JHA Feb 99.p65

JOURNAL FOR THE HISTORY O F

1999

A S T R O N O M Y

VOLUME 30

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EDITED BY M. A. HOSKIN

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Journal for the History of Astronomy

Vol. 30 Part 1

No. 98

C O N T E N T S

Regiomontanus’s Concentric-sphere Models for the Sun and Moon

N. M. SWERDLOW .............................................................................

A Career of Controversy: The Anomaly of T. J. J. See

THOMAS J. SHERRILL ......................................................................

The Babylonian First Visibility of the Lunar Crescent: Data and Criterion

LOUAY J. FATOOHI, F. RICHARD STEPHENSON and SHETHA
S. AL-DARGAZELLI ...........................................................................

Book Reviews ............................................................................................

Galileo on the World Systems, transl. and ed. by Maurice A. Finocchiaro
(William E. Carroll); From Baghdad to Barcelona, ed. by Josep
Casulleras and Julio Samsó (Owen Gingerich); Astronomische
Konzepte und Jenseitsvorstellungen in den Pyramidentexten, by Rolf
Krauss (Kurt Locher); The Quest for Longitude, ed. by William J. H.
Andrewes (Simon Schaffer); Of Time and Measurement, by A. J. Turner
(Jim Bennett); The History of Radio Astronomy and the National Ra-
dio Astronomy Observatory, by Benjamin K. Malphrus (Woodruff T.
Sullivan, III); The Measurement of Starlight, by J. B. Hearnshaw
(William Liller); Pierre-Simon Laplace, 1749–1827, by Charles
Coulston Gillispie (J. L. Heilbron); Humanismus zwischen Hof und
Universität, by Franz Graf-Stuhlhofer (Michael H. Shank); In Search
of Planet Vulcan, by Richard Baum and William Sheehan (Steven J.
Dick); The Einstein Tower, by Klaus Hentschel (Helge Kragh)

Notices of Books .......................................................................................

Notes on Contributors ...............................................................................

February 1999

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I N S T R U C T I O N S T O C O N T R I B U T O R S

JHA, xxx (1999)

REGIOMONTANUS’S CONCENTRIC-SPHERE MODELS FOR

THE SUN AND MOON

N. M. SWERDLOW, The University of Chicago

It seems curious that the astronomer and mathematician who did the most to estab-
lish a serious understanding of Ptolemy’s mathematical astronomy in Europe also
had a serious interest in concentric-sphere models for the motions of the heavens.
But such is undoubtedly true. The first known indication of Regiomontanus’s inter-
est appeared in a letter to Giovanni Bianchini published from the manuscript Nu-
remberg Cent V app. 56c by C. T. von Murr in 1786. The letter is undated, but must
fall between letters from Bianchini to Regiomontanus dated 21 November 1463
and 5 February 1464 since in it Regiomontanus responds to problems posed by
Bianchini in the letter of 21 November and in the letter of 5 February Bianchini
responds to problems posed by Regiomontanus in the undated letter. The principal
subject of the letter is a description of a set of tables, on which Regiomontanus
seems to have been working but had not yet completed, applicable to spherical
astronomy. These are in fact the Tabulae primi mobilis, eventually dedicated to
Matthias Corvinus while Regiomontanus was in Hungary in 1467–71 and pub-
lished in Vienna in 1514 in an edition by Georg Tannstetter. They are double-entry
tables for solutions to right spherical triangles in the form a = sin

–1

(sin

sin c), and

may be applied to all solutions based upon the law of sines by substituting the
complements of a,

or c.

and c are tabulated at 1° intervals from 1° to 90°, a and

differences of a for

+ 1° and c + 1° are given to seconds, which makes interpola-

tion quite secure. The tables run to 90 pages of 90 entries per page or, not counting
duplications, no fewer than 4095 solutions. Considering all the computation
Regiomontanus did in these tables, his two great sine tables for R = 6,000,000 and
R = 10,000,000, the Tabulae directionum, and the Ephemerides for 1475–1506, it is
my suspicion that he was a lightening calculator, and a very accurate one too.

After explaining the arrangement of the tables and giving the solutions to prob-

lems proposed by Bianchini in the preceding letter, Regiomontanus gives a list of
40 problems in spherical astronomy that may be solved using the tables. When the
Tabulae primi mobilis were completed, the list had grown to 63 problems with
detailed solutions and examples running to 38 double-column quarto pages in the
printed edition.

But the last two problems in the original list had been dropped, and

this is of some interest. The last four problems and Regiomontanus’s concluding
remarks to Bianchini are as follows:

37. To compute the equation of the eighth sphere according to the methods of
Alfonso.

N. M. Swerdlow

38. To compute the equation of the eighth sphere according to the theory of
Th

bit.

39. To compute the equation of the Sun.
40. To compute the equation of the anomaly of the Moon.

But where does this vexatious and audacious pen hasten? Will it perhaps

direct all things sought of astronomers to this singular table? I say that a great
part of such things as are sought will be found by means of this table if we shall
first have established a complete concentric astronomy. Why that? It will be
beautiful to save the irregularities of the motions of the planets through
concentrics. We have already provided the method for the Sun and Moon, while
concerning the rest some foundations have been laid through which, when com-
pleted, one will be permitted to compute the equations of all the planets by
means of this table. But concerning this matter, no more for the present lest, in
reading my letter, you experience a weariness greater than the delight I take in
writing. If I seem to have said any of these things more boldly than justly, you
will receive my reasons more clearly, I believe, in a following letter. I would,
nevertheless, prefer to treat of these things by speech rather than by the pen, for
it would be much more easy and convenient. As long as that is not possible, a
letter will take on the function of speech which, whatever it relates, will be
subject to correction by your judgement.

Now it is entirely sensible to provide solutions to the equation of the eight sphere,
the inequality of the motion of the fixed stars, in the Alfonsine Tables and in De
motu octauae sphaerae attributed to Th

bit because both are solutions of spherical

triangles, but it seems odd to treat the equations of the Sun and Moon as spherical
because the normal epicyclic and eccentric models are in the plane and use only
plane triangles. The reason becomes clear when Regiomontanus says that his tables
will be applicable to all things sought by astronomers once he has established a
“complete concentric astronomy”, which he thinks will be “beautiful” — pulchrum,
perhaps just “excellent” — and is obviously his intention. He has, he says, worked
out a method for the Sun and Moon, and at least laid some foundations by which,
when completed, the equations of all the planets will be computed with his tables.
Ultimately, he gave up on this, for solutions to the solar and lunar equations do not
appear in the Tabulae primi mobilis, which concludes with the two forms of the
equation of the eighth sphere just mentioned, and nothing more was heard of con-
centric spherical models for the planets. Nevertheless, just as he said, he had worked
out concentric spherical models for the Sun and Moon, but that was a discovery that
came many years after von Murr published the letter to Bianchini.

In 1953 Ernst Zinner published a brief description of a letter written in 1460 by

Regiomontanus, then in Grosswardein (Oradea), to Bishop Johann Vitez, in which
he describes just such models for the Sun and Moon.

The letter is contained in a

manuscript we shall call F, Florence, Magliabechiana XI, 144, ff. 16r–17v, which
also contains, among other works, the Epitome almagesti Ptolemaei, the Disputationes

Regiomontanus’s Concentric-sphere Models

contra Cremonensia in planetarum theoricas deliramenta, and Peurbach’s Theoricae
nouae planetarum. What makes F of particular interest, aside from being the unique
copy of this letter, is that it was copied in 1476 in Buda and presumably belonged to
Martin Ilkusch (Ilkusz), from about 1466 astronomer to King Matthias Corvinus.
Regiomontanus knew Ilkusch in Italy, for he is “Cracoviensis” who learns of the
faults of the old Theorica planetarum from “Viennensis” in the Disputationes, which
is set in Rome during the papal election between the death of Pius II on 8 August
1464 and the election of Paul II on 31 August. In F, and to my knowledge in F alone,
the two characters of the dialogue are called “Martinus” and “Joannes”, showing
that Ilkusch knew that he was “Cracoviensis”, meaning from the University of Cra-
cow, and Regiomontanus “Viennensis”, meaning from the University of Vienna. It
is nice to see people identifying themselves first and foremost with their universi-
ties in the fifteenth century.

Regiomontanus and Ilkush also knew each other dur-

ing 1467–71 when Regiomontanus was at Matthias’s and Vitez’s newly founded,
and short lived, University of Pressburg (Bratislava), so any manuscript associated
with Ilkusch has a particular authenticity, and indeed F is quite an excellent manu-
script, with notably detailed figures for Peurbach’s Theoricae nouae and a good
text of the Epitome, although prior to the final version in Venice lat. 328.

I first came across F about twenty years ago when collecting films of manu-

scripts of the Epitome, and at the time made a transcription and translation of the
text (after a fashion) along with some other works of Regiomontanus and Peurbach.
But I did nothing with it because I was, to say the least, puzzled by whatever
relation it might have to Regiomontanus’s notes on al-Bi

, written in his own

hand at ff. 45r–47v of Vin 5203, a large manuscript dating from his years in Vi-
enna, containing works of other authors, in particular Peurbach, some in
Regiomontanus’s hand, some not, along with various notes of his own. And all I
could learn from F. J. Carmody’s edition and study of the notes was that
Regiomontanus, far from being interested in concentric-sphere models, was highly
critical of the entire principle.

These difficulties were removed only recently

when Michael Shank published a new edition and the first translation of the text
in which he argued, convincingly I believe, that Regiomontanus’s notes are not
his own, but a copy of a criticism of al-Bi

written in Vienna or Klosterneuberg,

at some time after a solar eclipse of 1433 that the author says was annular and
seems to have observed himself. And this criticism was in turn based upon an
earlier criticism in a treatise on an instrument called a planitorbium, a kind of
equatory, written in 1310 by one G. Marcho, a Franciscan from Aquitaine, who
was then (or had been) a student in Paris and cites an annular eclipse of 1309.

follows that the notes are something Regiomontanus copied and do not necessar-
ily represent, in fact do not represent, his own thoughts on either al-Bi

concentric-sphere models in general, and this makes it possible to consider the
models described in the letter to Vitez independently of the notes on al-Bi

In fact, far from entirely rejecting al-Bi

, I believe that Bi

was the source

N. M. Swerdlow

of Regiomontanus’s models, but in a peculiar and critical way. Even if he was not
the author of the notes, Regiomontanus had every opportunity to study Bi

’s

work as he owned a manuscript containing the Latin version by Michael Scot
(Nuremberg, Cent V 53, ff. 74r–111v, not in Regiomontanus’s hand), which he
annotated, at times critically.

In Bi

’s model for the planets, an epicycle is

placed on the surface of a sphere removed from the pole of the celestial equator
by the obliquity of the ecliptic, and the planet is placed a quadrant from the epicy-
cle, thus near the ecliptic. Bi

presumes that as a point moves about the epicy-

cle in the anomalistic period, the planet, always a quadrant from the epicycle, will
take on an inequality in its motion in longitude and also a motion in latitude, both
with the anomalistic period. The model accounts for only the second or solar
inequality of the planets, and has nothing corresponding to the first or zodiacal
inequality, produced in Ptolemy’s model by equant motion in an eccentric. Bi

’s

model, and its considerable defects, are described very well by Bernard Goldstein
in his edition and translation of the Arabic text.

But Goldstein does something

more, and this turns out to be of great interest. After showing the problems of
Bi

’s model, he describes a modification of the model that can work properly,

at least for the second inequality in longitude, by letting the epicycle move at an
arbitrary distance about the pole of the ecliptic rather than the equator, with the
planet, still a quadrant from the epicycle, oscillating in the plane of the ecliptic
about its mean position. The principle of this model turns out to be identical,
except for the direction of motion on the epicycle, to Regiomontanus’s models
for the Sun and Moon. Now, we may safely exclude the possibility that
Regiomontanus read Goldstein’s account of Bi

’s planetary model, but he was

certainly clever enough to come up with the very same modification, except that
he first applied it to the Sun and Moon by changing the direction of motion on the
epicycle. His model is definitely not based upon Bi

’s solar model, in which

the Sun, in addition to moving with its own mean motion, is a quadrant from a
point that moves at twice that speed on a circle eccentric to the pole of the equa-
tor. But it could in principle be based upon modifying Bi

’s lunar model, the

last to be described in Bi

’s treatise, which is essentially the same as the plan-

etary model except for the direction of motion on the epicycle, in order to make
the Moon oscillate in the plane of its inclined circle, and likewise applied to make
the Sun oscillate in the plane of the ecliptic. In addition, Regiomontanus devises
a way of accounting for part of the second inequality of the Moon, not even con-
sidered by Bi

, that is also based upon the principle of converting motion about

an epicycle to oscillation along a great circle.

This is what I believe to be the origin of Regiomontanus’s models, a correction

of al-Bi

’s planetary, or perhaps lunar, model, and I can see no relation to other

concentric-spherical models for inequalities, as the motion of the eighth sphere
attributed to Th

bit. And it goes without saying that it has nothing whatever to do

with Eudoxus’s models, as described by Aristotle or Simplicius, or an attempt to

Regiomontanus’s Concentric-sphere Models

discover Eudoxus’s models. Why Regiomontanus was interested in concentric-sphere
models, I leave to heads wiser than my own. That he was serious about them is
shown by his intention to write a work, in four treatises no less, to refute “the old
theory of eccentrics and epicycles” and to propose and confirm by geometrical
proofs a theory of concentric spheres accounting for all inequalities. One thing
certain is that his motivation was physical and was not concerned with finding more
accurate models for the Sun, Moon, and planets. If anything, his goal was to devise
concentric-sphere models identical in effect to Ptolemy’s, which he surely under-
stood adequately to his task in 1460, and he evidently persevered in his search even
after he became a complete master of Ptolemy’s astronomy in writing the Epitome,
which predates the letter to Bianchini. Further, he must have known from the begin-
ning that the variation in the apparent size or brightness of the Moon and planets
indicates a variation of distance incompatible with concentric spheres, as is pat-
ently obvious and also pointed out in detail in the notes he copied on al-Bi

which devote particular attention to the variation of the lunar parallax and the ap-
parent size of the Moon and shadow in solar and lunar eclipses, citing the annular
eclipse of 1433 as evidence.

How he thought he could get around these problems,

I also leave to heads wiser than my own. In the criticism of the contemporary state
of astronomy that Regiomontanus wrote to Bianchini following Bianchini’s letter
of 5 February 1464, he singles out as a defect the effect of the variation of distance
implicit in Ptolemy’s models on the apparent sizes of Mars, Venus, and the Moon,
which are not observed to take place, but it is a far cry from this exaggerated vari-
ation to concentric spheres in which distances do not vary at all.

Perhaps despite

his best intentions, he gave up on concentric-sphere models because he ultimately
found them inapplicable, to the planets because he could devise no model combin-
ing the first inequality, second inequality, and motion in latitude, and to the Moon
because he could devise nothing corresponding to the correction of the direction of
the apogee of the epicycle as a function of the mean elongation, which is not present
in his model. Perhaps he just decided that the whole principle of concentric spheres
was without value after all. In any case, this must have occurred between the letter
to Bianchini at about the end of 1463 and the dedication of the Tabulae primi mobilis
to Matthias Corvinus, presumably before Regiomontanus left Hungary in 1471,
since, as noted, spherical solutions for the equations of the Sun and Moon are not
present in the instructions.

What follows is an edition of the text from F with a translation in which I have

added a few phrases in brackets for clarity. The text of F itself is excellent and
requires no emendation aside from punctuation and division into paragraphs, which
I have done as seems appropriate. The figures from the manuscript are shown as
Plates 1 and 2, and I have redrawn them in Figures 1 and 2. Note that in Plate 1 of
the solar model the letters L and M are reversed and in Plate 2 of the lunar model the
letters G and H are reversed. The analysis following the text and translation is purely
technical, and again I leave historical speculation to wiser heads.

N. M. Swerdlow

Text and Translation

[De sole]

Sol habet duos orbes mundo concentricos, quorum superior polos suos habet

sub polis zodiaci octauae sphaerae, et eclipticam sub ecliptica eiusdem. In huius
orbis concauo circulus est paruus habens polum extra eclipticam praedictam.
Sed orbi inferiori corpus solare infixum est.

Mouetur autem orbis superior regulariter super polis suis omni die naturali

per 59 minuta et 8 secunda fere. Orbis uero inferior hoc pacto in conuexo eius
est punctus ex directo centri corporis solaris inuaribiliter permanens, alius quoque
punctus a priori per quartam circuli magni distans. Horum unus mouetur
regulariter in circumferentia parui circuli praedicti, in eo tempore complendo
reuolutionem unam quo et orbis superior. Alius autem terminus istius quartae,
qui apud solem est, semper adhaeret eclipticae in orbe superiori signati.

Quod ut facilius appareat, pingenda est theorica in qua quidem puncta litteris

alphabeti nunc appellabo. Post uero cum maior fauebit commoditas, singulis
punctis nomina sua fingam.

Opus quoque nouum quatuor absoluam tractatibus, in quorum primo antiquam

LATE

1. Theorica solis absque eccentrico.

Regiomontanus’s Concentric-sphere Models

[On the Sun]

The Sun has two orbs concentric to the world, of which the higher has its poles

under the poles of the zodiac of the eighth sphere, and [its] ecliptic under the ecliptic
of the eighth sphere. In the concavity of this orb is a small circle with a pole outside
the ecliptic just mentioned. But the solar body is fixed in the lower orb.

Now the higher orb moves uniformly about its poles by about 0;59,8° in each

natural day. And the lower orb is so arranged that in the convexity of it there is a point
invariably remaining directly at the centre of the solar body, and also another point
distant from the first by a quadrant of a great circle. One of these points moves uni-
formly in the circumference of the small circle mentioned before, completing one
revolution in the same time as the higher orb. However, the other end of the quadrant,
which is at the Sun, always adheres to the ecliptic designated in the higher orb.

In order that this will more easily be clear, a representation should be drawn in

which I shall now call the points by letters of the alphabet. And later when the oppor-
tunity is more favourable, I shall assign to the individual points their names.

I shall also complete a new work in four treatises. In the first of these I shall present

the old theory of eccentrics and epicycles demolished by strong reasons and observa-
tions that will be made. In the second I shall clearly set out a theory of concentric orbs
by which all inequalities of the motions can be saved. And in the third I shall confirm
what is in the second by geometrical proofs. The fourth will contain the way by which

. 1. Theory of the Sun without an eccentric.

N. M. Swerdlow

speculationem de eccentricis et epicyclis rationibus firmis atque obseruationibus
futuris destructam dabo. In secundo speculationem orbium concentricorum
quibus omnes diuersitates motuum saluari poterint aperte ponam. In tertio uero
testimoniis geometricis ea quae in secundo tractatu sunt confirmabo. Quartus
quo pacto motus isti numerari et tabulae ad illas nouas radices fundari possint
continebit.

Se quorsum euagabar? Iam rediens describo eclipticam superioris orbis, quae

sit ABCD, cuius unus polus sit punctus Z, a quo descendat quarta circuli magni
ZA. In hac quarta signetur punctus E, super quo describatur circulus paruus
KFHG. Deinde in conuexo orbis inferioris estimetur quarta circuli magni, cuius
unus terminus adhaereat circumferentiae dicti circuli parui, quem punctum nota
K repraesentat. Reliquus uero terminus huius quartae, qui ex directo centri cor-
poris solaris est, semper adhaereat eclipticae superioris.

Mouetur itaque omnis punctus eclipticae ABCD regulariter circa centrum

mundi, et similiter mouetur paruus circulus KFHG. Quod si quarta KB in conuexo
orbis inferioris semper, ut dictum est, in eisdem punctis adhaereret eclipticae,
sol non haberet diuersitatem in motu suo, semper enim centrum solis ex directo
puncti B regulariter moti reperiretur. Sed non est ita, immo terminus quartae qui
adhaeret circumferentiae parui circuli mouetur in circumferentia parui circuli
uersus punctum F, et trahit secum reliquum terminum quartae, qui apud solem
est, adhaerente tamen eclipticae.

Intellige ergo arcum per polum eclipticae et terminum quartae usque ad

eclipticam transeuntem similiter moueri ad motum termini. Tunc quanta est portio
eclipticae quam claudunt duo arcus, quorum unus per polum eclipticae et polum
parui circuli transit, et alius per polum eclipticae et dictum quartae terminum,
tanta est etiam portio ea quae inter punctum B et terminum quartae adhaerentem
eclipticae deprehenditur.

Cum itaque terminus quartae circuiens ad punctum F perueniet, punctum,

inquam, in quo arcus ZN contingit paruum circulum, maxima est illa, de qua
dixi, portio eclipticae, unde et reliquus quartae terminus adhaerens maxime a
puncto B remouebitur. Postea uero portio haec pedetentim minuitur quousque
nulla fiet, quando scilicet terminus quartae circuiens in puncto H parui circuli
fuerit. Recedente autem termino quartae circuente a puncto H, augetur iterum
portio eclipticae inter duos arcus comprehensa, donec terminus quartae circuiens
ad aliud punctum contactus, quod est G, perueniet. Tunc iterum maxima est
huiusmodi portio, quae tandem, propter motum termini circueuntis, continue
decrescit donec reuolutio integra perficitur in paruo circulo.

Haec itaque est habitudo motuum solis. Nunc ad descriptiones terminorum

uenio.

Linea medii motus solis est quae a centro mundi exiens per punctum B usque

ad zodiacum protenditur.

Linea ueri motus a centro mundi per centrum corporis solaris usque ad

zodiacum continuatur.

Regiomontanus’s Concentric-sphere Models

the motions can be computed and tables [with] new epoch positions established for
them.

But where have I wandered? Now returning, I shall describe the ecliptic of the

higher orb, which let be ABCD, one pole of which let be point Z, from which let
descend a quadrant of a great circle ZA. In this quadrant let a point E be designated,
about which let the small circle KFHG be described. Then in the convexity of the
lower orb, let a quadrant of a great circle be estimated, one end of which let adhere to
the circumference of the small circle just mentioned, which point let letter K repre-
sent. And let the other end of this quadrant, [point B], which is directly at the centre of
the solar body, always adhere to the ecliptic of the higher orb.

Accordingly, every point of the ecliptic ABCD moves uniformly around the centre

of the world, and likewise the small circle moves [uniformly around the centre of the
world]. And if the quadrant KB in the convexity of the lower orb always, as was
mentioned, adhered to the ecliptic in the same points, the Sun would have no inequal-
ity in its motion, for the centre of the Sun would always be found directly at the point
B that is moved uniformly. But it is not so, rather, the end of the quadrant which
adheres to the circumference of the small circle moves in the circumference of the
small circle [from K] towards point F, and draws with it the other end of the quadrant,
which is at the Sun, yet adhering to the ecliptic.

Understand, therefore, that an arc, [as ZFN, ZHKA or ZGO], passing through the

pole of the ecliptic [Z] and the end of the quadrant [at the small circle, as F, H, G or K,
extended] as far as the ecliptic, [as to N, A or O], likewise moves in accordance with
the motion of the end [at the small circle]. Accordingly, as much as is the portion of
the ecliptic which two arcs contain, one of which [ZEA] passes through the pole of the
ecliptic and the pole of the small circle, and the other, [as ZFN, ZHKA or ZGO],
through the pole of the ecliptic and the end of the quadrant [at the small circle ex-
tended to the ecliptic], so much is also the portion [of the ecliptic] which is found
between point B and the end of the quadrant adhering to the ecliptic, [as L or M].

And thus when the revolving end of the quadrant arrives at point F, the point, I say,

in which arc ZN is tangent to the small circle, there the portion of the ecliptic [NA] of
which I have spoken is the greatest, and hence the other, adhering end of the quadrant
draws the farthest away from B, [namely to L]. But afterwards this portion gradually
decreases until it becomes zero, namely, when the revolving end of the quadrant is in
point H of the small circle. When, however, the revolving end of the quadrant recedes
from point H, once again the portion of the ecliptic contained between the two arcs
increases until the revolving end of the quadrant arrives at the other point of tangency,
which is G. Then once again the portion of this kind [AO] is greatest, which finally, on
account of the motion of the revolving end, decreases continuously until an entire
revolution in the small circle is completed.

And thus this is the disposition of the motions of the Sun. Now I come to the

description of the technical terms.

The line of the mean motion of the Sun is the line which, proceeding from the

centre of the world through point B, is extended as far as the zodiac.

N. M. Swerdlow

Medius motus et uerus [sunt arcus eclipticae] principio arietis et lineis suis

iam dictis intercipiuntur.

Aequatio solis est arcus eclipticae quam lineae ueri et medii motuum

concludunt. Haec nulla est cum terminus quartae circuiens est in puncto K parui
circuli. Cum autem est in puncto contactus, scilicet F, maxima contingit aequatio,
quam signat in figura arcus BL. Item in puncto H nulla est aequatio, sed tandem
maxima redit aequatio cum terminus quartae circuiens est in puncto G, quam
quidem aequationem arcus BM significat. Quamdiu autem terminus quartae
circuiens est in medietate parui circuli KFH, medius motus maior est uero, quare
tunc aequatio, ut uerus habeatur motus, a medio subtrahitur. In alia uero medi-
etate contra fit, quare tunc aequatio additur.

[De luna]

Luna quatuor requirit orbes mundo concentricos, quorum inferiores duo per

omnia se habent sicut in sole, hoc dempto, quod terminus quartae circuiens non
complet reuolutionem in eo tempore praecise, quo orbis secunda deferens paruum
circulum, suam reuolutionem perficit. Item quod terminus quartae adhaerens

LATE

2. Theorica lunae absque eccentricis et epicyclo.

Regiomontanus’s Concentric-sphere Models

The line of the true motion is extended from the centre of the world through the

centre of the solar body as far as the zodiac.

The mean and true motions [are the arcs of the ecliptic] cut off by the beginning of

Aries and their lines just mentioned.

The equation of the Sun is the arc of the ecliptic which the lines of the true and

mean motions contain. This is zero when the revolving end of the quadrant is in point
K of the small circle. When, however, it is in the point of tangency, namely F, the
greatest equation occurs, which arc BL designates in the figure. Likewise in point H
the equation is zero, but finally the greatest equation returns when the revolving end
of the quadrant is in point G, which equation arc BM designates. And as long as the
revolving end of the quadrant is in the half KFH of the small circle, the mean motion
is greater than the true motion, wherefore then the equation is subtracted from the
mean motion in order to obtain the true motion. But in the other half [HGK] it is the
contrary, wherefore then the equation is added.

[On the Moon]

The Moon requires four orbs concentric to the world, of which the lower two are

arranged in all respects just as for the Sun, with this exception, that the revolving end
of the quadrant does not complete a revolution in precisely the time in which the

. 2. Theory of the Moon without eccentrics and an epicycle.

N. M. Swerdlow

non adhaeret eclipticae, sed circulo decliui qui in orbe quarto signabitur.

Circulus autem ille paruus circulus argumenti lunae uocabitur. Tertius orbis

in sui concauitate paruum habet circulum, quem circulum centri medii nominabo,
et signatur hic in figura notis XQTR, cuius polus P tantum distat a polo Z quan-
tum punctus E, qui est polus circuli argumenti, a puncto A, qui in uia lunae
decliui est, remouetur. Dicta tamen quatuor puncto in uno circulo magno sunt.

Intellige denique quartam circuli magni in conuexo secundi orbis, cuius unus

terminus, qui est directe super punctum circuli argumenti, semper adhaereat
circumferentiae PZEA, reliquus uero terminus semper adhaereat circumferentiae
circuli centri medii.

Quartus et supremus orbis suos habet polos sub polis zodiaci, et in eo sunt

duo puncta diametraliter opposita, quorum quodlibet a polo dicto sibi uicino
distat per quinque gradus. Haec duo puncta sunt poli uiae decliuis ab ecliptica,
sub qua quidem uia luna semper reperitur. Mouetur autem orbis iste contra
successionem signorum, et transmutat sectiones draconis lunae.

Tertius uero orbis mouetur regulariter super polis uiae decliuis lunae secun-

dum successionem signorum omni die naturali 13 gradibus fere, et defert secum
circulum centri medii, qui in eo est, et circulum argumenti, qui in secundo orbe
est. Verum unus terminus quartae quam in conuexo secundi orbis dixi
imaginandam mouetur in circumferentia circuli centri medii, in mense lunari
aequali duas faciendo reuolutiones, et trahit consequenter secum circulum
argumenti. Hoc enim pacto argumentorum aequationes fiunt nunc maiores, nunc
minores.

De motibus reliquorum orbium superius uisum est. Definitiones autem

terminorum post, si Deus uolet, accipies. De reliquis planetis, nunc nihil.

Pauca haec scribere institui, ne hosce dies uentri modo indulgens inerti

praeterirem otio. Quod si rem uelis ampliorem, faue praesul dignissime reducere
me Vienna suscipiat. Iam enim Euclides, Ptolemaeus, caeteri quoque amici
plurimi cum quibus ante hac consueui, nisi animus me fallit, de spe reditus
decidere, quos apprime formido, ne si mora longiori detineat, perpetua me
obliuione deserant. Da precor o et praesidium et dulce decus meum praeceptorem
reuisere Georgium, qui res tuis placitura uotis absoluet, si prius discipulo mihi
quae prior quaeque posterior ueniat ordo dabitur.

Haec magister Joannes de Kunigsperg Germanus in Varadino domino Johanni

episcopo, anno domini 1460.

Regiomontanus’s Concentric-sphere Models

second orb carrying the small circle completes its revolution. Likewise, that the
adhering end of the quadrant does not adhere to the ecliptic, but to an inclined circle
which is designated in the fourth orb.

Now the small circle will be called the circle of the anomaly of the Moon. The

third orb [also] has a small circle in its concavity, which I shall call the circle of the
mean centre, and here it is designated in the figure by the letters XQTR. The pole P
of the small circle is distant as far from pole Z as point E, which is the pole of the
circle of the anomaly, is removed from point A, which is in the inclined path of the
Moon. Yet the four points just mentioned [PZEA] are in the same great circle.

Finally, understand a quadrant of a great circle in the convexity of the second

orb, of which one end, which is directly over the [centre] point of the circle of the
anomaly, let always adhere to the arc PZEA, while the other end let always adhere
to the circumference of the circle of the mean centre.

The fourth and highest orb has its poles under the poles of the zodiac, and in it

are two diametrically opposite points, of which each one is separated from the pole
of the zodiac near to it by 5°. These two points are the poles of the path inclined
from the ecliptic, under which path the Moon is always found. Now this orb moves
opposite to the order of the signs, and it shifts the intersections of the dragon of the
Moon.

But the third orb moves uniformly about the poles of the inclined path of the

Moon in the order of the signs by about 13° in each natural day, and it carries with
it the circle of the mean centre, which is in it, and the circle of the anomaly, which
is in the second orb. However, one end of the quadrant, which I have said is to be
imagined in the convexity of the second orb, moves in the circumference of the
circle of the mean centre, making two revolutions in a mean lunar month, and con-
sequently draws with it the circle of the anomaly. For in this way the equations of
the anomalies become now greater, now smaller.

It was evident earlier concerning the motions of the other orbs. If God wills, you

will receive the definitions of the technical terms later. Concerning the other plan-
ets, nothing now.

I have undertaken to write these things lest I pass these days in unproductive

idleness, merely giving in to the stomach. But if you wish something more substan-
tial, be well disposed, worthy Bishop, that Vienna may undertake to recall me. For
already Euclid, Ptolemy, and also many other friends to whom I was formerly ac-
customed, unless my mind fails me, have perished from hope of my return, which I
fear especially, lest if my return be detained by a longer delay, they may abandon
me to eternal oblivion. O grant, I pray, the aid and dear honour to again see my
teacher Georg [Peurbach], who will complete these things in a way pleasing to your
wishes, if first the order of what should come first and what after be given to me his
pupil.

This letter [is from] Johannes Germanus of Königsberg in Grosswardein to Lord

Bishop Johannes [Vitez],

. 1460.

N. M. Swerdlow

Analysis

The principle of Regiomontanus’s models is a conversion of circular to reciprocal
motion, which is illustrated in Figures 3(a) and 3(b) by a rigid linkage mechanism
in a plane. A rod of length r = AB rotates uniformly through angle

about A, and

attached to it is a rod of length l = BC > AB, which is constrained such that C
oscillates in a straight line over a distance s. The reciprocation may be either in-line
with A as in 3(a) or offset by a distance d = AA

′

as in 3(b). As illustrated in the

figure, the motions are reversible, that is, if the source of motion is at A, rotational
motion is converted to reciprocal, and if the source of motion is at C, reciprocal
motion is converted into rotational. One may think of the mechanical trains at-
tached to steam or internal combustion engines and electric motors. For example, a
rotational motion at A may drive a pump or a press at C, or the piston of a heat
engine at C may turn a wheel or crankshaft at A, as in a steam locomotive or auto-
mobile. In the theory of machines, the device is called a slider crank mechanism,
probably the most common of all mechanical systems, in the terminology of which
A is called the crankshaft, r the crank, B the crankpin, l the connecting rod, C the
wrist pin, s the stroke, and d the offset.

The maximum displacement of C from its centre position takes place when the

linkages r and l lie, either extended, l + r, or overlapping, l – r, in a straight line,
necessarily passing through A. However, the alignment of the rotation and reciprocation

3. Conversion between rotation and reciprocation.

Regiomontanus’s Concentric-sphere Models

is of importance and produces remarkable effects. If, as in 3(a), the constrained
path of C is in-line with A, it is obvious that the range of the displacement of C is
s = 2r and its limits are reached at

= (0°, 180°). However, if, as in 3(b), the line

of the reciprocation of C is removed from A by an offset d, the range of the dis-
placement of C is given by s = ((l + r)

– d

)

– ((l – r)

– d

)

. In the in-line

mechanism of 3(a), d = 0 and the formula reduces to s = (l + r) – (l – r) = 2r. But
in the offset mechanism of 3(b), in which d < (l – r) and r < l, considering the
triangle formed by (l + r), (l – r), and s, since the sum of any two sides of a triangle
is greater than the third side, (l – r) + s > (l + r), and since (l – r) + 2r = (l + r), thus s
> 2r and the range of the displacement is greater than in the in-line reciprocation.
Further, the displacement of C corresponding to any value of

differs greatly for in-

line and offset reciprocation, the offset reciprocation being highly irregular and hav-
ing almost no relation to the in-line reciprocation for the same value of

. Interest-

ingly, all of these difficulties disappear when the mechanism is transferred to spheres
under the special conditions chosen by Regiomontanus.

The conversion of this device to the motions of spheres as imagined by

Regiomontanus is shown in Figure 4. The spheres are hollow bodies, shells, of some
unspecified thickness, each having an outer, convex surface or convexity (conuexum,
conuexitas) and an inner, concave surface or concavity (concauum), all surfaces cen-
tred about the observer at O, and are taken in pairs, with the convex surface of the

. 4. Order of spheres and reciprocation.

N. M. Swerdlow

inner Sphere 2 touching the concave surface of the outer Sphere 1. The spheres must
also be rigid bodies, that is, solid spheres, for the motion of a pole is transferred to the
equator of the sphere, and motions are also transferred through quadrants of great
circles that behave like the rigid rods of Figure 3. The outer Sphere 1 is given a
rotational motion about its pole Z that carries both the equatorial great circle of the
sphere, located a quadrant from Z at A

′

, and a small circle with centre A located in its

concavity. In the convexity of Sphere 2, which is also carried about Z, is a point B that
moves uniformly through angle

in the circle about A, and at the end of a quadrant

from B is a point C, likewise in the convexity of Sphere 2, that oscillates over some
distance in the equatorial circle of Sphere 1 as B moves about the small circle. Now
this is very strange. One might imagine A to be a pole and AB the radius of a small
circle, both in the convexity of Sphere 2, so that B is carried around the circle as
Sphere 2 rotates about its pole at A. But it is clear from Regiomontanus’s description
that both A and the small circle are in the concavity of Sphere 1; hence point B of
Sphere 2 must be displaced about the small circle rather than rotate around a pole,
which is not what usually happens in concentric sphere models. And how, one might
ask, does point C manage to confine its oscillations to the equatorial circle of Sphere
1, as there is no guide, as in Figure 3, to keep it there?

What has just been described is actually the solar model, which is shown in Figure

5. The ecliptic is a circle in the higher of two spheres, rotating with the sphere through
the mean motion of the Sun in longitude

∆

, and let

}

be the mean anomaly of the

Sun measured from

, the longitude of the apogee in an eccentric or epicyclic model,

to the mean sun

. In this higher sphere, let a quadrant descend from the pole of the

. 5. Theory of the Sun.

Regiomontanus’s Concentric-sphere Models

ecliptic Z to the ecliptic at K

′

and move about Z through

′

}

′

}

– 90°. On

quadrant ZK

′

at a distance R from Z, let a point C be taken in the concavity of the

higher sphere, which will also move through

}

′

about Z, and thus parallel to the

ecliptic. C is the centre of a small circle of radius r, likewise in the concavity of the
higher sphere, about which a point L, in the convexity of the lower sphere, moves
through the mean anomaly

}

such that

}

= 0° and the direction of the motion of L is

opposite to the motion of C about Z when L lies at K, at the greatest distance from Z
on quadrant ZK

′

. Let a second quadrant descend from Z through L to meet the ecliptic

at L

′

, and as L moves about pole C, L

′

departs from K

′

by arc

. Next, in the convexity

of the lower sphere let a quadrant from K “adhere” to the ecliptic at the mean sun

which moves 90° ahead of K through the mean anomaly

}

′

+ 90° measured from

. Let a second quadrant from L “adhere” to the ecliptic at S, the true Sun, such that

as L rotates about C, S oscillates on either side of

through

, the equation of the

anomaly, in the plane of the ecliptic. Hence, the distance of S from

is the true

anomaly (not shown)

}

What Regiomontanus does not show is that K

′

and L

′

S in the ecliptic are equal, so

that S

= L

′

, which is not obvious but is true provided that K

and LS are both

quadrants. These relations were demonstrated by Bernard Goldstein in his own in-
genious correction of al-Bi

’s planetary model, and I must confess that, having

begun my analysis with reciprocation in a plane, I did not believe that Regiomontanus’s
model could work properly until I came upon Goldstein’s simple and elegant demon-
stration. And, as noted before, I believe that Regiomontanus devised the principle of
his model as a correction to al-Bi

, just as Goldstein did. Thus, since Z

= K

90° and ZKK

′

lie in the same great circle, K

′

= K

= 90°. And since ZS = LS = 90°

and ZLL

′

lie in the same great circle, L

′

S = LS = 90°. Hence, K

′

= L

′

S = 90° and S

′

. Nevertheless, although the geometry is satisfactory, it is hard to see how the

model can work mechanically. For although

may “adhere” to the ecliptic a quadrant

from the fixed point K without difficulty, one may reasonably ask how S is made to
“adhere” to and oscillate along the ecliptic a quadrant from the moving point L since
there is surely no slot or guide for S of the sort shown in Figure 3. To expect S to know
how to remain in the ecliptic while L moves about a circle is to expect a great deal.

Regiomontanus promises a treatise in which he will explain how to compute equa-

tions from his concentric-sphere models. It is not difficult. If

}

is measured from K

and the distance

= ZL, from the law of cosines,

= cos

–1

(cos r cos R – sin r sin R cos

}

), and then from the law of sines

= sin

–1

((sin r sin

}

)/sin

). With only derivatives

of the law of sines, for which the Tabulae primi mobilis may be used, drawing a
perpendicular from L to ZC, so that a = sin

–1

(sin

}

sin r) and b = cos

–1

(cos r/cos a), it

follows that

= cos

–1

(cos a cos (R + b)) and

= sin

–1

(sin a/sin

The equation

itself is determined by the distance R of C from Z and the ratio r/R. The distance R is
arbitrary, but once selected, the ratio r/R must be chosen such that sin

–1

(sin r/sin R) =

max

, for in this way angle CZL and arc L

′

will be equal to the required

, and

max

will occur when ZL

′

is tangent to the small circle and perpendicular to CL just below

N. M. Swerdlow

}

= ±(90° +

max

) because of the spherical excess in triangle CZL. In a planar epicyclic

or eccentric model the maximum equation occurs at

}

= ±(90° +

max

) exactly, but

because r/R is small, the difference will be small and, in general,

will differ only

slightly from a planar model for a corresponding

}

. After all, what Regiomontanus,

like al-Bi

, has done is to place an epicyclic model on the surface of a sphere, and

since neither Regiomontanus nor anyone else had any idea of how accurately a sim-
ple epicycle produces the solar equation, any small difference must be considered
harmless. Perhaps he even thought that in tabulating

the solar equation c

(

}

) from

the Alfonsine Tables could be used directly. The motivation of the model, as we have
noted, is entirely physical and has nothing to do with accuracy. It follows from the
condition for r/R that r = sin

–1

(sin

max

sin R). If, as appears reasonable, Regiomontanus

has in mind the solar equation of the Alfonsine Tables in which

max

= 2;10°, then if C

were located at K

′

in the ecliptic so that R = ZK

′

= 90°, r = sin

–1

(sin 2;10° sin 90°) =

2;10°. But if, say, R = ZC = 60°, then r = sin

–1

(sin 2;10° sin 60°) = 1;52,35°, and it may

be confirmed that

max

= sin

–1

(sin 1;52,35°/sin 60°) = 2;10°, as required.

So much for the Sun. We next consider the lunar model, shown in Figure 6, which

is more complex than the solar model but still works on the same principle. There are
four spheres, of which the two inner are for the equation of the first inequality at
syzygy, the third is for the variation of the equation due to the second inequality, and
the fourth and outermost, which is never illustrated, is for the motion of the nodes and
the inclined circle of the Moon along the ecliptic. The Moon is said to move in the
path of the inclined circle in the fourth sphere, although it is actually located in the
convexity of the innermost sphere, and Z, the pole of the inclined circle, is 5° from the
pole of the ecliptic. The first two spheres are analogous to the two spheres of the Sun,

. 6. Theory of the Moon.

Regiomontanus’s Concentric-sphere Models

that is, the convexity of the innermost contains the quadrants K

and LM extending

from the small circle to, respectively, the mean position

and true position M of

the Moon, and the concavity of the next higher contains the small circle itself,
called the “circle of the anomaly”, with centre C which moves on quadrant ZK

′

through the mean motion in longitude

∆

. In the case of the Moon, the mean

motions in longitude and anomaly differ notably, but if we define a moveable apo-
gee

, as in an eccentric or epicyclic model, we may consider the mean anomaly

}

measured from

to the mean moon

. The small circle of the anomaly with centre

C and the equation of the anomaly

are the same as for the Sun so that M

= L

′

as required. The distance R is arbitrary and again the ratio r/R has the condition
sin

–1

(sin r/sin R) =

max

, so that r = sin

–1

(sin

max

sin R). Taking the maximum equa-

tion of the Alfonsine Tables, in which at syzygy

max

= 4;56°, if R = 90°, meaning

that C is in the plane of the Moon’s inclined circle, r = 4;56°, and, as in the example
used for the Sun, if R = 60°, r = sin

–1

(sin 4;56° sin 60°) = 4;16,16°, and we may

confirm that

max

= sin

–1

(sin 4;16,16°/sin 60°) = 4;56°.

The second inequality, which alters the equation of the anomaly as a function of

the mean elongation

∼

of the Moon from the mean sun, is produced by another

small circle, called the “circle of the mean centre”, located in the concavity of a
third, higher sphere. Thus, D is the centre of this circle, located on arc K

′

CZ ex-

tended beyond Z in the concavity of a third sphere such that D is a quadrant from C,
from which it follows that ZD = K

′

C. A point G in the convexity of the lower sphere

carrying C moves in the circle about D of radius DG = r

′

, completing a rotation

through 2

∼

in one-half a mean synodic month — 2

∼

is called the “mean centre” in

medieval lunar theory, hence the name of the circle — such that G coincides with F,
at its least distance from Z, at syzygy when 2

∼

= 0°, and is at its great distance from

Z at quadrature when 2

∼

= 180°. The direction of rotation is arbitrary. A quadrant

extends from G to C, and as G rotates about the circle of the mean centre, the centre
of the circle of the anomaly C, which “adheres” to the arc DZK

′

, is drawn towards

Z, reaching its least distance at quadrature. The principle is exactly that of the in-
line reciprocation of Figure 3(a). The motion of C along arc ZK

′

reduces ZC = R

and thus increases the ratio r/R, which in turn increases the equation

such that r/

R and

are maximum at quadrature and minimum at syzygy. This is just what

happens in Ptolemy’s lunar model, in which the distance R of the centre of the
epicycle from the observer varies between syzygy and quadrature so that also r/R
and

are maximum at quadrature and minimum at syzygy.

The effect is shown in Figure 7, in which the centre of the circle of the anomaly, C

at syzygy, has been drawn along ZK

′

to C

by the motion of G in the small circle,

increasing the equation of the anomaly at syzygy

by the amount

. If we call the

least distance R

′

= R – 2r

′

, it is now required that sin

–1

(sin r/sin R

′

) = (

)

max

. Since

r is given by

1max

at syzygy, we find R

′

from R

′

= sin

–1

(sin r/sin (

)

max

), and the

radius r

′

of the circle of the mean centre then follows from r

′

(R – R

′

). In the

Alfonsine Tables the maximum equation at quadrature, (

)

max

= 7;34°. Thus, if R

N. M. Swerdlow

= 90°, so that C is in the Moon’s inclined circle at syzygy and r = 4;56°, R

′

= sin

–1

(sin

4;56°/sin 7;34°) = 40;46,25° and r

′

(90° – 40;46,26°) = 24;36,47°, which is very

large indeed. If, as in our previous example R = 60° and r = 4;16,16°, R

′

= sin

–1

(sin

4;16,16°/sin 7;34°) = 34;26,34° and r

′

(60° – 34;26,34°) = 12;46,43°; and we

confirm that (

)

max

= sin

–1

(sin 4;16,16°/sin 34;26,34°) = 7;34°. Table 1 shows R

′

and r

′

for selected values of R, assuming, as before, that

1max

= 4;56° and (

)

max

= 7;34°.

ABLE

′

5°

0;25,46°

3;15,47°

0;52, 7°

0;51,20

6;30,40

1;44,40

1;16,31

9;43,50

2;38, 5

2;27,52

19; 3,33

5;28,13,30

3;29,10

27;30, 6

8;44,57

4;16,16

34;26,34

12;46,43

4;55,34

39; 3,29

17;58,15,30

4;56

40;46,26

24;36,47

In every case, the circle of the mean centre r

′

is larger than the circle of the

anomaly r, in fact, from two to five times larger, just as in Ptolemy’s lunar model
the eccentricity of the second inequality is nearly twice the radius of the epicycle,
for the principle of increasing the ratio r/R by reducing R is the same in both mod-
els. But of course here there is no problem of an exaggerated variation in the dis-
tance of the Moon from the Earth because the distance does not vary at all.

The position of the Moon is given at syzygy by the quadrant L

, which

. 7. Second inequality of the Moon

Regiomontanus’s Concentric-sphere Models

“adheres” to the inclined circle of the Moon at M

, and with the correction for the

second inequality by quadrant L

, which “adheres” to the inclined circle at M

With the mean position of the Moon 90° ahead of K

′

, the Moon at syzygy is

90° ahead of L

′

at M

with equation

, and not at syzygy, with the additional

correction

for the second inequality, 90° ahead of L

′

at M

, for which the equa-

tion is thus

. For computing the equations, Regiomontanus may have in mind

using three columns of the Alfonsine Tables, that is, the equation c

(

}

) for syzygy,

the addition c

(

}

) for quadrature, and the coefficient of interpolation c

∼

) for

intermediate elongations in the form

= c

+ c

× c

. But since he mentions

that he intends to write a treatise on how motions and tables may be computed for
his new models, perhaps he has other ideas. The formulas for spherical solutions
given earlier for the Sun could be applied to

and to

, with columns then

tabulated for

and

= (

) –

, with some kind of coefficient of interpolation

a function of 2

∼

. Note that there is no equivalent in Regiomontanus’s model to the

inclination of the apogee of the epicycle in Ptolemy’s model, and thus no correction
of the mean anomaly by the second inequality as a function of the mean elongation,
that is, the correction c

∼

) in the Alfonsine Tables is simply ignored.

Finally, and this is not illustrated, the fourth and outermost sphere shifts the

intersections of the ‘dragon’ of the Moon, that is, the nodes of the Moon’s inclined
circle, opposite to the order of the signs, in the direction of decreasing longitude.
Thus, the poles of the fourth sphere coincide with the poles of the zodiac, and the
poles of the inclined circle in the fourth sphere are removed 5° from the poles of the
zodiac. As the sphere turns about the poles of the zodiac, the inclined circle in the
fourth sphere with its nodes and limits of latitude will slowly regress, and this mo-
tion of the inclined circle is transmitted to the three lower spheres.

REFERENCES

1. The Tabulae primi mobilis and the sine tables have been carefully analysed by E. Glowatzki and

H. Göttsche, Die Tafeln des Regiomontanus: Ein Jahrhundertwerk. Algorismus. Heft 2 (Munich,
1990). In the former, they find 1072 errors of ±1

″

, 48 of ±2

″

, 4 of ±3

″

, 2 of ±4

″

, 1 of +5

″

. The

sine table for R = 10,000,000 contains 1820 errors of ±1, 1 of +2, and 12 of –2 in 5400 entries.
Is there anyone who could do that today?

2. The best guide to the Tabulae primi mobilis, although they are nowhere mentioned, is the edition

of Johann Werner’s De meteoroscopiis libri sex by A. Björnbo and, following his death, J.
Würschmidt in Abhandlungen zur Geschichte der mathematischen Wissenschaften, xxiv/2
(1913). The reason is that Werner, using his instrument, the meteoroscope, which he also calls
a saphea, a universal astrolabe containing stereographic projection of circles of longitude and
latitude, provides solutions for all of the problems in the Tabulae primi mobilis, and a good
many more besides. It is a very interesting work, very well edited, and should be better known.
A description and illustration of such an instrument may be found in John North, Horoscopes
and history (Warburg Institute Surveys and Texts 13; London, 1986), 67–69. Obviously, the
precision of using the Tabulae primi mobilis far exceeds that of any instrument that could be
made.

3. Nuremberg Cent V app. 56c, f. 39v:

37. Aequationem octauae spherae secundum Alfonsi fundamenta numerare.

N. M. Swerdlow

38. Aequationem octauae spherae secundum imaginationem Tebith computare.
39. Aequationem solis colligere.
40. Aequationem argumenti lunae dinumerare.
Sed quo ruit calamus ille molestus atque audax? Forsitan omnia astronomorum quaesita
ad hanc unicam tabulam appellet? Dico ego bonam partem huiusmodi quaesitorum per
hanc repertum iri tabulam, si prius concentricam astronomiam totam fundauerimus. Quid
illud? Diuersitates motuum planetarum per concentricos saluare pulcrum erit. Iam soli et
lunae uiam dedimus, de reliquis autem quaedam initialia iacta sunt, quibus completis
aequationes omnium planetarum per hanc tabulam numerare licebet. De hac re nihil amplius
impraesentiarum, ne legendi scripta mea maius patiamini fastidium quam ego scribendo
uoluptatem habeam. Si quid harum rerum audentius aequo dixisse uideor, posteris litteris
rationes meas luculentius (sic puto) accipietis. Mallem tamen uoce quam calamo hisce de
rebus disserere, facilius enim multo et expeditius foret. Dum id fieri nequit, littere uoci
officia sumant, [margin: quae, quicquid afferent, uestro iudicio limandum erit].

M. Curtze’s text in Abhandlungen zur Geschichte der mathematischen Wissenschaften, xii
(1902), 218, is, as usual, faulty. While mine may not be perfect, it is at least better and
intelligible. For this passage, I have not checked the editions of von Murr (1786) and S. Magrini,
Atti e memorie della deputazione ferrarese di storia patria, xxii/3 (1917), which are always
preferable to Curtze’s. Regiomontanus follows this with the, possibly deleted, remark that he
intends to go to Milan on some business, and it appears that he did, for the following spring he
reports in his oration on the mathematical sciences delivered in Padua that he saw Giovanni de
Dondi’s astrarium kept safely by the Duke of Milan in his Castle of Pavia.

4. E. Zinner, “Neue Regiomontan-Forschungen und ihre Ergebnisse”, Sudhoff’s Archiv, xxxvii (1953),

107–8. Zinner again mentions the letter in Leben und Wirken des Joh. Müller von Königsberg
genannt Regiomontanus, 2nd edn (Osnabrück, 1968), 151, and the remarks in the letter to
Bianchini, 101. There is also a reference by H. Grossing, “Regiomontanus und Italien”,
Regiomontanus-Studien, ed. by G. Hamann, Sitzungsberichte der österreichische Akademie
der Wissenschaften, Phil.-hist. Kl., ccclxiv (1980), 223–4, p. 234, and discussions by A. Gerl,
Trignometrisch-astronomisches Rechnen kurz vor Copernicus (Boethius 21; Stuttgart, 1989),
210–13, and “The most recent results of research on Regiomontanus”, in E. Zinner,
Regiomontanus: His life and work, transl. by E. Brown (Amsterdam, 1990), 335–8. I would
politely suggest that not one of these accounts is based upon a study of the text or can withstand
scrutiny.

5. In the heading on f. 18r, the work is even addressed to Ilkusch: “Johannes Germanus ad Martinum

Ilkusch Cracoviensis in theoricas veteres a Gerardo aiunt Cremonensis editas.”

6. F. J. Carmody, “Regiomontanus’ Notes on al-Bi

’s astronomy”, Isis, xlii (1951), 121–30, which

Carmody wrote in connection with his edition of Michael Scot’s Latin translation, Al-Bi

De motibus celorum (Berkeley, 1952), and “The planetary theory of Ibn Rushd”, Osiris, x
(1952), 556–86.

7. M. H. Shank, “The ‘Notes on al-Bi

i’

attributed to Regiomontanus: Second thoughts”, Journal

for the history of astronomy, xxiii (1992), 15–30. The eclipses are those of 17 June 1433,
which seems to have been total, not annular, and 31 January 1310, which was annular and was
dated by Marcho to 1309 since the year in Paris began at Easter. Shank identifies G. Marcho
with the Francisan Guy de la Marche. See also M. H. Shank, “Regiomontanus and homocentric
astronomy”, Journal for the history of astronomy, xxix (1998), 157–66. I wish to thank Michael
Shank and Richard Kremer, who are engaged in a far more extensive study of Regiomontanus’s
interest in concentric-sphere models, for encouraging me to retrieve my transcription and
translation and write this paper.

8. Zinner, Regiomontanus (ref. 4), 61; Shank, op. cit. (ref. 7), 17.
9. B. R. Goldstein, Al-Bi

: On the principles of astronomy (2 vols, New Haven, 1971), 7–12.

10. Shank, op. cit. (ref. 7), 25–26.
11. N. M. Swerdlow, “Regiomontanus on the critical problems of astronomy”, Nature, experiment,

Regiomontanus’s Concentric-sphere Models

and the sciences, ed. by T. H. Levere and W. R. Shea (Dordrecht, 1990), 165–95, pp. 173–4.
Let me correct a mistranslation in this paper that has bothered me for years. On p. 172, paragraph
3, lines 2–3, for “familiarly known” substitute “obstinate” (inveterati, i.e. “chronic”). Then on
p. 183, paragraph 2, delete the first sentence. Regiomontanus’s point is that Jupiter and Saturn
do not present the long-standing problems of Mars.

12. If one asks why Regiomontanus did not simply put the mean sun at K

′

and the true Sun at L

′

, with

ZCK

′

in advance of

}

, the answer must be that ZK

′

and ZL

′

are not physical or structural

quadrants, as K

and LS, but just a way of measuring the equation

in the ecliptic; and such

an arrangement would not be a correction or modification of Bi

’s model, in which the

quadrant from the epicycle to the Sun, Moon or planet is essential.

13. This is the solution in De triangulis omnimodis IV, 28, for two sides and an included angle, adapted

to an exterior angle; V, 2 is equivalent to the law of cosines, although using versed sines, but
is not in a form suitable to this problem and one does not know whether Regiomontanus even
knew it when he wrote this work.

JHA, xxx (1999)

A CAREER OF CONTROVERSY: THE ANOMALY OF T. J. J. SEE

THOMAS J. SHERRILL, Los Altos, California

Few historical figures of early twentieth-century science inspire a degree of ran-
cour comparable to that evoked by the American astronomer Thomas Jefferson
Jackson See (Figure 1). At a time when the revolutionary developments of Ein-
stein’s theory of relativity and quantum mechanics were overturning the old phys-
ics, when new discoveries on the nature of the atom were astonishing the world,
and when technological breakthroughs were occurring almost weekly, public inter-
est in science grew to unprecedented levels. It seems perhaps odd that during this
productive period there should emerge as a major “spokesman” for science — con-
sulted by newspapers and other media to interpret scientific discoveries or worldly
events such as eclipses, earthquakes, or volcanic eruptions — a scientist whose
own theories ran counter to the revolution.

Although he had a solid background in celestial mechanics and was a respected

telescopic observer early in his career, when he turned to theoretical work T. J. J.
See began diverging from his astronomical colleagues in striking ways. He devel-
oped his own hypothesis of solar system evolution, as well as theories that ex-
plained the many diverse phenomena in the universe. In public lectures, numerous
books, and dozens of articles in popular science magazines he frequently managed
to convince a significant segment of the public that his unorthodox astronomical
views were to be preferred over more accepted contemporary theories. From as-
tronomy he ventured into other scientific fields, notably geology and physics, gen-
erating controversy after controversy. He helped lead scientific attacks on relativ-
ity, sought classical explanations for atomic and electromagnetic forces, and chal-
lenged Hubble’s concept of an expanding universe. With each controversy he alien-
ated himself further from the scientific establishment.

Despite his limited support among astronomers, See had a devoted public fol-

lowing who hailed him as “the American Herschel” and “the greatest astronomer in
the world”. This following was looked upon with embarrassment in the scientific
community, and it served as a constant reminder of the difficulty of explaining
science to the world at large. Once See had achieved some credibility with the
public, it was hard to counter his influence with reasoned arguments that might be
too technical for mass consumption.

Although his work is little known to today’s younger astronomers, it is perhaps

worthwhile to review See’s career, if only as a counterexample to the case for strict
application of the scientific method. While attempts have been made over the years
to ‘rehabilitate’ his reputation, or to suggest that some of his ideas were indeed
visionary for his time, the fact remains that many of his methods were deplorable
and eventually detrimental to science.

Thomas J. Sherrill

. 1. T. J. J. See, from the frontispiece of W. L. Webb’s Brief biography (ref. 1).

A Career of Controversy

Background and Education

Born near Montgomery City, Missouri, on 19 February 1866, Thomas Jefferson
Jackson was the sixth of nine children of Noah See, a well-to-do farmer. His early
education was typical for a farmer’s son in the post-Civil War era, consisting of no
more than four winter months a year in a country schoolhouse. Despite his obvious
brightness, it was only when he was seventeen years old that he was allowed to
attend a proper high school in the county seat, where he so distinguished himself in
science and mathematics that his father was persuaded to send him on to college.

At the State University of Missouri, in Columbia less than fifty miles from his

home, See continued to excel in all the sciences, but it was astronomy that drew him
most strongly. He was allowed to use the 7

-inch equatorial telescope at the univer-

sity’s small observatory to study the planets, comets, and stars; he took a particular
early interest in double stars. He graduated in 1889 as class valedictorian.

See was sent abroad for his graduate education, to the University of Berlin, which

had one of the world’s most respected faculties in the sciences, presided over by
Hermann von Helmholtz. The astronomy professors allowed the hard-working stu-
dent to observe and measure double stars with the Royal Observatory’s 9-inch re-
fractor. He learned the most modern techniques for calculating double star orbits,
and was to write his dissertation on the subject of the origin of such multiple sys-
tems. He received his Doctor of Philosophy and Master of Arts degrees magna cum
laude in December 1892.

At the University of Chicago

Upon graduation, See was offered an instructorship with the astronomy department
of the new University of Chicago by its president, William R. Harper, whom he had
met in Berlin. At the time the University’s astronomy department consisted solely
of the astrophysicist George Ellery Hale and a celestial mechanics specialist, Kurt
Laves. The department had considerable promise for the future, however, for Hale
and Harper had recently persuaded Charles T. Yerkes, a Chicago streetcar tycoon,
to purchase the 40-inch glass lenses then lying unground at the Massachusetts shop
of Alvan Clark and Sons. They were intended for the largest refracting telescope in
the world, to be the centrepiece of the planned Yerkes Observatory, a facility cost-
ing around $250,000.

In consultation with S. W. Burnham, the noted double star observer who was

awaiting a faculty appointment, it was decided that virtually all published double
star orbits — some of them decades old — required revision based on more recent
observations. See was assigned the task of leading a few graduate students in collect-
ing old and new observations, adding some of their own made at cooperating nearby
observatories, and systematically recalculating the orbits of the forty best-observed
binary systems. With such an ambitious project some shortcuts had to be taken, so
new graphical methods worked out with Burnham were utilized to speed up the
process of reducing the orbits.

Thomas J. Sherrill

See quickly realized that the project provided a fertile source of recognition, and

he began submitting papers almost monthly to the Astronomical journal in America
and the Astronomische Nachrichten in Germany, as the binary orbits were analysed
one by one.

This was the start of a prolific career as an astronomical writer and

popularizer, as he also began publishing articles in non-professional scientific month-
lies such as Popular astronomy.

In the meantime, the University of Chicago’s efforts to get the Yerkes Observa-

tory out of the planning stage had bogged down. After an observing session in
Europe, Hale was preoccupied with establishing the Astrophysical journal, and
Harper became increasingly worried about a projected estimate of $30,000 a year
which might be required to run the Observatory once it was built. At a meeting with
Harper, See offered to draw up a plan for running Yerkes on a much reduced budget,
and this offer was accepted. Supposedly this budget reduction earned the young
astronomer Hale’s animosity; among other things, See felt that this animosity was
behind the University’s reneging on a promise to publish his investigation of the
forty binary orbits in book form.

Thus See had to arrange to publish this work,

entitled Researches on the evolution of the stellar systems: Volume 1 (for he had
further plans for the subject), at his own expense.

In the spring of 1896, in consequence of See’s growing reputation as an ob-

server, Percival Lowell invited him to undertake a survey of the southern sky using
the 24-inch Clark refractor at Flagstaff, Arizona, for the discovery and measure-
ment of double stars. See accepted, and Harper offered him leave of absence to do
this work, with the rank of assistant professor. See, however, insisted on the posi-
tion of associate professor as his price to remain connected with Chicago. Since
this was the rank of the much more prominent Hale, Harper could not grant the
request, and See simply left.

Thus he lost the opportunity to work with the Yerkes

40-inch, which was completed and the Observatory opened in September 1897.

At the Lowell Observatory

The work for Lowell was another major undertaking for See, as many southern
doubles had not been measured since their discovery by Sir John Herschel during
his expedition to the Cape of Good Hope from 1834 to 1838. Because observations
of Mars had top priority at Flagstaff, the binary survey with the 24-inch (Figure 2)
had to be done when the planet was least accessible. During the winter of 1896–97
the telescope was transported to a site near Mexico City, where the low latitude
enabled the survey to reach as far south as declination –65° (again vying for time
with Lowell’s Mars work). The results, which included the discovery of 600 new
doubles and the re-measurement of 1400 previously recognized by Herschel, were
catalogued in the March 1898 issue of the Astronomical journal.

Although this work was generally well-received, there were some astronomers

who began to accuse See privately of carelessness as an observer.

In addition, they

felt that the young man’s overconfidence frequently led him to mischaracterize

A Career of Controversy

T. J. J. See (right) and his assistant, W. G. Cogshall, sweeping for double stars with the Lowell
Observatory’s 24-inch Clark refractor in Mexico City during the winter of 1896–97. Their po-
sitions were normally reversed, with See at the main telescope’s eyepiece and his assistant
recording the micrometer measurements and sketching the finder’s field. From Webb’s Brief
biography (ref. 1), plate following p. 66.

. 2.

Thomas J. Sherrill

results, and sometimes to engage in rank speculation in his writings. For example,
while reducing the forty binary orbits at Chicago he had written about one of them
in an October 1895 letter to the Astronomical journal:

Since August 20, when I first announced to you the existence of peculiar anoma-
lies in the motion of the companion of [70 Ophiuchi], I have succeeded in
showing conclusively that the system is perturbed by an unseen body.... I find
that the dark body has a period of approximately forty years.... The sudden
deviation of the companion from Schur’s ephemeris proves the existence of the
dark body here assumed.

Elsewhere, writing of his Lowell double star survey, he claimed that

Among these obscure objects about a half a dozen are truly wonderful, in that
they seem to be dark, almost black in color, and apparently are shining by a dull
reflecting light. It is unlikely that they will prove to be self-luminous.

See stopped just short of declaring these dark bodies to be “... the first case of
planets ... noticed among the fixed stars”.

In October 1897 See published his first article for a non-scientific national maga-

zine, Atlantic monthly — a nine-page dissertation highlighting his work on double
stars.

Apparently he wanted to ensure that his accomplishments received due no-

tice in the world at large, as well as in the scientific community.

It had been intended to extend the Lowell survey even farther south by temporar-

ily relocating the 24-inch refractor in Peru, but Percival Lowell suffered an unex-
pected nervous breakdown in 1898, so that most of his observatory projects had to
be suspended for over two years. In February 1899, on the recommendation of the
Secretary of the Navy, President William McKinley appointed See to a professor-
ship of mathematics in the Navy, on assignment to the U.S. Naval Observatory in
Washington D.C. In fairly short order he was put in charge of the Observatory’s
biggest telescope, the 26-inch Clark refractor.

This instrument was as excellent as

the Lowell 24-inch, although its achievements were limited by the unsteady skies
of Washington, which could seldom match the seeing at Flagstaff.

Thus, in 1899 the 33-year-old See had one of the most promising futures of any

young astronomer in the country.

The Dark Star

A comedown was in store. See had followed up his 1895 letter to the Astronomical
journal on the orbit of 70 Ophiuchi with a paper analysing the apparent systematic
departures of the 88-year-period binary from the orbit given earlier by Schur and
from one recalculated by See which included more recent observations. He confirmed
that the most likely explanation was an unseen satellite of the companion, whose
period he revised to approximately 36 years. He confidently stated that the nature
of the residuals between observed and computed positions “... would be a necessary

A Career of Controversy

consequence of the orbital motion of the visible companion about the common center
of gravity, and may be said to establish completely the reality of that phenomenon”.

In the 15 May 1899 issue of the Astronomical journal Forest Ray Moulton, who

had been a graduate student of See’s at the University of Chicago (and had not yet
been awarded his Ph.D.), published a paper which showed that the postulated dark
satellite could not exist. On the basis of the solution of the restricted three-body
problem, Moulton proved that the orbit of such a satellite would be highly unsta-
ble.

He pointed out that Eric Doolittle, another former student who had performed

most of the calculations for See’s paper, had in the meantime calculated a new orbit
for 70 Ophiuchi which represented the observations reasonably well without as-
suming the existence of a third body.

See could have considered this disclosure just a temporary setback, as double

star work is replete with examples of misidentifications of single stars or false con-
jectures of additional components.

However, he attempted to evade the charge of

coming to an erroneous conclusion. “Those who will examine my original papers
in A. J. 358, 363”, he wrote to the journal in response, “will see that I foresaw from
the first the difficulty of securing stability, and that while I assigned the unseen
body to the companion, ... I never entertained any very decided view as to which
star the dark body attended”.

The Astronomical journal did not print the bulk of See’s letter, so it is unknown

what additional claims he made on his behalf. But from their appended note it is
clear that the Journal’s editors felt that See was obscuring the issues:

Dr. See’s remarks were transmitted to Mr. Moulton to afford him the opportu-
nity, if he desired, to reply; but he declines, on perfectly correct and dignified
grounds, to do so; his essential and sufficient reason being that the statements
are not in accordance with the facts....

The present is as fitting an opportunity as any to observe that heretofore Dr. See
has been permitted, in the presentation of his views in this journal, the widest
latitude that even a forced interpretation of the rules of catholicity would allow;
but that hereafter he must not be surprised if these rules, whether as to sound-
ness, pertinency, discreetness or propriety, are construed within what may ap-
pear to him unduly restricted limits.

The Journal’s note, with its implicit threat to censor future contributions by See,

was interpreted as banishing him from the publication. Such an outright act was
almost unprecedented for a scientific journal, and represented a severe reverse for
someone in the process of making a name for himself as an astronomer. See contin-
ued to use the Astronomische Nachrichten as a vehicle for publishing detailed
technical papers (mostly in English), and Popular astronomy and other, wider-
circulation magazines for more popular articles on his work. If the articles he wrote
were sometimes self-serving, they were also widely read by a public anxious for
information on the latest developments in science.

Thomas J. Sherrill

aptain See in his of

fice a

t the small U

. Na

al Obser

tor

y a

t Mar

e Island

, Calif

nia. He is sho

wn e

xamining the plans of

illiam

Her

hel’

s 40-ft r

lector

rking up to eighteen hour

s a da

in this r

oom the indef

tig

le See wr

ote thousands of pa

ges e

anding

upon his scientif

ic theor

ies. F

rom

ebb’

ief bio

raph

. 1),

thir

d pla

te f

ollo

wing p. 82.

. 3.

A Career of Controversy

With the Navy

See was able to take full advantage of the 26-inch refractor at the Naval Observa-
tory, making micrometrical measurements of asteroids, faint satellites, and plan-
etary diameters. Although he did not publicly state so at the time, he later claimed
that he observed faint belts on Neptune and glimpsed crater-like markings on Mer-
cury during this period.

He also participated in the international effort to redetermine

the solar parallax by observing the asteroid Eros at its close approach to the Earth in
1901.

However, See did not take well to the highly organized program of work at the

Naval Observatory, and the tension and overwork he experienced there contributed
to a “breakdown” in 1902.

See himself described symptoms of stomach trouble

and insomnia, due to “a severe internal catarrhal condition approaching a mild form
of appendicitis”.

He was to suffer similar bouts off and on for several years.

Following a six-month leave of absence to recuperate, See was transferred to the

U.S. Naval Academy at Annapolis, where he was an instructor in mathematics for
one semester. He did not fully recover from his illness there, and so was transferred
once more in November 1903, this time to be placed in charge of the Naval Ob-
servatory at Mare Island, near Vallejo, California. The more healthful west coast
climate agreed with him, and he was to remain there for the rest of his life.

The Observatory, however, was little more than a chronometer and time station

attached to the huge naval shipyard, and had no telescope larger than a 5-inch re-
fractor. It became clear to See that if he was to make further discoveries, it would
not be as an observational astronomer. Instead, he was to turn to theoretical work
(Figure 3), with a view toward making the work the core of vol. ii of his Researches
on the evolution of the stellar systems.

The work proceeded only slowly. See’s Navy superiors at Mare Island, appar-

ently pleased to have an astronomer of some stature at their little observatory, al-
lowed him much leeway in what he chose to investigate. Working up to eighteen
hours a day, he was often sidetracked when some area captured his interest —
particularly if he thought his work on the subject would likewise capture public
interest.

Thus, after the great San Francisco earthquake of 1906, See embarked on a two-

year study to attempt to shed light on the origin of such events. He concluded that
the main cause of earthquakes was leakage of the ocean floor. Coming into contact
with lava beneath the sea bed, the leaking water generated steam, which expelled
the lava landward to produce the upheaving of the Earth’s crust during a coastal
earthquake. See also alleged that many repetitions of this process over time had
been responsible for the formation of mountain ranges. He expounded these views
most thoroughly in hundreds of pages in the Proceedings of the American Philo-
sophical Society of Philadelphia.

Professional geologists in the main were not impressed by See’s incursion into

their field, and except for a few European investigators tended to ignore his work.

Thomas J. Sherrill

In a letter to Science, See proclaimed that “I have proved that mountains are formed
by the sea, ... and ... that the oceans are gradually drying up and the land increas-
ing”.

He furthermore stated that his arguments had been so convincing that “...

geologists have discreetly kept silent”. In response, a noted Yale geologist, Joseph
Barrell, wrote to Science that ocean leakage was an old idea, and that See’s work
was merely

... a dressing out of this old and, to say the least, doubtful hypothesis with many
speculative additions, with much repetition of well-known facts and theories,
and with specific applications in such frequent discord with modern teaching
of the principles of physiography and known details of geologic structure and
history, that no geologist has felt called upon to comment.

But See was not deterred by attacks, and continued to explore other fields while

working on plans for his Researches. He travelled and lectured widely, and spent
most summers at his childhood home in Missouri. On one such visit, in June 1907,
he married Frances Graves, a physician’s daughter, in Montgomery City. See was
41. The couple were to have one surviving son, Ernest, although another son died in
infancy.

The Capture Theory of Cosmical Evolution

When See returned to astronomical subjects, he took up the popular topic of solar
system evolution. He had for years doubted the long-held eighteenth-century
Laplacian hypothesis that the gravitationally contracting solar nebula had depos-
ited gaseous rings at the orbital radii of the planets, and that these rings subse-
quently had condensed to form the planets themselves. Forest Ray Moulton had
shown in 1900 that this idea was not consistent with the Sun’s current rotation rate,
on the basis of the laws of conservation of angular momentum.

By the close of the

first decade of this century, most astronomers had come to reject Laplace’s hypoth-
esis, but there was no consensus in favour of a theory to replace it.

In 1904 Moulton and T. C. Chamberlin, a geologist at the University of Chicago,

developed the planetesimal hypothesis, which proposed that nebulous matter sur-
rounding the early Sun condensed into small solid bodies called planetesimals, which
eventually aggregated through collisions to form the planets.

Although they claimed

it was not required by the theory, they favoured as the origin of the solar nebula
tidal disruption of the Sun by an encounter with a passing star. Along with many
astronomers of the day, Moulton and Chamberlin came to believe that the stunning
time exposure photographs of spiral nebulae coming out of Lick Observatory and
other places represented direct evidence of forming solar systems. (The Shapley–
Curtis debate touching on whether the spirals were nearby nebulae or distant galax-
ies was still sixteen years in the future.) It was thought that the spiral’s nucleus was
condensing into a star like our Sun, while the knots and clumps of gaseous matter
arrayed along the spiral arms were the infant planets and satellites.

A Career of Controversy

See at first strongly opposed this interpretation of the nebula photographs, writ-

ing in a 1906 Popular astronomy article with characteristic assertiveness: “The specu-
lations on spiral nebulae have been decidedly overdone, and it is time to call a halt.
There is not the slightest probability that our solar system was ever a part of a spiral
nebula, and such a suggestion is simply misleading and mischievous.”

But See changed his mind, apparently feeling that he needed the evidence of the

suggestive photographs to make a case for his own developing theory. He was to
call his picture of solar system formation the capture theory after its central tenet:
that instead of being separated off from the Sun the planets had been captured
gravitationally from where they had formed farther out in the solar nebula. Their
initially eccentric orbits had been reduced in size and circularized by the resisting
action of the nebular gas surrounding the Sun. In a similar way, the planetary satel-
lites originally rotated about the Sun but were captured by the larger planets.

See developed these ideas, some of which originated with earlier investigators,

over a period of several years (Figure 4), and planned to showcase them in his
follow-up volume of the Researches. He decided to give a preview of this portion of
the work at a January 1909 meeting of the Astronomical Society of the Pacific at
Chabot Observatory in Oakland, California. However, he developed full-blown ap-
pendicitis about three weeks prior to the meeting, and lay in the hospital for sixteen
days before his doctors felt it was safe to operate.

Thus, T. J. J. See was not even present at the event he was to later characterize as

one of his life’s greatest triumphs. His paper was read before the open meeting by
Russell T. Crawford of the University of California at Berkeley, the Society’s secre-
tary. The front page of one section of the Sunday San Francisco Call on the follow-
ing day declared “Prof. See’s Paper Creates Sensation at Meeting of Astronomical
Society”,

while an article in the San Francisco Examiner was headlined “Scien-

tists in Furore over Nebulae”.

Over the next few days the opinions of astronomers

who were present at the meeting, as well as those of others who were not, were
solicited by the San Francisco newspapers. Charles Burckhalter of Chabot Observa-
tory was quoted as saying, “Professor See’s theory seems to me more reasonable
than any other that has yet been advanced.... I believe that See has not solved the
whole mystery of the universe, but he is enthusiastic in his discovery, which is a great
one.”

Crawford himself thought See’s theory was plausible, but was basically unde-

cided “until I am able to give a closer examination to the facts that Professor See has
compiled”.

John Brashear, the well-known astronomical instrument maker, issued a

signed statement from Pittsburgh that he could not tell from newspaper accounts ex-
actly what See was proposing, but that “there is little doubt Dr. See’s paper ... should
be given much weight, because he is a man whose researches and mathematical stud-
ies entitle him to a hearing among his scientific colleagues”.

Interviewed in his sick bed at Mare Island’s naval hospital, See asserted with

little modesty, “I am fairly convinced that I have solved the problem and that no
astronomer in the future will be able to disturb the chain of reasoning and

Thomas J. Sherrill

mathematics that I have worked out”.

A five-page paper summarizing his theory

appeared in the Astronomische Nachrichten on 24 February 1909, but it contained
no such mathematical chain.

This must have been a disappointment to those in the

astronomical community who seemed willing to listen, but it appears to have mat-
tered little to See. Rather, he seemed to relish the attention he was getting, whether
his peers embraced his hypotheses or not.

While his summary papers were at least serious and reasoned, See apparently

could not resist a desire to be recognized as a prophet: in a postscript submitted to
the Astronomische Nachrichten nine days after his summary paper, he predicted “...
that there is certainly one, most likely two, and probably three unknown planets
beyond Neptune”.

On the basis of unpublished work he had done in 1904, he

placed the nearest of the new bodies at a radius of 42.25 AU from the Sun, and the
others at 56 and 72 AU. He recommended a photographic search of a specific re-
gion of the ecliptic for the first body, which he tentatively named “Oceanus”. See

One of the sixty or so articles in Popular astronomy by which See established his firm reputa-
tion with the public. The frontispiece is a copy of a bookplate presented to him by California
admirers, and depicts (clockwise from upper left): M74; Kaulbach’s painting of Homer and
the Greeks; Plato; and the solar system. The Greek caption at the top reads: “T. J. J. See, the
geometer outside the library”, while that at the foot quotes the Platonic aphorism, “The Deity
always geometrizes”. From Popular astronomy, xix (1911), 528–9.

. 4.

A Career of Controversy

never revealed how he arrived at his predictions, but it seems most likely that he
applied some graphical technique to observed perturbations of Neptune. There is
no evidence that anyone seriously sought his postulated new planets.

In addition to his local exposure, See sought a wider audience for his latest ideas.

In a letter of 28 May 1909 to Science he attacked “... the inconsistent and purely
destructive criticisms recently put forth at Chicago by Chamberlin and Moulton....
Most of the recent speculations on cosmogony are not worth the paper they are
written on; and yet some of them have been published by the Astrophysical journal
and the Carnegie Institution.” He went on to promote his own competing theory:

It is only fair to say that no constructive results of consistent character had been
reached on this subject till my own investigation was completed last year, of
which an account is given in Astronomische Nachrichten.... As I have worked
on this subject uninterruptedly for twenty-five years, I am prepared to speak
with some degree of authority.

Forest Ray Moulton had been silent during the earlier debate over See’s theory,

but the Science letter represented direct and personal criticism. In a response pub-
lished in the 23 July issue of Science, he accused See of “extravagant pretensions”
regarding his (See’s) background in cosmogony (as cosmology was then called),
pointing out that See’s “alleged twenty-five years of uninterrupted work” in the
field had apparently resulted in only two published papers. He also castigated See’s
claim of consistency, contrasting his 1906 claim that there was “not the slightest
probability that our solar system was ever part of a spiral nebula” with his latest
paper’s statement that “The solar system was formed from a spiral nebula”. In fact,
Moulton averred that

In See’s paper there are only two points of divergence from the ideas fully
developed by Professor Chamberlin and myself. The first is that spiral nebulas
have their origin in “the meeting of two or more streams of cosmical dust”. The
second is that satellites are captured bodies.

Moulton strongly implied that See had deliberately adapted portions of the
planetesimal hypothesis to his own purposes without giving credit to its authors.

Moulton’s accusations were printed on the front page of the San Francisco Call,

under the headline “Astronomers Warring — Moulton Exposes See” and the sub-
heading “Chicago Professor Says Mare Island Observer Stole Discarded Theories”.

See responded the following day that the Chicago professors were “exercised” be-
cause See’s researches had been accepted by the scientific world and had com-
pletely upset several years’ worth of their work.

He also maintained in a letter of

reply to Science that “I have since developed a rigorous proof ... of just how the
capture of satellites comes about”.

The proof was not forthcoming, and Moulton’s

conflict with See continued to smoulder for nearly three more years.

Vol. ii of See’s Researches, subtitled The capture theory of cosmical evolution,

appeared late in 1910, running to some 735 oversize quarto pages. Beautifully printed

Thomas J. Sherrill

(again at his own expense) and profusely illustrated, it presented a review of many
topics in celestial mechanics and drew together much of See’s work since vol. i, but
it also contained much that was new. In See’s world view, most of the phenomena
of nature could be explained by suitable application of his capture theory and at-
tendant hypotheses. Besides his treatment of solar system evolution, some of his
key points were as follows:

The Moon’s craters were caused by the impact of other, smaller satellites of the

solar system, rather than by volcanic action.

The Earth and other planets once had craters like the Moon’s, but these have

since been obliterated by water and atmospheric erosion.

Direct (west to east) planetary rotation resulted from the cumulative effect of

collisions with smaller bodies, as did the tendency of a planet’s equatorial
plane to coincide with its orbital plane about the Sun.

Comets originate in the outer reaches of the remnant solar nebula, and periodic

comets are those that have been gathered in by the gravitational action of
Jupiter.

In addition to gravitational attraction, repulsive forces are at work in the uni-

verse, in the form of gas and dust continuously being expelled from stars.

The matter expelled from stars tends to aggregate in vacant regions toward the

poles of the Milky Way, which explains why spiral nebulae are more numer-
ous in these directions.

After stars form out of the spiral nebulae, they eventually drift back into the

plane of the Milky Way.

Diffuse nebulosity results when the gas expelled from stars is too tenuous to

condense into more compact form.

Collisions of smaller bodies are the cause of most of the light of nebulae.
All single stars have planetary systems revolving about them.
Double and multiple stars are formed when a large spiral nebula divides into two

or more parts, which condense separately.

Star clusters evolve from incredibly vast nebulae, and from the gathering in of

neighbouring stars under the clustering power of gravitation.

Variable stars occur when the orbits of attending dark companions cause them to

eclipse the light of the primary star, or occasionally when a companion gives
off light due to nebular resistance encountered when closest to the primary.

Novae result from the conflagration produced when a planetary body collides

with its central star.

The Milky Way is much more extensive than previously thought; extinction of

light by cosmic dust is so great that starlight from the farthest distances is cut
off.

Life is a general phenomenon of the physical universe, and almost as universal

as matter itself.

A Career of Controversy

Some of See’s ideas in the book were quite original and even prescient of more

modern theories, but many more were speculations presented with little justifica-
tion, and others were borrowed from his contemporaries. Still, he could fairly claim
that he had unified many of these concepts for the first time.

The astronomical community’s reaction to See’s tome was reasonably polite,

although some continued to be disappointed by the lack of sufficient evidence for
many of the author’s conjectures. His publisher issued a circular quoting about two
dozen scientists’ comments on the work, some of which must be taken with a grain
of salt (since they were undoubtedly solicited in exchange for a free copy). A few
were possibly left-handed compliments, such as that of the celestial mechanics spe-
cialist, E. W. Brown of Yale: “The beautiful printing and magnificent illustrations
are a very unusual feature, and make the book a welcome addition to any library,
quite apart from the contents.”

If some astronomers were equivocal in expressing their support, See himself

apparently had no qualms about claiming it. To Popular astronomy and elsewhere
he submitted an article asserting that E. W. Brown had verified his ideas of the
capture of satellites,

and in other articles he stated that the French mathematician

Henri Poincaré had adopted some material from See’s book into a course of lec-
tures in Paris.

Forest Ray Moulton, however, was in no way equivocal in his reaction to See’s

book. In an article in the February 1912 Popular astronomy entitled “Capture theory
and capture practice”, Moulton demonstrated that an important section of the work
had been “captured” from Moulton’s 1902 book Introduction to celestial mechan-
ics without credit.

The article reprinted three pages of See’s book and the corre-

sponding parts of Moulton’s text face-to-face to show that except for changes of
notation the equations involved were identical. The failure to give specific credit
might have been attributed to oversight — the chapter was after all a review of the
three-body problem and not claimed to be original, and See had referenced Moulton’s
book in the second chapter previous (his only such mention of it in the Researches)
— but Moulton also asserted that See’s discussion of the equations showed a seri-
ous lack of understanding of the fundamentals of celestial mechanics. Moulton
claimed that equations were misused, illustrations misdrawn, and important con-
cepts played havoc with. The critique made numerous sarcastic references to See’s
immodest claims on behalf of the capture theory, especially the claims that Brown
and Poincaré supported it, emphasizing that “these astronomers have not announced
in their publications that they have taken such a position”. As in some of his earlier
attacks, Moulton appeared galled by the fact that See was garnering wide attention
for a theory which he had developed largely from the efforts of others, without
having mathematically derived a significant number of his own results. Moulton
expressed contempt for “those who make books with shears”.

See never again wrote for Popular astronomy (except for an obituary piece on a

close astronomer friend in 1920

), although he had previously written some sixty

Thomas J. Sherrill

articles and letters over twenty years. It does not seem likely that the magazine’s
editors “banished” him as had the editors of the Astronomical journal, for he was a
popular contributor and the Moulton affair was just one black mark. Rather, See
was probably incensed and hurt that the editors would print such a scathing and
personal attack upon him.

A Growing Dichotomy

This crushing blow to his self-esteem served only to widen the gap between T. J. J.
See’s position within the professional astronomy community and his stature as per-
ceived by the public at large. On the one hand, except for a modest core of support-
ers, astronomers remained cool toward the Researches; the work was seldom cited
in professional papers. The public, on the other hand, was largely unaware of
Moulton’s highly technical critique, and knew little of See’s humiliation within the
scientific world. They saw his theories discussed in the New York Times and na-
tional magazines, as well as presented as the subject of editorials. In an era of
expanding scientific discovery, scientists who could expound impressively on their
ideas were held up to public adulation, and See was a grand example. In his naval
captain’s uniform (he was commissioned an officer in 1913), the six-foot four-inch,
athletically built professor must have been an imposing figure on the lecture plat-
form. At the time the public lecture was both a popular form of entertainment and
an educational experience, and a riveting speaker could transfix an audience with
the help of a lantern slide projector and never-before-seen astronomical photographs.
If the speaker was not quite accepted by the scientific establishment, his listeners
could probably convince themselves that they were witnessing the revelation of a
startling new view of the cosmos.

In 1913 a longtime admirer and amateur astronomer from Independence, Mis-

souri, William Larkin Webb, published the 300-page Brief biography and popular
account of the unparalleled discoveries of T. J. J. See. The introduction declares:

Professor See is universally recognized as the most intrepid and indefatigable
of the explorers of Nature; and since the death of Poincaré and Sir George
Darwin, in 1912, occupies easily the front place among living natural philoso-
phers.

Chapter after chapter cites See’s numerous accomplishments, leading up to “the
triumph of the Capture Theory”. Of the acceptance of the latter the book is blithely
optimistic:

Considering the extremely revolutionary character of See’s discoveries, it must
be held that they have had a very favorable reception from the scientific world....
[As] time has elapsed it is noticed that acceptance of the results is general, and
that acquiescence in See’s conclusions becomes more and more universal.

Considering the sometimes fawning prose in the biography, most reviews of the

A Career of Controversy

book were not overly unkind, although The nation’s review noted that it abounded
in “parlous surfeit of superlatives”. Less than one-half of the book actually de-
scribes events in See’s life (the remainder reprints several of his papers and lec-
tures), and The nation took the opportunity to poke fun at the hyperbole in the
scientist’s portrayal:

The infant See, we are told, first saw the light on the 393d anniversary of
Copernicus’s birth, ... [and] showed himself “every inch a natural philosopher”
by speculating on the origins of sun, moon, and stars at the tender age of two,
never so much as dreaming that he should grow into a “little boy with methodi-
cal methods”, and one day become “the greatest astronomer in the world”.

With considerable insight, the reviewer presented a more balanced view of the sci-
entific world’s actual reception of See’s theories:

During the past twelve years he [See] has pursued researches in universe build-
ing to which has not as yet been accorded that full acceptance which their au-
thor and his biographer seem to believe has been the case.... So far his revolu-
tionary theories seem only in small part acceptable to his scientific contempo-
raries.

New Theory of the Aether

While See’s astronomical views were at least treated with a modicum of respect,
his ensuing researches into more fundamental physics provoked reactions approach-
ing scorn. In April 1914 he announced to the press that he had discovered the cause
of gravitation, thereby answering a question that had puzzled scientists since the
days of Isaac Newton. He claimed that gravity results from particles being expelled
at the speed of light on electrical streams from the millions of stars in the universe.
The attractive force between two bodies is really only the apparent result of each
body screening the other from the bombardment of these particles from all direc-
tions; since each body experiences fewer collisions from the direction of the other,
they are forced together.

Like many of See’s earlier ideas, this one was essentially derivative, from hy-

potheses dating back two centuries. Natural philosophers in the time of Newton had
developed the basic concept, but the scheme was most clearly spelled out in the
“theory of ultramundane corpuscles” of George Louis Le Sage, published in 1818.

See’s alleged discovery was a secondary result of a discovery of the nature of

light, which he announced at the same time. This hypothesis stated that light con-
sists of egg-shaped particles of matter rotating about their shorter axes and bearing
an electrical charge on the sharper ends. See claimed to have proved his theory, and
overthrown the theory that light consists of waves transmitted through the ether.

Mainstream astronomers were quick to pronounce judgement on See’s new theo-

ries. The San Francisco Chronicle submitted a summary of them to the University
of California at Berkeley, where a committee of scientists that included the Lick

Thomas J. Sherrill

Observatory director, W. W. Campbell, met and issued a statement that “The whole
thing is an unsubstantiated theory and as such cannot be dealt with by scientists.
Until he shows proofs there can be no discussion. The scientific world will ignore
the theory as it now stands.”

See sent a 600-page account of his theory to the

Royal Society of London in November 1914, but it was disregarded. In 1917 he
privately published a revised version, which also received little serious attention.

Between 1920 and 1926 the ever-indulgent Astronomische Nachrichten finally

published See’s re-revised theory as the “New theory of the aether” (which he ap-
parently decided did exist after all), a series of eight papers comprising some 300
pages.

The theory asserted that gravity, electricity, and magnetism were all due to

ether waves propagating at the speed of light. The ether was an extremely rarefied
but enormously elastic gas, consisting of tiny particles called etherons, each one-
billionth the size of an electron and travelling at a velocity 57% faster than light.
Now, instead of his 1914 “screening” explanation, the attractive gravitational force
between two bodies was explained in terms of helical electrodynamic waves emit-
ted by each, as many rotating in a right-handed sense as in a left-handed sense.
When the waves from one body encountered oppositely-rotating waves from the
other, their interpenetration acted to undo the stress in the ether, so that the ether
contracted and drew the bodies together.

In See’s theory, virtually all of the phenomena of the universe — light, atomic

forces, radioactivity, molecular forces, explosive forces, sunspots, lightning, auro-
ras, magnetic storms, earth currents, etc., etc. — could be addressed in terms of
waves in the ether. Thus, his was a “theory of everything” which could be called
upon to explain physical happenings from the cosmic to the mundane.

Although See wrote hundreds of pages on these subjects, there was a serious lack

of the substantive kind of proofs that the Berkeley committee had asked for. There
were numerous historical anecdotes dating back to Laplace, Newton, or even the
ancient Greeks; there were dozens of equations from Maxwell, Lord Kelvin, or Poisson,
some of them irrelevant to the subject under discussion; there were trivial, hard-to-
follow, or spurious arguments connecting the equations; but little was proved or even
made to seem plausible. As an example of ‘non-sequitur’ reasoning, See deduced the
velocity of etherons from a relationship he had worked out between the mean mo-
lecular velocity v and the velocity V of sound wave propagation in monatomic gases,

v =

/2V,

but he failed to justify why particles one-billionth the size of an electron should
behave like a monatomic gas, or why electromagnetic waves should behave analo-
gously to sound waves.

In the last of the eight new papers See calculated the probability that his wave

theory was a correct interpretation of nature to be as infinity to the 200th power to
one (

∞

200

: 1)!

To his contemporaries the reasoning in the papers must have seemed

to be only so much smoke and mirrors. As the Berkeley group had foretold, his new
theory was not taken seriously, and went virtually undiscussed elsewhere in the

A Career of Controversy

scientific literature. (It may be speculated that the only reason the Astronomische
Nachrichten continued to publish his papers is that its longtime editor, Hermann
Kobold, was an old friend of See’s.) Only in the popular press did his case for
etherons get a hearing (Figure 5).

Adversarial Physics

During this same period See began attacking Albert Einstein’s theory of relativity,
which he considered a “crazy vagary”. Although many scientists of the day rejected
relativity, See was especially vitriolic in his criticism. As most of the scientific world
was applauding the confirmation of the theory’s prediction for the bending of light
rays passing near the Sun, based on solar eclipse observations in 1919 and 1922, See
accused Einstein of having plagiarized the formula for this effect from the 1801 result
of J. von Soldner, a German physicist, who had used Newton’s corpuscular theory of
light in his derivation.

See made much of the fact that Einstein had at first calculated

a value for the magnitude of the deflection exactly one-half of his theory’s final value,
and accused Einstein of revising the theory in order to hide the error.

Later on See claimed that Einstein had made more than eighty errors in his basic

calculations on relativity theory. See entered into numerous debates on the theory
with other scientists in articles and letters in the New York Times and elsewhere, and
never missed an opportunity to attack Einstein or promote his own ether wave theory.
The Cambridge astronomer Arthur S. Eddington branded See’s criticism “all bosh
and nothing to it”,

but Einstein himself avoided the fracas. Einstein’s only re-

corded comment regarding See came after his wife relayed a telegram to him in
Holland containing the text of See’s October 1924 claims to have demolished rela-
tivity: “Too bad about that long telegram from New York.”

See also rejected Edwin Hubble’s idea of an expanding universe almost from the

time it was first proposed in 1929. See contended that the observed increase in the red
shift of extragalactic nebula spectral lines with distance was due not to motion away
from the Milky Way galaxy but to physical changes of the light waves themselves. As
interpreted by his theory, light waves lost energy in collisions with cosmic dust, and
this loss produced a wavelength increase in proportion to the nebula’s distance.

See’s many controversial ideas attracted substantial public attention and put him

at odds with other scientists time and again. During this period he advanced a theory
that sunspots were caused by meteors raining down upon the Sun’s surface, di-
rected by the gravitational influence of Jupiter and Saturn. He deduced that the
eleven-year sunspot cycle period was a combination of the orbital periods of the
two giant planets. He received considerable press coverage from his declarations
that sunspots were responsible for climatic cycles of flood and drought on Earth.

See also announced his interpretation of several intercontinental radio signal ex-

periments which made news at the time. He claimed that radio waves travelled about
11% slower than light, bending around the Earth’s surface during long-distance trans-
missions.

He also considered that radio waves travelled preferentially over the night

Thomas J. Sherrill

A feature article on See’s ether wave theory in the Sunday edition of the San Francisco Exam-
iner, 11 March 1928, p. K-5. By this time See had largely stopped writing popular articles on
his astronomical work, as there were numerous journalists only too willing to do this for him.

. 5.

A Career of Controversy

hemisphere rather than the day hemisphere because the ether is quieter at night.

See retired from the Navy at age 64 in 1930, but he remained at Mare Island, now

free to work on his theories full time. As he became increasingly strident in ex-
pressing eccentric views, scientific publications shunned his papers. Following the
death of Hermann Kobold, even the Astronomische Nachrichten published no arti-
cles by him after 1938.

As the new physics gained acceptance by the scientific world and eventually by

the public in the 1930s, See’s views began to fall out of popular favour. Many
scientists were especially relieved when controversy over relativity died down.
Gradually, even the press stopped seeking out See’s opinions on such topics.

See was to write eleven more volumes expanding on his ether wave theory. Is-

sued under the collective title Wave-theory! between 1938 and 1952, these volumes
were published as rotographic prints of typewritten copy, with equations written in
and illustrations (Figure 6) drawn by hand.

In the preface to the first volume See

compared his struggles to get the definitive version of his theory published to the
Royal Society of London’s hedging on the publication of Newton’s Principia, which
Halley eventually printed at his own expense.

Wave-theory! re-covered much of the ground gone over in the eight Astronomische

Nachrichten papers, then went on to extend See’s ideas to further physical phenom-
ena and to scientific discoveries made since 1926. The arcane illustrations, most
drawn by the author himself, bore more of a resemblance to those seen in meta-
physical treatises of the period than to those in scientific works. Perhaps in an effort
to appear modern, See “proved” in vol. v that the developing quantum theory was
really just a branch of his wave theory, and “derived” the value of Planck’s constant
from his theory’s basic principles. Never reluctant to go out on a limb, in vol. ix he
calculated the age of the solar system as at least 10.44 trillion years, 3000 times the
age estimated by other astronomers at the time.

Conclusion

But by the time of the last Wave-theory! volume See was 86 years old, and most of the
scientific community had long ceased to take him seriously. For over thirty years few
scientists bothered to criticize his work in a public forum, as if to do so would dignify
it. See was debated mainly when he publicly attacked other scientists such as Ein-
stein, and in their responses others would seldom mention See’s own new theories.

An unhappy aspect of See’s becoming virtually a pariah to the scientific world is

the deterrent that this might present to later investigators with unorthodox or other-
wise unpopular views. Fortunately, most scientists are willing to grant a degree of
respect to those with opposing opinions, as long as these opinions have some rational
basis. They are all too aware that today’s unpopular theory can become tomorrow’s
fundamental truth. In addition, there is no permanent stigma attached to being wrong
on some issue: Albert Einstein himself could not accept some of the basic princi-
ples of quantum mechanics, as evidenced by his famous quote, “God does not play

Thomas J. Sherrill

Diagram illustrating See’s theory of gravitation, from p. 27 of vol. i (1938) of his Wave theory!
He saw the attraction between the Sun and Earth as arising from helical electrodynamic waves
emitted by each. Interpenetration of waves rotating in opposite directions acts to undo the
stress in the ether, so that the ether contracts and draws the bodies together.

. 6.

A Career of Controversy

dice”. See became anathema because he insisted on taking his case to the public at
large when he was unable to convince his peers. It was also considered questionable
in an age of growing specialization to venture outside of one’s field of training — as
See did into geology, climatology, and numerous branches of physics.

Nevertheless, See’s excesses should not be allowed completely to overshadow

his accomplishments. His early double star work was in large part sound, and his
observational skills were generally to be trusted. He was basically on the right track
in promoting — although in many cases he did not originate — the ideas that the
solar nebula was initially very cold, that stars constantly expel gaseous matter, that
cosmic dust gives rise to extinction of distant starlight, that comets originate in the
remnant outer regions of the solar nebula, and that the Moon’s surface gives evi-
dence of bombardment by small planetoids. In addition, capture phenomena, the
central feature of See’s ill-starred theory of solar system evolution, are today held
by many astronomers to be responsible for a large proportion of planetary satellites
(as well as for events such as the crash of Comet Shoemaker-Levy 9 into Jupiter in
1994). Finally, See deserves credit for pressing British scientific societies to pub-
lish Sir William Herschel’s collected works; this resulted in the release of a beauti-
ful two-volume edition in 1912.

See died at Oak Knoll Naval Hospital in Oakland, California, on 4 July 1962, at

the age of 96. Although he merited only a four-line obituary in Science,

the New

York Times saw fit to print almost an entire column of biographical material.

It is

sad that a promising astronomical career was sacrificed to See’s need for public
attention. Other than the controversy that he generated during his heyday, little is
remembered today of his astronomical work. But it cannot be denied that he played
a part in an exciting time for American science, when the man on the street was
beginning to develop a real passion for the subject, and to assign hero status to
some of its practitioners.

History has taken a divided view on Thomas Jefferson Jackson See. Much the

majority opinion is expressed by the Encyclopedia Americana: “Although he had
an unremarkable career and made no important contributions to science, See is
remembered for his numerous controversial papers on astronomical subjects and
his unfailing knack for espousing the discredited side of scientific theories.”

None-

theless, a revisionistic dissent is registered by the Dictionary of scientific biogra-
phy: “See’s numerous publications were considered unorthodox and were dismissed
by scientists of his time. Many of his ideas, however, are in striking agreement with
current theories.”

While it is desirable that See’s career be judged dispassionately,

it is to be hoped that one day his more eccentric theories are not ‘rediscovered’ and
made a part of the pseudo-science revolution!

Thomas J. Sherrill

REFERENCES

1. W. L. Webb, Brief biography and popular account of the unparalleled discoveries of T. J. J. See

(Lynn, Mass., 1913).

2. See, for example, See’s articles in Astronomical journal, xv (1895), 33, 54, 97, 101, 129, 155, 156,

161, 169, 171, 180, 188; xvi (1896), 17, 24, 41, 92, 125, 137; and in Astronomische Nachrichten,
cxxxvii (1895), cols 159, 359; cxxxviii (1895), cols 25, 55, 149, 345, 369, 373; cxxxix (1896),
cols 17, 63, 161, 163, 169, 341, 367; cxl (1896), cols 33, 35, 39; cxli (1896), col 7 (only first
pages/columns here listed).

3. See, for example, See’s articles in Popular astronomy, i (1893), 373; ii (1894), 103, 249, 289, 337,

385; iii (1895) 49, 178; iv (1896), 297, 533, 550 (only first pages here listed).

4. Webb, op. cit. (ref. 1), 59.
5. T. J. J. See, Researches on the evolution of the stellar systems: Volume 1 (Lynn, Mass., 1896).
6. J. Ashbrook, “The sage of Mare Island”, Sky and telescope, xxiv (1962), 193.
7. T. J. J. See, “Discoveries and measures of double and multiple stars in the Southern Hemisphere”,

Astronomical journal, xviii (1898), 181–7.

8. Ashbrook, op. cit. (ref. 6), states for example that W. H. van den Bos had pointed out that all of

See’s binary position angles for about a month had the same large systematic error, apparently
due to a failure to check the micrometer’s zero point each night.

9. T. J. J. See, “Perturbations in the motion of the double star F.70 Ophiuchi =

2272”, Astronomical

journal, xv (1895), 180.

10. T. J. J. See, “Recent discoveries respecting the origin of the universe”, Atlantic, lxxx (1897), 484–

92.

11. Ashbrook, op. cit. (ref. 6).
12. T. J. J. See, “Researches on the orbit of F.70 Ophiuchi, and on a periodic perturbation in the

motion of the system arising from the action of an unseen body”, Astronomical journal, xvi
(1896), 17–23.

13. F. R. Moulton, “The limits of temporary stability of satellite motion, with an application to the

question of the existence of an unseen body in the binary system F.70 Ophiuchi”, Astronomical
journal, xx (1899), 33–37.

14. E. Doolittle, “The orbit of F.70 Ophiuchi”, Astronomical journal, xvii (1897), 121–2.
15. Subsequently, 6.5-year and 17-year perturbations were postulated by others for 70 Ophiuchi, but

today these suggestions are discounted.

16. T. J. J. See, “Remarks on Mr. Moulton’s paper”, Astronomical journal, xx (1899), 56.
17. Editor’s Note, Astronomical journal, xx (1899), 56.
18. Webb, op. cit. (ref. 1), 72, and the plate following p. 74.
19. Webb, op. cit. (ref. 1), 76.
20. Ashbrook, op. cit. (ref. 6).
21. Webb, op. cit. (ref. 1), 78.
22. T. J. J. See, articles in Proceedings of the American Philosophical Society (Philadelphia), xlv

(1906), 222–87; xlvi (1907), 191–299, 369–415; xlvii (1908), 157–275.

23. T. J. J. See, “Fair play and toleration in science”, letter to editor of Science, xxix (1909), 858.
24. J. Barrell, “Fair play and toleration in criticism”, letter to editor of Science, xxx (1909), 21.
25. F. R. Moulton, “An attempt to test the nebular hypothesis by an appeal to the laws of dynamics”,

Astrophysical journal, xi (1900), 103–30.

26. See, for example, T. C. Chamberlin and F. R. Moulton, “The development of the planetesimal

hypothesis”, Science, xxx (1909), 642–5.

27. T. J. J. See, “Significance of the spiral nebulae’, Popular astronomy, xiv (1906), 614–16.
28. T. J. J. See, “On the cause of the remarkable circularity of the orbits of the planets and satellites

and on the origin of the planetary system”, Popular astronomy, xvii (1909), 263–72.

A Career of Controversy

29. “Solar system was larger than now”, San Francisco Call, 31 January 1909, p. 41.

30. “Scientists in furore over nebulae”, San Francisco Examiner, 1 February 1909, p. 3.
31. “See’s theory said to be reasonable”, San Francisco Call, 1 February 1909, p. 12.
32. Ibid.
33. “Takes issue with See”, San Francisco Call, 1 February 1909, p. 12.
34. T. J. J. See, “On the cause of the remarkable circularity of the orbits of the planets and satellites,

and on the origin of the planetary system”, Astronomische Nachrichten, clxxx (1909), cols
185–94.

35. T. J. J. See, Note to above paper, Astronomische Nachrichten, clxxx (1909), col. 194.

36. F. R. Moulton, “Remarks on recent contributions to cosmogony”, letter to editor of Science, xxx

(1909), 113–17.

37. “Astronomers warring — Moulton exposes See”, San Francisco Call, 4 August 1909, p. 1.
38. “See says Moulton was only menial”, San Francisco Call, 5 August 1909, p. 2.
39. T. J. J. See, “Geology and cosmogony”, letter to editor of Science, xxx (1909), 479–80.
40. T. J. J. See, Researches on the evolution of the stellar systems: Volume 2. The capture theory of

cosmical evolution (Lynn, Mass., 1910).

41. Webb, op. cit. (ref. 1), 246.
42. T. J. J. See, “Professor E. W. Brown’s verification of the capture of satellites”, Popular astronomy,

xix (1911), 422–5.

43. T. J. J. See, “The evolution of the starry heavens”, Popular astronomy, xix (1911), 529–47.
44. F. R. Moulton, “Capture theory and capture practice”, Popular astronomy, xx (1912), 67–82.
45. T. J. J. See, “Historical notice of John Nelson Stockwell of Cleveland”, Popular astronomy, xxviii

(1920), 565–84.

46. Webb, op. cit. (ref. 1), p. viii.
47. Ibid., 248.
48. “Professor See”, review of Brief biography and popular account of the unparalleled discoveries of

T. J. J. See, The Nation, xcviii (1914), 307–8.

49. “Dr. See solves gravity puzzle”, San Francisco Examiner, 25 April 1914, p. 8.
50. Traité physique mechanique par George Louis Le Sage, ed. by P. Prévost (Paris, 1818).
51. “Want proofs before discussing discovery”, San Francisco Chronicle, 25 April 1914, p. 13.
52. T. J. J. See, Electrodynamic wave-theory of physical forces: Volume 1 (Lynn, Mass., 1917).
53. T. J. J. See, “New theory of the aether”, Astronomische Nachrichten, ccxi (1920), cols 49–86, 137–

90; ccxii (1920), cols 233–302, 385–454; ccxiv (1921), cols 281–359; ccxv (1922), cols 49–
138; ccxvii (1922), cols 193–284; ccxxvi (1926), cols 401–97.

54. See, for example, the third of these papers (ref. 53), col. 233.
55. See the eighth of these papers, col. 493.
56. “Has mystery of ether at last been solved by science?”, San Francisco Examiner, 11 March 1928,

p. K-5.

57. T. J. J. See, “Capt. See scores Einstein”, letter to editor of New York Times, 1 May 1923, p. 20.
58. “Prof. See declares Einstein in error”, New York Times, 14 October 1924, p. 14.
59. “Denies error in relativity”, New York Times, 16 October 1924, p. 12.
60. “Einstein ignores Capt. See”, New York Times, 18 October 1924, p. 17.
61. T. J. J. See, Wave-theory!, v (Lynn, Mass., 1940).
62. “Meteoric rain on Sun blamed for heat wave”, San Francisco Chronicle, 9 July 1921, p. 1.
63. “Finds the radio wave slower than light; around the globe at 165,000 miles a second”, New York

Times, 12 May 1924, p. 1.

64. T. J. J. See, “Radio waves by night”, letter to editor of New York Times, 11 September 1924, p. 22.
65. T. J. J. See, Wave-theory!, i–xi (Lynn, Mass., 1938–52).
66. Webb, op. cit. (ref. 1), 268.

Thomas J. Sherrill

67. Science, cxxxvii (1962), 272.

68. “Capt. T. J. J. See, Astronomer, 96”, New York Times, 5 July 1962, p. 23.
69. S. D. Gossner, “See, Thomas Jefferson Jackson”, Encyclopedia Americana (New York, 1995),

515.

70. R. A. J. Schorn and L. D. G. Young, “See, Thomas Jefferson Jackson”, Dictionary of scientific

biography, xii, 280–1.

JHA, xxx (1999)

THE BABYLONIAN FIRST VISIBILITY OF THE LUNAR

CRESCENT: DATA AND CRITERION

LOUAY J. FATOOHI, F. RICHARD STEPHENSON, and

SHETHA S. AL-DARGAZELLI, University of Durham

1. Introduction

The problem of predicting the first visibility of the lunar crescent attracted attention
throughout much of the historical period, from the many nations who used lunar
calendars to regulate their activities. The oldest available records that reveal organ-
ized interest in this matter date back almost three thousand years — to the time of
the Babylonians. Predicting the first visibility of the lunar crescent aroused great
interest among medieval Muslim astronomers, largely because the dates of reli-
gious practices in Islam — such as the beginning and end of the fasting month of
Ramadhan — are determined by a lunar calendar.

In modern times, scientific interest in understanding the visibility of the lunar

crescent has been motivated mainly by two factors: (i) the need of historians cor-
rectly to interpret past records of nations that used the lunar calendar; and (ii) the
need of present-day Muslims to ascertain each month when the lunar crescent may
be visible for the first time after conjunction with the sun — and hence to know
when to look for it, and also to know when it cannot be seen.

Predicting the earliest visibility of the lunar crescent after conjunction is a matter

of considerable complexity. It is a problem where astronomical, atmospheric, opti-
cal and human factors are all at work. The fact that even modern astronomers can-
not agree on the best criterion for determining the first visibility of the lunar cres-
cent only attests to the complex nature of this matter.

Throughout history, attempts have been made to put forward criteria for predict-

ing when the young crescent will first be seen in any given month. Each attempt has
followed either an empirical or a theoretical approach. The empirical approach,
which is more frequently employed, is based on analysing a collection of observa-
tional data and then formulating a criterion that best fits the observations. On the
other hand, the theoretical method is embodied in attempts to resolve the problem
through considering the various factors affecting crescent visibility and designing a
descriptive mathematical model. While the Babylonian criterion was empirical, the
Arab astronomers took mostly a theoretical approach. Recent studies on the subject
have presented prediction models from both aspects: empirical and theoretical.

In this paper, we address the observational aspect of the Babylonian approach to

the problem of first visibility of the lunar crescent and also consider the criterion
that they have possibly used for predicting the first visibility of the crescent.

L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli

2. The Role of Observations in the Study of First Visibility of the Lunar Crescent

Real observations of first visibility of the lunar crescent are crucial for the formula-
tion of an empirical model, yet they are equally important for testing any theoretical
solution. Whether empirical or theoretical, the reliability of any criterion can be
established with confidence only by testing it against real observations of first vis-
ibility of the crescent. This critical role of observational data has urged researchers
into the problem of predicting the first visibility of the crescent, to compile such
data from the astronomical literature.

It was Fotheringham

who made the first such collection in 1910, when he com-

piled 76 observations of the new moon made by August Mommsen and Julius
Schmidt at Athens in the second half of the previous century. Fotheringham used
these observations to design his criterion for predicting the first visibility of the
lunar crescent. The most comprehensive lists of observations made by experienced
observers, including those compiled by Fotheringham, have recently been published
by Schaefer

and by Doggett and Schaefer.

These authors compiled and carefully

checked observations from a large number of publications as well as from
moonwatches that they organized.

The dates of the observational data compiled by Schaefer and Doggett range

from 1859 to 1996, and are from various northern and southern latitudes. The total
number of the observations they cite is 294, of which 23 are observations of last
visibility of the old moon — rather than first visibility of the new moon. One very
important aspect of the 271 evening observations is that they are not all positive
sightings: 81 are negative observations, i.e., unsuccessful attempts to spot the new
moon. Such negative observations are of exceptional importance in determining the
limits of first visibility of the lunar crescent.

In this paper, we present the oldest observations of the lunar crescent that have so

far come to light. We have extracted 209 positive observations from the Babylonian
“Astronomical Diaries”, with their dates ranging from –567 to –73 (568 to 74

.).

In the following sections we explain the Babylonian source of data, the conversion
of the Babylonian dates into Julian dates, and how we determined the exact Julian
date of first visibility of the lunar crescent. Finally, we discuss the possible visibil-
ity criterion that the Babylonians may have used.

3. The Babylonian “Astronomical Diaries”

The ancient Babylonians developed great interest in astronomical observations. This
interest was motivated mainly by their concern with astrology, though calendrical
needs contributed as well. In fact, there was never any distinction between the as-
tronomers who made observations and the astrologers who interpreted the observa-
tions; both tasks were performed by the same people.

From the eighth century

. onward, the Babylonians systematically and con-

tinuously recorded their astronomical observations on clay tablets. The Babylonian

The Babylonian First Visibility

heritage of astronomical cuneiform texts is usually classified, after Sachs,

into

four categories: (i) “Almanacs”, which are yearly lists of various predicted lunar
and planetary phenomena, solstices and equinoxes, etc.; (ii) “Goal-Year Texts”,
which were designed for the prediction of lunar and planetary phenomena based on
certain fundamental periods and were prepared from the “Astronomical Diaries”
(see below); (iii) “Normal-Star Almanacs”, texts on the positions of thirty-one stars,
close to the ecliptic, which the Babylonians used for reference and which were
denoted “Normalsterne” (“Normal stars”) by Epping

(a list of these stars, with

longitude and latitude at the epoch 164

., is given by Stephenson and Walker

);

and (iv) the “Astronomical Diaries”, the only category of interest for the purpose of
this study.

The Astronomical Diaries, or more briefly “diaries”, is the modern term used to

refer to the tablets known in Akkadian as nasaru ša ginê, which means “regular
watching”. These diaries represent records of daily astronomical observations made
in the Neo-Babylonian period by professionals who, according to excavated late
documents, were employed and paid specifically to make these observations. Their
job also included recording their observations in the diaries and preparing astro-
nomical tables and yearly almanacs. A diary usually covered about six months of
observation. The entries for each month typically include information on the fol-
lowing: the length of the previous month; lunar and solar eclipses; lunar and plan-
etary conjunctions with each other or with Normal stars; solstices and equinoxes;
heliacal risings and settings of planets and Sirius; meteors; and comets. In the dia-
ries, the Babylonians also systematically recorded the six time-intervals termed by
A. Sachs “Lunar Sixes”. These may be described as follows. On the first day of the
month the Babylonians recorded the time between sunset and moonset (na). Around
the middle of the month they recorded four intervals related to the full moon: the
time interval between moonset and sunrise when the moon set for the last time
before sunrise (ŠÙ); the interval between sunrise and moonset when the moon set
for the first time after sunrise (na); the interval between moonrise and sunset when
the moon rose for the last time before sunset (ME); and the interval between sunset
and moonrise when the moon rose for the first time after sunset (GE

). Finally, near

the end of the month the Babylonians recorded the time between moonrise and
sunrise when the waning crescent moon was visible for the last time (KUR). In
addition to the astronomical data, the diaries also contain some non-astronomical
information: on the weather, the prices of six basic commodities, the height of the
river Euphrates, and certain historical events.

It should be emphasized that although the major bulk of celestial phenomena

referred to in the diaries are actual observations, some of the recorded events are
not observations but rather predictions based on certain mathematical calculations.
Sometimes this is clearly stated whereas on other occasions it is implicit, as in the
case when the sky is mentioned as having been overcast.

Most of the available tablets containing the diaries are damaged to varying degrees

L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli

— often extensively. In some cases the date of the tablet is broken away. Such
tablets can often be dated by using a unique combination of astronomical data that
they record — for example, eclipses and lunar and planetary positions. This is how
Sachs and Hunger determined many of the dates of the diaries, which they recently
published in transliteration and translation in three volumes.

These volumes, which

form the exclusive source for the Babylonian data of the current study, cover diaries
from –651 (652

.) to –60 (61

.).

The following is an example of the diary reports, for the first seven days of the

lunar month whose first day corresponds to

. 163 August 11 (parentheses denote

editorial comment, square brackets indicate damaged text that has been restored by
the editors, while the number at the beginning of each paragraph indicates the line
number in the text):

1 Year 149 (Seleucid), king Antiochus. Month V, (the 1st of which was identi-
cal with) the 30th (of the preceding month), sunset to moonset: 10°, it was very
low; measured (despite) mist.

2 Night of the 2nd, the moon was 1 cubit behind

Virginis. Night of the 3rd,

the moon was 1 cubit above

Virginis, the moon having passed 0.5 cubit

3 to the east. The 3rd, the north wind blew. Night of the 4th, the moon was 4
cubits in front of

Librae. The 4th, the north wind blew. Night of the 5th,

4 beginning of the night, the moon was 2.5 cubits below

Librae. The 5th, the

east wind blew. Night of the 6th, beginning of the night, the moon was 20
fingers above

5 Scorpii. The 6th, ZI IR (unidentified), the east wind blew. Night of the 7th,
beginning of the night, the moon was 3 cubits in front of

Ophiuchi,

6 the moon being 2.5 cubits high to the north, it stood 1 cubit 8 fingers in front
of Mars to the west, the moon being 2 cubits high to [the north;]

7 last part of the night, Venus was 4 cubits below

Leonis. The 7th, clouds

were in the sky, ZI IR, the east wind blew.

As seen in the above example, a typical diary starts with a mention of the Babylonian
year and month. This is followed by a phrase stating that the first day of that month
was either “identical with” or “followed”

the 30th of the preceding month, so

indicating whether the previous month contained 29 or 30 days, the only lengths
permitted by the Babylonian time-reckoning. After that there is a mention of the
measured or predicted na interval, which is the time between sunset and moonset of
the first day of the month — usually known as ‘moonset lagtime’ in modern termi-
nology. This is one of the six quantities termed Lunar Sixes already mentioned.

During each month, the Babylonian observers recorded when the moon and planets

passed near to each other or near to normal stars. In a diary, the relative position of a
celestial body to another may be described by one of the terms “above” (e), “below”

The Babylonian First Visibility

(šap), “in front of” (ina IGI), or “behind” (ar). The terms “behind” and “in front
of ” are roughly synonymous with “to the east of” and “to the west of ”, respec-
tively, following the apparent rotation of the celestial sphere.

For the measurement of angles, such as the position of celestial bodies and

magnitudes of eclipses,

the Babylonians used the units ‘finger’ (SI) and ‘cubit’

(KÙŠ), which contained twenty-four fingers in the Neo-Babylonian period.

It was

previously suggested that the cubit was approximately equivalent to 2°.

However,

a recent investigation of Babylonian measurements of close planetary conjunctions
has shown that the cubit closely equalled 2.2°.

This last study has also shown that

the Babylonians did not use horizon coordinates (altitude and azimuth), but there
was little evidence to determine whether ecliptical or equatorial coordinates were
used. However, because of the Babylonians’ introduction of the concept of the zo-
diac around 400

. it appears more reasonable to suppose that the Babylonian

astronomers used an ecliptical system.

For the measurement of time intervals shorter than a day, such as the durations of

the phases of an eclipse,

the Babylonians used the unit uš. According to Neugebauer,

“The ‘degree’ (uš) is the fundamental unit for the measurement not only of arcs,
especially for the longitude, but also for the measurement of time, corresponding to
our modern use of right ascension. Therefore, 1 degree = 4 minutes of time”.

Accordingly, Sachs and Hunger, who translate uš as “time degree”, have converted
all measurements in uš in the diaries, especially those of the Lunar Sixes, into time-
degrees. We have confirmed, through the investigation of Babylonian records of
lunar eclipse durations, that the modern equivalence of the uš is accurately 4 min-
utes and have shown that the definition of this unit showed no variations over the
centuries covered by the Late Babylonian astronomical texts.

4. Determination of the Julian Date of First Visibility of the Lunar Crescent

We have thoroughly scanned Sachs and Hunger’s three volumes

and compiled a

list of dates of Julian years and Babylonian months in which the moon was first
sighted. This is not simply a list of each year and month cited in the extant diaries
because, as already mentioned, the Babylonians did not depend solely on observa-
tion when determining the first day of the month, though this seems to have been
the practice in ideal weather. The Babylonian astronomers did use mathematical
methods for determining the first day of the month, at least when visibility of the
lunar crescent was prevented by unfavourable weather conditions. Since our pur-
pose was to collect dates of actual observations rather than predictions of first vis-
ibility of lunar crescents we have selected only the entries that contain explicit
statements confirming that the moon was indeed sighted. Terms and phrases used
by the Babylonians to indicate actual sighting of the moon include “visible”, “seen”,
“first appearance”, and “earthshine”. Descriptions of the position of the moon or its
brightness, such as “low”, “could be seen”, “was low to the sun”, “faint” and “bright”,
are also indications of actual observations. Below are examples from different years

L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli

of reported first sightings of the lunar crescent:

Month V, (the 1st of which was identical with) the 30th (of the preceding month),
first appearance of the moon; sunset to moonset: 12°; the moon was 2 cubits in
front of Mercury.

[Julian date:

. 373 July 23]

[Month V,] the 1st (of which followed the 30th of the preceding month), sunset
to moonset: 15.5°; the moon was 1.66 cubits in front of

Virginis.

[Julian

date:

. 334 August 12]

Month IX, the 1st (of which followed the 30th of the preceding month), sunset
to moonset: 15°, measured; the moon stood 1.5 cubits in front of Mercury to
the west.

[Julian date:

. 274 December 4]

Month IX, (the 1st of which was identical with) the 30th (of the preceding
month), sunset to moonset: 17.5°; it was bright, earthshine, measured; it was
low to the sun.

[Julian date:

. 204 December 10]

[Month V, (the 1st of which was identical with) the 30th (of the preceding month),
sunset to] moonset: [nn°]; it was faint, it was low to the sun; (the moon) [stood]
3 cubits in front of Mars, 5 cubits in front of Saturn to the west.

[Julian date:

. 171 August 9]

In order to confine ourselves to actual sightings of the lunar crescent, we have

excluded all entries where the text contained explicit statements and terms imply-
ing invisibility of the moon, such as “I did not watch”, “I did not see the moon”,
“overcast”, “mist”, and “clouds”. We have also ruled out all entries in which the
moonset lagtime or interval between sunset and moonset (na) is said to have been
predicted as this might well be due to the fact that the moon was not seen. As an
essential measure of extra caution, we have discounted any entry that does not con-
tain a specific statement that the moon was seen, even if it does not contain any
explicit or implicit indication to the contrary. Accordingly, the final list of accept-
able entries, though numbering as many as 209 in total, was unavoidably only a
small part of the original material. The following are examples of the kinds of en-
tries that have been discarded for one or more of the reasons mentioned above:

[Month XI, (the 1st of which was identical with) the 30th (of the preceding
month),] sunset to moonset: 14°; there were dense clouds, so that I did not see
the moon.

[Julian date:

. 453 February 12]

Month VIII, the 1st (of which followed the 30th of the preceding month), sun-
set to moonset: 18.5°. Night of the 1st, clouds crossed the sky.

[Julian date:

. 271 November 2]

Month II, (the 1st of which was identical with) the 30th (of the preceding month,
sunset to moonset): 13°; dense clouds, I did not watch. Night of the 1st, [clouds]
crossed the sky.

[Julian date:

. 256 April 23]

The Babylonian First Visibility

[Diaries from month VII to the end] of month XII, year 113, which is the year
177, King Arsaces. Month VII, the 1st (of which followed the 30th of the pre-
ceding month), sunset to moonset: 11.5°; mist [...].

[Julian date:

. 135 Sep-

tember 30]

Having collected all reliable dates of first sightings of the moon after conjunc-

tion, we made a preliminary conversion of all dates, which are given by Sachs and
Hunger in terms of Julian year and Babylonian lunar month, to their full Julian
equivalents. This could have been achieved using the specially prepared tables of
Parker and Dubberstein

which cover the period 626

. to

. 75. However, the

use of these manual tables would not be very practical when a large number of data
are involved. Therefore, we used only the intercalary scheme from these tables, i.e.,
the recorded positions of the additional months (which always followed the 6th or
12th month). We then integrated this scheme in a specially designed program that
reads in the Babylonian date and converts it to its Julian equivalent, totally inde-
pendently of the tables.

The program uses the lunar visibility criterion suggested by Schoch

to deter-

mine the expected dates of first visibility of the crescents. This is the criterion on
which the tables of Parker and Dubberstein are based. The use of a specific lunar
visibility criterion for this purpose is of no critical importance, because the con-
verted dates, whether found manually by tables or by the program, could be consid-
ered only a first approximation anyway. The reason is that the date of actual obser-
vation of the crescent in any given month, which is the date that really matters for
the purpose of this study, is not necessarily the same as that predicted by any theo-
retical calculation. For instance, a crescent that in theory should have been easily
noticed could have set unseen because of unfavourable weather and its actual first
visibility could have occurred the next evening. Therefore, in each instance the
calculated date of first visibility must be checked against real observational data —
usually in the form of a time or positional measurement from the month under
consideration (see next section). In this way, one can be sure whether the theoreti-
cally calculated date is exact or in need of amendment. In practice, such amend-
ments never exceeded a single day, but even such a seemingly small discrepancy is
crucial for the purpose of crescent visibility studies.

In 136 of the 209 entries that we compiled, the measured moonset lagtime is

given; since the lagtime changes from one day to another by an average of 54 min-
utes (some 13.5°), this quantity could be used to determine the exact date of first
sighting of the lunar crescent. The following are two different explanatory exam-
ples:

Month III, (the 1st of which was identical with) the 30th (of the preceding
month), the moon became visible behind Cancer; it (i.e. the crescent) was thick;
sunset to moonset: 20°.

This observation is from year –567. According to the date conversion program, the

L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli

Julian date of this event is –567 June 20. From our further computations, the moonset
lagtime on that day was 89 minutes, i.e. 22.25 time-degrees, which is close to that
given in the Babylonian text; hence

. 568 June 20 is confirmed to be the exact

Julian date of observation.

Month VIII, the 1st (of which followed the 30th of the preceding month), sun-
set to moonset: 17°; it could be seen while the sun stood there.

This entry belongs to year –283. The calculated Julian date of this event is

. 284

October 26. However, the computed moonset lagtime on that date is 31 minutes, i.e.
7.75° time-degrees, which indicates that the exact date of observation was in fact
the next day, i.e.

. 284 October 27; on this latter date the lagtime was 69 minutes,

i.e. 17.25° time-degrees — almost the same quantity as measured by the Babylonians.

We found 9 entries where the difference between the measured and the com-

puted lagtime was more than 4°, i.e. more than 16 minutes of time. The difference
could well be due to inaccurate measurement of the lagtime or scribal error in the
original text, and does not necessarily indicate an error in the date. Measurement of
the na interval would be a difficult task since the young crescent moon can be seen
only for a short time about midway between sunset and moonset. However, as a
measure of caution, we re-checked these entries using additional data from the text.
For this purpose, we used observations of lunar horizontal separation (i.e. when the
moon is “behind”, “east”, “in front of ”, or “west”) from a star or planet recorded
during the same lunar month. Because the moon traverses about 13° every day, the
date of any lunar conjunction in the month can be exactly determined, and this date
can be used as a reference for verifying the date of the first day of the month, i.e. the
date of the observation. However, if the text did not mention the horizontal separa-
tion we used the vertical separation (i.e. when the moon is “above” or “below”)
because the latter would be given only when the moon was horizontally close to the
planet or star.

In the other 73 of the compiled 209 entries, the observed lagtime was missing,

mostly because the text is broken away. In this case, we used other astronomical
data from the same month to verify the date, exactly as in the case of the 9 entries
mentioned above. Table 1 includes the exact Julian dates of the 209 Babylonian
observations of the lunar crescent mentioned in the astronomical diaries.

For calculating the lunar coordinates, we designed a program that uses the semi-

analytical lunar ephemeris ELP2000-85.

Although Chapront-Touzé and Chapront

suggest that ELP2000-85 is valid over a time span of several thousand years, using
this theory for ancient times requires a significant modification. The ELP2000-85
solution assumes a value of –23.895

″

/cy

for the tidal secular acceleration of the

moon. However, recent results from lunar laser ranging (LLR) suggest a higher
lunar acceleration of –25.88 ± 0.5

″

/cy

In a recent communication to one of the

present authors,

J. L. Williams of the LLR team claims that consistent results for

lunar acceleration are being found in the range –25.8 to –26.0

″

/cy

. Although the

difference between these recent results and that assumed by ELP2000-85 may seem

The Babylonian First Visibility

ABLE

1. The 209 Babylonian observations of first visibility of the lunar crescent.

No.

Year

Month Day

No.

Year Month Day

No.

Year

Month Day No.

Year Month Day

−

567

−

284

107

−

192

160

−

143

−

567

−

283

108

−

192

161

−

143

−

567

−

281

109

−

190

162

−

143

−

566

−

277

110

−

190

163

−

142

−

566

−

277

111

−

189

164

−

141

−

418

−

277

112

−

189

165

−

141

−

381

−

273

113

−

188

166

−

140

−

381

−

266

114

−

187

167

−

140

−

378

−

266

115

−

187

168

−

140

−

374

−

264

116

−

185

169

−

139

−

374

−

255

117

−

183

170

−

137

−

372

−

255

118

−

183

171

−

136

−

372

−

251

119

−

183

172

−

134

−

372

−

250

120

−

181

173

−

133

−

370

−

249

121

−

179

174

−

133

−

370

−

246

122

−

179

175

−

133

−

368

−

246

123

−

178

176

−

133

−

366

−

246

124

−

178

177

−

132

−

366

−

246

125

−

178

−

132

−

346

−

245

126

−

176

179

−

131

−

345

−

245

127

−

176

180

−

129

−

342

−

237

128

−

175

181

−

124

−

333

−

237

129

−

175

182

−

123

−

333

−

234

130

−

173

183

−

123

−

332

−

234

131

−

173

184

−

119

−

328

−

233

132

−

172

185

−

119

−

328

−

233

133

−

170

186

−

118

−

324

−

232

134

−

170

187

−

117

−

324

−

231

135

−

170

188

−

111

−

324

−

225

136

−

169

189

−

111

−

324

−

218

137

−

169

190

−

111

−

322

−

217

138

−

168

191

−

107

−

321

−

210

139

−

168

192

−

105

−

321

−

209

140

−

164

193

−

105

−

321

−

207

141

−

164

194

−

105

−

321

−

207

142

−

163

195

−

105

−

321

−

203

143

−

163

196

−

105

−

307

−

201

144

−

163

197

−

104

−

307

−

200

145

−

162

198

−

302

−

198

146

−

162

199

−

302

−

197

147

−

162

200

−

302

−

197

148

−

161

201

−

302

−

197

149

−

158

202

−

302

−

196

150

−

158

203

−

301

−

195

151

−

156

204

−

301

−

194

152

−

154

205

−

294

100

−

194

153

−

151

206

−

293

101

−

194

154

−

149

207

−

291

102

−

193

155

−

145

208

−

291

103

−

193

156

−

145

209

−

291

104

−

193

157

−

144

−

289

105

−

192

158

−

144

−

286

106

−

192

159

−

144

L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli

small, it does nevertheless accumulate significant errors over a long period as in the
case of the Babylonian data. We have remedied this situation by using a special for-
mula given in the Astronomical almanac which accounts for the deficiency in the
tidal secular acceleration of the moon by modifying the Julian day number of the
event so that the computed lunar coordinates are for a lunar acceleration of –26

″

/cy

In order for the calculations to be valid for an ancient epoch such as the

Babylonian, it is also necessary to make allowance for the cumulative effect of
changes in the length of the day (

∆

T) which results from variations in the earth’s

rate of rotation due to tides and other causes.

For example,

∆

T is estimated to have

been as much as about 16800 seconds (4.66 hours) in the year –500 which corre-
sponds to changes of about 2.5° and 0.2° in the lunar longitude and latitude, respec-
tively. We have incorporated into our calculations

∆

T using the values recently de-

rived by Stephenson and Morrison

from their analysis of historical records of

astronomical events — mainly eclipses, including those from Babylon.

We computed the solar coordinates using the solution VSOP82 (stands for Vari-

ations Séculaires des Orbites Planétaires)

and the planetary positions using the

analytical theory VSOP87.

We designed a special program for calculating the stellar

coordinates.

5. The Babylonian Criterion of First Visibility of the Lunar Crescent

The accurate prediction of the evening of first visibility of the new crescent was of
major significance for the Babylonians. Indeed, this matter was of such importance
that it was the main goal of the Babylonian lunar theory in the Seleucid period (311
– 64

.).

The Babylonians succeeded in formulating a truly mathematical lunar

theory which they used for predicting various parameters of the lunar motion, as
found recorded in the lunar ephemerides they prepared.

Modern investigators of the problem of first visibility of the new crescent, who

are not themselves scholars of Babylonian astronomy, have systematically claimed
that the Babylonian conditions of visibility were that the age of the new moon is
more than 24 hours and that the arc of separation(s) should be equal to or greater
than 12°, i.e. that the moon sets at least 48 minutes after sunset. This supposed
Babylonian criterion is also often cited as being only S

≥

12°. It seems that Bruin

was the first modern researcher to attribute this criterion to the Babylonians and
that all subsequent researchers who reiterated this claim were simply relying on his
account.

However, it should be noted that Bruin cited no reference in support of

his claim. Bruin seems to have suggested it because he noted that the simple rule of
S

≥

12° was used by Arab astronomers from the seventh century onward; he be-

lieved that it might have transmitted to them from the Hindus who would have
learned it from the Babylonians. However, Bruin’s claim with regard to the
Babylonian condition of lunar visibility is, at best, inaccurate. The 12° equatorial
difference is indeed the crescent visibility criterion adopted by the Indian
Suryasiddhanta (c. 600) and the Khandakhadyaka (650), as pointed out by King.

The Babylonian First Visibility

However, even though Babylonian astronomical knowledge had passed to the Indi-
ans (by way of the Greeks), this does not necessarily imply that this was the
Babylonian criterion of crescent visibility.

Study of the Babylonian lunar ephemerides has revealed that they are based on

two somewhat different versions of lunar theory, usually referred to as “System A”
and “System B”. According to System A, the sun moves with constant velocities on
two different arcs of the ecliptic, whereas System B assumes that the solar velocity
changes with time in a linear zigzag function.

The difference between the two

theories is usually represented by Figure 1.

It is interesting to note that although System B must have been an improvement

of System A, both Systems were used simultaneously throughout the period 250–
50

. in preparing ephemerides. Neugebauer notes that such a practice, which is

contrary to our modern scientific concepts where new theories replace old ones, is
yet more prominent in the planetary theory.

The lunar ephemerides were used by

the Babylonians to predict the first and last visibility of the moon. A comparative
list of the main columns of computations of a complete ephemeris in the two sys-
tems is given in Table 2.

Although the existence of procedure texts that give criteria for determining the

first and last visibility of the moon is hard to doubt, so far, unfortunately, no such
texts have come to light. Therefore, it is only through the analysis of individual

One Year

System A

System B

Time

elocity of the Sun

. 1. The two representations of solar motion in the Babylonian lunar theory.

L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli

The columns of astronomical calculations included by Babylonian astronomers in each
ephemeris of System A and System B. As seen, some parameters are calculated in ephemerides
of both Systems whereas others are restricted to one System or the other. Although the last
four quantities are missing from the tables of System A, preserved procedural texts tell us
they were calculated; they would be necessary for finding the lagtime.

ABLE

cases in the ephemerides that certain criteria can be concluded.

Contrary to what is commonly assumed, Neugebauer

found from the study of

extant ephemerides that the moonset lagtime alone could not have been used as the
visibility criterion by the Babylonians in any of the two Systems. He suggests that
a criterion of the following form might have been used by the Babylonians for both
Systems:

elongation (L) + moonset lagtime (in degrees) (S)

constant.

System A

System B

Dates

Relative velocity of the moon with
respect to the sun(?)

Velocity of the sun

Longitude of the moon

Length of daylight

Half length of the night

Latitude of the moon

Magnitude of eclipses

Velocity of the moon

Length of the month in first approximation

Correction related to the next column

Correction in the length of the month caused by the variability of solar velocity

Second correction to the length of the
month

Length of the month

Date of syzygy, midnight epoch

Date of syzygy, evening epoch

Date of syzygy, evening or morning
epoch
Time difference between syzygy and
sunset or sunrise

Elongation of first or last visibility

Influence of the obliquity of the ecliptic

Influence of the latitude

Duration of first or last visibility (lagtime)

The Babylonian First Visibility

Neugebauer suggests that the rationale behind the inclusion of the elongation in the
criterion of first visibility would be that the elongation measures, in addition to the
angular distance between the sun and moon, the width of the visible crescent. There-
fore, this criterion would imply that the chance of sighting the new crescent in-
creases with the width of the crescent and with the time for which the crescent
remains above the horizon before setting.

As for the value of the constant in the above criterion, Neugebauer found from

his study of preserved texts that in the case of System A the constant could have
been about 21°. In other words, the Babylonian visibility criterion for System A is:

L + S

21°.

In the case of System B, Neugebauer found two ephemerides that suggest a value of
about 23° for the constant, whereas another suggests

≥

20° and a fourth accepts a

value as low as

≥

17°. This represents a considerable range.

Interestingly, Neugebauer notes that the moonset lagtime might have been used

alone for predicting the visibility of the new moon in some cases. He concludes this
from the existence of isolated lists of lagtimes that seem to have been collected for
several years in succession. The lowest values found in these texts are 11.33°, 11.66°,
and 11.83°, and these are followed by a phrase of unknown meaning. The highest
value of lagtime given is 25.16° without alternative, although an ephemeris pre-
served for the same year accepts instead 12°. One alternative solution of 20.5° for a
full month (30 days) and 10.5° for a hollow month (29 days) is also given.

We have found that the smallest value of L + S in the 209 observations is 22°

(observation 89), which is very close to the limits of 21° and 23° suggested by
Neugebauer for Systems A and B respectively. The highest value of L + S that we
have found is 57.9° (observation 143). Therefore, while exceeding the 22° limit
does not ensure visibility of the lunar crescent, this value may possibly have been
used by the Babylonians as the lowest limit for the visibility of the crescent.

The latitude of Babylon is about 32.6° N. To test the reliability of the above

criterion that the Babylonians might have used, we applied it to the observations of
Table 1 as well as all entries of latitudes within the range ± (30° – 35°) from the
modern compilations.

We assumed that the Babylonian criterion was L + S

≥

22°,

as this is the smallest value in the Babylonian data. We found that the quantity L + S
is less than 22° for only 2 of the 231 positive observations of latitudes close to that
of Babylon. But while this criterion misjudges only 0.9% of the positive observa-
tions, it has 7 of the 19 negative observations in the visibility zone, i.e. L + S greater
than 22°. The latter result represents a very high percentage of error, 36.8%. The
unreliability of this criterion becomes even more manifest when applied to the data
from all latitudes. Five of the total of 399 Babylonian and modern positive observa-
tions, i.e. 1.3%, are wrongly placed according to the Babylonian criterion, but as
many as 37 of the 81 negative observations, i.e. 45.7%, contradict the visibility
condition. Certainly, this would be a very bad global criterion.

L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli

There have been modern attempts to formulate modern crescent visibility crite-

ria that would predict the dates when the crescent could have been visible in Babylon.
These attempts were originally triggered by interest in determining the beginnings
of the Babylonian months, which would help in establishing the equivalent dates of
Babylonian records. One such solution was first attempted by Karl Schoch, who
designed tables for determining the evening of the first sighting of the lunar cres-
cent that are applicable to all places whose latitudes differ little from that of Babylon.
Schoch also presented his lunar visibility tables, following Fotheringham,

in the

form of a curve of true lunar altitude (h) (parallax is not accounted for) versus the
azimuthal difference between the sun and moon (

∆

Z) at sunset, so that the new

moon would be first visible on the first evening after conjunction in which the
moon falls above the curve (see Table 3).

However, the criterion of Schoch suffers

from the important flaw of being based on both observations and predictions of the
lunar crescent.

Even Schoch’s identification of what he considered to have been

observations was not totally sound. For instance, Schoch states that “The most valu-
able observations for my purpose are the most ancient, belonging to a time when
the Babylonians were unable to compute the appearance of the crescent, i.e. the
time from Rim-Sin to Ammizaduga and from Nebuchadnezzar to Xerxes”.

But

the fact that the Babylonians were at some stage of their history unable to predict
the first appearance of the crescent does not necessarily mean that they did not
follow some simple rules in fixing their calendar, the most probable and simplest of
such rules being that the month would be of either 29 or 30 days. If so basic a rule
was followed, then the lengths of the Babylonian months determined according to
this rule would have no implications whatsoever for the visibility of the moon. (It
should be stressed that the skies of Babylon are often cloudy in winter, for exam-
ple.) It was exactly to avoid using such pseudo-observational data that for the present
project we collected only actual observations of the lunar crescent. Although
Fotheringham

expresses his confidence in Schoch’s criterion for computing the

first visibility of the lunar crescent at Babylon, Schoch’s use of predictions in addi-
tion to observations in setting his criterion has been criticized by O. Neugebauer.

It seem fair to conclude that Schoch’s solution can be regarded as neither observa-
tional nor theoretical, and hence it is likely to lead to errors in predicting the dates
of first sightings of the lunar crescent in Babylon.

Another criterion for determining the first visibility of the lunar crescent at Babylon

was suggested by P. V. Neugebauer. This solution uses the same two parameters
employed by Schoch, i.e.

∆

Z and h, but the suggested curve lies a little below that

of Schoch for smaller

∆

Z and slightly above it for larger

∆

However, the differ-

ences between both curves are too small to be of any significance in practical use.
Neugebauer’s curve also extends to 23° of

∆

Z, in contrast to that of Schoch which

covers only up to 19° of

∆

Z (see Table 3 for both criteria). We did not come across

any other modern criterion that is based on Babylonian data or is designed to pre-
dict the lunar visibility in Babylon in particular. Researchers into the Babylonian

The Babylonian First Visibility

calendar have relied on one or the other of the above criteria (for example, Parker
and Dubberstein

used Schoch’s model while Huber

opted for that of Neugebauer).

We have examined both criteria of Schoch and Neugebauer using the 209 obser-

vations that we have collected from the Babylonian diaries. Because these are real
observations, they can serve as a very reliable indicator of the accuracy of both
criteria. We have plotted in Figure 2 the visibility curves of Schoch and Neugebauer
as well as the 209 Babylonian observations. The graph shows that both models are
reasonably good in predicting the observations. Of the 209 positive observations,
only 8 fell below the visibility curves. In other words, according to the criteria of
Schoch and Neugebauer about 3.8% of the sighted crescents would have been in-
visible. However, if the visibility curve is drawn downwards starting from about h =
9.45° for

∆

Z = 0°, then all of the observations would be above the visibility curve,

i.e. in the visibility zone.

It should be stressed, however, that the fact that this modified curve would have

almost all positive observations in the visibility zone does not tell us anything about
the suitability of this criterion for hypothetical negative observations from Babylon.
In other words, it is obvious that while lowering the dividing line would include all

The criteria of K. Schoch and of P. V. Neugebauer. At any specified azimuthal difference
from the sun, the crescent is expected to be visible when the moon is not lower than a critical
true altitude at sunset.

ABLE

True azimuthal

Minimum true lunar altitude (h)

difference (

∆

Schoch

Neugebauer

10.7

10.4

10.7

10.4

10.6

10.3

10.5

10.2

10.4

10.1

10.3

10.0

10.1

9.8

10.0

9.7

9.8

9.5

9.6

9.4

9.3

9.1

8.8

8.9

8.4

8.6

8.0

8.3

7.6

8.0

7.3

7.7

7.0

7.4

6.7

7.0

6.3

6.6

6.2

5.7

5.2

4.8

L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli

The visibility criteria of Schoch and P. V. Neugebauer together with the Babylonian positive
observations.

. 2.

The Babylonian First Visibility

the positive observation in the visibility zone, i.e. above the curve, the curve will
certainly become so low that it would have more negative observations in its vis-
ibility zone than would the original curves. While lowering the criterion curve would
definitely give better results as far as positive observations are concerned, it would
also increase the number of Babylonian months that actually began one day later
than the solution predicts. This drawback in the criteria of Neugebauer and Schoch
would have become manifest if the Babylonian data included actual negative obser-
vations in addition to the positive.

A realistic evaluation of the h

−

∆

Z criteria can be made with the help of the

modern lists of observations which, unlike the Babylonian collection, include nega-
tive in addition to the positive observations. Neugebauer’s curve misjudges 22 of
the 81 negative observations, i.e. 27.2%, and misses 50 of the 399 positive, i.e.
12.5%. Obviously, this criterion cannot be considered satisfactory. Schoch’s curve
would not give a significantly different results.

While Schoch suggested that his model is applicable to all latitudes close to that

of Babylon, Fotheringham claimed that his h

−

∆

Z criterion is independent of the

geographical latitude of the observer. We have used the data in Table 1 as well as
the modern lists to investigate whether or not the h

−

∆

Z criterion depends on the

observer’s latitude. We have, therefore, separated the observations into two catego-
ries according to the geographical latitude of the observers, including in the first
category only the observations made from latitudes ± (30° – 40°). These consisted
of 372 observations, 310 positive and 62 negative. The second group included all
the other 108 observations, 89 of which are positive and the remaining 19 negative.

We have plotted in Figure 3 the mid-latitudes data and Neugebauer’s form of the

−

∆

Z criterion. The curve has 27 of the 310 (7.7%) positive observations (denoted

by circles) in the invisibility zone and 13 of the 62 (21%) negative observations
(denoted by crosses) in the visibility zone. Figure 4 is similar to Figure 3 but it
includes the observational data from all the latitudes other than ± (30° – 40°). Here
the curve of Neugebauer has as many as 9 of the 19 (47.4%) negative observations
and 26 of the 89 (29.2%) positive in the wrong zone (though Figures 3 and 4 may
show smaller numbers of points because of coinciding data points).

It seems from Figures 3 and 4 that Neugebauer’s criterion gives much larger

errors when applied to latitudes away from that of Babylon. This shows that, con-
trary to Fotheringham’s assertion, this type of solution is latitude-dependent. This
and the high percentage of error that all forms of this criterion give cannot be over-
come by simply lowering or raising the curve or even changing its shape. Any such
changes can improve the reliability of the criterion with respect to some of the data
but only at the cost of worsening its assessment of the rest. For instance, lowering
the curve would decrease the number of positive observations that are already in the
invisibility area, but this would then raise more negative observations to the visibil-
ity zone. Similarly, any change to make the criterion more suitable to a certain
range of latitudes would make it more unreliable for other latitudes. The observational

L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli

. 3. The criterion of P. V. Neugebauer and the observations for latitudes ± (30° – 40°).

The Babylonian First Visibility

. 4. The criterion of P. V. Neugebauer and the observations for latitudes other than ± (30° – 40°).

L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli

data show that at azimuthal difference of 0.5° a crescent that is as low as 6.2° has
been seen. This is not an isolated observation. Another observer saw a crescent of
8.1° altitude and 0.4° azimuthal difference with the naked eye only. On the other
hand, still for very small

∆

Z, many crescents that are higher than 10° or even 11°

have been missed. Therefore, it seems fair to say that the h

−

∆

Z criterion, in its

present form, is itself inherently of limited utility for predicting the first visibility of
the lunar crescent on the global level. Neither this criterion nor the L + S that may
have been used by the Babylonians can be used confidently for predicting the first
visibility of the lunar crescent.

REFERENCES

1. J. K. Fotheringham, “On the smallest visible phase of the moon”, Monthly notices of the Royal

Astronomical Society, lxx (1910), 27–531.

2. B. E. Schaefer, “Visibility of the lunar crescent”, Quarterly journal of the Royal Astronomical

Society, xxix (1988), 511–23; idem, “Lunar crescent visibility”, ibid., xxxvii (1996), 759–68.

3. L. E. Doggett and B. E. Schaefer, “Lunar crescent visibility”, Icarus, cvii (1994), 388–403.
4. L. E. Doggett, P. K. Seidelmann and B. E. Schaefer, “Moonwatch — July 14, 1988”, Sky & telescope,

July 1988, 34–35.

5. J. Britton and C. B. F. Walker, “Astronomy and astrology in Mesopotamia”, in C. B. F. Walker

(ed.), Astronomy before the telescope (London, 1996), 42–67, p. 44.

6. A. J. Sachs, “A classification of the Babylonian astronomical tablets of the Seleucid period”,

Journal of cuneiform studies, ii (1948), 271–90.

7. J. Epping, Astronomische aus Babylon (Freiburg, 1889).
8. F. R. Stephenson and C. B. F. Walker, Halley’s Comet in history (London, 1985).
9. A. J. Sachs and H. Hunger, Astronomical diaries and related texts from Babylon, i: Diaries from

652

. to 262

. (Vienna, 1988); ii: Diaries from 261

. to 165

. (Vienna, 1989); iii:

Diaries from 164

. to 61

. (Vienna, 1996).

10. Sachs and Hunger, op. cit. (ref. 9, 1996), 25.
11. The phrases “identical with” and “followed”, which describe the length of the month, have been

introduced by Hunger in substitution of the very brief original cuneiform text.

12. F. R. Stephenson and L. J. Fatoohi, “The Babylonian unit of time”, Journal for the history of

astronomy, xxv (1994), 99–110.

13. Sachs and Hunger, op. cit. (ref. 9, 1988), 12.
14. F. X. Kugler, Sternkunde und Sterndienst in Babel, ii (Münster, 1909/1910), 547–50; O. Neugebauer,

Astronomical cuneiform texts: Babylonian ephemerides of the Seleucid period for the motion
of the sun, the moon, and the planets, i (Princeton, 1955), 39; Sachs and Hunger, op. cit. (ref.
9, 1988), 22.

15. L. J. Fatoohi and F. R. Stephenson, “Angular measurements in Babylonian astronomy”, Archiv für

Orientforschung, xliv/xlv (1997/98), 210–14.

16. F. R. Stephenson and L. J. Fatoohi, “Lunar eclipse times recorded in Babylonian history”, Journal

for the history of astronomy, xxiv (1993), 255–67.

17. Neugebauer, op. cit. (ref. 14), 39.
18. Stephenson and Fatoohi, op. cit. (ref. 12).
19. Sachs and Hunger, opera cit. (ref. 9).
20. Sachs and Hunger, op. cit. (ref. 9, 1988), 115.
21. Ibid., 167.
22. Ibid., 341.

The Babylonian First Visibility

23. Sachs and Hunger, op. cit. (ref. 9, 1989), 205.

24. Ibid., 451.
25. Sachs and Hunger, op. cit. (ref. 9, 1988), 59.
26. Ibid., 351.
27. Sachs and Hunger, op. cit. (ref. 9, 1989), 19.
28. Sachs and Hunger, op. cit. (ref. 9, 1996), 193.
29. R. A. Parker and W. H. Dubberstein, Babylonian chronology 626

. –

. 75 (Providence, 1956).

30. K. Schoch, “Astronomical and calendrical tables”, in S. Langdon and J. K. Fotheringham, The

Venus Tablets of Ammizaduga: A solution of Babylonian chronology by means of the Venus
observations of the First Dynasty (Oxford, 1928). For further details of the program, see Louay
J. Fatoohi, “A computer program for the conversion of Babylonian into Julian dates”, Journal
for the history of astronomy, xxix (1998), 378–9.

31. Sachs and Hunger, op. cit. (ref. 9, 1988), 49.
32. Ibid., 305.
33. M. Chapront-Touzé and J. Chapront, “ELP2000-85: A semi-analytical lunar ephemeris adequate

for historical times”, Astronomy and astrophysics, cxc (1988), 342–52.

34. Ibid.
35. J. O. Dickey et al., “Lunar laser ranging — a continuing legacy of the Apollo Program”, Science,

cclxv (1994), 482–90.

36. F. R. Stephenson, Historical eclipses and the rotation of the Earth (Cambridge, 1997).
37. Astronomical almanac, 1992 (Washington, D.C.), K8.
38. L. V. Morrison and F. R. Stephenson, “Contemporary geophysics from Babylonian clay tablets”,

Contemporary physics, xxxviii (1997), 13–23.

39. F. R. Stephenson and L. V. Morrison, “Long-term fluctuation in the Earth’s rotation: 700

. to

. 1990", Philosophical transactions of the Royal Society, A, cccli (1995), 165–202.

40. P. Bretagnon, “Théorie du mouvement de l’ensemble des planètes: Solution VSOP82", Astronomy

and astrophysics, cxiv (1982), 278–88; P. Bretagnon and J.-L. Simon, Planetary programs
and tables from –4000 to + 2800 (Richmond, Virginia, 1986).

41. P. Bretagnon and G. Francou, “Planetary theories in rectangular and spherical variables: VSOP87

solutions”, Astronomy and astrophysics, ccii (1988), 309–15.

42. Neugebauer, op. cit. (ref. 14), 41.
43. F. Bruin, “The first visibility of the lunar crescent”, Vistas in astronomy, xxi (1977), 331–58, p.

333.

44. See, for instance, M. Ilyas, “Lunar crescent visibility criterion and Islamic calendar”, Quarterly

journal of the Royal Astronomical Society, xxxv (1994), 425–61; Schaefer, op. cit. (ref. 2,
1988).

45. D. King, “Some early Islamic tables for determining lunar crescent visibility”, Annals of the New

York Academy of Sciences, d (1987), 185–225.

46. Neugebauer, op. cit. (ref. 14).
47. Neugebauer, The exact sciences in Antiquity (Providence, 1957), 115.
48. Table 2 is adapted from Neugebauer, op. cit. (ref. 14), 43.
49. Ibid., 43.
50. Ibid., 67 and 84; O. Neugebauer, A history of ancient mathematical astronomy (Berlin, 1975),

539–40.

51. Schaefer, opera cit. (ref. 2); Doggett and Schaefer, op. cit. (ref. 3).
52. Fotheringham, op. cit. (ref. 1).
53. Schoch, op. cit. (ref. 30), 95.
54. O. Neugebauer, “The Babylonian method for the computation of the last visibilities of Mercury”,

Proceedings of the American Philosophical Society, xcv (1951), 110–16.

L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli

55. Schoch, op. cit. (ref. 30), 98.

56. J. K. Fotheringham, “The visibility of the lunar crescent”, in Langdon and Fotheringham, The

Venus Tablets of Ammizaduga (ref. 30), 45–48, p. 48.

57. O. Neugebauer, op. cit. (ref. 54).
58. P. V. Neugebauer, Astronomische Chronologie, ii (Berlin and Leipzig, 1929), Table E 21.
59. Parker and Dubberstein, op. cit. (ref. 29).
60. P. J. Huber, “Astronomical dating of Babylonian I and UR III”, Monographic journals of the Near

East, Occasional papers, i/4 (1982), 107–99.

JHA, xxx (1999)

GALILEO’S DIALOGO

Galileo on the World Systems: A new abridged translation and guide. Translated

and edited by Maurice A. Finocchiaro (University of California Press, Los An-
geles, 1997). Pp. 448. $55 (hardcover), $19.95 (paperback).

Translations and abridgements of fundamental texts in the history of science are as
important for contemporary students as they are difficult to accomplish. Maurice
Finocchiaro has for some time been an important interpreter of Galileo, especially
from the point of view of the philosophy of science. His Galileo and the art of
reasoning (Reidel, 1980) is a comprehensive analysis of the arguments set forth in
Galileo’s Dialogue on the two chief world systems. More recently, in The Galileo
affair: A documentary history (University of California Press, 1987), he edited and
translated the principal documents concerning the theological and philosophical
controversies associated with Galileo’s defence of Copernican astronomy. His new
translation and abridgement, as part of a special National Endowment for the Hu-
manities program for “guided studies of historically significant scientific writings”,
is an excellent resource for both students and teachers. Since the original text is
both long and difficult, Finoccchiaro’s book is especially welcome.

Finocchiaro’s text contains about two-fifths of the original text along with sub-

stantial notes and commentary. He provides an extensive introduction in which he
displays his excellent analysis of the intellectual context in which the book needs to
be understood. The abridgement of the text is well done: Finocchiaro provides those
portions of Galileo’s text that go to the heart of the arguments concerning Aristote-
lian cosmology and the possibilities of the Earth’s daily rotation and annual revolu-
tion around the Sun. Finocchiaro is especially alert to the rhetoric of scientific dem-
onstration and the role of demonstrative claims in Galileo. Finocchiaro’s own analysis
is set forth in three appendices: on critical reasoning, methodological reflection,
and varieties of rhetoric. An extensive glossary at the end contains key historical,
philosophical, and scientific terms and concepts. The entire work reveals the clarity
and thoroughness that is characteristic of Finocchiaro’s writings.

Throughout the notes, commentary, and appendices we find Finocchiaro’s well-

established claim that Galileo, despite the rhetoric of demonstration, never suc-
ceeded in demonstrating that the Earth actually moves, even though such a goal
was important to the Tuscan scientist. In this light, I think that Finocchiaro’s deci-
sion to omit the brief opening discussion of the Fourth Day — the day in which the
argument from the motion of the tides (as effect) to the double motion of the Earth
(as cause) is set forth — is unfortunate. For here the type of argument that will
follow is described: a search for ‘true and primary causes’ from which the effects
(in this case the tides) necessarily follow. Here we can see evidence that for Galileo
a true scientific demonstration seeks to discover a unique causal nexus.

B O O K R E V I E W S

Book Reviews

ASPECTS OF THE EXACT SCIENCES IN ISLAM

From Baghdad to Barcelona: Studies in the Islamic Exact Sciences in Honour of

Prof. Juan Vernet. Edited by Josep Casulleras and Julio Samsó (Annuari de
Filologia (Universitat de Barcelona), xix (1996), B-2; Instituto “Millás Vallicrosa
de Historia de la Ciencia Arabe”, Barcelona, 1996). Pp. 830.

These two volumes contain the papers from a symposium of this title at the XIXth
International Congress of History of Science held in Zaragoza in 1993. Eighteen
well-credentialed specialists present papers that can provide a rich source of details
for fellow historians. Severely scholarly in nature, these contributions represent the
bricks from which the edifice of history of astronomy is built. Seldom do we glimpse
here the larger outlines of the structure itself.

An exception is the opening paper, by George Saliba, who attempts to correct the

commonly-received view that the transfer of Greek knowledge to the Islamic world
basically took place through a golden age of translations in Baghdad in the first half
of the nineteenth century, and that this was primarily a stepping-stone to their sub-
sequent transfer to the Latin West. Using neglected material that had been available
in English and German for nearly seventy years, Saliba paints a complex picture of
transformation as well as transfer.

In the papers that follow (mostly in English, but a few in Spanish), we can learn

particulars of astrolabes, of astronomical tables, of trepidation, and just a touch of
mathematical astrology and magic squares. Among these one paper in particular
caught my eye, John North’s inquiry into “Just whose were the Alfonsine Tables?”.
Emmanuel Poulle has argued in the pages of this journal that they were essentially
a Parisian invention from around 1320. He has compared the forms of the (no longer
extant) Castilian Tables, as specified in the existing canons, with those tables now
known as the Alfonsine, and has concluded that they are so different from any

The introduction, which includes a very good account of the geostatic world

view and the Copernican controversy, helps to make this translation and abridgement
an ideal text for courses in the history and philosophy of science. The extended
commentary found in the footnotes adds significantly to the understanding of the
text and also illuminates current scholarly discussion of Galileo’s work. Through-
out the translation, Finocchiaro provides succinct summaries of sections omitted in
the abridgement as well as references to Favaro’s Italian edition and to Stillman
Drake’s English translation.

Finocchiaro’s new book is an exceptional achievement and those of us who teach

undergraduates — not to mention those whom we teach — will benefit greatly
from it.

Cornell College, Mount Vernon, Iowa

ILLIAM

E. C

ARROLL

Book Reviews

Castilian predecessor that we must credit what survives to the Parisian school.

North, however, has probed deeply into the underlying parameters of the solar

and precessional theories and has made a persuasive case that the Parisian tables,
while original in form, are actually based on constants taken over from Alfonso’s
astronomers. Surely the last word has not yet been written on this fascinating con-
troversy, but at the moment the pendulum seems to have swung back towards an
essential input from the Alfonsine astronomers whose original tables still seem to-
tally lost.

Harvard-Smithsonian Center for Astrophysics

WEN

INGERICH

THE ECLIPTIC IN ANCIENT EGYPT

Astronomische Konzepte und Jenseitsvorstellungen in den Pyramidentexten. Rolf

Krauss (Harassowitz, Wiesbaden, 1997). Pp. xvi + 297. DM 118 (paperback).

Rolf Krauss, for two decades known as an authority on Egyptian chronology and
philology, has here placed himself in the company of the four authors of the most
voluminous scholarly books on ancient Egyptian astronomy issued this century,
namely O. Neugebauer and R. A. Parker, C. Leitz, and M. Clagett. At the same time
he ventured to extend the field of pertinent erudition back to the Egyptian Old
Kingdom, a task requiring philological skill to a larger degree than was necessary
for the later epochs covered by these other authors. Such a high philological stand-
ard is exemplified not only by Krauss himself but also by the four Egyptologists
who acted as referees for this work, which was previously submitted as an habilita-
tion thesis to Hamburg University.

Owing to this lengthy refereeing process the main features of its contents have

been known to insiders for some years, a fact which, for example, enabled M. Römer
to announce its central thesis in an article in the daily press in December 1994
(“Auf dem Himmelsgewässer” in the Frankfurter Allgemeine Zeitung, no. 290, p.
N6), an article warmly recommended as a supplement to this review. This thesis
states that the mythological Kha-canal that occurs dozens of times in the Pyramid
Texts meant a “sinuous” or “oblique” band along the ecliptic, and its equally fre-
quently mentioned ferrymen Mhntjw are the Moon and certain planets. This claim
puts the Egyptians’ knowledge of the ecliptic back by two millennia.

I have become fairly convinced of it, though having some residual resistence

mainly because of the occasionally occurring epithet “sinuous” of that ecliptical
canal. A rejection of this central thesis would fatally invalidate about half of Krauss’s
numerous further astronomical interpretations, and any critic of it would be forced
to deal with a considerable part of the author’s 1197 predominantly philological
footnotes.

Having often been one of Krauss’s collaborators in minor questions, I have been

able over many years to watch his steadily increasing familiarity with the sky and

Book Reviews

with astronomical notions. He has now achieved an astronomical reliability rarely
encountered in scholars whose background is in the humanities. His 34 astronomical
figures are correct and clear, with the exception only of no. 5c. They are computer-
generated mainly in Chapter 12, where he argues for the identification of certain
deities with Mercury and Venus, relying on their geometrical relations to the morn-
ing horizon as fairly clearly stated by the textual sources. This chapter is largely
independent of the above-mentioned ecliptical hypothesis.

Even less dependent are Chapters 7 and 8, which deal with Orion and Sirius,

whose identity with Egyptian deities has been largely incontestable since Plutarch,
and is paralleled in textual astronomy of the Middle Kingdom. Finally, Chapter 15
gives a comprehensive summary of the preceding parts without their detailed argu-
mentation, so that it may be helpful to read it first.

Römer’s preannouncement had a side-effect scarcely intended by Krauss but no

doubt helpful to the commercial success of the book. By uncritical readers the ecliptic
thus put back by 2000 years has been readily confused with or conjecturally con-
nected with the zodiac, though the textual sources clearly contradict any such idea.
These numerous readers are recruited from the semi-academic wave of theosophy
and esoterism, among whom Egyptology enjoys an increasing philosophical inter-
est in general, but who in particular are eager to absorb any historical clue that
might seem to prove their belief that their beloved astrology has roots far back in all
ancient cultures. I see this trend as a valuable challenge to historians of astronomy,
whom I recommend to look at Krauss’s book also from this somewhat distorted
standpoint.

Kantonsschule, Wetzikon, Switzerland

URT

OCHER

HARRISON’S RIGHTS AND WRONGS

The Quest for Longitude. Edited by William J. H. Andrewes (The Collection of

Historical Scientific Instruments, Harvard University, Cambridge, Mass., 1996).
Pp. 448. $75/£49.95.

This lavishly produced and beautifully illustrated volume presents the papers and
the associated documents generated at a Harvard conference held in 1993 to mark
the bicentenary of the birth of the Humberside clockmaker John Harrison. As its
editor points out, appetite for longitude stories seems inexhaustible. It was this
conference that also prompted Dava Sobell’s bestseller, Longitude, a paean to
Harrison’s virtues and a chronicle of his sufferings. In Umberto Eco’s recent bulky
pastiche of Baroque travellers’ tales, The island of the day before, visionary longi-
tude schemes occupy pride of place. Several, such as the use of the weapon-salve at
long range on a wounded dog, are discussed here by Owen Gingerich in a chapter
on “nutty solutions to the longitude problem”. The novelist Thomas Pynchon has
also imagined a vast panorama of eighteenth-century navigation, surveying and

Book Reviews

astronomy, Mason and Dixon, which gives speaking parts to the marine chronom-
eters tested by his protagonists in 1761 at the Cape and St Helena. Pynchon also
satirically defends his eponymous heroes against the machinations of the then As-
tronomer Royal, Nevil Maskelyne.

Maskelyne and his colleagues have not emerged unscarred from these stories. In

the volume under review, Harrison is privileged by eulogists and scholars. Chapters
are devoted to the wooden clocks this ingenious carpenter made before 1730 where
many of his key innovations were early introduced; to the designs of the series of
clocks from H1 to H4 that he offered for the Longitude Prize set up by the 1714
Act; and, notably, to a passionate argument by Martin Burgess, who has rebuilt a
version of Harrison’s regulator using modern materials and methods, that the fail-
ure to recognize Harrison’s achievements was due mainly to a “gross failure of
human relationships”. Several thus reproduce and justify Harrison’s own much pub-
licized sense of injury, of the prejudice of “priests and philosophers” against his
masterly clocks. At least part of the appeal of this collection is the opportunity it
offers to reconsider the roles of practical astronomy and chronometry, of naviga-
tional skill and instrument making, in the “quest for longitude”.

This quest rather resembles a complex and branching network than a single mo-

ment of heroic insight. Readers of this journal will be familiar with the argument of
J. A. Bennett (1993), but already present in the works of Rupert Gould (1923) and
Humphrey Quill (1966), that John Harrison was a superb social operator who won
enormous sums from the Board of Longitude, patronage from the monarch and
reward from the Royal Society, and who, in the phrase of Gould cited here in a fine
paper on late eighteenth-century French horology by Catherine Cardinal, “built a
wonderful house on the sand”. Harrison certainly showed the plausibility of the
chronometric method, but it was the designs of Pierre Le Roy and the remarkable
production techniques of John Arnold and Thomas Earnshaw that at last turned the
method into a viable approach capable of providing reliable clocks for hosts of
mariners.

An historian of astronomy will be impressed by the argument made here by

Albert van Helden that observations of the eclipses of Jupiter’s moons, especially
as systematized by the efficient programme of Giovanni Cassini between 1668 and
the 1690s, provided the key technology for land-based longitude measures. This
prompted ambitious early seventeenth-century programmes from Gassendi and
Peiresc, the foundation of the Paris Observatory in the 1660s, French then global
geodesy, and the key debates on light speed started by Cassini and Ole Roemer in
the 1670s.

Derek Howse complements this valuable reminder with his account of the lunar

longitude method, favoured by Maskelyne and his coterie, the method of choice for
navigators until the mid-nineteenth century. This choice relied on the co-ordination
of Hadley’s quadrant, Tobias Mayer’s lunar tables (1755), and the star tables of
John Flamsteed and of Nicolas-Louis de Lacaille (1757) in handbooks released
from Paris and Greenwich. Though the best chronometric methods offered double

Book Reviews

ESSAYS IN THE HISTORY OF HOROLOGY

Of Time and Measurement: Studies in the History of Horology and Fine Technol-

ogy. A. J. Turner (Variorum, Aldershot, 1993). Pp. xii + 301. $103.95.

In his preface Anthony Turner acknowledges the likelihood that collections of re-
published articles will be “marginalised by polite non-reviews”. The present review
will confirm this opinion, but it is difficult to do more. This is a disparate collection,
despite the relative unity of the subject: the pieces were written for different pur-
poses and different audiences and, although there is a common character that de-
rives from the individuality of the author, there is, of course, no sustained narrative
and no directional argument. How could there be? Even the retention of the variety
of layouts, typefaces and paginations signals a diversity of sources and intentions,
while in terms of impact on the subject, the important articles have already achieved
this. The reviewer is thrown back on the staple observation that it is convenient to
have them ready to hand in an accessible format. If this is marginalization, the
author can hardly blame the reviewer.

As for the facts, there are 22 articles originally published between 1972 and

1990. They range from notes of a page or two to major and influential articles, but
most, by the author’s characterization, are “investigations into details”. They are

the accuracy of the lunar method, the latter was still often required to calibrate
marine clocks. As Eric Forbes once neatly put it, at the key meeting of the Board of
Longitude in February 1765 where Maskelyne’s plan for a Nautical Almanac was
endorsed and the performance of H4 decisively assessed, the Board acutely judged
that Harrison had made the chronometric method practicable but not generally use-
ful — so he was awarded half the maximum prize; while the astronomers had made
the lunar method generally useful but not yet practicable — so Mayer’s heirs were
awarded half the minimum prize, and, thanks to remarks by Alexis-Claude Clairaut
published in May 1765, Leonhard Euler was compensated for his aid with Mayer’s
tabulations.

Polemics about Harrison’s sufferings and the claims of the makers and theorists

too often simply revisit the debates of that year. Add to all this the significance of
the superb cartography that enabled early modern mariners to travel the world without
a direct longitude method (a theme less thoroughly treated in this collection); the
fascinating stories, given careful attention here by David Penney, of artisan skill in
the metropolitan clockmakers’ shops of Paris and London; and the eventual devel-
opment of global positioning systems during this century. It is not hard to see why
the story of the quest for longitude rightly maintains a central place in our under-
standing of science, technology and society.

Darwin College, Cambridge

IMON

CHAFFER

Book Reviews

LAUDING THE NRAO

The History of Radio Astronomy and the National Radio Astronomy Observatory:

Evolution Toward Big Science. Benjamin K. Malphrus (Krieger Publishing Co.,
Melbourne, Florida, 1996). Pp. vi + 210. $49.50.

This book, an outgrowth of an Ed.D. thesis in education at West Virginia University
and published near the Cape Canaveral spaceport, is a celebratory history of the
U.S. National Radio Astronomy Observatory (NRAO) as seen through the develop-
ment of its major radio telescopes over the period 1956 to the present. Basing him-
self primarily on internal and annual NRAO reports and the published astronomical
literature, Malphrus unremittently gushes on with statements such as “The Green
Bank interferometer system ... has carried out a wide variety of excellent research
and made significant discoveries”. Although not a house publication, it could well
have been produced by the NRAO public relations folks. The book is of value

grouped between sun-dials, mechanical horology and precision instrumentation.

The highlights are the accounts of William Oughtred’s “horizontal instrument”,

of the historical background to the chronometry of Ferdinand Berthoud, and of the
instrument making of Philippe Danfrie, together with one of the earliest but most
influential among the articles included, the much-cited “Mathematical instruments
and the education of gentlemen”, originally published in 1973.

Readers of JHA may be most interested in, and possibly least familiar with, “The

pre-history, origins and development of the reflecting telescope” from the obscure
Bollettino del Centro Internazionale di Storia della Spazio e del Tempo. There are
some very interesting points here that deserve elaboration. Only with Newton and
James Gregory, for example, does Turner feel that we have a scheme for a practical
telescope, rivalling the refractor, instead of intriguing consequences of the optical
properties of mirrors coupled with experimentation on burning glasses. For him the
latter characterization covers the period from Digges to Mersenne. There are also
promising suggestions about the diffusion of technical information on the making
of reflectors into the London trade and the rise of commercial manufacture in this
area.

But the article also illustrates a problem with this form of republication, namely

that there is little scope for the kind of improvements that would come with a new
edition. This may be a particularly unfortunate example, since it appeared first in a
non-English publication, but it is littered with mistakes — mostly misspellings and
typographical errors, but also lack of clarity and signs of hurried production.

Despite these reservations, and at the risk of resorting to the commonplace ob-

servation, I have to admit that I will find it useful to have a good number of these
articles conveniently to hand.

University of Oxford

ENNETT

Book Reviews

primarily for its excellent illustrations, and as a starting outline for whoever might
want to do a critical history of this important institution.

Malphrus’s first chapter sets the stage for the establishment of NRAO in the late

1950s by looking at the origins and development of radio astronomy. The account,
however, is full of errors and misconceptions, starting with the preface’s first sen-
tence: “The science of radio astronomy began in the 1930s with Karl Guthe Jansky’s
discovery of radio emission from the galactic nucleus.” The term radio astronomy
was not even coined until 1948 and it was still many more years before one had a
recognizable specialty (and never a science). And Jansky was able to establish only
that the radio emission was coming from the general direction of the galactic cen-
tre, not precisely from its nucleus. On p. 10 Grote Reber’s remarkable 31-ft diam-
eter dish antenna, built in his backyard in Illinois in 1937, is illustrated and cap-
tioned as “the first true radio telescope” without any discussion of the problematic
meaning of ‘true’ or the astounding idea of combining the words ‘radio’ and
‘telescope’ together (which also did not happen until the late 1940s). Another ex-
ample (p. 23) is the citation of Joe Pawsey and John Bolton as examples of men
who represented a “diffusion of the great minds” from one research group to an-
other. In both cases Malphrus starts them off in Cambridge (England), inferring
that they were part of the leading postwar radio astronomy group there under Mar-
tin Ryle. But in fact Pawsey obtained his Ph.D. at Cambridge for ionospheric work
and returned to his native Australia before the War, and Bolton was only a wartime
physics undergraduate at Cambridge before joining the Royal Navy and eventually
emigrating to Australia. This first chapter is the only one that pays any attention to
the rest of the world besides NRAO; once Malphrus begins tracking NRAO’s his-
tory, with rare exception is any broader context ever drawn from other institutions,
research groups, or nations.

Chapter 2 describes the fascinating debates surrounding the creation of a na-

tional radio observatory, with key players such as Merle Tuve, Lloyd Berkner, Alan
Waterman of the National Science Foundation, and the U.S. Navy (through the ill-
fated Sugar Grove 600-ft dish project). But most of this chapter, the most satisfying
to a historian’s sensibilities, is simply a retelling of Alan Needell’s excellent study
published in Osiris in 1987. Nevertheless, one still encounters statements such as
“by 1954 there was a pervasive feeling that the US lagged behind other countries in
astronomy” — tell that to the rest of the world envying the Mt Wilson 100-inch and
Palomar 200-inch telescopes! For some reason the author also feels compelled to
insert a couple of paragraphs about how the NRAO staff have always been proud
that “research in radio astronomy [as opposed to nuclear physics] has no malevo-
lent applications”, and yet he himself points out the Navy’s use of NRAO telescopes
for precise astrometric work — why does he think the Navy wanted precise naviga-
tional and missile-aiming capabilities?

In sum, this is a book of little value for historians of science. Despite the term

“Big Science” in his subtitle, Malphrus never analyses the concept in the least,
apparently thinking it unproblematic; nor does he ever cite any of the voluminous

Book Reviews

MEASURING MAGNITUDES

The Measurement of Starlight: Two Centuries of Astronomical Photometry. J. B.

Hearnshaw (Cambridge University Press, Cambridge, 1996). Pp. xiv + 511. $95/
£65.

If only the photoelectric cell (or the CCD) had been invented two millennia ago! As
John Hearnshaw’s fine book so clearly underscores, a prodigious amount of time
and effort was spent first on defining a magnitude system that astronomers slav-
ishly linked to the 6-magnitude system used by Ptolemy in his Almagest, and then
searching for ways to measure magnitudes accurately using both the eye and the
photograph. As late as 1950, Stebbins, Whitford and Johnson showed that a scale
error of about 0.6 magnitudes still persisted in the photographically-determined
magnitudes for faint stars in the standard Selected Areas. Mercifully, five years
later, the International Astronomical Union put to rest the International System of
magnitudes and the use of the North Polar Sequence.

The first five chapters, just half of The measurement of starlight, takes us chrono-

logically through this difficult and frustrating quest, beginning with the first use of
stellar magnitudes followed by the various ways of measuring them visually. This
work resulted not only in several important star catalogues, the Bonner
Durchmusterung being the best known, but also the discovery of several hundred
variable stars. Chapter 4 describes the early days (1839–1922) of photographic
photometry, and Chapter 5 picks up the story of the origins of “photoelectric” pho-
tometry, where Hearnshaw uses this word to include photoconductive and photo-
voltaic cells as well as the photoelectric effect. This chapter takes us from 1892 to
1945 and the advent of the photomultiplier.

The scene then switches to “Photometry at longer wavelengths” beginning with

William Herschel’s discovery of “ultra-red” radiation from the Sun announced in
the year 1800. This chapter continues to 1970 by which time the galactic nucleus
had been discovered by Becklin and Neugebauer and circumstellar dust had been
detected around several stars. Meanwhile, back in the darkroom, photographs were
still being processed at a great rate, and Hearnshaw summarizes the on-going strug-
gle to measure magnitudes accurately, finally aided by the photoelectric multiplier
with which faint stars in the plate fields could be measured and used as standards.

Beginning in the twentieth century, a number of enormously important develop-

ments came about photographically despite the calibration problems: the explosion

historical literature on scientific institutions and postwar science. Instead, one is
left with ahistorical conclusions such as “[NRAO’s] cutting edge instrumentation
has allowed frontier research from which major contributions logically followed”.
Enough said.

University of Washington, Seattle

OODRUFF

T. S

ULLIVAN

, III

Book Reviews

of the discovery of variable stars, especially in globular clusters and the Magellanic
clouds, Russell’s and Shapley’s studies of binary stars, the outlining of the Galaxy,
and Henrietta Leavitt’s “remarkable discovery” of the period–luminosity law for
Cepheid variables. The final two chapters describe, respectively, the post-Second
World War successes of photometry made with photoelectric photomultipliers, and
image tubes and television systems, bringing us up to 1970, the year of the first
mention of the charge-coupled device (CCD) by Boyle and Smith at Bell Laboratories
and the cut-off date of the book.

Hearnshaw has successfully avoided making this history a dreary compilation of

abstracts, and has nicely linked together the steps that have led photometrists to
1970 by which time accurate magnitudes and colours had been established over
some 50 magnitudes — a factor of 1020 in brightness. Furthermore, he has made
the reading more lively by including excerpts from oral histories. Some of the re-
marks of Joel Stebbins, “one of the most notable of the early pioneers in stellar
photoelectric photometry” — and also one of the most humorous — are real treas-
ures.

In my opinion Hearnshaw has done a great service by weighting properly, I be-

lieve, the relative importance of European and American researches, and he notes
that much solid research was stifled in Europe because many observatories devoted
inordinate amounts of time to the making of the ill-fated Carte du Ciel. Hearnshaw
also notes the on-going East Coast–West Coast rivalry in twentieth-century USA.
As an undergraduate at Harvard in the late 1940s, I was able to experience both of
these since the oft-mentioned Harlow Shapley, Bart Bok, and Cecilia Payne-
Gaposchkin were all still active and visitors frequently came from overseas to speak
of their work.

One notable feature of The measurement of starlight is the large number of refer-

ences: I counted 1,825 of them. Also excellent are the name and subject indices,
which have obviously been made with some care.

On the down side, I was annoyed that a number of the figures, especially graphs,

had no labels on their axes; one often has to guess at what was being plotted. The
only other substantive criticism I have concerned “the author’s personal selection”,
which left out practically all mention of, for example, Hubble’s demonstration of
the extragalactic nature of the spiral nebulae, surely one of the larger milestones in
twentieth-century astrophysics; in the entire book, Hubble receives only two brief
references. Also, I would have at least mentioned Dorrit Hoffleit’s numerous con-
tributions and Arlo Landolt’s important establishment of UBV photoelectric se-
quences along the celestial equator begun in the 1960s.

This carefully researched and edited book should be much enjoyed by modern-

day photometrists and by astronomers interested in the development of one vital
part of astronomy. I highly recommend it to all of them.

Instituto Isaac Newton, Santiago, Chile

ILLIAM

ILLER

Book Reviews

THE DSB ON LAPLACE REPRINTED

Pierre-Simon Laplace, 1749–1827: A Life in Exact Science. Charles Coulston

Gillispie with the assistance of Robert Fox and Ivor Grattan Guiness (Princeton
University Press, Princeton, New Jersey, 1998). Pp. xii + 322. $49.50/£35.

The volume under review is a largely verbatim reprint of the lengthy article on
Laplace in the first supplement to the Dictionary of scientific biography. Apart from
a few new references and some light rewriting, the text dates from 1978. Gillispie
and his co-authors came to compile the entry and to place it in the supplement
because the contributor first engaged to write Laplace’s life had not finished when
the volume that was to contain it went to press. No doubt the assignment was bur-
densome within an article of standard size. Laplace’s writings were many and var-
ied, his bibliography twisted, and his life apart from his career poorly documented.
As editor-in-chief of the DSB, Gillispie could allow himself the space necessary to
summarize the writings and straighten out the bibliography. The life remains to be
written.

The reprint has the merits over the original of a convenient format and a useful

index. No advantage was taken of the opportunity to introduce illustrations or dia-
grams or to ease entry into Laplace’s work for readers unprepared for the rigours of
the DSB. Gillispie and the Princeton University Press deserve thanks for downsizing
and indexing the original article but not for giving the impression that the result is a
new work. The assertion on the jacket blurb, that the contributions of Gillispie et al.
will not be “duplicated” in our time, is good puffery but bad history.

Worcester College, Oxford

J. L. H

EILBRON

A SIXTEENTH-CENTURY VIENNESE INTELLECTUAL

Humanismus zwischen Hof und Universität: Georg Tanstetter (Collimitius) und sein

wissenschaftliches Umfeld im Wien des frühen 16. Jahrhunderts. Franz Graf-
Stuhlhofer (Schriftenreihe des Universitätsarchivs, Band 8; WUV-Universitüts
Verlag, 1996). 268 Schilling (paperback).

A Bavarian by birth and a master of arts from Ingolstadt, Georg Tanstetter Collimitius
(1482–1535) went on to become the leading teacher of astronomy and a well-
connected figure in early sixteenth-century Vienna. (The word “Collimitius”, which
is sometimes fashionably appended to his name, is the latinization of his home-
town, Rain, which means “border”.) His students included Petrus Apianus (the au-
thor of the spectacular Astronomicum Caesareum of 1540), and the Swiss humanist
Joachim Vadian was one of his best friends. He was also Emperor Maximilian’s
deathbed physician (1518–19), an advisor and Leibarzt to King Ferdinand of
Habsburg and his children, a computer of calendars, an editor, and an author in his

Book Reviews

own right. Not least, he contributed, as a biographer, to the history of astronomy in
fifteenth-century Vienna.

In 1980, Franz Stuhlhofer wrote a dissertation on Tanstetter for the University of

Vienna. He has now updated the fruits of his research in a more accessible form,
published under his hyphenated married name. The result is likely to remain for
some time the definitive reference on Tanstetter’s life. Indeed, the systematic and
exhaustive collection of information assembled here suggests that Tanstetter prob-
ably deserves an engaging narrative biography, in which his activities could be
fleshed out in the full richness of their context.

As the title hints, Tanstetter is significant for several reasons. As an important

academic, he held prominent teaching and administrative positions at the Univer-
sity of Vienna (including professor of astronomy and medicine, vice-chancellor,
dean, and rector). But his activities also illustrate the interaction between university
and court, medicine and astrology, and late-medieval and humanist trends, to say
nothing of their interest for the history of publishing and historiography. Since he
resists stereotyping according to traditionally polarized historiographical and disci-
plinary categories, his life offers an opportunity for an intriguing and salutary case-
study.

The book surveys all extant materials known to the author, and these encompass

an impressive range. Tanstetter is responsible for some twenty calendars, almanacs,
and judicia (1504–1526, several of them directed to the Viennese city fathers); a
proposal for calendar reform; a plague treatise for 1521; a map of Hungary; univer-
sity lectures on astronomy/astrology (including notes on the astronomical sections
of Pliny); editions of works in the mathematical sciences (from Proclus to Peurbach
and Regiomontanus, through Witelo, the latitude of forms, and John of Murs); and
— last and least — some forgettable poetry honouring a deceased youth with the
unforgettable name of Arbogast Strub.

The centre of gravity of Tanstetter’s activities was astrology, an endeavour that

connected his astronomical work, his involvement with the imperial court, his pub-
lishing ventures, and his later medical career. Among contemporaries, he was re-
nowned for his prediction of the Emperor Maximilian’s death six years before it
occurred.

For all of his multifarious activities, Tanstetter is remembered today primarily as

an historian of astronomy and editor of astronomical works. His Viri mathematici
quos inclytum Viennense gymnasium ordine celebres habunt (Vienna, 1514) is a
biographically-organized history of Viennese astronomy in the fifteenth century,
from Henry of Langenstein (d. 1397) to Tanstetter’s own times. It reflects Tanstetter’s
pride in belonging to an institution with such a glorious tradition. Graf-Stuhlhofer
conveniently provides the Latin text and a translation of this short, relatively rare
work.

Graf-Stuhlhofer raises once again the much-vexed problem of “humanist sci-

ence”, largely following in the footsteps of Helmuth Grössing’s Humanistische
Naturwissenschaft (Baden-Baden, 1983). He assigns Tanstetter an intermediate

Book Reviews

THE PERIHELION OF MERCURY

In Search of Planet Vulcan: The Ghost in Newton’s Clockwork Universe. Richard

Baum and William Sheehan (Plenum Publishing Corporation, New York, 1997).
Pp. x + 310. $28.95.

The subject of this interesting and clearly written volume is actually broader than
its title suggests. Not until halfway through the volume do we reach the problem of

position between the extreme “ideal types” of the humanist and the scholastic.
Tanstetter’s scholarly work, for example, is not oriented to Antiquity. On the con-
trary: apart from Proclus’s Sphere and his own comments on Pliny, his publishing
efforts encompassed what now pass for “medieval” works. Graf-Stuhlhofer never-
theless argues that Tanstetter saw himself as a humanist, categorizing him as a “hu-
manist dove”, not an agressive “humanist hawk”. Just the same, he suggests that in
terms of content one “should scarcely expect clearly recognizable differences be-
tween scholasticism and humanism” (p. 108) — apparently a distinction without a
difference.

In outlining Tanstetter’s life, Graf-Stuhlhofer sheds light on poorly-understood

aspects of early sixteenth-century university life in Vienna. In particular, he exam-
ines the fate of the famous “College of Poets” founded by Conrad Celtis, a Habsburg-
funded college associated with the university and outfitted with two chairs of po-
etry and rhetoric and two in the mathematical disciplines. He hypothesizes that this
college functioned as a kind of fourth higher faculty, effectively a graduate school
for the Faculty of Arts. Although scholars have doubted that the college survived
beyond Celtis’s death (1508), Graf-Stuhlhofer plausibly suggests that it did: in-
deed, it would explain the contemporary designation of Tanstetter as “ordinary pro-
fessor of mathematics”, despite the lack of references to such teaching in the Acts
of the Faculty of Arts itself.

While Graf-Stuhlhofer alludes to Tanstetter’s “reflection of contemporary poli-

tics and mentality” (p. 15), he does not develop these themes very much in the
book. The most sensitive exception is perhaps his brief treatment of Tanstetter’s
ambiguous relation to the religious upheavals of the day. While his friend and cor-
respondent Vadian — now back in Switzerland — had given his allegiance to the
emergent Reformation, Tanstetter the Habsburg advisor was not surprisingly reti-
cent on the subject. The book is well-organized and easy to use. It is helpfully
equipped with separate indices for proper names and all names appearing in
Tanstetter’s books. The twenty-two illustrations include the known and presumed
portraits of Tanstetter, and the title-pages of his books. In short, this is a useful
reference work on a prominent intellectual, teacher, and courtly advisor in six-
teenth-century Vienna.

University of Wisconsin–Madison

ICHAEL

H. S

HANK

Book Reviews

Vulcan. The first half, the best popular history of celestial mechanics I have seen,
describes in vivid terms the problems in celestial mechanics from Newton to the
discovery of Neptune in the mid-nineteenth century. In particular, it details how the
challenges to Newtonian gravitational theory were overcome one-by-one, from
Clairaut’s triumphant explanation in 1749 of the motion of the lunar apsides, to his
prediction (accurate within 33 days) of the 1759 perihelion passage of Halley’s
comet. It includes Laplace’s solution in 1784 to the problem of the great inequality
in the orbits of Jupiter and Saturn, and finally Le Verrier’s prediction of the location
of the Neptune.

All of this gives us a much greater appreciation for the intransigent problem

treated in the second half of the book, the advance in the perihelion of Mercury,
which is thus properly placed in the context of the history of celestial mechanics.
Le Verrier is the hero of this story, but there is much prior and lesser known history
as well. Predictions of the transits of Mercury (which occur considerably more
frequently than transits of Venus) gradually improved with respect to observation,
from one-day discrepancies in 1707, to hours in 1753, to 53 minutes in 1786, to 16
seconds in 1845 based on Le Verrier’s prediction. In 1859 Le Verrier began his
assault on Mercury, comparable to Kepler’s famous “battle with Mars” 250 years
earlier involving eight-minute-of-arc discrepancies. After taking into account the
theory of the Sun and errors of observation, Le Verrier found that planetary
perturbations accounted for 527 arcseconds per century in the advance of Mercu-
ry’s perihelion, leaving 38 arcseconds per century unexplained (later shown by Simon
Newcomb to be 43 arcseconds/century). This gave rise to his hypothesis that un-
known masses must exist between Mercury and the Sun, a suggestion that set off a
20-year observing frenzy. Already by 1860 the name “Vulcan”, the Roman god of
fire, was given to the hypothetical planet, even though no one knew whether it
might be a single object or many.

Le Verrier did not wait long for confirmation; in early 1859 the French country

doctor Edmond Lescarbault claimed to have observed the transit of such an object
across the Sun. This might not have had much historical effect, but after severe
questioning by Le Verrier of the details of Lescarbault’s observations, the Paris
Observatory Director made the triumphant announcement of a new intramercurial
planet to the Académie des Sciences. This was only the first of numerous observa-
tional claims, in a saga that Baum and Sheehan describe in considerable detail. In
the United States James Craig Watson became the champion of Vulcan, and claimed
actually to have observed it during the 1878 solar eclipse. He was bitterly opposed
by C. H. F. Peters, among others, but was supported by an observation of the comet
discoverer Lewis Swift. Further confirmation remained elusive, however, and even
Le Verrier realized that twenty Vulcans (based on a mass deduced from Lescarbault’s
measurement of Vulcan’s diameter) would be needed to explain the anomalous
motion of Mercury. As more eclipses passed without confirming observations, Vulcan
passed into history. As the authors point out, the whole Vulcan episode is another
illustration of (in David Brewster’s words) “those illusions of the eye or of the

Book Reviews

brain, which have sometimes disturbed the tranquillity of science”. Sheehan has
documented plenty more in his book Planets and perception.

But the compelling story of this volume is that of celestial mechanics, for as we

all know, the advance in the perihelion of Mercury in the end could not be ex-
plained by classical Newtonian physics. The answer came not from observational
astronomers, but from a physicist, Albert Einstein, whose General Theory of Rela-
tivity finally explained the infamous 43 arcsecond anomaly. That story, beyond the
scope of this book, has been well-told elsewhere. But Baum and Sheehan remind us
that the search for bodies “felt” before they have been seen continued with the
search for a trans-Neptunian planet, the trans-Plutonian Planet X, and continues in
ever more subtle form — and apparently finally successfully — with the detection
of gravitational wobbles induced by extrasolar planets. With the latter success, ce-
lestial mechanics now has before it the prospect of charting entirely new solar sys-
tems, a process that is already bringing fresh challenges for gravitational theory.

Although the authors state that this book is not intended as an academic history,

it is nevertheless well documented, full of insight, and (unlike many weightier tomes)
a joy to read.

U.S. Naval Observatory

TEVEN

J. D

ICK

EINSTEIN AND THE EINSTEIN TOWER

The Einstein Tower: An Intertexture of Dynamic Construction, Relativity Theory,

and Astronomy. Klaus Hentschel, translated by Ann M. Hentschel (Cambridge
University Press, Cambridge, 1998). Pp. xiv + 226. $45.

Whereas a whole publication industry has been erected around Einstein and his
theory of relativity, much less historical attention has been devoted to the more
secondary figures in the history of relativity and even less to the institutions that
were involved in the history. Klaus Hentschel’s book, a translation of the German
1992 original, is related to the Einstein literature but has neither Einstein nor his
theory as its focal subject. The main part of the book is devoted to an astronomer,
Erwin Finlay Freundlich, and an institution, the Potsdam solar observatory known
as the “Einstein Tower”. Contrary to what is often believed, Einstein was greatly
interested in the possibilities of testing his general theory of relativity. On the basis
of his 1911 theory he had found that a ray of light passing the limb of the Sun
should be deflected an angle of 0

″

.85, or half the value predicted by the fully devel-

oped theory of 1916. Influenced by Einstein, the young Berlin astronomer Freundlich
decided to test the “Einstein effect” and soon became Einstein’s mouthpiece in the
generally conservative German astronomical community.

Hentschel gives a fine biographical account of Freundlich, a passionate advocate

of relativity but also a difficult person who was constantly engaged in controversies

Book Reviews

and whose career was anything but smooth. Through Freundlich’s life story we get
to know not only the person but also, and even more interestingly, his social and
professional environments. Hentschel provides a fascinating insight in the Berlin
astronomical community during the Weimar republic and the dramatic changes that
followed in 1933 when the National Socialists came to power. The book is not an
ordinary biography of a scientist. As indicated by its title, it is as much concerned
with the observatory that Freundlich started to establish in 1919 with the explicit
purpose of testing Einstein’s theory. The Einstein Tower in the Berlin suburb Potsdam
was modelled after the 150-ft tower telescope at the Mount Wilson Observatory.
What made it famous and brought it on the front page of the news magazines was
not its scientific results (which were disappointing) but its innovative design, the
creation of the architect Erich Mendelsohn. This is the third of the book’s main
themes. Hentschel interweaves in the scientific, institutional, and political history
of the 1920s an informative and interesting account of German architectural history
with Mendelsohn in the focus.

The Einstein Tower is contextual history at its best. Contrary to many other works

in the fashionable contextual genre, Hentschel does not merely deal with the con-
texts but also with what these contexts are about, that is, the scientific questions.
And he does so expertly and in considerable detail. There are many detailed histori-
cal examinations of the early solar eclipse expeditions aiming at testing Einstein’s
light-bending prediction (e.g., by J. Crelinsten, D. Moyer, J. Earman and C. Glymour)
and Hentschel provides additional information about the later expeditions in the
1920s. When Freundlich finally succeeded in measuring the light deflection, in
Sumatra in 1929, he found a value considerably larger than the predicted 1

″

.75. An

undisturbed Einstein dismissed Freundlich’s result as being due to an “erroneous
calculation of the experimental results”.

Hentschel argues that in order to understand an episode in the history of science

we should pay attention not only to the main actors, say Einstein or Eddington, but
also to the more secondary figures (such as Freundlich and his antagonist Hans
Ludendorff) and the entire network of people, instruments and institutions in which
they operated. This view, neither particularly novel nor particularly controversial,
may or may not lead to good and interesting history. It all depends on the way it is
practised. In the case of Freundlich and the Einstein Tower, as analysed by Hentschel,
this kind of “common folk’s history” works well. Contributing to the fine result is
Hentschel’s meticulous scholarship, his careful examination of often obscure ar-
chival sources, and the many illustrations. It is not the author’s fault that Stanford
University Press charges $45 for a book of less than 250 pages.

Aarhus University

ELGE

RAGH

Tycho Brahe: Instruments of the Renewed Astronomy. Alena Hadravova, Petr Hadrava

and Jole R. Shackelford (Institutum Studiis Classicis Promovendis, Academia
Scientiarum Rei Publicae Bohemorum, Prague, 1996). Pp. xvi + 175. (Paperback.)

Tycho Brahe: Prístroje Obnovene Astronomie. Alena Hadravova, Petr Hadrava and

Jole R. Shackelford (Institutum Studiis Classicis Promovendis, Academia
scientiarum Rei Publicae Bohemorum, Prague, 1996). Pp. xvi + 188. (Paperback.)

These are handy new editions of Tycho Brahe’s Astronomiae instauratae mechanica
(1598), one in Czech and one in English (revised somewhat from the 1946 translation
by Raeder, Strömgren and Strömgren). The Czech version is a little longer because it
includes the poems omitted in the English translations. The English version does
however include the dedication to Rudolf II omitted in the earlier English version.

Dictionary of Minor Planet Names. Lutz D. Schmadel (Springer-Verlag, Heidelberg

and New York, 1997). Pp. xii + 940. DM 168.

This huge revised compendium lists the discoverers and discovery dates of the first
7041 asteroids, and gives succinct information about the source of the names. A
fascinating amount of miscellaneous detail is included, from obituary references of
some of the honorands to a list of the most prolific asteroid finders.

Doomsday Asteroid: Can We Survive? Donald W. Cox and James H. Chestek

(Prometheus Books, New York, 1996). Pp. 337. $26.95.

A popular book by two space enthusiasts, riding on the wave of interest generated
by several close approaches and the dinosaur extinction conclusions.

Exploring the Unknown: Selected Documents in the History of the U.S. Civil Space

Program, ii: External Relationships. Edited by John M. Logsdon with Dwayne
A. Day and Roger D. Launius (National Aeronautics and Space Administration,
Washington, D.C., 1996). Pp. xxxvi + 636. $40.

A thick book of documents, ranging from congressional testimony to memoranda
for the President, recording both civilian–military rivalries and the NASA-university-
industrial interplay. Included is a useful biographical appendix.

Exploring the Unknown: Selected Documents in the History of the U.S. Civil Space

Program, iii: Using Space. Edited by John M. Logsdon with Roger D. Launius,
David H. Onkst, and Stephen J. Garber (National Aeronautics and Space
Administration, Washington, D.C., 1998). Pp viii + 608. $41.

A continuation of the document series, with essays on the history of satellite com-
munications and observing the Earth from space.

N O T I C E S O F B O O K S

JHA, xxx (1999)

Notices of Books

Aiming at Targets: The Autobiography of Robert C. Seamans. Robert C. Seamans,

Jr (National Aeronautics and Space Administration, Washington, D.C. 1996).
Pp. x + 291. $25 (paperback).

Seamans was a Deputy Administrator of NASA during the Apollo period; this lively
account is part of the ever-burgeoning NASA History Series.

Stages to Saturn: A Technological History of Apollo/Saturn Launch Vehicles. Roger

E. Bilstein (National Aeronautics and Space Administration, Washington, D.C.,
1996). Pp. viii + 511. $37 (paperback).

A reprint of a 1980 study of the development of the Saturn launch vehicle used in
the Apollo program; this is another of the NASA History Series.

L’Astrolabe. Raymond d’Hollander (Les Astrolabes du Musée Paul Dupuy de Tou-

louse, Toulouse, 1993). Pp. xii + 151. 270 FrF (paperback).

A book filled with pictures, diagrams, and formulas, primarily about the common
planispheric astrolabe; included is an astrolabe rete on a transparent disk.

Total Eclipses of the Sun. J. B. Zirker (Princeton University Press, Princeton, New

Jersey, 1995). Pp. 228. $12.95/ £10.95 (paperback).

Zirker’s book explains well why modern astronomers still chase eclipses, what they
have found and what they are still looking for. The opening chapter gives a succinct
historical background.

Greenwich Time and the Longitude. Derek Howse (Philip Wilson Publishers and

National Maritime Museum, London, 1997). Pp. 199. £19.95.

This “official millennium edition” of the late Derek Howse’s 1980 book is now in a
larger format with many more illustrations. For example, instead of a small black-
and-white detail of Flamsteed from the ceiling painting of Greenwich Hospital,
there is now a full-page colour plate. The original book was reviewed in JHA in the
February 1982 issue.

Preceptum Canonis Ptolomei. David Pingree (Corpus des Astronomes Byzantins,

viii; Academia-Bruylant, Louvain-la-Neuve, 1997). Pp. 174. 850 Belgium Francs
or 140 FF (paperback).

Composed around

. 534, this Latin treatise gives instructions for using Ptolemy’s

Handy tables. This critical edition, based on six surviving manuscripts, includes an
English translation and 24 pages of commentary with copious passages in Greek.
In the end Pingree concludes that the Preceptum was an inadequate guide to the
Handy tables.

Notes on Contributors

N O T E S O N C O N T R I B U T O R S

HETHA

S. A

-D

ARGAZELLI

obtained her Ph.D. in Nuclear Physics from Durham

University in 1979. She is interested in Historical Astronomy in general and
Islamic astronomy in particular. She is currently Research Fellow in the Elec-
tronic Engineering and Computer Science Department at Aston University.

ENNETT

, Keeper of the Museum of the History of Science, Oxford, is currently

occupied with a major redevelopment at the Museum, which will probably re-
main closed until the year 2000.

ILLIAM

E. C

ARROLL

is professor of European intellectual history and the history

of science at Cornell College (Iowa). He is the director of Cornell’s interdiscipli-
nary program in science and religion. His work includes studies of the reception
of Aristotelian thought in the Latin Middle Ages as well as the controversy be-
tween Galileo and the Inquisition.

TEPHEN

J. D

ICK

is an historian of science at the U.S. Naval Observatory in Wash-

ington, D.C., President of IAU Commission 41 (History of Astronomy), and the
author of The biological universe (Cambridge University Press, 1996). He is
writing the history of the U.S. Naval Observatory.

OUAY

ATOOHI

has recently been awarded his Ph.D. from Durham University for a

thesis on “First visibility of the lunar crescent and other problems in historical
astronomy”. He is currently Visiting Fellow in the Physics Department at Dur-
ham University.

Galileo: Decisive Innovator. Michael Sharratt (Cambridge University Press, Cam-

bridge, 1996). Pp. xiv + 247. £35/$54.95 (paperback).

The paperback edition of a book reviewed in the February 1996 issue of JHA.

Histoire générale des sciences (4 volumes: La science antique et médiévale; La

science moderne; La science contemporaine, (i) Le xix

siècle; and La science

contemporaine, (ii) Le xx

siècle). Edited by René Taton (Quadrige / Presses

Universitaires de France, 1995). Pp. 3472. 498 FF (boxed set of four paperbacks).

A large number of authors contributed in 1957 to the original edition of this sweep-
ing survey of the history of science from Antiquity to the twentieth century. In 1966
it was revised, bringing the history up to 1960. The four volumes have now ap-
peared in a handy boxed reprint.

Notes on Contributors

WEN

INGERICH

notes with alarm the increase in stolen copies of Copernicus’s De

revolutionibus; using data from his census he has assisted in identifying and
recovering some copies from Eastern Europe, but others are still missing.

OHN

EILBRON

, formerly professor of history and vice-chancellor at the University

of California, Berkeley, is a senior research fellow at Worcester College, Oxford.
His book, The sun in the church, a history around and about meridian lines in
Catholic churches, is in press with Harvard University Press.

ELGE

RAGH

is professor in the History of Science Department of Aarhus Univer-

sity, where he works in the history of the modern physical sciences. His book on
twentieth-century physics will be published next year by Princeton University Press.

ILLIAM

ILLER

has worked in Chile since 1981 as “a reborn amateur astronomer”

after serving for twenty years as a professor of astronomy at Harvard University.
His wide-ranging interests have included stellar photometery, Easter Island
archaeoastronomy, and musical composition.

URT

OCHER

(Rebrain 39, 8624 Grüt, Switzerland) is a college teacher of physics

with a special interest in pre-Ptolemaic astronomy.

IMON

CHAFFER

is Fellow of Darwin College and Reader in the History and Phi-

losophy of Science, University of Cambridge. He is currently taking part in a
collaborative project on the history of instrumentation and scientific travel in the
eighteenth and nineteenth centuries.

ICHAEL

H. S

HANK

is currently immersed in Regiomontanus research. He is com-

pleting a book on the text and contexts of the Disputationes and a detailed study
of the printing of that work, and is beginning with Richard Kremer a major study
of the “Defence of Theon against George of Trebizond”.

HOMAS

J. S

HERRILL

(226 Solana Drive, Los Altos, CA 94022, USA) is an astrono-

mer whose background is in celestial mechanics. He worked on the Hubble Space
Telescope project for Lockheed Martin Corp. for 18 years, and developed the
HST Design Reference Mission, a simulation of 30 days of orbital observations
used as a reference for spacecraft design. He continues to consult for Lockheed
Martin on the development of the Space Infrared Telescope Facility (SIRTF).

ICHARD

TEPHENSON

continues his work on various aspects of Applied Historical

Astronomy. He was on the organizing committee of the Third International Con-
ference on Oriental Astronomy at Fukuoka, Japan, which took place in October last.

N. M. S

WERDLOW

is professor in the Department of Astronomy and Astrophysics at

The University of Chicago. He is currently working on a book on Galileo’s
astronomy.

OODY

ULLIVAN

is a Professor of Astronomy and Adjunct Professor of History at

the University of Washington in Seattle. He has long been researching and writ-
ing a monograph on the early worldwide history of radio astronomy (prior to
1954). His passion is gnomonics.