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1 he moon IMOIYI a plioLoguipb Like u at the I uk Obscivatoiy 

A Short History 





Wagnct Verzeiht ' es ist etn gross Ei get/en 
Sich in den Gust dcr Zeiten zu versct/en, 
Zu bchauen wic vor unb em weiser Mann gedacht, 
Und wie wir's dann zulctzt so herihch weit gebracht 

Faust O ja, bis an die Stei ne weit ' 





intension flfeanuals, 



This Series is primarily designed to aid the University Extension 
Movement throughout Great Britain and America, and to supply 
the need, so -widely felt by students, of Text-books for study and 
reference, in connection with the authorised Comscs of Lcctwes 

Volumes dealing 'with separate departments of Literature, Science, 
Art, and History have been assigned to representative literary men, 
to University Professors, or to Extension Lecturers connected with 
Oxford, Cambridge, London, or the Universities of Scotland and 

The Manuals are not intended for purposes of Elementary Edu- 
cation, but for students who have made some advance in the subject 
dealt with The statement of details is meant to illustrate the working 
of general laws, and the development of principles , while, the historical 
evolution of the subject dealt with is kept in view, along with its 
philosophical significance 

The remarkable success which has attended University JSvtetinon 
in Britain has been partly due to the combination of- scientific treat- 
ment with popularity, and to the union of wmphcity with thorough- 
ness This movement, however, can only teach those resident in the 
larger centres of population, while all over the count? y thne arc 
thoughtful persons who dente the same kind of teaching. It M fat 
them also that this Series is designed Its aim u to wpply the 
general reader with the same kind of teaching a^ is given in the 
Lectures, and to reflect the spirit which has characterised the move- 
ment, vis the combi?iation of principles with facts, and oj methods 
with results 

The Manuals are also intended to be contributions to the Literature 
of the Subjects with which they respectively deal, quite apart pom 
University Extension , and some of them will be found to meet a general 
rather than a special want 


I HAVF tried to give in this book an outline of the history 
of astronomy from the earliest historical times to the present 
day, and to piesent it in a form which shall be intelligible 
to a reader who has no special knowledge of either astronomy 
or mathematics, and has only an ordinal y educated person s 
power of following scientific reasoning 

In order to accomplish my object within the limits of 
one small volume it has been necessaiy to pay the strictest 
attention to compression , this has been effected to some 
extent by the omission of all but the scantiest treatment 
of several branches of the subject which would figure 
prominently in a book written on a different plan or on 
a different scale I have dehbeiately abstained from giving 
any connected account of the astionomy of the Egyptians, 
Chaldaeans, Chinese, and othas to whom the early develop 
ment of astronomy is usually attributed On the one 
hand, it does not appear to me possible to foim an in 
dependent opinion on the subject without a first hand 
knowledge of the documents and inscriptions from which 
our information is derived , and on the other, the vanous 
Onental scholars who have this knowledge still differ so 
widely from one another m the interpretations that they 
give that it appears premature to embody their results in 

vi Preface 

the dogmatic form of a text-book It has also seemed 
advisable to lighten the book by omitting except in a very 
few simple and important cases all accounts of astro- 
nomical instruments , I do not remember ever to have 
derived any pleasure or profit from a written description 
of a scientific instrument before seeing the instrument 
itself, or one very similar to it, and I have abstained 
from attempting to give to my readers what I have never 
succeeded in obtaining myself The aim of the book 
has also necessitated the omission of a number of im- 
portant astronomical discoveries, which find their natural 
expression in the technical language of mathematics I 
have on this account only been able to describe in the 
briefest and most general way the wonderful and beautiful 
superstructure which several generations of mathematicians 
have erected on the foundations laid by Newton For 
the same reason I have been compelled occasionally 
to occupy a good deal of space in stating in ordinary 
English what might have been expressed much more 
briefly, as well as more cleaily, by an algebiaical formula 
for the benefit of such mathematicians as may happen to 
read the book I have added a few mathematical footnotes , 
otherwise I have tried to abstain scmpulously from the 
use of any mathematics beyond simple arithmetic and a 
few technical terms which are explained in the text. A 
good deal of space has also been saved by the total 
omission of, or the briefest possible reference to, a very 
large number of astronomical facts which do not bear on 
any well-established general theory, and foi similar icasons 
I have geneially abstained from noticing speculative 
theories which have not yet been established or icfuted 
In paiticular, for these and for other reasons (stated more 
fully at the beginning of chaptei xni ), I have dealt m the 
briefest possible way with the immense mass of obseivations 

Preface vii 

which modern astronomy has accumulated , it would, for 
example, have been easy to have filled one or more volumes 
with an account of observations of sun-spots made during 
the last half-century, and of theories based on them, but 
I have in fact only given a page or two to the subject 

I have given short biographical sketches of leading astio- 
nomers (other than living ones), whenever the material 
existed, and have attempted m this way to make their 
personalities and surroundings tolerably vivid , but I 
have tried to lesist the temptation of filling up space 
with merely picturesque details having no real bearing on 
scientific progress The trial of Keplei's mother for witch- 
craft is piobably quite as interesting as that of Galilei 
before the Inquisition, but I have entirely omitted the first 
and given a good deal of space to the second, because, 
while the former appealed to be chiefly of curious interest, 
the latter appeared to me to be not merely a striking inci- 
dent in the life of a great astionomei, but a part of the 
history of astronomical thought I have also inserted a 
large number of dates, as they occupy veiy little space, and 
may be found useful by some readers, while they can be 
ignoied with great case by others 9 to facilitate rcfeience 
the dates of birth and death (when known) of every 
astronomer of note mentioned in the book (othei than 
living ones) have been put into the Index of Names. 

I have not scrupled to give a good deal of space to 
dcsciiptions of such obsolete theories as appealed to me to 
foim an integral pait of astronomical piogiess One of the 
icasons why the history of a science is woith studying is 
that it sheds light on the processes whereby a scientific 
theory is formed m ordei to account for certain facts, 
and then undergoes successive modifications as new facts 
aie gradually In ought to beat on it, and is perhaps 
finally abandoned when its disci epancies with facts can 

vin Preface 

no longer be explained or concealed For example, no 
modern astronomei as such need be concerned with 
the Gieek scheme of epicycles, but the history of its 
invention, of its giadual peifection as fresh obseivations 
were obtained, of its subsequent failure to stand moie 
stringent tests, and of its final abandonment in favour of 
a moie satisfactory theory, is, I think, a valuable and 
interesting object-lesson in scientific method I have at 
any late written this book with that conviction, and have 
decided veiy laigely fiom that point of view what to omit 
and what to include 

The book makes no claim to be an original contribution 
to the subject , it is written largely from second-hand 
souices, of which, however, many are not veiy accessible to 
the general reader. Particulars of the authonties which 
have been used are given in an appendix 

It lemams gratefully to acknowledge the help that I have 
received in my work Mr W W Rouse Ball, Tutoi of 
Tiimty College, whose gieat knowledge of the history of 
mathematics a subject very closely connected with astro- 
nomy has made his criticisms of special value, has been 
kind enough to read the proofs, and has theieby saved me 
from several eriors, he has also given me valuable mfoi- 
mation with legaid to portraits of astionomers Miss H 
M Johnson has undei taken the laborious and tedious task 
of leading the whole book in manuscript as well as in 
proof, and of verifying the cioss-iefercnccs Miss F 
HardCtistle, of Girton College, has also read the proofs, 
and verified most of the numerical calculations, as well as 
the ci oss-references To both I am indebted for the 
detection of a large number of obscurities in expression, 
as well as of clerical and othei eirois and of mispnnts 
Miss Johnson has also saved me much time by making the 
Index of Names, and Miss Haidcastle has rendered me 



a fuither service of gieat value by drawing a consider- 
able number of the diagrams I am also indebted to 
Mi C E Inghs, of this College, for fig 81 , and I have 
to thank Mi W H Wesley, of the Royal Astronomical 
Society, foi vanous references to the literature of the 
subject, and in particular for help in obtaining access to 
vanous illustrations 

I am further indebted to the following bodies and 
individual astionomers for permission to reproduce photo- 
graphs and diawmgs, and in some cases also for the gift 
of copies of the originals the Council of the Royal Society, 
the Council of the RoyaL Astionomical Society, the Director 
of the Lick Observatory, the Dnector of the Institute 
Geogiaphico-Mihtaie of Florence, Professoi Barnard, 
Major Darwin, Di Gill, M Janssen, M Loewy, Mr E 
W Maunder, Mr H Pain, Piofessoi E C Pickenng, 
Dr Schuster, Di Max Wolf 








ASTRONOMY, $ 1-18 
I Scope of astronomy 

2-5 Fust notions the motion of the sun the motion 
and phases oi the moon daily motion of the 



4j 6 Pi ogress due to early civilised peoples Egyptians, 

Chinese, Indians, and Chaldaeans 3 

<j 7 The celestial bphc? e its scientific value apparent dis- 
tance between the stars the measurement of 
angles 4 

^ 8-9 The rotation of the celestial sphue the North and 
South poles the daily motion the celestial 
equator cwcttmpolar stars 7 

10-11 The annual motion oi the sun great circles 
the ecliptic and its obliquity the equinoxes and 
equinoctial points the solstices and solstitial 
points % 

^ 12-13 Ihc constellations the oodiat, signs of the aotftac, 
and zodiacal constellations the first point oj 
Aries (T), and ihcjtrst point of Libra (=:) 12 

4j 14 The five planet* dvcct and rcbogtade motions 

stationary points H 

15 The Older of neatness of the planets ocu4tation* 

s it pci tor and inferior planets J 5 


16 Measurement of time the day and its division into 

hours the lunar month the year the week 17 

17 Eclipses, fhesaros 1 9 

18 The rise of Astrology 20 



400 AD), 19-54 21 -7S 

$. 19-20 Astronomy up to the time of Aristotle, The 
Greek calendar full and empty months 
the octaetens Meton's cycle . . 21 

21. The Roman calendar introduction of the 

Julian Calendar 22 

22 The Gregorian Calendar 23 

$ 23 Early Greek speculative astronomy Thales 

and Pythagoras the spherical form of the 
earth the celestial spheres the music of 
the spheres . . 24 

^ 24 Phtlolaus and other Pythagoreans : early be- 

lievers in the motion of the earth Atist- 
archus and Seleucus 25 

{j 25 Plato uniform circulai and spherical motions 26 

<Sj 26 Eudo\MS lepresentation of the celestial 

motions by combinations of spheres de- 
scription of the constellations Calhppus 27 

^ 27-30 Aristotle his spheres the phases ot the rnoon 
proofs that the earth is spherical his 
arguments against the motion of the eaith 
relative distances of the celestial bodies 
other speculations estimate oi his astio- 
nomical work 29 

31-2 The early Alexandrine school : its rise Arist- 
archus his estimates of the distances of the 
sun and moon Observations by Timochani* 
and Anstyllns . 34 

33-4 Development of sphcucs the Phenomena of 
Euclid the horizon, the senzth, poles of a 
great circle, verticals, declination cuclcs, the 
meridian, celestial latitude and longitude^ 
t ight ascension and decimation Sun-dials 36 

Contents xui 


35 The division of the surface of the eailh into 

zones 37 

36 Eratosthenes his measurement of the earth 

and of the obliquity of the ecliptic . 39 

^ 37 HipparchUi : his life and chief contributions to 
astronomy Apollomuds representation of 
the celestial motions by means of cucles 
General account of the theory of eccentncs 
and epicycles . . 4 

^ 38-9 Hipparchus's repiesentation of the motion of 
the sun, by means of an eccentric apogee,, 
pengee, line of apses, etcentncity equation of 
the centre the epicycle and the defeient 41 

<j 40 Theory of the rnoon lunation or synodic month 

and sidereal month motion of the moon's 
nodes arid apses dtcuomttc month and 
anomalistic month 47 

(j 41 Observations of planets eclipse method of con- 

necting the distances of the sun and moon 
estimate of their distances . . 49 

^42 His star catalogue Discovery of the precession 

of the eyiimo&cs ' the tropical year and the 
sidcicalycat . . 5 1 

43 Eclipses oi the sun and moon conjunction 

and opposition* partial, total, and annular 
eclipses parallax . 5& 

^.44 Delambre's estimate of I hppai thus 61 

^ 45 The slow progress ol astronomy alter the time of Hip- 
parchub PFm^s proof that the cat th ib round 
new ineasmemuits oi the caith by Posidontus 61 
^ 46 Ptolemy The Ahnagest and the Oplics> theory of 

tcft action 62 

ij 47 Account oi the Almagest * Ptolemy's postulates 

arguments against the- motion of the caith 63 
^ 48 The theory of the moon ejection and /06WS2!sS 65 

^49 "J he attoolabc Parallax, and distances of the 

sun and moon , 67 

^ 50 The stai catalogue: piccession - 68 

^ 51 Theory of the planets the cquant 69 

^ 52, Estimate of Ptolemy . 73 

53 Ihe doc*iy of ancient astiouomy Thcon and llypatta 73 
54 Summary and estimate of Greek astiononry 74 

xiv Contents 




I$00 AD), 55-69 . . . 76-91 

^ 55 The slow development of astronomy duimg this 

period . 76 

$> 56 The East, The formation of an astiononncal school 
at the court of the Caliphs icvival of 
astrology translations from the Greek by 
Honnn ben Ishak, Ishak ben Honcin, Tabit 
ben Korra, and others 76 

{? 57~8 The Bagdad observatory Measurement of the 
earth Corrections of the ash onomical data 
of the Greeks trepidahon 78 

59 Albategnms discovery of the motion of the 

sun's apogee 79 

ij 60 Abul Wafa supposed discovery of the variation 

of the moon Ibn Yunos the Hakcmtte 
Tables , 70, 

6 1 Development of astronomy in the Mahometan 

dominions in Morocco and Spam * Ai sachet 
the Toletan Tables So 

^ 62 Nasstr Eddm and his school Ilkhamc Tablet* 

more accurate value of precession 81 

<vj 63 Taitai astronomy Ulugh Begh his stai cata- 

logue . 82 

ij 64 Estimate of oriental astronomy of this peiiod 

Arabic numerals survivals of Aiabic names 
of stars and astronomical terms nadit 82 

65 The West General stagnation after the fall of the 
Roman Empiie Bede Revival of learning 
at the court of Chailemagne Alcum 83 

66 Influence of Mahometan learning' Gerbcrti 

translations from the Arabic Plato ofTivoli^ 
Athelard of Bath, Gheravdo of Cremona 
Alfonso X and his school . the Alfonsine 
Tables and the Ltbios del Saber 84 

67 The schoolmen of the thirteenth century, 

Albertus Magnus, Cecco d'Ascoh, Roger 
Bacon Sacrobosco's Sphaera Mundi 85 

Contents xv 


68 Purbach and Regiomontanus influence of the 

original Greek authors the Nurnbei g school 
Walther employment of printing conflict 
between the views of Aristotle and of 
Ptolemy the celestial spheres of the Middle 
Ages the firmament &nd theprimum mobile 86 

69 Ltonardo da Vinci earthshme Fracastor and 

Apian observations of comets Nonius 
FernePs measurement of the earth 90 


COPPERNICUS (FROM 1473 AD TO 1543 A D ), 7O-Q2 Q2-I24 

70 Ihe Revival of Learning 92 

71-4 Lite of Coppermcus growth of his ideas publi- 
cation of the Comnientanolus Rheticus and the 
Pnma Narmho publication of the De Revo- 
lutiombus . . 93 

^ 75 The ccntial idea in the work of Coppernicus 

relation to earhei writers . 99 

^ 76-9 Ihc De Hevolutionibus The first book the 
postulates the principle of relative motion, 
with applications to the apparent annual 
motion of the sun, and to the daily motion 
of the celestial sphcie 100 

80 Ihc two motions of the earth answers to 

objections 105 

^ 8 1 The motion of the planets 106 

<j 82 The seasons . 108 

^. 83 Fnd of fiist book The second book decrease 

m the obliquity ot the ecliptic the star 
catalogue no 

^ 84 The thn d hook piecession no 

ij 85 Tht third book the annual motion of the earth 

aphelion and penhdion The fourth book 
theoiy oi the moon distances of the sun 
and moon eclipses . in 

^ 86-7. Ihc fifth and $>t.\t!) books theory of the planets 

synodic and &ide>cal pet-tod^ 112 

88 Jtocplimation of the btationaiy points 118 



89~9 Detailed theory of the planets detects of the 

theory . 12 1 

91 Coppernicus's use of epicycles . 122 

92 A difficulty in his system 123 


TO ABOUT 1601 AD), 93-112 . 125-144 

^ 93~4 The first reception of the De Rcvolutiombus 

Reinhold the Prussian Tables . 125 

$ 95 Coppermcanism m England Field, Recorde, Digger 127 
96 Difficulties in the Coppernican system the need foi 

progress m dynamics and for fresh observations 127 
97~3 The Cassel Observatory the Landgrave Wtlhani 
IV ', Rothmann } and Biugt' the stai catalogue 
Burgi's invention of the pendulum clock 128 

99 Tyeho Brahe his early life 130 

100 The new star of 1572 travels in Germany 131 

101-2 His establishment in Hveen Uraniborg and 

Stjerneborg life and work in Hveen 132 

103 The comet of 1577, and otheis . 135 

104 Books on the new star and on the comet of 1577 136 

105 Tycho's system of the world quarrel with 

Reyrn&sBai 136 

106 Last years at Hveen breach with the King 138 

107 Publication of the Astrononuac lustaitratac 

Mechamca and of the star catalogue in- 
vitation from the Emperor . 139 
108 Life at Benatek co-opeiation of ICeplei death 140 
$109 Pate of Tycho's instruments and obseivations 141 
^ no Estimate of Tycho's work the accuracy ot his 
observations, improvements in the ait of 
observing . 141 
ill Improved values of astronomical constants 
Theory of the moon the variation and the 
annual equation 143 
^ H2 The star catalogue rejection of tiepidation 

unfinished work on the planets , 144 

Contents XV11 

GALILEI (FROM 1564 A D TO 1642 A D ), 113-134 145-178 

113 Early life 

04 The pendulum ^ 

^115 Diversion from medicine to mathematics his first 

book ^ g 

"6 Professorship at Pisa experiments on falling 
bodies protests against the principle of 
authority M7 

^ 117 Professorship at Padua adoption of Coppcimcan 

views I4 g 

118 The telescopic discoveries. Invention of the tele- 
scope by Ltppershenn its application to 
astronomy by Harriot, Simon Manns, and 
Galilei I4 Q 

119 The Sidcic%ts Nunaus observations of the moon 150 

9 120 New stars resolution of poitions of the Milkv 

Way IS1 

? 121 The discovery of Jupiter's satellites then im- 

portance for the Coppernican controversy 
controversies j,-j 

122 Appointment at the Tuscan court 153 

^ 123 Observations of Saturn Discovery of the 

phases of Venus l ^ 

^ 124 Obseivations of sun-spots by Fabncius, Kimot, 

Schemer, and Galilei the Macchtc Solan 
pi oof that the spots wci e not planets obsei - 
vations of the umbra Mid penumbra 1 54 

S^ 125 Quarrel with Schemei and the Jesuits theological 
controversies Letter to the Grand Dnt,ha>s 

S S 126 Visit to Rome The Hrst condemnation pi ohibition 

of Coppei mean books ! qo 

127 Method foi finding longitude Contiovcisy on 

comets HSaggtatote , .160 

<j 128 Dialogue on the Two Chief Systems of the World 

Its preparation and publication 162 

129 The speakers aigmnent for the Coppcimcan 

system based on the telescopic discoveries 
discussion of stellar pal atlax the differential 
method of parallax . ^ 

xvin Contents 


^ 130 Dynamical arguments in favour of the motion of 

the earth the First Law of 'Motion The tides 165 

131 The trial and condemnation The thinly veiled 
Coppernicamsm of the Dialogue the re- 
markable preface l68 

132 Summons to Rome trial by the Inquisition 

condemnation, abjuration, and punishment 
prohibition of the Dialogue 169 

133 Last years life at Aicetn hbration of the moon 
the Two New Sciences uniform acceleration, and 
the first law of motion Blindness and death i7 3 

134 Estimate of Galilei's work his scientific method 176 


KEPLER (FROM 1571 AD TO 1630 AD), iSB-^ 1 i79- I 97 
135 Early life and theological studies 179 

136 Lectureship on mathematics at GiaU astronomical 
studies and speculations the Mystet mm Cosmo- 
graphicum I 

137 Religious troubles in Styn a woi k with Tycho 181 

<j 138 Appointment by the Emperoi Rudolph as successor 
to Tycho writings on the new star of 1604 and 
on Optics theory of refraction and a new form 
of telescope ^ 2 

139 Study of the motion of Mars unsuccessful attempts 

to explain it r ^3 

140-1 The ellipse discovery of the first two of Keplrfs 
Laws for the case of Mars the Commentaries 
on Mars l8 4 

^ 142 Suggested extension of Keplei's Laws to the othci 

planets l86 

& id^ Abdication and death of Rudolph appointment at 

Linz , ' 8S 

144 The Harmony of the World disco veiy of Kepler'* 

Third Law the " music of the sphucs " 188 

145 Epitome of the Copermcan Astronomy its pio- 
hibition fanciful conection of the distance of 
the sun obseivation of the sun's corona 191 

146 Treatise on Comets *93 

147 Religious troubles at Lmz * removal to Ulm 194 

Contents xix 


$ 148 The Rudolphinc Tables . I 94 

^ 149 Work under Wallenstem death 195 

^ 150 Minor discoveries speculations on gravity . . 195 

151 Estimate of Kepler's work and intellectual character 197 



ABOUT 1687 AD), 152-163 . 198-209 

152- The general character of astronomical progress 

duung the period . ^8 

^ I53 Schemer's obsei vations oifaculac on the sun Hewl 
his Selenography and his wntmgs on comets 
his star catalogue Riccioh 's New Almagest 198 

154 Planetary observations * Huygens's discovery of a 

satellite of Saturn and of its ring . 109 

155 Gascotgne's and Auzout's invention of the micro- 
meter Picatd's telescopic "sights " . 202 

156 Hoirocks extension of Kepler's theoiy to the 

moon observation of a tiansit of Venus 202 

^ I57~8 Huygens's icdiscovery of the pendulum clock 

his theory of circular motion 203 

ij 159 Measurements ol the earth by Snell, Norwood, and 

Picai d 204 

i? 1 60 The Pans Observatory Domcnico Cassiw his 
discoveries ol lour new satellites of Satuin his 
other woik . 204 

ij 161 Ridier* s expedition to Cayenne pendulum observa- 
tions observations of Mais in opposition hori- 
zontal paratta v annual or Cellar pat allax 205 

<Jj 162 Roancr and the velocity ol light , 208 

^ 163 Descartes . , t 208 



% 164-195 . , . 210-246 

^ 164 Division oi Nnvton's life into thice penocls , . 210 

i? 165, Eaily hfc, 1643 to 1665 210 

^ 166 Great i)io(luctivc pciiocl, 1665-87 211 



167 Chief divisions of his work astronomy, optics, pure 

mathematics . 
168 Optical discoveries the reflecting telescopes of 

Gregory and Newton the spectrum - 211 

& 169 Newton's description of his discoveries in 1665-6 212 
170 The beginning of his work on gravitation the 
falling apple previous contributions to the 
subject by Kepler, Borelli, and Huygens 213 

4> 171 The problem of circular motion acceleration ^ 214 

4> 172 The law of the mvet se square obtained from Kepler s 
Third Law for the planetary orbits, treated as 
circles * 

fc 173 Extension of the earth's gravity as far as the moon : 

imperfection of the theory 2I 7 

174 HooMs and Wren's speculations on the planetary 
motions and on gravity Newton's second calcu- 
lation of the motion of the moon agreement 
with obseivation 221 

175-6 Solution of the problem of elliptic motion 

Halley's visit to Newton 221 

177 Presentation to the Royal Society of the tract DC 

Motu publication of the Pnncipta 222 

178 The Prmcipaa its divisions 22 3 

179-80 The Laws of Motion the First Law acceleia- 
tion in its general form mab& and force 
the Third Law 22 3 

181 Law of universal gravitation enunciated . 227 

^182 The attraction of a sphere - 22 

^ 183 The general problem of accounting for the 

motions of the solai system by means of 
gravitation and the Laws of Motion 
pertM battons 22 9 

^ 184 Newton's lunar theoiy 2 3 

^ 185 Measurement of the mass of a planet by means 

of its attraction of its satellites . .231 

186 Motion of the sun cento e oj gtavity ot the bolai 

system * iclativity of motion 2 3 1 

^ 187 Thenon-&phencalformofthccaith,andof Jupitci 233 

188 Explanation oi pi ccession . * 2 34 

<t 189 The tides the mass of the moon deduced horn 

tidal observations 2 35 

4j 190 The motion b of comets * parabolic oibits . . 237 

Contents xxi 


191 Reception of the Pnncipia 239 

^ 192 Third period of Newton's life, 1687-1727 Pailia- 
mentary career impiovement of the lunar 
theory appointments at the Mint and removal 
to London publication of the Optics and of the 
second and third editions of the Pnncipia } edited 
by Cotes and Pemberton death 240 

^ 193 Estimates of Newton's workby Leibniz, by Lagrange, 

and by himself 241 

^194 Comparison of his astronomical work with that of 
his piedeccssors "explanation" and "de- 
scription " conception of the material univeise 
as made up of bodies attracting one another 
according to certain laws 242 

4J 195 Newton's scientific method " Hypotheses non jingo " 245 



CENTURY, 196-227 . 247-286 

^196 Gi avitational asttonoiny its development due 
almost entirely to Continental astronomers use 

of analysis , English observational astronomy 247 
^ 197-8 Flam^teed foundation of the Gicenwicli Ob- 

seivatoiy his star catalogue 249 

^199 Halley catalogue of Southein stais 253 

$ 200 Halley's comet 253 

^ 201 Scculai acceleration of the moon's mean motion 254 

ij 202 Tiansits of Venus . 254 

ij 203 P)opn motions of the fixed stats 255 
4J 204-5 Lunar and planetaiy tables caicei at Gieen- 

wich minoi woik , 255 

^ 206 Bradley caieei . 257 
^ 207-11 Discovwy and explanation of aberration the 

constant oj abei t alum 258 

$ 212 Failure to detect paiallax , 265 

^ 213-5 Discovery ol nutation MacJun 265 
^ 216-7 fables ot Jupitci's satclhtts by JJradley and by 
Watgcnttn determination o( longitudes, 

and othci woik 269 

ij 2|8 His obsci vations , eduction 271 

xxii Contents 


219 The density of the earth Maskelyne the Cavendish 

experiment 2 73 

^ 220 The Cassim-Mamldi school in France 275 

^ 221 Measurements of the earth ; the Lapland and 

Peruvian arcs ; Maupertuis 275 

^ 222-4 Lacazlle , his careei expedition to the Cape 

star catalogues, and other work 279 

225-6 Tobias Mayer , his observations lunar tables : 

the longitude prize 282 

227 The transits of Venus in 1761 and 1769 distance 

of the sun . , 284 



228-250 , 287-322 

228 Newton's problem the problem of three bodies 
methods of approximation lunar theory and 
planetary theory 287 

229 The progress of Newtonian principles in France 
popularisation by Voltaire The five great 
mathematical astronomers the pre-eminence of 
France 290 

230 Eider his caieer St Peteisburg and Berlin 

extent of his writings 291 

231 Clairaut figuie of the earth rettun of Halley's 

comet 293 

232 UAlembert his dynamics - precession and nuta- 
tion his versatility nvalry with Clairaut 295 

2 33-4 The lunai theoiies and lunar tables of Euler, 
Clairaut, and D'Alembcrt , advance on Newton's 
lunar theory 297 

^ 235 Planetary theory ; Clairaut's deteimination of the 

masses of the rnoon and of Venus : Lalande 299 

236 Eulei's planctaiy theory r method ot the variation 

of elements or parameter s . S^ 1 

237 Lagtange his career Berlin and Pans the 

Metamque Analytique . 34 

238 Laplace his caieer the Mccamque Celeste and the 
Systeme du Monde , political appointments and 
Distinctions , f , , 306 

xxiv Contents 


brightness as a test of nearness measurement 
of brightness " space-penetrating " power of a 
telescope 33 2 

259 Nebulae and star dusters Herschel's great cata- 
logues 33 6 

260 Relation of nebulae to star clusters the "island 
universe " theory of nebulae the " shining fluid " 
theory distribution of nebulae 337 

261 Condensation of nebulae into clusters and stars 339 

262 The irresolvabihty of the Milky Way 340 

263 Double stars their proposed employment for find- 
ing parallax catalogues probable connection 
between members of a pair 341 

264 Discoveries of the revolution of double stars 

binary stats their uselessness for parallax 343 

^ 265 The motion of the sun in space the various 

positions suggested for the apex 344 

266 Variable stars Mtta and Algol catalogues of 
comparative brightness method of sequences 
variability of a Hercuhs 346 

267 Herschel's work on the solar system new satellites 

observations of Saturn, Jupiter, Venus, and Mars 348 

268. Observations of the sun Wilson theory of the 

structure of the sun 35 

269 Suggested variability of the sun 351 

270. Other researches 35 2 

^271 Comparison of Heischel with his contemporaries 

Schtoeter 35 2 


THE NINETEENTH CENTURY, 272-320 354-409 

272 The three chief divisions of astionomy, observa- 
tional, gravitational, and descriptive 354 
ij 273 The gicat growth of descnptive astronomy in the 

nineteenth century . 355 

274 Observational Astronomy Instrumental advances 

the introduction of photography 357 

^ 275 The method oi least squat cs Lcgemhc and Gan^ 357 

^276 Olhei work by Gauss the Theorm Motits le- 

discoveiy of the minor planet Ccics 358 

Contents xxv 


277 Bessel his improvement in methods of re- 

duction his table of refraction the Funda- 
menta Nova and Tabulae Regiowontanae 359 
278 The parallax of 6 1 Cygnt its distance 360 

279 Henderson's parallax of a Centaun and Struve's 

of Vega later parallax determinations 362 

4j 280 Star catalogues the photographic chart 362 

281-4 The distance of the sun transits of Venus 
observations of Mars and of the minor planets 
in opposition diwnal method gravitational 
methods, lunar and planetary methods 
based on the velocity of light summary of 
results 363 

ij 285 Variation in latitude rigidity of the earth 367 

^ 286 Gravitational Astronomy Lunar theory Damoi- 
seau 9 Potssou t Ponte'coulant, Lubbock, Hansen, 
Delaunqy, Professor Newcowb, Adams, Dr 
Hill . 367 

287 Secular acceleration of the moon's mean motion 

Adams's collection of Laplace Delaunay's 
explanation by means of tidal friction 369 

^.288 Planetary theoiy Lcvcrnct, Gylden, M Poincare 370 

289 The discovery of Neptune by Leverner and Dr 

Gallc Adams's woik 371 

290 Lunar and planetary tables outstanding dis- 

ci epancies between theory and observation 372 

<ij 291 Cometaiy orbits return of Halley's comet in 

1835 Enckc's and other periodic comets 372 

292 Theory of tides analysis of tidal observations 

by Lubbock, Wlicwell^ Lord Kelvin, and 
Professor Darwin bodily tides in the eaith 
and its ugidily 373 

293 Ihc stability oi the solar system 374 

^ 294 Descriptive Astronomy, Disco veiy of the minor 
planctb 01 asteroids their number, dis- 
tribution, and size 376 

{j 295 Di&coveiics of satellites ot Neptune, Satuin, 

Uianus, Mais, and "fupitei, and of the a ape 
t tug ol Saturn , 3^ 

^. 296 Ihc huifticc of the moon nils the hmai atmo- 

sphcie , , t 3&2 

i Contents 


297 The surfaces of Mars, Jupiter, and Saturn the 

canals on Mars Maxwell's theoiy of Saturn's 
rings the rotation of Mercury and of Venus 383 

298 The surface of the sun Schwabs' s discovery of 

the periodicity of sun-spots connection be- 
tween sun-spots and terrestrial magnetism 
Cairingtoris observations of the motion and 
distnb ntion of spots Wilson's theory of spots 385 

^ 299-300 Spectrum analysts Newton, Wollaston, Fraun- 

hofer, Knchhoff the chemistry of the sun 386 

^301 Eclipses of the sun the corona, chromosphere, 

and fit eminences spectroscopic methods of 
observation 3^9 

^302 Spectioscopic method of determining motion to 

or from the observer Doppler's principle 
application to the sun 39 * 

^ 303 The constitution of the sun 39 2 

^ 304-5 Observations of comets : nucleus theory of the 
formation of then tails their spectra re- 
lation between comets and meteors 393 

^ 306-8 Sidereal astronomy career of John Herschcl his 
catalogues of nebulae and of double stars 
the expedition to the Cape measurement of 
the sun's heat by Herschel and by PowUet 396 

^309 Double stars observations by Stiuve and 

others orbits of binary stais 39$ 

310 Lord Rossc\ telescopes, his observations of 

nebulae revival of the "island univeise" 
theory 4 

ij 311 Application of the spectroscope to nebulae 

distinction between nebulae and clusters 401 
312 Spectroscopic classification of stars by Sccchi 

chemistiy of stars stais with bright-line 
spectra . 4 O1 

3I3-4- Motion of stars m the line of sight Discovery 
of binary stais by the spectroscope eclipse 
theory of variable stais 4 2 

^315 Observations of variable stais 43 

316 Stellai photometry Pogsoris light ratio the 

Oxfoi d, Harvard, and Potsdam photometries 403 

317 Structure of the sidereal system relations of 

stars and nebulae , 4") 

Contents XXVH 


318-20 Laplace's nebular hypothesis in the light of 
later discoveries the sun's heat Helmholtz's 
shrinkage theoiy Influence of tidal friction on 
the development of the solar system Professor 
Darwin's theory of the birth of the moon 
Summary 406 






The moon Frontispiece 

1 The celestial sphere 5 

2 The daily paths of circumpolai stars To face p 8 

3 The circles of the celestial spheie 9 

4 The equator and the ecliptic 1 1 

5 1 he Gi eat Bear . To face p 12 

6 The apparent path of Jupitei 16 

7 The apparent path of Mercury 17 
8- 1 1 The phases of the moon 30, 31 

12 The curvature of the eai th . . 32 

13 The method of Austarchus for comparing the distances of 

the sun and moon 34 

14 The cquatoi and the ecliptic 36 

15 The cquatoi, the hoiizon, and the meridian 38 

1 6 Flic meafauicmont ot the earth 39 

17 The ucccntiic ... 44 

1 8 I he position of the sun's apogee 45 

19 The epicycle and the dcfcient . 47 

20 1 he eclipse method ot connecting the di&tanccb ot the sun 

and moon .... 30 

21 The mucase of the longitude oi a stai ,. 52 

22 flic movement oi the oquatoi 53 
23, 24. Hu pieeossion oi the equinoxes , 53, 54 

25 1 ho oai th's shadow , . 57 

26 The ecliptic and the moon's path 57 

27 riio sun aud moon .. 58 

28 Put U ill eclipse oi UK moon ,. 58 

29 Fotal i chpst" oi the moon . 58 

30 Aunulfu eclipse oi tlu sun , , "59 

31 Paiallax *,, , 60 

32 Rcii action by the atmosphcic , 63 


xxx List of Illustrations 


33 Parallax . 68 

34 Jupiter's epicycle and deferent , 7 

35 The equant 71 

36 The celestial spheres - , , 89 

37 Relative motion . 102 

38 The relative motion of the sun and moon . 103 

39 The daily rotation of the earth 104 

40 The solar system according to Coppernicus 107 
41, 42 Coppernican explanation of the seasons 108, 109 

43 The orbits of Venus and of the earth 113 

44 The synodic and sidereal periods of Venus 114 

45 The epicycle of Jupiter .. 116 

46 The relative sizes of the orbits of the earth and of a supenoi 

planet . "7 

47 The stationary points of Mercury .. . 119 

48 The stationary points of Jupiter 1 20 

49 The alteration in a planet's apparent position due to an 

alteration m the earth's distance from the sun 122 

50 Stellar parallax . .124 

51 Uramborg . ., 133 

52 Tycho's system of the world 137 

53 One of Galilei's drawings of the moon 150 

54 Jupiter and its satellites as seen on January 7, 1610 152 

55 Sun-spots To face p 154 

56 Galilei's proof that sun-spots are not planets 156 

57 The differential method of parallax 165 
PORTRAIT OF GALILEI .. To face p, 171 

58 The daily libiation of the moon .. 173 
PORTRAIT OF KEPLER . To face p. 183 

59 An ellipse 185 

60 Kepler's second law . 1 86 

6 1 Diagram used by Kepler to establish his laws of planetary 

motion . .. 187 

62 The " music of the spheres " according to Kepler 190 

63 Kepler's idea of gravity . 196 

64 Saturn s ring, as diawn by Huygens To face p 200 

65 Saturn, with the ring seen edge-wise 200 

66 The phases of Saturn's ring 201 

67 Eaily drawings of Saturn To face p 202 

68 Mais in opposition 206 

List of Illustrations xxxi 


69 The parallax of a planet 206 

70 Motion m a circle 214 

71 The moon as a projectile 220 

72 The spheroidal form of the earth 234 

73 An elongated ellipse and a parabola 238 
PORTRAIT OF NEWTON . . To face p 240 

74, 75 The aberration of light 262, 263 

76 The aberrational ellipse 264 

77 Precession and nutation 268 

78 The varying curvature of the earth 277 

79 Tobias Mayer's map of the moon To face p 282 

80 The path of Halley's comet 294 

8 1 A varying ellipse 33 

82 Herschel's forty-foot telescope 3 2 9 

83 Section of the sidereal system 333 

84 Illustrating the effect of the sun's motion m space 345 

85 6 1 Cygm and the two neighbouring stars used by Bessd 360 

86 The parallax of 6 1 Cygm . 3 6t 

87 The path of Halley's comet 373 

88 Photographic trail of a mmoi planet To face p 377 

89 Paths of minor planets 37^ 

90 Comparative sizes of three minor planets and the moon 379 

91 Saturn and its system 3% 

92 Mars and its satellites 3& 1 

93 Jupiter and its satellites . 3^ 2 

94 The Apennines and the adjoining regions) To /ace p 383 

of the moon / 

95 Saturn and its rings . 384 

96 A group of sun-spots , 3^5 

97 Fraunhofer's map ot the solar spectrum 387 

98 The total solar eclipse of 1886 . 390 

99 The great comet of 1882 393 

100 The nebula about 17 Argus . ,, 397 

10 1 The orbit of Ursae 399 

102 Spual nebulae To face p. 400 

103 The spectrum of ]8 Aungae ,, 403 

104 The Milky Way near the cluster m Pei sens 405 




"The nevcr-weancd Sun, the Moon exactly round, 
And all those Stars with which the brows of ample heaven aie 


Orion, all the Pleiades, and those seven Atlas got, 
The close beamed Hyades, the Bear, surnam'd the Chariot 
That turns about heaven's axle tree, holds ope a constant eye 
Upon Onon, and of all the cressets m the sky 
His golden foiehcad nevei bows to th' Ocean empery" 

The Iliad (Chapman's translation) 

i ASTRONOMY is the science which treats of the sun, the 
moon, the stais, and other objects such as comets which are 
seen m the sky It deals to some extent also with the earth, 
but only m so far as it has pioperties m common with the 
heavenly bodies In early times astronomy was concerned 
almost entirely with the observed motions of the heavenly 
bodies At a later stage astronomers were able to discover 
the distances and sizes of many of the heavenly bodies, 
and to weigh some of them , and more recently they have 
acquired a considerable amount of knowledge as to then 
nature and the material of which they arc made 

2 We know nothing of the beginnings of astronomy, 
and can only conjecture how certain of the simpler facts 
of the science particularly those with a direct influence on 
human life and comfortgradually became familiar to early 
mankind, very much as they are familiar to modern savages, 

2 A Short History of Astronomy [CH I 

With these facts it is convenient to begin, taking them in 
the order m which they most readily present themselves to 
any ordinary observer 

3 The sun is daily seen to rise in the eastern part of 
the sky, to travel across the sky, to reach its highest position 
in the south in the middle of the day, then to sink, and 
finally to set in the western part of the sky But its daily 
path across the sky is not always the same the points of 
the horizon at which it rises and sets, its height in the sky 
at midday, and the time from sunrise to sunset, all go 
through a series of changes, which are accompanied by 
changes in the weather, in vegetation, etc , and we aie 
thus able to recognise the existence of the seasons, and 
their recurrence after a ceitam interval of time which is 
known as a year 

4 But while the sun always appears as a bright circulai 
disc, the next most conspicuous of the heavenly bodies, the 
moon, undergoes changes of form which readily strike the 
observei, and are at once seen to take place in a regular ordei 
and at about the same intervals of time A little more caie, 
however, is necessary in order to observe the connection 
between the form of the moon and her position m the sky 
with respect to the sun Thus when the moon is first 
visible soon after sunset near the place where the sun has set, 
her form is a thin crescent (cf. fig n on p 31), the hollow 
side being turned away from the sun, and she sets soon 
after the sun Next night the moon is farther from the 
sun, the descent is thicker, and she sets later, and so on, 
until after rather less than a week from the first appearance 
of the crescent, she appears as a semicircular disc, with 
the flat side turned away from the sun The semicircle 
enlarges, and after another week has giown into a complete 
disc , the moon is now nearly m the opposite direction to 
the sun, and theiefore rises about at sunset and sets about 
at sunnse. She then begins to appioach the sun on the 
other side, rising before it and setting m the daytime , 
hei size again diminishes, until after another week she is 
again semicircular, the flat side being still turned away 
fioni the sun, but being now turned towards the west 
instead of towards the east The semicucle then becomes 
a gradually diminishing crescent, and the time of rising 

$ 36] The Beginnings of Astronomy 3 

approaches the time of sunrise, until the moon becomes 
altogether invisible After two or thiee nights the new 
moon reappears, and the whole series of changes is repeated 
The different forms thus assumed by the moon are now 
known as her phases , the time occupied by this series of 
changes, the month, would natuially suggest itself as a con- 
venient measure of time , and the day, month, and year 
would thus form the basis of a rough system of time- 
measui ement 

5 From a few observations of the stars it could also 
clearly be seen that they too, like the sun and moon, 
changed their positions in the sky, those towards the east 
being seen to rise, and those towards the west to sink and 
finally set, while others moved acioss the sky from east to 
west, and those in a certain noithern part of the sky, though 
also in motion, were never seen either to rise or set. Although 
anything like a complete classification of the stars belongs 
to a more advanced stage of the subject, a few star groups 
could easily be lecogmsed, and their position in the sky 
could be used as a rough means of measuring time at night, 
just as the position of the sun to indicate the time of day, 

6 To these rudimentary notions important additions 
were made when rather more caieful and prolonged obser- 
vations became possible, and some little thought was 
devoted to their interpretation 

Several peoples who i cached a high stage of civilisation 
at an early period claim to have made impoitant pi ogress 
m astionomy Gieek traditions assign considerable astro- 
nomical knowledge to Egyptian priests who lived some 
thousands of years B c , and some of the peculiauties of 
the pyramids which were built at some such period aie at 
any late plausibly interpreted as evidence of pietty accurate 
astronomical observations, Chinese records describe observa- 
tions supposed to have been made in the 25th century B c., 
some of the Indian sacred books icfer to astronomical 
knowledge acquired several centimes before this time, and 
the first observations of the Chaldacan priests of Babylon 
have been attributed to times not much later 

On the other hand, the eaihest recorded astronomical 
observation the authenticity of which may be accepted 
without scruple belongs only to the 8th century B c. 

4 A Short History of Astronomy ecu I 

For the purposes of this book it is not woith while to 
make any attempt to disentangle from the mass of doubtful 
tradition and conjectural interpretation of inscriptions, bear- 
ing on this early astionomy, the few facts which lie embedded 
therein, and we may proceed at once to give some account 
of the astronomical knowledge, other than that aheady dealt 
with, which is discovered in the possession of the earliest 
really historical astronomers -the Greeks- at the beginning 
of their scientific history, leaving it an open question what 
portions of it were derived from Egyptians, Chaldaeans, their 
own ancestors, or other sources 

7. If an observer looks at the stars on any clear night 
he sees an appaiently innumerable * host of them, which 
seem to lie on a portion of a spherical surface, of which he 
is the centie This spherical surface is commonly spoken 
of as the sky, and is known to astionomy as the celestial 
sphere, The visible part of this sphere is bounded by the 
earth, so that only half can be seen at once , but only the 
slightest effort of the imagination is required to think of 
the other half as lying below the earth, and containing other 
stars, as well as the sun. This sphere appears to the 
observer to be very large, though he is incapable of forming 
any precise estimate of its size \ 

Most of us at the present day have been taught in child- 
hood that the stars are at different distances, and that this 
spheie has in consequence no real existence The early 
peoples had no knowledge of this, and for them the celestial 
spheie really existed, and was often thought to be a solid 
sphere of crystal 

Moreover modern astionomers, as well as ancient, find 
it convenient for very many purposes to make use of this 
sphere, though it has no material existence, as a means 
of repiesenting the directions in which the heavenly bodies 
are seen and their motions For all that direct observation 

* In our climate 2,000 is about the greatest number ever visible 
at once, even to a keen-sighted person 

t Owing to the greater brightness of the stais oveinead they 
usually seem a little nearer than those near the horizon, and con- 
sequently the visible poition of the celestial sphere appears to be 
lather less than a half of a complete sphere 1 his is, however, of no 
importance, and will for the futui e be ignored 


The Celestial Sphere 

can tell us about the position of such an object as a star 
is its direction, its distance can only be ascertained by 
indirect methods, if at all If we diaw a sphere, and 
suppose the observer's eye placed at its centre o (fig T), 
and then draw a straight line from o to a star s, meeting 
the surface of the sphere in the point s , then the star 
appears exactly in the same position as if it were at s, 
nor would its appaient position be changed if it were 
placed at any other point, such as s' or s", on this same 

FIG i The celestial sphcic 

line When we speak, therefoie, of a star as being at 
a point s on the celestial sphere, all that we mean is that 
it is in the same direction as the point ^, or, m othci 
words, that it is situated somewhere on the straight line 
through o and s The advantages of this method of rcpic- 
sentmg the position of a stai become evident when we wish 
to compaie the positions of scvoal stars The difference 
of direction of two stars is the angle between the lines 
drawn fiom the eye to the stars , eg., if the stars are R, s, it 
is the angle R o s Similarly the difference of direction of 

6 A Short History of Astronomy CCH I 

another pair of stars, p, Q, is the angle p o Q The two stars 
p and Q appear nearer together than do R and s, or farther 
apart, accoidmg as the angle P o Q is less or greater than 
the angle R o s But if we represent the stais by the 
corresponding points p, q, r, s on the celestial sphere, then 
(by an obvious property of the spheie) the angle P o Q 
(which is the same as p o q) is less or greater than the 
angle R o s (01 r o s) according as the arc joining p q 
on the sphere is less or greater than the arc joining r s, 
and in the same proportion ; if, foi example, the angle R o s 
is twice as great as the angle p o Q, so also is the arc p q 
twice as gieat as the arc rs We may therefore, m all 
questions relating only to the directions of the stars, leplace 
the angle between the directions of two stars by the aic 
joining the corresponding points on the celestial sphere, or, 
m other words, by the distance between these points on 
the celestial sphere But such arcs on a sphere are 
easier both to estimate by eye and to treat geometrically 
than angles, and the use of the celestial sphere is therefore 
of gieat value, apart from its historical origin It is im- 
portant to note that this apparent distance of two stais, 
i e their distance from one another on the celestial sphere, 
is an entirely dififeient thing from their actual distance from 
one another in space In the figuie, for example, Q is 
actually much nearer to s than it is to p, but the apparent 
distance measured by the arc q s is several times greater 
than qp The apparent distance of two points on the 
celestial sphere is measured numerically by the angle 
between the lines joining the eye to the two points, 
expressed in degrees, minutes, and seconds, 15 

We might of course agree to regaid the celestial sphere 
as of a particular size, and then express the distance be- 
tween two points on it m miles, feet, or inches , but it is 
practically very inconvenient to do so To say, as some 
people occasionally do, that the distance between two stars 
is so many feet is meaningless, unless the supposed sue of 
the celestial sphere is given at the same time 

It has already been pointed out that the obseiver is 
always at the centre of the celestial spheie , this remains 

* A light angle is divided into ninety dcgiecs (90), a degree into 
sixty minutes (60'), and a minute into sixty seconds (60") 

s] The Celestial Sphere its Poles 7 

true even if he moves to another place. A sphere has, 
however, only one centre, and theiefore if the sphere 
remains fixed the observer cannot move about and yet 
always remain at the centre. The old astronomers met 
this difficulty by supposing that the celestial sphere was so 
large that any possible motion of the observer would be 
insignificant in comparison with the radius of the sphere and 
could be neglected. It is often more convenient when 
we are using the sphere as a mere geometrical device for 
representing the position of the stars to regard the sphere 
as moving with the observer, so that he always remains at 
the centre 

8 Although the stars all appeal to move across the 
sky ( 5), and their rates of motion differ, yet the distance 
between any two stars remains unchanged, and they weie 
consequently regarded as being attached to the celestial 
sphere Moreover a little careful observation would have 
shown that the motions of the stars in different parts of the 
sky, though at first sight very different, weie just such 
as would have been produced by the celestial sphere with 
the stars attached to it turning about an axis passing 
through the centre and through a point in the northern 
sky close to the familiar pole-star. This point is called 
the pole. As, however, a straight line drawn through the 
centre of a sphere meets it m two points, the axis of 
the celestial sphere meets it again in a second point, 
opposite the fhst, lying in a part of the celestial sphere 
which is permanently below the horizon This second 
point is also called a pole., and if the two poles have to 
be distinguished, the one mentioned first is called the 
north pole, and the other the south pole, The direction 
of the rotation of the celestial sphere about its axis is 
such that stars near the noith pole are seen to move round 
it in circles in the direction opposite to that m which the 
hands of a clock move ; the motion is uniform, and a 
complete revolution is performed in four minutes less than 
twenty-four hours , so that the position of any stai m the 
sky at twelve o'clock to-night is the same as its position at 
four minutes to twelve to-moriow night. 

The moon, like the stars, shares this motion of the 
celestial sphere, and so also does the sun, though this 

S A Short History of Astronomy [Cn I 

is rnoie difficult to recognise owing to the fact that the sun 
and stais are not seen together 

As other motions of the celestial bodies have to be dealt 
with, the general motion just described may be conveniently 
refeired to as the daily motion or daily rotation of the 
celestial sphere 

9. A further study of the daily motion would lead to the 
recognition of certain important cucles of the celestial spheie. 

Each star describes in its daily motion a circle, the size 
of which depends on its distance from the poles Fig. 2 
shews the paths described by a number of stars near the 
pole, recorded photographically, during part of a night. 
The pole-star describes so small a cncle that its motion can 
only with difficulty be detected with the naked eye, stars a 
little farther off the pole describe largei circles, and so on, 
until we come to stars half-way between the two poles, which 
describe the largest circle which can be drawn on the 
celestial sphere The circle on which these stars he and 
which is described by any one of them daily is called the 
equator. By looking at a diagram such as fig 3, or, better 
still, by looking at an actual globe, it can easily be seen 
that half the equatoi (E Q w) lies above and half (the 
dotted part, w R E) below the horizon, and that m conse- 
quence a star, such as s, lying on the equator, is in its daily 
motion as long a time above the honzon as below If 
a star, such as s, lies on the noith side of the equator, i e 
on the side on which the noith pole p lies, more than half 
of its daily path lies above the horizon and less than half 
(as shewn by the dotted line) lies below, and if a star 
is near enough to the noith pole (more precisely, if it is 
neaiei to the north pole than the nearest point, K, of the 
horizon), as <r, it nevei sets, but lemains continually above 
the honzon. Such a star is called a (northern) circumpolar 
star. On the other hand, less than half of the daily path of 
a star on the south side of the equator, as s', is above the 
horizon, and a star, such as <r', the distance of which from 
the north pole is gi eater than the distance of the farthest 
point, n, of the horizon, or which is nearer than n to the 
south pole, remains continually below the horizon 

10. A slight familiarity with the stars is enough to shew 
any one that the same stars are not always visible at the 

1<IG 2 The paths oi cncumpolai stars, Chewing then move- 
ment during seven houis Fiom a. photogiaph by Mi 
II Pain "1 he thickest line is the path oi the pole stai 

[ / o fin c p 8 

$ 9. io] The Daily Motion of the Celestial Sphere 9 

same time of night Rather more caieful observation, 
carried out for a considerable time, is necessaiy m order 
to see that the aspect of the sky changes m a regular way 
from night to night, and that after the lapse of a yeai the 
same stais become again visible at the same time The 
explanation of these changes as clue to the motion of 
the sun on the celestial sphere is more difficult, and the 

FIG 3 The cncleb ot the celestial s>phcic 

unknown discoveiei of this fact certainly made one of 
the most impoitant steps m early astronomy 

If an observer notices soon after sunset a star somewheic 
in the west, and looks foi it again a few evenings latei at 
about the same time, he finds it lower down and nearer to 
the sun , a few evenings latei still it is invisible, while Us 
place has now been taken by some othei sUn which was at 
first farthei east in the sky This stai can in turn be 
observed to appioach the sun evening by evening Or if 
the stais visible after sunset low down m the east are 

I0 A Short History of Astronomy LCH i 

noticed a few days later, they are found to be higher up 
m the sky, and their place is taken by other stars at 
first too low down to be seen Such observations of 
stars rising or setting about sunrise or sunset shewed to 
early observers that the stais were giadually changing their 
position with respect to the sun, or that the sun was 
changing its position with respect to the stais 

The changes just described, coupled with the fact that 
the stars do not change their positions with respect to one 
another, shew that the stais as a whole perform then daily 
revolution rather more rapidly than the sun, and at such a 
rate that they gam on it one complete revolution in the 
course of the yeai. This can be expressed otherwise in 
the form that the stars aie all moving westwaid on the 
celestial sphere, relatively to the sun, so that stars on the 
east are continually approaching and those on the west 
continually receding from the sun. But, again, the same 
facts can be expressed with equal accuracy and greater 
simplicity if we regard the stars as fixed on the celestial 
sphere, and the sun as moving on it from west to east 
among them (that is, in the direction opposite to that of 
the daily motion), and at such a rate as to complete a 
circuit of the celestial sphere and to return to the same 
position aftei a year 

This annual motion of the sun is, howevei, readily seen 
not to be merely a motion from west to east, for if so the 
sun would always rise and set at the same points of the 
horizon, as a star does, and its midday height m the sky 
and the time from sunrise to sunset would always be the 
same We have already seen that if a star lies on the 
equator half of its daily path is above the horizon, if 
the star is north of the equator more than half, and if south 
of the equator less than half, and what is tiue of a star is true 
for the same reason of any body sharing the daily motion of 
the celestial sphere During the summei months theiefore 
(March to Septembei), when the day is longer than the night, 
and more than half of the sun's daily path is above the 
horizon, the sun must be noith of the cquatoi, and dmmg 
the winter months (September to Maich) the sun must be 
south of the equator The change in the sun's distance 
from the pole is also evident from the fact that m the winter 


The Annual Motion of the Sun 

months the sun is on the whole lower down in the sky than 
in summer, and that m particular its midday height is less 

ii The sun's path on the celestial sphere is theiefore 
oblique to the equator, lying partly on one side of it and 
partly on the other A good deal of caieful observation 
of the kind we have been describing must, however, have 
been necessary befoie it was ascertained that the sun's 
annual path on the celestial sphere (see fig 4) is a great 
circle (that is, a circle having its centre at the centre of 
the sphere) This great cncle is now called the ecliptic 
(because eclipses take place only when the moon is in 
or near it), and the angle at which it cuts the equator is 
called the obliquity of the ecliptic The Chinese claim to 
have measured the obliquity in noo B c , and to have found 
the remarkably accurate value 23 52' (cf chapter n , 35), 
The truth of this statement may reasonably be doubted, but 
on the other hand the statement of some late Greek writers 
that either Pythagoras or Anaximander (6th century B c ) was 
the first to discover the 
obliquity of the ecliptic is NORTH POLE 

almost ceitamly wrong It 
must have been known with 
reasonable accuiacy to both 
Chaldacans and Egyptians 
long befoie 

When the sun crosses the 
equator the day is equal to 
the night, and the times 
when this o ecu is are con- 
sequently known as the 
equinoxes, the vernal equi- 
nox occurring when the sun 
ciosses the equator from 
south to noith (about Mai eh 
2ist), and the autumnal 
equinox when it ciosses back (about September 23rd) 
The points on the celestial sphere where the sun crosses 
the eqiuitoi (A, c in fig 4), ic wheic ecliptic and equatoi 
cross one anothei, aic called the equinoctial points, 
occasionally also the equinoxes. 

After the vernal equinox the sun m its path along the 




4 The equatoi and the 

12 A Short History of Astronomy CCH 1 

ecliptic recedes from the equator towards the north, until it 
reaches, about thiee months afterwards, its greatest distance 
from the equator, and then approaches the equator again. 
The time when the sun is at its greatest distance from the 
equator on the north side is called the summer solstice, 
because then the northwaid motion of the sun is arrested 
and it temporarily appeals to stand still Similarly the sun 
is at its greatest distance from the equator towaids the 
south at the winter solstice The points on the ecliptic 
(B, D in fig 4) where the sun is at the solstices aic called 
the solstitial points, and are half-way between the equinoctial 

12 The earliest observers piobably noticed particular 
groups of stars remaikable for their form or for the presence 
of bright stars among them, and occupied their fancy by 
tracing resemblances between them and familial objects, etc 
We have thus at a very early period a rough attempt at 
dividing the stars into groups called constellations and at 
naming the latter 

In some cases the stars regarded as belonging to a con- 
stellation form a well-marked group on the sky, sufficiently 
separated from other stars to be conveniently classed 
together, although the resemblance which the group bears 
to the object after which it is named is often very slight 
The seven bright stars of the Great Leai, for example, form 
a group which any observei would veiy soon notice and 
naturally make into a constellation, but the lescmblance 
to a beai of these and the fainter stars of the constellation 
is sufficiently remote (see fig. 5), and as a matter of fact 
this part of the Bear has also been called a Waggon and 
is in Amenca familiarly known as the Dipper ; another 
constellation has sometimes been called the Lyre and 
sometimes also the Vultuie In very many cases the choice 
of stars seems to have been made in such an arbitraiy 
manner, as to suggest that some fanciful figure was first 
imagined and that stais were then selected so as to represent 
it in some rough sort of way In fact, as Sir John Hcrschel 
remarks, " The constellations seem to have been pmposely 
named and delineated to cause as much confusion and 
inconvenience as possible Innumerable snakes twine 
through long and contorted areas of the heavens where no 

$$ is, n] The Constellations the Zodiac 13 

memory can follow them , bears, lions, and fishes, large and 
small, confuse all nomenclature." (Outlines of Astronomy ', 

3 O1 ) 

The constellations as we now have them are, with the 
exception of a certain number (chiefly in the southern 
skies) which have been added in modern times, substantially 
those which existed in early Greek astronomy , and such 
mfoimation as we possess of the Chaldaean and Egyptian 
constellations shews resemblances indicating that the Greeks 
borrowed some of them The names, as for as they are 
not those of animals or common objects (Bear, Seipent, 
Lyre, etc ), are largely taken from characters in the Greek 
mythology (Hercules, Perseus, Orion, etc ) The con- 
stellation Berenice's Hair, named after an Egyptian queen 
of the 3rd century B.C , is one of the few which com- 
memorate a historical personage* 

13 Among the constellations which first received names 
were those through which the sun passes in its annual 
circuit of the celestial sphere, that is those through which 
the ecliptic passes The moon's monthly path is also a great 
circle, never differing very much from the ecliptic, and the 
paths of the planets ( 14) are such that they also are never 
fai from the ecliptic Consequently the sun, the moon, 
and the five planets weic always to be found within a legion 
of the sky extending about 8 on each side of the ecliptic 
This strip of the celestial spheie was called the zodiac, 
because the constellations in it weie (with one exception) 
named after living things (Greek f<3ov, an animal) ; it was 
divided into twelve equal paits, the signs of the zodiac, 
ihiough one of which the sun passed evciy month, so that 
the position of the sun at any time could be roughly 
described by stating in what " sign " it was The stars in 
each " sign ' J were formed into a constellation, the "sign' 7 
and the constellation each icceivmg the same name. Thus 

"* I luve made no attempt eithu hue 01 elscwhcic to descubc the 
constellations and their positions, as I believe such vcibal clesciip- 
tions to be almost useless Foi a beginner who wishes to become 
familial with them the best plan is to get some bettei infoimed 
friend to point out a few of the moie conspicuous ones, in difluent 
pa its of the sky, Otheis can then be readily added by means of a 
slan -atlas, or of the stai-maps given in many textbooks 

T4 A Short Histoiy of Astronomy [Cn I 

arose twelve zodiacal constellations, the names of which 
have come down to us with unimportant changes from 
early Greek times * Owing, however, to an alteration of 
the position of the equator, and consequently of the 
equinoctial points, the sign Anes, which was defined by 
Hipparchus in the second centuiy c c (see chapter n , 42) 
as beginning at the vernal equinoctial point, no longer 
contains the constellation Anes, but the preceding one, 
Pisces ; and there is a corresponding change throughout 
the zodiac The more precise numerical methods of 
modern astronomy have, however, rendered the signs of 
the zodiac almost obsolete , but the first point of Anes ( r ), 
and the first point of Libra (==), are still the recognised 
names for the equinoctial points 

In some cases individual stars also received special 
names, or were called after the part of the constellation in 
which they were situated, eg Sinus, the Eye of the Bull, 
the Heart of the Lion, etc ; but the majority of the present 
names of single stars are of Arabic origin (chapter in , 64) 

14 We have seen that the stars, as a whole, letam 
invariable positions on the celestial sphere,t whereas the 
sun and moon change their positions It was, howevei, 
discovered in prehistoric times that five bodies, at first 
sight barely distinguishable fiom the other stars, also changed 
their places. These five Mercury, Venus, Mars, Jupiter, 
and Saturn with the sun and moon, were called planets, | 
or wanderers, as distinguished from the fixed stars 

* The names, m the customary I atm forms, are Aries, Taurus, 
Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capncoinus, 
Aquarius, and Pisces, they are easily remembered by the doggeiel 

The Ram, the Bull, the Hea\enly Twins, 
And next the dab, the Lion shines, 

The Virgin and the Scales, 
The Scorpion, Aichei, and He-Goat, 
The Man that bears the Watei ing-pot, 

And Fish with glitteiing tails 

f This statement leaves out of account small motions nearly 01 
quite invisible to the naked eye, some of which aie among the most 
interesting discoveries of telescopic astronomy , see, for example, 
chapter x, ^ 207-215 

J The custom of calling the sun and moon planets has now died 
out, and the modern usage will be adopted henceforwaid in this 

i 4 , is] The Planets 15 

Mercury is nevei seen except occasionally neai the horizon 
just after sunset or before sunrise, and in a climate like 
ours requires a good deal of looking for y and it is rather 
remarkable that no record of its discovery should exist. 
Venus is conspicuous as the Evening Star or as the 
Morning Stai The discovery of the identity of the 
Evening and Morning Stars is attnbuted to Pythagoras 
(6th century EC), but must almost certainly have been 
made earlier, though the Homeric poems contain references 
to both, without any indication of their identity Jupiter is 
at times as conspicuous as Venus at her brightest, while 
Mars and Saturn, when well situated, lank with the brightest 
of the fixed stars. 

The paths of the planets on the celestial sphere are, as 
we have seen ( 13), never veiy far fiom the ecliptic , but 
whereas the sun and moon move continuously along their 
paths from west to east, the motion of a planet is some- 
times from west to east, or direct, and sometimes from east 
to west, or retrograde. If we begin to watch a planet when 
it is moving eastwards among the stars, we find that aftei 
a time the motion becomes slowei and slowei, until the 
planet hardly seems to move at all, and then begins to 
move with giadually increasing speed in the opposite 
dnection, after a time this westward motion becomes 
slower and then ceases, and the planet then begins to move 
eastwards again, at first slowly and then faster, until it 
returns to its original condition, and the changes are 
repeated When the planet is just reversing its motion it 
is said to be stationary, and its position then is called a 
stationary point. The time during which a planet's motion 
is retrogiade is, however, always consideiably less than that 
dunng which it is direct, Jupiter's motion, foi example, 
is direct for about 39 weeks and ictrograde for 17, while 
Mercury's direct motion lasts 13 or 14 weeks and the retio- 
grade motion only about 3 weeks (see figs. 6, 7) On the 
whole the planets advance from west to east and describe 
circuits round the celestial sphere m periods which are 
different foi each planet The explanation of these irregu- 
larities m the planetary motions was long one of the great 
difficulties of astionomy. 

15 The idea that some of the heavenly bodies are 

1 6 

A Short History of Astronomy 

[CM I 

nearer to the earth than others must have been suggested 
by eclipses (17) and occupations, ze passages of the 
moon over a planet or fixed star In this way the moon 
would be recognised as nearei than any of the other 
celestial bodies No direct means being available for 
determining the distances, rapidity of motion was employed 
as a test of probable nearness Now Saturn returns to the 
same place among the stars in about 29! years, Jupitei in 
12 years, Mais in 2 years, the sun m one year, Venus in 225 


jr IG 6 The apparent path of Jupiter from Oct, 28, 1897, to 
Sept 3, 1898 The dates printed in the diagram shew the 
positions of Jupiter 

days, Mercury in 88 days, and the moon m 27 days, and 
this order was usually taken to be the order of distance, 
Saturn being the most distant, the moon the neaiest The 
stars being seen above us it was natural to think of the 
most distant celestial bodies as being the highest, and 
accordingly Saturn, Jupiter, and Mars being beyond the 
sun were called superior planets, as distinguished from the 
two inferior planets Venus and Mercury. This division 
corresponds also to a difference in the observed motions, 
as Venus and Mercury seem to accompany the sun m its 

l6 J The Measurement of Tune ij 

annual journey, being never moie than about 47 and 29 
respectively distant from it, on eithei side , while the other 
planets are not thus restricted in their motions. 

1 6 One of the purposes to which applications of 
astronomical knowledge was fust applied was to the 
measurement of time, As the alternate appearance and 
disappeaiance of the sun, bringing with it light and heat, 
is the most obvious of astionomical facts, so the day is 


FIG 7 The appaicnt path oi Mcicniy fioin Aug I lo Oct 3, 
1898. The dates punted in capital Icttcis shew the, positions 
of the sun; the othei dates shew those oi Mcieury. 

the simplest unit of time.* Some of the early civilised 
nations divided the time fiom suniisc to sunset and also 
the night each into 12 equal houis, According to this 
airangement a day-horn was in summei longei than a 

* It maybe noted that our woul "day" (and the com* spun chnp, 
woid in othci languages) is commonly used in two scnsos, either lot 
the time between sunnfec and sunset (day as distinguished iioin 
night), or foi the whole period of 24 hours or day-and-ni^ht. The 
Greeks, however, used for the latter a special woul, 

1 8 A Short History of Astronomy [CH. I 

night-hour and m winter shorter, and the length of an hour 
varied during the year At Babylon, for example, where 
this arrangement existed, the length of a day-hour was at 
midsummer about half as long again as in midwinter, and 
in London it would be about twice as long It was there- 
fore a great improvement when the Gieeks, in comparatively 
late times, divided the whole day into 24 equal hours 
Other early nations divided the same period into 1 2 double 
hours, and others again into 60 hours 

The next most obvious unit of time is the lunar month, 
or period during which the moon goes through her phases 
A third independent unit is the year Although the year 
is for oidmary life much more important than the month, 
yet as it is much longer and any one time of year is harder 
to recognise than a paiticular phase of the moon, the length 
of the year is moie difficult to determine, and the earliest 
known systems of time-measurement were accoidingly 
based on the month, not on the year The month was 
found to be neaily equal to 29^ days, and as a period 
consisting of an exact number of days was obviously con- 
venient for most oidmary purposes, months of 29 01 30 
days were used, and subsequently the calendar was brought 
into closer accord with the moon by the use of months 
containing alternately 29 and 30 days (cf chapter n,, 19) 

Both Chaldaeans and Egyptians appear to have known 
that the year consisted of about 365^ days, and the lattei, 
foi whom the importance of the yeai was emphasised by 
the rising and falling of the Nile, were probably the first 
nation to use the yeai m preference to the month as a 
measure of time They chose a year of 365 days 

The oiigm of the week is quite different from that of 
the month or year, and rests on certain astrological ideas 
about the planets To each houi of the day one of the 
seven planets (sun and moon included) was assigned as a 
"ruler," and each day named after the planet which luled 
its fiist hour The planets being taken in the order 
already given ( 15), Saturn ruled the first hour of the 
fiist day, and therefore also the 8th, i5th, and 2 2nd hours 
of the first day, the 5th, i2th, and igth of the second clay, 
and so on, Jupiter ruled the 2nd, 9th, i6th, and 23rd 
hours of the first day, and subsequently the ist hour of 

iy] The Measurement of Time Edipse^ 19 

the 6th day. In this way the first hours of successive 
days fell respectively to Saturn, the Sun, the Moon, Mars, 
Mercury, Jupiter, and Venus. The first three are easily 
recognised in our Saturday, Sunday, and Monday , in the 
other days the names of the Roman gods have been 
replaced by their supposed Teutonic equivalents Mercury 
by Wodan, Mars by Thues, Jupiter by Thor, Venus by 
Freia * 

17, Eclipses of the sun and moon must from very early 
times have excited great interest, mingled with superstitious 
terroi, and the hope of acquiring some knowledge of them 
was probably an important stimulus to early astronomical 
work That eclipses of the sun only take place at new 
moon, and those of the moon only at full moon, must have 
been noticed after very little observation ; that eclipses of 
the sun are caused by the passage of the moon in front 
of it must have been only a little less obvious , but the 
discovery that eclipses of the moon aie caused by the 
earth's shadow was probably made much latei In fact 
even in the time of Anaxagoras (5th centuiy B c ) the idea 
was so unfamiliai to the Athenian public as to be regarded 
as blasphemous 

One of the most remarkable of the Chaldaean con- 
tributions to astronomy was the discovery (made at any 
rate several centimes BC) of the recurrence of eclipses 
after a period, known as the saros, consisting of 6,585 days 
(or eighteen of our yeais and ten or eleven days, accoiding 
as five or foui leap-yeais are included) It is probable 
that the cliscovciy was made, not by calculations based on 
knowledge of the motions of the sun and moon, but by 
meie study of the dates on which eclipses were recorded 
to have taken place As, however, an eclipse of the sun 
(unlike an eclipse of the moon) is only visible over a small 
part of the suiface of the earth, and eclipses of the sun 
occurring at intervals of eighteen yeais are not geneiaily 
visible at the same place, it is not at all easy to see how 
the Chaldaeans could have established their cycle for this 
case, nor is it in fact clear that the saros was supposed to 
apply to solai as well as to lunar eclipses The saros may 

* Compare the Fiench . Mardi, Mercredi, Jeudi, Vendredi, or 1 
better still the Italian * Martedi, Mcrcoledi, Giovedi, Venerdi. 

2> A Short History of Astronomy [Cii I , 18 

be illustrated in modern times by the eclipses of the sun 
which took place on July i8th, 1860, on July 29th, 1878, 
and on August 9th, 1896, but the first was visible in 
Southern Europe, the second in North America, and the 
third in Northern Europe and Asia 

1 8. To the Chaldaeans may be assigned also the doubtful 
honour of having been among the first to develop astrology, 
the false science which has professed to ascertain the in- 
fluence of the stars on human affans, to predict by celestial 
observations wars, famines, and pestilences, and to discover 
the fate of individuals from the positions of the stars at 
their birth A belief in some form of astrology has always 
prevailed in oriental countries , it flourished at times among 
the Greeks and the Romans , it formed an important pait 
of the thought of the Middle Ages, and is not even quite 
extinct among ourselves at the present day.* It should, 
however, be remembered that if the histoiy of astrology is 
a painful one, owing to the numerous illustrations which 
it affords of human credulity and knavery, the belief in 
it has undoubtedly been a powerful stimulus to genuine 
astronomical study (cf, chapter in , 56, and chapter v., 
99> I0 ) 

* See, for example, Old Moore's or ZadkiePs Almanack, 



"The astionomei discoveis that gcomctiy, a pine abstraction of the 
human mind, is the measure of planetaiy motion " 


19 IN the earlier penod of Greek history one of the 
chief functions expected of astionomers was the pioper 
regulation of the calendar The Greeks, like earlier 
nations, began with a calendar based on the moon. In 
the time of Hesiod a year consisting of 12 months of 30 
days was m common use , at a later date a year made up 
of 6 Ml months of 30 days and 6 empty months of 29 days 
was mtioduced To Solon is attributed the merit of 
having introduced at Athens, about 594 EC, the piactice 
of adding to every alternate year a "full" month Thus a 
penod of two yeais would contain 13 months of 30 days 
and 12 of 29 days, 01 738 days in all, distributed among 
2 5 months, giving, for the average length of the year and 
month, 369 clays and about 29] days respectively. This 
airangement was furthei impioved by the introduction, 
probably during the 5th century B c , of the octaeteris, or 
eight-year cycle, in three of the years of which an additional 
" full " month was introduced, while the remaining years 
consisted as before of 6 " full " and 6 " empty " months 
By this arrangement the average length of the year was 
icduced to 365] days, that of the month remaining neaily 
unchanged As, however, the Greeks laid some stress on 
beginning the month when the new moon was first visible, 
it was necessary to make from time to time arbitiaiy 
alterations m the calendar, and considerable confusion 

22 A Short Histoiy of Astronomy [CH n, 

resulted, of which Aristophanes makes the Moon complain 
m his play The Clouds^ acted in 423 B c. 

" Yet you will not maik youi days 

As she bids you, but confuse them, jumbling them all sorts of ways 
And, she says, the Gods in chorus shower reproaches on her head, 
When, in bitter disappointment, they go supperless to bed, 
Not obtaining festal banquets, duly on the festal day " 

20 A little later, the astronomer Meton (born about 
460 BC) made the discovery that the length of 19 yeais 
is very neaily equal to that of 235 lunar months (the 
difference being in fact less than a day), and he devised 
accordingly an arrangement of 12 years of 12 months and 
7 of 13 months, 125 of the months m the whole cycle 
being "full' 3 and the others "empty" Nearly a centuiy 
later Callippus made a slight improvement, by substituting 
m every fourth period of 19 years a "full" month foi one of 
the " empty " ones. Whether Meton's cycle, as it is called, 
was introduced for the civil calendar or not is unceitam, 
but if not it was used as a standard by reference to which 
the actual calendai was from time to time adjusted The 
use of this cycle seems to have soon spread to other paits 
of Greece, and it is the basis of the present ecclesiastical 
rule for fixing Easter The difficulty of ensuring satisfactory 
correspondence between the civil calendar and the actual 
motions of the sun and moon led to the practice of publish- 
ing from time to time tables (Trapa^/mra) -not unlike 
our modern almanacks, giving for a series of years the 
dates of the phases of the moon, and the rising and setting 
of some of the fixed stars, together with predictions of the 
weather Owing to the same cause the early wnteis on 
agriculture (eg Hesiod) fixed the dates for agricultural 
opeiations, not by the calendar, but by the times of the 
rising and setting of constellations, i e the times when 
they first became visible before sunrise or were last visible 
immediately after sunset a practice which was continued 
long after the establishment of a fairly satisfactory calendar, 
and was appaiently by no means extinct in the time of 
Galen (2nd century A D.) 

21 The Roman calendar was m early times even more 
confused than the Greek There appeals to have been 

24 A Short History of Astronomy [CH II 

Gregory XIII introduced therefore, m 1582, a slight change; 
ten days were omitted from that year, and it was arranged 
to omit for the future three leap-years in four centimes 
(viz in 1700, 1800, 1900, 2100, etc, the yeais 1600, 2000, 
2400, etc , remaining leap-years) The Gregorian Calendar, 
01 New Style, as it was commonly called, was not adopted 
in England till 1752, when n days had to be omitted, 
and has not yet been adopted in Russia and Gieece, 
the dates there being now 12 days behind those of 
Western Europe 

23. While their oriental predecessors had confined 
themselves chiefly to astronomical observations, the eaihei 
Greek philosophers appear to have made next to no 
observations of importance, and to have been far moie 
interested in inquiring into causes of phenomena Thalcs, 
the founder of the Ionian school, was credited by latei 
writers with the introduction of Egyptian astronomy into 
Greece, at about the end of the 7th century B c ; but both 
Thales and the majority of his immediate successors appear 
to have added little or nothing to astronomy, except some 
rather vague speculations as to the foim of the earth 
and its relation to the rest of the world On the other 
hand, some real progress seems to have been made by 
Pythagoras* and his followers Pythagoras taught that 
the earth, m common with the heavenly bodies, is a sphere, 
and that it rests without requmng support in the middle 
of the universe Whether he had any real evidence in 
support of these views is doubtful, but it is at any mte 
a reasonable conjecture that he knew the moon to be 
bright because the sun shines on it, and the phases to 
be caused by the greater or less amount of the illuminated 
half turned towards us , and the curved form of the 
boundary between the bright and dark portions of the 
moon was correctly interpreted by him as evidence that 
the moon was spherical, and not a flat disc, as it appears 
at first sight Analogy would then piobably suggest that the 
earth also was spherical However this may be, the belief 
in the spherical form of the earth never disappeared from 

* We have little definite knowledge of his life. He was bom m 
the earlier part of the 6th century B c , and died at the end of the 
same century or beginning of the next, 

$ 2i, 24] The Pythagoreans 25 

Greek thought, and was in later times an established part 
of Greek systems, whence it has been handed down, 
almost unchanged, to modern times This belief is thus 
2,000 years oldei than the belief in the lotation of 
the earth and its i evolution lound the sun (chapter iv ), 
doctrines which we are sometimes inclined to couple with 
it as the foundations of modern astionomy. 

In Pythagoras occuis also, peihaps foi the first time, an 
idea which had an extremely important influence on ancient 
and mediaeval astionomy Not only weie the stars supposed 
to be attached to a crystal spheie, which revolved daily 
on an axis ihiough the earth, but each of the seven 
planets (the sun and moon being included) moved on a 
spheie of its own The distances of these spheres from 
the earth were fixed in accoi dance with certain speculative 
notions of Pythagoras as to numbers and music , hence 
the spheres as they revolved produced harmonious sounds 
which specially gifted persons might at times heai this 
is the origin of the idea of the music of the spheres which 
recurs continually in mediaeval speculation and is found 
occasionally in modern literature At a latei stage these 
spheies of Pythagoras weic developed into a scientific 
repiesentation of the motions of the celestial bodies, which 
remained the basis of astronomy till the time of Kepler 
(chaptei vii ) 

24 The Pythagorean PJulolaus^ who lived about a 
century later than his master, introduced for the fiist tune 
the idea of the motion of the caith he appears to have 
icgarded the earth, as well as the sun, moon, and five 
planets, as levolvmg round some central fire, the earth 
lotatmg on its own axis as it i evolved, appaiently in oider 
to ensuic that the central fiie should always remain in- 
visible to the inhabitants of the known parts of the earth 
That the scheme was a purely fanciful one, and entirely 
diffcient from the modern doctnne of the motion of the 
earth, with which later writers confused it, is sufficiently 
shewn by the invention as pait of the scheme of a purely 
imaginary body, the counter-earth (am^v), which brought 
the numbei of moving bodies up to ten, a sacred Pytha- 
gorean number The suggestion of such an important 
as that of the motion of the eaith ? an idea so 

26 A Short History of Astronomy [CH n 


repugnant to unmstructed common sense, although piesented 
in such a crude form, without any of the evidence required 
to win general assent, was, however, undoubtedly a valuable 
contribution to astronomical thought It is well worth 
notice that Coppeimcus in the great book which is the 
foundation of modern astionomy (chapter iv , 75) especi- 
ally quotes Philolaus and othei Pythagoreans as authorities 
for his doctrine of the motion of the earth 

Three other Pythagoreans, belonging to the end of 
the 6th century and to the 5th century B c , Hicetas of 
Syracuse, Herachtus, and Ecphantus, are explicitly mentioned 
by later writers as having believed in the rotation of the 

An obscure passage in one of Plato's dialogues (the 
Twiaeus) has been mteipreted by many ancient and modern 
commentators as implying a belief in the ictation of the 
eaith, and Plutaich also tells us, paitly on the authority 
of Theophrastus, that Plato in old age adopted the belief 
that the centre of the universe was not occupied by the 
earth but by some better body * 

Almost the only scientific Greek astronomer who believed 
m the motion of the earth was Anstarchus of Samos, who 
lived m the fiist half of the 3rd century B c , and is best 
known by his measmements of the distances of the sun 
and moon ( 32) He held that the sun and fixed stars 
were motionless, the sun being in the centre of the sphere 
on which the latter lay, and that the earth not only rotated 
on its axis, but also described an orbit louncl the sun 
Seleucns of Seleucia, who belonged to the middle of the 
2nd century B c , also held a similar opinion Unfor 
tunately we know nothing of the giounds of this belief in 
either case, and their views appear to have found little 
favour among their contemporanes or successors. 

It may also be mentioned in this connection that Aristotle 
( 27) clearly realised that the apparent daily motion of the 
stars could be explained by a motion either of the stars or 
of the earth, but that he rejected the latter explanation 

25 Plato (about 428-347 BC) devoted no dialogue 
especially to astronomy, but made a good many references 

Theophrastus was born about half a ccntiny, Plutarch neaily 
ftve centuries, later than Plato, 

s> 26] Anstarchits Plato 


to the subject in various places He condemned any 
careful study of the actual celestial motions as degrading 
rather than elevating, and apparently icgaided the subject 
as worthy of attention chiefly on account of its connection 
with geometiy, and because the actual celestial motions 
suggested ideal motions of gi eater beauty and interest 
This view of astronomy he contrasts with the popular 
conception, according to which the subject was useful 
chiefly foi giving to the agriculturist, the navigator, and 
otheis a knowledge of times ancl seasons ! At the end 
of the same dialogue he gives a shoit account of the 
celestial bodies, according to \\hich the sun, moon, planets, 
and fixed stais revolve on eight concentric and closely 
fitting wheels or circles lound an axis passing thiough the 
earth Beginning with the body neaiest to the caith, the 
order is Moon, Sun, Mercury, Venus, Mars, Jupitei, Satuin, 
stars The Sun, Mercury, and Venus are said to peiform 
then revolutions in the same time, while the other planets 
move more slowly, statements which shew that Plato was at 
any rate aware that the motions of Venus and Mercury are 
diffeient from those of the other planets. He also states 
that the moon shines by reflected light received from 
the sun 

Plato is said to have suggested to his pupils as a worthy 
pioblem the explanation of the celestial motions by means 
of a combination of uniform cnculai or spherical motions 
Anything like an accurate theory of the celestial motions, 
agieemgwith actual obseivation, such as Hipparchus and 
Ptolemy afteiwaids constructed with fair success, would 
hardly seem to be in accordance with Plato s ideas of the 
true astronomy, but he may well have wished to see 
established some simple and haimonious geometrical 
scheme which would not be altogether at variance with 
known facts 

26 Acting to some extent on this idea of Plato's, Eudo&m 
of Cnidus (about 409-356 BC) attempted to explain the 
most obvious peculiarities of the celestial motions by means 
of a combination of unifoim circular motions He may be 
regarded as repi cscntative of the tiunsition from speculative 

" Republic, VII. 529, 530, 

28 A Short History of Astronomy [Cn n 

to scientific Greek astronomy As in the schemes of 
several of his predecessors, the fixed stais he on a sphere 
which revolves daily about an axis through the earth , the 
motion of each of the othei bodies is produced by a com- 
bination of other spheies, the centre of each sphere lying 
on the surface of the preceding one Foi the sun and 
moon three spheres were in each case necessary one to 
produce the daily motion, shared by all the celestial 
bodies ; one to pioduce the annual or monthly motion in 
the opposite direction along the ecliptic , and a third, with 
its axis inclined to the axis of the preceding, to produce 
the smaller motion to and from the ecliptic Eudoxus 
evidently was well aware that the moon's path is not 
coincident with the ecliptic, and even that its path is not 
always the same, but changes continuously, so that the third 
spheie was m this case necessary , on the other hand, he 
could not possibly have been acquainted with the minute 
deviations of the sun from the ecliptic with which modern 
astronomy deals Either therefore he used enoneous 
observations, 01, as is more probable, the sun's third sphere 
was introduced to explain a purely imaginary motion con- 
jectured to exist by " analogy " with the known motion of 
the moon For each of the five planets four spheres were 
necessary, the additional one serving to produce the variations 
in the speed of the motion and the reversal of the direction of 
motion along the ecliptic (chapter i , 14, and below, 51) 
Thus the celestial motions were to some extent explained 
by means of a system of 27 spheres, i for the stars, 6 foi 
the sun and moon, 20 foi the planets There is no cleai 
evidence that Eudoxus made any serious attempt to arrange 
either the size or the time of revolution of the spheres so as 
to produce any precise agreement with the observed motions 
of the celestial bodies, though he knew with considerable 
accuracy the time required by each planet to return to the 
same position with respect to the sun , in othei words, his 
scheme represented the celestial motions qualitatively but 
not quantitatively On the other hand, there is no reason 
to suppose that Eudoxus regarded his spheres (with the 
possible exception of the sphere of the fixed stars) as 
material , his known devotion to mathematics rendcis it 
probable that m his eyes (as m those of most of the 

** 2 ?> 2 8] Eitdoxus Aristotle 29 

scientific Gieek astronomers who succeeded him) the 
spheres were mere geometrical figures, useful as a means 
of resolving highly complicated motions into simpler 
elements Eudoxus was also the first Greek recorded to 
have had an observatory, which was at Cmdus, but we have 
few details as to the instruments used or as to the observa- 
tions made. We owe, however, to him the first systematic 
description of the constellations (see below, 42), though 
it was probably based, to a large extent, on rough observa- 
tions borrowed from his Gieek predecessors or from the 
Egyptians He was also an accomplished mathematician, 
and skilled m various other blanches of learning. 

Shortly aftei wards Calhppus ( 20) further developed 
Eudoxus's scheme of revolving spheres by adding, for 
icasons not known to us, two spheres each for the sun 
and moon and one each foi Venus, Mercury, and Mars, 
thus bringing the total number up to 34. 

27 We have a tolerably full account of the astronomical 
views of Aristotle (384-322 B c ), both by means of inci- 
dental references, and by two treatisesthe Meteordoqica 
and the De Coelo though another book of his, dealing 
specially with the subject, has unfortunately been lost. He 
adopted the planetary scheme of Eudoxus and Calhppus, 
but imagined on " metaphysical grounds " that the spheres 
would have certain disturbing effects on one another, and 
to counteract these found it necessaiy to add 22 fresh 
sphcies, making 56 m all At the same time he treated the 
spheres as matenal bodies, thus converting an ingenious and 
beautiful gcometncal scheme into a confused mechanism/ 1 
Anstotle's sphcics weie, however, not adopted by the 
leading Greek astronomeis who succeeded him, the systems 
of Hippaichus and Ptolemy being geometncal schemes 
based on ideas more like those of Eudoxus, 

28 Aristotle, m common with other philosophers of his 
time, believed the heavens and the heavenly bodies to be 
spherical. In the case of the moon he supports this belief 
by the aigument attributed to Pythagoias ( 23), namely 
that the obscived appcaiances of the moon 'in its sevcial 

* Confused, because the mechanical knowledge ol the time was 
quite unequal to giving any explanation of the way in which these 
fopheieb acled on one another. 

3 A Short Jfistory of Astronomy [CH n 

phases are those which would be assumed by a spherical 
body of which one half only is illuminated by the sun. 
Thus the visible portion of the moon is bounded by two 
planes passing nearly through its centie, perpendicular 
respectively to the lines joining the centre of the moon to 
those of the sun and earth In the accompanying diagram, 
which repiesents a section through the centres of the sun 

/ B 


8 The phases of the moon 

(s), earth (E), and moon (M), A B c D representing on a 
much enlarged scale a section of the moon itself, the 
portion DAB which is turned away from the sun is dark, 
while the portion ADC, being turned away from the 
observer on the eaith, is in any case invisible to him The 
part of the moon which appears bright is therefore that of 
which B c is a section, or the poition 
represented by F B G c in fig 9 (which 
lepiesents the complete moon), which 
consequently appears to the eye as 
bounded by a semicircle F c G, and a 
portion F B G of an oval curve (actually 
an ellipse) The breadth of this bright 
surface clearly varies with the iclative 
positions of sun, moon, and eaith , so 
that in the course of a month, during 
which the moon assumes successively the positions relative 
to sun and earth represented by i, 2, 3, 4, 5, 6, 7, 8 in 
rig 10, its appearances are those represented by the cor- 
responding numbers m fig n, the moon thus passing 

FIG 9 The phases 
o the moon 

29] Anstotle the Phases of the Moon 31 

through the familiar phases of crescent, half full, gibbous. 
full moon, and gibbous, half full, crescent again * 

C > 



FIG 10 The phases of the moon 

Anstotle then argues that as one heavenly body 1 is 
spherical, the others must be so also, and supports^ this 
conclusion by another argument, equally inconclusive to 



FIG 1 1 The phases of the moon 

us, that a spherical foim is appiopnate to bodies moving as 
the heavenly bodies appear to do 

29 His proofs that the eaith is spherical are moie in- 
teresting After discussing and rejecting various other 
suggested forms, he points out that an eclipse of the moon 
is caused by the shadow of the eaith cast by the sun, and 

* I have introduced here the lamihar explanation ol the phases of 
the moon, and the aigument based on it for the spherical shape ot 
the moon, because, although pi obably known before Anstotlc, there 
is, as iai as I know, no clcai and definite statement of the mattci in 
any eailici wnter, and aitci his time it becomes an accepted pait of 
Greek clcmentaiy astronomy It may be noticed that the explanation 
is unaffected either by the question of the rotation of the eaith or 
by that of its motion round the bun 

32 A Short History of Astronomy [Cn. n 

aigues fiom the circular form of the boundary of the shadow 
as seen on the face of the moon dunng the progress of the 
eclipse, or in a partial eclipse, that the earth must be 
spherical , for otheiwise it would cast a shadow of a dif- 
feient shape A second reason for the spherical form of 
the earth is that when we move noith and south the stais 
change their positions with respect to the horizon, while 
some even disappear and fresh ones take their place This 
shows that the direction of the stars has changed as com- 
pared with the observer's horizon , hence, the actual direction 
of the stars being imperceptibly affected by any motion of 
the observer on the earth, the horizons at two places, noith 
and south of one another, arc m different directions, and the 
eaith is therefore curved For 
example, if a star is visible to an 
observei at A (fig 12), while to 
an observer at B it is at the same 
time invisible, i e hidden by the 
earth, the surface of the earth 
FIG 12 The curvature of at A must be m a different direc- 
theeaith tion from that at B Anstotle 

quotes further, in confirmation of 

the roundness of the eaith, that travellers from the far 
East and the far West (practically India and Morocco) 
alike reported the presence of elephants, whence it may be 
inferred that the two regions in question are not very far 
apart He also makes use of some rather obscuie arguments 
of an a priori character 

There can be but little doubt that the readiness with 
which Aristotle, as well as other Greeks, admitted the 
sphencal form of the earth and of the heavenly bodies, 
was due to the affection which the Greeks always seem 
to have had for the circle and sphere as being "perfect," 
z.e perfectly symmetrical figures 

30 Aristotle argues against the possibility of the revo- 
lution of the earth round the sun, on the ground that this 
motion, if it existed, ought to produce a corresponding 
apparent motion of the stais We have heie the first 
appearance of one of the most serious of the many objections 
ever brought against the belief m the motion of the earth, 
an objection really only finally disposed of during the 

$ 30] Aristotle 33 

present centuiy by the discovery that such a motion of 
the stars can be seen in a few cases, though owing to the 
almost inconceivably great distance of the stars the motion 
is imperceptible except by extremely lefined methods of 
observation (cf chapter XIIL, 278, 279) The question 
of the distances of the several celestial bodies is also 
discussed, and Aristotle ainves at the conclusion that the 
planets are farther off than the sun and moon, supporting 
his view by his observation of an occupation of Mars by 
the moon (z e a passage of the moon in front of Mars), and 
by the fact that similar observations had been made in the 
case of other planets by Egyptians and Babylonians It 
is, however, difficult to see why he placed the planets 
beyond the sun, as he must have known that the intense 
brilliancy of the sun renders planets invisible in its neigh- 
bourhood, and that no occupations of planets by the sun 
could really have been seen even if they had been reported 
to have taken place. He quotes also, as an opinion of 
" the mathematicians," that the stars must be at least nine 
times as far off as the sun 

There are also in Aristotle's writings a number of astro- 
nomical speculations, founded on no solid evidence and of 
little value , thus among other questions he discusses the 
nature of comets, of the Milky Way, and of the stars, why 
the stars twinkle, and the causes which produce the various 
celestial motions 

In astronomy, as in other subjects, Aristotle appears 
to have collected and systematised the best knowledge of 
the time, but his original contributions are not only not 
comparable with his contubutions to the mental and moral 
sciences, but are mfenoi in value to his work in other 
natuial sciences, eg Natural History Unfoitunately the 
Greek astronomy of his time, still m an undeveloped state, 
was as it were crystallised in his writings, and his gieat 
authority was invoked, centuries afterwards, by comparatively 
unintelligent or ignorant disciples in suppoit of doctimes 
which were plausible enough in his time, but which subse- 
quent lesearch was shewing to be untenable The advice 
which he gives to his readeis at the beginning of his ex- 
position of the planetary motions, to compare his views 
with those which they arrived at themselves 01 met with 


34 A Short History of Astronomy [dr n 

elsewhere, might with advantage have been noted and 
followed by many of the so-called Aristotelians of the 
Middle Ages and of the Renaissance * 

31 After the time of Aristotle the centre of Gieck 
scientific thought moved to Alexandna Founded by 
Alexandei the Great (who was for a time a pupil of 
Aristotle) m 332 EC, Alexandria was the capital of Egypt 
during the reigns of the successive Ptolemies These 
kings, especially the second of them, surnamed Phila- 
delphos, were patrons of learning, they founded the 
famous Museum, which contained a magnificent library 
as well as an observatory, and Alexandria soon became 
the home of a distinguished body of mathematicians and 
astronomers During the next five centuries the only 
astronomers of importance, with the great exception of 
Hippaichus ( 37), were Alexandrines 

32 Among the earlier members of the Alexandrine 
school were Anstarchus of Samos, Anstylfas, and Timo- 
charis, three nearly contemporaiy astronomers belonging 


FIG 13 The method of Anstarchus for comparing the distances 
of the sun and moon. 

to the first half of the 3rd centuiy B c The views of 
Anstarchus on the motion of the earth have already been 
mentioned (24) A treatise of his On the Magnitudes 
and Distances of the Sun and Moon is still extant . he thci e 
gives an extiemely ingenious method for ascertaining the 
comparative distances of the sun and moon. If, in the 
figure, E, s, and M denote respectively the centres of the 
earth, sun, and moon, the moon evidently appeals to an 
observer at E half full when the angle E M s is a light 
angle If when this is the case the angular distance 
between the centres of the sun and moon, i e the angle 
M E s, is measuied, two angles of the tuangle M K s are 

* See, for example, the account of Galilei's controversies, in 
chaptei vj 

$* i*> rl Anstarchiu 35 

known, its shape is thcrcfoic complete!) clctei mined, and 
the tatio of its sides E M, & s can be calculated without 
much difficulty In fact, it being known (by a well-known 
Jesuit m elemental y geometiy) that the angles at E and s 
au k togethei equal to a light angle, the angle at & is 
obtained by subti acting the angle s K M fiom a right angle. 
Anstaichus made the angle at s about 3, and hence 
calculated that the distance of the sun was" from 18 to 20 
times that of the moon, wheieas, m fact, the sun is about 400 
times as distant as the moon The enoimous eiroi is due 
to the difficulty of detci mining with sufficient accuiacy the 
moment when the moon is half full the boundaiy separating 
the bnght and daik paits of the moon's face i& in reality 
(owing to the 11 regularities on the sin face of the moon) an ill- 
defined and broken line (cf fig 53 and the frontispiece), so that 
the observation on which Anstaichus based his work could 
not have been made with any accuiacy even with our modem 
instruments, much less with those available m his time. 
Anstarchus further estimated the apparent sizes of the sun 
and moon to be about equal (as is shewn, for example, at 
an eclipse of the sun, when the moon sometimes rather more 
than hides the surface of the sun and sometimes does not 
quite cover it), and inferred correctly that the real chameteis 
of the sun and moon weie in proportion to their distances 
By a method based on eclipse observations which was 
afterwards developed by Ilippaichus (41), he also found 
that the diameter of the moon was about \ that of the 
earth, a lesult vciy near to the truth, and the same 
method supplied data from which the distance of the moon 
could at once have been expressed in terms of the radius 
of the earth, but his woik was spoilt at this point by a 
grossly man mate estimate of the apparent si/e of the moon 
(2 instead of ]), and his conclusions seem to contradict 
one another. He appeals also to have believed the dis- 
tance of the lived stars to be immeasurably great as 
computed with that of the sun Both his speculative 
opinions and his actual results mark therefore a decided 
advance in astronomy. 

Tnnochtins and Anstyllus weie the fust to ascertain and 
to leroul the positions of the chief stars, by means of 
numerical measurements of then distances fiom lixecl 

A Short History of Astronomy 

[Or II 

positions on the sky , they may thus be regarded as the 
authors of the first real star catalogue, earlier astronomers 
having only attempted to fix the position of the stars by 
more or less vague verbal descriptions They also made a 
number of valuable observations of the planets, the sun, 
etc, of which succeeding astionomers, notably Hippaichus 
and' Ptolemy, were able to make good use 

33 Among the important contributions of the Cnecks 
to astronomy must be placed the development, chiefly from 
the mathematical point of view, of the consequences of the 
rotation of the celestial sphere and of some of the simpler 
motions of the celestial bodies, a development the indi- 
vidual steps of which it is difficult to tiace We have, 

FIG 14 The equator and the ecliptic, 

however, a series of minor treatises or textbooks, written 
for the most part during the Alexandnne pcnod, dealing 
with this branch of the subject (known geneially as 
Spherics, or the Doctrine of the Sphere), of which the 
Phenomena of the famous geometer Euclid (about 300 B c ) 
is a good example In addition to the points and circles 
of the sphere already mentioned (chaptci i, 8-n), we 
now find explicitly recognised the horizon, or the great 
circle in which a hoiizontal plane through the observer 
meets the celestial spheie, and its pole,"* the zenith, t 01 

* The poles of a great circle on a sphere aie the ends of a diamciei 
perpendicular to the plane of the great circle Every point on the 
great circle is at the same distance, 90, from each pole 

f The woid "zenith " is Aiabic, not Greek cf chapter m , 6| 

** 33-35] Spherics 37 

point on the celestial sphere vertically above the observer 
the verticals, or great circles through the zenith, meeting the 
horizon at right angles , and the declination circles which 
pass through the north and south poles and cut the 
equator at right angles Another important great circle 
was the meridian, passing through the zenith and the poles 
The well-known Milky Way had been noticed, and was 
regarded as foimmg another great circle There are also 
traces of the two chief methods in common use at the 
present day of indicating the position of a star on the 
celestia sphere, namely, by leference either to the equatoi 
or to the ecliptic If through a star s we draw on the 
sphere a portion of a great circle s N, cutting the ecliptic r N 
at right angles in N, and another great circle (a declination 
circle) cutting the equator at M, and if r be the first point of 
A"es ( 13). where the ecliptic crosses the equator, then 
the position of the star is completely defined either by the 
lengths of the arcs TN, N s, which are called the celestial 
longitude and latitude respectively, or by the arcs TM M - 
called respectively the right ascension and declination * 
*or some purposes it is more convenient to find the 
position of the star by the first method, , e by reference 
to he ecliptic , for other puiposes m the second way b y 
making use of the equator y 

34 One of the applications of Sphencs was to the con- 
struction of sun-dials, which were supposed to have been 
onginally mtioduced into Gieece from Babylon, but which 
were much improved by the Greeks, and extensively used 
both m Greek and m mediaeval times The pioper gradua- 
tion of sun-dials placed m various positions, horizontal, 
vertical, and oblique, required considerable mathematical 
skill Much attention was also given to the time of the 
rising and setting of the vanous constellations, and to 
similai questions 

35 The discovery of the spheiical foim of the earth 
led to a scientific treatment of the differences between the 
seasons m diffeicnt parts ol the earth, and to a correspond- 
ing division of the earth into zones We have ahead y 
seen that the height of the pole above the horuon vanes in 

Most oi tlic.bc namcb arc not Greek, but oi latei origin 

3 8 A Short History of Astronomy ten II 

different places, and that it was recognised that, if a traveller 
were to go fai enough noith, he would find the pole to 
coincide with the zenith, whereas by going south he would 
reach a legion (not ver^ far beyond the lunits of actual 
Greek travd) where the pole would ^ on the horizon 
and the equator consequently pass through the zenith in 
regions stdl farther south the north pole would be per- 
rnTently invisible, and the south pole would appear above 

tlie Fur ther"if m the figure H t ic w represents the horizon, 
meeting the equator Q E R w in the cast and west points B w, 
and thS m en q d,an H Q Z r K in the.uth and^ north pjjn* 

and P the pole, then it is 
easily seen that Q z is equal 
to P K, the height of the 
pole above the horizon 
Any celestial body, there- 
fore, the distance of which 
from the equator towaids 
the north (decimation) is 
less than r K, will ciosb 

the meridian to the south 
of the zenith, whereas if 
its decimation be greater 
than p K, it will cross to 
the noith of the zenith 
Now the greatest distance 
of the sun fiom the equatoi is equal to the ^ between 
the ecliptic and the equator, or about 23] Consequently 
at places at which the height of the pole is less than 23] 
the sun will, duimg part of the year, cast shadows at midday 
owaids the south This was known actually to be the case 
not very fai south of Alexandria. It was similarly recog- 
nised that on the other side of the equator theie must be 
a region m which the sun oidmarily cast shadows towaids 
the south, but occasionally towards the noith Ihese two 
icmons are the ton id zones of modem geogiaphers. 

Again, if the distance of the sun from the equator 
is 2<4, its distance from the pole is 66f, theiefoie in 
regions so far north that the height P K of the north pole 

Fit, 15 

~ Ihe cqiutoi, the honzon, 
and the mendian 

s6i The Measurement of the Eatth 39 

is more than 663, the sun passes in summer into the 
region of the cucumpolar stais which never set (chapter i , 
9), and therefore during a portion of the summer the sun 
remains continuously above the hon^on Similarly in the 
same regions the sun is in winter so near the south pole 
that for a time it lemains continuously below the honzon 
Regions in which this occurs (our Arctic regions) were 
unknown to Gieek travellers, but their existence was cleaily 
indicated by the astronomeis 

36 To Eratosthenes (276 BC to 195 or 196 BC), another 
member of the Alexandrine school, we owe one of the fust 
scientific estimates of the size of the earth He found 

FIG 1 6 The measurement of the earth 

that at the summer solstice the angular distance of the 
sun from the zenith at Alexandria was at midday -g^th of 
a complete circumference, or about 7, whereas at Syene 
in Upper Egypt the sun was known to be vertical at 
the same time From this he inferred, assuming Syene 
to be due south of Alexandria, that the distance from 
Syene to Alexandria was also 5 \th of the circumference 
of the earth. Thus if m the figure s denotes the sun, A 
and B Alexandria and Syene respectively, c the centre of 
the earth, and A z the direction of the zenith at Alexandria, 
Eratosthenes estimated the angle s A z, which, owing to 
the great distance of s, is sensibly equal to the angle s c A, 
to be 7, and hence mfeired that the arc A B was to the 
circumference of the earth in the proportion of 7 to 360 
or i to 50 The distance between Alexandria and Syene 

40 A Short History of Astronomy [Cn II 

being known to be 5,000 stadia, Eratosthenes thus arrived 
at 250,000 stadia as an estimate of the circumference 
of the earth, a number altered into 252,000 in order to 
give an exact number of stadia (700) for each degree on the 
earth It is evident that the data employed were rough, 
though the principle of the method is perfectly sound 9 
it is, however, difficult to estimate the correctness of the 
result on account of the uncertainty as to the value of 
the stadium used If, as seems probable, it was the 
common Olympic stadium, the result is about 20 per cent 
too great, but according to another interpretation * the 
lesult is less than i per cent in error (cf chapter x , 221) 

Another measurement due to Eiatosthenes was that 
of the obliquity of the ecliptic, which he estimated at 
f| of a right angle, or 23 51', the eiror in which is only 
about 7'. 

37 An immense advance in astronomy was made by 
Hipparchus, whom all competent critics have agreed to 
rank far above any other astronomer of the ancient world, 
and who must stand side by side with the greatest astro- 
nomers of all time Unfortunately only one unimportant 
book of his has been preserved, and our knowledge of 
his work is derived almost entirely fiom the writings of his 
great admirer and disciple Ptolemy, who lived nearly three 
centuries later ( 46 seqq ) We have also scarcely any 
information about his life He was born either at Nicaea 
in Bithyma or in Rhodes, m*'which island he erected an 
observatory and did most of his work. There is no 
evidence that he belonged to the Alexandrine school, 
though he probably visited Alexandria and may have made 
some obseivations there Ptolemy mentions observations 
made by him in 146 BC, 126 is c , and at many inter- 
mediate dates, as well as a rather doubtful one of 161 DC 
The period of his greatest activity must therefore have been 
about the middle of the 2nd century B c 

Apart from individual astronomical discoveries, his chief 
services to astronomy may be put under four heads He 
invented or greatly developed a special branch of mathe- 

* That of M Paul Tannery Recherche* sur VHtbtotrc dc FAstoo* 
nonue Ancicnnc, chap v 

37, 38] HipparcJms 41 

matics,* which enabled processes of numerical calculation 
to be applied to geometrical figures, whether in a plane or 
on a spheie He made an extensive series of observations, 
taken with all the accuracy that his instruments would 
permit He systematically and critically made use of old 
observations for comparison with later ones so as to 
discover astronomical changes too slow to be detected 
within a single lifetime Finally, he systematically employed 
a particular geometrical scheme (that of eccentrics, and to 
a less extent that of epicycles) for the representation of the 
motions of the sun and moon 

38. The merit of suggesting that the motions of the 
heavenly bodies could be represented more simply by com- 
binations of uniform circular motions than by the revolv- 
ing spheres of Eudoxus and his school ( 26) is generally 
attubuted to the great Alexandrine mathematician Apol- 
lomus of Perga, who lived in the latter half of the 3rd 
century B c , but there is no clear evidence that he worked 
out a system in any detail. 

On account of the important part that this idea played 
in astronomy for neaily 2,000 years, it may be worth 
while to examine in some detail Hipparchus's theory of 
the sun, the simplest and most successful application of 
the idea, 

We have already seen (chaptei i , 10) that, in addition 
to the daily motion (from east to west) which it shares with 
the rest of the celestial bodies, and of which we need here 
take no further account, the sun has also an annual motion 
on the celestial sphere in the reverse direction (from west 
to east) in a path oblique to the equator, which was eaily 
recognised as a great circle, called the ecliptic It must 
be lemembered further that the celestial sphere, on which 
the sun appeals to lie, is a mere gcometucal fiction 
introduced for convenience ; all that direct observation 
gives is the change in the sun's direction, and therefore 
the sun may consistently be supposed to move in such a 
way as to vary its distance fiom the earth m any arbitrary 
manner, provided only that the alteiations in the apparent 
size of the sun, caused by the variations in its distance, 
agree with those observed, 01 that at any rate the differences 
* Tiigonomctry 

42 A Short History of Astronomy [CH II 

are not great enough to be peiceptible It was, moreover, 
known (probably long before the time of Hipparchus) that 
the sun's apparent motion in the ecliptic is not quite 
uniform, the motion at some times of the year being 
slightly more rapid than at others 

Supposing that we had such a complete set of observa- 
tions of the motion of the sun, that we knew its position 
from day to day, how should we set to work to record and 
describe its motion ? For practical purposes nothing could 
be more satisfactory than the method adopted in our 
almanacks, of giving from day to day the position of the 
sun ; after observations extending over a few years it would 
not be difficult to verify that the motion of the sun is (after 
allowing for the irregularities of our calendar) from year to 
year the same, and to predict in this way the place of the 
sun from day to day in future years 

But it is clear that such a description would not only 
be long, but would be felt as unsatisfactory by any one 
who appi cached the question from the point of view of 
intellectual curiosity or scientific interest Such a person 
would feel that these detailed facts ought to be capable 
of being exhibited as consequences of some simpler geneial 

A modern astronomer would effect this by expressing 
the motion of the sun by means of an algebraical formula, 
t e he would repiesent the velocity of the sun or its 
distance from some fixed point m its path by some 
symbolic expression repiesentmg a quantity undergoing 
changes with the time in a ceitam definite way, and 
enabling an expert to compute with ease the required 
position of the sun at any assigned instant * 

The Gieeks, however, had not the requisite algebiaical 
knowledge for such a method of lepicsentation, and Hip- 
parchus, like his piedecessois, made use of a geometrical 

* The process may be worth illustrating by means of a simple* 
problem A heavy body, falling trcely under gravity, is found (the 
icsistcincc of the an being allowed for) to fall about 16 l< tt in 
I second, 64 tcet in 2 seconds, 144 ieet in 3 seconds, 256 iect in 
4 seconds, 400 feet in 5 seconds, and so on This series ot figuies 
carried on as far as may be required would satisfy practical ic- 
quirementSy supplemented if desiicd by the coi responding figures 
for ti action s ot seconds, but the mathematician repiescnts the same 

$ 39] Hipparchus 43 

^representation of the lequued variations in the sun's motion 
in the ecliptic, a method of repie&entation which is in some 
respects more intelligible and vivid than the use of algebra, 
but which becomes unmanageable in complicated cases 
It mns moieover the risk of being taken for a mechanism 
The circle, being the simplest curve known, would naturally 
be thought of, and as any motion other than a uniform 
motion would itself requne a special representation, the 
idea of Apollomus, adopted by Hipparchus, was to devise 
a proper combination of uniform circular motions 

39 The simplest device that was found to be satisfactory 

in the case of the sun was the use of the eccentric, i e a 

circle the centre of which (c) does not coincide with the 

position of the observer on the earth (E) If in fig 17 a 

point, s, describes the eccentric circle A F o B uniformly, 

so that it always passes over equal arcs of the circle in 

equal times and the angle ACS increases umfoimly, then 

it is evident that the angle A E s, or the apparent distance 

of s from A, does not increase uniformly When s is near 

the point A, which is farthest from the earth and hence 

called the apogee, it appears on account of its greater 

distance from the ob&eiver to move more slowly than when 

near i< or o , and it appears to move fastest when near B, 

the point neaiest to E, hence called the perigee Thus the 

motion of s varies m the same soit of way as the motion 

of the sun as actually observed Before, however, the 

eccentric could be considered as satisfactory, it was neces- 

saiy to show that it was possible to choose the direction 

of the line B E c A (the line of apses) which deteimmcs the 

positions of the sun when moving fastest and when moving 

most slowly, and the magnitude of the ratio of E c to the 

radius c A of the circle (the eccentricity), so as to make 

the calculated positions of the sun in various paits of its 

path differ from the observed positions at the corresponding 

facts more simply and m a way more satisfactory to the mind by the 
formula 6 = 16 t 2 , where s denotes the number of feet fallen, and 
t the numbei ot seconds By giving t any assigned value, the 
con expending space fallen through is at once obtained bimilaily 
the motion of the sun can be repicscnted approximately by the 
moie complicated foimula I nt -t- 2 c s^n nt, where / is the 
distance from a fixed point in the orbit, t the time, and , e cei tain 
numciical quantities 


A Short History of Astronomy 

[Cii II 

times of year by quantities so small that they might fauly 
be attributed to errors of observation. 

This problem was much more difficult than might at fiist 
sight appear, on account of the great difficulty experienced 
in Greek times and long afterwards in getting satisfactory 
observations of the sun As the sun and stars are not 
visible at the same time, it is not possible to measure 
directly the distance of the sun from neighbouring stars 
and so to fix its place on the celestial sphere. But it 

FIG 17 1 he eccentric 

is possible, by measuring the length of the shadow cast by 
a rod at midday, to ascertain with fair accuracy the height 
of the sun above the horizon, and hence to deduce its 
distance from the cquatoi, or the declination (figs 3, 14) 
This one quantity does not suffice to fix the sun's position, 
but if also the sun's right ascension ( 33), or its distance 
east and west from the stars, can be accurately ascei tamed, 
its place on the celestial spheie is completely determined 
Ihe methods available for determining this second quantity 
were, however, veiy imperfect One method was to note 
the time between the passage of the sun acioss some fixed 
position m the sky (eg. the meridian), and the passage of 




a star across the same place, and thus to ascertain the 
angular distance between them (the celestial sphere being 
known to turn through 15 in an houi), a method which 
with modern clocks is extremely accurate, but with the 
rough water-clocks or sand-glasses of former times was very 
uncertain In another method the moon was used as a 
connecting link between sun and stars, her position relative 

FIG 1 8. The position of the sun's apogee 

to the latter being obseived by mght, and with respect to 
the former by day, but owing to the rapid motion of the 
moon in the interval between the two observations, this 
method also was not susceptible of much accuracy 

In the case of the particular problem of the detei- 
rnmation of the line of apses, Hipparchus made use of 
anothei method, and his skill is shewn in a stnkmg mannei 
by his recognition that both the eccentncity and position 
of the apse line could be determined from a knowledge of 

46 A Short History of Astronomy [Cn II 

the lengths of two of the seasons of the year, z.e of the 
intervals into which the year is divided by the solstices 
and the equinoxes ( u) By means of his own observa- 
tions, and of otheis made by his predecessors, he ascer- 
tained the length of the spring (from the vernal equinox to 
the summer solstice) to be 94 days, and that of the summer 
(summer solstice to autumnal equinox) to be 92^ days, the 
length of the year being 365! days As the sun moves 
in each season through the same angular distance, a right 
angle, and as the spring and summer make together more 
than half the year, and the spring is longei than the 
summer, it follows that the sun must, on the whole, be 
moving more slowly during the spring than in any other 
season, and that it must therefore pass through the apogee 
m the spring. If, therefore, m fig 18, we diaw two 
perpendiculai lines Q E s, p E R to represent the directions 
of the sun at the solstices and equinoxes, p corresponding 
to the vernal equinox and K to the autumnal equinox, the 
apogee must lie at some point A between P and Q. So 
much can be seen without any mathematics the actual 
calculation of the position of A and of the eccentricity is 
a matter of some complexity The angle PEA was found 
to be about 65, so that the sun would pass through its 
apogee about the beginning of June ; and the eccentricity 
was estimated at -% 

The motion being thus represented geometrically, it 
became merely a matter of not very difficult calculation to 
construct a table from which the position of the sun for 
any day m the year could be easily deduced This was 
done by computing the so-called equation of the centre, 
the angle c s E of fig 17, which is the excess of the actual 
longitude of the sun over the longitude which it would 
have had if moving umfoimly 

Owing to the imperfection of the observations used 
(Hipparchus estimated that the times of the equinoxes and 
solstices could only be relied upon to within about half a 
day), the actual results obtained were not, according to 
modern ideas, very accurate, but the theory represented 
the sun's motion with an accuracy about as gieat as that 
of the observations It is woith noticing that with the 
same theory, but with an improved value of the eccentricity. 

* 40] Hipparchus 47 

the motion of the sun can be represented so accurately 
that the enor never exceeds about i', a quantity insensible 
to the naked eye 

The theory of Hipparchus lepresents the variations in 
the distance of the sun with much less accuiacy, and 
whereas in fact the angular diametei of the sun vanes by 
about -jjyth part of itself, or by about i' m the course of 
the year, this variation according to Hipparchus should be 
about twice as great But this erroi would also have been 
quite imperceptible with his instruments 

Hipparchus saw that the motion of the sun could equally 
well be represented by the other device suggested by 
Apollomus, the epi- 
cycle, The body the 
motion of which is to be 
represented is supposed 
to move uniforml) / 
round the circumference / 
of one circle, called the / 
epicycle, the centre of ! 
which in turn moves on \ 
another circle called the \ 
deferent. It is in fact \ 
evident that if a circle 
equal to the eccentric, 
but with its centre at E 

(fig 19), be taken as FIG 1 9, The epicycle and the dcfeient 

the deferent, and if s' 

be taken on this so that L s' is parallel to c s, then s' s is 
parallel and equal to E c ; and that therefoie the sun s, moving 
unifoimly on the eccentric, may equally well be regarded 
as lying on a circle of radius s' s, the centie &' of which 
moves on the defeient The two constructions lead in 
fact in this paiticular problem to exactly the same result, 
and Hipparchus chose the eccentric as being the simpler 
40 The motion of the moon being much more com- 
plicated than that of the sun has always piesented difficulties 
to astronomers, 1 and Hipparchus required for it a more 
elaborate construction Some further descuption of the 

* At the present time there is still a small discrepancy between the 
observed and calculated places of the moon Sec chaptei xni., 290. 

48 A Short History of Astronomy [Cn n 

moon's motion is, however, necessary before discussing his 

We have already spoken (chapter i , 16) of the lunar 
month as the period during which the moon returns to the 
same position with respect to the sun, more piecisely this 
penod (about 29^ days) is spoken of as a lunation or 
synodic month, as, however, the sun moves eastward on 
the celestial sphere like the moon but more slowly, the 
moon returns to the same position with respect to the 
stars in a somewhat shortei time, this period (about 27 
days 8 hours) is known as the sidereal month. Again, the 
moon's path on the celestial sphere is slightly inclined to 
the ecliptic, and may be regarded approximately as a great 
circle cutting the ecliptic in two nodes, at an angle which 
Hipparchus was probably the first to fix definitely at 
about 5. Moreover, the moon's path is always changing 
in such a way that, the inclination to the ecliptic remaining 
nearly constant (but cf chapter v, in), the nodes move 
slowly backwards (from east to west) along the ecliptic, 
perfoimmga complete revolution in about 19 years. It is 
therefore convenient to give a special name, the dracomtic 
month,* to the period (about 27 days 5 hours) during which 
the moon returns to the same position with respect to the 

Again, the motion of the moon, like that of the sun, is 
not uniform, the variations being greater than in the case 
of the sun Hippaichus appears to have been the first to 
discover that the part of the moon's path in which the 
motion is most rapid is not always in the same position on 
the celestial sphere, but moves continuously , or, in othei 
words, that the line of apses (39) of the moon's path 
moves The motion is an advance, and a complete circuit 
is described in about nine years Hence arises a fourth 
kind of month, the anomalistic month, which is the penod 
in which the moon returns to apogee or perigee 

To Hipparchus is due the ciedit of fixing with gieatei 

* The name is interesting as a icmnant oi a veiy caily supersti- 
tion Eclipses, which always occui near the nodes, were at one 
time supposed to be caused by a dragon which clevouied the sun 
or moon The symbols S3 2S still used to denote the two nodes 
are supposed to represent the head and tail ol the diagon. 

41] Hipparckus 49 

exactitude than before the lengths of each of these months 
In ordei to determine them with accuracy he recognised 
the importance of comparing obseivations of the moon 
taken at as great a distance of time as possible, and saw 
that the most satisfactory results could be obtained by 
using Chaldaean and other eclipse obseivations, which, 
as eclipses only take place neai the moon's nodes, were 
simultaneous records of the position of the moon, the 
nodes, and the sun 

To represent this complicated set of motions, Hipparchus 
used, as m the case of the sun, an eccentnc, the centre of 
which described a circle round the earth m about nine 
yeais (corresponding to the motion of the apses), the plane 
of the eccentnc being inclined to the ecliptic at an angle 
of 5, and sliding back, so as to lepiesent the motion of 
the nodes already described 

The result cannot, however, have been as satisfactory as 
in the case of the sun The variation in the rate at which 
the moon moves is not only greater than in the case of 
the sun, but follows a less simple law, and cannot be ade- 
quately lepresented by means of a single eccentnc ; so 
that though Hipparchus' work would have represented the 
motion of the moon m certain paits of her orbit with fair 
accuracy, there must necessarily have been elsewhere dis- 
crepancies between the calculated and observed places. 
There is some indication that Hipparchus was aware of 
these, but was not able to reconstruct his theory so as to 
account for them 

41 In the case of the planets Hipparchus found so 
small a supply of satisfactory observations by his prede- 
cessors, that he made no attempt to construct a system 
of epicycles or eccentncs to lepiesent their motion, but 
collected fiesh observations for the use of his successors 
He also made use of these observations to determine with 
more accuracy than before the aveiage times of revolution 
of the several planets 

He also made a satisfactory estimate of the size and 
distance of the moon, by an eclipse method, the leading 
idea of which was due to Anstaichus ( 32), by obseivmg 
the angular diameter of the earth's shadow (Q i<) at the 
distance of the moon at the time of an eclipse, and comparing 



A Short History of Astronomy 


FIG 20 The eclipse method 
of connecting the distances 
of the sun and moon 

it with the known angulai dia- 
meters of the sun and moon, 
he obtained, by a simple cal- 
culation,* a relation between 
the distances of the sun and 
moon, which gives either when 

* In the figure, which is taken 
from the De Revol^ombus of 
Coppermcus (chapter iv , ^ 85), 
let D, K, M represent respectively 
the centres of the sun, earth, and 
moon, at the time of an eclipse of 
the moon, and let s Q G, s R E denote 
the boundaries of the shadow-cone 
cast by the earth , then Q R, drawn 
at right angles to the axis of the 
cone, is the breadth of the shadow 
at the distance of the moon We 
have then at once from similar 


Hence if K D = n M K and 
also AD = n (radius of moon), n 
being 19 according to Anstarchus, 
GK-QM n (radius of moon) G K 

I .n 
n (radius of moon) G K 

= n GK H QM 

radius of moon 4- radius of 

= +^) (radius of earth). 
By observation the angular ladius 
of the shadow was found to be 
about 40' and that of the moon to 
be 15', so that 

radius ot shadow = Radius of moon, 
. radius oi moon 

= A (* + ~) (radius of caith), 

But the angulai radius of the moon 

being 15', its distance is necessarily 

about 220 times its radius, 

and distance of the moon 

= 60 (i + ~) (ladius of the earth), 

which is loughly Hippaichus's 
result, if n be any fairly laige 

4] Hipparchus 51 

the other is known Hippaichus knew that the sun was 
veiy much more distant than the moon, and appears to 
have tried more than one distance, that of Anstarchus among 
them, and the result obtained in each case shewed that 
the distance of the moon was nearly 59 times the radius 
of the earth Combining the estimates of Hipparchus and 
Anstarchus, we find the distance of the sun to be about 1,200 
times the radius of the earth a number which remained sub- 
stantially unchanged for many centuries (chaptei vm , 161) 

42 The appearance in 134 B c of a new star m the 
Scorpion is said to have suggested to Hipparchus the 
construction of a new catalogue of the stats. Fie included 
i, 080 stars, and not only gave the (celestial) latitude and 
longitude of each star, but divided them according to then 
brightness into six magnitudes The constellations to which 
he refers are nearly identical with those of Eudoxus ( 26), 
and the list has undergone few alterations up to the present 
day, except for the addition of a numbei of southern con- 
stellations, invisible in the civilised countries of the ancient 
world. Hipparchus recorded also a number of cases in 
which three or more stars appealed to be in line with one 
another, or, more exactly, lay on the same gieat circle, 
his object being to enable subsequent observers to detect 
more easily possible changes in the positions of the stars. 
The catalogue remained, with slight alterations, the standard 
one for nearly sixteen centuries (cf chaptei in , 63) 

The construction of this catalogue led to a notable 
discoveiy, the best known probably of all those which 
Hipparchus made In comparing his observations of certain 
stars with those of Timochans and Anstyllus ( 33), made 
about a century and a half caiher, Hipparchus found that 
then distances from the equinoctial points had changed 
Thus, in the case of the bright star Spica, the distance 
from the equinoctial points (measured eastwards) had 
increased by about 2 in 150 ycais, or at the rate of 48" pei 
annum Further inquiry showed that, though the roughness 
of the obscivations pioduced consideiable variations in the 
case of difleient stais, there was evidence of a gcncial 
increase m the longitude of the stars (mcastued from west 
to east), unaccompanied by any change of latitude, the 
amount of the change being estimated by Hipparchus as 

52 A Short History of Astronomy [di II 

at least 36" annually, and possibly more The agreement 
between the motions of different stais was enough to 
justify him in concluding that the change could be 
accounted for, not as a motion of individual stars, but 
rather as a change in the position of the equinoctial 
points, from which longitudes were measured Now these 
points are the intersection of the equator and the ecliptic 
consequently one or another of these two cncles must have 
changed But the fact that the latitudes of the stars had 
undergone no change shewed that the ecliptic must have 
letamed its position and that the change had been caused 


FIG 21 The increase of the longitude of a star 

by a motion of the equator Again, Hipparchus measined 
the obliquity of the ecliptic as several of his predecessors 
had done, and the results indicated no appreciable change. 
Hipparchus accordingly inferred that the equatoi was, as 
it were, slowly sliding backwards (i e from east to west), 
keeping a constant inclination to the ecliptic 

The argument may be made clearer by figiues In 
fig 21 let TM denote the ecliptic, TN the equatoi, s a 
stai as seen by Timochans, s M a gieat cnclc drawn pei- 
pendicular to the ecliptic. Then s M is the latitude, TM 
the longitude Let s' denote the stai as seen by Hippaichus 9 

42] fftffarckns 53 

then he found that s' M was equal to the formei s M, 
but that TM' was gieatei than the former rn, 01 that M' 

FIG 22 The movement of the equator 

was slightly to the east of M This change M M' being 

nearly the same for all stars, it was simpler to attribute it 

to an equal motion in the 

opposite direction of the 

point r, say from r to T' 

(fig 22), ze* by a motion of 

the equator from TN to 

r ' N', its inclination N' r 1 M 

remaining equal to its foimer 

amount N T M. The general 

effect of this change is shewn 

in a diffeient way in fig, 23, 

wheie r T' ^ ==' being the 

ecliptic, A B c D icpresents 

the equator as it appeared 

in the time of Tunochaus, 

A f B' c' B' (pi inted in red) FIG. 23 ~~ I he pi cccssion of the 

the same in the time of equinoxes 

Hippatchus, r, ^= being the 

earlier positions of the two equinoctial points, and r', *' 
the later positions. 

54 A Short History of Astronomy E CH n 

The annual motion r r ' was, as has been stated, estimated 
by Hipparchus as being at least 36" (equivalent to one 
degree m a century), and probably more, Its true value is 
considerably more, namely about 50" 

An important consequence of the motion of the equatoi 
thus discovered is that the sun in its annual journey lound 
the ecliptic, after starting fiom the equinoctial point, returns 
to the new position of the equinoctial point a little befoic 
returning to its original position with respect to the stais, 
and the successive equinoxes occur slightly earlier than they 

FIG 24 The precession of the equinoxes 

otherwise would From this fact is derived the name pre- 
cession of the epinoxes, or more shortly, precession, which 
is applied to the motion that we have been considering 
Hence it becomes necessary to recognise, as Hippaichus 
did, two different kinds of year, the tropical year or period 
required by the sun to leturn to the same position with 
respect to the equinoctial points, and the sidereal year 01 
period of return to the same position with respect to the 
stars If r r' denote the motion of the equinoctial point 
during a tropical year, then the sun after starting from the 

42] Hipfarclms 55 

equinoctial point at r arrives at the end of a tropical 
year at the new equinoctial point at r', but the sidereal 
year is only complete when the sun has further described 
the arc r'r and returned to its original staitmg-pomt T. 
Hence, taking the modern estimate 50" of the arc r r', the 
sun, in the sideieal yeai, describes an arc of 360, m the 
tropical year an aic less by 50", or 359 5 9' 10" , the lengths 
of the two years are therefore m this proportion, and the 
amount by which the sidereal year exceeds the tropical 
year bears to either the same ratio as 50" to 360 (or 

1,296,000"), and is theiefore - , days or about 20 

79 n 1296000 J 


Another way of expressing the amount of the precession 
is to say that the equinoctial point will describe the 
complete circuit of the ecliptic and leturn to the same 
position after about 26,000 years 

The length of each kind of year was also fixed 
by Hipparchus with considerable accuracy That of 
the tropical year was obtained by comparing the times 
of solstices and equinoxes observed by earlier astrono- 
mers with those observed by himself He found, for 
example, by comparison of the date of the summer solstice 
of 280 B.C , observed by Anstaichus of Sainos, with that 
of the year 135 BC, that the cuirent estimate of 365 
days for the length of the year had to be diminished 
by rlirth f a day or about five minutes, an estimate 
confirmed roughly by othei cases It is interesting to 
note as an illustiation of his scientific method that he 
discusses with some care the possible error of the observa- 
tions, and concludes that the time of a solstice may be 
eironeous to the extent of about | day, while that of an 
equinox may be expected to be within | day of the truth 
In the illustration given, this would indicate a possible 
eiror of i~] days m a penod of 145 years, or about 15 
minutes m a year Actually his estimate of the length of 
the yeai is about six minutes too great, and the error is 
thus much less than that which he indicated as possible. 
In the couise of this work he considered also the possibility 
of a change m the length of the year, and arrived at the 
conclusion that, although his observations weie not precise 

56 A Short History of Ashonomy [Cn n 

enough to show definitely the invariability of the year, there 
was no evidence to suppose that it had changed. 

The length of the tiopical year being thus evaluated at 
365 days 5 hours 55 minutes, and the difference between 
the two kinds of year being given by the observations of 
precession, the sidereal yeai was ascei tamed to exceed 
3 65 \ days by about 10 minutes, a result agreeing almost 
exactly with modern estimates, That the addition of two 
erroneous quantities, the length of the tropical year and the 
amount of the precession, gave such an accurate result was 
not, as at first sight appears, a mere accident. The chief 
source of error m each case being the erroneous times of 
the several equinoxes and solstices employed, the eirors 
in them would tend to produce errors of opposite kinds 
in the tropical year and in precession, so that they would m 
part compensate one another. This estimate of the length 
of the sidereal year was probably also to some extent 
verified by Hipparchus by comparing eclipse obseivations 
made at different epochs 

43 The great improvements which Hippaichus effected 
m the theories of the sun and moon naturally enabled him 
to deal more successfully than any of his predecessors with 
a problem which in all ages has been of the greatest interest, 
the prediction of eclipses of the sun and moon. 

That eclipses of the moon were caused by the passage 
of the moon through the shadow of the earth thiown by 
the sun, or, m other words, by the interposition of the 
earth between the sun and moon, and eclipses of the sun 
by the passage of the moon between the sun and the 
observer, was perfectly well known to Greek astronomers 
in the time of Aristotle ( 29), and probably much eailier 
(chapter i, 17), though the knowledge was probably 
confined to comparatively few people and superstitious 
terrors were long associated with eclipses 

The chief difficulty m dealing with eclipses depends 
on the fact that the moon's path does not coincide 
with the ecliptic. If the moon's path on the celestial 
sphere weie identical with the ecliptic, then, once eveiy 
month, at new moon, the moon (M) would pass exactly 
between the earth and the sun, and the latter would be 
eclipsed, and once every month also, at full moon, the 

' 43] 



moon (M') would be in the opposite direction to the sun 
as seen from the earth, and would consequently be obscured 
by the shadow of the earth 

As, however, the moon's path is inclined to the ecliptic 
( 4)> the latitudes of the sun and moon may differ by 
as much as 5, either when they are in conjunction, / e 
when they have the same longitudes, or when they are 

FIG 25 1 he cai th's shadow 

m opposition, te when then longitudes differ by 180, 
and they will then m either case be too far apart for an 
eclipse to occur Whether then at any full or new moon 
an eclipse will occui or not, will depend primarily on the 
latitude of the moon at the time, and hence upon her 
position with respect to the nodes of her orbit ( 40) If 
conjunction takes place when the sun and moon happen 


FIG, 26 The ecliptic and the moon's path 

to be near one of the nodes (N), as at s M in fig 26, the 
sun and moon will be so close togethei that an eclipse 
will occur , but if it occurs at a considerable distance fiom 
a node, as at s' M', their centres are so fai apart that no 
eclipse takes place. 

Now the appaient diameter of either sun or moon is, 
as we have seen ( 32), about ] 9 consequently when their 
discs just touch, as in fig 27, the distance between their 
centres is also about ~] If then at conjunction the dis- 
tance between then centres is less than this amount, an 

A Short History of Astronomy 

[Cii II 

eclipse of the sun will take place , if not, theic will be no 
eclipse It is an easy calculation to determine (in fig 26) 
the length of the side N s or N M of the triangle N M s, 
when s M has this value, and hence to 
deteimme the greatest distance from the 
node at which conjunction can take place 
if an eclipse is to occui An eclipse of 
the moon can be treated in the same way, 
except that we there have to deal with the 
moon and the shadow of the earth at the 
distance of the moon The apparent si/e 
of the shadow is, however, consideiably 
greater than the apparent size of the moon, 
and an eclipse of the moon takes place if 
the distance between the centre of the nioon and the centre 
of the shadow is less than about i. As before, it is easy 
to compute the distance of the moon or of the centre of the 
shadow from the node when opposition occurs, if an eclipse 
just takes place As, however, the appaient sizes of both 
sun and moon, and consequently also that of the earth's 
shadow, vary accoiding to the distances of the sun and 

FIG 27 The sun 
and moon 

FIG 28 Partial eclipse of 
the moon 

FIG 29 Total eclipse of 
the moon 

moon, a variation of which Hippaichus had no acemate 
knowledge, the calculation becomes leallya good deal moie 
complicated than at first sight appeals, and was only dealt 
with imperfectly by him 

Eclipses of the moon are divided into partial or total, 
the former occurring when the moon and the earth's 
shadow only overlap partially (as in % 28), the latter 

43] Hipparchus 59 

when the moon's disc is completely immersed in the 
shadow (fig 29) In the same way an eclipse of the sun 
may be partial 01 total; but as the sun's disc may be at 
times slightly larger than that of the moon, it sometimes 
happens also that the whole disc of the sun is hidden 
by the moon, except a narrow ring icund the edge (as 
in fig 30) such an eclipse is called annular. As the 
earth's shadow at the distance of the moon 
is always largei than the moon's disc, annular 
eclipses of the moon cannot occur 

Thus eclipses take place if, and only if, 
the distance of the moon from a node at 

the time of conjunction 01 opposition lies I<IG 30 Annulai 

within ceitam limits approximately known , eclipse of the 
and the pioblem of piedicting eclipses sun 
could be roughly solved by such knowledge 
of the motion of the moon and of the nodes as Hippaichus 
possessed Moreover, the length of the synodic and 
dracomtic months ( 40) being once ascertained, it became 
merely a matter of arithmetic to compute one or more 
periods after which eclipses would lecur nearly m the same 
manner For if any period of time contains an exact 
number of each kind of month, and if at any time an 
eclipse occurs, then after the lapse of the period, con- 
junction -(or opposition) again takes place, and the moon 
is at the same distance as before from the node and the 
eclipse recuis very much as before The saros, foi example 
(chapter i , 17), contained very neaily 223 synodic 01 
242 dracomtic months, dirTcimg from eithci by less than 
an hour Hipparchus saw that this penod was not com- 
pletely reliable as a means of predicting eclipses, and 
showed how to allow for the inegulanties m the moon's 
and sun's motion ( 39, 40) which weie ignored by it, 
but was unable to deal fully with the difficulties arising 
from the variations m the appaient diameters ol the sun 
or moon 

An important complication, howevei, arises in the case 
of eclipses of the sun, which had been noticed by eaihei 
wntcis, but which Hipparchus was the fiist to deal with 
Since an eclipse of the moon is an actual darkening of the 
rroon ? it is visible to anybody, wheievei situated, v\ho can 

60 A Shoit History of Astronomy [Cn II 

see the moon at all, foi example, to possible inhabitants 
of other planets, just as we on the earth can see precisely 
similar eclipses of Jupiter's moons. An eclipse of the sun 
is, however, merely the screening off of the sun's light from 
a particulai obseiver, and the sun may thciefoic be eclipsed 
to one observer while to another elsewhere it is visible as 
usual Hence in computing an eclipse of the sun it is 
necessary to take into account the position of the obseivcr 
on the earth. The simplest way of doing this is to make 
allowance for the difference of direction of the moon as 
seen by an observer at the place in question, and by an 
observer in some standaid position on the earth, preferably 


FIG v Parallax 

an ideal observer at the centre of the eaith If, in 
fig 31, M denote the moon, c the centre of the earth, 
A a point on the earth between c and M (at which thciefore 
the moon is overhead), and B any other point on the earth, 
then observers at c (or A) and B see the moon in slightly 
different directions, c M, B M, the difference between which 
is an angle known as the parallax, which is equal to the 
angle BMC and depends on the distance of the moon, 
the size of the earth, and the position of the observer 
at B In the case of the sun, owing to its great distance, 
even as estimated by the Greeks, the paiallax was in all 
cases too small to be taken into account, but m the case 
of the moon the parallax might be as much as 1 and 
could not be neglected. 

t4f 45] Hifparchus 61 

If then the path of the moon, as seen from the centre 
of the earth, were known, then the path of the moon as 
seen from any particular station on the earth could be 
deduced by allowing for parallax, and the conditions of 
an eclipse of the sun visible theie could be computed 

From the time of Hippaichus onwards lunar eclipses 
could easily be predicted to within an houi or two by 
any ordinary astronomer , solai eclipses probably with less 
accuracy; and in both cases the prediction of the extent of 
the eclipse, ze of what poition of the sun 01 moon would 
be obscured, probably left very much to be desired 

44 The great services rendered to astionomy by Hippai- 
chus can hardly be better expiessed than in the words of 
the great Fiench historian of astronomy, Delambie, who is 
in geneial no lenient critic of the work of his piedecessors 

" When we consider all that Hipparchus invented or perfected, 
and reflect upon the number of his works and the mass oi 
calculations which they imply, we must regard him as one of 
the most astonishing men ot antiquity, and as the greatest oi all 
in the sciences which are not puiely speculative, and which 
requne a combination oi geometrical knowledge with a 
knowledge of phenomena, to be observed only by diligent 
attention and refined instruments " * 

45 Foi nearly three centuries after the death of Hippai- 
chus, the history of astionomy is almost a blank Several 
textbooks wnttcn dunng this period aie extant, shewing 
the gradual popularisation of his great discoveries Among 
the few things of interest in these books may be noticed 
a statement that the stars are not necessanly on the sur- 
face of a spheic, but may be at difleient distances from 
us, which, however, there are no means of estimating , a 
conjecture that the sun and stais are so fai of! that the eaith 
would be a mcie point seen fioin the sun and invisible 
from the stars , and a rc-statcment of an old opinion 
traditionally attributed to the Egyptians (whether of the 
Alexandrine pcnod or eorhci is imceitam), that Venus and 
Meicuiy revolve icund the sun Jt seems also that in this 
period some attempts wcie made to explain the planctaiy 

ic Ancwnnc, Vol L, p 185 

62 A Short History of Astronomy [CH ir 

motions by means of epicycles, but whether these attempts 
maiked any advance on what had been done by Apollonms 
and Hipparchus is uncertain 

It is interesting also to find in Phny (A D 23-79) tne 
well-known modern aigument foi the spherical form of the 
earth, that when a ship sails away the masts, etc , lemam 
visible after the hull has disappeared from view 

A new measurement of the circumference of the eaith by 
Posidomus (born about the end of Hipparchus's life) may 
also be noticed , he adopted a method similar to that of 
Eratosthenes ( 36), and arrived at two different results 
The later estimate, to which he seems to have attached 
most weight, was 180,000 stadia, a result which was about 
as much below the truth as that of Eratosthenes was 
above it 

46. The last great name in Greek astronomy is that 
of Claudius Ptolemaeus, commonly known as Ptolemy, of 
whose life nothing is known except that he lived in 
Alexandria about the middle of the 2nd century AD 
His reputation lests chiefly on his gieat astronomical 
treatise, known as the Almagest* which is the source 
from which by far the greater part of our knowledge of 
Greek astronomy is derived, and which may be fairly 
regarded as the astronomical Bible of the Middle Ages 
Several other minor astronomical and astrological treatises 
are attributed to him, some of which are probably not 
genuine, and he was also the author of an important work 
on geography, and possibly of a treatise on Of tics, which 
is, however, not certainly authentic and maybe of Aiabian 
origin _ The Of tics discusses, among other topics, the 
refraction 01 bending of light, by the atmosphere on the 
earth it is pointed out that the light of a stai 01 othci 
heavenly body s, on entering our atmosphere (at \) and on 
penetrating to the lowei and denser portions of it, must 
be gradually bent or refracted, the lesult being that the 

* The chief Mb bears the title ^7^77 o-tfm^s, or great composi- 
tion .though the author refers to his book elsewhere as /wtflmtartd) 

(mathematical composition) The Arabian translators eithci 
thiough admiration 01 caiele&sncss, converted peyfaif, great, into 
^y^rrj, greatest, and hence it became known by the Axabs as 
At Magistt, whence the Latin Almageshim and oui 

1 46, 47] 


stai appeais to the observer at B nearer to the zenith z 
than it actually is, i e the light appeals to come from s' 
instead of from s , it is shewn further that this effect must 
be gieater for bodies near the horizon than for those near 
the zenith, the light fiom the former travelling thiough 
a greater extent of atmosphere, and these results are 
shewn to account for certain observed deviations m the 
daily paths of the stars, by which they appear unduly 
raised up when near the horizon Refraction also explains 
the well-known flattened appearance of the sun 01 moon 
when rising or setting, the lower edge being raised by 

FIG 32 Refraction by the atmosphcic 

refraction more than the upper, so that a contraction of 
the veitical diametei lesults, the horizontal contraction 
being much less. * 

47 The Almagest w avowedly based largely on the woik 
of cailtci astionomers, and in particular on that of Hippai- 
chus, for whom Ptolemy continually expresses the greatest 
admiration and respect Many of its contents have there- 
fore already been dealt with by anticipation, and need not 
be discussed again in detail. The book plays, however, 
such an mipoHont part in astronomical history, that it 
may be worth while to give a shoit outline of its contents, 

* The bettei known appaienl cnlaigemcnl ot the sun or moon 
when using 01 setting has nothing to do with icii action It is an 
optical illusion not veiy satisfactory explained, but probably due to 
the lessei bnlhancy oi the sun at the time, 

64 A Short History of Astronomy [CH n 

in addition to dealing more fully with the parts m which 
Ptolemy made important advances 

The Almagest consists altogether of 13 books The 
first two deal with the simpler observed facts, such as the 
daily motion of the celestial sphere, and the general 
motions of the sun, moon, and planets, and also with a 
number of topics connected with the celestial sphere and 
its motion, such as the length of the day and the times 
of rising and setting of the stais m different zones of the 
earth 3 there aie also given the solutions of some important 
mathematical problems, 1 ' and a mathematical tablet of 
considerable accuracy and extent But the most interest- 
ing parts of these introductory books deal with what may 
be called the postulates of Ptolemy's astronomy (Book I , 
chap 11.) The first of these is that the earth is spherical ; 
Ptolemy discusses and rejects various alternative views, 
and gives several of the usual positive arguments foi a 
spherical form, omitting, however, one of the strongest, 
the eclipse argument found m Aristotle ( 29), possibly 
as being too lecondite and difficult, and adding the 
argument based on the increase in the aiea of the eaith 
visible when the observer ascends to a height. In his 
geography he accepts the estimate given by Posidonius 
that the circumfeience of the earth is 180,000 stadia The 
other postulates which he enunciates and for which he 
argues are, that the heavens are spherical and revolve like 
a sphere , that the earth is m the centre of the heavens, 
and is merely a point in comparison with the distance of 
the fixed stars, and that it has no motion. The position 
of these postulates in the treatise and Ptolemy's general 
method of piocedure suggest that he was treating them, not 
so much as important results to be established by the best 
possible evidence, but rather as assumptions, more pio- 
bable than any otheis with which the author was acquainted, 
on which to base mathematical calculations which should 
explain observed phenomena. $ His attitude is thus 

* In spherical trigonometry 

j- A table of choids (or double sines of half-angles) foi every ?, 
from o to 1 80 

J His proceduie may be compared with that of a political 
economist of the school of Ricardo, who, in order to establish some 

48] The Almagest 65 

essentially different from that either of the early Greeks, 
such as Pythagoras, or of the controversialists of the i6th 
and early i7th centuries, such as Galilei (chapter vi ), for 
whom the truth or falsity of postulates analogous to those 
of Ptolemy was of the very essence of astronomy and was 
among the final objects of inquiry The arguments which 
Ptolemy produces in support of his postulates, arguments 
which were probably the commonplaces of the astronomical 
wilting of his time, appeal to us, except in the case of 
the shape of the earth, loose and of no great value 
The other postulates were, in fact, scarcely capable of 
eithei proof or dispioof with the evidence which Ptolemy 
had at command His argument in favour of the immo- 
bility of the earth is interesting, as it shews his clear 
peiception that the more obvious appearances can be 
explained equally well by a motion of the stais or by a 
motion of the earth , he concludes, however, that it is 
easier to attribute motion to bodies like the stars which 
seem to be of the nature of fiie than to the solid earth, 
and points out also the difficulty of conceiving the earth to 
have a rapid motion of which we are entirely unconscious. 
He does not, however, discuss seiiously the possibility that 
the earth or even Venus and Mercury may i evolve round 
the sun 

The thud book of the Almagest deals with the length of 
the year and theory of the sun, but adds nothing of import- 
ance to the work of Hipparchus 

48 The fomth book of the Almagest, which treats of 
the length of the month and of the theoiy of the moon, 
contains one of Ptolemy's most impoiiant discoveries We 
have seen that, apait from the motion of the moon's oibit 
as a whole, and the revolution of the line of apses, the 
chief irregularity or inequality was the so-called equation 
of the centre ( 39, 40), represented fairly accurately by 

rough explanation of economic phenomena, starts with certain simple 
assumptions as to human nature, which at any rate aie more plausible 
than any other equally simple set, and deduces horn them a numbci 
oi abfatiact conclusions, the applicability ol which to ical life has 
to he considered in individual cases But the pcifunctoiy discussion 
which such a wnter gives ot the qualities oi the "economic man" 
cannot of course be legarded as his deliberate and final estimate 
of human natuie, 

66 A Short History of Astronomy [CH n 

means of an eccentric, and depending only on the position 
of the moon with respect to its apogee Ptolemy, however, 
discovered, what Hipparchus only suspected, that theie 
was a further inequality in the moon's motion to which 
the name evection was afterwaids given and that this 
depended partly on its position with respect to the sun 
Ptolemy compared the observed positions of the moon with 
those calculated by Hipparchus m various positions lelativc 
to the sun and apogee, and found that, although there was 
a satisfactory agreement at new and full moon, theie was a 
considerable eiror when the moon was half- full, provided 
it was also not very neai perigee or apogee Hipparchus 
based his theory of the moon chiefly on observations of 
eclipses, 2 e on observations taken necessarily at full or new 
moon ( 43), and Ptolemy's discovery is due to the fact 
that he checked Hipparchus's theory by observations taken 
at other times, To represent this new inequality, it was 
found necessary to use an epicycle and a deferent, the latter 
being itself a moving eccentric circle, the centie of which 
revolved round the earth To account, to some extent, for 
certain remaining discrepancies between theory and obser- 
vation, which occuired neither at new and full moon, nor 
at the quadratures (half-moon), Ptolemy introduced fuither 
a certain small to-and-fro oscillation of the epicycle, an 
oscillation to which he gave the name of prosneusis * 

h The equation of the centre and the evection may be expressed 
tngonometncally by two terms in the expiession foi the moon's 
longitude, a sm 6 -t- b sm (20- 0), wheie a, b aie two numerical 
quantities, m round numbcis 6 and i, 6 is the angular distance oi 
the moon fiom perigee, and </> is the angular distance fiom the sun 
At conjunction and opposition is o or 180, and the two teims 
i educe to (a ) stn 9 This would be the lorm in which the 
equation of the centre would have presented itself to Hipparchus 
Ptolemy's correction is therefore equivalent to adding on 

b [stn 6 4* stn (2 0)], or 2 6 sm cos (00), 
which vanishes at conjunction or opposition, but reduces at the 
quadratures to 2 b sin 0, which again vanishes if the moon is at apogee 
or perigee (8 = o or 180), but has its gieatest value half-way 
between, when 6 = 90 Ptolemy's construction gave rise also to 
a still smaller teim of the type, 

c sm 2 <p [cos (2 + 0) H- 2 cos (2 0)], 

which, it will be observed, vanishes at quadratures as well as at 
conjunction and opposition, 

s^ 19] The Almagest 67 

Ptolemy thus succeeded in fitting his theory on to his 
observations so well that the error seldom exceeded 10', 
a small quantity m the astionomy of the time, and on 
the basis of this constmction he calculated tables from 
which the position of the moon at any requned time could 
be easily deduced 

One of the inherent weaknesses of the system of epi- 
cycles occurred in this theoiy in an aggiavated foim It 
has already been noticed in connection with the theory of 
the sun ( 39), that the eccentric or epicycle pioduced an 
erroneous variation in the distance of the sun, which was, 
however, imperceptible in Greek times Ptolemy's system, 
however, repiesented the moon as being sometimes nearly 
twice as far off as at others, and consequently the appaient 
diameter ought at some times to have been not much moie 
than half as great as at otheis a conclusion obviously 
inconsistent with observation It seems piobable that 
Ptolemy noticed this difficulty, but was unable to deal with 
it , it is at any late a significant fact that when he is dealing 
with eclipses, foi which the apparent diameters of the sun 
and moon are of importance, he entirely rejects the estimates 
that might have been obtained fiom his lunai theory and 
appeals to duect observation (cf also 51, note) 

49 The fifth book of the Almagest contains an account 
of the construction and use of Ptolemy's chief astronomical 
instiument, a combination of graduated circles known as 
the astrolabe. * 

Then follows a detailed discussion of the moon's 
paiallav ( 43), and of the distances of the sun and moon 
Ptolemy obtains the distance of the moon by a parallax 
method which is substantially identical with that still in use 
If we know the direction of the line c M (fig 33) joining the 
centres of the earth and moon, 01 the direction of the 
moon as seen by an observer at A , and also the direction 
of the line B M, that is the dnection of the moon as seen 
by an observer at B, then the angles of the triangle c B M 
are known, and the mtio of the sides c B, CM is known 

* Heic, as elsewhere, I have given no detailed account ot astro- 
nomical mstiuments, believing such descuptions to be m gcncial 
neither mteiesting nor intelligible to those who have not the actual 
mslj.umen.ts before them, and to be of little use to those who have 

68 A Short History of Astronomy [Cn II 

Ptolemy obtained the two directions lequired by means 
of observations of the moon, and hence found that c M 
was 59 times c B, or that the distance of the moon was 
equal to 59 times the radius of the earth He then uses 
Hipparchus's eclipse method to deduce the distance of the 
sun from that of the moon thus ascertained, and finds 
the distance of the sun to be 1,210 times the radius of 
the earth This number, which is substantially the same 
as that obtained by Hippaichus (41), is, however, only 

FIG 33. -Parallax 

about -JTJ of the tme number, as indicated by modem 
work (chapter xni , 284) 

The sixth book is devoted to eclipses, and contains no 
substantial additions to the work of Hippaichus 

50 The seventh and eighth books contain a catalogue of 
stars, and a discussion of precession ( 42) The catalogue, 
which contains 1,028 stais (three of which are duplicates), 
appears to be nearly identical with that of Hippaiehus 
It contains none of the stars which weie visible to Ptolemy 
at Alexandna, but not to Hipparchus at Rhodes Moi tr- 
over, Ptolemy professes to deduce fiom a companson of 
his observations with those of Hippaichus and othets the 
(erroneous) value 36" for the precession, which Hipparchus 
had given as the least possible value, and which Ptolemy 
regards as his final estimate, But an examination of 

so, 51] The Almagest 69 

the positions assigned to the stars in Ptolemy's catalogue 
agrees better with their actual positions in the time of 
Hipparchus, corrected for precession at the supposed rate of 
36" annually, than with their actual positions in Ptolemy's 
time It is therefoie probable that the catalogue as a 
whole does not represent genuine observations made by 
Ptolemy, but is substantially the catalogue of Hipparchus 
coriected foi precession and only occasionally modified by 
new observations by Ptolemy or others. 

51. The last five books deal with the theory of the 
planets, the most important of Ptolemy's original contribu- 
tions to astionomy The problem of giving a satisfactory 
explanation of the motions of the planets was, on account 
of their far greater irregularity, a much more difficult one 
than the corresponding pioblem for the sun or moon The 
motions of the lattei are so nearly uniform that their 
irregularities may usually be regaided as of the natme of 
small corrections, and for many purposes may be ignoied 
The planets, however, as we have seen (chapter i , 14), do 
not even always move from west to east, but stop at intervals, 
move in the reverse dnection foi a time, stop again, and 
then move again in the original direction It was probably 
recognised in early times, at latest by Eudoxus ( 26), that 
in the case of three of the planets, Mais, Jupiter, and Saturn, 
these motions could be represented roughly by supposing 
each planet to oscillate to and fro on each side of a fictitious 
planet, moving uniformly round the celestial spheie in or 
near the ecliptic, and that Venus and Mercury could 
similaily be regarded as oscillating to and fro on each side 
of the sun These lough motions could easily be inter- 
preted by means of revolving spheres or of epicycles, as was 
clone by Eudoxus and piobably again with more precision 
by Apollomus In the case of Jupitei, for example, we 
may regaid the planet as moving on an epicycle, the centre 
of which, y, describes uniformly a deferent, the centre of 
which is the eaith The planet will then as seen Irom the 
caith appear alternately to the cast (as at TI) and to the 
west (as at Q of the fictitious planet j } and the extent of 
the oscillation on each side, and the mtcival between suc- 
cessive appearances in the extiemc positions (j b J 2 ) on eithei 
side, can be made right by choosing appropriately the size 

A Short History of Astronomy 

I 1 -- 11 

and rapidity of motion of the epicycle It is moreovei 
evident that with this arrangement the appaient motion 
of Jupiter will vary considerably, as the two motions Out 
on the epicycle and that of the centre of the epicycle on 
the defeient are sometimes m the same direction, so as 
to increase one another's effect, and at other times m 
opposite directions Thus, when Jupiter is most distant 
from the earth, that is at J 3 , the motion is most rapid, at 
j, and J 9 the motion as seen from the earth is nearly the 
same as" that of j, while at j, the two motions are in 

opposite directions, and. the 
size and motion of the epi- 
cycle having been chosen in 
the way indicated above, 
it is found in fact that the 
motion of the planet m the 
epicycle is the gi eatei of the 
two motions, and that thcio- 
fore the planet when in 
this position appeals to be 
moving from east to west 
(from left to light m the 
figure), as is actually the 
case As then at ]\ and 
j, the planet appears to 
be moving fiom west to 
east, and at J 4 in the opposite direction, and sudden 
changes of motion do not occui m astionomy, there must 
be a position between ] l and j t , and another between 
j, and j,, at which the planet is just reveismg its direction 
of motion, and therefoie appears for the instant at rest 
We thus arrive at an explanation of the stationaiy points 
(chapter i , 14) An exactly similar scheme explains 
roughly the motion of Meicuiy and Venus, except that 
the centre of the epicycle must always be m the direction 
of the sun 

Hipparchusj as we have seen ( 41), found the cunent 
lepresentations of the planetary motions macanate, and 
collected a number of fresh observations These, with 
fresh observations of his own, Ptolemy now employed 
in order to construct an impioved planetary system. 

FIG 34 Jupiter's epicycle 
and deferent 

si] The Almagest 71 

As m the case of the moon, he used as deferent an 
eccentric circle (centre c), but instead of making the 
centre j of the epicycle move uniformly in the deferent, he 
introduced a new point called an eguant (E'), situated at 
the same distance from the centie of the deferent as the 
earth but on the opposite side, and legulated the motion of 
j by the condition that the apparent motion as seen from the 
equant should be uniform , m other words, the angle A E' j 
was made to increase uniformly In the case of Mercury 
(the motions of which have been found troublesome by 
astronomers of all periods), 
the relation of the equant to 
the centre of the epicycle was 
different, and the latter was 
made to move in a small 
circle The deviations of the 
planets from the ecliptic 
(chapter i , 13, 14) were 
accounted for by tilting up 
the planes of the several 
deferents and epicycles so 
that they were inclined to the 
ecliptic at various small angles 

By means of a system of this FIG 35 The equant 
kind, worked out with gieat 

care, and evidently at the cost of enormous labour, Ptolemy 
was able to repicsent with very fan exactitude the motions 
of the planets, as given by the observations m his possession. 

It has been pointed out by modern cutics, as well as by 
some mediaeval writeis, that the use of the equant (which 
played also a small part in Ptolemy's lunai theory) was a 
violation of the principle of employing only uniform cucular 
motions, on which the systems of Hipparchus and Ptolemy 
were supposed to be based, and that Ptolemy himself 
appeared unconscious of his inconsistency It may, how- 
evei, fairly be doubted whether Hipparchus or Ptolemy 
ever had an abstract belief in the exclusive virtue of such 
motions, except as a convenient and easily intelligible 
way of icpresentmg certain more complicated motions, 
and it is difficult to conceive that Hipparchus would have 
scrupled any moie than his great follower, in using an 

72 A Short History of Astronomy pen n 

equant to represent an irregular motion, if he had found 
that the motion was thereby represented with accuracy 
The criticism appears to me in fact to be an anachronism 
The earlier Gieeks, whose astronomy was speculative rather 
than scientific, and again many astronomers of the Middle 
Ages, felt that it was on a priori grounds necessary to re- 
present the " perfection " of the heavenly motions by the 
most "perfect" or regular of geometrical schemes, so that 
it is highly probable that Pythagoras or Plato, or even 
Aristotle, would have objected, and certain that the 
astronomers of the i4th and i5th centuries ought to have 
objected (as some of them actually did), to this innova- 
tion of Ptolemy's But there seems no good reason foi 
attributing this a priori attitude to the later scientific Greek 
astronomers (cf also 38, 47) * 

It will be noticed that nothing has been said as to the 
actual distances of the planets, and in fact the appaient 
motions are unaffected by any alteiation in the scale on 
which defeient and epicycle aie constructed, piovided that 
both are altered proportionally Ptolemy expiessly states that 
he had no means of estimating numerically the distances of 
the planets, or even of knowing the order of the distance of 
the several planets He followed tradition in accepting 
conjecturally lapidity of motion as a test of nearness, and 
placed Mars, Jupiter, Satuin (which peiform the cncuit 
of the celestial spheie in about 2, 12, and 29 years re- 
spectively) beyond the sun m that order As Venus and 

* The advantage derived from the use of the equant can be made 
clearei by a mathematical comparison with the elliptic motion in- 
troduced by Kepler In elliptic motion the angulai motion and 
distance are lepresented approximately by the foimulse nt + 2e 6z;/ jf, 
a (i c cos nt} respectively, the coiiesponclma, foimuUxj given by 
the use of the simple eccentric aie nt + e' tin tit, a (i e f cos tit) 
To make the angulai motions agree we must thercfoie take <?' = 2c, 
but to make the distances agree we must take c' = e , the two con- 
ditions are theicfore inconsistent But by the introduction oi an 
equant the formulae become itt + 2c' sin nt, a (i c' co& ;//), and 
both agree if we take c' = c Ptolemy's lunai theory could have 
been neaily liced fiom the serious difficulty aheacly noticed (^ 48) 
if he had used an equant to represent' the chief inequality ot the 
moon, and his planetaiy theory would have been made accuiatc 
to the first order of small quantities by the use of an equant both 
for the deferent and the epicycle. 

52, ssl Ptolemy and Jus Successors 73 

Mercury accompany the sun, and may therefore be legarded 
as on the aveiage performing their revolutions m a year, 
the test to some extent failed in their case, but Ptolemy 
again accepted the opinion of the " ancient mathematicians " 
(i e probably the Chaldaeans) that Mercmy and Venus he 
between the sun and moon, Mercury being the nearei to 
us (Cf chapter i , 15 ) 

52 There has been much difference of opinion among 
astronomers as to the merits of Ptolemy Throughout the 
Middle Ages his authority was regarded as almost final on 
astronomical matters, except where it was outweighed by 
the even greatei authority assigned to Aristotle Modem 
ciiticism has made clear, a fact which indeed he nevei 
conceals, that his work is to a large extent based on that 
of Hipparchus , and that his observations, if not actually 
fictitious, weie at any rate in most cases poor. On the 
other hand his work shews clearly that he was an accom- 
plished and original mathematician * The most important 
of his positive contnbutions to astronomy were the discovery 
of evection and his planetary theoiy, but we ought probably 
to rank above these, important as they are, the seivices 
which he tendered by picservtng and developing the great 
ideas of Hipparchus ideas which the other astronomers 
of the time weie probably incapable of appreciating, and 
which might easily have been lost to us if they had not 
been embodied in the Almagest 

53 The histoiy of Gieek astronomy practically ceases 
with Ptolemy The practice of observation died out so 
completely that only eight obseivations are known to have 
been made during the eight and a half centuries which 
sepaiate him from Albategnius (chapter in , 59) The 
only Greek wiiters aftci Ptolemy's time are compileis and 
commentatois, such as Theon (// A D 365), to none of 
whom original ideas of any mipoitance can be attributed. 
The murder of his daughtei Hypatia (AD 415), herself 
also a writer on astionomy, maiks an epoch m the decay 
of the Alexandrine school , and the end came in \ D 640, 
when Alcxanclna was captuicd by the Aiabs t 

* De Moigan classes him as a geomctei with Archimedes, Euclid, 
and Apollomus, the thiee great gcomctcis of antiquity 
f The legend that the books in the hbiaiy bcivcd foi &ix months as 

74 A Short History of Astronomy [Cn n 

54 It remains to attempt to estimate buefly the value of 
the contributions to astronomy made by the Greeks and of 
their method of investigation It is obviously umeasonable 
to expect to find a brief formula which will characterise the 
scientific attitude of a series of astronomers whose lives 
extend over a period of eight centuries , and it is futile 
to explain the inferiority of Greek astronomy to our own on 
some such ground as that they had not discovered the method 
of induction, that they were not careful enough to obtain 
facts, or even that then ideas were not clear In habits 
of thought and scientific aims the contrast between Pytha- 
goras and Hipparchus is probably greater than that between 
Hipparchus on the one hand and Coppermcus or even 
Newton on the other, while it is not unfan to say that the 
fanciful ideas which peivade the work of even so great a 
discoverer as Kepler (chaptei vii , 144, 151) place his 
scientific method in some respects behind that of his great 
Greek predecessoi 

The Gieeks inherited from their piedecessors a number 
of observations, many of them executed with considerable 
accuracy, which were nearly sufficient for the lequirements 
of piactical life, but in the matter of astronomical theory 
and speculation, m which their best thinkers were very 
much more interested than in the detailed facts, they 
received virtually a blank sheet on which they had to write 
(at first with indifferent success) their speculative ideas 
A considerable interval of time was obviously necessaiy to 
bridge over the gulf separating such data as the eclipse 
observations of the Chaldaeans from such ideas as the 
harmonical spheres of Pythagoras , and the necessary 
theoretical structuie could not be erected without the use 
of mathematical methods which had giadually to be in 
vented That the Greeks, paiticularly in early times, paid 
little attention to making obseivations, is tiue enough, bill 
it may fanly be doubted whether the collection of nesb 
material foi observations would leally have camcc 
astronomy much beyond the point reached by the 
Chaldaean observel s When once speculative ideas, made 

iuel for the iurnaccs of the public baths is i ejected by Gibbon anc 
otlicis One good leason for not accepting it is that by this tmi< 
there were probably veiy few bookb left to burn 

$ s-0 Estimate of Greek Astronomy 75 

definite by the aid of geometiy, had been sufficiently 
developed to be capable of comparison with observation, 
rapid progress was made The Greek astronomers of the 
scientific penod, such as Anstarchus, Eiatosthenes, and 
above all Hipparchus, appear moi cover to have followed 
in their researches the method \\hich has always been 
fruitful in physical science namely, to frame provisional 
hypotheses, to deduce their mathematical consequences, 
and to compare these with the lesults of observation 
There are few better illustrations of genuine scientific 
caution than the way in which Hipparchus, having tested 
the planetary theories handed down to him and having 
discovered their insufficiency, dehbeiately abstained from 
building up a new theory on data which he knew to be 
insufficient, and patiently collected fresh matenal, never to 
be used by himself, that some future astronomer might 
thereby be able to arrive at an impiovcd theory 

Of positive additions to our astronomical knowledge 
made by the Greeks the most stnkmg m some ways is the 
discovery of the approximately spherical foim of the earth, 
a result which later woik has only slightly modified But 
then explanation of the chief motions of the solai system 
and their resolution of them into a compaiatively small 
number of simpler motions was, in reality, a far more im- 
portant contribution, though the Greek epicychc scheme 
has been so remodelled, that at first sight it is difficult to 
recognise the relation between it and our modern views 
The subsequent histoiy will, howevci, show how completely 
each stage in the progress of astronomical science has 
depended on those that preceded 

When we study the gieat conflict in the time of Coppei- 
mcus between the ancient and modern ideas, our sympathies 
naturally go out towards those who supported the lattei, 
which are now known to be moic accuiate, and we are apt to 
foiget that those who then spoke in the name of the ancient 
astionomy and quoted Ptolemy weic indeed believers in 
the doctrines which they had cleaved fiom the Greeks, but 
that then methods of thought, their frequent refusal to face 
facts, and their appeals to authority, weic all entirely 
foreign to the spirit of the great men whose disciples they 
believed themselves to be 



"The lamp burns low, and through the casement bais 
Grey morning glimmers feebly " 

BROWNING'S Paracelsus 

55 ABOUT fourteen centuries elapsed between the publica- 
tion of the Almagest and the death of Coppernicus (1543), 
a date which is in astronomy a convenient landmaik on the 
boundaiy between the Middle Ages and the modern world 
In this penod, nearly twice as long as that which separated 
Thales from Ptolemy, almost four times as long as that 
which has now elapsed since the death of Coppernicus, no 
astronomical discovery of first-rate importance was made. 
There were some impoitant advances in mathematics, and 
the art of observation was improved , but theoretical 
astronomy made scarcely any pi ogress, and m some respects 
even went backwaid, the current doctrines, if m some 
points slightly moie coriect than those of Ptolemy, being 
less intelligently held 

In the Western World we have already seen that there 
was little to record for nearly five centimes after Ptolemy 
Aftei that time ensued an almost total blank, and several 
moie centimes elapsed before there was any appreciable 
revival of the interest once felt in astronomy 

56 Meanwhile a rcmaikablc development of science had 
taken place m the East during the ;th century The 
descendants of the wild Aiabs who had earned the bannei 
of Mahomet ovei so large a part of the Roman empuc, as 
well as over lands lying farthei east, soon began to feel the 
influence of the civilisation of the peoples whom they had 
subjugated, and Bagdad, which m the 8th century became 


CH in , < ss, 56] The Bagdad School 77 

the capital of the Caliphs, rapidly developed into a centre of 
literary and scientific activity Al Mansur, who leigned 
from AD 754 to 775, was noted as a patron of science, 
and collected round him learned men both from India and 
the West In particular we are told of the arrival at his 
court in 772 of a scholar from India bearing with him an 
Indian treatise on astronomy/ which was translated into 
Arabic by order of the Caliph, and remained the standard 
treatise foi nearly half a centuiy Fiom Al Mansui's time 
onwards a body of scholais, m the first instance chiefly 
Syrian Christians, were at work at the court of the Caliphs 
translating Gieek wntings, often through the medium of 
Syriac, into Arabic The first translations made were of 
the medical tieatises of Hippocrates and Galen, the 
Anstotelian ideas contained in the latter appear to have 
stimulated interest in the writings of Anstotle himself, and 
thus to have enlarged the range of subjects legaided as 
worthy of study Astronomy soon followed medicine, and 
became the favourite science of the Arabians, partly no doubt 
out of genuine scientific interest, but probably still more for 
the sake of its practical applications Certain Mahometan 
ceiemonial obseivances requned a knowledge of the 
dnection of Mecca, and though many woi shippers, living 
anywhere between the Indus and the Stiaits of Gibraltar, 
must have satisfied themselves with icugh-and-ieady 
solutions of this problem, the assistance which astionomy 
could give in fixing the tme direction was welcome in 
larger centies of population The Mahometan calendai, 
a lunar one, also required some attention in order that 
fasts and feasts should be kept at the pioper times Moie- 
over the belief in the possibility of piedicting the futuie 
by means of the stais, which had flounshed among the 
Chaldaeans (chapter i , 18), but which remained to a gicat 
extent m abeyance among the Gieeks, now revived rapidly 
on a congenial oncntal soil, and the Caliphs were probably 
quite as much interested in seeing that the learned men of 

* The data as to Indian astronomy aic so unccitam, and the 
evidence ot any impoitant oiigmal contnbulions is so slight, that I 
have not thought it woith while to entci into the subject in any 
detail The chicl Indian treatises, including the one leicned to in 
the text, bear strong maiks oi having been based on Gieck writings 

78 A Short History of Astronomy [Cn in. 

their courts were proficient in astrology as in astronomy 

The first translation of the Almagest was made by oider 
of Al Mansur's successor Harun al Rasid (AD 765 01 766 
-A D. 809), the hero of the Arabian Nzg/its It seems, 
however, to have been found difficult to translate , fresh 
attempts weie made by Honem ben Ishak ("MS 7 3) and 
by his son Ishak ben Honem (^-910 or 911), and a final 
version by Tabit ben Koira (836-901) appealed towaicls 
the end of the Qth century Ishak ben Honem translated 
also a number of other astionomical and mathematical 
books, so that by the end of the gth century, after which 
translations almost ceased, most of the more important 
Greek books on these subjects, as well as many mmoi 
treatises, had been translated. To this activity we owe 
our knowledge of several books of which the Greek originals 
have perished. 

57 Dm ing the penod m which the Caliphs lived at 
Damascus an observatory was erected theie, and another on 
a moie magnificent scale was built at Bagdad in 829 by the 
Caliph Al Mamun The instruments used were supenoi both 
in size and in woikmanship to those of the Greeks, though 
substantially of the same type. The Arab astronomeis 
introduced moreover the excellent piactice of making 
regular and as far as possible nearly continuous observa- 
tions of the chief heavenly bodies, as well as the custom 
of noting the positions of known stars at the beginning 
and end of an eclipse, so as to have aftei wards an exact 
record of the times of their occuircnce So much import- 
ance was attached to coiiect observations that \ve aie told 
that those of special interest weie recorded in formal 
documents signed on oath by a mixed body of astronomeis 
and lawyers 

Al Mamun ordered Ptolemy's estimate of the size of the 
earth to be verified by his astronomers Two separate 
measurements of a portion of a meridian were made, which, 
however, agreed so closely with one another and with 
the erroneous estimate of Ptolemy that they can haidly 
have been independent and careful measurements, but 
rather rough verifications of Ptolemy's figures 

58 The careful observations of the Arabs soon shewed 

n 57-60] The Bagdad School Albategmus 79 

the defects in the Greek astronomical tables, and new tables 
were from time to time issued, based on much the same 
principles as those in the Almagest, bat with changes in 
such numencal data as the relative sizes of the vanous 
circles, the positions of the apogees, and the inclinations 
of the planes, etc 

ToTabit ben Koira, mentioned above as the translatoi of 
the Almagest, belongs the doubtful honour of the disco\eiy 
of a supposed variation in the amount of the pieccssion 
(chapter n , 42, 50) To account for this he devised a 
complicated mechanism which pioduced a certain alteration 
in the position of the ecliptic, thus introducing a pmely 
imaginary complication, known as the trepidation, which 
confused and obscured most of the astronomical tables 
issued during the next five 01 six centuries 

59 A far greater astronomei than any of those mentioned 
in the pieceding articles was the Arab prince called 
from his birthplace Al Eattani, and bettei known by the 
Latinised name Albategnms^ who carried on obseivations 
from 878 to 918 and died in 929 He tested many of 
Ptolemy's lesults by fiesh observations, and obtained 
moie accuiate values of the obliquity of the ecliptic 
(chapter i, u) and of precession He wrote also a 
treatise on astronomy which contained improved tables 
of the sun and moon, and included his most notable dis- 
covery namely, that the direction of the point m the 
sun's orbit at which it is farthest from the taith (the 
apogee), or, in other woicls, the dnection of the centte of 
the ecccntnc icpie&enting the sun's motion (chapter n, 
39), was not the same as that given m the Almagest > 
from which change, too great to be aUnbutcd to ineie 
eirors of observation or calculation, it might lanly be 
mfencd that the apogee was slowly moving, a lesult which, 
however, he did not explicitly state Albategmus was also 
a good mathematician, and the authoi of some notable 
impiovements m methods of calculation l 

60, The last of the Bagdad astronomers was A bit I \Vafa 

Y lie intioduccd into tngonomUiy the use ol A/WS, and made also 
some little use ol ////'//&, without appai<iitly mihsmg tlien im- 
portaneL he also used SOUK new ionmiUr !<n the solution ol 
bpheiical tiianglcs. 

So A Short History of Astronomy [Cn in 

(939 or 94 ~998), the author of a voluminous treatise on 
astronomy also known as the Almagest., which contained 
some new ideas and was written on a different plan from 
Ptolemy's book, of which it has sometimes been supposed 
to be a translation In discussing the theory of the moon 
Abul Wafa found that, after allowing for the equation of 
the centre and foi the evection, there remained a fuither 
irregularity m the moon's motion which was imperceptible 
at conjunction, opposition, and quadratuie, but appieciable 
at the intermediate points It is possible that Abul AVafa 
here detected an inequality rediscovered by Tycho Biahe 
(chapter v., in) and known as the variation, but it 
is equally likely that he was merely restating Ptolemy's 
prosneusis (chapter n , 48) * In either case Abul Wafa's 
discovery appears to have been entirely ignored by his 
successors and to have borne no fruit He also earned 
further some of the mathematical improvements of his 

Another neaily contemporary astronomer, commonly 
known -as Ibn Yunos (?-ioo8), worked at Cano under 
the patronage of the Mahometan lulers of Egypt He 
published a set of astronomical and mathematical tables, 
the Hakemite Tables , which remained the standaid ones for 
about two centuries, and he embodied m the same book 
a number of his own obseivations as well as an extensive 
series by earlier Arabian astronomers 

6 1 About this time astronomy, in common with othci 
branches of knowledge, had made some progress in the 
Mahometan dominions m Spam and the opposite coast 
of Africa A great library and an academy were founded 
at Cordova about 970, and centres of education and learning 
were established in rapid succession at Coidova, Toledo, 
Seville, and Morocco 

The most important work produced by the aslronomeis 
of these places was the volume of astronomical tables 
published under the direction of ArzaJiel m 1080, and 
known as the Toletan Talks, because calculated for an 
observer at Toledo, where Aizachel probably lived To 

!! A prolonged but indecisive contioveisy has been earned on, 
chiefly by Fiench scholars, with regard to the iclations of Ptolemy. 
Abul Wafa, and Tycho m this matter, 

$ 6i, 62] 77^ Spanish School Nassir Eddin 81 

the same school are due some improvements m instru- 
ments and m methods of calculation, and several writings 
weie published in criticism of Ptolemy, without, however, 
suggesting any improvements on his ideas 

Giadually, however, the Spanish Christians began to drive 
back then Mahometan neighbouis Coiclova and Seville 
were captuied in 1236 and 1248 respectively, and with their 
fall Arab astronomy disappeaied fioni histoiy 

62 Eefoie we pass on to considei the pi ogress of 
astionomy in Euiope, two more astronomical schools of 
the East deserve mention, both of which illustrate an 
extiaordinanly rapid growth of scientific interests among 
barbaious peoples Hulagu Khan, a giandson of the 
Mongol conquei or Genghis Khan, captuied Bagdad in 1258 
and ended the rule of the Caliphs theie Some years 
befoie this he had received into favoui, partly as a political 
adviser, the astionomer Nassir Eddin (bom in 1201 at Tus 
in Khoiassan), and subsequently piovided funds foi the 
establishment of a magnificent observatoiy at Meraga, near 
the north-west fiontiei of modern Persia Heie a number 
of astionomers worked under the general supenntendence 
of Nassir Eddin The instruments they used were lemark- 
able foi their size and careful construction, and weie 
probably better than any used m Euiope in the time of 
Coppermcus, being surpassed fust by those of Tycho Brahe 
(chapter v ) 

Nassir Eddin and his assistants tianslated or commented 
on nearly all the more important available Greek writings 
on astionomy and allied subjects, including Euclid's 
Elements^ several books by Archimedes, and the Almagest 
Nassn Eddin also wrote an abstract of astronomy, maiked 
by some little originality, and a tieatise on geometry He 
does not appear to have accepted the authonty of Ptolemy 
without question, and objected m paiticulai to the use 
of the equant (chaptei n, 51), which he replaced by 
a new combination of spheies Many of these tieatises 
had for a long time a gieat leputation in the East, and 
became m their turn the subject-matter of commentary. 

But the gicat work of the Meiaga astionomers, which 
occupied them 12 years, was the issue of a levised set of 
astronomical tables, based on the Hakemite Tables of Ibn 


82 A Short History of Astronomy [Cn, in 

Yunos ( 60), and called in honour of their patron the 
Ilkhamc Tables They contained not only the usual tables 
for computing the motions of the planets, etc , but also a 
stai catalogue, based to some extent on new obseivations 

An important result of the obseivations of fixed stars 
made at Meraga was that the precession (chaptei n , 42) 
was fixed at 51", or within about i'' of its tiue value Nassu 
Eddm also discussed the supposed tiepidation ( 58), but 
seems to have been a little doubtful of its reality He died 
in 1273, soon after his patron, and with him the Meiaga 
School came to an end as rapidly as it was formed 

63 Nearly two centuries latei Ulugh Begh (born in 1394), 
a grandson of the savage Tartar Tameilane, developed a 
great personal interest in astronomy, and built about 1420 an 
observatory at Samarcand (in the present Russian Turkestan), 
wheie he worked with assistants He published fresh 
tables of the planets, etc , but his most important work 
was a star catalogue, embracing nearly the same stars as 
that of Ptolemy, but obseived afresh This was probably 
the first substantially independent catalogue made since 
Hipparchus The places of the stais were given with 
unusual piecision, the minutes as well as the degrees 
of celestial longitude and latitude being recorded, and 
although a comparison with modern observation shews 
that there were usually errors of several minutes, it is 
probable that the instruments used were extremely good 
Ulugh Begh was muidered by his son in 1449, an( ^ Wlt ^ 
him Tartar astronomy ceased 

64 No great original idea can be attubuted to any of the 
Arab and other astronomers whose work we have sketched 
They had, however, a remarkable aptitude for absorbing 
foreign ideas, and cany ing them slightly further. They 
were patient and accurate observers, and skilful calculators. 
We owe to them a long series of obseivations, and the 
invention or introduction of several important improve- 
ments in mathematical methods * Among the most 
important of their services to mathematics, and hence to 
astronomy, must be counted the introduction, from India, 

* For example, the practice of ti eating the trigonometrical functions 
as algebraic quantities to be manipulated by formulae, not meiely 
as geometrical lines. 

H 63-65] Ulugh Begk Estimate of Arab Astronomy 83 

of our present system of writing numbers, by which the 
value of a numeral is altered by its position, and fiesh 
symbols are not wanted, as in the clumsy Greek and 
"Roman systems, for higher numbers An immense sim- 
plification was thereby introduced into arithmetical work * 
More important than the actual original contnbutions of 
the Aiabs to astronomy was the service that they performed 
in keeping alive interest in the science and preset ving the 
discoveries of their Greek predecessors. 

Some curious relics of the time when the Aiabs weie 
the great masters in astronomy have been preserved in 
astronomical language Thus we have derived from them, 
usually in very coriupt foims, the cunent names of many 
individual stars, eg Aldebaran, Altan, Bctelgeux, Rigel, 
Vega (the constellations being mostly known by Latin 
translations of the Greek names), and some common 
astronomical terms such as zcmth and nadir (the invisible 
point on the celestial sphere opposite the zenith); while 
at least one such woid, almanack, has passed into common 
language. / 

65 In Europe the period of confusion following the break- 
up of the Roman empne and preceding the definite formation 
of feudal Europe is almost a blank as regards astronomy, 
or indeed any other natural science The best intellects 
that were not absorbed in practical life were occupied 
with theology. A few men, such as the Venerable Bede 
(67 2 -735)) hvmg fo r the most part in secluded monasteries, 
were noted for then learning, which included in general 
some portions of mathematics and astronomy , none were 
noted for then additions to scientific knowledge. Some 
advance was made by Chailemagnc (742-814), who, m 
addition to introducing something like older into his 
extensive dominions, made energetic attempts to develop 
education and learning In 782 he summoned to his court 
oui learned countryman Alcum (735-804) to givemsti action 
in astronomy, arithmetic, and rhetoric, as well as in othei 
subjects, and invited other scholars to join him, foimmg 
thus a kind of Academy of which Alcum was the head. 

* Any one who has not realised this may do so by pcilormmg 
with Roman numcials the simple opei ation oJt multiplying by ilseU 
a number such as MDCCCXCVIII 

84 A Short History of Astronomy ten ill. 

Charlemagne not only founded a higher school at his 
own court, but was also successful in urging the ecclesi- 
astical authorities m all parts of his dominions to do 
the same. In these schools were taught the seven liberal 
arts divided into the so-called tnvmm (giammar, rhctonc, 
and dialectic) and quadnvium, which included astionomy 
in addition to arithmetic, geometry, and music 

66. In the loth century the fame of the Arab learning 
began slowly to spread through Spam into othei paits of 
Europe, and the immense learning of Gerbert, the most 
famous scholar of the century, who occupied the papal 
chair as Sylvester II from 999 to 1003, was attributed in 
lar^e part to the time which he spent in Spam, either m 
or near the Moorish dominions He was an ardent student, 
indefatigable in collecting and reading laie books, and 
was especially interested m mathematics and astionomy 
His skill in making astiolabes (chapter n , 49) and other 
instruments was such that he was popularly supposed^ to 
have acquired his powers by selling his soul to the Evil 
One Other scholars shewed a similar inteiest in Aiabic 
learning, but it was not till the lapse of another centuiy 
that the Mahometan influence became impoitant 

At the beginning of the i2th century began a senes of 
tianslations from Arabic into Latin of scientific and 
philosophic treatises, paitly original woiks of the Arabs, 
partly Arabic translations of the Gieek books One of the 
most active of the translators was Plato of Tivoli, who 
studied Arabic in Spam about 1116, and translated Alba- 
tegnms's Ashonoiny ( 59), as well as other astionomical 
books At about the same time Euclid's Element*, among 
other books, was translated by Athelard of Bath G he tat do 
of Cremona (1114-1187) was even more mclustiious, and 
is said to have made tianslations of about 70 scientific 
treatises, including the Almagest, and the Tolctan lablcs 
of Arzachel ( 61) The beginning of the i3th centuiy was 
marked by the foundation of several Universities, and at 
that of Naples (founded m 1224) the Empeioi Roderick II , 
who had come into contact with the Mahometan learning 
in Sicily, gathered together a number of scholars whom he 
duected to make a fiesh series of translations from the 

* 66, 6?3 The Revival of Astwnomy m the West 85 

Aristotle's writings on logic had been pieserved m 
Latin translations from classical times, and were already 
much esteemed by the scholars of the nth and i2th 
centuries His other writings were first met with m Arabic 
versions, and were translated into Latin during the end 
of the 1 2th and during the i 3 th centuries, m one or two 
cases translations were also made from the original Greek 
The influence of Aristotle over mediaeval thought, already 
considerable, soon became almost supreme, and his works 
were by many scholars regarded with a reverence equal to 
or greater than that felt for the Chnstian Fathers 

Western knowledge of Aiab astronomy was very much 
increased by the activity of Alfonso X of T eon and Castile 
(1223-1284), who collected at Toledo, a lecent conquest 
fiom the Arabs, a body of scholars, Jews and Christians 
who calculated undei his general superintendence a set of 
new astronomical tables to supeisede the Toletan Tables 
ihese Alfonsine Tables were published in 1252, on the 
day of Alfonso's accession, and spread lapidly 'thiou*h 
Euiope They embodied no new ideas, but several 
numerical data, notably the length of the year were 
given with greater accuiacy than before To Alfonso is 
due also the publication of the Libros del Saber, a volu- 
minous encyclopaedia of the astionomical knowledge of 
the time, which, though compiled largely fiom Arab sources 
was not, as has sometimes been thought, a mere collection 
of translations One of the cunosities in this book is a 
diagram rcpiesentmg Mercuiy's oibit as an ellipse the 
eaith being in the centre (cf chapter vii , T4 o), this 
being probably the first trace of the idea of repiesentmg 
the celestial motions by means of cuives other than circles 
67 To the i3th century belong also several of the great 
scholars, such as Albertus Ma^nm, Roger Bacon, and 
Lecco dAscoh (from whom Dante learnt), who took all 
knowledge for their province. Rogei Bacon, who was born 
m Somersetshire about 1214 and died about 1294, wrote 
three pnncipal books, called lespccnvely the Opus Ma -m* 
Opus Minus, and Opu, Tertntm, which contained not only 
tieatiscs on most existing branches of knowledge, but also 
some extremely mteicstmg discussions of their relative 
impoitancc and of the right method foi the advancement 

86 A Short History of Astronomy [CH in 

of learning. He inveighs warmly against excessive aclhei - 
ence to authority, especially to that of Aristotle, whose 
books he wishes burnt, and speaks stiongly of the impoit 
ance of experiment and of mathematical icasoning m 
scientific inquiries He evidently had a good knowledge 
of optics and has been supposed to have been acquainted 
with the telescope, a supposition which we can haidly 
regard as confirmed by his story that the invention was 
known to Caesar, who when about to invade Liitam sui- 
veyed the new country from the opposite shores of Gaul 
with a telescope ! . . 

Another famous book of this penod was written by the 
Yorkshireman John Halifax or Holywood, bcttei known 
by his Latinised name Sacrobosco, who was foi some time 
a well-known teacher of mathematics at Pans, wheie he 
died about 1256 His Sphaera Mundi was an elemental y 
treatise on the easier parts of cmrent astronomy, dealing 
in fact with little but the more obvious results of the 
daily motion of the celestial sphere It enjoyed immense 
popularity for three or four centuries, and was frequently 
re-edited, translated, and commented on it was one of 
the very first astronomical books ever punted , 25 editions 
appeared between 1472 and the end of the century, and 
40 more by the middle of the iyth century 

68 The European writers of the Middle Ages whom we 
have hitherto mentioned, with the exception of Alfonso and 
his assistants, had contented themselves with collecting and 
rearranging such portions of the astronomical knowledge 
of the Greeks and Arabs as they could mastei , theie weie 
no serious attempts at making progress, and no obsewations 
of importance were made A new school, however, giew 
up m Germany during the I5th century which suceei-ded 
in making some additions to knowledge, not in themselves 
of first-rate impoitance, but significant of the gieatei inde- 
pendence that was beginning to inspire scientific woik 
George Purbach^ born in 1423, became m 1450 professoi 
of astronomy and mathematics at the Umveisily of Vienna, 
which had soon after its foundation (1365) become a 
centre for these subjects He theic began an fipitom? 
of Astronomy based on the Almaget> and also a Latin 
veision of Ptolemy's planetary theoiy, intended pailly 

68j Sacrobosco, Purbach^ Regiomontamts 87 

as a supplement to Sacrobosco's textbook, from which 
this part of the subject had been omitted, but m part 
also as a treatise of a highei oidei , but he was hindered 
m both undertakings by the badness of the onlj available 
veisions of the Almage* /--Latin translations which had 
been made not duectly from the Gieek, but thiouo-h 
the medium at any late of Arabic and veiy possibly of 
bynac as well (cf 56), and which consequently swarmed 
with mistakes He was assisted m this work by his moie 
famous pupil John Muller of Komgsberg (m Franconia) 
hence known as Regiomontanus, who was attracted to 
Vienna at the age of 16 (1452) by Purbach's reputation 
ine two astronomers made some observations, and were 
strengthened m then conviction of the necessity of astio- 
nomical reforms by the serious inaccuracies which they 
discovered in the Alfonsme Tables, now two centimes old 
an eclipse of the moon, for example, occurimg an houi late 
and Mais being seen 2 from its calculated place Purbach 
and Regiomontanus were invited to Rome by one of the 
Caidmals, laigely with a view to studying a copy of the 
Almagest contained among the Greek manuscripts which 
since the fall of Constantinople (1453) had come into Italy 
m consideiable numbers, and they were on the point of 
starting when the eldei man suddenly died (1461) 

Regiomontanus, who decided on going notwithstanding 
Purbach s death, was altogether seven yeais m Italy he 
there acquned a good knowledge of Greek, which he had 
already begun to study in Vienna, and was thus able to lead 
the Almagest and other tieatises in the original, he completed 
lui bach's Epitome of Autonomy, made some obscivations 
lectured, wrote a mathematical treatise f of considerable 
ment, and finally returned to Vienna in 1468 with originals 
or copies of several important Gieek manuscripts He 
was for a short time professor there, but then accepted an 
invitation fiom the King of Hungary to arrange a valuable 
collection of Greek manuscripts The king, howevei, soon 

On tngonomctiy He icintroduced the MM, which had been 

forgotten, and made some use of the tangent, but like Albatcgnius 

J 59 ) did not icahsc its importance, and thus jtmamed behind 

bn \unos and Ahul Wala An impoitant conliibnlion to mnlhc- 

aucs was fi table of ,smt,s calculated loi cvciy minute horn o to 90, 

88 A Short History of Astronomy [CH in 

turned his attention from Greek to fighting, and Regiornon- 
tanus moved once more, settling this time in Nurnberg, then 
one of the most flourishing cities in Germany, a special 
attraction of which was that one of the early printing 
presses was established there The Nurnberg citizens 
received Regiomontanus with great honour, and one nch 
man in particular, Bernard Walther (1430-1504), not only 
supplied him with funds, but, though an older man, became 
his pupil and worked with him The skilled artisans of 
Nurnberg were employed in constructing astronomical 
instruments of an accuracy hitherto unknown in Europe, 
though probably still inferior to those of Nassir Eddin and 
Ulugh Begh ( 62, 63) A number of observations weie 
made, among the most interesting being those of the comet 
of 1472, the first comet which appears to have been 
regarded as a subject for scientific study rather than for 
superstitious terror Regiomontanus recognised at once the 
importance for his woik of the new invention of printing, 
and, finding probably that the existing presses were unable 
to meet the special requirements of astronomy, started a 
printing press of his own Here he brought out m 1472 
or 1473 an edition of Purbach's book on planetary theoiy, 
which soon became popular and was frequently reprinted. 
This book indicates clearly the discrepancy already being 
felt between the views of Aristotle and those of Ptolemy. 
Aristotle's original view was that sun, moon, the five 
planets, and the fixed stais were attached respectively to 
eight spheres, one inside the othei , and that the outer 
one, which contained the fixed stars, by its revolution was 
the primary cause of the apparent daily motion of all the 
celestial bodies The discoveiy of precession required on 
the part of those who earned on the Anstotelian tradition 
the addition of another sphere. According to this scheme, 
which was probably due to some of the translators or 
commentators at Bagdad ( 56), the fixed stars were on 
a spheie, often called the firmament, and outside this was 
a ninth sphere, known as the primum mobile, which moved 
all the others , another sphere was added by Tabit ben 
Koira to account for trepidation ( 58), and accepted by 
Alfonso and his school, an eleventh sphere was added 
towards the end of the Middle Ages to account for the 


The Celestial Spheres 

supposed changes in the obliquity of the ecliptic A few 
writers invented a largei number Outside these spheres 
mediaeval thought usually placed the Empyrean or Heaven 
The accompanying diagram illustiates the whole ariange- 

FIG 36 The celestial spheres*. Fioin Apian'b 

These spheics, which weie almost cntncly fanciful and 
in no senous way even professed to account foi the details 
of the celestial motions, are of coinse quite diflcicnt fioin 
the cucles known as deferents and epicycles, which Ilippni- 
chus and Ptolemy used These wcie meic gcometncal 

90 A Short History of Astronomy [Cn in 

abstractions, which enabled the planetaiy motions to be 
represented with tolerable accuracy Each planet moved 
freely in space, its motion being lepiescnted 01 described 
(not controlled] by a particulai geometrical aiiangcment 
of circles Par bach suggested a compiomisc by hollowing 
out Anstotle's ciystal sphcies till theic was loom foi 
Ptolemy's epicycles inside ' 

From the new Nurnberg pi ess were issued also a suc- 
cession of almanacks which, like those of to-day, gave the 
public useful information about moveable feasts, the phases 
of the moon, eclipses, etc ; and, in addition, a volume of 
less popular Ephemendcs^ with astionomical infoimation 
of a fuller and more exact chaiacter for a period of about 
30 years This contained, among othei things, astionomical 
data for finding latitude and longitude at sea, foi which 
Regiomontanus had invented a new method f 

The superiority of these tables ovei any others available 
was such that they were used on several of the great voyages 
of discovery of this period, probably by Columbus himseli 
on his first voyage to Amenca 

In 1475 Regiomontanus was invited to Rome by the 
Pope to assist in a reform of the calendar, but died theic 
the next year at the early age of forty 

Walther carried on his friend's work and took a nunibci 
of good observations , he was the first to make any 
successful attempt to allow foi the atmospheric lefi notion 
of which Ptolemy had piobably had some knowledge (clup- 
tei n, 46) , to him is clue also the practice of obtaining 
the position of the sun by companson with Venus instead of 
with the moon (chapter n , 59), the much slower motion 
of the planet rendering greatei accuiacy possible 

After Walther's death other observe! & of lessraent cat tied 
on the work, and a Nurnbeig astionomical school of some 
kind lasted into the lyth centuiy 

69 A few minoi discoveries in astionomy belong to this 
or to a slightly later period and may conveniently be dealt 
with here 

Lwnardo da Vina (1452-1519), who was not only a 

gieat painter and sculptoi, but also an anatomist, engmcci, 

mechanician, physicist, and mathematician, was the fnst 

Tli at of (i lunai 

$ 6 ^ Regiomontamts and Others 91 

to explain correctly the dim illumination seen ovei the 
rest of the suiface of the moon when the bright part is 
only a thin ciescent He pointed out that \vhen the 
moon was nearly new the half of the earth which was 
then illuminated by the sun was turned nearly duectly 
towaids the moon, and that the moon was in consequence 
illuminated slightly by this earthshme, just as we arc by 
moonshine. The explanation is interesting in itself, and 
was also of some value as shewing an analogy between 
the eaith and moon which tended to bieak down the 
supposed barnei between teriestnal and celestial bodies 
(chapter vi, 119) 

Jerome Fracastor (1483-1543) and Peter Apian (1495- 
T 5S 2 )j tw voluminous wnteis on astronomy, made obser- 
vations of comets of some interest, both noticing that 
a comet's tail continually points away from the sun, as 
the comet changes its position, a fact which has been 
used in modern times to throw some light on the structure 
of comets (chapter xin , 304) 

Peter Nonius (1492-1577) deseives mention on account 
of the knowledge of twilight which he possessed , several 
problems as to the duration of twilight, its vanation in 
different latitudes, etc , were coirectly solved by him , but 
otheiwise his numerous books are of no great interest * 

A new determination of the sue of the earth, the first 
since the time of the Caliph Al Mamun ( 57), was made 
about 1528 by the French doctor /<?// Ferncl (1497-1558), 
who ainved at a icsult the en or m winch (less than i pei 
cent ) was fai less than could reasonably have been ex- 
pected fiom the lough methods employed 

The life of llegiomontanus overlapped that of Coppei- 
nicus by three yeais, the four wnteis last named wcic 
noaily his contemporaries, and we may theicfore be said to 
have come to the end of the compaiatively stationaiy period 
dealt with in this chaptei 

* He did not invent the measuimg instrument called the veimei 
often attubutcd to him, but something quite different and of vciv 
inferior value f ^ 



"But in this our age, one laie witte (seeing the continuall eirois 
that irom time to time more and more continually have been dis- 
coveied, besides the infinite absurdities in their Theoucks, which 
they have been forced to admit that would not confesse any Mobihtie 
in the ball of the Earth) hath by long studye, paynfull piactise, 
and rare invention delivered a new Theonck 01 Model of the woild, 
shewing that the Earth resteth not m the Centci of the whole woild 
or globe of elements, which encircled and enclosed in the Moone's 
orbit, and togethei with the whole globe ol moitahty is earned 
yearly round about the Sunne, which like a king in the middest of 
all, rayneth and giveth laws of motion to all the rest, sphaencally 
dispersing his glonous beanies of light thiough all this sacied 
coelestiall Temple " 


70 THE growing mteiest in astronomy shewn by the 
work of such men as Regiomontanus was one of the eaily 
results in the legion of science of the gicat movement of 
thought to diffeient aspects of which aie given the names 
of Revival of Learning, Renaissance, and Reformation 
The movement may be regaided pumaiily as a general 
quickening of intelligence and of interest in matters of 
thought and knowledge The invention of printing eaily 
m the i5th century, the stimulus to the study of the Greek 
authois, due in part to the scholais who weie driven west- 
wards after the captuie of Constantinople by the Tuiks 
(1453), and the discovery of America by Columbus in 
1492, all helped on a movement the beginning of which 
has to be looked foi much earhei 

Every stimulus to the intelligence natuially brings with it 
a tendency towauls inquiry into opinions received through 
tiadition and based on some great atithonty The effective 


CH iv , 7 o, 7 i] The Revival of Learning 93 

discoveiy and the study of Greek philosophers other 
than Aristotle naturally did much to shake the supreme 
authority of that gieat philosopher, just as the Reformers 
shook the authority of the Church by pointing out what 
they considered to be inconsistencies between its doctrines 
and those of the Bible At first theie was little avowed 
opposition to the principle that truth was to be derived 
from some authority, rather than to be sought independ- 
ently by the light of reason , the new scholars replaced 
the authority of Aristotle by that of Plato or of Greek and 
Roman antiquity m general, and the religious Reformers 
leplaced the Chuich by the Bible Naturally, however 
the conflict between authonties produced m some minds 
scepticism as to the principle of authority itself, when 
fieedom of judgment had to be exeicised to the extent 
of deciding between authorities, it was but a step further 
a step, it is true, that comparatively few tookto use 
the individual judgment on the mattei at issue itself 

In astronomy the conflict between authorities had already 
ansen, paitly m connection with certain divergencies be- 
tween Ptolemy and Aiistotle, partly m connection with 
the various astronomical tables which, though on sub- 
stantially the same lines, differed in minor points The 
time was therefore ripe for some fundamental criticism of 
the traditional astronomy, and for its reconstruction on a 
new basis 

Such a fundamental change was planned and worked 
out by the gieat astionomer whose work has next to be 

71 NicJiolas Coppeimc or Coppet mws * was born on 
February iQth, 1473, m a house still pointed out m the little 
trading town of Thorn on the Vistula Thorn now lies 
just within the eastern frontier of the piesent kingdom of 
liussia, in the time of Coppermcus it lay m a legion over 
which the King of Poland had some sort of suzerainty, the 

* The name is spelled in a laige number of different ways both by 
Coppermcus and by his tontcmporaucs He himself usually wiote 
his name Coppunic, and m leained productions commonly used the 
Latin foim Coppcimcus The spelling Copemicus is so much less 
commonly used by him that I have thought it better to discard it 
even at the nsk of appearing pedantic 

94 A Short History of Astronomy [Cn IV 

precise nature of which was a continual subject of quarrel 
between him, the citizens, and the order of Teutonic knights, 
who claimed a good deal of the neighbouring country 
The astronomei's father (whose name was most commonly 
written Koppemigk) was a merchant who came to Thorn 
from Cracow, then the capital of Poland, in 1462 Whether 
Coppernicus should be counted as a Pole or as a German 
is an intricate question, over which his biographers have 
fought at great length and with some acrimony, but which 
is not worth further discussion heie 

Nicholas, after the death of his fathei in 1483, was undei 
the care of his uncle, Lucas Watzehode, afterwards bishop 
of the neighbouimg diocese of Eimland, and was destined 
by him from a very early date for an ecclesiastical career 
He attended the school at Thorn, and at the age of 17 
entered the Umveisity of Cracow Here he seems to have 
first acquired (or shewn) a decided taste foi astionomy 
and mathematics, subjects m which he probably received 
help from Albert Brudzewski, who had a great leputation 
as a learned and stimulating teacher } the lectuie lists of 
the University show that the comparatively modern treatises 
of Purbach and Regiomontanus (chapter in , 68) were 
the standard textbooks used Coppernicus had no intention 
of graduating at Cracow, and probably left aftei thiee 
years (1494) During the next year or two he lived 
partly at home, partly at his uncle's palace at Heilsberg, 
and spent some of the time in an unsuccessful candidature 
for a canonry at Frauenburg, the cathedral city of his 
uncle's diocese 

The next nine or ten years of his life (from 1496 to 
1505 or 1506) weie devoted to studying in Italy, his stay 
theie being broken only by a short visit to Frauenbuig m 
1501 He worked chiefly at Bologna and Padua, but 
graduated at Fenara, and also spent some time at Rome, 
where his astronomical knowledge evidently made a favour- 
able impression Although he was supposed to be in 
Italy primarily with a view to studying law and medicine, 
it ib evident that much of his best work was being put 
into mathematics and astronomy, while he also paid a good 
deal of attention to Greek. 

During his absence he was appointed (about 1497) to 


\To )(UC f> 91 

1 72j Life of Coppermcus 


a canonry at Frauenburg, and at some uncertain date 
he also received a sinecure ecclesiastical appointment at 

72 On returning to Frauenburg from Italy Coppermcus 
almost immediately obtained fresh leave of absence, and 
joined his uncle at Heilsberg, ostensibly as his medical 
adviser and really as his companion 

It was probably during the quiet years spent at Heilsberg 
that he first put into shape his new ideas about astronomy 
and wrote the first draft of his book He kept the 
manuscript by him, revising and rewriting from time to 
time, partly from a desire to make his work as perfect as 
possible, partly from complete indifference to reputation, 
coupled with dislike of the contioveisy to which the 
publication of his book would almost certainly give use 
In 1509 he published at Ciacow his first book, a Latin 
translation of a set of Greek letteis by Theophylactus, 
inteiestmg as being probably the fast translation from the 
Greek evei published m Poland or the adjacent districts. 
In 1512, on the death of his uncle, he finally settled in 
Frauenburg, in a set of rooms which he occupied, with shoit 
intervals, for the next 31 years Once fairly m residence, 
he took his share in conducting the business of the 
Chapter he acted, for example, moie than once as their 
lepresentative in various quarrels with the King of Poland 
and the Teutonic knights, m 1523 he was general 
administrator of the diocese for a few months after the 
death of the bishop ; and for two periods, amounting alto- 
gether to six years (1516-1519 and 1520-1521), he lived at 
the castle of Allenstem, administering some of the outlying 
propei ty of the Chapter. In 1521 he was commissioned to 
draw up a statement of the grievances of the Chapter 
against the Teutonic knights for presentation to the 
Prussian Estates, and m the following yeai wrote a memo- 
randum on the debased and confused state of the coinage 
m the district, a paper which was also laid before the 
Estates, and was afterwards rewritten in Latin at the special 
request of the bishop He also gave a certain amount 
of medical advice to his fnends as well as to the pooi of 
Frauenburg, though he never piactiscd regularly as a 
physician , but notwithstanding these various occupations 

9 6 A Short History of Astronomy [Cn iv 

it is probable that a very large part of his time dunng the 
last 30 years of his life was devoted to astronomy 

73. We are so accustomed to associate the revival of 
astronomy, as of other branches of natural science, with 
increased care in the collection of observed facts, and to 
think of Coppernicus as the chief agent in the revival, that 
it is woith while here to emphasise the fact that he was m 
no sense a great observei His mstmments, which were 
mostly of his own construction, were fai infenoi to those 
of Nassir Eddm and of Ulugh Begh (chaptei in , ^ 62, 63), 
and not even as good as those which he coulcl have pro- 
cured if he had wished fiom the workshops of Nurnberg , 
his observations were not at all numerous (only 27, which 
occur in his book, and a dozen or two besides being known), 
and he appears to have made no serious attempt to secure 
great accuracy His determination of the position of one 
star, which was extensively used by him as a standard of 
reference and was therefore of special impoi lance, was in 
error to the extent of nearly 40' (more than the apparent 
bieadth of the sun 01 moon), an eiror which Hippaichus 
would have considered very serious His pupil Rheticus 
( 74) reports an interesting discussion between his master 
and himself, in which the pupil urged the importance of 
making observations with all imaginable accuiacy, Coppei- 
nicus answered that minute accuracy was not to be looked 
for at that time, and that a rough agreement between theoiy 
and observation was all that he could hope to attain 
Coppernicus moreover points out in more than one place 
that the high latitude of Fraucnbuig and the thickness of 
the an were so detnraental to good observation that, foi 
example, though he had occasionally been able to see the 
planet Mercury, he had never been able to obseive it 

Although he published nothing of importance till towauls 
the end of his life, his reputation as an astionomei and 
mathematician appears to have been established among 
experts from the date of his leaving Italy, and to have 
steadily increased as time went on 

In 1515 he was consulted by a committee appointed by 
the Lateran Council to consider the refoim of the calendar, 
which had now fallen into some confusion (chaptei a , 

73] Life of Coppermcus 97 

22), but he declined to give any advice on the ground 
that the motions of the sun and moon weie as yet too 
imperfectly known for a satisfactory reform to be possible 
A few years later (1524) he wrote an open letter, intended 
for publication, to one of his Cracow friends, in reply to a 
tract on precession, m which, after the manner of the time, 
he used strong language about the enors of his opponent ** 
It was meanwhile gradually becoming known that he 
held the novel doctrine that the earth was m motion and 
the sun and stars at rest, a doctune which was sufficiently 
startling to attract notice outside astionomical circles 
About 1531 he had the distinction of being ridiculed on 
the stage at some populai performance in the neighbour- 
hood , and it is interesting to note (especially m view of 
the famous persecution of Galilei at Rome a centuiy later) 
that Luther in his Table Talk frankly described Coppeimcus 
as a fool for holding such opinions, which were obviously 
contraiy to the Bible, and that Melanchthon, perhaps the 
most learned of the Reformers, added to a somewhat similar 
criticism a bioad hint that such opinions should not be 
tolerated Coppermcus appears to have taken no notice of 
these or similar attacks, and still continued to publish nothing 
No observation made later than 1529 occuis in his gieat 
book, which seems to have been nearly in its final form by that 
date , and to about this time belongs an exti emely interest- 
ing paper, known as the Commentanoliis^ which contains a 
short account of his system of the woild, with some of the 
evidence for it, but without any calculations It was 
appai entry written to be shewn or lent to friends, and was 
not published , the manuscript disappeared after the death 
of the author and was only rediscovered m 1878 The 
Commcntanolus was probably the basis of a lectuie on 
the ideas of Coppermcus given m 1533 by one of the 
Roman astionomers at the icquest of Pope Clement VII 
Thiee years latei Cardinal Schombcrg wrote to ask 
Coppermcus for fuithcr information as to his views, the 
Icttci showing that the chief features weie already pietty 
accmately kno\vn 

1 Nnllo dcinian loto tnf/>tioi rs/ quant itbt minis pucnlitet 

hallucmatn} Nowhue is he moic (oohsh tluai where he sufteis 

from delusions ol too childish a chaiactei 


98 A Short History of Astronomy [Cn iv 

74 Similar requests must have been made by others, but 
his final decision to publish his ideas seems to have been 
due to the arrival at Frauenburg m 1539 of the enthusiastic 
young astronomer generally known as Rheticus } Bom in 
1514, he studied astronomy under Schoner at Nurnberg, 
and was appointed in 1536 to one of the chans of 
mathematics created by the influence of Melanchthon at 
Wittenberg, at that time the chief Protestant University 

Having heard, probably through the Commentanolu^^ of 
Coppermcus and his doctrines, he was so much interested 
in them that he decided to visit the great astiononiei at 
Frauenburg Coppermcus received him with extreme 
kindness, and the visit, which was originally intended to 
last a few days or weeks, extended over nearly two years 
Rheticus set to work to study Coppermcus's manuscript, 
and wrote within a few weeks of his arrival an extiemely 
interesting and valuable account of it, known as the First 
Narrative (Prima Narratw\ in the form of an open lettei 
to his old master Schoner, a letter which was printed in the 
following spring and was the first easily accessible account 
of the new doctrines t 

When Rheticus returned to Wittenbeig, towards the end 
of 1541, he took with him a copy of a purely mathematical 
section of the great book, and had it punted as a textbook 
of the subject (Trigonometry) , it had probably been already 
settled that he was to superintend the printing of the com- 
plete book itself Coppermcus, who was now an old man 
and would natuially feel that his end was appioachmg, sent 
the manuscript to his fnend Giese, Bishop of Kulm, to do 
what he pleased with Giese sent it at once to Rheticus, 
who made arrangements for having it printed at Nurnberg 
Unfortunately Rheticus was not able to see it all thiongh 
the press, and the work had to be entrusted to Osianclei, 
a Lutheian preacher interested in astronomy Osianclei 

* His real name was Geoig Joachim, that by which he is known 
having been made up by himself from the Latin name of the district 
where he was born (Rhsetia) 

f The Commentanolus and the Prima Nartatio give most icaclcis 
a better idea of what Coppermcus did than his larger book, in which 
it is comparatively difficult to disentangle his leading ideas liom the 
mass of calculations based on them, 

74,7s] Publication of the " De Rewlutiombus' 


appears to have been much alarmed at the thought of the 
disturbance which the heretical ideas of Coppernicus would 
cause, and added a prefatory note of his own (which he 
omitted to sign), praising the book m a vulgar way, and 
declaring (what was quite contrary to the views of the 
author) that the fundamental principles laid down in it 
were merely abstract hypotheses convenient for purposes 
of calculation, he also gave the book the title De 
ttevolutwmbus Orbmm Celestmm (On the Revolutions of 
the Celestial Spheres), the last two words of which were 
probably his own addition The printing was finished m 
the winter 1542-3, and the author received a copy of his 
book on the day of his death (May 24th, 1543), when his 
memory and mental vigour had already gone 

75 The central idea with which the name of Coppernicus 
is associated, and which makes the De Rewhitwnibus one 
of the most important books in all astronomical literature, by 
the side of which perhaps only the Almagest and Newton's 
Prmcipia (chapter ix , 177 seqq} can be placed, is that 
the apparent motions of the celestial bodies are to a great 
extent not real motions, but are due to the motion of the 
earth carrying the observer with it Coppernicus tells us 
that he had long been struck by the unsatisfactory nature 
of the current explanations of astronomical observations, 
and that, while searching in philosophical writings for some 
better explanation, he had found a reference of Cicero to 
the opinion of Hicetas that the eaith turned round on its 
axis daily He found similar views held by other Pytha- 
goreans, while Philolaus and Anstarchus of Samos had 
also held that the eaith not only lotates, but moves 
bodily round the sun or some other centre (cf chapter n , 
24) The opinion that the eaith is not the sole centre 
of motion, but that Venus and Mercury revolve round the 
sun, he found to be an old Egyptian belief, supported 
also by Martianus Capella, who wrote a compendium of 
science and philosophy m the 5th or 6th century A,D 
A more modern authority, Nicholas of Citsa (1401-1464), a 
mystic writer who refers to a possible motion of the earth, 
was ignored or not noticed by Coppernicus None of 
the writers here named, with the possible exception of 
Anstaichus of Samos, to whom Coppernicus apparently 

ioo A Short History of Astronomy [CH iv 

paid little attention, presented the opinions quoted as 
more than vague speculations , none of them gave any 
substantial reasons for, much less a proof of, their views , 
and Coppemicus, though he may have been glad, after the 
fashion of the age, to have the support of recognised 
authorities, had practically to make a fresh start and 
elaborate his own evidence for his opinions 

It has sometimes been said that Coppemicus proved 
what earlier wiiters had guessed at or suggested , it would 
perhaps be truer to say that he took up certain floating ideas, 
which were extremely vague and had never been worked 
out scientifically, based on them certain definite funda- 
mental principles, and from these principles developed 
mathematically an astronomical system which he shewed to 
be at least as capable of explaining the observed celestial 
motions as any existing variety of the traditional Ptolemaic 
system The Coppermcan system, as it left the hands of 
the author, was in fact decidedly superior to its rivals as 
an explanation of ordinary observations, an advantage which 
it owed quite as much to the mathematical skill with which 
it was developed as to its first principles 3 it was in many 
respects very much simpler, and it avoided ccitain 
fundamental difficulties of the older system. It was how- 
ever liable to certain serious objections, which were only 
overcome by fresh evidence which was subsequently 
brought to light For the predecessors of Coppemicus 
there was, apart from variations of minor impoi lance, but 
one scientific system which made any senous attempt to 
account for known facts , for his immediate successors theie 
were two, the newer of which would to an impartial mind 
appear on the whole the more satisfactory, and the further 
study of the two systems, with a view to the discovery of 
fresh arguments or fresh obseivations tending to suppoit 
the one or the other, was immediately suggested as an 
inquiry of first-rate impoi tance 

76 The plan of the De Revolutionibus bears a general 
resemblance to that of the Almagest In form at least 
the book is not primarily an argument m favour of the 
motion of the earth, and it is possible to lead much of 
it without ever noticing the piesence of this doctnne, 

Coppemicus, like Ptolemy, begins with certain first pnn- 

$$ 76, 7?3 The Motion of the Earth roi 

ciples or postulates, but on account of their novelty takes 
a little more trouble than his predecessoi (cf chapter n , 
47) to make them at once appear probable With 
these postulates as a basis he proceeds to develop, by 
means of elaborate and rather tedious mathematical reason- 
ing, aided here and there by references to observations, 
detailed schemes of the various celestial motions , and it 
is by the agreement of these calculations with observations, 
far more than by the general reasoning given at the 
beginning, that the various postulates are in effect justified 
His first postulate, that the universe is spherical, is 
supported by vague and inconclusive reasons similar to 
those given by Ptolemy and others , foi the spherical form 
of the earth he gives several of the usual valid arguments, 
one of his proofs for its curvature from east to west being 
the fact that eclipses visible at one place are not visible 
at another A third postulate, that the motions of the 
celestial bodies are uniform circular motions or are com- 
pounded of such motions, is, as might be expected, sup 
ported only by reasons of the most unsatisfactory character 
He aigues, foi example, that any want of uniformity in 

"must arise either from irregularity in the moving power, 
whether this be within the body or foreign to it, or irom some 
inequality of the body in revolution Both of which things 

the intellect shimks irom with horror, it being unworthy to hold 
such a view about bodies which are constituted m the most 
perfect order " 

77 The discussion of the possibility that the earth may 
move, and may even have more than one motion, then 
follows, and is more satisfactoiy though by no means con- 
clusive Coppemicus has a firm grasp of the principle, 
which Austotle had also enunciated, sometimes known as 
that of relative motion, which he states somewhat as 

" For all change in position which is seen is due to a motion 
either oi the observer or of the thing looked at, or to changes 
in the position of both, provided that these are different For 
when things are moved equally relatively to the same things, 

102 A Short History of Astronomy [Cn IV 

no motion is perceived, as between the object seen and th< 
observer " * 

Coppernicus gives no proof of this pimciple, regarding 
it probably as sufficiently obvious, when once stated, tc 
the mathematicians and astronomers for whom he wa< 
writing It is, however, so fundamental that it may be 
worth while to discuss it a little more fully 

Let, for example, the observer be at A and an object ai 
B, then whether the object move from B to B', the observe! 
remaining at rest, or the observer move an equal distance 
in the opposite direction, from A to A', the object remaining 
at rest, the effect is to the eye exactly the same, since in 

FIG 37 Relative motion 

either case the distance between the obseiver and object 
and the direction in which the object is seen, icpiesented 
m the first case by A B' and in the second by A' rs, aic the 

Thus if m the course of a yeai either the sun passes 
successively through the positions A, B, c, D (fig 38), the 
earth remaining at rest at E, or if the sun is at icst and 
the earth passes successively through the positions a, l>, c, //, 

* Onims emm qucc vidctur sccundwn locum niittatio, a?tt cst }n o/>t(>t 
locum tmttaho, ant est proptet spectator ici motmn, aut vidmtts, am 
ccrte dibparem ittnusqttc imitatwncm Nam inter mota <vqitahi?> 
ad eadem non perctpitw motus, inter tew visam dico, et vzdmtcm {!)(,' 
Rev , I v ) 

I have tried to remove some of the ciabbcdncss of the ougiuul 
passage by translating fieely 

v8] Relative Motion 103 

at the corresponding times, the sun remaining at rest at s, 
exactly the same effect is produced on the eye, provided 
that the lines as, b s, ^s, d$ are, as in the figure, equal in 
length and parallel in direction to E A, E B, E c, E D re- 
spectively The same being true of intermediate points, 
exactly the same apparent effect is produced whether the 
sun describe the circle A B c D, or the earth describe at 
the same rate the equal circle abed It will be noticed 
further that, although the corresponding motions in the 
two cases are at the same times m opposite directions (as 
at A and a), yet each circle as a whole is described, 


FIG 38 The relative motion of the sun and moon 

as indicated by the arrow heads, in the wine direction 
(contiary to that of the motion of the hands of a clock, 
in the figures given) It follows in the same sort of way 
that an apparent motion (as of a planet) may be explained 
as due paitially to the motion of the object, partially to 
that of the obseivei 

Coppeimcus gives the famihai illustiation of the 
passenger m a boat who sees the land apparently moving 
away fiom him, by quoting and explaining Vugil's line 

" Provchimur portu, terrccque urbcsque reccdunt " 

78 The application of the same ideas to an apparent 
rotation round the observer, as in the case of the apparent 
daily motion of the celestial sphere, is a little more difficult. 
It must be rcmembeied that the eye has no means of 

A Short History of Astronomy [Cn iv 

judging the duection of an object taken by itself, it can 
only judge the difference between the direction of the 
object and some other duection, whether that of anothei 
object or a direction fixed in some way by the body 
of the obseiver Thus when aftei looking at a star twice 
a-t an interval of time we decide that it has moved, this 
means that its direction has changed relatively to, say, some 
tree 01 house which we had noticed nearly in its direction, 
or that its duection has changed relatively to the duection 
*n which we aie directing oui eyes 01 holding our bodies 
Such a change can evidently be mterpieted as a change of 

direction, eithei of the star 
or of the line fiom the eye 
to the tree which we used 
as a line of leference To 
apply this to the case of the 
celestial sphere, let us sup- 
pose that s lepresents a star 
on the celestial spheie, which 
(for simplicity) is overhead 
to an observer on the eaith 
at A, this being determined 
by comparison with a line 
A B drawn upright on the 
earth Next, eaith and ce- 
lestial sphere being supposed 
to have a common centie 
T at o, let us suppose firstly 

that the celestial sphere turns lound (in the duection of 
the hands of a clock) till s comes to s', and that the 
observei now sees the star on his horuon or in a direction 
at right angles to the ongmal duection A B, the an"le 
turned thiough by the celestial sphere being s o s' and 
secondly that, the celestial sphere being unchanged, the 
earth turns round m the opposite duection, till A u comes 
to A B, and the star is again seen by the obscivei on his 
horizon Whichevei of these motions has taken place 
the observer sees exactly the same appaient motion m the 
sky and the figure shews at once that the angle s o s' 
through which the celestial sphere was supposed to turn 
in the first case is equal to the angle A o A' thiough which 

Fig 39 I he daily rotation of 
the eaith 

4* 79, So] The Motion of the Earth IOS 

the earth turns in the second case, but that the two 
rotations are in opposite directions A similar explanation 
evidently applies to more complicated cases 

Hence the apparent daily rotation of the celestial sphere 
about an axis through the poles would be produced equally 
well, either by an actual rotation of this charactei, or by 
a rotation of the earth about an axis also passing through 
the poles, and at the same iate ; but in the opposite 
direction, / e from west to east This is the first motion 
wmcn Coppermcus assigns to the earth 

79 The apparent annual motion of the sun, in accordance 
with which it appears to revolve round the earth in a path 
which is neaily a circle, can be equally well explained by 
supposing the sun to be at rest, and the earth to describe 
an exactly equal path round the san, the direction of the 
i evolution being the same This is virtually the second 
motion which Coppeimcus gives to the earth, though, on 
account of a peculiarity m his geometncal method he 
resolves this motion into two otheis, and combines with 
one of these a further small motion which is required for 
precession * 

80 Coppernicus's conception then is that the earth 
revolves round the sun in the plane of the ecliptic, while 
rotating daily on an axis which continually points to the 
poles of the celestial spheie, and therefore retains (save for 
precession) a fixed direction in space 

It should be noticed that the two motions thus assigned 
to the earth are perfectly distinct, each icquires its own 
pi oof, and explains a different set of appearances. It was 
quite possible, with perfect consistency, to believe m one 
motion without believing in the othei, as in fact a veiy 
lew of the 16th-century astronomeis did (chaptei v , ioO 

In giving his reasons for believing in the motion of the 


f hls c ntc poianes, as well as to 

the rrf , s o 

Inntl ' SlmP ' e&t folm f a revolut 'n of one body ,onnd 

a "?ri ,!"? a , m0 T In Wluch the revolving body moved as Tf 
ngidly attached to the central body Thus ,n the case of the ea, t 

mchnori 2 m < T S Sl J Ch * at the aX1S Of the ^ icmoiucd 
the cfore rl,t C n /f /" gle l thc llnc J " n g * and sun, and 
tneiciore changed its direction in space In ordci then to mil . th, 

'' -- nocesl^y to *d 

I0 6 A Short History of Astronomy LCn iv 

earth Coppernicus discusses the chief objections which had 
been urged by Ptolemy To the objection that if the eaith 
had a rapid motion of rotation about its axis, the earth 
would be in danger of flying to pieces, and the air, as well 
as loose objects on the surface, would be left behind, he 
replies that if such a motion weie dangerous to the solid 
earth, it must be much more so to the celestial sphere, which, 
on account of its vastly greater size, would have to move 
enormously faster than the eaith to complete its daily 
rotation, he enters also into an obscuie discussion of 
difference between a natural " and an "artificial ? motion, 
of which the former might be expected not to disturb 
anything on the earth 

Coppernicus shews that the earth is very small compared 
to the sphere of the stars, because wherevei the observer 
is on the earth the horizon appears to divide the celestial 
sphere into two equal paits and the observer appears always 
to be at the centie of the sphere, so that any distance 
through which the observer moves on the earth is im- 
peiceptible as compared with the distance of the stais 

8 1 He goes on to argue that the chief irregularity in the 
motion of the planets, in virtue of which they move back- 
wards at intervals (chapter i , 14. and chapter IT , 51), 
can readily be explained in general by the motion of the 
earth and by a motion of each planet louncl the sun, in its 
own time and at its own distance From the fact that 
Venus and Mercury were never seen very fai from the sun, 
it could be inferred that their paths weie neaiei to the sun 
than that of the earth, Mercury being the nearer to the sun 
of the two, because nevei seen so far from it m the sky as 
Venus The other three planets, being seen at times in a 
direction opposite to that of the sun, must necessauly 
evolve round the sun m orbits larger than that of the 
earth, a view confirmed by the fact that they weie brightest 
when opposite the sun (m which positions they would be 
nearest to us) The older of then lespective distances 
from the sun could be at once inferred from the dibttubing 
effects produced on their apparent motions by the motion 
of the earth , Saturn being least affected must on the whole 
be farthest from the earth, Jupiter next, and Mais next 
The eaith thus became one of six planets revolving round 

$ 8i] The Arrangement of the Solar System 107 

the sun, the order of distance Mercury, Venus, Earth, 
Mars, Jupiter, Saturn being also in accordance with the 
rates of motion round the sun, Mercury performing its 
revolution most rapidly (in about 88 days *), Saturn most 
slowly (in about 30 years) On the Coppernican system 

FIG 40 The solai system according to Coppemicus Fiom the 
DC Revohitionibus, 

the moon alone still revolved louncl the earth, being the 
only celestial body the status of which was substantially 

* In tins preliminary discussion, as in fig 40, Coppcrnicus gives 
50 days, but in the moie detailed ticatraent given in Book V he 
corrects this to 88 days. 

loS A Short History of Astronomy [Cii iv 

unchanged, and thus Coppernicus was able to give the 
accompanying diagram of the solar system (fig 40), lepie- 
sentmg his view of its general arrangement (though not of 
the right proportions of the different paits) and of the 
various motions 

82 The effect of the motion of the eaith lound the sun 
on the length of the day and othei seasonal effects is 

FIG 41 Coppeimcan explanation oi the seasons Fioin the 
De Revohttiombus 

discussed in some detail, and illustrated by diaguims which 
aie heie reproduced * 

In fig 41 A, B, c, D repicscnt the centic of the caith in four 
positions, occupied by it about December 2310!, Mai eh sist, 
June 22nd, and Septembei 2 2nd respectively (/ e. at the 

15 Fig 42 has been slightly altered, so <is to make it a^icc with 
% 41 

82] The Seasons, according to Copper nmis 109 

beginnings of the four seasons, according to astronomical 
reckoning) , the circle F G H i m each of its positions 
represents the equator of the earth, i e a great circle on 
the eaith the plane of which is perpendicular to the axis 
of the earth and is consequently always parallel to the 
celestial equator This ciicle is not m the plane of 
the ecliptic, but tilted up at an angle of 23 J, so that F 
must always be supposed below and H above the plane of 
the papei (which represents the ecliptic) } the equator cuts 
the ecliptic along G i The diagram (in accordance with the 
common custom in astronomical diagrams) repiesents the 
various circles as seen from the north side of the equator 
and ecliptic When the earth is at A, the north pole (as is 
shewn more clearly m fig 42, in which p, p' denote the 
noith pole and south pole respectively) is turned away 

Partes Boreae J^ 


|L E M 

Partes Auftrinae. 

FIG 42 Coppemican explanation of the seasons From the 
De Revoliitiombiis 

from the sun, E, which is on the lowei or south side of the 
plane of the equator, and consequently inhabitants of the 
noithern hemisphere see the sun for less than half the day, 
while those on the southern hemispheie see the sun for more 
than half the day, and those beyond the line K L (in fig 42) 
see the sun during the whole day Three months later, 
when the eaith's centre is at B (fig 41), the sun lies m the 
plane of the equator, the poles of the earth are turned 
neither towards nor away from the sun, but aside, and all 
over the eaith daylight lasts foi 12 hours and night for an 
equal time Three months later still, when the earth's 
centre is at c, the sun is above the plane of the equator, 
and the inhabitants of the northern hemispheie see the 
sun for more than half the clay, those on the southern 
hemispheie for less than half, while those in parts of the 
eaith faither north than the line M N (in fig 42) see the 
sun foi the whole 24 hours. Finally, when, at the autumn 

no A Short History of Astronomy [CH iv 

equinox, the earth has reached D (fig 41), the sun is again 
in the plane of the equatoi, and the day is eveiywhere equal 
to the night 

83 Coppermcus devotes the first eleven chaptei s of the 
first book to this preliminary sketch of his system, the 
remainder of this book he fills with some mathematical 
propositions and tables, which, as pieviously mentioned 
( 74), had already been separately printed by Rheticus 
The second book contains chiefly a number of the usual 
results relating to the celestial sphere and its apparent 
daily motion, treated much as by eailier writeis, but with 
greater mathematical skill Incidentally Coppermcus gives 
his measurement of the obliquity of the ecliptic, and mfeis 
from a comparison with earlier observations that the 
obliquity had decreased, which was in fact the case, though 
to a much less extent than his imperfect observations 
indicated The book ends with a catalogue of stars, which 
is Ptolemy's catalogue, occasionally corrected by fresh 
observations, and reairanged so as to avoid the effects of 
precession * When, as frequently happened, the Greek 
and Latin versions of the Almagest gave, owing to copyists' 
or printers' errors, different results, Coppermcus appears to 
have followed sometimes the Latin and sometimes the 
Greek version, without in general attempting to ascertain 
by fresh observations which was right 

84 The third book begins with an elaborate discussion 
of the precession of the equinoxes (chaptei n , 42) Fiom 
a comparison of results obtained by Timochans, by latoi 
Greek astronomers, and by Albategmus, Coppermcus mfeis 
that the amount of precession has varied, but that its 
average value is 50" 2 annually (almost exactly the true 
value), and accepts accordingly Tabit ben Ivoria's unhappy 
suggestion of the tiepidation (chaptei in , 58) An 
examination of the data used by Coppermcus shews that 
the erroneous or fraudulent observations of Ptolemy 
(chapter n , 50) are chiefly responsible for the perpetua- 
tion of this mistake 

* Coppermcus, instead of giving longitudes as mcasuicd from the 
first point of Aries (or vemal equinoctial point, chapter i., & ir is) 
which moves on account of precession, mcasuied the longiluclcs'l 
a standard fixed star (a Artetts) not far Jtrom this point. 


8 3 85] Precession 


Of much more interest than the detailed discussion of tre- 
pidation and of geometrical schemes for representing it is 
the interpretation of precession as the result of a motion of 
the earth's axis Precession was originally recognised by 
Hipparchus as a motion of the celestial equator, in which 
its inclination to the ecliptic was sensibly unchanged 
Now the ideas of Coppermcus make the celestial equator 
dependent on the equator of the eaith, and hence on its 
axis; it is in fact a great circle of the celestial sphere 
which is always perpendicular to the axis about which the 
earth rotates daily Hence precession, on the theory of 
Coppermcus, arises from a slow motion of the axis of the 
earth, which moves so as always to remain inclined at the 
same angle to the ecliptic, and to return to its original 
position after a penod of about 26,000 years (since a 
motion of 50" 2 annually is equivalent to 360 or a complete 
circuit in that period), in other words, the earth's axis 
has a slow conical motion, the central line (or axis) of the 
cone being at right angles to the plane of the ecliptic 

85 Precession being dealt with, the greater part of the 
remainder of the third book is devoted to a discussion in 
detail of the apparent annual motion of the sun round the 
eaith, corresponding to the real annual motion of the earth 
round the sun The geometrical theory of the Almagest 
was capable of being immediately applied to the new system, 
and Coppermcus, like Ptolemy, uses an eccentric He 
makes the calculations afresh, arrives at a smaller and more 
accurate value of the eccentricity (about -^ instead of -r 3 ^), 
fixes the position of the apogee and perigee '(chaptei n , 39), 
or rather of the equivalent aphelion and perihelion (2 e the 
points m the earth's orbit where it is respectively farthest 
from and nearest to the sun), and thus verifies Albalegnms's 
discovery (chapter in , 59) of the motion of the line of 
apses. The theory of the earth's motion is worked out in 
some detail, and tables are given whereby the apparent place 
of the sun at any time can be easily computed 

The fourth book deals with the theory of the moon As 
has been already noticed, the moon was the only celestial 
body the position of which m the universe was substantially 
unchanged by Coppermcus, and it might hence have been 
expected that little alteration would have been required m 

ii2 A Short History of Astronomy [CH iv 

the traditional theory Actually, however, there is scarcely 
any part of the subject m which Coppeimcus did more to 
dimmish the discrepancies between theory and observation 
He rejects Ptolemy's equant (chapter n , 51), partly on 
the ground that it produces an irregular motion unsuitable 
for the heavenly bodies, partly on the more substantial 
ground that, as aheady pointed out (chapter u , 48), 
Ptolemy's theory makes the apparent size of the moon at 
times twice as great as at others By an anangement of 
epicycles Coppemicus succeeded in representing the chief 
irregularities in the moon's motion, including evection, but 
without Ptolemy's prosneusis (chapter n , 48) or Abul 
Wafa's inequality (chapter in , 60), while he made the 
changes in the moon's distance, and consequently m its 
apparent size, not very much greater than those which 
actually take place, the difference being impeiceptible by 
the rough methods of obseivation which he used * 

In discussing the distances and sizes of the sun and 
moon Coppernicus follows Ptolemy closely (chapter n , 49 3 
cf also fig 20) , he ainves at substantially the same estimate 
of the distance of the moon, but makes the sun's distance 
1,500 times the earth's radius, thus improving to some extent 
on the traditional estimate, which was based on Ptolemy's. 
He also develops in some detail the effect of parallax on 
the apparent place of the moon, and the variations in the 
apparent size, owing to the variations in distance f and the 
book ends with a discussion of eclipses 

86 The last two books (V and VI ) deal at length with 
the motion of the planets 

In the cases of Mercuiy and Venus, Ptolemy's explana- 
tion of the motion could with little difficulty be icarrangcd 
so as to fit the ideas of Coppernicus We have seen 
(chapter n , 51) that, minor irregularities being ignored, 
the motion of either of these planets could be repicscnted 
by means of an epicycle moving on a deferent, the centre of 

! Accoidmg to the theory of Coppernicus, the diameter of the 
moon when greatest was about \ greatei than its aveiagc amount, 
modern observations make this fraction about ^ Oi, to put it othci- 
wisc, the diameter of the moon when greatest ought to exceed its 
value when least by about 8' accoidmgto Coppcmicus, and by About 5' 
accoi cling to modern observations 

> 86] 

The Motion of the Planets 


the epicycle being always in the direction of the sun, the 
ratio of the sizes of the epicycle and deferent being fixed, 
but the actual dimensions being practically arbitrary 
Ptolemy preferred on the whole to regaid the epicycles of 
both these planets as lying between the earth and the sun 
The idea of making the sun a centre of motion having once 
been accepted, it was an obvious simplification to make 
the centre of the epicycle not merely lie m the direction 
of the sun, but actually be the sun In fact, if the planet 

FIG 43 The orbits oi Venus and of the earth 

m question revolved lound the sun at the pioper distance 
and at the propci rate, the same appearances would be 
pioduced as by Ptolemy's epicycle and defeient, the path 
of the planet round the sun leplacing the epicycle, and the 
apparent path of the sun lound the earth (or the path of 
the earth round the sun) replacing the deferent 

In discussing the time of revolution of a planet a dis- 
tinction has to be made, as m the case of the moon (chap- 
ter ii., 40), between the synodic and sidereal periods of 
revolution Venus, foi example, is seen as an evening star 

1 14 A Short History of Astronomy [CH iv 

at its greatest angular distance from the sun (as at v in 
% 43) at intervals of about 584 days This is theiefore 
the time which Venus takes to return to the same position 
relatively to the sun, as seen fiom the earth, or relatively 
to the earth, as seen from the sun, this time is called 
the synodic period But as during this time the line E s 
has changed its direction, Venus is no longer in the 
same position relatively to the stars, as seen eithei from 
the sun or from the earth If at first Venus and the 

FIG 44 The synodic and sideieal penods of Venus 

earth are at v lf E, respectively, after 584 days (or about 
a year and seven months) the earth will have performed 
rather more than a revolution and a half round the 
sun and will be at E 2 , Venus being again at the greatest 
distance from the sun will therefore be at v Ibut.'will 
evidently be seen in quite a different part of the sky 
and will not have performed an exact revolution round the 
sun, It is important to know how long the line s v, takes 
to return to the same position, ic how long Venus takes 
to leturn to the same position with respect to the stars 

87] The Motion of the Planets 115 

as seen from the sun, an mteival of time known as the 
sidereal period. This can evidently be calculated by a 
simple rule-of-three sum from the data given For Venus 
has in 584 days gamed a complete revolution on the 
earth, or has gone as far as the earth would have gone in 
54 -f 365 or 949 days (fractions of days being omitted for 
simplicity) hence Venus goes in 584 x ^ days as far 
as the earth m 365 days, te Venus completes a revolution 
m 584 x r #j. 01 225 days This is therefore the sidereal 
period of Venus The process used by Coppermcus was 
different, as he saw the advantage of using a long period of 
time, so as to dimmish the error due to minor irregularities 
and he therefore obtained two observations of Venus at 
a considerable interval of time, in which Venus occupied 
very nearly the same position both with respect to the sun 
and to the stars, so that the mteival of time contained veiv 
nearly an exact number of sidereal periods as well as of 
synodic periods By dividing therefore the observed 
interval of time by the number of sidereal periods (which 
being a whole number could readily be estimated) the 
sidereal period was easily obtained A similar process 
shewed that the synodic period of Mercuiy was about 116 
clays, and the sidereal period about 88 days 

The comparative sizes of the orbits of Venus and 
Mercury as compared with that of the earth could easily 
be ascertained from observations of the position of either 
planet when most distant from the sun Venus for 
example, appears at its greatest distance from the sun when 
at a point Vl (fig 44) such that v, E, touches the circle m 
which Venus moves, and the angle E, v. s is then (by 
a known property of a cuclc) a nght angle The angle 
s E t Y! being obseived, the shape of the triangle s E v, is 
known and the latio of its sides can be ieadily calculated 
Ihus Coppermcus found that the average distance of 
Venus from the sun was about 72 and that of Mercury 
about 36 the distance of the earth from the sun bcmi 
taken to be 100 , the coiiespondmg modem figuics are 
72 3 and 38 7 

87 In the case of the superior planets, Mars, Jupitei, 
and Saturn, it was much more difficult to iccognise that 
then motions could be explained by supposing them to 


A Short History of Astronomy 


revolve round the sun, since the centre of the epicycle 
did not always lie in the direction of the sun, but might 
be anywhere in the ecliptic One peculianty, howevei, 
m the motion of any of the supenor planets might easily 
have suggested their motion round the sun, and was either 
completely overlooked by Ptolemy or not lecogmsed by 
him as important It is possible that it was one of the 
clues which led Coppermcus to his system This peculi- 
arity is that the mdms of the epicycle of the planet, 
7j, is always parallel to the line ES joining the eaith 
and sun, and consequently performs a complete ie- 

volution in a year This 
connection between the 
motion of the planet and 
that of the sun leceived 
no explanation from 
Ptolemy's theoiy Now 
if we draw E j' paiallcl 
to j j and equal to it in 
length, it is easily seen * 
that the line j' j is equal 
and parallel to K/, that 
consequently r describes 
a circle lound / just as 
j iound E. Hence the 
motion of the planet can 
equally well be icpie- 

sented by supposing it to move in an epicycle (represented 
by the large dotted cncle in the figure) of which / is the 
centre and j' j the ladius, while the centie of the epicycle, 
remaining always in the direction of the sun, describes 
a defeient (lepresented by the small cncle iound i',) of which 
the earth is the centie By this method of icpiesentation 
the motion of the supenor planet is exactly like that ol 
an infenoi planet, except that its epicycle is laigei than 
its deferent^ the same reasoning as befoic shows that the 
motion can be lepresented simply by supposing the centie 
j' of the epicycle to be actually the sun Ptolemy's epicycle 
and deferent aie theiefore capable of being replaced, with- 
out affecting the position of the planet m the bky, by a 

* Fuclid, I 33 

FIG 45 The epicycle of Jupiter 

s? I The Motion of the Planets 117 

motion of the planet m a circle lound the sun, while the 
sun moves round the earth, or, moie simply, the earth 
lound the sun 

The synodic period of a superior planet could best be 
determined by observing when the planet was in opposition, 
2 e when it was (neaily) opposite the sun, or, more 
accurately (since a planet does not move exactly in the 
ecliptic), when the longitudes of the planet and sun differed 
by 180 (or two right angles, chapter n , 43). The 

FIG. 46 The iclativc sizes of the orbits ot the caith and of a 
superior planet 

sideieal period could then be deduced neaily as m the case 
of an infenor planet, with this difference, that the supenor 
planet moves moie slowly than the earth, and therefore loses 
one complete revolution in each synodic period, or the 
sideieal penod might be found as before by obseivmg 
when oppositions occurred neaily m the same part of the 
sky* Coppernicus thus obtained veiy fanly accurate 

* If P be the synodic penod of a planet (m ycais), and s the 
sideieal penod, then we evidently have * + I = * foi an mieiior 

planet, and I ^ 

^ foi a supcnoi planet, 

n8 A Short History of Astronomy [Cn iv 

values for the synodic and sidereal periods, viz 780 days 
and 687 days respectively for Mais, 399 days and about 
12 years foi Jupiter, 378 days and 30 years for Saturn 
(cf fig 40) 

The calculation of the distance of a superior planet 
from the sun is a good deal more complicated than that 
of Venus 01 Mercury If we ignore vanous details, the 
process followed by Coppermcus is to compute the position 
of the planet as seen from the sun, and then to notice 
\vhen this position differs most from its position as seen 
from the earth, i e when the earth and sun are farthest apart 
as seen from the planet This is clearly when (fig 46) 
the line joining the planet (p) to the earth (E) touches the 
circle described by the earth, so that the angle s P E is 
then as great as possible The angle p E s is a right 
angle, and the angle s P E is the difference between the 
observed place of the planet and its computed place as 
seen from the sun , these two angles being thus known, the 
shape of the triangle s p E is known, and therefore also 
the latio of its sides In this way Coppemicus found 
the average distances of Mars, Jupiter, and Saturn from the 
sun to be respectively about i|, 5, and 9 times that of the 
earth ; the corresponding modem figures are i 5, 5 2, 9 5 

88 The explanation of the stationary points of the 
planets (chapter i , 14) is much simplified by the ideas of 
Coppermcus If we take first an mfenoi planet, say Mercury 
(fig 47), then when it lies between the earth and sun, as 
at M (or as on Sept 5 in fig 7), both the eaith and Mei- 
cury are moving m the same direction, but a comparison 
of the sizes of the paths of Mercury and the earth, and of 
their respective times of performing complete circuits, shews 
that Mercury is moving faster than the earth Consequently 
to the observer at E, Mercury appears to be moving from 
left to right (in the figure), or from east to west , but this 
is contrary to the general direction of motion of the planets, 
le Mercuiy appears to be retiogiadmg On the othei 
hand, when Mercury appears at the greatest distance fiom 
the sun, as at M, and M_>, its own motion is dneclly towaids 
or away from the earth, and is therefore impeiceptible , 
but the earth is moving towards the observers nght, and 
therefoie Mercury appears to be moving towards the left, 

$ 88 1 Stationary Points 119 

or from west to east. Hence between M t and M its motion 
has changed from direct to retrograde, and therefoie at 
some intermediate point, say ;, (about Aug. 23 m fig 7), 
Mercury appears for the moment to be stationary, and 
similarly it appears to be stationary again when at some point 
m 3 between M and M^ (about Sept 13 m fig 7) 
In the case of a superior planet, say Jupiter, the argument 

FIG 47 The stationary points of Mercury 

is nearly the same When in opposition at j (as on 
Mar 26 m fig 6), Jupiter moves more slowly than the 
earth, and in the same direction, and theiefore appeal s to 
be moving m the opposite direction to the earth, i e as seen 
from E (fig 48), from left to right, or from east to west, that 
is in the rctrogiade direction But when Jupiter is m 
either of the positions j, or j (m which the earth appears 
to the ob&eivei on Jupiter to be at its gieatest distance 


A Short History of Astronomy [Cn iv 

from the sun), the motion of the earth itself being directly 
to or from Jupiter produces no effect on the apparent 
motion of Jupiter (since any displacement directly to or 
fiom the observer makes no difference m the object's 
place on the celestial sphere) , but Jupiter itself is actually 
moving towards the left, and therefoie the motion of 

FIG 48 The stationary points of Jupiter 

Jupiter appears to be also fiom light to left, or from west 
to east Hence, as before, between j, and j and between 
j and ] 2 there must be points / j 2 (Jan 24 and May 27, 
in fig 6) at which Jupiter appears for the moment to be 

The actual discussion of the stationary points given by 
Coppermcus is a good deal more elaborate and more 
technical than the outline given here, as he not only shews 

89, go] The Motion of the Planets 121 

that the stationary points must exist, but shews how to 
calculate their exact positions 

89 So far the theory of the planets has only been 
sketched very roughly, m order to bring into prominence 
the essential differences between the Coppermcan and the 
Ptolemaic explanations of their motions, and no account 
has been taken of the minor irregularities for which Ptolemy 
devised his system of equants, eccentrics, etc , nor of the 
motion m latitude, i e to and from the ecliptic Copper- 
nicus, as already mentioned, rejected the equant, as being 
productive of an 11 regularity "unworthy'' of the celestial 
bodies, and constructed for each planet a fairly complicated 
system of epicycles Foi the motion m latitude dis- 
cussed m Book VI he supposed the orbit of each planet 
round the sun to be inclined to the ecliptic at a small 
angle, different for each planet, but found it necessary, m 
order that his theory should agiee with observation, to 
introduce the wholly imaginary complication of a regular 
increase and dcciease m the inclinations of the orbits of 
the planets to the ecliptic. 

The actual details of the epicycles employed are of no 
great mtciest now, but it may be worth while to notice that 
for the motions of the moon, eaith, and five other planets 
Coppermcus required altogether 34 circles, mz four for the 
moon, three for the eaith, seven for Mercury (the motion 
of which is peculiarly irregulai), and five for each of the 
other planets , this number being a good deal less than 
that icquired m most versions of Ptolemy's system 
Fiacastoi (chaptei in, 69), for example, writing m 1538, 
lequired 79 spheres, of which six were lequncd for the 
fixed stars 

90 The planetary theory of Coppermcus necessanly 
suffered from one of the essential defects of the system of 
epicycles. It is, in fact, always possible to choose a system 
of epicycles m such a way as to make either the direction of 
any body or its distance vaiy m any lequired manner, but 
not to satisfy both requnements at once In the case of the 
motion of the moon round the earth, or of the earth round 
the sun, cases m which vanations in distance could not 
icadily be obseived, epicycles might theiefore be expected 
to give a satisfactory le&ult, at any rate until methods of 

122 A Short History of Astronomy [CH iv 

observation were sufficiently improved to measure with some 
accuracy the apparent sizes of the sun and moon, and so 
check the variations in their distances But any variation 
in the distance of the earth from the sun would affect not 
merely the distance, but also the direction m which a planet 
would be seen , in the figure, for example, when the planet 
is at P and the sun at s, the apparent position of the planet, 
as seen from the earth, will be different according as the 
earth is at E or E' Hence the epicycles and eccentrics of 
Coppermcus, which had to be adjusted in such a way that 

E E' S 

FIG 49 The alteration in a planet's apparent position due to an 
alteration m the earth's distance from the sun 

they necessarily involved incorrect values of the distances 
between the sun and earth, gave rise to coi responding 
errors m the observed places of the planets The obser- 
vations which Coppermcus used were hardly extensive 01 
accurate enough to show this discrepancy clearly; but a 
crucial test was thus vntually suggested by means of which, 
when further observations of the planets had been made, 
a decision could be taken between an epicyclic representa- 
tion of the motion of the planets and some other geometrical 
PT The merits of Coppermcus are so great, and the part 

$ 9*1 9a] The Use of Epicycles by Coppermcus 123 

which he played m the overthrow of the Ptolemaic system 
is so conspicuous, that we are sometimes liable to forget 
that, so far fiom rejecting the epicycles and eccentrics of 
the Greeks, he used no other geometncal devices, and was 
even a more orthodox " epicyclist " than Ptolemy himself, 
as he rejected the equants of the latter * Milton's famous 
description (Par Lost, VIII 82-5) of 

"The Sphere 

With Centric and Eccentric scribbled o'er, 
Cycle and Epicycle, Orb in Orb," 

applies theiefore just as well to the astronomy of Copper- 
mcus as to that of his predecessors, and it was Kepler 
(chapter vn ), writing more than half a century later, not 
Coppermcus, to whom the rejection of the epicycle and 
eccentric is due 

92 One point which was of importance m later 
controversies deserves special mention here The basis 
of the Coppermcan system was that a motion of the 
earth carrying the observer with it produced an apparent 
motion of other bodies The apparent motions of the 
sun and planets were thus shewn to be in great part 
explicable as the result of the motion of the earth round 
the sun Similar reasoning ought apparently to lead 
to the conclusion that the fixed stars would also appear 
to have an annual motion There would, in fact, be a 
displacement of the apparent position of a star due to 
the alteration of the earth's position m its orbit, closely 
resembling the alteration in the apparent position of the 
moon due to the alteration of the observer's position 
on the earth which had long been studied under the name 
of parallax (chapter n , 43) As such a displacement 
had nevei been observed, Coppermcus explained the 
apparent contiadiction by supposing the fixed stars so 

K Recent biogiapheis have called attention to a cancelled passage 
in the manuscript of the DC Revolutionists in which Coppermcus 
jshcws* that an ellipse can be generated by a combination of cncular 
motions The pioposition is, howevei, only a piece of pure mathe- 
matics, and has no relation to the motions of the planets round the 
sun It cannot, thciefoie, fairly be icgarded as in any way aj> 
anticipation of the ideas of Kcplu (chapter yn ), 


A Short History of Astronomy CH iv , $ 92 

fai off that any motion due to this cause was too small 
to be noticed If, for example, the earth moves in six 
months from E to E', the change in direction of a star at 
s' is the angle E' s' E, which is less than that of a nearer 
star at s 3 and by supposing the star s' sufficiently remote, 
the angle E' s' E can be made as small as may be required 
For instance, if the distance of the star were 300 times 
the distance E E', ^ e 600 times as far from the eaith as 

FIG 50 Stellar parallax 

the sun is, the angle E s' E' would be less than 12', 
a quantity which the instruments of the time were bai cly 
capable of detecting * But more accurate obseivations 
of the fixed stars might be expected to throw fuithei light 
on this problem 

1 It may be noticed that the differential method of parallax 
(chapter vi , 129), by which such a quantity as 12' could have 
been noticed, was put out of court by the geneial supposition, shared 
by Coppernicus, that the stars were all at the same distance fiom 



" Preposleioas wits that cannot low at ease 
On the smooth channel of our common seas, 
And such are those, in my conceit at least, 
Those clerks that think think how absuid a jest ' 
That neither heavens nor stars do turn at all, 
Noi clance about this great round Earthly Ball, 
But the Eaith itself, this massy globe of ouis, 
Tui ns round about once every twice twelve hours ' " 

Du BARIAS (Sylvester's translation) 

93 THE publication of the De Revolutionists appears to 
have been received much more quietly than might have 
been expected from the staithng nature of its contents 
The book, in fact, was so wiitten as to be unintelligible except 
to mathematicians of considerable knowledge and ability, 
and could not have been read at all generally Moieover 
the preface, inserted by Osiandei but geneially supposed 
to be by the author himself, must have done a good deal 
to disarm the hostile criticism due to prejudice and custom, 
by repiesentmg the fundamental principles of Coppemicus 
as mere geometrical absti actions, convenient foi calcu- 
lating the celestial motions Although, as we have seen 
(chapter iv , 73), the contradiction between the opinions 
of Coppemicus and the common interpretation of vanous 
passages in the Bible was promptly noticed by Luther, 
Melanchthon, and others, no objection was laised either 
by the Pope to whom the book was dedicated, or by his 
immediate successois 

The enthusiastic advocacy of the Coppermcan vie\vs by 
Rhelicus has alieady been refeired to The only olhei 

126 -^ Short History of Agronomy [Cn v 

astionomer of note who at once accepted the new views 
W , aS o h ',r lend and c llea g u e Erasmus Remhold (bom 
at Saalfeld in 1511), who occupied the chief chaii of 
mathematics and astionomy at Wittenbeig fiom 15-^6 to 
1553, and it thus happened, curiously enough, that* the 
doctrines so emphatically condemned by two of the meat 
Protestant leadeis were championed principally m what 
was generally legarded as the vety centre of Protestant 

94 Rheticus, after the publication of the Narratio 
Pnma and of an Ephemens or Almanack based on 
Coppemican principles ( I5S o), occupied himself principally 
with the calculation of a veiy extensive set of mathematical 
tables, which he only succeeded m finishing just bcfoie his 
death in 1576 

Remhold icndeied to astionomy the extremely rmpoitant 
service of calculating, on the basis of the De Revolution^*, 
tables of the motions of the celestial bodies, which weie 
published m 1551 at the expense of Duke Albeit of Piussia 
and hence called Tabula Prufetucas, or Prussian Tables 
-Remhold levised most of the calculations made by Coppei- 
mcus, whose arithmetical woik was occasionally at fault 
but the chief object of the tables was the development m 
great detail of the woik in the Dt Revolutionists, such 
a foim that the places of the chief celestial bodies at any 
lequued time could be ascertained with ease The author 
claimed for his tables that from them the places of all the 
heavenly bodies could be computed foi the past 3,000 veais 
and would agree with all observations recofdeddunng that 
period The tables were indeed found to be on the whole 
decided y supenoi to their predecessor the Alfonso 
Tables chapter in , 66), and gradually came mo.e and 
moie into favour, until superseded three-quarters of a cen- 
tuiy later by the RudolpJune Table, of Kepler (chapter vn , 
148) This supenouty of the new tables was only 
indirectly connected with the difference m the principles 
on which the two sets of tables were based, and was kS 
due to the facts that Remhold was a much bettei compute 
than the assistants of Alfonso, and that Coppeimcus rf 
not a bettei mathematician than Ptolemy, at an? ate ha 1 
bettei mathematical tools at command Never belts he 

94,95] The Reception of the Coppernican Ideas 127 

tables naturally had gieat weight in inducing the astio- 
nomical world gradually to recognise the merits of the 
Coppernican system, at any late as a basis for calculating 
the places of the celestial bodies 

Remhold was unfortunately cut off by the plague in 
1553, and with him disappeaied a commentaiy on the De 
Revolutionism which he had piepared but not published 

95 Very soon afteiwaids we find the first signs that the 
Coppernican system had spread into England In 1556 
John Field published an almanack foi the following year 

avowedly based on Coppermcus and Remhold, and a 
passage m the Whetstone of Witte (1557) by Robert Recorde 
(1510-1558), our fiist wntei on algebia, shews that the 
author regarded the doctrines of Coppeimcus with favour, 
even if he did not believe in them entirely A few years 
latei Thomas Digges (?-i595)> m his Alae sive ScaZae Mathe- 
maticae (1573), an astronomical tieatise of no gieat import- 
ance, gave warm piaise to Coppermcus and his ideas 

96 For nearly half a century after the death of Remhold 
no important contributions were made to the Coppernican 
controversy Remhold's tables were doubtless slowly 
doing their work in familiarising men's minds with the 
new ideas, but certain definite additions to knowledge had 
to be made before the evidence for them could be regarded 
as really conclusive 

The serious mechanical difficulties connected with the 
assumption of a rapid motion of the eaith which is quite 
imperceptible to its inhabitants could only be met by 
further progress in mechanics, and specially in knowledge 
of the laws according to which the motion of bodies is 
pioduced, kept up, changed, or destroyed , in this direction 
no considerable progress was made befoie the time of 
Galilei, whose woik falls chiefly into the eaily i7th centuiy 
(cf chapter vi , 116, 130, 133) 

The objection to the Coppernican scheme that the stais 
shewed no such apparent annual motions as the motion 
of the eaith should pioduce (chapter iv , 92) would also 
be eithci answcied or strengthened according as improved 
methods of obseivation did or did not tevcal the required 

Moieover the Prussian Table^ although moie accurate 

128 A Short History of Astronomy [CH v 

than the Alfonsine^ haidly claimed, and certainly did not 
possess, minute accuracy Coppermcus had once told 
Rheticus that he would be extravagantly pleased if he 
could make his theory agree with observation to within 10', 
but as a matter of fact disci epancies of a much more 
serious character were noticed from time to time The 
comparatively small numbei of observations available and 
their roughness made it extremely difficult, eithei to find 
the most satisfactory numerical data necessaiy for the 
detailed development of any theory, or to test the theory 
properly by comparison of calculated with observed places 
of the celestial bodies Accordingly it became evident to 
more than one astronomer that one of the most piessmg 
needs of the science was that observations should be taken 
on as laige a scale as possible and with the utmost 
attainable accuracy. To meet this need two schools of 
observational astronomy, of veiy unequal excellence, de- 
veloped during the latter half of the i6th century, and 
provided a mass of material for the use of the astionomers 
of the next generation Fortunately too the same period was 
marked by rapid progress m algebra and allied branches of 
mathematics Of the three great inventions which have so 
enormously diminished the labour of numerical calculations, 
one, the so-called Arabic notation (chapter in , 64), 
was already familiar, the other two (decimal fractions and 
logarithms) were suggested m the i6th century and were 
in working order early in the lyth century 

97 The first important set of observations taken after 
the death of Regiomontanus and Walther (chapter in , 68) 
were due to the energy of the Landgrave William JV of 
Hesse (1532-1592) He was remarkable as a boy for his 
love of study, and is reported to have had his interest m 
astronomy created or stimulated when he was little more 
than 20 by a copy of Apian's beautiful Astronomicitm 
Caesareum, the cardboard models in which he caused to be 
imitated and developed m metal-work He went on with 
the subject seriously, and in 1561 had an observatory built 
at Cassel, which was remarkable as being the first which had 
a revolving roof, a device now almost universal. In this he 
made extensive observations (chiefly of fixed staib) dunrig 
the next six years The death of his father then compelled 

$$ 97, 98] The Cassel Observatory 129 

him to devote most of his energy to the duties of govern 
ment, and his astronomical ardour abated A few years 
later, however (1575), as the result of a short visit from 
the talented and enthusiastic young Danish astronomer 
Tycho Brahe ( 99), he renewed his astronomical work, and 
secured shortly afterwaids the sei vices of two extremely able 
assistants, Christian Rothmann (in 1577) zxAJoost Burgi 
(in 1579). Rothmann, of whose life extremely little is 
known, appears to have been a mathematician and theo- 
retical astronomei of considerable ability, and was the 
author of several improvements in methods of dealing 
with various astronomical problems He was at first a 
Coppermcan, but shewed his independence by calling 
attention to the needless complication introduced by 
Coppermcus in resolving the motion of the earth into 
three motions when two sufficed (chapter iv , 79) His 
faith in the system was, however, subsequently shaken by 
the errors which observation revealed in the Prussian Tables 
Burgi (1552-1632) was originally engaged by the Landgrave 
as a clockmaker, but his remarkable mechanical talents 
were soon turned to astronomical account, and it then 
appealed that he also possessed unusual ability as a 
mathematician * 

98. The chief work of the Cassel Observatory was the 
foimation of a stai catalogue The positions of stars were 
compared with that of the sun, Venus 01 Jupiter being 
used as connecting links, and then positions relatively to 
the equatoi and the first point of Aries (r) deduced, 
allowance was regularly made foi the cirois due to the 
refraction of light by the atmosphere, as well as for the 
paiallax of the sun, but the most notable new departure 
was the use of a clock to lecord the time of observa- 
tions and to measuie the motion of the celestial spheie 
The constiuction of clocks of sufficient accuiacy for the 
purpose was rendered possible by the mechanical genius 
of Burgi, and in paiticulai by his discovery that a clock 
could be regulated by a pendulum, a discovery which he 

" There is hitle doubt that he invented what were substantially 
logarithms independently of Napier, but, with chaiactenstic inability 
or unwillingness to proclaim his discovenes, allowed the invention 
to die with him 

130 A Short History of Astronomy [Cn v 

appears to have taken no steps to publish, and which had 
in consequence to be made again independently befoie it 
received general recognition * By 1586 121 stars had been 
carefully observed, but a more extensive catalogue which 
was to have contained more than a thousand stars was 
never finished, owing to the unexpected disappeaiance of 
Rothmann in 1590 f and the death of the Landgiave two 
yeais later 

99 The woik of the Cassel Obseivatoiy was, however, 
overshadowed by that earned out nearly at the same time 
by Tycho (Tyge) Brake He was born in 1546 at Knudstiup 
in the Danish province of Scania (now the southern 
extremity of Sweden), being the eldest child of a nobleman 
who was afterwards governoi of Helsmgborg Castle He 
was adopted as an infant by an uncle, and brought up 
at his country estate When only 13 he went to the 
University of Copenhagen, where he began to study 
rhetoric and philosophy, with a view to a political career 
He was, however, very much interested by a small eclipse 
of the sun which he saw in 1560, and this stimulus, added 
to some taste for the astrological ait of casting horoscopes, 
led him to devote the greater pait of the icmaimng two 
years spent at Copenhagen to mathematics and astronomy. 
In 1562 he went on to the University of Leip/ig, accom- 
panied, according to the custom of the time, by a tutoi, 
who appears to have made persevering but unsuccessful 
attempts to induce his pupil to devote himself to law 
Tycho, however, was now as always a difficult person to divett 
from his purpose, and went on steadily with his astronomy 
In 1563 he made his first recorded observation, of a close 
approach of Jupiter and Saturn, the time of which he noticed 
to be predicted a whole month wrong by the Alfoimnc 
Tables (chapter in , 66), while the Prussian Tables ( 94) 
were several days in erroi While at Leipzig he bought 
also a few rough mstiuments, and anticipated one of the 
great improvements afterwards earned out systematically, 

* A similar discovery was in fact made twice again, by Galilei 
(chapter vi, 114) and by Huygens (chapter vxii , ^ 157) 

t He obtained leave of absence to pay a visit to Tycho Hnihc 
and never returned to Cassel He must have died between 1599 

99, .oo] Early Ltfe of TycJio Brake 

uTstrunien ^ eSt ' mate and to allow for the error s of his 
In 1565 Tycho returned to Copenhagen, probably on 
account of the war with Sweden which had just broken out 
and stayed about a year, during the course of which he lost 
his uncle. He then set out again (1566) on his travels 
and visited Wittenberg, Rostock, BaslehrlgolstadtXgsbut 
and other centres of learning, thus making acquaintance 
with several of the most notable astronomers of Germany 
At Augsburg he met the brothers Hauuel, rich cUizens 
with a taste for science, for one of whom he des lg ned and 
had constructed an enormous quadraat (quarter-circled 
with a radius of about I0 feet" the rim ^ which was 
graduated to single minutes ; and he began also here the 
construction of his great celestial globe, five feet in diameter, 
on which he marked one by one the pos.tions of the stars 
as he afterwards observed them 

In 1570 Tycho returned to his father at Helsmgbonr 
and soon after the death of the latter (1571) went ftr 
a long visit to Steen Bille, an uncle with scientific tastes" 
Curing this visit he seems to have devoted most of his 
time to chemistry (or peihaps rather to alchemy), and his 
astronomical studies fell into abeyance for a time 

loo His mteiest in astronomy was fortunately revived 
by the sudden appearance, in November 1572, of a brilliant 
new star m the constellation Cassiopeia Of this Tycho 
took a number of extremely careful obseivations , he noted 
the gradual changes in its brilliancy from its first appearance, 
when ,t rivalled Venus at her brightest, down to us final 
disappearance 16 months later He repeatedly measured 
its angular distance fiom the chief stars in Cassiopeia, 
and applied a variety of methods to asceitam whether it 
had any perceptible parallax (chapter n , 43 4g ) N O 
parallax could be definitely detected, and he deducedaccord 
mgly that the stai must certainly be faither off than the moon 
as moreover it had no share in the planetary motions, he 
inferred that it must belong to the reg.on of the fixed stars. 
lo us of to-day this result may appeal fairly commonplace, 
but most astronomers of the time held so firmly to Aristotle's 
doctrine that the heavens generally, and the region of the 
fixed stars in particular, were incouuptible and unchange- 

I 3 2 A Short History of Astronomy [Cn v,ioi 

able, that new stars were, like comets, almost universally 
ascribed to the highei regions of our own atmosphere 
Tycho wrote an account of the new star, which he was ulti- 
mately induced by his friends to publish (1573), together 
with some portions of a calendar for that year which he had 
prepared His reluctance to publish appeals to have been 
due m great part to a belief that it was unworthy of the 
dignity of a Danish nobleman to wnte books ' The 
book m question (De Nova Stella) compares veiy 

favourably with the numerous other writings which the 
star called forth, though it shews that Tycho held the 
common beliefs that comets were in our atmosphere, and 
that the planets were carried round by solid ciystallme 
spheres, two delusions which his subsequent work did 
much to destroy. He also dealt at some length with the 
astrological importance of the star, and the great events 
which it foreshadowed, utterances on which Keplci sub- 
sequently made the very sensible criticism that "if that 
star did nothing else, at least it announced and produced 
a great astronomer " 

In 1574 Tycho was lequested to give some astronomical 
lectures at the University of Copenhagen, the fust of which, 
dealing largely with astrology, was printed in 1610, after his 
death. When these were finished, he set off again on his 
travels (1575) After a short visit to Cassel ( 97), during 
which he laid the foundation of a lifelong friendship with 
the Landgiave, he went on to Frankfoit to buy books, 
thence to Basle (where he had serious thoughts of settling) 
and on to Venice, then back to Augsburg and to Regens- 
burg, where he obtained a copy of the Commentariolu* of 
Coppermcus (chaptei iv., 73), and finally came home 
by way of Saalfeld and Wittenberg 

101 The next year (1576) was the beginning of a 
new epoch m Tycho's career. The King of Denmaik, 
Frederick II., who was a zealous patron of science and 
literature, determined to provide Tycho with endowments 
sufficient to enable him to carry out his astronomical work 
m the most effective way He accordingly gave him for 
occupation the little island of Hveen m the Sound (now 
belonging to Sweden), promised money for building a 
house and observatory, and supplemented the income 

134 A Short History of Astronomy [CH v 

derived from the rents of the island by an annual paymen 
of about ;ioo Tycho paid his first visit to the island n 
May, soon set to work building, and had already begun tc 
make regular observations in his new house before the 
end of the year 

The buildings were as remarkable for their magnificence 
as for their scientific utility Tycho never forgot that he wa ( 
a Danish nobleman as well as an astronomer, and built ir 
a manner suitable to his rank. 1 His chief building (fig 51) 
called Uraniborg (the Castle of the Heavens), was in the 
middle of a large square enclosure, laid out as a garden 
the corners of which pointed North, East, South, and West 
and contained several observatories, a library and laboratory 
in addition to living rooms Subsequently, when the numbe 
of pupils and assistants who came to him had increased 
he erected (1584) a second building, Stjerneborg (Sta 
Castle), which was remarkable for having undergrounc 
observatories. The convenience of being able to cairy ou 
all necessaiy work on his own premises induced hm 
moreover to establish woikshops, where nearly all hi< 
instruments were made, and afterwards also a printing pres- 
and paper null Both at Uraniborg and Stjerneborg no 
only the rooms, but even the instruments which wen 
gradually constructed, were elaborately painted or otherwise 

102 The expenses of the establishment must have beer 
enormous, particularly as Tycho lived in magnificent stylt 
and probably paid little attention to economy His income 
was derived from various sources, and fluctuated from tim< 
to time, as the King did not merely make him a fixec 
annual payment, but added also temporaiy grants of land 
or money Amongst other benefactions he received n 
1579 one of the canonnes of the cathedral of Roshlde 
the endowments of which had been practically seculansec 
at the Reformation. Unfortunately most of his propert 
was held on tenures which involved corresponding obliga 
tons, and as he combined the irritability of a genm 
with the haughtiness of a mediaeval nobleman, contmua 
quarrels were the result Very soon after his arrival a 

* He even did not forget to provide one of the most necessar 
parts of a mediaeval castle, a prison ' 

$$ 102, IDS] Life at Hveen 135 

Hveen his tenants complained of work which he illegally 
forced from them , chapel services which his canonry 
required him to keep up were neglected, and he entirely 
refused to make certain recognised payments to the widow 
of the previous canon Further difficulties arose out of a 
lighthouse, the maintenance of which was a duty attached 
to one of his estates, but was regularly neglected Nothing 
shews the King's good feeling towards Tycho more than 
the trouble which he took to settle these quarrels, often 
ending by paying the sum of money under dispute. Tycho 
was moreover exti emery jealous of his scientific reputation, 
and on more than one occasion broke out into violent 
abuse of some assistant or visitor whom he accused of 
stealing his ideas and publishing them elsewhere 

In addition to the time thus spent m quarrelling, a good 
deal must have been occupied in entertaining the numerous 
visitois whom his fame attracted, and who included, m 
addition to astronomers, persons of rank such as several 
of the Danish royal family and James VI of Scotland 
(afterwards James I of England) 

Notwithstanding these distractions, astronomical work 
made steady progress, and during the 21 years that Tycho 
spent at Hveen he accumulated, with the help of pupils 
and assistants, a magnificent series of observations, far 
transcending in accuracy and extent anything that had 
been accomplished by his predecessors A good deal of 
attention was also given to alchemy, and some to medicine. 
He seems to have been much impressed with the idea 
of the unity of Nature, and to have been continually 
looking out for analogies or actual connection between 
the different subjects which he studied 

103 In 1577 appeared a brilliant comet, which Tycho 
observed with his customary care, and, although he had 
not at the time his full complement of instruments, his 
observations were exact enough to satisfy him that the 
comet was at least three times as far off as the moon, and 
thus to refute the populai belief, which he had himself 
held a few yeais befoie ( 100), that comets were generated 
m oui atmosphere. His observations led him also to the 
belief that the comet was revolving round the sun, at a 
distance from it greater than that of Venus, a conclusion 

136 A Short History of Astronomy [Or v 

which mterfeied seriously with the common doctrine of 
the solid crystalline spheres. He had further opportunities 
of observing comets in 1580, 1582, 1585, 1590, and 1596, 
and one of his pupils also took observations of a comet 
seen in 1593 None of these comets attracted as much 
general attention as that of 1577, but Tycho's observations, 
as was natural, gradually improved in accuracy 

104 The valuable results obtained by means of the new 
star of 1572, and by the comets, suggested the propriety of 
undertaking a complete treatise on astronomy embodying 
these and other discoveries Accoidmg to the original 
plan, there were to be three preliminary volumes devoted 
respectively to the new stai, to the comet of 1577, and to 
the later comets, while the mam tieatise was to consist of 
several moie volumes dealing with the theories of the sun, 
moon, and planets Of this magnificent plan compaiatively 
little was ever executed The fiist volume, called the 
Astronomiae Instauratae Progymnasmota^ or Introduction 
to the New Astronomy, was hardly begun till 1588, and, 
although mostly printed by 1592, was never quite finished 
during Tycho's lifetime, and was actually published by 
Kepler in 1602 One question, in fact, led to another 
in such a way that Tycho felt himself unable to give 
a satisfactory account of the star of 1572 without 
dealing with a number of preliminary topics, such as the 
positions of the fixed stars, precession, and the annual 
motion of the sun, each of which necessitated an 
elaborate investigation The second volume, dealing with 
the comet of 1577, called De Mundi aether ei recent lonbw 
Phaenomems Liber secundus (Second book about recent 
appearances in the Celestial World), was finished long 
before the first, and copies were sent to fuends and 
correspondents in 1588, though it was not regularly pub- 
lished and on sale till 1603 The third volume was never 
written, though some material was collected foi it, and the 
rnam tieatise does not appear to have been touched 

105 The book on the comet of 1577 is of special 
{interest, as containing an account of Tycho's system of the 
world, which was a compromise between those of Ptolemy 
and of Coppernicus Tycho was too good an astronomei 
not to realise many of the simplifications which the 

$ 104, IDS] Tychds System of the World 137 

Coppernican system introduced, but was unable to answer 
two of the serious objections , he regarded any motion of 

FIG. 52 fycho's system of the world From his book on the 
comet of 1577 

" the sluggish and heavy earth " as contrary to " physical 
principles," and he objected to the great distance of the 

J 3^ A Short History of Astronomy [CH v 

stars which the Coppernican system required, because a vast 
empty space would be left between them and the planets, 
a space which he regarded as wasteful * Biblical difficul- 
ties t also had some weight with him He accordingly 
devised (1583) a new system according to which the five 
planets revolved round the sun (c, in fig 52), while the sun 
revolved annually round the earth (A), and the whole celestial 
sphere performed also a daily revolution lound the earth 
The system was nevei worked out in detail, and, like many 
compromises, met with little support, Tycho nevertheless 
was extremely proud of it, and one of the most violent and 
prolonged quarrels of his life (lasting a dozen years) was with 
Reymers Bar or Ursus (?-i6oo), who had communicated 
to the Landgrave m 1586 and published two years later a 
system of the world very like Tycho's Reymeis had been 
at Hveen for a short time in 1584, and Tycho had no hesita- 
tion m accusing him of having stolen the idea from some 
manuscript seen there Reymers naturally retaliated with 
a counter-charge of theft against Tycho Theie is, how- 
ever, no good reason why the idea should not have occurred 
independently to each astronomer , and Reymers made m 
some respects a great improvement on Tycho's scheme by 
accepting the daily rotation of the earth, and so doing 
away with the daily rotation of the celestial sphere, which 
was certainly one of the weakest parts of the Ptolemaic 

1 06 The same year (1588) which saw the publication of 
Tycho's book on the comet was also marked by the death 
of his patron, Frederick II The new King Christian was 
a boy of n, and for some years the country was managed 
by four leading statesmen The new government seems to 
have been at first quite friendly to Tycho , a large sum was 
paid to him for expenses incurred at Hveen, and additional 
endowments were promised, but as time went on Tycho's 
usual quarrels with his tenants and others began to produce 

* It would be mteiestmg to know what use he assigned to the 
(presumably) still vaster space beyond the stars 

f Tycho makes m this connection the delightful remark that 
Moses must have been a skilled astronomer, because he refers to 
the moon as "the lesser light," notwithstanding the fact that the 
apparent diameters of sun and moon are very nearly equal J 

[To face / 

** Io6 ' I0 7l Last Years at Hveen 139 

their effect In 1594 he lost one of his chief supporters 
at court, the Chancellor Kaas, and his successor, as well as 
two 01 three other important officials at court, were not 
very friendly, although the stones commonly told of violent 
personal animosities appear to have little foundation As 
early as 1591 Tycho had hinted to a correspondent that 
he might not remain permanently in Denmark, and m 1594 
he began a correspondence with representatives of the 
Emperor Rudolph II , who was a pation of science But 
his scientific activity during these years was as great as 
ever, and m 1596 he completed the printing of an 
extremely interesting volume of scientific con espondence 
between the Landgrave, Rothmann, and himself The 
accession of the young King to power in 1596 was at once 
followed by the withdrawal of one of Tycho's estates, and 
m the following year the annual payment which had been 
made since 1576 was stopped It is difficult to blame the 
King for these economies , he was evidently not as much 
interested in astronomy as his father, and consequently re- 
garded the heavy expenditure at Hveen as an extravagance, 
and it is also probable that he was seriously annoyed at 
Tycho's maltreatment of his tenants, and at other pieces of 
unruly conduct on his part Tycho, however, regarded the 
forfeiture of his annual pension as the last stiaw, and left 
Hveen early in 1597, taking his moie portable pioperty 
with him After a few months spent in Copenhagen, he 
took the decisive step of leaving Denmark for Germany, 
in return for which action the King deprived him of his 
canonry. Tycho thereupon wiote a remonstrance in 
which he pointed out the impossibility of carrying on his 
work without proper endowments, and offered to return 
if his services were properly appreciated The King, 
however, was by this time seriously annoyed, and his reply 
was an enumeration of the various causes of complaint 
against Tycho which had arisen of late years Although 
Tycho made some more attempts through various friends 
to regain royal favour, the breach lemamed final. 

107 Tycho spent the winter 1597-8 with a friend near 
Hambuig, and, while there, issued, under the title of 
Astronomiae Instauratae Mechanica, a description of his 
instruments, togethei with a short autobiography and an 

14 -A Short History of Astronomy [Cn v 

interesting account of his chief discoveries About the 
same time he circulated manuscript copies of a catalogue 
of ijooo fixed stars, of which only 777 had been properly 
observed, the rest having been added hurriedly to make 
up the traditional number The catalogue and the 
Mechamca were both intended largely as evidence of his 
astronomical eminence, and were sent to various influential 
persons Negotiations went on both with the Emperor 
and with the Prince of Orange, and after another year spent 
in various parts of Germany, Tycho definitely accepted an 
invitation of the Emperoi and arrived at Prague in June 

108 It was soon agreed that he should inhabit the 
castle of Benatek, some twenty miles fiom Pi ague, where he 
accordingly settled with his family and smaller instruments 
towards the end of 1599 He at once started observing, 
sent one of his SODS to Hveen foi his laiger instruments, 
and began looking about for assistants He secured one of 
the most able ol his old assistants, and by good fortune 
was also able to attract a far greater man, John Kepler, to 
whose skilful use of the materials collected by Tycho the 
latter owes no inconsiderable part of his great reputation. 
Kepler, whose life and work will be dealt with at 
length in chaptei vn , had recently published his fiist 
important work, the Mystenum Cosmographicum ( 136), 
which had attracted the attention of Tycho among others, 
and was beginning to find his position at Gratz in Styna 
uncomfoi table on account of impending religious disputes 
After some hesitation he joined Tycho at Benatek early 
m 1600 He was soon set to work at the study of Mais 
for the planetaiy tables which Tycho was then preparing, 
and thus acquired special familianty with the observations 
of this planet which Tycho had accumulated The re- 
lations of the two astronomers were not altogether happy, 
Kepler being then as always anxious about money matters, 
and the disturbed state of the country rendering it 
difficult for Tycho to get payment from the Emperor 
Consequently Kepler very soon left Benatek and returned 
to Prague, where he definitely settled after a short visit 
to Gratz 9 Tycho also moved there towards the end of 
1600, and they then worked together harmoniously for 

108-ixo] TycMs Last Years 141 

the short lemamder of Tycho's life Though he was 
by no means an old man, there were some indications 
that his health was failing, and towards the end of 1601 
he was suddenly seized with an illness which terminated 
fatally after a few days (November 24th) It is charac- 
teristic of his devotion to the great work of his life that 
in the delirium which preceded his death he cried out 
again and again his hope that his life might not prove to 
have been fruitless (Nefrustra mxisse videar) 

109 Partly owing to difficulties between Kepler and 
one of Tycho's family, partly owing to growing political 
disturbances, scarcely any use was made of Tycho's instru- 
ments after his death, and most of them penshed during 
the Civil Wars m Bohemia Kepler obtained possession 
of his observations , but they have never been published 
except in an impeifect form. 

no. Anything like a satisfactory account of Tycho's 
sei vices to astronomy would necessarily deal largely with 
technical details of methods of observing, which would 
be out of place heie It may, however, be worth while 
to attempt to give some general account of his charac- 
teristics as an observer before referring to special dis- 

Tycho realised more fully than any of his predecessors 
the importance of obtaining observations which should not 
only be as accurate as possible, but should be taken so 
often as to preserve an almost continuous record of the 
positions and motions of the celestial bodies dealt with,, 
wheieas the prevailing custom (as illustrated for example 
by Coppermcus) was only to take obseivations now and 
then, either when an astronomical event of special interest 
such as an eclipse or a conjunction was occurring, or to 
supply some particular datum required for a point of theory. 
While Coppermcus, as has been already noticed (chapter iv , 
73), only used altogether a few dozen observations m 
his book, Tycho to take one instance observed the sun 
daily for many yeais, and must therefore have taken some 
thousands of observations of this one body, in addition to the 
many thousands which he took of other celestial bodies. 
It is true that the Arabs had some idea of observing con- 
tinuously (cf chapter in, 57), but they had too little 

1 42 A Short History of Astronomy [Cn v 

speculative powei or originality to be able to make much use 
of their observations, few of which passed into the hands of 
European astronomers Regiomontanus (chapter in., 68), 
if he had lived, might probably have to a considei- 
able extent anticipated Tycho, but his shoit life was 
too fully occupied with the study and interpretation of 
Greek astronomy for him to accomplish very much in 
other departments of the subject The Landgrave and his 
staff, who were in constant communication with Tycho, 
were woikmg in the same direction, though on the whole 
less effectively Unlike the Arabs, Tycho was, however, 
fully impressed with the idea that obseivations were only 
a means to an end, and that mere observations without 
a hypothesis or theory to connect and interpret them weie 
of little use 

The actual accuracy obtained by Tycho in his observa- 
tions naturally varied considerably according to the nature 
of the observation, the care taken, and the period of his 
career at which it was made The places which he assigned 
to nine stars which were fundamental in his star catalogue 
differ from their positions as deduced from the best modern 
observations by angles which are in most cases less than i', 
and in only one case as great as 2' (this error being chiefly 
due to refraction (chapter n , 46), Tycho's knowledge of 
which was necessarily imperfect) Other star places were 
presumably less accurate, but it will not be far from the truth 
if we assume that in most cases the errors m Tycho's obsei- 
vations did not exceed i' or 2' Kepler in a famous passage 
speaks of an error of 8' in a planetary observation by 
Tycho as impossible This great mciease in accuracy can 
only be assigned in part to the size and careful construction 
of the instruments used, the chaiactenstics on which the 
Arabs and other observers had laid such stress Tycho 
certainly used good instruments, but added veiy much to 
their efficiency, partly by minoi mechanical devices, such ns 
the use of specially constructed " sights " and of a particular 
method of graduation,* and partly by using instruments 
capable only of restricted motions, and therefore of much 
gieater steadiness than instruments which were able to point 
to any part of the sky Another extremely impoitant idea 

* By transversals 

in] Estimate of Tychds Work 143 

was that of systematically allowing as far as possible for 
the inevitable mechanical imperfections of even the best 
constructed instruments, as well as for other permanent 
causes of error It had been long known, for example, 
that the refraction of light through the atmosphere had 
the effect of sl'ghtly raising the apparent places of stars 
m the sky. Tycho took a series of observations to ascer- 
tain the amount of this displacement for different parts of 
the sky, hence constructed a table of refractions (a very 
imperfect one, it is true), and in future observations regularly 
allowed for the effect of refraction Again, it was known 
that observations of the sun and planets were liable to be 
disturbed by the effect of parallax (chapter n , 43, 49), 
though the amount of this correction was uncertain In 
cases where special accuracy was required, Tycho accord- 
ingly observed the body in question at least twice, choosing 
positions in which parallax was known to produce nearly 
opposite effects, and thus by combining the observations 
obtained a result nearly free from this particular source of 
error He was also one of the first to realise fully the 
importance of repeating the same observation many times 
under different conditions, in oider that the various acci- 
dental sources of error in the separate observations should 
as far as possible neutralise one another 

in Almost every astronomical quantity of importance 
was le-determmed and generally corrected by him The 
annual motion of the sun's apogee relative to r , for example, 
which Coppei metis had estimated at 24", Tycho fixed at 
45", the modern value being 61" , the length of the year 
he determined with an error of less than a second 3 and he 
constructed tables of the motion of the sun which gave Us 
place to within i', previous tables being occasionally 15' or 
20' wrong By an unfortunate omission he made no inquiry 
into the distance of the sun, but accepted the extremely 
inaccurate value which had been handed down, without 
substantial alteration, from astronomer to astronomer since 
the time of Hipparchus (chapter n,, 41). 

In the theory of the moon Tycho made several important 
discoveries He found that the irregularities m its move- 
ment were not fully represented by the equation of the 
centre and the evection (chapter n , 39, 48), but that 

i 4 4 A Short History of Astronomy [C v , * 

theie was a further irregularity which vanished at opposition 
and conjunction as well as at quadratures, but m inter- 
mediate positions of the moon might be as great as 4 
This irregularity, known as the variation, was, as has been 
already mentioned (chapter in , 60), veiy possibly dis- 
covered by Abul Wafa, though it had been entuely lost 
subsequently At a later stage in his career, at latest 
during his visit to Wittenberg m 1598-9, Tycho found that 
it was necessary to introduce a further small inequality 
known as the annual equation, which depended on the 
position of the earth m its path round the sun , this, how- 
ever, he never completely investigated He also ascertained 
that the inclination of the moon's orbil to the ecliptic was 
not, as had been thought, fixed, but oscillated regulaily, 
and that the motion of the moon's nodes (chapter n , 40) 
was also variable 

112 Reference has already been made to the stai 
catalogue. Its construction led to a study of precession, 
the amount of which was determined with considerable 
accuracy; the same investigation led Tycho to reject the 
supposed irregularity in precession which, under the name 
of trepidation (chapter in , 58), had confused astronomy 
for several centuries, but from this time forward rapidly lost 
its popularity. 

The planets were always a favourite subject of study 
with Tycho, but although he made a magnificent scries of 
observations, of immense value to his successors, he died 
before he could construct any satisfactoiy theoiy of the 
planetary motions He easily discovered, however, that their 
motions deviated considerably from those assigned by any 
of the planetary tables, and got as far as detecting some 
regularity in these deviations. 



"Dans la Science nous sommes tous disciples de Galilee " 

" Bacon pointed out at a distance the road to true philosophy 
Galileo both pointed it out to others, and made himself considerable 
advances in it " DAVID HUME 

113 To the generation which succeeded Tycho belonged 
two of the best known of all astionomers, Galilei and Kepler. 
Although they were nearly contemporaries, Galilei having 
been bom seven years earlier than Kepler, and surviving 
him by twelve years, their methods of work and their 
contributions to astronomy were so different in character, 
and then influence on one another so slight, that it is 
convenient to make some departure from strict chrono- 
logical oider, and to devote this chapter exclusively to 
Galilei, leaving Kepler to the next 

Galileo Galilei was born m 1564, at Pisa, at that time 
in the Grand Duchy of Tuscany, on the day of Michel 
Angelo's death and m the year of Shakespeare's birth 
His father, Vincenzo, was an impovenshed member of a 
good Floientme family, and was distinguished by his skill 
m music and mathematics Galileo's talents shewed them- 
selves early, and although it was originally intended that 
he should earn his living by trade, Vincenzo was wise 
enough to see that his son's ability and tastes rendered him 
much more fit for a professional career, and accordingly 
he sent him in 1581 to study medicine at the University 
of Pisa Here his unusual gifts soon made him con- 
spicuous, and he became noted m particular for his 
unwillingness to accept without question the dogmatic 
statements of his teachers, which were based not on direct 

I4S 10 

146 A Short History of Astronomy [Cn vi, 

evidence, but on the authority of the great writers of the 
past This valuable characteristic, which marked him 
throughout his life, coupled with his skill in argument, 
earned for him the dislike of some of his professors, and 
from his fellow-students the nickname of The Wrangler 

114 In 1582 his keen observation led to his first scien- 
tific discovery Happening one day in the Cathedral of 
Pisa to be looking at the swinging of a lamp which was 
hanging from the roof, he noticed that as the motion 
gradually died away and the extent of each oscillation 
became less, the time occupied by each oscillation remained 
sensibly the same, a result which he verified more precisely 
by comparison with the beating of his pulse Further 
thought and trial shewed him that this property was not 
peculiar to cathedral lamps, but that any weight hung by 
a string (or any other form of pendulum) swung to and fro 
in a time which depended only on the length of the string 
and other characteristics of the pendulum itself, and not 
to any appreciable extent on the way in which it was set 
in motion or on the extent of each oscillation He devised 
accordingly an instrument the oscillations of which could 
be used while they lasted as a measure of time, and which 
was in practice found very useful by doctors for measuring 
the rate of a patient's pulse 

115. Before very long it became evident that Galilei had 
no special taste for medicine, a study selected for him 
chiefly as leading to a reasonably lucrative professional 
caieer, and that his real bent was for mathematics and its 
applications to experimental science He had received 
little or no formal teaching in mathematics before his second 
year at the University, m the course of which he happened 
to overhear a lesson on Euclid's geometiy, given at the 
Grand Duke's court, and was so fascinated that he con- 
tinued to attend the course, at first surreptitiously, afterwards 
openly 3 his interest in the subject was thereby so much 
stimulated, and his aptitude for it was so marked, that he 
obtained his father's consent to abandon medicine in favour 
of mathematics 

In 1585, however, poverty compelled him to quit the 
University without completing the regular course and 
obtaining a degree, and the next four years were spent 

114-116] The Pendulum Falling Bodies 147 

chiefly at home, where he continued to read and to think 
on scientific subjects. In the year 1586 he wrote his first 
known scientific essay, * which was circulated in manuscript, 
and only printed during the present century 

116 In 1589 he was appointed for three years to a 
professorship of mathematics (including astionomy) at Pisa 
A miserable stipend, equivalent to about five shillings a 
week, was attached to the post, but this he was to some 
extent able to supplement by taking private pupils. 

In his new position Galilei had scope for his remarkable 
power of exposition, but far from being content with giving 
lectures on traditional lines he also earned out a series of 
scientific investigations, important both in themselves and 
on account of the novelty m the method of investigation 

It will be convenient to discuss more fully at the end 
of this chapter Galilei's contributions to mechanics and to 
scientific method, and merely to refer here briefly to his 
first experiments on falling bodies, which were made at this 
time Some weie pei formed by dropping various bodies 
from the top of the leaning tower of Pisa, and others by 
rolling balls down giooves airanged at different inclinations 
It is difficult to us nowadays, when scientific experiments 
aie so common, to realise the novelty and importance at 
the end of the i6th century of such simple experiments 
The mediaeval tradition of carrying out scientific investiga- 
tion largely by the interpretation of texts in Aristotle, Galen, 
01 other great wnters of the past, and by the deduction 
of results from general principles which were to be found 
in these wntcis without any fresh appeal to observation, 
still prevailed almost undisturbed at Pisa, as elsewhere 
It was m paiticular commonly asserted, on the authority 
of Anstotle, that, the cause of the fall of a heavy body 
being its weight, a heavier body must fall faster than a 
lighter one and m propoition to its greater weight It may 
perhaps be doubted whether any one before Galilei's time 
had clear enough ideas on the subject to be able to give 
a definite answer to such a question as how much farther 
a ten-pound weight would fall m a second than a one-pound 

* On an instrument which he had invented, called the hydrostatic 

i 4 8 A Short History of Astronomy LUl V1 

weight , but if so he \\ouldprobably have said that it would 
fall ten times as far, or else that it would require ten times 
as long to fall the same distance To actually try the 
experiment, to vary its conditions, so as to icmove as many 
accidental causes of error as possible, to increase m some 
way the time of the fall so as to enable it to be measuied 
with more accuracy, these ideas, put into piactice by Galilei, 
were entiiely foieign to the prevailing habits of scientific 
thought, and were indeed regarded by most of his col- 
leagues as undesirable if not dangerous innovations A 
few simple experiments were enough to prove the complete 
falsity of the current beliefs m this matter, and to establish 
that m general bodies of diffeient weights fell nearly the 
same distance m the same time, the difference being not 
more than could reasonably be ascribed to the resistance 
offeied by the an 

These and other results were embodied in a tract, which, 
like most of Galilei's eaiher writings, was only cuculatcd 
in manuscript, the substance of it being first printed in the 
great treatise on mechanics which he published towards 
the end of his life ( 133) 

These innovations, coupled with the slight respect that 
he was in the habit of paying to those who differed fiom 
him, evidently made Galilei far from popular with his 
colleagues at Pisa, and either on this account, or on account 
of domestic troubles consequent on the death of his fathci 
(1591), he resigned his professorship shortly before the 
expiration of his term of office, and returned to his mother's 
home at Florence 

117 After a few months spent at Florence he was 
appointed, by the influence of a Venetian friend, to a 
professorship of mathematics at Padua, which was then in 
the territory of the Venetian republic (1592). The ap- 
pointment was m the first instance for a pcnod of six years, 
and the salary much larger than at Pisa During the first 
few years of Galilei's career at Padua his activity seems 
to have been very great and veiy varied , in addition to 
giving his regular lectures, to audiences which rapidly in- 
creased, he wrote tracts, for the most pait not printed at 
the time, on astronomy, on mechanics, and on fortification, 
and invented a variety of scientific mstiumcnts 

ii7, 8] First Astronomical Discoveries 149 

No record exists of the exact time at which he first 
adopted the astronomical views of Coppermcus, but he 
himself stated that m 1597 he had adopted them some 
years before, and had collected arguments in their support 

In the following year his professorship was renewed foi 
six years with an increased stipend, a renewal which was 
subsequently made for six years more, and finally for life, 
the stipend being increased on each occasion. 

Galilei's fiist contribution to astronomical discovery was 
made in 1604, when a star appeared suddenly in the con- 
stellation Seipentarms, and was shewn by him to be at 
any rate moie distant than the planets, a lesult confiiming 
Tycho's conclusions (chaptei v , 100) that changes take 
place m the celestial regions even beyond the planets, and 
are by no means confined as was commonly believed 
to the earth and its immediate surroundings 

118 By this time Galilei had become famous through- 
out Italy, not only as a brilliant lecturer, but also as a 
learned and original man of science The discovenes 
which first gave him a European reputation weie, howevei, 
the series of telescopic observations made in 1609 and the 
following years 

Roger Bacon (chapter in , 67) had claimed to have de- 
vised a combination of lenses enabling distant objects to be 
seen as if they were near , a similai invention was probably 
made by our countryman Leonard Dtgges (who died about 
1571), and was described also by the Italian Porta in 1558 
If such an instrument was actually made by any one of the 
three, which is not ceitam, the discovery at any rate 
attracted no attention and was again lost The effective 
discovery of the telescope was made in Holland in 1608 
by Hans Lippersheim (^-1619), a spectacle-maker of Middle- 
burg, and almost simultaneously by two other Dutchmen, 
but whether independently or not it is impossible to say 
Early in the following year the report of the invention 
reached Galilei, who, though without any detailed mfoima- 
tion as to the structure of the instrument, succeeded after 
a few trials m arranging two lenses one convex and one 
concave- m a tube in such a way as to enlarge the 
apparent sue of an object looked at , his first instrument 
made objects appear three times neaiei, consequently 

15 A- Short History of Astronomy [CH vi 

three times greater (in breadth and height), and he was 
soon able to make telescopes which in the same way 
magnified thirty-fold 

That the new instrument might be applied to celestial 
as well as to terrestrial objects was a fairly obvious idea, 
which was acted on almost at once by the English mathe- 
matician Thomas Harriot (1560-1621), by Simon Manus 
(1570-1624) in Geimany, and by Galilei That the ciedit 
of first using the telescope for astronomical purposes is 
almost invariably attributed to Galilei, though his first 
observations weie in all probability slightly later in date 
than those of Harriot and Manus, is to a gieat extent 
justified by the peisistent way in which he examined object 
after object, whenever there seemed any reasonable prospect 
of results following, by the energy and acuteness with which 
he followed up each clue, by the independence of mind 
with which he interpreted his observations, and above all 
by the insight with which he realised their astronomical 

119 His first series of telescopic discoveries were pub- 
lished early in 1610 m a little book called Sidereus Nutums, 
or The Sidereal Messenger His first observations at 
once thiew a flood of light on the nature of oui nearest 
celestial neighbour, the moon It was commonly believed 
that the moon, like the other celestial bodies, was perfectly 
smooth and spherical, and the cause of the familiar dark 
markings on the surface was quite unknown * 

Galilei discoveied at once a number of sraallei maikmgs, 
both bright and dark (fig 53), and recognised many of 
the latter as shadows of lunai mountains cast by the 
sun, and fuither identified bright spots seen near the 
boundary of the illuminated and dark portions of the moon 
as mountain-tops just catching the light of the rising or 
setting sun, while the surrounding lunar area was still in 
daikness. Moreover, with characteristic ingenuity and love 
of precision, he calculated from observations of this nature 
the height of some of the more conspicuous lunai moun- 

* A fair idea of mediaeval views on the subject may be derived fiom 
one of the most tedious Cantos in Dante's great poem (Pmadiso, II ), 
in which the poet and Beatrice expound two diffeient " explanations " 
of the spots on the moon. 

IMG 53 -One ol Gahlci'b chawings oi the moon From t the 

SiddensNunnns [To face p 150 

iig i2i] Observations of the Moon 151 

tains, the largest being estimated by him to be about four 
miles high, a result agreeing closely with modern estimates 
of the greatest height on the moon The large dark spots 
he explained (erroneously) as possibly caused by water, 
though he evidently had less confidence in the correctness 
of the explanation than some of his immediate scientific 
successors, by whom the name of seas was given to 
these spots (chapter vin , 153) He noticed also the 
absence of clouds Apart however from details, the really 
significant results of his obseivations were that the moon 
was in many important respects similar to the earth, that 
the traditional belief in its perfectly spherical form had 
to be abandoned, and that so far the received doctrine of 
the sharp distinction to be drawn between things celestial 
and things terrestrial was shewn to be without justification , 
the importance of this in connection with the Coppermcan 
view that the earth, instead of being unique, was one of 
six planets revolving round the sun, needs no comment 

One of Galilei's numerous scientific opponents * attempted 
to explain away the apparent contradiction between the old 
theory and the new observations by the ingenious sugges- 
tion that the apparent valleys in the moon were in reality 
filled with some invisible crystalline material, so that the 
moon was in fact perfectly spherical To this Galilei 
replied that the idea was so excellent that he wished to 
extend its application, and accordingly maintained that 
the moon had on it mountains of this same invisible sub- 
stance, at least ten times as high as any which he had 

120 The telescope revealed also the existence of an 
immense number of stars too faint to be seen by the 
unaided eye , Galilei saw, for example, 36 stars m the 
Pleiades, which to an ordinary eye consist of six only 
Portions of the Milky Way and various nebulous patches 
of light were also discovered to consist of multitudes of 
faint stais clustered together , m the cluster Prsesepe (in 
the Crab), for example, he counted 40 stars 

121 By far the most striking discovery announced in the 
Sidereal Messenger was that of the bodies now known as 

* Liulovico (idle Colombe in a tiact Contra II Moto della Terra, 
which ib reprinted m the national edition ot Galilei's works, Vol III 

I S 2 A Short History of Astronomy [CH vi 

the moons or satellites of Jupiter. On January 7th, 1610, 
Galilei turned his telescope on to Jupiter, and noticed 
three faint stars which caught his attention on account of 
their closeness to the planet and their airangement nearly 
in a straight line with it He looked again next night, and 
noticed that they had changed their positions relatively 
to Jupiter, but that the change did not seem to be such 
as could result from Jupiter's own motion, if the new bodies 
were fixed stars Two nights later he was able to confix m 
this conclusion, and to infer that the new bodies were not 
fixed stars, but moving bodies which accompanied Jupitei 
m his movements A fourth body was noticed on 
January ijth, and the motions of all foui were soon recog- 
nised by Galilei as being motions of revolution lound 
Jupiter as a centre With characteristic thoioughness he 

Oii. * * O * Oc 

FIG 54 Jupiter and its satellites as seen on Jan 7, 1610 
From the Sidereits Nuncius 

watched the motions of the new bodies night after night, 
and by the date of the publication of his book had aheady 
estimated with very fair accuracy their periods of revolution 
round Jupiter, which ranged between about 42 hours and 
17 days, and he continued to watch their motions for 

The new bodies were at first called by their discoveier 
Medicean planets, m honour of his pation Cosmo de 
Medici, the Grand Duke of Tuscany ; but it was evident 
that bodies i evolving lound a planet, as the planets them- 
selves revolved round the sun, formed a new class of bodies 
distinct from the known planets, and the name of satellite 
suggested by Keplei as applicable to the new bodies as 
well as to the moon, has been generally accepted 

The discovery of Jupiter's satellites shewed the falsity 
of the old doctrine that the earth was the only centre of 
motion,, it tended, moreover, seriously to discredit the 
infallibility of Aristotle and Ptolemy, who had clearly no 
knowledge of the existence of such bodies; and again 
those who had difficulty in believing that Venus and 

I22 1 The Satellites of Jupiter 153 

Meictiry could revolve round an apparently moving body, 
the sun, could not but have their doubts shaken when 
shewn the new satellites evidently performing a motion 
of just this character , and most important consequence 
of all the very leal mechanical difficulty involved in the 
Coppermcan conception of the moon revolving round the 
moving eaith and not dioppmg behind was at any rate 
shewn not to be insuperable, as Jupiter's satellites succeeded 
m performing a precisely similar feat. 

The same reasons which rendered Galilei's telescopic 
discoveries of scientific importance made them also objec- 
tionable to the supporters of the old views, and they were 
accordingly attacked m a number of pamphlets, some of 
which are still extant and possess a certain amount of 
interest One Martin Horky, for example, a young German 
who had studied under Kepler, published a pamphlet in 
which, after piovmg to his own satisfaction that the satel- 
lites of Jupiter did not exist, he discussed at some length 
what they were, what they were like, and why they existed 
Another writer gravely argued that because the human 
body had seven openings m it the eyes, ears, nostrils, and 
mouth therefore by analogy there must be seven planets 
(the sun and moon being included) and no more How- 
ever, confnmation by other observers was soon obtained 
and the pendulum even began to swing in the opposite 
direction, a number of new satellites of Jupiter being 
announced by various observers. None of these, however, 
turned out to be genuine, and Galilei's four remained the 
only known satellites of Jupiter till a few yeais ago 
(chapter xm , 295). 

122 The reputation acquired by Galilei by the publica- 
tion of the Messenger enabled him to bring to a satisfactory 
issue negotiations which he had for some time been carrying 
on with the Tuscan court Though he had been well 
treated by the Venetians, he had begun to feel the burden 
of legular teaching somewhat nksome, and was anxious to 
devote more time to research and to writing A republic 
could hardly be expected to provide him with such a 
smecme as he wanted, and he accordingly accepted m the 
summer of 1610 an appointment as professor at Pisa, and 
also as " First Philosopher and Mathematician " to the Grand 

154 A Short History of Astronomy [Cn VI 

Duke of Tuscany, with a handsome salary and no definite 
duties attached to either office 

123. Shortly before leaving Padua he tuined his telescope 
on to Saturn, and observed that the planet appeared to 
consist of three parts, as shewn in the first drawing of 
fig 67 (chapter vm , 154) On subsequent occasions, 
howevei, he failed to see more than the central body, and 
the appearances of Saturn continued to present perplexing 
variations, till the mystery was solved by Huygens m 1655 
(chapter via, 154) 

The first discovery made at Florence (October 1610) was 
that Venus, which to the naked eye appears to vary very 
much in brilliancy but not in shape, was in reality at times 
crescent-shaped like the new moon and passed thiough 
phases similar to some of those of the moon This shewed 
that Venus was, like the moon, a dark body in itself, deriv- 
ing its light from the sun ; so that its similarity to the earth 
was thereby made more evident 

124 The discovery of dark spots on the sun completed 
this series of telescopic discoveries According to his own 
statement Galilei first saw them towards the end of 1 6 TO,* 
but apparently paid no particular attention to them at the 
time ; and, although he shewed them as a matter of 
curiosity to various fuends, he made no formal announce- 
ment of the discovery till May 1612, by which time the 
same discovery had been made independently by Harriot 
( 118) in England, by John Fabncms (1587-^1615) m 
Holland, and by the Jesuit Christopher Schemer (1575-1650) 
in Germany, and had been published by Fabncms (June 
1611) As a matter of fact dark spots had been seen with 
the naked eye long before, but had been generally supposed 
to be caused by the passage of Mercury m front of the sun 
The presence on the sun of such blemishes as black spots, 
the "mutability" involved m their changes m foim and 
position, and their formation and subsequent disappearance, 
were all distasteful to the supporters of the old views, 

* In a letter of May 4th, 1612, he says that he has seen them for 
eighteen months, in the Dialogue on the Two Systems (III , p 312, 
in Salusbury's translation) he says that he saw them while he still 
lectured at Padua, i c piesumably by September 1610, as he moved 
to Florence in that month 

55 Sun-spots Fiom Galilei's Macchtc Solan 

[To face /> 154 

$$ 123,124] Phases of Venus * Sim-spots 155 

according to which celestial bodies were perfect and un- 
changeable The fact, noticed by all the early observers, 
that the spots appeared to move across the face of the sun 
from the eastern to the western side (i e roughly from left 
to right, as seen at midday by an observer in our latitudes), 
gave at first sight countenance to the view, championed by 
Schemer among others, that the spots might really be small 
planets revolving round the sun, and appearing as dark 
objects whenever they passed between the sun and the 
observer In three letters to his friend Welser, a merchant 
prince of Augsburg, written in 1612 and published in the 
following year,* Galilei, while giving a full account of his 
observations, gave a crushing refutation of this view , proved 
that the spots must be on or close to the surface of the 
sun, and that the motions observed were exactly such as 
would result if the spots were attached to the sun, and it 
revolved on an axis m a period of about a month ; and 
further, while disclaiming any wish to speak confidently, 
called attention to several of their points of resemblance 
to clouds, 

One of his arguments against Schemer's views is so 
simple and at the same time so convincing, that it may 
be worth while to reproduce it as an illustration of Galilei's 
method, though the controveisy itself is quite dead 

Galilei noticed, namely, that while a spot took about 
fourteen days to cross from one side of the sun to the 
other, and this time was the same whether the spot passed 
through the centre of the sun's disc, or along a shorter 
path at some distance from it, its rate of motion was by 
no means uniform, but that the spot's motion always 
appeared much slower when near the edge of the sun 
than when near the centre This he recognised as an 
effect of foreshortening, which would result if, and only if, 
the spot were near the sun 

If, for example, m the figure, the circle represent a 
section of the sun by a plane through the obseiver at o, 
and A, B, c, D, E be points taken at equal distances along 
the surface of the sun, so as to rcpiesent the positions 
of an object on the sun at equal intervals of time, on 
the assumption that the sun levolvcs uniformly, then the 

* Histona c Qimost) axiom intotno ctlle Macdite Solan 

156 A Short History of Astronomy [Cn vi 

apparent motion from A to B, as seen by the observer 
at o, is measured by the angle A o B, and is obviously 
much less than that from D to E, measured by the angle 
DOE, and consequently an object attached to the sun 
must appear to move more slowly from A to B, t e. near 
the sun's edge, than from D to E, near the centre On the 
other hand, if the spot be a body revolving round the sun 
at some distance from it, eg along the dotted circle c d e, 
then iff, d) e be taken at equal distances from one anothei, 
the appaient motion from c to d> measuied again by the 
angle c o d, is only veiy slightly less than that from d to e, 
measuied by the angle d o e Moreover, it required only 
a simple calculation, peiformed by Galilei in several cases, 

FIG 56 Galilei's proof that sun-spots aie not planetb 

to express these results in a numerical shape, and so to 
infer from the actual observations that the spots could not 
be more than a very moderate distance from the sun The 
only escape from this conclusion was by the assumption 
that the spots, if they were bodies revolving round the sun, 
moved irregularly, m such a way as always to be moving 
fastest when they happened to be between the centre of 
the sun and the earth, whatever the earth's position might 
be at the time, a piocedure for which, on the one hand, 
no sort of reason could be given, and which, on the othei, 
was entnely out of harmony with the uniformity to which 
mediaeval astionomy clung so firmly 

The rotation of the sun about an axis, thus established, 
might evidently have been used as an argument in support 
of the view that the earth also had such a motion, but, 
as far as I am aware, neither Galilei nor any contemporary 
noticed the analogy. Among other facts relating to the 

* *25] Sun-spots 157 

spots observed by Galilei were the greater darkness of the 
central parts, some of his drawings (see fig 55) shewing, 
like most modern drawings, a fairly well-marked line of 
Division between the central part (or umbra) and the less 
dark fringe (or penumbra) surrounding it , he noticed also 
that spots frequently appeared m groups, that the members 
of a group changed their positions relatively to one another, 
that individual spots changed their sue and shape con- 
siderably during then lifetime, and that spots were usually 
most plentiful m two regions on each side of the sun's 
equatoi, corresponding roughly to the tropics on our own 
globe, and were never seen far beyond these limits 

Similar observations weie made by other telescopists, 
and to Schemer belongs the credit of fixing, with consider- 
ably more accuracy than Galilei, the position of the sun's 
axis and equatoi and the time of its rotation 

125 The contioversy with Schemer as to the nature 
of spots unfortunately developed into a personal quarrel 
as to then respective claims to the discovery of spots, 
a controversy which made Schemer his bitter enemy, and 
probably contributed not a little to the hostility with which 
Oalilei was henceforward regarded by the Jesuits Galilei's 
uncompiormsmg championship of the new scientific ideas, 
the slight respect which he shewed for established and 
traditional authority, and the biting sarcasms with which 
he was m the habit of greeting his opponents, had won 
for him a large number of enemies in scientific and 
l>hilosophic circles, particularly among the large party 
who spoke in the name of Aristotle, although, as Galilei 
was never tired of reminding them, their methods of 
thought and their conclusions would m all piobabihty 
have been rejected by the great Greek philosopher if he 
had been alive 

It was probably m part owing to his consciousness of a 
growing hostility to his views, both in scientific and in 
ecclesiastical circles, that Galilei paid a short visit to Rome 
in 1 6 1 1, when he met with a most honourable reception 
and was treated with gieat friendliness by several cardinals 
and other persons in high places 

"Unfortunately he soon began to be diawn into a contro- 
versy as to the relative validity m scientific matteis of 

158 A Short History of Astronomy [Cn VI 

observation and reasoning on the one hand, and of the 
authority of the Church and the Bible on the other, a 
controversy which began to take shape about this time and 
which, though its battle-field has shifted from science to 
science, has lasted almost without interruption till modern 

In 1611 was published a tract maintaining Jupitei's 
satellites to be unscnptural In 1612 Galilei consulted 
Cardinal Conti as to the astronomical teaching of the Bible, 
and obtained from him the opinion that the Bible appeared 
to discountenance both the Aristotelian doctrine of the 
immutability of the heavens and the Coppernican doctrine 
of the motion of the earth A tract of Galilei's on floating 
bodies, published in 1612, roused fresh opposition, but on 
the other hand Cardinal Barbenni (who afteiwaids, as 
Urban VIII , took a leading part m his persecution) 
specially thanked him for a piesentation copy of the book 
on sun-spots, in which Galilei, foi the first time, clearly 
proclaimed m public his adherence to the Coppernican 
system In the same year (1613) his friend and follower, 
Father Castelh, was appointed professor of mathematics 
at Pisa, with special instructions not to lecture on the 
motion of the eaith Within a few months Castelh was 
diawn into a discussion on the relations of the Bible to 
astronomy, at the house of the Grand Duchess, and quoted 
Galilei m support of his views } this caused Galilei to 
express his opinions at some length m a letter to Castelh, 
which was circulated m manuscript at the couit To this 
a Dominican preacher, Caccmi, replied a few months 
afterwards by a violent seimon on the text, " Ye Galileans, 
why stand ye gazing up into heaven?"* and m 1615 
Galilei was secretly denounced to the Inquisition on the 
strength of the letter to Castelh and other evidence In 
the same year he expanded the letter to Castelh into a 
more elaborate treatise, in the form of a Letter to the Grand 
Duchess Christine, which was circulated m manuscupt, but 
not printed till 1636 The discussion of the bearing of 
particular passages of the Bible (eg the account of the 
miracle of Joshua) on the Ptolemaic and Coppernican 

" Acts i ii The pun is not quite so bad in its Latin low , Vw 
Gahlaei, etc 

I26 1 The First Condemnation of Galilei 159 

systems has now lost most of its interest } it may, however, 
be worth noticing that on the more general question Galilei 
quotes with approval the saying of Cardinal Baronius, 
" That the intention of the Holy Ghost is to teach us not 
how the heavens go, but how to go to heaven," * and the 
following passage gives a good idea of the general tenor 
of his argument 

"Methmks, that in the Discussion of Natural Problemes we 
ought not to begin at the authority of places of Scripture , but 
at Sensible Experiments and Necessary Demonstrations For 
Nature being inexorable and immutable, and never passing 
the bounds of the Laws assigned her, as one that nothing careth, 
whether her abstruse reasons and methods of operating be or 
be not exposed to the capacity of men, I conceive that that 
concerning Natural Effects, which either sensible experience 
sets before our eyes, or Necessary Demonstrations do prove unto 
us, ought not, upon any account, to be called into question, 
much less condemned upon the testimony of Texts of Scripture, 
which may under their words, couch senses seemingly contrary 
thereto " |- 

126 Meanwhile his enemies had become so active that 
Galilei thought it well to go to Rome at the end of 1615 
to defend his cause Early in the next year a body of 
theologians known as the Qualifiers of the Holy Office 
(Inquisition), who had been instructed to examine certain 
Coppermcan doctrines, reported 

"That the doctrine that the sun was the centre of the world 
and immoveable was false and absurd, formally heretical and 
contrary to Scripture, whereas the doctrine that the earth was 
not the centre of the world but moved, and has further a daily 
motion, was philosophically false and absurd and theologically 
at least erroneous " 

In consequence of this repoit it was decided to censure 
Galilei, and the Pope accordingly instructed Cardinal 
Bellarmine "to summon Galilei and admonish him to 

* Spintm sancto mentcni fitissc nos doccrc, quo modo ad Coeluni 
catur, non auUm, quomodo Coelum gt adtatnr 

f Fiorn the translation by Salusbury, m Vol I of his Mathematical 


i6o A Short History of Astronomy 

abandon the said opinion," which the Cardinal did ^ 
Immediately afterwards a deciee was issued condemning 
the opinions m question and placing on the well-known 
Index, of Prohibited Books three books containing Coppei- 
mcan views, of which the De Reoolutiombus of Coppci nu us 
and another were only suspended " until they should 
be collected," while the third was altogether prohibited, 
The necessary corrections to the De jRevolutionifnt\ wm 
officially published in 1620, and consisted only of a few 
alterations which tended to make the essential piinnples 
of the book appear as mere mathematical hypotheses, 
convenient for calculation Galilei seems to have been 
on the whole well satisfied with the issue of the inquiry, 
as far as he was personally concerned, and after obtaining 
from Cardinal Bellarmme a certificate that he had ncithci 
abjured his opinions nor done penance for them, stayed 
on in Rome for some months to shew that he was in 
good repute there 

127 During the next few yeais Galilei, who was now 
more than fifty, suffered a good deal from ill-health and 
was comparatively inactive He carried on, howcvei, a 
correspondence with the Spanish court on a method of 
ascertaining the longitude at sea by means of Jupitei's 
satellites. The essential problem m finding the longitude* 
is to obtain the time as given by the sun at the lequued 
place and also that ,at some place the longitude of which 
is known If, for example, midday at Rome omns an 
hour earlier than m London, the sun takes an hom to 
travel from the meridian of Rome to that of London, and 
the longitude of Rome is 15 east of that of London 
At sea it is easy to ascertain the local time, e& by 
observing when the sun is highest in the sky, but the 
gieat difficulty, felt in Galilei's time and long after wauls 
(chapter x , 197, 226), was that of ascertaining the time at 
some standard place Clocks were then, and long altei 
wards, not to be relied upon to keep tune accurately dunng 

* The only point of any importance in connection with (ahl<n% 
lelations with the Inquisition on which theie seems to ht loom f*n 
any serious doubt is as to the stringency of this warning It is 
probable that Galilei was at the same time specifically ioibuldui to 
"hold, teach, or defend in any way, whether verbally or in writing," 
the obnoxious doctrine. 

i2 7 ] The Problem of Longitude Comets 161 

a long ocean voyage, and some astronomical means of 
determining the time was accordingly wanted Galilei's 
idea was that if the movements of Jupiter's satellites, and 
in particular the eclipses which constantly occurred when 
a satellite passed into Jupiter's shadow, could be predicted, 
then a table could be prepared giving the times, according 
to some standard place, say Rome, at which the eclipses 
would occur, and a sailor by observing the local time 
of an eclipse and comparing it with the time given in 
the table could ascertain by how much his longitude 
differed from that of Rome. It is, however, doubtful 
whether the movements of Jupiter's satellites could at that 
time be predicted accurately enough to make the method 
practically useful, and in any case the negotiations came 
to nothing 

In 1618 three comets appeared, and Galilei was soon 
drawn into a controversy on the subject with a Jesuit 
of the name of Grassi The controversy was marked by 
the personal bitterness which was customary, and soon 
developed so as to include larger questions of philosophy 
and astronomy Galilei's final contribution to it was 
published in 1623 under the title // Saggiatore (The 
Assayer), which dealt incidentally with the Copper-mean 
theory, though only in the indirect way which the edict 
of 1616 rendered necessary. In a characteristic passage, 
for example, Galilei says 

" Since the motion attributed to the earth, which I, as a pious 
and Catholic person, consider most false, and not to exist, 
accommodates itself so well to explain so many and such 
different phenomena, I shall not feel sure that, false as it 

is, it may not just as deludmgly correspond with the phenomena 
ot comets " , 

and again, m speaking of the rival systems of Coppermcus 
and Tycho, he says 

"Then as to the Copermcan hypothesis, if by the good 
iortune of us Catholics we had not been freed from error 
and our "blindness illuminated by the Highest Wisdom, I do 
not believe that such grace and good fortune could have 
been obtained by means of the leasons and observations given 
by Tycho " 

162 A Short History of Astronomy [di vi 

Although in scientific importance the s gf* ranks 
far belSw many others of Galilei's writings, it had a great 
reWtatL as a piece of brilliant controversial writing, and 
notwnhstandmg its thinly veiled Coppernicamsm, the new 
Pope, Urban VIII , to whom it was dedicated was so much 
plerad with it that he had it read aloud to him at meals 
The book must, however, have strengthened the hands 
of Galilei's enemies, and it was probably with a view to 
counteracting their influence that he went to Rome next 
year, to pay his respects to Urban and congratulate him 
on his recent elevation The visit was in almost every 
way a success , Urban granted to him several friendly 
interviews, promised a pension for his son, gave him several 
presents, and finally dismissed him with a lettei of special 
recommendation to the new Grand Duke of I uscany, who 
had shewn some signs of being less friendly to Galilei 
than his father On the other hand, however, the Pope 
refused to listen to Galilei's request that the decree of 1616 
should be withdrawn 

128 Galilei now set seriously to work on^ the gieat 
astronomical treatise, the Dialogue on the 2 'wo Chief 
Systems of the World, the Ptolemaic ami Coppernican, 
which he had had in mind as long ago as 1610, and in 
which he proposed to embody most of his astronomical 
work and to collect all the available evidence beaimg on 
the Coppernican controversy The foim of a dialogue was 
chosen, partly for literary reasons, and still moie because 
it enabled him to present the Coppernican case as strongly 
as he wished through the mouths of some of the speakers, 
without necessarily identifying his own opinions with theirs 
The manuscript was almost completed In 1629, and m the 
following year Galilei went to Rome to obtain the necessary 
licence for printing it The censor had some alterations 
made and then gave the desired permission for pimtmg at 
Rome, on condition that the book was submitted to him 
again befoie being finally printed off Soon aftei Galilei's 
return to Florence the plague broke out, and quarantine 
difficulties rendered it almost necessary that the book 
should be printed at Florence instead of at Rome This 
required a fresh licence, and the difficulty experienced m 
obtaining it shewed that the Roman censor was getting 

$ las, xa 9 ] The Dialogue on the Two Chief Systems 163 

more and more doubtful about the book Ultimately, 
however, the introduction and conclusion having been sent 
to Rome for approval and probably to some extent re- 
written there, and the whole work having been approved 
by the Florentine censor, the book was printed and the 
first copies were ready early in 1632, bearing both the 
Roman and the Florentine imprimatur 

129 The Dialogue extends over four successive days, 
and is carried on by three speakers, of whom Salviati is a 
Coppernican and Simphcio an Aristotelian philosopher, 
while Sagredo is avowedly neutral, but on almost every 
occasion either agrees with Salviati at once or is easily 
convinced by him, and frequently joins in casting ridicule 
upon the arguments of the unfortunate Simphcio Though 
many of the arguments have now lost their immediate 
interest, and the book is unduly long, it is still very read- 
able, and the specimens of scholastic reasoning put into 
the mouth of Simphcio and the refutation of them by 
the othei speakers strike the modern reader as excellent 

Many of the arguments used had been published by 
Galilei m earlier books, but gam impressiveness and cogency 
by being collected and systematically arranged The 
Aristotelian dogma of the immutability of the celestial 
bodies is once more belaboured, and shewn to be not 
only inconsistent with observations of the moon, the sun, 
comets, and new stars, but to be in reality incapable of 
being stated in a form free from obscurity and self-con- 
tradiction The evidence in favour of the earth's motion 
derived from the existence of Jupiter's satellites and from 
the undoubted phases of Venus, from the suspected phases 
of Mercury and from the variations in the apparent size of 
Mars, are once more insisted on The greater simplicity 
of the Coppernican explanation of the daily motion of the 
celestial sphere and of the motion of the planets is forcibly 
urged and illustrated m detail It is pointed out that on 
the Coppernican hypothesis all motions of i evolution or 
rotation take place m the same direction (from west to 
east), whereas the Ptolemaic hypothesis requires some 
to be m one direction, some in another Moreover the 
apparent daily motion of the stars, which appears simple 

I64 A Short History of Astronomy [di vi 

enough if the stars aie regarded as rigidly attached to a 
material sphere, is shewn in a quite diffcient aspect if, 
as even Simphcio admits, no such sphere exists, and each 
star moves in some sense independently A star near the 
pole must then be supposed to move far more slowly than 
one near the equator, since it describes a much smaller 
circle in the same time, and furthei-an aigiiment very 
characteristic of Galilei's ingenuity in drawing conclusions 
from known facts owing to the precession of the equinoxes 
(chapter n , 42, and iv , 84) and the consequent change 
of the position of the pole among the stais, some of those 
stars which in Ptolemy's time were describing veiy small 
circles, and therefore moving slowly, must now be describing 
large ones at a greater speed, and Dice vena An extremely 
complicated adjustment of motions becomes thcrefoie 
necessary to account for observations which Coppeinicus 
explained adequately by the rotation of the earth and a 
simple displacement of its axis of rotation 

Salviati deals also with the standing difficulty that the 
annual motion of the earth ought to cause a corresponding 
apparent motion of the stars, and that if the stars be 
assumed so far off that this motion is imperceptible, then 
some of the stars themselves must be at least as large as 
the earth's orbit round the sun Salviati points out that 
the apparent or angular magnitudes of the fixed stars, 
avowedly difficult to determine, are in reality almost entnely 
illusory, being due m great part to an optical effect known 
as irradiation, in virtue of which a bright object always 
tends to appear enlarged , * and that there is m consequence 
no reason to suppose the stars nearly as large as they might 
otherwise be thought to be. It is suggested also that the 
most promising way of detecting the annual motion of stai s 
resulting from the motion of the eaith would be by 
observing the relative displacement of two stars close 
together in the sky (and therefore nearly m the same clhec- 
tion), of which one might be presumed from its greater 

* This is illustrated by the well-known optical illusion wheieby a 
white circle on a black backgiound appeals larger than an equal 
black one on a white background The appaient si/e of the hot 
filament in a modern incandescent electric lamp is another good 

13] The Dialogue on the Two Chief Systems 165 

brightness to be nearer than the othei It is, for example, 
evident that if, m the figure, E, E' represent two positions of 
the earth in its path round the sun, and A, B two stars at 
different distances, but nearly in the same direction, then 
to the observer at E the star A appears to the left of B, 
whereas six months afterwards, when the observer is at E', 
A appears to the right of B Such a motion of one star with 
respect to another close to it would be much more easily 
observed than an alteration of the same amount in the 
distance of the star from some standard point such as the 
pole. Salviati points out that accurate observations of 


FIG 57 The differential method of parallax 

this kind had not been made, and that the telescope might 
be of assistance for the purpose This method, known as 
the double-star or differential method of parallax, was in 
fact the first to lead two centuries later to a successful 
detection of the motion m question (chapter xin , 278) 

130 Entirely new ground is broken m the Dialogue 
when Galilei's discoveries of the laws of motion of bodies 
are applied to the problem of the earth's motion His 
great discovery, which threw an entirely new light on the 
mechanics of the solar system, was substantially the law 
afterwards given by Newton as the first of his three laws 
of motion, in the form Every body continues in its state of 
rest or of uniform motion in a straight hne, except in so far 
as it is compelled by force applied to it to change that state 
Putting aside for the present any discussion of force, a 
conception first made really definite by Newton, and only 
imperfectly grasped by Galilei, we may interpret this law 
as meaning that a body has no more inherent tendency to 
dimmish its motion or to stop than it has to increase its 
motion or to stait, and that any alteiation m either the 
speed or the direction of a body's motion is to be explained 
by the action on it of some other body, or at any rate by 

1 66 A Short History of Astronomy CCH vi 

some other assignable cause. Thus a stone thrown along 
a road comes to rest on account of the friction between 
it and the ground, a ball thrown up into the air ascends 
more and more slowly and then falls to the ground on account 
of that attraction of the earth on it which we call its 
weight As it is impossible to entirely isolate a body fiom 
all others, we cannot experimentally realise the state of 
things in which a body goes on moving indefinitely m the 
same direction and at the same rate, it may, however, 
be shewn that the more we remove a body from the 
influence of others, the less alteration is there m its motion 
The law is therefore, like most scientific laws, an abstrac- 
tion referring to a state of things to which we may 
approximate in nature Galilei introduces the idea in the 
Dialogue by means of a ball on a smooth inclined plane 
If the ball is projected upwards, its motion is gradually 
letarded, if downwards, it is continually accelerated This 
is true if the plane is fairly smooth like a well-planed 
plank and the inclination of the plane not very small 
If we imagine the experiment performed on an ideal plane, 
which is supposed perfectly smooth, we should expect the 
same results to follow, however small the inclination of 
the plane Consequently, if the plane were quite level, 
so that there is no distinction between up and down, we 
should expect the motion to be neithei retarded nor 
accelerated, but to continue without alteration Othei 
more familiar examples are also given of the tendency 
of a body, when once in motion, to continue in motion, 
as m the case of a rider whose horse suddenly stops, or of 
bodies in the cabin of a moving ship which have no tendency 
to lose the motion imparted to them by the ship, so that, 
eg, a body falls down to all appearances exactly as if the 
rest of the cabin were at rest, and therefoic, m reality, 
while falling retains the forward motion which it shares 
with the ship and its contents Salviati states also that 
contrary to general belief a stone dropped from the nubt- 
head of a ship m motion falls at the foot of the mast, not 
behind it, but there is no reference to the experiment 
having been actually performed 

This mechanical principle being once established, it 
becomes easy to deal with several common objections to 

iso] The Dialogue on the Two Chief Systems 167 

the supposed motion of the earth The case of a stone 
dropped from the top of a tower, which if the earth be 
in reality mowng rapidly from west to east might be 
expected to fall to the west m its descent, is easily shewn 
to be exactly parallel to the case of a stone dropped from 
the mast-head of a ship in motion The motion towards 
the east, which the stone when resting on the tower shares 
with the tower and the earth, is not destroyed in its 
descent, and it is therefore entnely in accordance with the 
Coppermcan theory that the stone should fall as it does at 
the foot of the tower K Similaily, the fact that the clouds, 
the atmosphere in general, birds flying in it, and loose 
objects on the surface of the earth, shew no tendency to 
be left behind as the earth moves rapidly eastward, but 
are apparently unaffected by the motion of the earch, is 
shewn to be exactly parallel to the fact that the flies m 
a ship's cabin and the loose objects there are m no way 
affected by the uniform onward motion of the ship (though 
the irregular motions of pitching and rolling do affect them) 
The stock objection that a cannon-ball shot westward 
should, on the Coppermcan hypothesis, cany farther than 
one shot eastward undei like conditions, is met in the 
same way , but it is further pointed out that, owing to 
the imperfection of gunneiy piacttce, the experiment could 
not really be tued accurately enough to yield any decisive 

The most unsatisfactory pait of the Dialogue is the 
fourth day's discussion, on the tides, of which Galilei 
suggests with great confidence an explanation based merely 
on the motion of the earth, while i ejecting with scoin the 
suggestion of Kepler and otheis coirect as far as it 
went that they weie caused by some influence emanating 
from the moon It is hardly to be wondered at that the 
rudimentary mechanical and mathematical knowledge at 
Galilei's command should not have enabled him to deal 

* Actually, since the top of the towei is describing a slightly larger 
circle than its foot, the stone is at first moving eastward slightly 
faster than the foot of the tower, and theiefoie should reach the 
giound slightly to the east of it This displacement is, ho w ever, 
very minute, and can only be detected by more delicate experiments 
than any devised by Galilei 

168 A Short History of Astronomy [Cn VI 

correctly with a problem of which the vastly moie powerful 
resources of modern science can only give an imperfect 
solution (cf chapter xi , 248, and chapter xm , 292) 

131 The book as a whole was in effect, though not in 
form, a powerful indeed unanswerableplea for Copper- 
mcamsm. Galilei tried to safeguard his position, paitly 
by the use of dialogue, and partly by the very remaikable 
introduction, which was not only read and appioved by the 
licensing authorities, but was in all probability in pait 
the composition of the Roman censoi and of the Pope 
It reads to us like a piece of elaborate and thinly veiled 
irony, and it throws a curious light on the intelligence 
or on the seriousness of the Pope and the censoi, that 
they should have thus approved it 

"Judicious reader, there was published some years since in 
Rome a salutiferous Edict, that, for the obviating of the dangeious 
Scandals of the present Age, imposed a reasonable Silence upon 
the Pythagorean Opinion of the Mobility of the Earth 1 here 
want not such as unadvisedly affirm, that the Decree was not 
the production of a sober Scrutiny, but ol an ilHormed passion , 
and one may hear some mutter that Consultors altogethei 
ignorant of Astronomical observations ought not to chpp the 
wings of speculative wits with rash prohibitions My /eale 
cannot keep silence when I hear these inconsiderate complaints 
I thought fit, as being thoroughly acquainted with that prudent 
Determination, to appeal openly upon the Theatre of the World 
as a Witness of the naked Truth I was at that tune in Rome, 
and had not only the audiences, but applauds oi the most 
Eminent Prelates of that Court , nor was that Decree published 
without Previous Notice given me thereof fhereloie it is my 
resolution in the present case to give Foreign Nations to see, 
that this point is as well understood in Italy > and partieuUnly 
in Rome, as Transalpine Diligence can imagine it to be and 
collecting together all the proper speculations that ecmceme the 
Copermcan Systeme to let them know, that the notice of all 
preceded the Censure of the Roman Lomt, and that there 
proceed from this Climate not only Doctrines for the health oi 
the Soul, but also ingenious Discoveries for the recreating of 
the Mind I hope that by these considerations the world 

will know, that if other Nations have Navigated more than we, 
we have not studied less than they , and that oiu returning to 
assert the Earth's stability, and to take the contraiy only for 
a Mathematical Capncao, proceeds not from inadvertency oi 
what others have thought thereof, but (had one no other 

isi, 132] Galileos Trial 169 

inducements), from these reasons that Piety, Religion, the 
Knowledge of the Divine Ommpotency, and a consciousness 
of the incapacity of man's understanding dictate unto us " * 

132 Natuially Galilei's many enemies were not long m 
penetrating these thin disguises, and the immense success 
of the book only intensified the opposition which it excited , 
the Pope appears to have been persuaded that Simphcio 
the butt of the whole dialogue was intended for himself, 
a supposed insult which bitterly wounded his vanity , and 
it was soon evident that the publication of the book could 
not be allowed to pass without notice In June 1632 a 
special commission was appointed to inquire into the 
matteran unusual procedure, probably meant as a mark 
of consideration for Galilei and two months later the 
further issue of copies of the book was prohibited, and in 
September a papal mandate was issued requiring Galilei 
to appeal personally before the Inquisition He was evi- 
dently frightened by the summons, and tried to avoid com- 
pliance through the good offices of the Tuscan court and 
by pleading his age and infirmities, but after considerable 
delay, at the end of which the Pope issued instructions to 
bring him if necessary by force and in chains, he had 
to submit, and set off for Rome early in 1633 Here he 
was treated with unusual consideration, for whereas m 
general even the most eminent offenders under trial by the 
Inquisition were confined m its prisons, he was allowed to 
live with his fnend Niccohni, the Tuscan ambassador, 
throughout the trial, with the exception of a peiiod of 
about three weeks, which he spent within the buildings 
of the Inquisition, in comfortable rooms belonging to one of 
the officials, with pei mission to correspond with his friends, 
to take exercise in the gaiden, and other privileges At 
his fiist heaiing before the Inquisition, his reply to the 
chaige of having violated the decree of 1616 ( 126) was 
that he had not understood that the decree or the admoni- 
tion given to him forbade the teaching of the Coppermcan 
theory as a mere " hypothesis," and that his book had not 
upheld the doctrine in any other way Between his first 
and second hearing the Commission, which had been 

* From the translation by Salusbury, m Vol I of his Mathematical 

i yo A Short History of Astronomy ecu vi 

examining his book, reported that it did distinctly defend 
and maintain the obnoxious doctrines, and Galilei, having 
been meanwhile privately advised by the Commissary- 
General of the Inquisition to adopt a moie submissive 
attitude, admitted at the next hearing that on reading his 
book again he recognised that parts of it gave the arguments 
for Coppermcamsm more strongly than he had at fust 
thought The pitiable state to which he had been i educed 
was shewn by the offer which he now made to wntc a 
continuation to the Dialogue which should as far as possible 
refute his own Coppernican arguments At the hnal 
hearing on June 2ist he was examined under threat of 
torture,* and on the next day he was bi ought up for 
sentence He was convicted "of believing and holding 
the doctrines false and contrary to the Holy and Divine 
Scriptures that the sun is the centie of the woild, and 
that it does not move from east to west, and that the earth 
does move and is not the centre of the world , also that an 
opinion can be held and supported as probable aftei it has 
been declared and decreed contrary to the Holy Scnptuics " 
In punishment, he was required to "abjuie, cuisu, and 
detest the aforesaid errors," the abjuration being at once 
read by him on his knees , and was furthei condemned to 
the "formal prison of the Holy Office 7 ' during the pleasure 
of his judges, and required to repeat the seven penitential 
psalms once a week for three years On the following day 
the Pope changed the sentence of imprisonment into con- 
finement at a country-house neai Rome belonging to the 
Grand Duke, and Galilei moved there on June 24th t On 
petitioning to be allowed to return to Florence, he was at 
first allowed to go as far as Siena, and at the end of the 
year was peimitted to retire to his country-house at Aicetn 
near Florence, on condition of not leaving it for the futuic 
without permission, while his intercourse with scientific and 
other friends was jealously watched 

* The official minute is. Et ei dicto quod dual veiiiatci t (that 
devemetur ad to? tut am 

) The three days June 21-24 are the only ones winch Gallic* 
could have spent in an actual prison, and there seems no icason t< 
suppose that they were spent elsewhere than m the eomlotUbk 
rooms in which it is known that he lived dining most oi April, 

* i32] The Second Condemnation of Gahlei 171 

The story of the trial reflects little ciedit either on 
Gahlei or on his persecutors. For the latter, it may be 
inged that they acted with unusual leniency considering 
the customs of the time ; and it is probable that many 
of those who were concerned m the trial were anxious to 
do as little injury to Galilei as possible, but were practically 
forced by the party personally hostile to him to take some 
notice of the obvious violation of the decree of 1616 It 
is easy to condemn Gahlei for cowaidice, but it must be 
borne m mind, on the one hand, that he was at the time 
nearly seventy, and much shaken in health, and, on the 
other, that the Roman Inquisition, if not as cruel as the 
Spanish, was a very real power m the early iyth century, 
during Galilei's life-time (1600) Giordano Bruno had been 
burnt alive at Rome foi wntmgs which, m addition to 
containing religious and political heresies, supported the 
Coppermcan astronomy and opposed the traditional 
Anstotelian philosophy Moreover, it would be unfair to 
regard his submission as due merely to considerations of 
personal safety, forapart from the question whether his 
beloved science would have gamed anything by his death 
or permanent imprisonment there can be no doubt that 
Gahlei was a pcifectly sincere member of his Church, and 
although he did his best to convince individual officers 
of the Chuich of the correctness of his views, and to 
minimise the condemnation of them passed in 1616, yet 
he was probably picpaied, when he found that the con- 
demnation was seriously meant by the Pope, the Holy 
Office, and others, to believe that m some senses at least 
his views must be wrong, although, as a matter of observa- 
tion and puie icason, he was unable to see how or why 
In fact, like many other excellent people, he kept water- 
tight compartments m his mind, respect for the Church 
being in one and scientific investigation in another 

Copies of the sentence on Galilei and of his abjuration 
were at once circulated m Italy and in Roman Catholic 
circles elsewhere, and a decree of the Congregation of the 
Index was also issued adding the Dialogue to the three 
Coppermcan books condemned in 1616, and to Kepler's 
Epitome of the Coppermcan Astronomy (chapter vn , 145), 
which had been put on the Index shoitly afterwards It 

172 A Short History of Astronomy [Cii vi,i33 

may be of interest to note that these five books still remained 
in the edition of the Index of Prohibited Books which was 
issued in 1819 (with appendices dated as late as 1821), 
but disappeared from the next edition, that of 1835 

133 The rest of Galilei's life may be described very 
briefly With the exception of a few months, during -which 
he was allowed to be at Floience for the sake of medical 
treatment, he remained continuously at Arcetn, evidently 
pretty closely watched by the agents of the Holy Office, 
much restricted in his intercourse with his friends, and 
prevented from carrying on his studies in the directions 
which he liked best. He was moreover veiy infiim, and 
he was afflicted by domestic troubles, especially by the 
death in 1634 of his favourite child, a nun in a neighbouring 
convent But his spirit was not broken, and he went on 
with several important pieces of work, which he had begun 
earlier in his career He carried a little further the study 
of his beloved Medicean Planets and of the method of finding 
longitude based on their movements ( 127), and negotiated 
on the subject with the Dutch government He made also 
a further discovery relating to the moon, of sufficient 
importance to deserve a few words of explanation 

It had long been well known that as the moon describes 
her monthly path round the earth we see the same markings 
substantially in the same positions on the disc, so that 
substantially the same face of the moon is turned towards 
the earth It occurred to Galilei to inquire whether this 
was accurately the case, or whethei, on the contraiy, some 
change m the moon's disc could be observed. He saw 
that if, as seemed likely, the line joining the centies of the 
earth and moon always passed through the same point 
on the moon's surface, nevertheless certain alterations in 
an observer's position on the earth would enable him to 
see different portions of the moon's surface from time to 
time. The simplest of these alterations is due to the daily 
motion of the earth. Let us suppose for simplicity that 
the observer is on the earth's equator, and that the moon is 
at the time in the celestial equator Let the larger circle 
in fig 58 represent the earth's equator, and the smaller 
circle the section of the moon by the plane of the equator 
Then in about 12 hours the earth's rotation caines the 

174 A Short History of Astronomy [CH. vi 

observer from A, where he sees the moon rising, to B, where 
he sees it setting When he is at c, on the line joining the 
centres of the earth and moon, the point o appears to be in 
the centre of the moon's disc, and the portion c o c is visible, 
c R c invisible. But when the observer is at A, the point p, 
on the right of o, appears in the centre, and the portion 
a P ci is visible, so that d a' is now visible and a c invisible 
In the same way, when the observer is at B, he can see the 
portion c b, while V c' is invisible and Q appears to be in 
the centre of the disc Thus m the course of the day 
the portion a o V (dotted in the figure) is constantly visible 
and b R a 1 (also dotted) constantly invisible, while acb 
and a' c' b r alternately come into view and disappear In 
other words, when the moon is rising we see a little 
more of the side which is the then uppermost, and when 
she is setting we see a little more of the other side which is 
uppermost in this position A similar explanation applies 
when the observer is not on the earth's equator, but the 
geometiy is slightly more complicated In the same way, as 
the moon passes from south to north of the equator and back 
as she revolves round the earth, we see alternately more and 
less of the northern and southern half of the moon This 
set of changes the simplest of several somewhat similar 
ones which are now known as librations of the moon being 
thus thought of as likely to occur, Galilei set to work to test 
their existence by observing certain markings of the moon 
usually visible near the edge, and at once detected altera- 
tions in their distance from the edge, which were m general 
accordance with his theoretical anticipations A more 
precise inquiry was however interrupted by failing sight, 
culminating (at the end of 1636) in total blindness. 

But the most important work of these years was the 
completion of the great book, m which he summed up 
and completed his discoveries in mechanics, Mathe- 
matical Discourses and Demonstrations concerning Two 
New Sciences, relating to Mechanics and to Local Motion 
It was written in the foim of a dialogue between the same 
three speakers who figured m the Dialogue on the Systems, 
but is distinctly inferior m literary merit to the earlier 
work We have here no concern with a large part of 
the book, which deals with the conditions under which 

133 ] Libration the Two New Sciences 175 

bodies are kept at rest by forces applied to them (statics), 
and certain problems relating to the lesistance of bodies 
to fiacture and to bending, though in both of these 
subjects Galilei broke new ground More important 
astronomically and probably intrinsically also is what he 
calls the science of local motion,* which deals with the 
motion of bodies He builds up on the basis of his early 
experiments ( 116) a theory of falling bodies, in which 
occurs for the first time the important idea of uniformly 
accelerated motion, or uniform acceleration, i e motion 
in which the moving body receives in every equal interval 
of time an equal increase of velocity. He shews that the 
motion of a falling body is except m so far as it is dis- 
turbed by the air of this nature, and that, as already 
stated, the motion is the same for all bodies, although 
his numerical estimate is not at all accurate t From this 
fundamental law he works out a number of mathematical 
deductions, connecting the space fallen through, the velocity, 
and the time elapsed, both for the case of a body falling 
freely and for one falling down an inclined plane He 
gives also a correct elementary theory of projectiles, m 
the course of which he enunciates more completely than 
before the law of inertia already referred to ( 130), 
although Galilei's form is still much less general than 

Conceive a body projected or thrown along a horizontal 
plane, all impediments being removed Now it is clear by 
what we have said before at length that its motion will 
be uniform and perpetual along the said plane, if the plane 
extend indefinitely 

In connection with projectiles, Galilei also appears to 
realise that a body may be conceived as having motions 
in two different directions simultaneously, and that each 
may be treated as independent of the other, so that, 
for example, if a bullet is shot horizontally out of a 
gun, its downward motion, due to its weight, is unaffected 

* Equivalent to portions of the subject now called dynamics or 
(more correctly) kinematics and kinetics 

f He estimates that a body falls m a second a distance of 4 
"bracchia," equivalent to about 8 feet, the true distance being 
slightly ovei 16 

I7 6 A Short History of Astronomy [Oi vi 

by its horizontal motion, and consequently it i caches 
the ground at the same time as a bullet simply allowed 
to drop, but Galilei gives no geneial statement of this 
principle, which was afterwards embodied by Newton in 
his Second Law of Motion 

The treatise on the Two New Sciences was finished in 
1636, and, since no book of Galilei's could be printed in 
Italy, it was published after some little delay at Leyden 
in 1638 In the same year his eyesight, which he hud 
to some extent recoveied after his first attack of blindness, 
failed completely, and four, years later (January 8th, 1642) 
the end came 

134 Galilei's chief scientific discovcncs have already 
been noticed The telescopic discoveries, on which mu< h 
of his popular reputation lests, have probably attracted 
more than their fair shaie of attention, many of them 
were made almost simultaneously by others, and the test, 
being almost inevitable results of the invention of the 
telescope, could not have been delayed long But the 
skilful use which Galilei made of them as arguments for 
the Coppernican system, the no less important suppoit 
which his dynamical discoveries gave to the same cause, 
the lucidity and dialectic brilliance with which he maishalled 
the arguments in favour of his views and demolished 
those of his opponents, together with the sensational in- 
cidents of his persecution, formed conjointly a contnbution 
to the Coppernican controversy which was m effect 
decisive Astronomical text-books still continued to give 
side by side accounts of the Ptolemaic and of the Coppei - 
mean systems, and the authors, at any rate if they weie 
good Roman Catholics, usually expressed, in some vnoio 
or less perfunctory way, their adherence to the fonnei, but 
there was no real life left in the traditional astionomy , 
new advances in astronomical theory were all on Coppei- 
nican lines, and in the extensive scientific correspondence 
of Newton and his contemporaries the truth of the 
Coppernican system scarcely ever appeal s as a subject foi 

Galilei's dynamical discoveries, which aie only m p.irt 
of astronomical importance, are m many respects Ins 
most remarkable contribution to science For whcicas in 

i34l Estimate of Galilei's Work 177 

astronomy he was building on foundations laid by pre- 
vious generations, in dynamics it was no question of im- 
piovmg or developing an existing science, but of creating 
a new one From his predecessors he inherited nothing 
but erroneous traditions and obscure ideas , and when these 
had been discarded, he had to arrive at clear fundamental 
notions, to devise experiments and make obseivations, to 
interpret his experimental results, and to follow out the 
mathematical consequences of the simple laws first arrived 
at The positive results obtained may not appear numerous, 
if viewed fiom the standpoint of our modern knowledge, 
but they sufficed to constitute a secure basis for the super- 
structure which later investigators added 

It is customary to associate with our countryman Francis 
Bacon (1561-1627) the reform m methods of scientific 
discovery which took place during the seventeenth century, 
and to which much of the rapid progress m the natural 
sciences made since that time must be attubuted The 
value of Bacon's theory of scientific discovery is very 
differently estimated by different critics, but there can be 
no question of the singular ill-success which attended his 
attempts to apply it in particular cases, and it may fairly 
be questioned whether the scientific methods constantly 
referied to incidentally by Galilei, and brilliantly exemplified 
by his practice, do not really contain a large part of what 
is valuable in the Baconian philosophy of science, while at 
the same time avoiding some of its errors Reference has 
already been made on several occasions to Galilei's protests 
against the cuirent method of dealing with scientific 
questions by the interpretation of passages in Aristotle, 
Ptolemy, or other writers , and to his constant insistence 
on the necessity of appealing directly to actual observation 
of facts. But while thus agreeing with Bacon m these 
essential points, he differed from him in the recognition 
of the importance, both of deducing new results from 
established ones by mathematical or other processes of 
exact reasoning, and of using such deductions, when 
compared with fresh experimental results, as a means of 
verifying hypotheses provisionally adopted This method 
of proof, which lies at the base of nearly all important 
scientific discovery, can hardly be described better than by 

i 7 8 A Short Htstory of Astronomy [CH VI , 134 

Galilei's own statement of it, as applied to a particular 

case .- 

" Let us therefore take this at present as a Postnlatum, the 
truth whereof we shall afterwards find established, when we 
shall see other conclusions built upon this Hypothes^s, to answer 
and most exactly to agree with Experience " * 

* Two New Sciences, translated by Weston, p 255 



" His celebrated laws were the outcome of a lifetime of speculation, 
for the most part vain and groundless But Kepler's name was 

destined to be immortal, on account of the patience with which he 
submitted his hypotheses to comparison with observation, the candour 
with which he acknowledged failure aftei failure, and the persever- 
ance and ingenuity with which he renewed his attack upon the 
riddles of nature " 


135 JOHN KEPLER, 01 Keppler,* was bom in 1571, seven 
years after Galilei, at Weil in Wurtemberg , his parents were 
m reduced circumstances, though his father had some claims 
to noble descent. Though Weil itself was predominantly 
Roman Catholic, the Keplers were Protestants, a fact which 
frequently stood in Kepler's way at various stages of his 
career But the father coulcl have been by no means 
zealous m his faith, for he enlisted m the army of the 
notorious Duke of Alva when it was engaged in trying to 
suppress the revolt of the Netherlands against Spanish 

John Kepler's childhood was maiked by more than the 
usual number of illnesses, and his bodily weaknesses, 
combined with a promise of great intellectual ability, seemed 
to point to the Church as a suitable career for him After 
attending various elementary schools with great irregulauty 
due partly to ill-health, partly to the requirements of 

* The astronomer appears to have used both spellings of his name 
almost indifferently For example, the title-page of his most 
important book, the Commentates on the Motions of Mars ( 141), 
has the form Kcplei, while the dedication of the same book is signed 



180 A Short History of Astronomy [CH vn 

manual work at home he was sent in 1584 at the public 
expense to the monastic school at Adelberg, and two years 
later to the moie advanced school or college of the 
same kind at Maulbronn, which was connected with the 
University of Tubingen, then one of the great centies of 
Protestant theology 

In 1588 he obtained the B A degree, and mthe following 
year entered the philosophical faculty at Tubingen 

There he came under the influence of Maestlm, the 
professor of mathematics, by whom he was in private 
taught the principles of the Coppermcan system, though 
the professorial lectures were still on the traditional lines 

In 1591 Kepler graduated as M A , being second out of 
fourteen candidates, and then devoted himself chiefly to 
the study of theology 

136 In 1594, however, the Protestant Estates of Styna 
applied to Tubingen for a lecturei on mathematics (in- 
cluding astronomy) for the high school of Gratz, and the 
appointment was offered to Kepler Having no special 
knowledge of the subject and as yet no taste for it, he 
naturally hesitated about accepting the offer, but finally 
decided to do so, expiessly stipulating, however, that he 
should not thereby forfeit his claims to ecclesiastical 
prefeiment m Wurtemberg, The demand for higher 
mathematics at Gratz seems to have been slight ; during 
his first year Kepler's mathematical lectures were attended 
by very few students, and m the following year by none, 
so that to prevent his salary from being wasted he was 
set to teach the elements of vanous other subjects It 
was moreover one of his duties to prepare an annual 
almanack or calendar, which was expected to contain not 
merely the usual elementary astronomical information such 
as we are accustomed to in the calendars of to-day, but 
also astrological information of a more interesting charactei, 
such as predictions of the weather and of remarkable events, 
guidance as to unlucky and lucky times, and the like 
Kepler's first calendar, for the year 1595, contained some 
happy weather-prophecies, and he acquired accordingly a 
considerable popular reputation as a prophet and astrologer, 
which remained throughout his life 

Meanwhile his official duties evidently left him a good 

136, is?] Kepler's Early Astronomical Work 181 

deal of leisure, which he spent with characteristic energy 
in acquiring as thorough a knowledge as possible of 
astronomy, and in speculating on the subject 

According to his own statement, "there were three 
things in particular, viz the number, the size, and the 
motion of the heavenly bodies, as to which he searched 
zealously for reasons why they were as they were and not 
otheiwise", and the results of a long course of wild 
speculation on the subject led him at last to a result with 
which he was immensely pleased a numeiical relation 
connecting the distances of the several planets from the 
sun with certain geometrical bodies known as the regular 
solids (of which the cube is the best known), a relation 
which is not very accurate numerically, and is of absolutely 
no significance or importance * This discovery, together 
with a detailed account of the steps which led to it, as well 
as of a number of other steps which led nowhere, was 
published in 1596 in a book a poition of the title of which 
may be tianslated as The Forerunner of Dissertations on 
the Universe, containing the Mystery of the Universe, 
commonly refeired to as the Mysterium Cosmographicum 
The contents were piobably much more attractive and 
seemed more valuable to Kepler's contemporanes than 
to us, but even to those who weie least inclined to attach 
weight to its conclusions, the book shewed evidence 
of considerable astronomical knowledge and very great 
ingenuity , and both Tycho Brahe and Galilei, to whom 
copies were sent, recognised m the authoi a rising 
astronomer likely to do good work 

137 In 1597 Kepler married In the following year the 
religious troubles, which had for some years been steadily 
growing, were increased by the action of the Archduke 
Ferdinand of Austria (afterwards the Emperor Ferdinand II ), 
who on his return from a pilgrimage to Loretto started a 

* The regular solids being taken in the order cube, tetrahedron, 
dodecahedron, icosahedron, octohcdron, and of such magnitude that 
a spheie can be circumscnbed to each and at the same time inscribed 
in the piecedmg solid oi the series, then the ladu of the six spheres 
so obtained were shewn by Kepler to be approximately proportional 
to the distances fiom the sun oi the six planets Saturn, Jupiter, Mais, 
Earth, Venus, and Meicury 

82 A Short History of Astronomy [Cn vii 

vigorous persecution of Protestants in his dominions, one 
step in which was an order that all Protestant ministers 
and teachers in Styna should quit the country at once 
(1598) Kepler accordingly fled to Hungary, but returned 
after a few weeks by special permission of the Archduke, 
given apparently on the advice of the Jesuit party, who had 
hopes of converting the astronomer Kepler's hearers had, 
however, mostly been scattered by the persecution, it be- 
came difficult to ensure regular payment of his stipend, 
and the rising tide of Catholicism made his position in- 
creasingly insecure Tycho's overtures were accordingly 
welcome, and in 1600 he paid a visit to him, as already 
described (chapter v , 108), at Benatek and Prague He 
returned to Gratz in the autumn, still uncertain whether to 
accept Tycho's offer or not, but being then definitely 
dismissed from his position at Gratz on account of his 
Protestant opinions, he returned finally to Prague at the 
end of the year 

138. Soon after Tycho's death Kepler was appointed his 
successor as mathematician to the Emperor Rudolph (1602), 
but at only half his predecessor's salary, and even this was 
paid with great irregularity, so that complaints as to an ears 
and constant pecuniary difficulties played an important part 
in his future life, as they had done during the later years 
at Gratz Tycho's instruments never passed into his pos- 
session, but as he had little taste or skill for observing, the 
loss was probably not great , fortunately, after some diffi- 
culties with the heirs, he secured control of the greater part 
of Tycho's incomparable series of observations, the working 
up of which into an improved theory of the solar system 
was the mam occupation of the next 25 years of his life 
Before, however, he had achieved any substantial result m 
this direction, he published several minor works for ex- 
ample, two pamphlets on a new star which appeared in 1604, 
and a treatise on the applications of optics to astronomy 
(published in 1604 with a title beginning Ad Vitelhonem 
Parahpomena quibus Astrononnae Pars Opttca Traditur ), 
the most interesting and important part of which was a 
considerable improvement in the theory of astronomical 
refraction (chapter u , 46, and chapter v, no). A 
later optical treatise (the Dioptnce of 1611) contained a 

[To face p 183. 

is8, ISP! Optical Work Study of Mars 183 

suggestion for the construction of a telescope by the use 
of two convex lenses, which is the form now most commonly 
adopted, and is a notable improvement on Galilei's instru- 
ment (chapter vi , 118), one of the lenses of which is 
concave ; but Kepler does not seem himself to have had 
enough mechanical skill to actually construct a telescope 
on this plan, or to have had access to workmen capable 
of doing so for him , and it is probable that Galilei's 
enemy Schemer (chapter VL, 124, 125) was the first 
person to use (about 1613) an instrument of this kind. 

139 It has already been mentioned (chapter v, 108) 
that when Tycho was dividing the work of his observatory 
among his assistants he assigned to Kepler the study of 
the planet Mars, probably as presenting more difficulties 
than the subjects assigned to the others It had been 
known since the time of Coppermcus that the planets, 
including the earth, revolved round the sun in paths that 
were at any rate not very different from circles, and 
that the deviations from uniform circular motion could be 
represented roughly by systems of eccentrics and epicycles 
The deviations from uniform circular motion were, however, 
notably different m amount in different planets, being, 
for example, very small in the case of Venus, relatively large 
m the case of Mars, and larger still in that of Mercury 
The Prussian Tables calculated by Reinhold on a Copper- 
mean basis (chapter v , 94) weie soon found to represent 
the actual motions very imperfectly, errors of 4 and 5 
having been noted by Tycho and Kepler, so that the 
principles on which the tables were calculated were evi- 
dently at fault 

The solution of the problem was cleaily more likely 
to be found by the study of a planet in which the de- 
viations from circulai motion were as great as possible 
In the case of Meicury satisfactory observations were 
scarce, whereas m the case of Mars there was an abundant 
series recorded by Tycho, and hence it was true insight on 
Tycho's part to assign to his ablest assistant this paiticular 
planet, and on Kepler's to continue the research with un- 
weaned patience The particular system of epicycles used 
by Coppemicus (chapter iv , 87) having proved defective, 
Kepler set to woik to devise other geometrical schemes, the 

184 A Short History of Astronomy [CH vn 

results of which could be compared with observation The 
places of Mars as seen on the sky being a combined result 
of the motions of Mars and of the earth in their respective 
orbits round the sun, the irregularities of the two oibits 
were apparently inextricably mixed up, and a great simpli- 
fication was accordingly effected when Kepler succeeded, 
by an ingenious combination of observations taken at suit- 
able times, in disentangling the irregularities due to the 
earth from those due to the motion of Mars itself, and 
thus rendering it possible to concentrate his attention on 
the latter His fertile imagination suggested hypothesis 
after hypothesis, combination after combination of eccentric, 
epicycle, and equant, he calculated the lesults of each and 
compared them rigorously with obseivation , and at one 
stage he arnved at a geometrical scheme which was capable 
of representing the observations with eriors not exceeding 
8' * A man of less intellectual honesty, 01 less convinced 
of the necessity of subordinating theory to fact when the 
two conflict, might have rested content with this degiee 
of accuracy, or might have supposed Tycho's icfractoiy 
observations to be m error. Kepler, however, thought 

" Since the divine goodness has given to us in Tycho Brahe a 
most careful observer, from whose observations the error of 8' 
is shewn in this calculation, it is right that we should with 
gratitude recognise and make use of this gift of God For if 
I could have treated 8' of longitude as negligible I should have 
already corrected sufficiently the hypothesis discovered m 

chapter xvi But as they could not be neglected, these 8' 
alone have led the way towards the complete reformation of 
astronomy, and have been made the subiect-matter of a great 
part of this work " f 

140 He accordingly started afresh, and after trying a variety 
of other combinations of circles decided that the path of 
Mars must be an oval of some kind At first he was in- 
clined to believe in an egg-shaped oval, larger at one end than 
at the other, but soon had to abandon this idea Finally 

* Two stars 4' apart only just appear distinct to the naked eye of 
a person with average keenness oi sight 
f Commentates on the Motions of Mars, Part II , end of chapter xix 

$ i4o] The Discovery of the Elliptic Motion of Mars 185 

he tried the simplest known oval curve, the ellipse,* and 
found to his delight that it satisfied the conditions of the 
problem, if the sun were taken to be at a focus of the ellipse 
described by Mars. 

It was further necessaiy to formulate the law of variation 
of the rate of motion of the planet m different parts of its 
orbit Heie again Kepler tried a number of hypotheses, m 
the course of which he fairly lost his way m the intricacies 
of the mathematical questions involved, but fortunately 
arrived, after a dubious process of compensation of errors, 
at a simple law which agreed with observation He found 
that the planet moved fast when near the sun and slowly 
when distant from it, in such a way that the area described 
or swept out m any time by the line joining the sun to 
Mars was always proportional to the time Thus m fig 6ot 
the motion of Mars is most rapid at the point A nearest to 
the focus s where the sun is, least rapid at A', and the 

* An ellipse is one of several curves, known as conic sections, 
which can be formed by taking a section of a cone, and may also be 
defined as a curve the sum of the distances of any point on which 
trom two fixed points inside it, known as the foci, is always the same 

Thus if, in the figure, s and H are the foci, and P, Q are any two 

An ellipse 

points on the cuive, then the distances s P, n P added together are 
efual to the distances s Q, Q H added together, and each sum is equal 
to the length A A' of the ellipse The ratio of the distance s H to 
the length A A' is known as the eccentricity, and is a convenient 
measure of the extent to which the ellipse differs from a circle 

f The ellipse is more elongated than the actual path of Mars, an 
accuiate drawing of which would be undistmguishable to the eye 
from a circle. The eccentricity is J in the figuie, that of Mars being $, 

1 86 A Short History of Astronomy CCH vn 

shaded and unshaded portions of the figure represent equal 
areas each corresponding to the motion of the planet duung 
a month Kepler's triumph at arriving at this result is 
expressed by the figure of victory in the corner of the 
diagram (fig 61) which was used in establishing the last 
stage of his proof. 


Kepler's second law. 

141 Thus were established for the case of Mars the two im- 
portant results generally known as Kepler's first two laws 

1 The planet describes an ellipse -, the sun being in onefoai\. 

2 The straight line joining the planet to the sun sweeps out 
equal areas in any two equal intervals of time 

The full history of this investigation, with the results 
alieady stated and a number of developments and results 
of minor importance, together with innumerable digressions 
and quaint comments on the progress of the inquiry, was 
published in 1609 m a book of considerable length, the 
Commentaries on the Motions of Mars * 

142. Although the two laws of planetary motion just 
given were only fully established for the case of Mars, 

* Astronomia Nova cuVtoXt^ros seu Physica Coekbtts, tradita Com- 
mentams de Motibus Stellae Marhs Ex Obscrvatiombu&> G. K 
Tychoms Bt ahe 

, i42] Kepler's First and Second Laws 


Kepler stated that the earth's path also must be an oval 
of some kind, and was evidently already convinced aided 
by his firm belief in the harmony of Nature that all the 
planets moved in accordance with the same laws This view 
is indicated in the dedication of the book to the Emperor 
Rudolph, which gives a fanciful account of the work as a 

FIG 6l Diagram used by Kepler to establish his laws of planetary 
motion From the Commentaries on Mars, 

struggle against the rebellious War-God Mars, as the result 
of which he is finally brought captive to the feet of the 
Emperor and undertakes to live for the future as a loyal 
subject As, however, he has many relations in the 
etheieal spaces his father Jupiter, his grandfather Saturn, 
his dear sister Venus, his faithful brother Mercury and he 
yearns for them and they for him on account of the similarity 
of their habits^ he entieats the Emperor to send out an 

i88 A Short History of Astronomy [Cn VII 

expedition as soon as possible to capture them also, and 
with that object to provide Kepler with the " smews of 
war " m order that he may equip a suitable army 

Although the money thus delicately asked for was only 
supplied very 11 regularly, Kepler kept steadily m view the 
expedition for which it was to be used, or, m plainer words, 
he worked steadily at the problem of extending his elliptic 
theory to the other planets, and constructing the tables of 
the planetary motions, based on Tycho's observations, at 
which he had so long been engaged 

143 In 1611 his patron Rudolph was forced to abdicate 
the imperial crown m favour of his brother Matthias, who 
had little interest in astronomy, or even m astrology ; and 
as Kepler's position was thus rendered more insecure than 
evei, he opened negotiations with the Estates of Upper 
Austria, as the result of which he was promised a small 
salary, on condition of undertaking the somewhat varied 
duties of teaching mathematics at the high school of Linz, 
the capital, of constructing a new map of the province, and 
of completing his planetary tables For the piesent, how- 
ever, he decided to stay with Rudolph. 

In the same year Kepler lost his wife, who had long 
been m weak bodily and mental health 

In the following year (1612) Rudolph died, and Kepler 
then moved to Linz and took up his new duties there, 
though still holding the appointment of mathematician to 
the Emperor and occasionally even receiving some portion 
of the salary of the office In 1613 he married again, after 
a careful consideration, recorded m an extraordinary but 
very characteristic letter to one of his friends, of the relative 
merits of eleven ladies whom he regarded as possible } and 
the provision of a proper supply of wine for his new house- 
hold led to the publication of a pamphlet, of some mathe- 
matical interest, dealing with the proper way of measuring 
the contents of a cask with curved sides * 

144 In the years 1618-1621, although m some ways the 
most disturbed years of his life, he published three books 
of importance an Epitome of the Copernican Astronomy ', 
the Harmony of the World^ and a treatise on Comets. 

* It contains the germs of the method of infinitesimals, 
j" Hw momces Mundi Libn V^ 

143, 144] 

Keller's Third Law 


The second and most important of these, published in 
1619, though the leading idea in it was discovered early 
m 1618, was legarded by Kepler as a development of his 
early Mystenum Cosmographicum ( 136) His specula- 
tive and mystic temperament led him constantly to search 
for relations between the various numerical quantities occui- 
nng m the solar system ; by a happy inspiration he thought 
of trying to get a relation connecting the sizes of the orbits 
of the various planets with their times of revolution round 
the sun, and after a number of unsuccessful attempts dis- 
covered a simple and important relation, commonly known 
as Keplei's third law 

The squares of the times of revolution of any two planets 
(including the earth) about the sun are proportional to the 
cubes of their mean distances ft om the sun 

If, for example, we express the times of revolution of 
the various planets in terms of any one, which may be con- 
veniently taken to be that of the eaith, namely a year, and m 
the same way express the distances in terms of the distance 
of the eaith from the sun as a unit, then the times of 
i evolution of the several planets taken m the ordei Mercury, 
Venus, Earth, Mars, Jupiter, Saturn are appioximately 24, 
615, i, i 88, ii 86, 29457, and their distances from the 
sunaie respectively 387, 723, i, 1524, 5203, 9539; if 
now we take the squares of the first series of numbeis (the 
squaie of a numbei being the number multiplied by itself) 
and the cubes of the second series (the cube of a numbei 
being the number multiplied by itself twice, or the square 
multiplied again by the number), we get the two senes of 
numbers given approximately by the table 







Square of] 
periodic V 
time J 







Cube of] 
mean I 







Here it will be seen that the two series of numbers, in the 

190 A Short History of Astronomy [CH vn 

upper and lower row respectively, agree completely for as 
many decimal places as are given, except in the cases of 
the two outer planets, where the lower numbers are slightly 
m excess of the upper For this discrepancy Newton after- 
wards assigned a reason (chapter ix , 186), but with the 
somewhat imperfect knowledge of the times of revolution 
and distances which Kepler possessed the discrepancy 
was barely capable of detection, and he was therefore 
justified from his standpoint in speaking of the law as 
" precise " * 

It should be noticed further that Kepler's law requues 
no knowledge of the actual distances of the several planets 

Saturnus Jupiter Marsfcie Tcira 

Venus *"* Mercunus Hie locum habetcciam] 

FIG 62 The " music of the spheres," according to Kepler 
From the Harmony of the World 

from the sun, but only of their relative distances, i.e the 
numbei of times farther off from the sun or nearer to the 
sun any planet is than any other In other words, it is 
necessary to have or to be able to construct a map of the 
solar s>stem coriect in its proportions^ but it is quite 
unnecessary for this purpose to know the scale of the map 

Although the Harmony of the ]Vorld is a large book, 
there is scarcely anything of value m it except what has 
already been given. A good deal of space is occupied 
with lepetitions of the earlier speculations contained m the 

* There may be some interest m Kepler's own statement of the 
law "Res est certissima exactissimaque, quod proportions quae 
est inter bmorurn quorumque planetarum tempora periodica, sit 
praecise sesquialtera proportionis mediarum distantiarum, id est 
orbium ipsorum " Hatmony of the World^ Book V , chapter HI 

i4s] The Harmony of the World and the Epitome 191 

Mysterium Cosmographuum^ and most of the rest is filled 
with worthless analogies between the proportions of the 
solar system and the relations between various musical 

He is bold enough to write down in black and white the 
" music of the spheres " (in the form shewn in fig 62), while 
the nonsense which he was capable of writing may be 
further illustrated by the remark which occurs in the same 
part of the book " The Earth sings the notes M I, F A, M I, 
so that you may guess from them that in this abode of ours 
Misery (imserid) and FAmme (fames) prevail " 

145 The Epitome of the Copernican Astronomy ', which 
appeared in parts m 1618, 1620, and 1621, although there 
are no very striking discoveries in it, is one of the most 
attractive of Kepler's books, being singularly free from the 
extravagances which usually render his writings so tedious 
It contains within moderately short compass, in the form 
of question and answer, an account of astronomy as known 
at the time, expounded from the Coppermcan standpoint, 
and embodies both Kepler's own and Galilei's latest dis- 
coveries Such a text-book supplied a decided want, and 
that this was recognised by enemies as well as by friends 
was shewn by its prompt appearance in the Roman Index 
of Prohibited Books (cf chapter vi , 126, 132) The 
Epitome contains the first clear statement that the two 
fundamental laws of planetary motion established for the 
case of Mars ( 141) were true also for the other planets 
(no satisfactory proof being, however, given), and that they 
applied also to the motion of the moon round the earth, 
though in this case there were further irregularities which 
complicated matters The theory of the moon is worked 
out m considerable detail, both evection (chapter n , 48) 
and variation (chapter in, 60, chapter v, in) being 
fully dealt with, though the " annual equation " which 
Tycho had just begun to recognise at the end of his life 
(chapter v, in) is not discussed Another interesting 
development of his own discoveries is the recognition 
that his third law of planetary motion applied also to 
the movements of the four satellites round Jupitei, as 
recorded by Galilei and Simon Manus (chapter vi , 118) 
Kepler also introduced in the Epitome a considerable 

IQ 2 A Short History of Astronomy [Oi VII 

improvement in the customary estimate of the distance of 
the earth from the sun, from which those of the othei 
planets could at once be deduced 

If, as had been generally believed since the time of 
Hipparchus and Ptolemy, the distance of the sun were 
1,200 times the ladius of the earth, then the parallax 
(chapter n , 43, 49) of the sun would at times be as 
much as 3', and that of Mars, which in some positions is 
much nearer to the earth, proportionally larger But Keplei 
had been unable to detect any parallax of Mars, and there- 
fore inferred that the distances of Mars and of the sun 
must be greater than had been supposed Having no 
exact data to go on, he produced out of his imagination 
and his ideas of the harmony of the solar system a distance 
about three times as great as the traditional one He 
argued that, as the earth was the abode of measuring 
creatures, it was reasonable to expect that the measurements 
of the solar system would bear some simple relation to the 
dimensions of the earth Accordingly he assumed that 
the volume of the sun was as many times gi eater than the 
volume of the earth as the distance of the sun was greater 
than the radius of the earth, and from this quaint assumption 
deduced the value of the distance aheady stated, which, 
though an improvement on the old value, was still only 
about one-seventh of the true distance 

The Epitome contains also a good account of eclipses 
both of the sun and moon, with the causes, means of 
predicting them, etc The faint light (usually reddish) with 
which the face of the eclipsed moon often shines is coirectly 
explained as being sunlight which has passed through 
the atmosphere of the earth, and has there been bent from 
a straight course so as to reach the moon, which the light 
of the sun m general is, owing to the mteiposiUon of the 
eaith, unable to reach Kepler mentions also a ring of 
light seen round the eclipsed sun in 1567, when the 
eclipse was probably total, not annular (chapter n , 43), 
and ascribes it to some sort of luminous atmospheie round 
the sun, referring to a description in Plutarch of the same 
appearance This seems to have been an early obseivation, 
and a rational though of course very imperfect explanation, 
of that remarkable solar envelope known as the corona 

146] Kepler's Epitome and his Book on Comets 193 

which has attracted so much attention m the last half- 
century (chapter xm , 301) 

146 The treatise on Comets (1619) contained an account 
of a comet seen m 1607, afterwaids famous as Halley's 
comet (chapter x , 200), and of three comets seen m 1618 
Following Tycho, Kepler held firmly the view that comets 
were celestial not terrestrial bodies, and accounted for their 
appearance and disappearance by supposing that they moved 
in straight lines, and therefore after having once passed 
near the earth receded indefinitely into space , he does 
not appear to have made any serious attempt to test this 
theoiy by comparison with observation, being evidently 
of opinion that the path of a body which would never 
reappear was not a suitable object for serious study He 
agreed with the observation made by Fiacastor and Apian 
(chaptei in , 69) that comets' tails point away from the 
sun, and explained this by the supposition that the tail is 
formed by rays of the sun which penetrate the body of 
the comet and cany away with them some portion of its 
substance, a theory which, allowance being made for the 
change in our views as to the nature of light, is a curiously 
correct anticipation of modern theories of comets 7 tails 
(chapter xm , 304) 

In a book intended to have a popular sale it was 
necessary to make the most of the "meaning" of the 
appearance of a comet, and of its influence on human 
affairs, and as Kepler was wilting when the Thirty Years' 
War had just begun, while religious persecutions and wars 
had been going on m Europe almost without interruption 
during his lifetime, it was not difficult to find sensational 
events which had happened soon after or shortly before 
the appearance of the comets referred to Keplei himself 
was evidently not inclined to attach much importance to 
such coincidences , he thought that possibly actual contact 
\vith a comet's tail might produce pestilence, but beyond 
that was not piepared to do more than cndoise the pious if 
somewhat neutral opinion that one of the uses of a comet is 
to remind us that we are mortal. His belief that comets are 
veiy numerous is expressed in the curious form "There 
are as many arguments to prove the annual motion of the 
earth round the sun as there are comets in the heavens " 

194 ^ Short History of Astronomy [Cn vn 

147 Meanwhile Kepler's position at Lmz had become 
more and more uncomfortable, owing to the rising tide 
of the religious and political disturbances which finally 
led to the outbreak of the Thirty Years' War in 1618 ; but 
notwithstanding this he had refused in 1617 an offer of 
a chair of mathematics at Bologna, partly through attach- 
ment to his native country and partly through a well-founded 
distrust of the Papal party in Italy. Three years afteiwaids 
he rejected also the overtuies made by the English 
ambassador, with a view to securing him as an ornament 
to the court of James I , one of his chief grounds for lefusal 
in this case being a doubt whether he would not suffer 
from being cooped up within the limits of an island 
In 1619 the Emperor Matthias died, and was succeeded 
by Ferdinand II , who as Archduke had started the peisc- 
cution of the Protestants at Gratz ( 137) and who had 
few scientific interests Kepler was, however, after some 
delay, confirmed in his appointment as Imperial Mathe- 
matician In 1620 Lmz was occupied by the Imperialist 
troops, and by 1626 the oppression of the Protestants by 
the Roman Catholics had gone so far that Kepler made 
up his mind to leave, and, after sending his family to 
Regensburg, went himself to Ulm 

148 At Ulm Kepler published his last great work 
For more than a quarter of a century he had been 
steadily working out in detail, on the basis of Tycho's 
observations and of his own theories, the motions of the 
heavenly bodies, expiessmg the results in such convenient 
tabular form that the determination of the place of any 
body at any required time, as well as the investigation 
of other astronomical events such as eclipses, became 
merely a matter of calculation according to fixed rules , 
this great undertaking, in some sense the summing up of 
his own and of Tycho's work, was finally published in 1627 
as the Rudolphine Tables (the name being given in honour 
of his former patron), and remained for something like 
a century the standard astronomical tables 

It had long been Kepler's intention, after finishing the 
tables, to write a complete treatise on astronomy, to be 
called the New Almagest , but this scheme was never fanly 
started, much less earned out 

$ 147-iso] The Rudolphine Tables 195 

149 After a number of unsuccessful attempts to secure 
the arrears of his salary, he was told to apply to Wallenstem, 
the famous Imperialist general, then established in Silesia 
in a semi-independent position, who was keenly mteiested 
in astrology and usually took about with him one or more 
representatives of the art. Kepler accordingly joined 
Wallenstem in 1628, and did astrology for him, in addition 
to writing some minor astronomical and astrological treatises 
In 1630 he travelled to Regensburg, where the Diet was 
then sitting, to press in person his claims for various arrears 
of salary , but, worn out by anxiety and by the fatigues of 
the journey, he was seized by a fever a few days after his 
arrival, and died on November 151*1 (N s ), 1630, in his c;oth 

The inventory of his property, made after his death, 
shews that he was in possession of a substantial amount, 
so that the effect of extreme poverty which his letters 
convey must have been to a considerable extent due to his 
over-anxious and excitable temperament 

150 In addition to the great discoveries already men- 
tioned Keplei made a good many minor contributions to 
astronomy, such as new methods of finding the longitude, 
and various improvements in methods of calculation required 
for astronomical problems He also made speculations of 
some interest as to possible causes underlying the known 
celestial motions Whereas the Ptolemaic system required 
a number of motions round mere geometrical points, centres 
of epicycles or eccentucs, equants, etc, unoccupied by any 
real body, and many such motions were still required by 
Coppernicus, Kepler's scheme of the solar system placed a 
real body, the sun, at the most important point connected 
with the path of each planet, and dealt similarly with the 
moon's motion round the earth and with that of the four 
satellites round Jupiter Motions of revolution came in 
fact to be associated not with some central point but with 
some central body, and it became therefore an inquiry of 
interest to asceitam if there were any connection between 
the motion and the cential body The property possessed 
by a magnet of attiactmg a piece of iron at some little 
distance from it suggested a possible analogy to Kepler, 
who had read with care and was evidently impressed by 


A Short History of Astronomy [CH vii 

the treatise On the Magnet (De Magnate) published in 
1600 by our countryman William Gilbert of Colchestei 
(1540-1603) He suggested that the planets might thus 
be regarded as connected with the sun, and therefore as 
sharing to some extent the sun's own motion of revolution 
In other words, a certain "carrying virtue" spread out 
from the sun, with or like the rays of light and heat, and 
tried to carry the planets round with the sun 

"There is there- 
fore a conflict be- 
tween the carrying 
power of the sun and 
the impotence 01 
material sluggishness 
[inertia] of the 
planet , each enjoys 
some measure of 
victory, for the former 
moves the planet 
from its position and 
the latter frees the 
planet's body to some 
extent from the bonds 
in which it is thus 
held, but only to 
be captured again by 
another portion of 

FIG 63 -Kepler's adea of gravity thlS r0tatOr y Virtue " * 

From the Epitome The annexed 

diagram is given 

by Kepler m illustration of this rather confused and vague 

He believed also in a more general "gravity," which he 
defined f as "a mutual bodily affection between allied bodies 
tending towards their union or junction/' and regarded the 
tides as due to an action of this sort between the moon and 
the water of the earth. But the speculative ideas thus 
thrown out, which it is possible to regard as anticipations 
of Newton's discovery of universal gravitation, were not in 
any way developed logically, and Kepler's mechanical ideas 

* Epitome, Book IV , Pait 2 

t Introduction to the Commentaries on the Motions of Mars. 

isi] Estimate of Kepler^ s Work 197 

were too impeifect for him to have made real progress in 
this direction. 

151 There are few astronomers about whose merits such 
different opinions have been held as about Kepler There 
is, it is true, a general agreement as to the great import- 
ance of his three laws of planetary motion, and as to the 
substantial value of the Rudolphine Tables and of various 
minor discoveries These results, however, fill but a small 
part of Kepler's voluminous writings, which are encumbered 
with masses of wild speculation, of mystic and occult 
fancies, of astrology, weather prophecies, and the like, which 
are not only worthless from the standpoint of modern 
astronomy, but which unlike many erroneous 01 imperfect 
speculations in no way pointed towards the direction in 
which the science was next to make progress, and must 
have appeared almost as unsound to sober-minded con- 
temporaries like Galilei as to us Hence as one reads 
chapter after chapter without a lucid still less a correct idea, 
it is impossible to refrain from regrets that the intelligence 
of Kepler should have been so wasted, and it is difficult 
not to suspect at times that some of the valuable results 
which lie imbedded m this gteat mass of tedious specula- 
tion were arrived at by a mere accident On the other 
hand, it must not be forgotten that such accidents have a 
habit of happening only to great men, and that if Kepler 
loved to give reins to his imagination he was equally im- 
pressed with the necessity of scrupulously compaimg 
speculative results with observed facts, and of surrendering 
without demur the most beloved of his fancies if it was 
unable to stand this test If Kepler had burnt three- 
quarters of what he printed; we should in all probability 
have formed a higher opinion of his intellectual grasp and 
sobriety of judgment, but we should have lost to a great 
extent the impression of extraordinary enthusiasm and 
industry, and of almost unequalled intellectual honesty, 
which we now get from a study of his works. 



"And now the lofty telescope, the scale 
By which they venture heaven itself t'assail, 
Was raised, and planted full against the moon " 


152 BETWEEN the publication of Galilei's Two New 
Sciences (1638) and that of Newton's Pnncipia (1687) a 
period of not quite half a century elapsed 9 during this 
interval no astronomical discovery of first-rate importance 
was published, but steady progiess was made on lines 
already laid down 

On the one hand, while the impetus given to exact observa- 
tion by Tycho Brahe had not yet spent itself, the invention 
of the telescope and its gradual improvement opened out an 
almost indefinite field for possible discovery of new celestial 
objects of interest On the other hand, the remarkable 
character of the three laws in which Kepler had summed 
up the leading characteristics of the planetary motions 
could haidly fail to suggest to any intelligent astionomer 
the question why these particular laws should hold, or, m 
other words, to stimulate the inquiry into the possibility of 
shewing them to be necessary consequences of some 
simpler and more fundamental law or laws, while Galilei's 
researches into the laws of motion suggested the possibility 
of establishing some connection between the causes under- 
lying these celestial motions and those of ordinary terrestrial 

153 It has been already mentioned how closely Galilei 
was followed by other astronomers (if not in some cases 
actually anticipated) in most of his telescopic discoveries. 

CH vm , 152-154] Telescopic Discoveries 199 

To his rival Christopher Schemer (chapter vi , 124, 125) 
belongs the credit of the discovery of bright cloud-like 
objects on the sun, chiefly visible near its edge, and from 
their brilliancy named facnlae (little torches) Schemer made 
also a very extensive series of observations of the motions 
and appearances of spots 

The study of the surface of the moon was carried on 
with great care by John Hevel of Danzig (1611-1687), who 
published m 1647 his Selenographia, or descnption of the 
moon, magnificently illustrated by plates engraved as well 
as drawn by himself The chief features of the moon 
mountains, craters, and the dark spaces then believed to be 
seas were systematically described and named, for the 
most part after corresponding featuies of our own earth 
Hevel's names for the chief mountain ranges, e.g the 
Apennines and the Alps^ and for the seas, eg Mare 
Serenitatis or Pacific Ocean, have lasted till to-day , but 
similar names given by him to single mountains and crateis 
have disappeared, and they aie now called after various 
distinguished men of science and philosophers, eg Plato 
and Coppermcus, in accoi dance with a system introduced 
by John Baptist Riccioh (1598-1671) in his bulky treatise 
on astronomy called the New Almagest (1651) 

Hevcl, who was an indefatigable worker, published two 
large books on comets, Prodromus Cometicus (1654) and 
Cometographa (1668), containing the first systematic account 
of all recorded comets He constiucted also a catalogue 
of about 1,500 stars, observed on the whole with accmacy 
rather greater than Tycho's, though still without the use of 
the telescope , he published in addition an improved set 
of tables of the sun, and a variety of othei calculations and 

154 The planets were also watched with mteicst by a 
number of observers, who detected at different times bnght 
01 dark markings on Jupiter, Mars, and Venus. The two 
appendages of Saturn which Galilei had discovered in 1610 
and had been unable to see two years later (chapter vi , 123) 
were seen and described by a number of astionomcrs 
under a perplexing variety of appearances, and the mystery 
was only unravelled, nearly half a century after Galilei's first 
observation, by the gieatest astionomei of this period, 

200 A Short History of Astronomy [Cn vi 11,^154 

Chnstiaan Huygens (1629-1695), a native of the Hague, 
Huygens possessed remarkable ability, both practical and 
theoretical, m several different directions, and his contribu- 
tions to astronomy were only a small part of his services 
to science Having acquired the art of grinding lenses 
with unusual accuracy, he was able to construct telescopes 
of much greater powei than his predecessors By the help of 
one of these instruments he discovered m 1655 a satellite of 
Saturn (Titan) With one of those remnants of mediaeval 
mysticism from which even the soberest minds of the century 
freed themselves with the greatest difficulty, he asserted that, 
as the total numbei of planets and satellites now reached the 
perfect number 12, no more remained to be disco veied a 
prophecy which has been abundantly falsified since ( i6o ; 
chapter xn , 253, 255 , chapter xiu , 289, 294, 295) 

Using a still finer telescope, and aided by his acuteness 
m interpreting his observations, Huygens made the much 
more interesting discovery that the puzzling appearances 
seen round Saturn were due to a thin ring (fig 64) inclined at 
a considerable angle (estimated by him at 31) to the plane 
of the ecliptic, and therefore also to the plane in which 
Saturn's path round the sun lies This result was fast 
announced according to the curious custom of the time 
by an anagram, in the same pamphlet in which the dis- 
covery of the satellite was published, De Saturm Luna 
Observatio Nova (1656), and three years afterwaids (1659) 
the larger Systema Saturmum appeared, m which the in- 
terpretation of the anagram was given, and the varying 
appearances seen both by himself and by earlier observers 
were explained with admirable lucidity and thoioughncss. 
The ring being extremely thin is invisible either when 
its edge is presented to the observer or when it is pie- 
sented to the sun, because in the latter position the ic&t 
of the ring catches no light Twice m the course of 
Saturn's revolution round the sun (at B and D in fig 66), 
i e at intervals of about 15 years, the plane of the ring 
passes for a short time through or very close both to the 
earth and to the sun, and at these two periods the ring is 
consequently invisible (fig. 65) Near these positions (as at 
Q, R, s, T) the ring appears much foreshortened, and pre- 
sents the appearance of two arms projecting from the body 

FIG 64 Saturn's ring, as drawn by Huygens From the 
Systenin Saturnnnn 

65 Satuin, with the nng seen edge-wise Fiom the 

Sy sterna Saturnnwn [To /ace /> 200 

202 A Short History of Astronomy [Cn vni 

of Saturn , farther off still the ring appeals wider and the 
opening becomes visible, and about seven years before 
and after the periods of invisibility (at A and c) the ring 
is seen at its widest Huygens gives for comparison with 
his own results a number of drawings by earlier observers 
(reproduced in fig 67), fiom which it may be seen how 
near some of them were to the discoveiy of the ring 

155 To our countryman William Gascoigne (1612 ^-1644) 
is due the first recognition that the telescope^ could be utilised, 
not merely for observing generally the appearances of celestial 
bodies, but also as an instrument of piecision, which would 
give the directions of stars, etc , with greater accuracy than 
is possible with the naked eye, and would magnify small 
angles in such a way as to facilitate the measurement 
of angular distances between neighbouring stars, of the 
diameters of the planets, and of similar quantities He was 
unhappily killed when quite a young man at the battle 
of Marston Mooi (1644), but his letters, published many 
years afterwards shew that by 1640 he was familiar with 
the use of telescopic "sights," for determining with 
accuracy the position of a star, and that he had constructed 
a so-called micrometer * with which he was able to measure 
angles of a few seconds Nothing was known of his dis- 
covenes at the time, and it was left for Huygens to invent 
independently a micrometer of an inferior kind (1658), and 
for Adiien Auzoitt (^-1691) to introduce as an improvement 
(about 1666) an instrument almost identical with Gascoigne's 

The systematic use of telescopic sights for the legular 
work of an observatory was first introduced about 1667 by 
Auzout's friend and colleague Jean Picard (1620-1682) 

156 With Gascoigne should be mentioned his friend 
Jeremiah Horrocks (1617 ?-i 641), who was an enthusiastic 
admirer of Kepler and had made a consideiable improve- 
ment m the theory of the moon, by taking the elliptic oibit 
as a basis and then allowing for various irregularities He 
was the first observer of a transit of Venus, i e a passage 
of Venus over the disc of the sun, an event which took 
place in 1639, contrary to the prediction of Kepler m the 
Rudolphme Tables^ but m accordance with the rival tables 

* Substantially the filar micrometer of modem astronomy 

FIG 67 Eaily drawings of Saturn From the Sy sterna Satnrmum 

[To face p 202 

155158] Gascoigne^ Horrocks^ Huygens 203 

of Philips von Lansberg ( 1561-163 2), which Horrocks had 
verified for the purpose It was not, however, till long 
afterwards that Halley pointed out the importance of the 
transit of Venus as a means of ascertaining the distance of 
the sun from the earth (chapter x , 202) It is also worth 
noticing that Horrocks suggested the possibility of the 
irregularities of the moon's motion being due to the disturb- 
ing action of the sun, and that he also had some idea of 
certain irregularities in the motion of Jupiter and Saturn, 
now known to be due to their mutual attraction (chapter x , 
204, chapter xi, 243) 

157 Another of Huygens's discoveries revolutionised the 
art of exact astronomical observation This was the inven- 
tion of the pendulum-clock (made 1656, patented in 1657). 
It has been already mentioned how the same discovery 
was made by Eurgi, but virtually lost (see chapter v , 98) , 
and how Galilei again introduced the pendulum as a time- 
measurer (chapter vi , 1 14) Galilei's pendulum, however, 
could only be used for measuring very short times, as there 
was no mechanism to keep it in motion, and the motion 
soon died away Huygens attached a pendulum to a clock 
driven by weights, so that the clock kept the pendulum going 
and the pendulum regulated the clock* Henceforward 
it was possible to take reasonably accurate time-observa- 
tions, and, by noticing the interval between the passage 
of two stars across the meridian, to deduce, from the known 
rate of motion of the celestial sphere, their angular distance 
east and west of one another, thus helping to fix the position 
of one with respect to the other It was again Picard (155) 
who first recognised the astronomical importance of this 
discovery, and introduced regular time-observations at the 
new Observatory of Pans 

158 Huygens was not content with this practical use 
of the pendulum, but worked out m his treatise called 
O sallatormm Horologmm or The Pendulum Clock (1673) a 
number of important results m the theory of the pendulum, 
and m the allied problems connected with the motion of 
a body in a circle or other cuive The greater part of these 

* Galilei, at the end of his life, appears to have thought of contriving 
a pendulum with clockwork, but there is no satisfactory evidence that 
he ever carried out the idea 

204 A Short History of Astronomy [Cn vni 

investigations lie outside the field of astronomy, but his 
formula connecting the time of oscillation of a pendulum 
with its length and the intensity of gravity * (or, m other 
words, the rate of falling of a heavy body) afforded a prac- 
tical means of measuring gravity, of far greater accuracy 
than any direct expenments on falling bodies, and his 
study of circular motion, leading to the result that a body 
moving in a circle must be acted on by some force towaids 
the centre, the magnitude of which depended in a definite 
way on the speed of the body and the size of the circlc,t is 
of fundamental importance in accounting for the planetary 
motions by gravitation 

159 During the iyth century also the first measurements 
of the earth were made which were a definite advance on 
those of the Greeks and Arabs (chapter n , 36, 45, 
and chapter in , 57) Willebrord Snell (1591-1626), best 
known by his discovery of the law of zefraction of light, 
made a series of measurements in Holland in 1617, from 
which the length of a degree of a meridian appeared to be 
about 67 miles, an estimate subsequently alteied to about 
69 miles by one of his pupils, who corrected some errors 
m the calculations, the result being then within a few 
hundred feet of the value now accepted Next, Richard 
Norwood(i$go ^-1675) measured the distance from London 
to York, and hence obtained (1636) the length of the 
degree with an error of less than half a mile. Lastly, 
Picard in 1671 executed some measurements near Pans 
leading to a result only a few yards wrong The length 
of a degree being known, the circumference and ladms of 
the earth can at once be deduced 

1 60 Auzout and Picard weie two members of a group 
of observational astronomers working at Pans, of whom the 
best known, though probably not really the greatest, was 
Giovanni Domenico Cassim (1625-1712) Bom in the 
north of Italy, he acquired a great reputation, partly by 
some rather fantastic schemes for the construction of 
gigantic instruments, partly by the discoveiy of the rotation 

* In modern notation time of oscillation = 2 TT A/ /T^ 
f I e he obtained the familiar formula v*/t t and several equivalent 
forms for cenh ifugal force 

i59-*6i] Measurements of the Earth Cassim 205 

of Jupiter (1665), of Mars (1666), and possibly of Venus 
(1667), and also b y hls tables of the motions of Jupiter's 
moons (1668) The last caused Picard to procure for him 
an invitation from Louis XIV (1669) to come to Pans 
and to exercise a general superintendence over the Obser- 
vatory, which was then being built and was substantially 
completed in 1671 Cassini was an industrious observer 
and a voluminous writer, with a remarkable talent for 
impressing the scientific public as well as the Court He 
possessed a strong sense of the importance both of himself 
and of his work, but it is more than doubtful if he had as 
clear ideas as Picaid of the really important pieces of work 
which ought to be done at a public observatory, and of 
the way to set about them But, notwithstanding these 
defects, he tendered valuable services to various departments 
of astronomy He discovered four new satellites of Saturn 
Japetus in 1671, Rhea in the following year, Dione and 
Thetis m 1684, and also noticed m 1675 a dark Barking 
in Saturn's ring, which has subsequently been more dis- 
tinctly recognised as a division of the ring into two, an 
inner and an outer, and is known as Cassim's division 
(see fig 95 facing p. 384) He also improved to some 
extent the theory of the sun, calculated a fresh table of 
atmospheric refraction which was an improvement on 
Kepler's (chapter vii , 138), and issued in 1693 a fresjl set 
of tables of Jupiter's moons, which were much more accurate 
than those which he had published in 1668, and much the 
best existing 

1 6 1 It was probably at the suggestion of Picard or Cassmi 
that one of their fellow astronomers, /^w Richer (?-i6g6), 
otherwise almost unknown, undertook (1671-3) a scientific 
expedition to Cayenne (in latitude 5 N ) Two important 
lesults were obtained It was found that a pendulum of 
given length beat more slowly at Cayenne than at Pans, 
thus shewing that the intensity of gravity was less near the 
equator than in higher latitudes This fact suggested that the 
earth was not a perfect sphere, and was afterwards used in 
connection with theoretical investigations of the problem of 
the earth's shape (cf chapter ix , 187) Again, Richer's 
observations of the position of Mars m the sky, combined 
with observations taken at the same time by Cassim, Picard, 


A Short History of Astronomy [Cn vni 

and others in France, led to a reasonably accurate estimate 
of the distance of Mars and hence of that of the sun 
Mars was at the time in opposition (chapter n , 43), so 

that it was nearer to the eaith 
than at other times (as shewn 
in fig 68), and therefore 
favourably situated for such 
observations The principle 
of the method is extremely 
simple and substantially iden- 
tical with that long used in 
the case of the moon (chap- 
ter ii , 49) One observer 
is, say, at Paris (p, in fig 69), 
and observes the direction in 
which Mars appears, i e the 
direction of the line P M 9 the 
other at Cayenne (c) observes similarly the direction of 
the line CM The line CP, joining Pans and Cayenne, is 
known geographically , the shape of the triangle c p M and 

FIG 68 Mars in opposition 

FIG 69 The parallax of a planet 

the length of one of its sides being thus known, the 
lengths of the other sides are leadily calculated. 

The result of an investigation of this soit is often most 
conveniently expressed by means of a certain angle, from 

i6i] Parallax 207 

which the distance m terms of the ladius of the earth, and 
hence m miles, can readily be deduced when desned 

The parallax of a heavenly body such as the moon, the 
sun, or a planet, being m the first instance defined geneially 
(chapter n , 43) as the angle (o M p) between the lines 
joining the heavenly body to the observer and to the 
centie of the earth, varies in general with the position of 
the observer It is evidently greatest when the obseiver 
is in such a position, as at Q, that the line M Q touches the 
earth, m this position M is on the obseiver's horizon 
Moreover the angle o Q M being a right angle, the shape 
of the triangle and the ratio of its sides are completely 
known when the angle o M Q is known Since this angle 
is the parallax of M, when on the observer's horizon, it is 
called the horizontal parallax of M, but the word horizontal 
is frequently omitted It is easily seen by a figure that 
the more distant a body is the smaller is its horizontal 
parallax , and with the small parallaxes with which we aie 
concerned m astronomy, the distance and the horizontal 
parallax can be treated as inversely pioportional to one 
another , so that if, for example, one body is twice as 
distant as another, its parallax is half as great, and so on 

It may be convenient to point out here that the word 
"paiallax" is used m a different though analogous sense when 
a fixed star is in question The apparent displacement 
of a fixed star due to the earth's motion (chapter iv , 92), 
which was not actually detected till long afterwards 
(chaptei xin , 278), is called annual or stellar parallax 
(the adjective being frequently omitted) , and the name 
is applied in particular to the greatest angle between the 
direction of the star as seen from the sun and as seen from 
the earth in the couise of the year If m fig 69 we regard 
M as representing a star, o the sun, and the circle as being 
the eaith's path round the sun, then the angle OM Q is the 
annual parallax of M 

In this particular case Cassmi deduced from Richer 's 
observations, by some rather doubtful processes, that the 
sun's parallax was about 9" 5, corresponding to a distance 
from the eaith of about 87,000,000 miles, or about 360 
times the distance of the moon, the most probable value, 
according to modern estimates (chapter xm , 284), being 

2 8 A Short History of Astronomy [CH viu 

a little less than 93,000,000 Though not really an accurate 
result, this was an enormous improvement on anything 
that had gone before, as Ptolemy's estimate of the sun's 
distance, corresponding to a parallax of 3', had survived 
up to the earlier part of the lyth century, and although 
it was generally believed to be seriously wiong, most 
corrections of it had been purely conjectural (chapter vn , 

162 Another famous discovery associated with the early 
days of the Pans Observatory was that of the velocity 
of light In 1671 Picard paid a visit to Denmark to 
examine what was left of Tycho Brahe's observatory at 
Hveen, and brought back a young Danish astronomer, 
Olaus ^^7/^^(1644-1710), to help him at Pans Roemer, 
in studying the motion of Jupiter's moons, observed (1675) 
that the intervals between successive eclipses of a moon 
(the eclipse being caused by the passage of the moon into 
Jupiter's shadow) were regularly less when Jupiter and the 
eaith were approaching one another than when they were 
receding This he saw to be readily explained by the 
supposition that light travels through space at a definite 
though very great speed Thus if Jupiter is approaching 
the earth, the time which the light from one of his moons 
takes to reach the earth is gradually decreasing, and con- 
sequently the interval between successive eclipses as seen 
by us is apparently diminished From the difference of 
the intervals thus observed and the known lates of motion 
of Jupiter and of the earth, it was thus possible to form a 
rough estimate of the rate at which light travels. Roemer 
also made a number of instrumental improvements of 
importance, but they are of too technical a character to 
be discussed here 

163 One great name belonging to the period dealt with 
in this chapter remains to be mentioned, that of Rene 
Descartes* (1596-1650) Although he ranks as a great 
philosopher, and also made some extremely impoitant 
advances in pure mathematics, his astronomical writings 
were of little value and in many respects positively harmful 
In his Principles of Philosophy (1644) he gave, among 
some wholly erroneous propositions, a fuller and more 

* Also frequently referred to by the Latin name Cartestus, 

** i6a, i6 3 ] The Velocity of Light Descartes 209 

general statement of the first law of motion discovered 
by Galilei (chapter vi , 130, 133), but did not support it 
by any evidence of value. The same book contained an 
exposition of his famous theory of vortices, which was an 
attempt to explain the motions of the bodies of the solar 
system by means of a certain combination of vortices or 
eddies The theory was unsupported by any experimental 
evidence, and it was not formulated accurately enough to 
be capable of being readily tested by comparison with 
actual obseivation, and, unlike many eironeous theories 
(such as the Gieek epicycles), it in no way led up to 
or suggested the truer theories which followed it But 
" Cartesiamsm," both m philosophy and m natural science, 
became extremely popular, especially in France, and its 
vogue contributed notably to the oveithrow of the authority 
of Aristotle, already shaken by thinkers like Galilei and 
Bacon, and thus rendered men's minds a little more ready 
to receive new ideas m this indirect way, as well as by 
his mathematical discoveries, Descaites probably con- 
tributed something to astronomical progress 




"Nature and Nature's laws lay hid in night, 
God said ' Let Newton be ' ' and all was light " 


164. NEWTON'S life may be conveniently divided into three 
portions First came 22 years (1643-1665) of boyhood 
and undergraduate life ; then followed his great productive 
period, of almost exactly the same length, culminating in 
the publication of the Pnnapia in 1687 , while the lest of 
his life (1687-1727), which lasted nearly as long as the 
other two periods put together, was largely occupied with 
official work and studies of a non-scientific character, and 
was marked by no discoveries ranking with those made 
in his middle period, though some of his earlier work 
received important developments and several new results 
of decided interest were obtained 

165. Isaac Newton was born at Woolsthorpe, near 
Grantham, m Lincolnshire, on January 4th, 1643,* tnls 
was very nearly a year after the death of Galilei, and a 
few months after the beginning of our Civil Wars His 
taste for study does not appear to have developed very 
early in life, but ultimately became so marked that, after 

* According to the unreformed calendar (OS) then in use m 
England, the date was Christmas Day, 1642 To facilitate comparison 
with events occurring out of England, I have used throughout this 
and the following chapters the Gregorian Calendar (N S ), which was 
at this time adopted in a large part of the Continent (cf chapter n , 


CH ix, ; 164-168] Newton's Early Life 2II 

some unsuccessful attempts to turn him mto a farmer he 
was entered at Trmity College, Cambridge, in 1661 

Although probably at first rather more backward than 
most undergraduates, he made extremely rapid progress 
in mathematics and allied subjects, and evidently Ravi his 
teachers some trouble by the rapidity with which he 
absorbed what little they knew He met with Euclid's 
Elements of Geometry for the first time while an under- 
graduate, but is reported to have soon abandoned it as 
being a trifling book," m favour of moie advanced reading 

he sraduated m the ordmary course as 

1 66 The external events of Newton's life during the 
next 22 years may be very briefly dismissed He was 
elected a Fellow m 1667, became M A m due course m 

IfJ i Wlng year> and was a PP lnt ed Lucasian Professor 
of Mathematics, m succession to his friend Isaac Barrow, 
m 1669 Three years later he was elected a Fellow of the 
recently founded Royal Society With the exception of 
some visits to his Lincolnshire home, he appears to have 
spent almost the whole period in quiet study at Cambridge 
and the history of his life is almost exclusively the history 
of his successive discoveries y 

167 His scientific work falls into three mam groups 
r fT m r (ln , clUdmg dynamics), optics, and pure mathe- 
matics. He also spent a good deal of time on experimental 
work in chemistry, as well as on heat and other branches 
of physics, and m the latter half of his life devoted much 
attention to questions of chronology and theology, m none 
of these subjects, however, did he produce results of much 

1 68 In forming an estimate of Newton's semus it is of 
course important to bear m mind the range of subiects 
with which he dealt , from oui present pomt of view, how- 
ever, his mathematics only piesents itself as a tool to be 
used m astronomical work, and only those of his optical 
discoveries which are of astionomical impoitance need be 
mentioned here In 1668 he constructed a reflecting 
telescope, that is, a telescope in which the rays of light from 
the object viewed are concentiatcd by means of a curved 
mirror instead of by a lens, as in the refracting telescopes 

2i2 A Short History of Astronomy LCH ix 

of Galilei and Kepler. Telescopes on this principle, differ- 
ing however in some important particulars from Newton s, 
had already been described in 1663 by James Gregory 
(1638-1675), with whose ideas Newton was acquainted, but 
it does not appear that Gregory had actually made an 
instrument Owing to mechanical difficulties in construction, 
half a century elapsed befoie reflecting telescopes were 
made which could compete with the best refractors of the 
time, and no important astronomical discoveries were made 
with them before the time of William Herschel (chapter xn ), 
more than a century after the original invention 

Newton's discovery of the effect of a prism m resolving 
a beam of white light into different colours is in a sense 
the basis of the method of spectrum analysis (chapter xni , 
299), to which so many astronomical discoveries of the 
last 40 years are due 

169 The ideas by which Newton is best known in each 
of his three great subjectsgravitation, his theory of 
colours, and fluxionsseem to have occurred to him 
and to have been partly thought out within less than two 
years after he took his degree, that is before he was 24 
His own account written many years afterwards gives 
a vivid picture of his extraordinary mental activity at this 

"In the beginning of the year 1665 I found the method of 
approximating Series and the Rule for reducing any dignity oi 
any Binomial into such a series The same year in May 1 
found the method of tangents of Gregory and Slusius, and m 
November had the direct method of Fluxions, and the next 
year in January had the Theory of Colours, and in May following 
I had entrance into the inverse method of Fluxions And the 
same yeai I began to think of gravity extending to the orb 
of the Moon, and having found out how to estimate the force 
with which [a] globe revolving within a sphere presses the 
surface ot the sphere, from Kepler's Rule of the periodical times 
of the Planets being in a sesquialterate proportion of their 
distances from the centers of their orbs I deduced that the 
forces which keep the Planets in their orbs must [be] reciprocally 
as the squares of their distances from the centers about which 
they revolve and thereby compared the force requisite to keep 
the Moon m her orb with the force of gravity at the surface 
of the earth, and found them answer pretty nearly All this 

i6g, 170] First Discoveries Gravity 213 

was in the two plague years of 1665 and 1666, for in those 
days I was in the prime of my age for invention, and minded 
Mathematicks and Philosophy more than at any time since " * 

170 He spent a considerable part of this time (1665- 
1666) at Woolsthorpe, on account of the prevalence of 
the plague 

The well-known stoiy, that he was set meditating on 
giavity by the fall of an apple in the orchard, is based 
on good authority, and is perfectly credible in the sense 
that the apple may have reminded him at that particular 
time of certain problems connected with gravity That 
the apple seriously suggested to him the existence of the 
problems or any key to their solution is wildly improbable 

Several astronomers had already speculated on the 
cc cause " of the known motions of the planets and satellites , 
that is they had attempted to exhibit these motions as 
consequences of some more fundamental and more general 
laws Kepler, as we have seen (chapter vn , 150), had 
pointed out that the motions in question should not be 
considered as due to the influence of mere geometrical 
points, such as the centres of the old epicycles, but to 
that of other bodies ; and in particular made some attempt 
to explain the motion of the planets as due to a special 
kind of influence emanating from the sun He went, 
however, entirely wrong by looking for a force to keep 
up the motion of the planets and as it were push them 
along Galilei's discovery that the motion of a body 
goes on indefinitely unless there is some cause at work 
to alter or stop it, at once put a new aspect on this as 
on other mechanical problems , but he himself did not 
develop his idea m this particular direction Giovanni 
Alfonso Borelh (1608-1679), m a book on Jupiter's satellites 
published in 1666, and theiefore about the time of Newton's 
first work on the subject, pointed out that a body revolving 
in a circle (or similar cmve) had a tendency to recede 
from the centre, and that in the case of the planets this 
might be supposed to be counteracted by some kind of 
attraction towards the sun We have then here the idea 

* From a MS among the Portsmouth Papers, quoted m the Preface 
to the Catalogue of the Portsmouth Papers, 


A Short History of Astronomy 


in a very indistinct foim certainly that the motion of a 
planet is to be explained, not by a force acting in the 
direction m which it is moving, but by a force directed 
towards the sun, that is about at right angles to the 
direction of the planet's motion. Huygens carried this 
idea much further though without special reference to 
astronomy and obtained (chapter vm , 158) a numerical 
measure for the tendency of a body moving in a circle 
to recede from the centre, a tendency which had in some 
way to be counteracted if the body was not to fly away 
Huygens published his work in 1673, some years after 
Newton had obtained his corresponding result, but before 
he had published anything ; and there can be no doubt 
that the two men worked quite independently 

171 Viewed as a purely general question, apart from 
its astronomical applications, the problem may be said to 

be to examine under 
what conditions a body 
can revolve with uniform 
speed in a circle. 

Let A lepresent the 
position at a certain 
instant of a body which 
is revolving with uniform 
speed m a circle of 
centre o Then at this 
instant the body is 
moving in the direction 
of the tangent A a to 
the circle Conse- 
quently by Galilei's Fust 
Law (chapter vi , 
130, 133), if left to 

FIG 7 Motion in a circle 

itself and uninfluenced by any other body, it would con- 
tinue to move with the same speed and m the same 
direction, i e along the line A a, and consequently would 
be found after some time at such a point as a But 
actually it is found to be at B on the circle Hence some 
influence must have been at work to bring it to B instead 
of to a But B is neaier to the centre of the circle than 
a is ; hence some influence must be at work tending 

$$'7i,i72] Motion in a Circle 215 

constantly to draw the body towards o, or counteracting 
the tendency which it has, m virtue of the First Law of 
Motion, to get farther and farther away from o To 
express either of these tendencies numerically we want a 
more complex idea than that of velocity or rate of motion, 
namely acceleration or rate of change of velocity, an idea 
which Galilei added to science in his discussion of the 
law of falling bodies (chapter vi, 116, 133) A falling 
body, for example, is moving after one second with the 
velocity of about 32 feet per second, after two seconds 
with the velocity of 64, after three seconds with the velocity 
of 96, and so on , thus m every second it gams a downward 
velocity of 32 feet per second, and this may be expressed 
otherwise by saying that the body has a downward accele- 
ration of 32 feet per second per second A further in- 
vestigation of the motion in a circle shews that the motion 
is completely explained if the moving body has, in addition 
to its original velocity, an acceleration of a certain magnitude 
directed towards the centre of the circle It can be shewn 
further that the acceleration may be numerically expressed 
by taking the square of the velocity of the moving body 
(expressed, say, m feet per second), and dividing this by 
the radius of the cucle m feet If, for example, the body 
is moving m a circle having a radius of four feet, at the 
late of ten feet a second, then the acceleration towards 

the centre is ( x I0 = ) 25 feet per second per second 

These results, with others of a similar character, were 
fust published by Huygens not of course precisely in this 
form in his book on the Pendulum Clock (chapter vm , 
158) , and discoveied independently by Newton in 1666 

If then a body Is seen to move m a circle, its motion 
becomes intelligible if some other body can be discovered 
which produces this acceleration In a common case, such 
as when a stone is tied to a string and whirled round, 
this acceleration is produced by the string which pulls 
the stone , in a spinning-top the acceleration of the outer 
parts is produced by the foices binding them on to the 
inner pait, and so on. 

172 In the most important cases of this kind which 
occui in astronomy, a planet is known to icvolve round 

2i 6 A Short History of Astronomy [CH ix 

the sun in a path which does not differ much from a 
circle If we assume for the present that the path is 
actually a circle, the planet must have an acceleration to- 
wards the centre, and it is possible to attribute this to the 
influence of the central body, the sun In this way arises 
the idea of attributing to the sun the power of influencing 
in some way a planet which revolves round it, so as to 
give it an acceleration towards the sun , and the question 
at once anses of how this " influence " differs at different 
distances To answer this question Newton made use of 
Kepler's Third Law (chapter vn , 144) We have seen 
that, according to this law, the squaies of the times of 
revolution of any two planets are proportional to the cubes 
of their distances from the sun , but the velocity of the 
planet may be found by dividing the length of the path 
it travels m its revolution lound the sun by the time of 
the i evolution, and this length is again proportional to the 
distance of the planet from the sun Hence the velocities 
of the two planets are proportional to their distances from 
the sun, divided by the times of revolution, and conse- 
quently the squares of the velocities are proportional to 
the squares of the distances from the sun divided by the 
squares of the times of revolution Hence, by Kepler's 
law, the squares of the velocities aie pioportional to the 
squares of the distances divided by the cubes of the dis- 
tances, that is the squares of the velocities are inversely 
proportional to the distances, the more distant planet 
having the less velocity and vice versa. Now by the 
formula of Huygens the acceleration is measured by the 
square of the velocity divided by the radius of the cucle 
(which in this case is the distance of the planet fiom the 
sun) The accelerations of the two planets towards the 
sun are theiefore inversely proportional to the distances 
each multiplied by itself, that is are inversely proportional 
to the squares of the distances Newton's first result 
therefore is that the motions of the planets regarded as 
moving m circles, and m strict accordance with Keplei's 
Thud Law can be explained as due to the action of the 
sun, if the sun is supposed capable of pioducmg on a 
planet an acceleration towards the sun itself which is 
proportional to the inverse square of its distance from 

i 7 3] The Law of the Inverse Square 217 

the sun , le at twice the distance it is \ as great, at three 
times the distance as great, at ten times the distance -^ 
as great, and so on 

The argument may perhaps be made clearer by a 
numerical example. In round numbers Jupiter's distance 
from the sun is five times as great as that of the earth, 
and Jupiter takes 12 years to perform a revolution round 
the sun, whereas the earth takes one Hence Jupiter goes 
in 12 years five times as far as the earth goes in one, and 
Jupiter's velocity is therefore about ^ that of the earth's, 
or the two velocities are in the ratio of 5 to 12, the 
squares of the velocities are therefore as 5x5 to 12 x 12, 
01 as 25 to 144 The accelerations of Jupiter and of the 
earth towards the sun are therefore as 25 5 to 144, 
or as 5 to 144 , hence Jupiter's acceleration towards the 
sun is about -^V tnat f tne earth, and if we had taken 
more accurate figures this fraction would have come out 
more nearly /- Hence at five times the distance the 
acceleration is 25 times less. 

This law of the inverse square, as it may be called, is 
also the law according to which the light emitted from the 
sun or any other bright body varies, and would on this 
account also be not unlikely to suggest itself in connection 
with any kind of influence emitted from the sun 

173 The next step in Newton's investigation was to see 
whether the motion of the moon round the earth could be 
explained in some similar way By the same argument as 
before, the moon could be shewn to have an acceleration 
towaids the earth Now a stone if let drop falls down- 
wards, that is in the direction of the centre of the earth, 
and, as Galilei had shewn (chapter vi , 133), this 
motion is one of uniform acceleration , if, m accordance 
with the opinion generally held at that time, the motion 
is regaided as being due to the earth, we may say that 
the earth has the power of giving an acceleration towards 
its own centie to bodies near its surface Newton noticed 
that this power extended at any late to the tops of moun- 
tains, and it occurred to him that it might possibly extend 
as far as the moon and so give rise to the required 
acceleration, Although, however, the acceleration of falling 
bodies, as far as> was known at the time, was the same for 

2i8 A Short History of Astronomy [CH ix 

terrestrial bodies wherever situated, it was probable that 
at such a distance as that of the moon the acceleration 
caused by the earth would be much less. Newton assumed 
as a working hypothesis that the acceleration diminished 
according to the same law which he had previously arrived 
at in the case of the sun's action on the planets, that is 
that the acceleration produced by the eaith on any body 
is inversely proportional to the square of the distance of 
the body fiom the centre of the earth 

It may be noticed that a difficulty arises heie which did 
not present itself in the corresponding case of the planets 
The distances of the planets from the sun being large 
compared with the size of the sun, it makes little difference 
whether the planetary distances are measured from the 
centre of the sun or from any other point in it The same 
is true of the moon and earth 3 but when we are comparing 
the action of the earth on the moon with that on a stone 
situated on or near the ground, it is clearly of the utmost 
importance to decide whether the distance of the stone 
is to be measured from the nearest point of the earth, 
a few feet off, from the centre of the earth, 4000 miles 
off, or from some other point Provisionally at any rate 
Newton decided on measuring from the centre of the 

It remained to verify his conjecture in the case of the 
moon by a numerical calculation , this could easily be done 
if certain things were known, viz the acceleration of a 
falling body on the earth, the distance of the surface of 
the earth from its centre, the distance of the moon, and 
the time taken by the moon to perform a revolution lound 
the earth The first of these was possibly known with fair 
accuracy ; the last was well known , and it was also known 
that the moon's distance was about 60 times the radius of 
the earth How accurately Newton at this time knew the 
size of the earth is uncertain Taking moderately accuiate 
figures, the calculation is easily performed In a month of 
about 27 days the moon moves about 60 times as far as 
the distance round the earth, that is she moves about 
60 x 24,000 miles in 27 days, which is equivalent to about 
3,300 feet per second The acceleration of the moon is 
therefore measured by the square of this, divided by the 

173] Extension of Gravity to the Moon 219 

distance of the moon (which is 60 times the radius of the 

earth, or 20,000,000 feet), that is, it is 3>3 X 3>3QQ 

60 x 20,000,000' 

which reduces to about ^ Consequently, if the law of 
the inverse square holds, the acceleration of a falling body 
at the surface of the earth, which is 60 times nearer to the 

centre than the moon is, should be 6o x 6o , or between 


32 and 33 , but the actual acceleration of falling bodies 
is rather more than 32 The aigument is therefore 
satisfactory, and Newton's hypothesis is so far verified. 

The analogy thus indicated between the motion of the 
moon round the earth and the motion of a falling stone 
may be illustrated by a comparison, due to Newton, of the 
moon to a bullet shot horizontally out of a gun from a 
high place on the earth Let the bullet start from B m 
fig 71, then moving at first horizontally it will describe a 
curved path and reach the ground at a point such as c, 
at some distance from the point A, vertically underneath 
its starting point If it were shot out with a greater velocity, 
its path at fust would be flatter and it would reach the 
ground at a point c' beyond c , if the velocity were greater 
still, it would leach the giound at c" or at c'" ; and it 
requires only a slight effort of the imagination to conceive 
that, with a still greater velocity to begin with, it would miss 
the earth altogether and describe a circuit round it, such 
as BDE This is exactly what the moon does, the only 
diffeicnce being that the moon is at a much greater distance 
than we have supposed the bullet to be, and that her 
motion has not been produced by anything analogous to 
the gun , but the motion being once theie it is immaterial 
how it was produced or whether it was ever produced m 
the past We may m fact say of the moon "that she is a 
falling body, only she is going so fast and is so far off that 
she falls quite round to the other side of the earth, instead 
of hitting it , and so goes on for ever " * 

In the memorandum already quoted ( 169) Newton 
speaks of the hypothesis as fitting the facts "pretty 
nearly", but m a letter of earlier date (June 2oth, 1686) 

* W K Clifford, Aims and Instruments of Scientific Thought 


A Short History of Astronomy 


he refers to the calculation as not having been made accu- 
rately enough It is probable that he used a seriously 
inaccurate value of the size of the earth, having overlooked 
the measurements of Snell and Norwood (chapter vm , 
159) it is known that even at a later stage he was unable 

FIG 71 The moon as a projectile. 

to deal satisfactorily with the difficulty above mentioned, 
as to whether the earth might for the pui poses of the 
problem be identified with its centre , and he was of course 
aware that the moon's path differed considerably fiom a 
circle The view, said to have been derived from Newton's 
conversation many years afterwards, that he was so dis- 
satisfied with his results as to regaid his hypothesis as 

174, ITS] The Motion of the Moon> and of the Planets 221 

substantially defective, is possible, but by no means certain , 
whatever the cause may have been, he laid the subject 
aside for some years without publishing anything on it, and 
devoted himself chiefly to optics and mathematics 

174. Meanwhile the problem of the planetary motions 
was one of the numerous subjects of discussion among the 
remarkable group of men who were the leading spirits of 
the Royal Society, founded in 1662. Robert Hooke (1635- 
1703), who claimed credit for most of the scientific dis- 
coveries of the time, suggested with some distinctness, not 
later than 1674, that the motions of the planets might be 
accounted for by atti action between them and the sun, and 
referied also to the possibility of the earth's attraction on 
bodies varying according to the law of the inverse square. 
Christopher ^^(1632-1723), better known as an architect 
than as a man of science, discussed some questions of this 
sort with Newton in 1677, and appears also to have thought 
of a law of attraction of this kind A letter of Hooke's to 
Newton, written at the end of 1679, dealing amongst other 
things with the curve which a falling body would describe, 
the rotation of the earth being taken into account, stimulated 
Newton, who professed that at this time his " affection to 
philosophy " was " worn out," to go on with his study of 
the celestial motions Picard's more accurate measurement 
of the earth (chapter vm , 159) was now well known, and 
Newton lepeated his formei calculation of the moon's 
motion, using Picard's improved measurement, and found 
the result more satisfactory than befoie 

175 At the same time (1679) Newton made a further 
discovery of the utmost importance by overcoming some of 
the difficulties connected with motion m a path othei than 
a circle 

He shewed that if a body moved round a central body, 
in such a way that the line joining the two bodies sweeps 
out equal areas in equal times, as in Kepler's Second Law 
of planetary motion (chapter vn , 141), then the moving 
body is acted on by an attraction directed exactly towards 
the central body ; and further that if the path is an ellipse, 
with the central body m one focus, as in Kepler's First Law 
of planetary motion, then this attraction must vary in 
different parts of the path as the inverse square of the 

222 A Short History of Astronomy [CH ix 

distance between the two bodies Keplei's laws of planetaiy 
motion were in fact shewn to lead necessarily to the 
conclusions that the sun exerts on a planet an attraction 
inversely proportional to the squaie of the distance of the 
planet from the sun, and that such an attraction affords a 
sufficient explanation of the motion of the planet 

Once more, however, Newton published nothing and 
" threw his calculations by, being upon other studies " 

176 Nearly five years later the matter was again brought 
to his notice, on this occasion by Edmund Halley (chap- 
ter x , 199-205), whose friendship played henceforward 
an important pait in Newton's life, and whose unselfish 
devotion to the great astronomer foims a pleasant contrast 
to the quarrels and jealousies prevalent at that time 
between so many scientific men Halley, not knowing 
of Newton's work m 1666, rediscovered, early m 1684, the 
law of the inverse square, as a consequence of Kepler's 
Third Law, and shortly afterwards discussed with Wren 
and Hooke what was the curve in which a body would 
move if acted on by an attraction varying according to 
this law y but none of them could answer the question * 
Later m the year Halley visited Newton at Cambridge 
and learnt from him the answer Newton had, character- 
istically enough, lost his previous calculation, but was 
able to work it out again and sent it to Halley a few 
months afterwards This time fortunately his attention 
was not diverted to other topics , he woikcd out at once a 
number of other problems of motion, and devoted his usual 
autumn course of Univeisity Icctuies to the subject 
Perhaps the most interesting of the new results was that 
Keplei's Third Law, from which the law of the inverse 
square had been deduced in 1666, only on the supposition 
that the planets moved m cnclcs, was equally consistent 
with Newton's law when the paths of the planets were 
taken to be ellipses 

177. At the end of the year 1684 Halley went to 
Cambridge again and urged Newton to publish his results 
In accordance with this request Newton wrote out, and sent 

* It is mteiestmg to read that Wren offered a pn/e of 405 to 
whichever ot the other two should solve this the central pioblcm of 
the solar system 

** 176-179] Elliptic Motion the Pnncipia 223 

to the Royal Society, a tract called Propositions de Motu, 
the ii propositions of which contained the results already 
mentioned and some others relating to the motion of 
bodies under attraction to a centre Although the pro- 
positions were given m an abstract form, it was pointed out 
that certain of them applied to the case of the planets 
Further pressure from Halley persuaded Newton to give 
his results a more peimanent form by embodying them m 
a larger book As might have been expected, the subject 
giew under his hands, and the great treatise which resulted 
contained an immense quantity of material not contained 
in the De Motu By the middle of 1686 the rough diaft 
was finished, and some of it was ready for press Halley 
not only undertook to pay the expenses, but superintended 
the printing and helped Newton to collect the astronomical 
data which were necessary After some delay in the press, 
the book finally appeared eaily m July 1687, under the 
title Philosophiae Naturahs Pnncipia Mathematica 

178 The Pnncipia, as it is commonly called, consists of 
three books m addition to introductory matter the first 
book deals generally with problems of the motion of bodies, 
solved for the most part m an abstract form without special 
refeience to astionomy, the second book deals with the 
motion of bodies tmough media which resist their motion, 
such as ordinary fluids, and is of comparatively small 
astronomical mipoitance, except that m it some glaring 
inconsistencies in the Cartesian theory of vortices are 
pointed out, the thud book applies to the circumstances 
of the actual solar system the results aheady obtained, and 
is m fact an explanation of the motions of the celestial 
bodies on Newton's mechanical principles 

179 The introductory portion, consisting of " Definitions " 
and "Axioms, or Laws of Motion," forms a very notable 
contribution to dynamics, being m fact the first coheient 
statement of the fundamental laws according to which the 
motions of bodies are produced or changed Newton 
himself does not appear to have regarded this part of 
his book as of very great importance, and the chief 
results embodied m it, being overshadowed as it were by 
the more striking discovenes m other parts of the book, 
attracted comparatively little attention Much of it must be 

224 A Short History of Astronomy [Or ix 

passed over here, but certain results of special astronomica 
importance require to be mentioned 

Galilei, as we have seen (chapter vi , 130, 133) 
was the first to enunciate the law that a body when one* 
in motion continues to move in the same direction an< 
at the same speed unless some cause is at work to mak 
it change its motion This law is given by Newton 11 
the form already quoted in 130, as the first of thre 
fundamental laws, and is now commonly known as th 
First Law of Motion. 

Galilei also discovered that a falling body moves wit] 
continually changing velocity, but with a unifoim accelers 
tion (chapter vi , 133), and that this acceleration is th 
same for all bodies (chaptei vi., 116). The tendency c 
a body to fall having been generally recognised as du 
to the earth, Galilei's discovery involved the lecogmtio: 
that one effect of one body on another may be an accelers 
tion produced in its motion Newton extended this ide 
by shewing that the earth produced an acceleiation in th 
motion of the moon, and the sun in the motion of th 
planets, and was led to the general idea of acceleration i 
a body's motion, which might be due in a variety of way 
to the action of other bodies, and which could convementl 
be taken as a measure of the effect produced by one bod 
on another 

1 80 To these ideas Newton added the very importar 
and difficult conception of mass. 

If we are companng two different bodies of the sara 
material but of different sizes, we are accustomed to thin 
of the larger one as heaviei than the other In the sam 
way we readily think of a ball of lead as being heavie 
than a ball of wood of the same size The most prommer 
idea connected with " heaviness " and " lightness " is th* 
of the muscular effort required to support or to lift th 
body m question , a greatei effort, for example, is require 
to hold the leaden ball than the wooden one. Again, th 
leaden ball if supported by an elastic string stretches 
farther than does the wooden ball 3 or again, if they ai 
placed m the scales of a balance, the lead sinks and tl: 
wood rises. All these effects we attribute to the " weight 
of the two bodies, and the weight we are mostly accustome 

$ i so] Newt on? s Laws of Motion Mass 225 

to attribute in some way to the action of the earth on 
the bodies The ordinary process of weighing a body in 
a balance shews, further, that we are accustomed to think 
of weight as a measurable quantity On the other hand, 
we know from Galilei's result, which Newton tested very 
carefully by a seiies of pendulum experiments, that the 
leaden and the wooden ball, if allowed to drop, fall with 
the same acceleration If therefore we measure the effect 
which the eaith produces on the two balls by their 
acceleration, then the earth affects them equally, but if 
we measuie it by the power which they have of stretching 
strings, 01 by the powei which one has of supporting the 
other m a balance, then the effect which the earth produces 
on the leaden ball is greater than that produced on the 
wooden ball Taken m this way, the action of the earth 
on either ball may be spoken of as weight, and the weight 
of a body can be measured by comparing it in a balance 
with standard bodies 

The difference between two such bodies as the leaden 
and wooden ball may, however, be recognised in quite 
a different way We can easily see, for example, that a 
greater effort is needed to set the one m motion than 
the other , or that if each is tied to the end of a string 
of given kind and whirled round at a given rate, the 
one string is more tightly stretched than the other In 
these cases the attraction of the earth is of no impoitance, 
and we recognise a distinction between the two bodies 
which is independent of the attraction of the earth This 
distinction Newton regarded as due to a difference in 
the quantity of matter or material m the two bodies, 
and to this quantity he gave the name of mass It may 
fairly be doubted whether anything is gained by this par- 
ticular definition of mass, but the leally important step 
was the distinct recognition of mass as a property of bodies, 
of fundamental importance m dynamical questions, and 
capable of measurement 

Newton, developing Galilei's idea, gave as one measure- 
ment of the action exerted by one body on another the pio- 
duct of the mass by the acceleration produced a quantity 
for which he used different names, now replaced by 
force The weight of a body was thus identified with the 


226 A Short History of Astronomy [Cn IX 

force exerted on it by the earth. Since the earth produces 
the same acceleration in all bodies at the same place, 
it follows that the masses of bodies at the same place are 
proportional to their weights , thus if two bodies are com- 
pared at the same place, and the weight of one (as shewn, 
for example, by a pair of scales) is found to be ten times 
that of the other, then its mass is also ten times as 
great But such experiments as those of Richer at Cayenne 
(chapter vin , 161) shewed that the acceleration of falling 
bodies was less at the equator than in higher latitudes , 
so that if a body is carried from London or Pans to 
Cayenne, its weight is alteied but its mass remains the 
same as before Newton's conception of the earth's 
gravitation as extending as far as the moon gave fuithei 
importance to the distinction between mass and weight } 
for if a body were removed from the earth to the moon, 
then its mass would be unchanged, but the acceleration 
due to the earth's attraction would be 60 x 60 times less, 
and its weight diminished in the same proportion 

Rules are also given for the effect produced on a 
body's motion by the simultaneous action of two or more 
forces * 

A further principle of great importance, of which only 
very indistinct traces are to be found before Newton's 
time, was given by him as the Third Law of Motion in 
the form "To every action there is always an equal 
and contraiy reaction , or, the mutual actions of any two 
bodies are always equal and oppositely directed " Here 
action and reaction aie to be interpreted primarily in the 
sense of force If a stone rests on the hand, the force with 
which the stone pi esses the hand downwards is equal to 
that with which the hand presses the stone upwards ., if 
the earth attracts a stone downwards with a certain force, 
then the stone attracts the earth upwaids with the same 
force, and so on It is to be carefully noted that if, as 
m the last example, two bodies are acting on one another, 
the accelerations produced are not the same, but since force 

* The familial parallelogram offerees, of which earlier writers had 
had indistinct ideas, was clearly stated and proved in the intro- 
duction to the Pnnapia, and was, by a curious coincidence, published 
also m the same ^ear by Vangnon and Lami 

i8i] Mass Action and Reaction 227 

is measured by the product of mass and acceleration, the 
body with the larger mass receives the lesser acceleration 
In the case of a stone and the earth, the mass of the 
latter being enormously greater,* its acceleration is enor- 
mously less than that of the stone, and is theiefore (m 
accordance with our experience) quite insensible 

1 8 1 When Newton began to write the Prmcipia he had 
probably satisfied himself ( 173) that the attracting power 
of the earth extended as far as the moon, and that the 
acceleration thereby produced in any body whether the 
moon, or whether a body close to the earth is inversely 
proportional to the square of the distance from the centre 
of the earth With the ideas of force and mass this lesult 
may be stated in the form the earth attracts any body with 
a force inversely proportional to the square of the distance 
from the earths centre^ and also proportional to the mass of 
the body 

In the same way Newton had established that the 
motions of the planets could be explained by an attraction 
towards the sun producing an acceleration inversely pro- 
portional to the square of the distance from the sun's 
centre, not only in the same planet in different parts of its 
path, but also in different planets Again, it follows from 
this that the sun attracts any planet with a force inversely 
proportional to the square of the distance of the planet 
from the sun's centre, and also propoitional to the mass 
of the planet 

But by the Third Law of Motion a body experiencing an 
attraction towards the earth must in turn exert an equal 
attraction on the earth , similarly a body experiencing an 
attraction towards the sun must exert an equal attraction 
on the sun If, for example, the mass of Venus is seven 
times that of Mars, then the force with which the sun 
attracts Venus is seven times as great as that with which 
it would attract Mars if placed at the same distance , and 
therefore also the force with which Venus attracts the 
sun is seven times as great as that with which Mars would 
attract the sun if at an equal distance from it. Hence, m 
all the cases of attraction hitherto considered and in 

* It is between 13 and 14 billion billion pounds See chapter x , 

228 A Short History of Astronomy [Cn ix 

which the comparison is possible, the force is proportional 
not only to the mass of the attracted body, but also to 
that of the attracting body, as well as being inversely pro- 
portional to the square of the distance Gravitation thus 
appears no longer as a property peculiar to the central 
body of a revolving system, but as belonging to a planet 
in just the same way as to the sun, and to the moon or 
to a stone in just the same way as to the eaith 

Moreover, the fact that separate bodies on the surface 
of the earth are atti acted by the earth, and therefore in 
turn attract it, suggests that this power of attracting other 
bodies which the celestial bodies are shewn to possess 
does not belong to each celestial body as a whole, but to 
the separate particles making it up, so that, for example, 
the force with which Jupiter and the sun mutually attract 
one another is the result of compounding the forces with 
which the separate particles making up Jupiter attract 
the separate particles making up the sun Thus is 
suggested finally the law of gravitation in its most general 
form every f article of matter attracts every other particle 
with a force proportional to the mass of each) and inversely 
proportional to the square of the distance between them."* 

182. In all the astronomical cases already referred to 
the attractions between the various celestial bodies have 
been treated as if they were accurately directed towards 
their centres, and the distance between the bodies has 
been taken to be the distance between their centres 
Newton's doubts on this point, m the case of the earth's 
attraction of bodies, have been already referred to ( 173) , 
but early m 1685 he succeeded in justifying this assumption. 
By a singularly beautiful and simple course of reasoning 
he shewed (Prmcipia^ Book I , propositions 70, 71) that, if 
a body is spherical in form and equally dense throughout, 
it attracts any particle external to it exactly as if its whole 
mass were concentrated at its centre He shewed, further, 
that the same is true for a sphere of variable density, 
provided it can be regarded as made up of a series of 
spherical shells, having a common centre, each of uniform 

* As far as I know Newton gives no short statement of the law 
m a perfectly complete and general form , separate parts of it are 
given m different passages of the Pnnapia. 

i8 2 , 183] Universal Gravitation 229 

density throughout, different shells being, however, of 
different densities For example, the result is true for a 
hollow mdiarubber ball as well as for a solid one, but 
is not true for a sphere made up of a hemisphere of wood 
and a hemisphere of iron fastened together 

183 The law of gravitation being thus provisionally 
established, the great task which lay before Newton, and 
to which he devotes the greater part of the first and third 
books of the Principle was that of deducing from it and 
the "laws of motion" the motions of the various members 
of the solar system, and of shewing, if possible, that the 
motions so calculated agreed with those observed If this 
were successfully done, it would afford a verification of the 
most delicate and rigorous chaiacter of Newton's pnnciples 

The conception of the solar system as a mechanism, each 
member of which influences the motion of every other 
member in accordance with one universal law of attraction, 
although extremely simple m itself, is easily seen to give rise 
to very serious difficulties when it is proposed actually to 
calculate the various motions If in dealing with the 
motion of a planet such as Mars it were possible to regard 
Mars as acted on only by the attraction of the sun, and to 
ignore the effects of the other planets, then the problem 
would be completely solved by the propositions which 
Newton established in 1679 ( I 75)? an( i by their means the 
position of Mars at any time could be calculated with any 
required degree of accuracy But in the case which 
actually exists the motion of Mars is affected by the forces 
with which all the other planets (as well as the satellites) 
attract it, and these forces in turn depend on the position of 
Mars (as well as upon that of the other planets) and hence 
upon the motion of Mars A problem of this kind m all 
its generality is quite beyond the powers of any existing 
mathematical methods Fortunately, however, the mass 
of even the largest of the planets is so very much less than 
that of the sun, that the motion of any one planet is only 
slightly affected by the others , and it may be regarded as 
moving very nearly as it would move if the other planets 
did not exist, the effect of these being afterwards allowed 
for as producing disturbances or perturbations m its path 
Although even m this simplified form the problem of the 

2 3 o A Short History of Astronomy LC ix 

motion of the planets is one of extreme difficulty (cf 
chapter xi , 228), and Newton was unable to solve it with 
anything like completeness, yet he was able to point out 
certain general effects which must result fiom the mutual 
action of the planets, the most interesting being the slow 
forward motion of the apses of the eaith's orbit, which had 
long ago been noticed by observing astronomers (chaptci in , 
59) Newton also pointed out that Jupiter, on account 
of its great mass, must produce a considerable pertuibation 
in the motion of its neighbour Saturn, and thus gave some 
explanation of an irregularity first noted by Horrocks 
(chapter vin., 156) 

184 The motion of the moon presents special difficulties, 
but Newton, who was evidently much interested in the 
problems of lunar theory, succeeded in overcoming them 
much more completely than the corresponding ones 
connected with the planets 

The moon's motion round the earth is primarily due to 
the attraction of the earth, the perturbations due to the 
other planets are insignificant , but the sun, which though 
at a very great distance has an enormously greater mass 
than the earth, produces a very sensible disturbing effect 
on the moon's motion Certain irregularities, as we have 
seen (chapter n , 40, 48 , chapter v , n i), had aheady 
been discovered by observation Newton was able to 
shew that the disturbing action of the sun would neces- 
sarily produce perturbations of the same general character 
as those thus recognised, and m the case of the motion of 
the moon's nodes and of her apogee he was able to get a 
very fairly accurate numerical result,* and he also dis- 
covered a number of other irregularities, for the most part 
very small, which had not hitherto been noticed He 
indicated also the existence of certain irregularities m the 
motions of Jupiter's and Saturn's moons analogous to those 
which occur in the case of our moon 

* It is commonly stated that Newton's value of the motion of the 
moon's apses was only about half the true value In a scholium 
of the Prmctpia to prop 35 of the third book, given m the finst 
edition but afterwards omitted, he estimated the animal motion at 
40, the observed value being about 41 In one of his unpublished 
papers, contained m the Portsmouth collection, he arrived at 39 by 
a process which he evidently regarded as not altogether satisfactoiy. 

i84 186] Universal Gravitation 231 

185 One group of results of an entirely novel character 
resulted from Newton's theory of gravitation It became 
for the first time possible to estimate the masses of some 
of the celestial bodies, by comparing the attractions exerted 
by them on other bodies with that exerted by the earth 

The case of Jupiter may be given as an illustration The 
time of revolution of Jupiter's outermost satellite is known 
to be about 16 days 16 hours, and its distance from 
Jupiter was estimated by Newton (not very coriectly) at 
about four times the distance of the moon from the earth. 
A calculation exactly like that of 172 or 173 shews that 
the acceleiation of the satellite due to Jupiter's attraction 
is about ten times as great as the acceleration of the moon 
towards the earth, and that therefore, the distance being 
four times as great, Jupiter attracts a body with a force 
10 x 4 x 4 times as great as that with which the earth 
attracts a body at the same distance , consequently Jupiter's 
mass is 1 60 times that of the earth This process of 
reasoning applies also to Saturn, and in a very similar way 
a comparison of the motion of a planet, Venus for example, 
round the sun with the motion of the moon round the 
earth gives a relation between the masses of the sun and 
earth In this way Newton found the mass of the sun to 
be 1067, 3021, and 169282 times greater than that of 
Jupiter, Saturn, and the earth, respectively The corre- 
sponding figuies now accepted are not far from 1047, 3530, 
324439 The large error in the last number is due to the 
use of an erroneous value of the distance of the sun then 
not at all accurately known upon which depend the othei 
distances in the solar system, except those connected with 
the earth-moon system As it was necessary for the em- 
ployment of this method to be able to observe the motion 
of some other body attracted by the planet m question, it 
could not be applied to the other three planets (Mars, 
Venus, and Mercury), of which no satellites were known 

1 86 From the equality of action and reaction it follows 
that, since the sun attracts the planets, they also attract the 
sun, and the sun consequently is in motion, though owing 
to the comparative smallness of the planets only to a very 
small extent It follows that Kepler's Third Law is not 
Strictly accurate, deviations from it becoming sensible in 

232 A Short History of Astronomy [Cii IX 

the case of the large planets Jupiter and Saturn (cf chap- 
ter vn , 144) It was, however, proved by Newton that 
in any system of bodies, such as the solar system, moving 
about m any way under the influence of their mutual 
attractions, there is a particular point, called the centre of 
gravity, which can always be treated as at rest , the sun 
moves relatively to this point, but so little that the distance 
between the centre of the sun and the centre of giavity can 
never be much more than the diameter of the sun 

It is perhaps rather curious that this result was not sewed 
upon by some of the supporters of the Church in the con- 
demnation of Galilei, now rather more than half a century 
old , for if it was far from supporting the view that the 
earth is at the centre of the world, it at any rate negatived 
that part of the doctrine of Coppernicus and Galilei which 
asserted the sun to be at rest in the centre of the world. 
Probably no one who was capable of undei standing 
Newton's book was a serious supporter of any anli- 
Coppermcan system, though some still professed them- 
selves obedient to the papal decrees on the subject.* 

* Throughout the Coppermcan controversy up to Newton's time 
it had been generally assumed, both by Coppermcans and by then 
opponents, that there was some meaning m speaking of a body simply 
as being "at rest" or ' m motion," without any icfucncc to any 
other body But all that we can really observe is the motion of one 
body relative to one or more others Astronomical observation tells 
us, for example, of a certain motion relative to one another of the 
earth and sun, and this motion was expressed in two quite diilcicnt 
ways by Ptolemy and by Coppernicus From a modem standpoint 
the question ultimately involved was whethei the motions ol the 
various bodies of the solar system relatively to the earth or lelativcly 
to the sun were the simpler to express If it is found convenient to 
express them as Coppernicus and Galilei did m relation to the 
sun some simplicity of statement is gamed by speaking of the sun 
as fixed and omitting the qualification relative to the sun " m 
speaking of any other body The same motions might have bu*n 
expressed relatively to any other body chosen at will eg to one of 
the hands of a watch carried by a man walking up and clown on the 

f rt L P ? n a T! h sea ' m thls case lfc 1S clear that the motions 
ot the other bodies of the solar system relative to this body would be 
excessively complicated , and it would therefore be highly inconvenient 
though still possible to treat this particular body as ''fixed " 

a tte m nt W i\ SP M t 5 * C pr blem presents ltself > however, when an 
attempt-like Newton's-is made to explain the motions of bodies of 
the solar system as the result of forces exerted on one anothei by 

$ *8 7 ] Relative Motion the Shape of the Earth 233 

187 The variation of the time of oscillation of a 
pendulum in different parts of the earth, discovered by 
Richer m 1672 (chapter vm , r6r), indicated that the 
earth was probably not a sphere Newton pointed out 
that this departure from the spherical form was a conse- 
quence of the mutual gravitation of the particles making 
up the earth and of the earth's lotation He supposed a 
canal of water to pass from the pole to the centre of the 
earth, and then from the centre to a point on the equator 
(BO^A in fig 72), and then found the condition that these 
two columns of water o B, o A, each being attracted towards 
the centre of the earth, should balance This method 
involved certain assumptions as to the inside of the earth, 
of which little can be said to be known even now, and 
consequently, though Newton's general result, that the 
earth is flattened at the poles and bulges out at the equator, 
was right, the actual numerical expression which he found 
was not very accurate If, in the figure, the dotted line is 
a circle the radius of which is equal to the distance of the 

those bodies If, for example, we look at Newton's First Law of 
Motion (chapter vi , 130), we see that it has no meaning, unless we 
know what are the body or bodies relative to which the motion is 
being expressed, a body at rest relatively to the earth is moving 
relatively to the sun or to the fixed stars, and the applicability oi the 
First Law to it depends therefore on whether we are dealing with its 
motion relatively to the earth or not For most terrestrial motions 
it is sufficient to regard the Laws of Motion as referring to motion 
relative to the earth , or, in other words, we may for this purpose 
treat the eaith as "fixed" But if we examine certain terrestrial 
motions more exactly, we find that the Laws of Motion thus interpreted 
are not quite true , but that we get a more accurate explanation oi 
the observed phenomena if we regard the Laws of Motion as reiernng 
to motion relative to the centre of the sun and to lines drawn fiom it 
to the stars , or, in other words, we treat the centre of the sun as a 
" fixed " point and these lines as " fixed " directions But again when 
we aie dealing with the solar system generally this interpretation is 
slightly inaccurate, and we have to treat the centre ot gravity of the 
solar system instead of the sun as " fixed " 

From this point of view we may say that Newton's object in the 
Pnncipia was to shew that it was possible to choose a certain point 
(the centre of gravity of the solar system) and certain directions 
(lines joining this point to the fixed stais), as a base oi reference, 
such that all motions being treated as relative to this base, the Laws 
ol Motion and the law of gravitation affoid a consistent explanation 
ol the obseived motions of the bodies of the solar system. 

2 34 

A Short History of Astronomy 

[Cn IX 

pole B from the centre of the earth o, then the actua 
surface of the earth extends at the equator beyond thi* 
circle as far as A, where, according to Newton, a A is aboul 
zfa of o B or o A, and according to modern estimates, basec 
on actual measurement of the earth as well as upon theor} 
(chapter x , 221), it is about ^ of o A. Both Newton' 8 
fraction and the modern one are so small that the le&ultmj. 
flattening cannot be made sensible in a figure ; in fig 7 2 

FIG 72 The spheroidal form of the earth 

the length a A is made, for the sake of distinctness, ncarl) 
30 times as great as it should be 

Newton discovered also in a similar way the flattening 
of Jupiter, which, owing to its more rapid rotation, i< 
considerably more flattened than the earth , this was alsc 
detected telescopically by Domenico Cassini four yean 
after the publication of the Pnnajna 

1 88 The discovery of the form of the earth led tc 
an explanation of the precession of the equinoxes, a 
phenomenon which had been discovered i ? 8oo years beibr( 

$ IBS, 189] The Shape of the Earth Precession 235 

(chapter n , 42), but had remained a complete mysteiy 
ever since 

If the earth is a perfect sphere, then its attraction on 
any other body is exactly the same as if its mass were all 
concentrated at its centie ( 182), and so also the attraction 
on it of any other body such as the sun or moon is 
equivalent to a single force passing through the centre o of 
the earth ; but this is no longer true if the earth is not 
spherical In fact the action of the sun or moon on the 
spherical part of the earth, inside the dotted circle in 
fig. 72, is equivalent to a force through o, and has no 
tendency to turn the earth in any way about its centre ; 
but the attraction on the remaining portion is of a different 
character, and Newton shewed that from it resulted a 
motion of the axis of the earth of the same general 
character as precession The amount of the precession as 
calculated by Newton did as a matter of fact agree pretty 
closely with the observed amount, but this was due to the 
accidental compensation of two errors, arising from his 
imperfect knowledge of the form and construction of the 
earth, as well as from erroneous estimates of the distance 
of the sun and of the mass of the moon, neither of which 
quantities Newton was able to measure with any accuracy * 
It was further pointed out that the motion in question was 
necessarily not quite uniform, but that, owing to the unequal 
effects of the sun in different positions, the earth's axis 
would oscillate to and fro every six months, though to a 
very minute extent. 

189, Newton also gave a general explanation of the tides 
as due to the disturbing action of the moon and sun, the 
former being the more important If the earth be regarded 
as made of a solid spherical nucleus, covered by the ocean, 
then the moon attracts different parts unequally, and in 
particular the attraction, measured by the acceleration pro- 
duced, on the water nearest to the moon is greater than 

* He estimated the annual precession due to the sun to be about 
9", and that due to the moon to be about four and a half times as 
great, so that the total amount due to the two bodies came out about 
50", which agrees within a fraction of a second with the amount 
shewn by observation , but we know now that the moon's share as 
not much more than twice that of the sun, 

236 A Short History of Astronomy [Cn TX, 

that on the solid earth, and that on the water farthest from 
the moon is less Consequently the water moves on the 
surface of the earth, the general character of the motion 
being the same as if the portion of the ocean on the side 
towards the moon were attracted and that on the opposite 
side repelled Owing to the rotation of the earth and 
the moon's motion, the moon returns to neaily the 
same position with respect to any place on the earth in 
a period which exceeds a day by (on the aveiage) about 50 
minutes, and consequently Newton's argument shewed 
that low tides (or high tides) due to the moon would follow 
one another at any given place at intervals equal to about 
half this period , or, m other words, that two tides would 
m general occur daily, but that on each day any particulai 
phase of the tides would occur on the average about 50 
minutes later than on the preceding day, a result agreeing 
with observation Similar but smaller tides were shewn 
by the same argument to arise from the action of the 
sun, and the actual tide to be due to the combination of 
the two It was shewn that at new and full moon the 
lunar and solar tides would be added together, whcicas 
at the half moon they would tend to counteract one anothei 
so that the observed fact of greater tides every fortnight 
received an explanation A number of other pccuhaiities 
of the tides were also shewn to result from the same 

Newton ingeniously used observations of the height of 

p & A When , the SUn and moon acted togethci and 
when they acted m opposite ways to compare the tide- 
rawing powers of the sun and moon, and hence to estimate 
tne mass of the moon m terms of that of the sun and 
consequently m terms of that of the earth ( x8?f The 
resulting mass of the moon was about twice what it ought 
to be according to modern knowledge, but as before 

no one kn of 


me moons mass even m the roughest way, and this lesult 
had to be disentangled from the innumerab e cmiipl iciion! 


*9] Tides and Comets 237 

problem at all manageable, but which were certainly not 
true, and consequently, as he was well aware, important 
modifications would necessarily have to be made, in order 
to bung his results into agreement with actual facts The 
mere presence of land not covered by water is, for example, 
sufficient by itself to produce important alterations in tidal 
effects at different places Thus Newton's theory was by 
no means equal to such a task as that of predicting the 
times of high tide at any required place, or the height of 
any required tide, though it gave a satisfactory explanation 
of many of the general characteristics of tides 

190 As we have seen (chapter v, 103, chapter vii , 
146), comets until quite recently had been commonly 
regarded as terrestrial objects produced in the higher 
regions of our atmosphere, and even the more enlightened 
astronomers who, like Tycho, Kepler, and Galilei, recog- 
nised them as belonging to the celestial bodies, were un- 
able to give an explanation of their motions and of their 
apparently quite irregular appearances and disappearances 
Newton was led to consider whether a comet's motion 
could not be explained, like that of a planet, by gravitation 
towards the sun If so then, as he had proved near the 
beginning of the Prmapia^ its path must be either an ellipse 
or one of two other allied curves, the parabola and 
hyperbola If a comet moved in an ellipse which only 
differed slightly from a circle, then it would never recede 
to any very great distance from the centre of the solar 
system, and would therefore be regularly visible, a result 
which was contrary to observation If, however, the ellipse 
was very elongated, as shewn in fig 73, then the period 
of revolution might easily be very great, and, during the 
greater part of it, the comet would be so far from the sun 
and consequently also from the earth as to be invisible 
If so the comet would be seen for a short time and become 
invisible, only to reappear after a very* long time, when 
it would naturally be regarded as a new comet If again 
the path of the comet were a parabola (which may be 
regarded as an ellipse indefinitely elongated), the comet 
would not return at all, but would merely be seen once 
when in that part of its path which is near the sun But 
if a comet moved in a parabola, with the sun in a focus, 

238 A Short History of Astronomy [Cu IX 

then its positions when not very far from the sun would 
be almost the same as if it moved in an elongated ellipse 
(see fig 73), and consequently it would hardly be possible 
to distinguish the two cases Newton accordingly worked 
out the case of motion in a parabola, which is mathemati- 
cally the simpler, and found that, in the case of a comet 
which had attracted much attention m the winter 1680-1, 
a parabolic path could be found, the calculated places of 
the comet m which agreed closely with those observed 
In the later editions of the Pnnafia the motions of a 
number of other comets were investigated with a similai 

FIG 73 An elongated ellipse and a parabola 

result It was thus established that in many cases a 
comet's path is either a parabola or an elongated ellipse, 
and that a similar result was to be expected in other cases 
This reduction to lule of the apparently arbitrary motions 
of comets, and their inclusion with the planets in the same 
class of bodies moving round the sun under the action 
of gravitation, may fairly be regarded as one of the most 
striking of the innumerable discoveries contained m the 

In the same section Newton discussed also at some 
length the nature of comets and m particular the structure 
of their tails, arriving at the conclusion, which is in geneial 
agreement with modern theories (chapter xin , 304), that 

igi] Comets Reception of the Prmcipia 239 

the tail is formed by a stream of finely divided matter 
of the nature of smoke, rising up fiom the body of the 
comet, and so illuminated by the light of the sun when 
tolerably near it as to become visible. 

191 The Prmcipia was published, as we have seen, in 
1687. Only a small edition seems to have been printed, 
and this was exhausted in three or four years Newton's 
earlier discovenes, and the piesentation to the Royal 
Society of the tract De Motu ( 177), had prepared the 
scientific world to look for important new results in the 
Prmcipia, and the book appears to have been read by 
the leading Continental mathematicians and astronomers, 
and to have been very warmly received in England The 
Cartesian philosophy had, however, too firm a hold to be 
easily shaken , and Newton's fundamental principle, in- 
volving as it did the idea of an action between two bodies 
separated by an interval of empty space, seemed impossible 
of acceptance to thinkers who had not yet fully grasped 
the notion of judging a scientific theory by the extent 
to which its consequences agree with observed facts 
Hence even so able a man as Huygens (chapter vni , 
154, 157, 158), regarded the idea of gravitation as 
"'absurd," and expressed his surprise that Newton should 
have taken the trouble to make such a number of laborious 
calculations with no foundation but this principle, a remark 
which shewed Huygens to have had no conception that 
the agreement of the results of these calculations with 
actual facts was proof of the soundness of the principle 
Personal reasons also contributed to the Continental neglect 
of Newton's work, as the famous quarrel between Newton 
and Leibniz as to their respective claims to the invention 
of what Newton called fluxions and Leibniz the differen- 
tial method (out of which the differential and integral 
calculus have developed) grew in intensity and fresh com- 
batants were drawn into it on both sides Half a century 
m fact elapsed before Newton's views made any substantial 
progiess on the Continent (cf chaptei XL, 229) In our 
country the case was different , not only was the Prmcipia 
read with admiration by the few who were capable of 
understanding it, but scholars like Bentlcy, philosophers 
like Locke, and courtiers like Halifax all made attempts 

24 o A Short History of Astronomy [Cn ix 

to grasp Newton's general ideas, even though the details 
of his mathematics were out of their range It was more- 
over soon discovered that his scientific ideas could be 
used with advantage as theological arguments 

192 One unfortunate result of the great success of the 
Pnnapia was that Newton was changed from a quiet 
Cambridge professoi, with abundant leisure and a slendei 
income, into a public charactei, with a continually increas- 
ing portion of his time devoted to public business of one 
sort or another 

Just before the publication of the Pnnafia he had beer 
appointed one of the representatives of his Univeisity tc 
defend its rights against the encroachments of James II 
and two years later he sat as member for the Umversit) 
in the Convention Parliament, though he retired after if 

Notwithstanding these and many other distractions, he 
continued to work at the theory of giavitation, paying 
particular attention to the lunar theory, a difficult subjec 
with his tieatment of which he was never quite satisfied 
He was fortunately able to obtain from time to time first 
rate observations of the moon (as well as of other bodies 
from the Astionomer Royal Flamsteed (chapter x , 197-8] 
though Newton's continual requests and Flamsteed's occa 
sional refusals led to strained relations at intervals It i 
possible that about this time Newton contemplated wntm 
a new treatise, with more detailed treatment of vanou 
points discussed m the Prmapia 9 and in 1691 there wa 
already some talk of a new edition of the Prmcipia, possibl 
to be edited by some younger mathematician In an 
case nothing serious in this direction was done for som 
years, perhaps owing to a serious illness, apparently som 
nervous disorder, which attacked Newton in 1692 an 
lasted about two years. During this illness, as he himsc 
said, " he had not his usual consistency of mind," and it 
by no means ceitam that he ever recovered his full ment; 
activity and power. 

Soon after recovering from this illness he made son 

* He once told Halley m despair that the lunar theory "mac 
his head ache and kept him awake so often that he would think 
it no more " 

n fau /> v\ 

$$ *92, 193] Neivtorfs Later Life 241 

preparations for a new edition of the Pnncipia^ besides 
going on with the lunar theory, but the work was again 
interrupted in 1695, when he received the valuable appoint- 
ment of Warden to the Mint, from which he was promoted 
to the Mastership four years later He had, in conse- 
quence, to move to London (1696), and much of his time 
was henceforward occupied by official duties. In 1701 
he resigned his professorship at Cambridge, and in the 
same year was for the second time elected the Parliamentary 
representative of the University In 1703 he was chosen 
President of the Royal Society, an office which he held till 
his death, and in 1705 he was knighted on the occasion of 
a royal visit to Cambridge 

During this time he published (1704) his treatise on 
Of tics ) the bulk of which was probably written long before 
and in 1709 he finally abandoned the idea of editing the 
Pnncipia himself, and arranged for the work to be done by 
Roger Cotes (1682-1716), the brilliant young mathematician 
whose untimely death a few years later called from Newton 
the famous eulogy, " If Mr Cotes had lived we might 
have known something." The alterations to be made were 
discussed in a long and active correspondence between the 
editor and author, the most important changes being 
improvements and additions to the lunar theory, and to 
the discussions of precession and of comets, though there 
were also a very large number of minor changes , and the 
new edition appeared in 1713 A third edition, edited by 
Pemberton, was published m 1726, but this time Newton, 
who was over 80, took much less part, and the alterations 
were of no great importance This was Newton's last piece 
of scientific work, and his death occuried in the following 
year (March 3rd, 1727). 

193 It is impossible to give an adequate idea of the 
immense magnitude of Newton's scientific discoveries 
except by a free use of the mathematical technicalities in 
which the bulk of them were expressed The criticism 
passed on him by his peisonal enemy Leibniz that, 
"Taking mathematics fiom the beginning of the world 
to the time when Newton lived, what he had done was 
much the better half," and the remark of his great suc- 
cessor Lagrange (chapter xi , 237), "Newton was the 


24 2 A Short History oj Astronomy [Cn ix 

greatest genius that ever existed, and the most fortunate 
for we cannot find more than once a system of the world 
to establish," shew the immense respect for his work fel 
bv those who were most competent to judge it 

With these magnificent eulogies it is pleasant to compart 
Newton's own grateful recognition of his predecessors 
If I have seen further than other men, it is because 
have stood upon the shoulders of the giants, ' and hi 
modest estimate of his own performances 

"I do not know what I may appear to the world , but t 
myself I seem to have been only like a boy playing on the sea 
ffi and diverting myself in now and then finding a smooths 
pebble or a prettitr shell than ordinary, whilst the great ocea 
of truth lay all undiscovered before me ' 

1 04 It is sometimes said, in explanation of the diffei 

ence between Newton's achievements and those of earlu 

astronomers, that whereas they discovered how the celesti: 

bodies moved, he shewed why the motions were as the 

were, 01, in other words, that they described motions whi 

he explained them or ascertained their cause 1 1 i 

however, doubtful whether this distinction between Ho 

and Why though undoubtedly to some extent convemer 

has any real validity. Ptolemy, for example, represent* 

the motion of a planet by a certain combination of q 

cycles , his scheme was equivalent to a particular methc 

of describing the motion , but if any one bad asked hi 

why the planet would be in a particular position at 

particular time, he might legitimately have answeied ft 

it was so because the planet was connected with this p. 

ticular system of epicycles, and its place could be deduc 

from them by a rigorous process of calculation, But 

any one had gone further and asked wby the plane 

epicycles were as they were, Ptolemy could have given 

answer Moreover, as the system of epicycles differed 

some important respects from planet to planet, I tolem 

system left unanswered a number of questions whi 

obviously presented themselves Then Coppermcus gr 

a partial answer to some of these questions lo 1 

question why certain of the planetary motions, correspoi 

mg to certain epicycles, existed, he would have replied tl 

it was because of certain motions of the eaith, from wn 

244 A Short Hutory f Astronom y [Cn IX 

planets are of ceitam sizes, at certain distances from the 
sun, etc, and to these questions again Newton could give 

n Bu\ S whereas the questions left unanswered by Ptolemy, 
Coppernicus, and Kepler were in whole or in part answered 
bv their successes, that is, then unexplained facts or 
laws were shewn to be necessaiy consequences of othei 
simpler and more general laws, it happens that up to the 
present day no one has been able to answer, in any satis- 
factory way, these questions which Newton left unansweied 
In this particular direction, theiefore, Newton s laws mark 
the boundary of our present knowledge But if any one 
were to succeed this year or next in shewing gravitation to 
be a consequence of some still more geneial law, this new 
law would still bring with it a new Why 

If however, Newton's laws cannot be regarded as an 
ultimate explanation of the phenomena of the solar system, 
except in the historic sense that they have not yet been 
shewn to depend on other moie fundamental laws, their 
success in " explaining," with fair accuracy, such an immense 
mass of observed results in all parts of the solai system, 
and their universal chaiacter, gave a powerful impetus to 
the idea of accounting for observed facts in othei depart- 
ments of science, such as chemistiy and physics, in some 
similar way as the consequence of forces acting between 
bodies, and hence to the conception of the material universe 
as made up of a certain numbei of bodies, each acting on 
one anothci with definite foices in such a way that all the 
changes which can be obseivcd to go on ate necessary 
consequences of these foices, and are capable of picchction 
by any one who has sufficient knowledge of the foices and 
sufficient mathematical skill to develop their consequences 

Whether this conception of the matcnal univeise is 
adequate or not, it has undoubtedly exercised a very 
important influence on scientific discovery as well as on 
philosophical thought, and although it was never formulated 
by Newton, and parts of it would probably have beei 
repudiated by him, there aie indications that some sucl 
ideas were in his head, and those who held the conceptior 
most fiimly undoubtedly derived their ideas directly o 1 
indirectly fiom him, 

'*9s] Newton *s Scientific Method 245 

195 Newton's scientific method did not differ essentially 
from that followed by Galilei (chapter vi , 134), which 
has been variously described as complete induction or 
as the inverse deductive method, the difference in name 
corresponding to a difference m the stress laid upon 
different parts of the same general process Facts are 
obtained by observation or experiment ; a hypothesis or 
provisional theory is devised to account for them , from 
this theory are obtained, if possible by a rigorous process 
of deductive reasoning, ceitam consequences capable of 
being compared with actual facts, and the comparison is 
then made In some cases the first process may appear 
as the more important, but m Newton's work the really 
convincing part of the proof of his results lay in the 
verification involved m the two last processes This has 
perhaps been somewhat obscured by his famous remark, 
Hypotheses nonfingo (I do not invent hypotheses), dissociated 
from its context The words occur m the conclusion of 
the Principle after he has been speaking of universal 

" I have not yet been able to deduce (deducere) from 
phenomena the reason of these properties of gravitation, and 
I do not invent hypotheses For any thing which cannot be 
deduced from phenomena should be called a hypothesis " 

Newton probably had m his mind such speculations as 
the Cartesian vortices, which could not be deduced directly 
from observations, and the consequences of which either 
could not be worked out and compared with actual facts 
or were inconsistent with them Newton in fact rejected 
hypotheses which were unvenfiable, but he constantly made 
hypotheses, suggested by observed facts, and verified by 
the agreement of their consequences with fresh observed 
facts The extension of gravity to the moon ( 173) is a 
good example he was acquainted with certain facts as to 
the motion of falling bodies and the motion of the moon ; 
it occurred to him that the earth's attraction might extend 
as far as the moon, and certain other facts connected with 
Kepler's Third Law suggested the law of the inverse 
square If this were right, the moon's acceleration towards 
the earth ought to have a certain value, which could be 

246 A Short History of Astronomy [Cn ix , 195 

obtained by calculation The calculation was made and 
found to agree roughly with the actual motion of the 

moon r . 

Moreovei it may be fairly urged, m illustration of the 
great importance of the process of verification, that 
Newton's fundamental laws were not ngoiously established 
by him, but that the deficiencies in his proofs have 
been to a great extent filled up by the elaborate pro- 
cess of verification that has gone on since I^or the 
motions of the solar system, as deduced by Newton from 
gravitation and the laws of motion, only agieed roughly 
with observation , many outstanding disciepancies weie 
left, and though there was a strong presumption that 
these were due to the necessary imperfections of Newton & 
processes of calculation, an immense expenditure of labour 
and ingenuity on the part of a senes of mathematicians has 
been required to remove these discrepancies one by one, 
and as a matter of fact there remain even to-day a few 
small ones which are unexplained (chapter xin , 290) 



"Through Newton theory had made a great advance and was 
ahead ot observation, the latter now made efforts to come once 
more level with theory ' BESSEL 

196 NEWTON virtually created a new department of 
astronomy, gravitational astronomy, as it is often called, 
and bequeathed to his successors the problem of deducing 
more fully than he had succeeded in doing the motions of 
the celestial bodies from their mutual gravitation 

To the solution of this problem Newton's own country- 
men contributed next to nothing throughout the i8th 
century, and his true successois were a group of Continental 
mathematicians whose woik began soon after his death, 
though not till neaily half a century after the publication 
of the Pnncipia 

This failure of the British mathematicians to develop 
Newton's discoveries may be explained as due in part to 
the absence 01 scarcity of men of real ability, but in part 
also to the peculiarity of the mathematical form in which 
Newton presented his discoveries The Pnncipia is written 
almost entirely in the language of geometry, modified in 
a special way to meet the requirements of the case 3 nearly 
all subsequent progress in gravitational astronomy has 
been made by mathematical methods known as analysis 
Although tne distinction between the two methods cannot 
be fully appreciated except by those who have used them 
both, it may perhaps convey some impression of the differ- 
ences between them to say that in the geometrical treatment 
of an astronomical problem each step of the reasoning is 


248 A Short History of Astronomy Cdi x 

expressed in such a way as to be capable of being inter- 
preted in terms of the original problem, whereas in the 
analytical treatment the problem is first expressed by 
means of algebraical symbols , these symbols are manipulated 
according to certain purely formal iiiles, no regaid being 
paid to the interpretation of the intermediate steps, and 
the final algebraical result, if it can be obtained, yields ^011 
interpretation the solution of the original problem The 
geometrical solution of a problem, if it can be obtained, 
is frequently shorter, clearer, and more elegant , but, on 
the other hand, each special problem has to be considered 
separately, whereas the analytical solution can be con- 
ducted to a great extent according to fixed rules applicable 
in a larger numbei of cases In Newton's time modern 
analysis was only just coming into being, some of the most 
important parts of it being in fact the creation of Leibniz 
and himself, and although he sometimes used analysis to 
solve an astronomical problem, it was his piacticc to tianslatc 
the result into geometrical language before publication , in 
doing so he was probably influenced to a large extent by 
a personal preference for the elegance of geometrical proofs, 
partly also by an unwillingness to increase the numeious 
difficulties contained in the Prmapia^ by using mathematical 
methods which were comparatively unfamihai But though 
in the hands of a master like Newton geometrical methods 
were capable of producing astonishing results, the Icssei 
men who followed him were scarcely ever capable of using 
his methods to obtain results beyond those which he 
himself had reached Excessive reverence for Newton and 
all his ways, combined with the estrangement which long 
subsisted between British and foreign mathematicians, as 
the result of the fluxional controversy (chapter ix , 191), 
prevented the former from using the analytical methods 
which were being rapidly perfected by Leibniz's pupils and 
other Continental mathematicians Our mathematicians 
remained, therefore, almost isolated during the whole of the 
1 8th century, and with the exception of some adnmabie 
work by Colin Maclaunn (1698-1746), which earned 
Newton's theory of the figure of the earth a stage further, 
nothing of importance was done in our country for nearly 
a century after Newton's death to develop the theory of 

$ 197] Continental Analysis and English Observation 249 

gravitation beyond the point at which it was left in the 

In other departments of astronomy, however, important 
progress was made both during and after Newton's lifetime, 
and by a curious inversion, while Newton's ideas were 
developed chiefly by French mathematicians, the Observa- 
tory of Pans, at which Picard and others had done such 
admirable work (chapter vm., 160-2), produced little of 
real importance for nearly a century afterwards, and a large 
part of the best observing work of the i8th century was 
done by Newton's countrymen It will be convenient to 
separate these two departments of astronomical work, and 
to deal in the next chapter with the development of the 
theory of gravitation 

197 The first of the great English observers was 
Newton's contemporary John Flamsteed, who was born near 
Derby in 1646 and died at Greenwich in 1720.* Unfor- 
tunately the character of his work was such that, marked 
as it was by no brilliant discoveries, it is difficult to present 
it in an attractive form or to give any adequate idea of 
its real extent and importance He was one of those 
laborious and careful investigators, the results of whose 
work are invaluable as material for subsequent research, 
but are not striking in themselves. 

He made some astronomical observations while quite a 
boy, and wrote several papers, of a technical character, on 
astronomical subjects, which attracted some attention In 
1675 he was appointed a member of a Committee to report 
on a method for finding the longitude at sea which had 
been offered to the Government by a certain Fienchman 
of the name of St Pierre The Committee, acting largely 
on Flamsteed's advice, reported unfavourably on the 
method in question, and memonalised Charles II. in 
favour of founding a national observatory, in order that 
better knowledge of the celestial bodies might lead to a 
satisfactory method of finding the longitude, a problem 
which the rapid increase of English shipping rendered of 
great practical importance The King having agreed, 
Flamsteed was m the same year appointed to the new 
* December 3ist, 1719, according to the unreformed calendar (OS) 
then in use m England 

250 A Short History of Astronomy idr x 

office of Astronomer Royal, with a salaiy of ^"TOO a ycai, 
and the warrant for building an Obseivatory at Gieenwich 
was signed on June i2th, 1675. About a year was ore upiecl 
in building it, and Flarnsteed took up his residence theie 
and began work m July 1676, five years aftci Cassim 
entered upon his duties at the Obscivatoiy of Paris 
(chapter vm , 160) The Greenwich Obseivatoiy was, 
however, on a very different scale fiom the magnificent 
sister institution The King had, it is true, piovuled 
Flamsteed with a building and a veiy small salaiy, but 
furnished him neither with instruments nor with an assist- 
ant A few instruments he possessed already, n few moie 
were given to him by rich friends, and he gt actually made 
at his own expense some further instrumental additions of 
importance Some years after his appointment the Govern 
ment provided him with "a silly, surly labourer" to help 
him with some of the rough work, but he was compelled 
to provide more skilled assistance out of his own pocket, 
and this necessity in turn compelled him to devote some 
part of his valuable time to taking pupils 

198 Flamsteed's great work was the construction of a 
more accurate and moie extensive star catalogue than any 
that existed, he also made a number of obseivations of 
the moon, of the sun, and to a less extent of othei bodies 
Like Tycho, the author of the last great star catalogue 
(chapter v , 107), he found pioblems continually presenting 
themselves in the course of his woik which had to be 
solved before his mam object could be accomplished, and 
we accordingly owe to him the invention of sevcial improve- 
ments in practical astronomy, the best known being his 
method of finding the position of the first point of A ties 
(chapter n,, 42), one of the fundamental points with 
reference to which all positions on the celestial sphere are 
defined He was the fiist astronomer to use a clock 
systematically for the determination of one of the two 
fundamental quantities (the right ascension) necessary to 
fix the position of a star, a method which was first suggested 
and to some extent used by Picard (chapter vm, & 157), 
and, as soon as he could get the necessary instruments, 
he regularly used the telescopic sights of Gascoigne and 
Auzout (chapter vm , 155), instead of making naked-eye 

igB] Flamsteed 251 

observations Thus while Hevel (chapter vm , 153) 
was the last and most accurate observer of the old school, 
employing methods not diffenng essentially from those 
which had been in use for centuries, Flamsteed belongs 
to the new school, and his methods differ rather in detail 
than in principle from those now in vogue for similar woik 
at Greenwich, Pans, or Washington This adoption of 
new methods, together with the most scrupulous care in 
details, rendeied Flamsteed's observations considerably 
more accuiate than any made m his time or eailier, the 
first definite advance afterwards being made by Bradley 
( 218) 

Flamsteed compared favourably with many observers 
by not merely taking and recoiding observations, but by 
performing also the tedious process known as reduction 
( 218), whereby the results of the observation are put 
into a form suitable for use by other astronomers,, this 
process is usually pei formed in modern observatories by 
assistants, but m Flamsteed's case had to be done almost 
exclusively by the astronomer himself From this and 
other causes he was extremely slow m publishing observa- 
tions , we have already alluded (chapter ix , 192) to the 
difficulty which Newton had m extracting lunai observations 
from him, and after a time a feeling that the object for 
which the Observatory had been founded was not being ful- 
filled became pietty general among astronomers Flamsteed 
always suffered from bad health as well as from the 
pecuniary and other difficulties which have been refeired 
to , moreover he was much more anxious that his observa- 
tions should be kept back till they were as accurate as 
possible, than that they should be published in a less 
perfect form and used for the researches which he once 
called " Mr Newton's ciotchets " , consequently he took 
lemonstrances about the delay in the publication of his 
observations in bad part Some painful quarrels occurred 
between Flamsteed on the one hand and Newton and 
Halley on the other The last straw was the unauthorised 
publication m 1712, under the editorship of Halley, of a 
volume of Flamsteed's observations, a proceeding to which 
Flamsteed not unnaturally leplied by calling Halley a 
"malicious thief" Three years later he succeeded in 

252 A Short History of Astronomy [Cn X 

getting hold of all the unsold copies and in destroying 
them, but fortunately he was also stimulated to prepare 
for publication an authentic edition The Histona Coelestis 
Bntanmcci) as he called the book, contained an immense 
series of observations made both before and during his 
career at Greenwich, but the most important and per- 
manently valuable part was a catalogue of the places of 
nearly 3,000 stars + 

Flamsteed himself only lived just long enough to finish 
the second of the three volumes, the third was edited 
by his assistants Abraham Sharp (1651-1742) and Joseph 
Crostkwait , and the whole was published in 1725 Four 
years later still appeared his valuable Star-Atlas, which 
long remained in common use 

The catalogue was not only three times as extensive as 
Tycho's, which it virtually succeeded, but was also very 
much more accurate It has been estimated t that, whereas 
Tycho's determinations of the positions of the stars were 
on the average about i' in error, the corresponding errors 
in Flamsteed's case were about 10" This quantity is the 
apparent diameter of a shilling seen from a distance of 
about 500 yards, so that if two marks were made at 
opposite points on the edge of the com, and it were placed 
at a distance of 500 yards, the two marks might be taken 
to represent the true direction of an average star and its 
direction as given in Flamsteed's catalogue. In some 
cases of course the error might be much gi eater and in 
others considerably less 

Flamsteed contributed to astronomy no ideas of first-rate 
importance , he had not the ingenuity of Picard and of 
Roemer in devising instrumental improvements, and he 
took little interest in the theoretical woik of Newton ,J 
but by unflagging industry and scrupulous care he succeeded 
m bequeathing to his successors an immense treasure of 

* The apparent number is 2,935, but 12 of these are duplicates 

t By Bessel (chapter xni , 277) 

j The relation between the work of Flamsteed and that of Newton 
was expressed with more correctness than good taste by the two 
astronomers themselves, in the course of some quarrel about the 
lunar theory "Sir Isaac worked with the ore I had dug" "If he 
dug the ore, I made the gold ring " 

i 9 9, 200] Flamstee&s Observations Halky 253 

observations, executed with all the accuracy that his in- 
strumental means permitted 

199 Flamsteed was succeeded as Astronomer Royal 
by Edmund Halley, whom we have already met with 
(chapter ix , 176) as Newton's friend and helper 

Born m 1656, ten years after Flamsteed, he studied 
astronomy in his schooldays, and published a paper on the 
orbits of the planets as early as 1676 In the same year 
he set off for St Helena (in latitude 16 S ) in order to 
make observations of stars which were too near the south 
pole to be visible in Europe The climate turned out to 
be disappointing, and he was only able after his return 
to publish (1678) a catalogue of the places of 341 southern 
stars, which constituted, however, an important addition 
to precise knowledge of the stars The catalogue was also 
remarkable as being the first based on telescopic observa- 
tion, though the observations do not seem to have been 
taken with all the accuracy which his instruments rendered 
attainable During his stay at St Helena he also took 
a number of pendulum observations which confirmed the 
results obtained a few years before by Richer at Cayenne 
(chapter vni , 161), and also observed a transit of Mercury 
across the sun, which occurred in November 1677 

Aftei his return to England he took an active part in 
current scientific questions, particularly in those connected 
with astronomy, and made several small contributions to 
the subject. In 1684, as we have seen, he first came 
effectively into contact with Newton, and spent a good 
part of the next few years in helping him with the 

200 Of his numerous contributions to astronomy, which 
touched almost every branch of the subject, his work 
on comets is the best known and probably the most 
important He observed the comets of 1680 and 1682 3 
he worked out the paths both of these and of a number 
of other recorded comets m accordance with Newton's 
principles, and contributed a good deal of the material 
contained m the sections of the Prmcipia dealing with 
comets, particularly m the later editions In 1705 he 
published a Synopsis of Cometary Astronomy m which no 
less than 24 cometary orbits were calculated Struck by 

254 -d Short History of Astronomy FCn x 

the resemblance between the paths desctibed by the 
comets of 1531, 1607, and 1682, and by the approximate 
equality in the intervals between their respective appear- 
ances and that of a fourth comet seen in 1456, he was 
shrewd enough to conjecture that the three later comets, 
if not all foui, were really different appeal ances of the same 
comet, which revolved round the sun m an elongated 
ellipse in a period of about 75 01 76 years He explained 
the difference between the 76 years which sepaiate the 
appearances of the comet in 1531 and 1607, and the slightly 
shorter period which elapsed between 1607 and 1682, as 
probably due to the perturbations caused by planets near 
which the comet had passed, and finally piedicted the 
probable reappearance of the same comet (which now 
deservedly bears his name) about 76 years after its last 
appearance, te about 1758, though he was again aware 
that planetary perturbation might alter the time of its 
appearance , and the actual appearance of the comet about 
the predicted time (chapter xi , 231) marked an impoitant 
era in the progress of our knowledge of these extieincly 
troublesome and erratic bodies 

201 In 1693 Halley read before the Royal Society a 
paper m which he called attention to the difficulty of 
reconciling certain ancient eclipses with the known motion 
of the moon, and referred to the possibility of some slight 
increase in the moon's average rate of motion round the 

This irregularity, now known as the secular acceleration 
of the moon's mean motion, was subsequently moie 
definitely established as a fact of observation , and the 
difficulties met with m explaining it as a lesult of guxvitatum 
have rendered it one of the most interesting of the 
moon's numerous irregularities (cf chapter xi , 240, and 
chapter xm , 287) 

202 Halley also rendered good seivice to astronomy 
by calling attention to the importance of the expected 
transits of Venus acioss the sun m 1761 and 1769 as a 
means of ascertaining the distance of the sun The 
method had been suggested rather vaguely by Keplei, uml 
more definitely by James Gregory m his Optics published 
m 1663 The idea was first suggested to Halley by 

201204] Halky 255 

his observation of the transit of Mercury in 1677 In 
three papers published by the Royal Society he spoke 
warmly of the advantages of the method, and discussed 
in some detail the places and means most suitable for 
observing the transit of 1761 He pointed out that the 
desired result could be deduced from a comparison of 
the durations of the tiansit of Venus, as seen from different 
stations on the Dearth, i e of the intervals between the first 
appearance of Venus on the sun's disc and the final dis- 
appearance, as seen at two or more different stations He 
estimated, moreover, that this interval of time, which would 
be several hours in length, could be measured with an 
error of only about two seconds, and that in consequence 
the method might be relied upon to give the distance of 
the sun to within about -^ pait of its true value As the 
current estimates of the sun's distance differed among one 
another by 20 or 30 per cent , the new method, expounded 
with Halley's customary lucidity and enthusiasm, not un- 
naturally stimulated astronomers to take great trouble to 
carry out Halley's recommendations The results, as we 
shall see ( 227), were, however, by no means equal to 
Halley's expectations 

203 In 1718 Halley called attention to the fact that 
three well-known stars, Sinus, Procyon, and Arcturus, had 
changed their angular distances from the ecliptic since 
Greek times, and that Sinus had even changed its position 
peiceptibly since the time of Tycho Brahe Moreover 
comparison of the places of other stars shewed that the 
changes could not satisfactorily be attributed to any motion 
of the ecliptic, and although he was well awaie that the 
possible errors of observation were such as to introduce 
a considerable unceitamty into the amounts involved, he 
felt sure that such errors could not wholly account foi 
the discrepancies noticed, but that the stars in question 
must have really shifted their positions in relation to the 
rest, and he naturally inferred that it would be possible 
to detect similar proper motions (as they are now called) in 
other so-called "fixed" stais 

204 He also devoted a good deal of time to the stand- 
ing astronomical problem of improving the tables of the 
moon and planets, particularly the former He made 

256 A Short History of Astronomy [Cn x 

observations of the moon as early as 1683, and by means 
of them effected some improvement in the tables In 
1676 he had already noted defects in the existing tables 
of Jupiter and Saturn, and ultimately satisfied himself of 
the existence of certain irregularities in the motion of these 
two planets, suspected long ago by Horrocks (chapter vm , 
156), these irregularities he attributed correctly to the 
perturbations of the two planets by one anothei, though 
he was not mathematician enough to work out the theory ; 
from observation, however, he was able to estimate the 
irregularities in question with fair accuiacy and to improve 
the planetary tables by making allowance for them But 
neither the lunar nor the planetary tables were ever com- 
pleted in a form which Halley thought satisfactory By 
1719 they were printed, but kept back from publication, 
in hopes that subsequent improvements might be effected 
After his appointment as Astronomer Royal m succession 
to Flamsteed (1720) he devoted special attention to getting 
fresh observations foi this purpose, but he found the 
Observatory almost bare of instruments, those used by 
Flamsteed having been his private property, and having 
been removed as such by his heirs or creditors Although 
Halley procured some instruments, and made with them 
a number of observations, chiefly of the moon, the age (63) 
at which he entered upon his office prevented him from 
initiating much, or from carrying out his duties with great 
energy, and the obseivations taken were in consequence 
only of secondary importance, while the tables for the 
improvement of which they were specially designed were 
only finally published in 1752, ten years after the death 
of their author Although they thus appeared many years 
after the time at which they were virtually prepared and 
owed little to the progress of science during the interval, 
they at once became and for some time remained the 
standard tables for both the lunai and planetary motions 
(cf 226, and chapter xi , 247) 

205 Halley's remarkable versatility m scientific work is 
further illustrated by the labour which he expended in 
editing the writings of the great Greek geometer Apollonms 
(chapter u , 38) and the star catalogue of Ptolemy 
(chapter n , 50) He was also one of the first of modern 

2os, 206] ' Halley 257 

astronomers to pay careful attention* to the effects to be 
observed during a total eclipse of the sun, and in the 
vivid description which he wrote of the eclipse of 1715, 
besides referring to the mysterious corona, which Kepler 
and others had noticed before (chapter vn , 145), he 
called attention also to " a very narrow streak of a dusky 
but strong Red Light," which was evidently a portion of 
that remarkable envelope of the sun which has been so 
extensively studied in modern times (chapter xm , 301) 
under the name of the chromosphere 

It is worth while to notice, as an illustration of Halley's 
unselfish enthusiasm for science and of his power of looking 
to the future, that two of his most important pieces of work, 
by which certainly he is now best known, necessarily 
appeared during his lifetime as of little value, and only 
bore their fruit after his death (1742), for his comet only 
returned in 1759, when he had been dead 17 years, and 
the first of the pair of transits of Venus, from which he 
had shewn how to deduce the distance of the sun, took 
place two years later still ( 227) 

206 The third Astronomer Royal, James Bradley, is 
popularly known as the author of two memorable dis- 
coveries, viz the aberration of light and the nutation 
of the earth's axis Remarkable as these are both m 
themselves and on account of the ingenious and subtle 
reasoning and minutely accurate observations by means of 
which they were made, they were in fact incidents m a long 
and active astronomical career, which resulted in the 
execution of a vast mass of work of great value 

The external events of Bradley's life may be dealt with 
very briefly Born in 1693, he proceeded m due course 
to Oxford (B A 1714, MA 1717), but acquired his first 
knowledge of astronomy and his marked taste for the 
subject from his uncle fames Pound, for many years rector 
of Wansted in Essex, who was one of the best observers of 
the time Bradley lived with his uncle for some years after 
leaving Oxford, and carried out a number of observations 
m concert with him The first recorded observation of 
Bradley's is dated 1715, and by 1718 he was sufficiently 
well thought of m the scientific world to receive the honour 
of election as a Fellow of the Royal Society But, as his 

258 A Short History of Astronomy [Cn X 

biographer K remarks, " it could not be foreseen that his 
astronomical labours would lead to any establishment in 
life, and it became necessary foi him to embiace a pio- 
fession " He accordingly took orders, and was fortunate 
enough to be presented almost at once to two livings, the 
duties attached to which do not seem to have mteifeied 
appreciably with the prosecution of his astronomical studies 
at Wansted 

In 1721 he was appointed Savilian Piofessoi of Astio- 
nomy at Oxford, and resigned his livings The woik of the 
professorship appears to have been vciy light, and for moie 
than ten years he continued to reside chiefly at Wansted, 
even after his uncle's death in 1724 In 1732 he took a 
house in Oxford and set up there most of his instalments, 
leaving, however, at Wansted the most impoitant of all, 
the "zenith-sector," with which his two famous discovenes 
weie made Ten years aftei wards Halley's death lemleied 
the post of Astronomer Royal vacant, and Biadley icceived 
the appointment 

The work of the Observatoiy had been a good deal 
neglected by Halley during the last few yeais of his life, 
and Bradley's first care was to effect nccessaiy icpaiis in 
the instruments. Although the equipment of the Obsei- 
vatory with instruments woithy of its position and of the 
state of science at the time was a work of yeais, Biadley 
had some of the most impoitant mstiuments in good 
working order within a few months of his appointment, 
and observations weie hencefoiwaid made systematically 
Although the 20 remaining yeais of his life (1742-1762) 
were chiefly spent at Greenwich in the discharge of the 
duties of his office and in lesearches connected with them, 
he retained his professorship at Oxfoid, and continued to 
make observations at Wansted at least up till 1747 

207 The discovery of abei ration resulted fiom an attempt 
to detect the parallactic displacement of stats whu h should 
result from the annual motion of the eaith Evei since 
the Coppernican contioversy had called attention to the 
importance of the pioblem (cf ciiapter iv, 92, and 
chaptei vi, 129), it had natuially exerted a fascination 

* Rigaud, in the memoirs prefixed to Biadlcy'b 

[To fau p 258 

$ 2 7] Bradley Aberration 259 

on the minds of observing astronomers, many of whom had 
tried to detect the motion in question, and some of whom 
(including the "universal claimant" Hooke) professed to 
have succeeded Actually, however, all previous attempts 
had been failures, and Bradley was no more successful than 
his predecessors in this particular undertaking, but was 
able to deduce from his observations two results of great 
interest and of an entirely unexpected character. 

The problem which Bradley set himself was to examine 
whether any star could be seen to have m the course of the 
year a slight motion lelative to others or relative to fixed 
points on the celestial sphere such as the pole. It was 
known that such a motion, if it existed, must be very 
small, and it was therefoie evident that extreme delicacy 
in instrumental adjustments and the greatest caie in obser- 
vation would have to be employed Bradley worked at first 
in conjunction with his friend Samuel Molyneux (1689-1 728), 
who had erected a telescope at Kew In accordance with the 
method adopted in a similar investigation by Hooke, whose 
results it was desired to test, the telescope was fixed in a 
nearly vertical position, so chosen that a paiticular star m 
the Dragon (y Diacoms) would be visible through it when 
it ciossed the meridian, and the telescope was mounted 
with great caie so as to maintain an invariable position 
throughout the year If then the star in question were to 
undergo any motion which altered its distance from the 
pole, there would be a corresponding alteiation m the posi- 
tion in which it would be seen in the field of view of 
the telescope The first observations weie taken on 
December i4th, 1725 (N S ), and by December 28th 
Biadley believed that he had already noticed a slight dis- 
placement of the star towards the south This motion 
was clearly verified on January ist, and was then observed 
to continue } in the following March the star reached its 
extreme southern position, and then began to move north- 
wards again In September it once more altered its 
direction of motion, and by the end of the year had 
completed the cycle of its changes and returned to its 
original position, the greatest change in position amounting 
to nearly 40' 

The star was thus observed to go through some annual 

260 A Short History of Astronomy [Cii X 

motion It was, howevei, at once evident to Bradley that 
this motion was not the parallactic motion of which he 
was in search, for the position of the star was such that 
parallax would have made it appear faithest south in 
December and farthest noith m June, or in each case thiee 
months earlier than was the case in the actual obscivalions 
Anothei explanation which suggested itself was that the 
earth's axis might have a to-and-fio oscillatory motion oj 
nutation which would alter the position of the celestial pole 
and hence produce a corresponding alteration in the position 
of the star Such a motion of the celestial pole would 
evidently pioduce opposite effects on two stars situated on 
opposite sides of it, as any motion which bi ought the pole 
nearer to one star of such a pan would necessanly move 
it away fiom the other Within a fortnight of the decisive 
observation made on January i st a star * had ah eady been 
selected for the application of this test, with the result whit h 
can best be given in Bradley's own words 

<( A nutation of the earth's axis was one of the first things thai 
offered itself upon this occasion, but it was soon lound to be 
insufficient , for though it might have accounted for the change 
of decimation in y Draconis, yet it would not at the same time 
agree with the phaenomena in other stars , particularly in a small 
one almost opposite in right ascension to y Draconis, at about 
the same distance from the north pole of the equator for though 
this star seemed to move the same way as a nutation o( the 
earth's axis would have made it, yet, it changing its declination 
but about half as much as y Draconis m the same time, (as 
appeared upon comparing the observations of both made upon 
the same days, at different seasons oi the year,) this plainly 
proved that the apparent motion of the stars was not occasioned 
by a real nutation, since, if that had been the cause, the altera- 
tion in both stars would have been near equal >J 

One or two other explanations were tested and found 
insufficient, and as the result of a series of observations 
extending over about two years, the phenomenon m ques- 
tion, although amply established, still remained quite 

By this time Bradley had mounted an instrument of his 

* A telescopic star named 37 Camelopardi m Flamsteed's 

2o8] Aberration 261 

own at Wansted, so arianged that it was possible to observe 
through it the motions of stars other than y Draconis 

Several stars were watched carefully throughout a year, 
and the observations thus obtained gave Bradley a fairly 
complete knowledge of the geometncal laws according to 
which the motions varied both from star to star and in 
the course of the yeai, 

208 The true explanation of aberration, as the pheno- 
menon in question was afterwards called, appears to have 
occuired to him about September, 1728, and was published 
to the Royal Society, after some further venfication, early 
in the following year. According to a well-known story,* 
he noticed, while sailing on the Thames, that a vane on 
the masthead appeared to change its direction every time 
that the boat altered its course, and was informed by the 
sailois that this change was not due to any alteration m 
the wind's direction, but to that of the boat's course In 
fact the apparent dnection of the wind, as shewn by the 
vane, was not the true dnection of the wind, but resulted 
from a combination of the motions of the wind and of the 
boat, being more precisely that of the motion of the wind 
relative to the boat Replacing in imagination the wind 
by light coming from a star, and the boat shifting its 
course by the earth moving round the sun and continually 
changing its direction of motion, Bradley ai rived at an 
explanation which, when worked out in detail, was found 
to account most satisfactorily for the apparent changes in 
the dnection of a star which he had been studying. His 
own account of the matter is as follows 

" At last I conjectured that all the phaenomena hitherto men- 
tioned proceeded from the progressive motion of light and the 
earth's annual motion m its orbit For I perceived that, if light 
v\as propagated in time, the apparent place of a fixed object 
would not be the same when the eye is at rest, as when it is 
moving in any other direction than that of the line passing 
through the eye and object , and that when the eye is moving 

* The story is given in T Thomson's History of the Royal Society, 
published more than 80 years afterwards (1812), but I have not been 
able to find any eaiher authority for it Bradley's own account of 
his difacoveiy gives a number of details, but has no allusion to this 


A Short History of Astronomy 

[CH X 

in different directions, the apparent place of the object would be 

" I considered this matter in the following manner I imagined 
c A to be a ray of light, falling perpendicularly upon the line 
B D, then if the eye is at rest at A, the object must appear in 
the direction A c, whether light be propagated m time or m an 
instant But if the eye is moving from B towards A, and light 
is propagated in time, with a velocity that is to the velocity of 
the eye, as c A to B A , then light moving from c to A, whilst 
the eye moves from B to A, that particle of it by which the ob]ect 
will be discerned when the eye in its 
motion comes to A, is at c when the eye 
is at B Joining the points B, c, I sup- 
posed the line c B to be a tube (inclined 
t the line B D m the angle D B c) of such 
a diameter as to admit of but one particle 
of light , then it was easy to conceive that 
the particle of light at c (by which the 
object must be seen when the eye, as it 
moves along, arrives at A) would pass 
through the tube B c, if it is inclined to 
B D m the angle DEC, and accompanies 
the eye in its motion irom B to A , and 
that it could not come to the eye, placed 
behind such a tube, if it had any other 
inclination to the line B D 

11 Although therefore the true or real 
place of an object is perpendicular to the 
line in which the eye is moving, yet the 
visible place will not be so, since that, 
no doubt, must be m the direction of the 
tube , but the difference between the true 
and apparent place will be (caeteris pan- 

D A B 

FIG 74 The aberra- 

the Phil Trans 

tion of light From DUS ) greater * or less, according to" the 
paper m different proportion between the velocity 
of hght and that of the eye SQ that 

we could suppose that light was propa- 
gated m an instant, then there would be no difference between 
the real and visible place of an object, although the eye were 
in motion , for in that case, A c being infinite with respect 
to A B, the angle A c B (the difference between the true and 
visible place) vanishes But if light be propagated m time, 
(which I presume will readily be allowed by most of the 
philosophers of this age,) then it is evident from the foregoing 
considerations, that there will be always a difference between 
the real and visible place of an object, unless the eye is moving 
either directly towards or from the object " 



Bradley's explanation shews that the apparent position of 
a star is determined by the motion of the star's light relative 
to the earth, so that the star appears slightly nearer to the 
point on the celestial sphere towards which the earth is 
moving than would otherwise be the case A familiar 
illustration of a precisely analogous effect may perhaps be 
of service Any one walking on a rainy but windless day 
piotects himself most effectually by holding his umbrella, 
not immediately over his head, but a little in front, exactly 
as he would do if he were at rest and there were a slight 
wind blowing in his face In fact, if he were to ignore 
his own motion and pay attention only to the dnection in 
which he found it advisable to point his umbrella, he would 
believe that there was a slight head-wind blowing the ram 
towards him 

209 The passage quoted from Bradley's paper deals 
only with the simple case in which the star is at right angles 
to the direction of the earth's motion He 
shews elsewhere that if the stai is in any 
other direction the effect is of the same kind 
but less m amount In Bradley's figure 
(fig 74) the amount of the star's displace 
ment from its true position is represented by 
the angle B c A, which depends on the pro- 
portion between the lines A c and A B , but 
if (as in fig 75) the earth is moving (without 
change of speed) in the direction A B' instead 
of A B, so that the direction of the star is 
oblique to it, it is evident from the figure 
that the star's displacement, represented by 
the angle A c B', is less than before , and 
the amount varies according to a simple 
mathematical law* with the angle between 
the two directions It follows therefore 
that the displacement in question is different 
foi different stars, as Bradley's observations 
had aheady shewn, and is, moreover, dif- 
feient for the same star in the course of the 
year, so that a star appears to descube a 
ciuve which is very nearly an ellipse (fig 76), the centre (s) 
* It is k sin CAB, where k \$ the constant of aberration, 

aberration of 


A Short History of Astronomy 

[CH X 

corresponding to the position which the stai would occupy 
if aberration did not exist It is not difficult to see that, 
wherever a star is situated, the eaith's motion is twice a 
year, at intervals of six months, at right angles to the direc- 
tion of the star, and that at these times the stai leceives the 
greatest possible displacement from its mean position, and 
is consequently at the ends of the greatest axis of the 
ellipse which it descnbes, as at A and A', whereas at inter- 
mediate times it 
undergoes its least 
displacement, as at 
B and B' The 
greatest displace- 
ment s A, or half of 
A A', which is the 
same foi all stars, 
is known as the con- 
stant of aberration, 
and was fixed by 
Bradley at between 
20" and 2oJ", the 

p IG 76 The aberrational ellipse 

value at present accepted being 20" 47 The least displace- 
ment, on the other hand, s B, or half of B B', was shewn 
to depend in a simple way upon the star's distance fiom 
the ecliptic, being greatest for stars farthest fiom the 

210 The constant of aberration, which is represented by 
the angle A c B m fig 74, depends only on the ratio between 
A c and A B, which are m turn propoitional to the velocities 
of light and of the earth Obseivations of abenation give 
then the ratio of these two velocities Fiom Biadley's 
value of the constant of abenation it follows by an easy 
calculation that the velocity of light is about 10,000 times 
that of the earth , Bradley also put this result into the form 
that light travels from the sun to the earth m 8 minutes 13 
seconds From observations of the eclipses of Jupiter's 
moons, Roemer and others had estimated the same interval 
at from 8 to n minutes (chapter vin , 162) ; and Bradley 
was thus able to get a satisfactory confirmation of the truth 
of his discovery Aberration being once established, the 
same calculation could be used to give the most accurate 

210213] Aberration 265 

measure of the velocity of light in terms of the dimensions 
of the earth's orbit, the determination of aberration being 
susceptible of considerably greater accuracy than the 
conesponding measurements lequired foi Roemer's method 

211 One difficulty in the theory of aberration deserves 
mention Bradley's own explanation, quoted above, refers 
to light as a material substance shot out from the star or 
other luminous body This was in accordance with the 
corpuscular theory of light, which was supported by the 
gieat weight of Newton's authority and was commonly 
accepted in the i8th century Modem physicists, however, 
have entirely abandoned the corpuscular theory, and regard 
light as a particular form of wave-motion transmitted 
through ether. From this point of view Bradley's ex- 
planation and the physical illustrations given are far less 
convincing, the question becomes in fact one of considerable 
difficulty, and the most careful and elaborate of modem 
investigations cannot be said to be altogether satisfactory 
The curious inference may be drawn that, if the more 
correct modern notions of the nature of light had prevailed 
in Bradley's time, it must have been very much more 
difficult, if not impracticable, for him to have thought of his 
explanation of the stellar motions which he was studying , 
and thus an erroneous theory led to a most important 

212 Bradley had of course not forgotten the original 
object of his investigation He satisfied himself, however, 
that the agreement between the observed positions of y Dra- 
conis and those which resulted from aberration was so 
close that any displacement of a star due to parallax which 
might exist must certainly be less than 2", and probably 
not more than |", so that the large parallax amounting to 
nearly 30", which Hooke claimed to have detected, must 
certainly be rejected as erroneous 

Fiom the point of view of the Coppermcan controversy, 
however, Bradley's discovery was almost as good as the 
discoveiy of a parallax , since if the earth were at rest 
no explanation of the least plausibility could be given of 
abei ration 

213 The close agreement thus obtained between theory 
and observation would have satisfied an astronomer less 

266 A Short History of Astronomy [Cn x 

accurate and careful than Bradley But in his paper on 
aberration (1729) we find him writing 

" I have likewise met with some small varieties m the declina- 
tion of other stars in different years which do not seem to 
proceed Irom the same cause But whether these small 

alterations proceed from a regular cause, or are occasioned by 
any change in the materials, etc , of my instrument, I am not yet 
able fully to determine " 

The slender clue thus obtained was caiefully followed 
up and led to a second striking discovery, which affords 
one of the most beautiful illustrations of the important 
results which can be deduced from the study of " residual 
phenomena" Aberration causes a stai to go through a 
cyclical series of changes m the course of a year , if there- 
fore at the end of a year a star is found not to have 
leturned to its original place, some other explanation of 
the motion has to be sought Precession was one known 
cause of such an alteration , but Bradley found, at the end 
of his first year's set of observations at Wansted, that the 
alterations in the positions of various stars differed by a 
minute amount (not exceeding 2") from those which would 
have resulted from the usual estimate of precession, and 
that, although an alteration in the value of precession would 
account for the observed motions of some of these stars, 
it would have increased the discrepancy m the case of 
others A nutation or nodding of the earth's axis had, 
as we have seen ( 207), already piesented itself to him 
as a possibility,, and although it had been shewn to be 
incapable of accounting for the mam phenomenon due to 
aberration it might prove to be a satisfactory explanation 
of the much smaller residual motions It soon occurred 
to Bradley that such a nutation might be due to the action 
of the moon, as both observation and the Newtonian 
explanation of precession indicated 

" I suspected that the moon's action upon the equatorial parts 
of the earth might produce these effects for if the precession 
of the equinox be, according to Sir Isaac Newton's principles, 
caused by the actions of the sun and moon upon those parts, 
the plane of the moon's orbit being at one time above ten 
degrees more inclined to the plane of the equator than at 
another, it was reasonable to conclude, that the part of the 

sis] Nutation 267 

whole annual precession, which arises from her action, would 
in different years be varied m its quantity , whereas the plane 
of the ecliptic, wherein the sun appears, keeping always nearly 
the same inclination to the equator, that part of the precession 
which is owing to the sun's action may be the same every year , 
and from hence it would follow, that although the mean annual 
precession, proceeding from the joint actions of the sun and 
moon, were 5") yet the apparent annual precession might 
sometimes exceed and sometimes fall short of that mean 
quantity, according to the various situations of the nodes of 
the moon's orbit " 

Newton in his discussion of precession (chapter ix , 188 , 
Principle Book III, proposition 21) had pointed out 
the existence of a small irregularity with a period of six 
months But it is evident, on looking at this discussion 
of the effect of the solar and lunar attractions on the 
protuberant parts of the earth, that the various alterations 
m the positions of the sun and moon relative to the earth 
might be expected to produce 11 regularities, and that the 
uniform precessional motion known from obseivation and 
deduced from gravitation by Newton was, as it were, only 
a smoothing out of a motion of a much more complicated 
charactei Except for the allusion referred to, Newton 
made no attempt to discuss these megularities, and none 
of them had as yet been detected by observation 

Of the numerous irregularities of this class which are now 
known, and which may be referred to generally as nutation, 
that indicated by Bradley in the passage just quoted is 
by far the most important As soon as the idea of an 
irregularity depending on the position of the moon's nodes 
occurred to him, he saw that it would be desirable to watch 
the motions of several stars during the whole period (about 
19 years) occupied by the moon's nodes in performing the 
circuit of the ecliptic and returning to the same position 
This inquiry was successfully carried out between 1727 and 
1747 with the telescope mounted at Wansted When the 
moon's nodes had performed half their revolution, i e 
after about nine years, the correspondence between the 
displacements of the stars and the changes in the moon's 
orbit was so close that Bradley was satisfied with the general 
correctness of his theory, and m 1737 he communicated the 
result pnvately to Maupertuis ( 221), with whom he had 


A Short History of Astronomy 

[Cn X 

had some scientific correspondence Maupertuis appeals 
to have told others, but Bradley himself waited patiently 
for the completion of the period which he regarded as 
necessary for the satisfactory verification of his theory, and 
only published his results definitely at the beginning of 

214 Bradley's observations established the existence of 
certain alterations in the positions of various stars, which 

FIG 77 Precession and nutation 

could be accounted for by supposing that, on the one 
hand, the distance of the pole from the ecliptic fluctu- 
ated, and that, on the other, the precessional motion of 
the pole was not uniform, but varied slightly in speed. 
John Machin (? -1751), one of the best English mathe- 
maticians of the time, pointed out that these effects would 
be produced if the pole were supposed to describe on the 
celestial sphere a minute circle in a period of rather less 

$ 2i4 2i6] Nutation 269 

than 19 years being that of the revolution of the nodes 
of the moon's orbit round the position which it would 
occupy if there were no nutation, but a uniform precession 
Bradley found that this hypothesis fitted his observations, 
but that it would be better to replace the circle by a 
slightly flattened ellipse, the greatest and least axes of which 
he estimated at about 18" and 16" respectively * ! This 
ellipse would be about as large as a shilling placed m a 
slightly oblique position at a distance of 300 yards from 
the eye. The motion of the pole was thus shewn to be 
a double one, as the result of precession and nutation 
combined it describes round the pole of the ecliptic " a 
gently undulated ring,' 7 as represented in the figure, in 
which, however, the undulations due to nutation are 
enormously exaggerated 

215 Although Biadley was aware that nutation must 
be produced by the action of the moon, he left the 
theoretical investigation of its cause to more skilled 
mathematicians than himself 

In the following year (1749) the French mathematician 
D'Alembert (chapter xi , 232) published a treatise t in 
which not only precession, but also a motion of nutation 
agreeing closely with that observed by Bradley, were shewn 
by a rigorous process of analysis to be due to the attraction 
of the moon on the protuberant parts of the earth round 
the equatoi (cf. chapter ix , 187), while Newton's ex- 
planation of piecession was confirmed by the same piece 
of work Euler (chapter xi , 236) published soon after- 
wards another investigation of the same subject, and it 
has been studied afresh by many mathematical astronomers 
since that time, with the result that Bradley's nutation 
is found to be only the most important of a long series 
of minute irregularities in the motion of the earth's axis 

216 Although abei ration and nutation have been dis- 
cussed first, as being the most important of Biadley ? s 

" His observations as a matter of fact point to a value rather 
gi eater than 18", but he preferred to use round numbers The 
figures at piesent accepted are i8"42 and 13" 75, so that his ellipse 
was decidedly less flat than it should have been 

f Recheiches sur la precession des equinoxes et sur la nutation de 
Vaxe de la teire. 

270 A Short History of Astronomy [CH x 

discovenes, other investigations were earned out by him 
befoie or during the same time 

The earliest important piece of work which he accom- 
plished was in connection with Jupiter's satellites His 
uncle had devoted a good deal of attention to this subject, 
and had diawn up some tables dealing with the motion of 
the first satellite, which were based on those of Domemco 
Cassmi, but contained a good many improvements Biadley 
seems for some yeais to have made a practice of frequently 
obseiving the eclipses of Jupiter's satellites, and of noting 
discrepancies between the observations and the tables ; and 
he was thus able to detect several hitheito unnoticed 
peculiarities m the motions, and theieby to foim improved 
tables The most interesting discovery was that of a 
period of 437 days, aftei which the motions of the three 
inner satellites recuired with the same nregulanties. 
Biadley, like Pound, made use of Roemei's suggestion 
(chapter vm , 162) that light occupied a finite time in 
travelling fiom Jupiter to the earth, a theory which Cassim 
and his school long rejected Bradley's tables of Jupiter's 
satellites were embodied in Halley's planetary and lunar 
tables, printed in 1719, but not published till more than 
30 years afterwards ( 204) Before that date the Swedish 
astronomer JPehr Vilhelm Wargentm (1717-1783) had in- 
dependently discovered the period of 437 days, which he 
utilised for the construction of an extiemely accuiate set 
of tables foi the satellites published in 1746 

In this case as m that of nutation Bradley knew that his 
mathematical powers were unequal to giving an explanation 
on gravitational principles of the inequalities which obseiva- 
tion had revealed to him, though he was well aware of the 
importance of such an undertaking, and definitely expressed 
the hope "that some geometer,* in imitation of the gieat 
Newton, would apply himself to the investigation of these 
irregularities, from the certain and demonstiative principles 
of gravity " 

On the othei hand, he made in 1726 an mteiestmg 
practical application of his superior knowledge of Jupiter's 

* The word "geometer" was formerly used, as "geometie" still 
is in French, in the wider sense in which " mathematician " is now 

2 i7,2i8] Bradley's Minor Work his Observations 271 

satellites by determining, m accordance with Galilei's 
method (chaptei vi , 127), but with remarkable accuracy, 
the longitudes of Lisbon and of New York 

217 Among Bradley's minor pieces of work may be 
mentioned his obseivations of several comets and his 
calculation of their respective oibits according to Newton's 
method , the construction of improved tables of refraction, 
which remained m use for neaily a century, a share in 
pendulum experiments earned out in England and Jamaica 
with the object of venfymg the variation of gravity m 
diffeient latitudes , a careful testing of Mayer's lunar tables 
( 226), togethei with impiovements of them, and lastly, 
some woik m connection with the reform of the calendar 
made m 1752 (cf chapter n , 22) 

218 It remains to give some account of the magnificent 
series of observations cained out during Bradley's admims- 
tiation of the Greenwich Observatory 

These observations fall into two chief divisions of unequal 
merit, those after 1749 having been made with some more 
accurate mstiuments which a grant from the government 
enabled him at that time to piocure 

The mam work of the Observatory undei Bradley con- 
sisted m taking observations of fixed stars, and to a lesser 
extent of other bodies, as they passed the meridian, the 
instruments used (the " mural quadrant " and the " transit 
instrument") being capable of motion only in the meridian, 
and being therefore steadier and susceptible of greater 
accuracy than those with more freedom of movement 
The most important observations taken duimg the years 
1750-1762, amounting to about 60,000, were published long 
after Bradley's death in two large volumes which appeared 
m 1798 and 1805 A selection of them had been used 
eaiher as the basis of a small star catalogue, published m 
the Nautical Almanac foi 1773, but it was not till 1818 
that the publication of Bessel's Fundamenta Astronomiae 
(chapter xni , 277), a catalogue of more than 3000 stars 
based on Bradley's observations, rendered these observations 
thoroughly available for astronomical work. One reason 
for this apparently excessive delay is to be found in 
Bradley's way of working Allusion has already been 
made to a variety of causes which prevent the appaient 

272 A Short History of Astronomy [CH x 

place of a star, as seen m the telescope and noted at the 
time, from being a satisfactory permanent record of its 
position There are various instrumental errors, and errors 
due to refraction, again, if a star's places at two different 
times are to be compared, precession must be taken into 
account, and Bradley himself unravelled in aberration and 
nutation two fresh sources of error In order therefore 
to put into a form satisfactory for permanent reference a 
number of star observations, it is necessary to make cor- 
rections which have the effect of allowing foi these vauous 
sources of error This process of reduction, as it is techni- 
cally called, involves a certain amount of rather tedious 
calculation, and though m modem observatories the process 
has been so far systematised that it can be carried out 
almost according to fixed rules by comparatively unskilled 
assistants, in Bradley's time it required more judgment, 
and it is doubtful if his assistants could have performed 
the work satisfactorily, even if their time had not been fully 
occupied with other duties Bradley himself probably 
found the necessary calculations tedious, and prefeired 
devoting his energies to work of a higher order It is 
true that Delambre, the famous French historian of 
astronomy, assures his readers that he had never found 
the reduction of an observation tedious if performed the 
same day, but a glance at any of his books is enough to 
shew his extraordinary fondness for long calculations of 
a fairly elementary chaiacter, and assuredly Bradley is not 
the only astronomer whose tastes have in this resg&qt 
differed fundamentally from Delambre's Moreovei fKTucmg } 
an observation is generally found to be a duty that, like ' 
answering letters, grows harder to perform the longer it 
is neglected , and it is not only less interesting but also 
much more difficult for an astronomer to deal satisfactonlvj 
with some one else's observations than with his own -at 
is not therefore surprising that after Bradley's death a 
long interval should have elapsed before an astronomer 
appeared with both the skill and the patience necessary 
for the complete reduction of Bradley's 60,000 observations. 
A variety of circumstances combined to make Bradley's 
observations decidedly superior to those of his predecessors. 
He evidently possessed m a marked degree the personal 

$ aip] Bradley 's Observations 273 

charactenstics of eye and judgment which make a first- 
rate observer , his instruments were mounted in the best 
known way for securing accuracy, and were constructed by 
the most skilful makers ; he made a point of studying very 
carefully the defects of his instruments, and of allowing 
for them , his discoveries of aberration and nutation 
enabled him to avoid sources of error, amounting to a 
considerable number of seconds, which his predecessors 
could only have escaped imperfectly by taking the average 
of a number of obseivations } and his improved tables of 
refraction still further added to the correctness of his 

Bessel estimates that the errors in Bradley's observations 
of the declination of stars were usually less than 4", while 
the corresponding errors m right ascension, a quantity which 
depends ultimately on a time-observation, were less than 15", 
or one second of time His observations thus shewed a 
considerable advance in accuracy compared with those of 
Flamsteed ( 198), which represented the best that had 
hitherto been done. 

219. The next Astronomer Royal was Nathaniel Bliss 
(1700-1764), who died after two years He was in turn 
succeeded by Neuil Maskelyne (1732-1811), who carried 
on for nearly half a century the tradition of accurate 
observation which Biadley had established at Greenwich, 
and made some improvements in methods 

To him is also due the first serious attempt to measure 
the density and hence the mass of the earth By com- 
paring the attraction exerted by the earth with that of 
the sun and other bodies, Newton, as we have seen 
(chapter ix , 185), had been able to connect the masses 
of several of the celestial bodies with that of the earth 
To connect the mass of the whole earth with that of a 
given terrestrial body, and so express it in pounds or tons, 
was a problem of quite a different kind It is of course 
possible to examine portions of the eaith's surface and 
compare their density with that of, say, water , then to 
make some conjecture, based on rough observations m 
mines, etc , as to the rate at which density increases as 
we go from the surface towards the centre of the earth, 
and hence to infer the average density of the earth Thus 


274 A Short History of Astronomy [LH x. 

the mass of the whole earth is compaied with that of a 
globe of water of the same size, and, the size being known, 
is expressible in pounds or tons 

By a process of this soit Newton had in fact, with extra- 
ordinary insight, estimated that the density of the earth 
was between five and six times as great as that of watei * 

It was, however, clearly desirable to solve the problem 
in a less conjectural manner, by a direct comparison of 
the gravitational attraction exerted by the earth with that 
exerted by a known mass a method that would at the 
same time afford a valuable test of Newton's theory of the 
gravitating properties of portions of the earth, as distinguished 
from the whole earth In their Peruvian expedition (221), 
Bouguer and La Condamme had noticed certain small deflec- 
tions of the plumb-line, which indicated an attraction by 
Chimborazo, near which they were working , but the obser- 
vations were too uncertain to be depended on Maskelyne 
selected for his purpose Schehalhen in Perthshire, a narrow 
ridge running east and west The direction of the plumb- 
line was observed (1774) on each side of the ndge, and 
a change m direction amounting to about 12" was found 
to be caused by the attraction of the mountain As the 
direction of the plumb-line depends on the attraction of 
the earth as a whole and on that of the mountain, this 
deflection at once led to a comparison of the two attrac- 
tions Hence an intricate calculation performed by Charles 
Hutton (1737-1823) led to a comparison of the average 
densities of the earth and mountain, and hence to the final 
conclusion (published in 1778) that the earth's density was 
about 4| times that of water As Hutton's estimate of the 
density of the mountain was avowedly almost conjectural, 
this result was^of course coirespondmgly uncertain 

A few years \&teijohn Muhell (1724-1793) suggested, and 
the famous chemist and electrician Henry Cavendish (1731- 
1810) carried out (1798), an experiment in which the 
mountain was replaced by a pair of heavy balls, and their 
attraction on another body was compared with that of the 
earth, the result being that the density of the earth was 
found to be about 5^ times that of water, 

* Prtnctpta, Book III , proposition 10 

$$ 220, 221] Jlfo Density of the Earth 275 

The Cavendish experiment, as it is often called, has 
since been repeated by various other experimenters in 
modified forms, and one or two other methods, too technical 
to be described here, have also been devised All the 
best modern experiments give for the density numbers 
converging closely on 5|, thus verifying in a most striking 
way both Newton's conjecture and Cavendish's original 

With this value of the density the mass of the earth is 
a little more than 13 billion billion pounds, or more 
piecisely 13,136,000,000,000,000,000,000,000 Ibs 

220 While Greenwich was furnishing the astronomical 
world with a most valuable senes of observations, the Pans 
Observatory had not fulfilled its early promise. It was 
in fact suffering, like English mathematics, from the evil 
effects of undue adherence to the methods and opinions of 
a distinguished man Domenico Cassmi happened to hold 
several erroneous opinions in important astronomical 
matters , he was too good a Catholic to be a genuine 
Coppernican, he had no belief in gravitation, he was firmly 
persuaded that the earth was flattened at the equator instead 
of at the poles, and he rejected Roemer's discovery of the 
velocity of light After his death in 1712 the directorship 
of the Obseivatory passed in turn to three of his descendants, 
the last of whom resigned office m 1793, and several 
members of the Maraldi family, into which his sister had 
married, worked in co-operation with their cousins Un- 
fortunately a good deal of their energy was expended, first 
in defending, and afterwards m gradually withdrawing from, 
the errors of their distinguished head. Jacques Cassini, for 
example, the second of the family (1677-1756), although 
a Coppernican, was still a timid one, and rejected Kepler's 
law of areas , his son again, commonly known as Cassmi de 
Thury (1714-1784), still defended the ancestral errors as 
to the form of the earth , while the fomth member of the 
family, Count Cassim (1748-1845), was the fast of the 
family to accept the Newtonian idea of gravitation 

Some planetary and other observations of value were 
made by the Cassim-Maraldi school, but little of this work 
was of first-rate importance 

221 A series of important measurements of the earth, 

276 A Short History of Astronomy [CH x 

in which the Cassmis had a considerable share, were made 
during the i8th century, almost entirely by Frenchmen, 
and resulted m tolerably exact knowledge of the earth's 
size and shape 

The variation of the length of the seconds pendulum 
observed by Richer m his Cayenne expedition (chapter vin , 
161) had been the first indication of a deviation of the 
earth from a spherical form Newton inferred, both from 
these pendulum experiments and from an independent 
theoretical investigation (chapter ix , 187), that the earth 
was spheroidal, being flattened towards the poles; and 
this view was strengthened by the satisfactory explanation 
of precession to which it led (chapter ix , 188) 

On the other hand, a comparison of various measurements 
of arcs of the meridian m different latitudes gave some 
support to the view that the earth was elongated towards 
the poles and flattened towards the equator, a view cham- 
pioned with great ardour by the Cassini school It was 
clearly important that the question should be settled by 
more extensive and careful earth-measurements 

The essential part of an ordinary measurement of the 
earth consists in ascertaining the distance in miles between 
two places on the same meridian, the latitudes of which 
differ by a known amount From these two data the length 
of an arc of a meridian corresponding to a difference of 
latitude of i at once follows The latitude of a place is 
the angle which the vertical at the place makes with the 
equator, or, expressed m a slightly different form, is the 
angular distance of the zenith from the celestial equator 
The vertical at any place may be defined as a direction 
perpendicular to the surface of still water at the place in 
question, and may be regarded as perpendicular to the 
true surface of the earth, accidental irregularities m its form 
such as hills and valleys being ignored * 

The difference of latitude between two places, north and 
south of one another, is consequently the angle between 
the verticals there Fig 78 shews the verticals, marked 
by the arrowheads, at places on the same meridian in 

* !t 1S important for the purposes of this discussion to notice that 
the vertical is not the line drawn from the centre of the earth to the 
place of observation. 

1 221] 

The Shape of the Earth 


latitudes differing by 10 , so that two consecutive verticals 
are inclined in every case at an angle of 10 

If, as in fig 78, the shape of the earth is drawn in accoid- 
ance with Newton's views, the figure shews at once that 
the arcs A A I; A, A^ etc , each of which corresponds to 10 of 
latitude, steadily increase as we pass from a point A on the 
equator to the pole B If the opposite hypothesis be 

FIG. 78. The varying curvature of the earth, 

adopted, which will be illustiated by the same figure if we 
now regard A as the pole and B as a point on the equator, 
then the successive aics decrease as we pass from equator 
to pole A comparison of the measurements made by 
Eiatosthenes in Egypt (chapter IT., 36) with some made 
m Europe (chapter vin , 159) seemed to indicate that a 
degree of the meridian near the equator was longer than 
one in higher latitudes ; and a similar conclusion was in- 
dicated by a comparison of diffeient portions of an extensive 

27 g A Short History of Astronomy [Cn. X 

French arc, about 9 m length, extending from Dunkirk 
to the Pyrenees, which was measured undei the super- 
intendence of the Cassmis in continuation of Picaids arc, 
the result being published by J Cassmi in 1720 In 
neither case, however, were the data sufficiently accuiate to 
justify the conclusion, and the first decisive evidence was 
obtained by measurement of arcs in places diffeimg far 
more widely m latitude than any that had hitheito been 
available The French Academy organised an expedition 
to Peru, under the management of three Academicians, 
Pierre Bouguer (1698-1758), Charles Mane de La Conda- 
mine (1701-1774), and Louis Godin (1704-1760), with 
whom two Spanish naval officers also co-operated. 

The expedition started m 1735, and, owing to various 
difficulties, the work was spread out over neaily ten years* 
The most important result was the measmement, with very 
fair accuracy, of an arc of about 3 in length, close to the 
equator , but a number of pendulum experiments of value 
were also performed, and a good many miscellaneous 
additions to knowledge were made 

But while the Peruvian party were still at their work a 
similar expedition to Lapland, under the Academician 
Pierre Louis Moreau de Maupertuis (1698-1759), had much 
more rapidly (1736-7), if somewhat carelessly, effected the 
measurement of an arc of nearly i close to the aicticcncle* 

From these measurements it resulted that the lengths 
of a degree of a meridian about latitude 2 S. (Peru), 
about latitude 47 N (France) and about latitude 66 N. 
(Lapland) were respectively 362,800 feet, 364,900 feet, and 
367,100 feet.* There was therefore clear evidence, from 
a comparison of any two of these arcs, of an meiease of 
the length of a degree of a meridian as the latitude increases; 
and the general correctness of Newton's views as against 
Cassmi's was thus definitely established 

The extent to which the earth deviates from a sphere 
is usually expiessed by a fraction known as the ellipticity, 
which is the difference between the lines c A, c B of fig. 78 
divided by the greater of them. From comparison of the 
three arcs just mentioned several very different values of the 
* 69 miles is 364,320 feet, so that the two northern degrees were 
a little more and the Peruvian are a little less than 69 miles. 

$ 222] The Shape of the Earth 279 

ellipticity were deduced, the discrepancies being partly due 
to different theoretical methods of interpreting the results 
and partly to errors in the arcs. 

A measurement, made by Jons Svanberg (177 1-1851) in 
1801-3, of an arc near that of Maupertuis has in fact 
shewn that his estimate of the length of a degree was 
about 1,000 feet too large 

A large number of other arcs have been measured m 
different parts of the earth at various times during the 
1 8th and i9th centuries The details of the measurements 
need not be given, but to prevent recurrence to the subject 
it is convenient to give here the results, obtained by a 
comparison of these different measurements, that the 
ellipticity is very nearly -j^-j, and the greatest radius of the 
earth (c A in fig 78) a little less than 21,000,000 feet or 
4,000 miles It follows from these figures that the length 
of a degree in the latitude of London contains, to use Sir 
John Herschel's ingenious mnemonic, almost exactly as 
many thousand feet as the year contains days 

222. Reference has already been made to the supremacy 
of Greenwich during the i8th century in the domain of 
exact observation France, however, produced during this 
period one great obseiving astronomer who actually accom- 
plished much, and under more favourable external conditions 
might almost have rivalled Bradley 

Nicholas Louis de Lacaille was born m 1713 After he 
had devoted a good deal of time to theological studies 
with a view to an ecclesiastical career, his interests were 
diverted to astronomy and mathematics He was intro- 
duced to Jacques Cassmi, and appointed one of the 
assistants at the Pans Obseivatory 

In 1738 and the two following years he took an active 
part m the measurement of the French aic, then m process 
of verification While engaged m this work he was ap- 
pointed (1739) to a poorly paid professorship at the 
Mazarm College, at which a small observatoiy was erected. 
Here it was his regular practice to spend the whole night, 
if fine, in obseivation, while "to fill up usefully the hours 
of leisuie which bad weather gives to observeis only too 
often " he undertook a variety of extensive calculations and 
wrote innumerable scientific memoirs It is therefore not 

280 A Short History of Astronomy [CH x 

sui prising that he died comparatively early (1762) and that 
his death was generally attributed to overwork 

223. The monotony of Lacaille's outward life was bioken 
by the scientific expedition to the Cape of Good Hope 
(1750-1754) organised by the Academy of Sciences and 
placed under his direction 

The most striking piece of work undertaken during this 
expedition was a systematic survey of the southern skies, 
m the course of which more than 10,000 stars were 

These observations, together with a carefully executed 
catalogue of nearly 2,000 of the stars* and a star-map, were 
published posthumously in 1763 under the title Coelum 
Australe Stelhferum, and entirely superseded Halley's much 
smaller and less accurate catalogue ( 199) Lacailie 
found it necessary to make 14 new constellations (some 
of which have since been generally abandoned), and to 
restore to their original places the stars which the loyal 
Halley had made into King Charles's Oak Incidentally 
Lacailie observed and described 42 nebulae, nebulous stars, 
and star-clusters, objects the systematic study of which 
was one of Herschel's great achievements (chapter xn , 

He made a laige number of pendulum experiments, at 
Mauritius as well as at the Cape, with the usual object of 
determining m a new part of the world the acceleration 
due to gravity, and measured an arc of the meridian ex- 
tending over rather more than a degree He made also 
careful observations of the positions of Mars and Venus, 
m order that from comparison of them with simultaneous 
observations m northern latitudes he might get the parallax 
of the sun (chapter VIIL, 161) These observations of 
Mars compared with some made in Europe by Bradley and 
others, and a similar treatment of Venus, both pointed to 
a solar parallax slightly m excess of 10", a result less 
accurate than Cassim's (chapter vni , 161), though 
obtained by more reliable processes 

A large number of observations of the moon, of which 
* The remaining 8,000 stars were not "reduced" by Lacailie 
The whole number were first published m the "reduced" form by 
the British Association in 1845. 

$$ 22 3 , 224] Lacaille 281 

those made by him at the Cape formed an important part, 
led, after an elaborate discussion in which the spheroidal 
form of the earth was taken into account, to an improved 
value of the moon's distance, first published in 1761 

Lacaille also used his observations of fixed stars to 
improve our knowledge of lefraction, and obtained a 
number of observations of the sun in that part of its orbit 
which it traverses in our winter months (the summer of 
the southern hemisphere), and m which it is therefore 
too near the horizon to be observed satisfactorily in 

The results of this one of the most fruitful scientific 
expeditions ever undertaken were published in separate 
memoirs or embodied in various books published aftei his 
return to Pans 

224 In 1757, under the title Astronomiae Fundamenta, 
appeared a catalogue of 400 of the brightest stars, observed 
and reduced with the most scrupulous care, so that, not- 
withstanding the poverty of Lacaille's instrumental outfit, 
the catalogue was far superior to any of its predecessors, 
and was only surpassed by Bradley's observations as they 
were gradually published It is characteristic of Lacaille's 
unselfish nature that he did not have the Fundamenta sold 
m the ordinary way, but distributed copies gratuitously to 
those interested m the subject, and earned the money 
necessary to pay the expenses of publication by calculating 
some astronomical almanacks 

Another catalogue, of rather more than 500 stais situated 
in the zodiac, was published posthumously 

In the following year (1758) he published an excellent 
set of Solar Tables, based on an immense series of obseiva- 
tions and calculations These were remarkable as the first 
m which planetary perturbations were taken into account 

Among Lacaille's minor contributions to astronomy may 
be mentioned improved methods of calculating cometary 
orbits and the actual calculation of the orbits of a large 
number of recoided comets, the calculation of all eclipses 
visible m Europe since the year i, a warning that the 
transit of Venus would be capable of far less accurate 
observation than Halley had expected ( 202), observations 
of the actual transit of 1761 ( 227), and a number of 

282 A Short History of Astronomy [Cn. X 

improvements in methods of calculation and of utilising 

In estimating the immense mass of work which Lacaille 
accomplished during an astronomical career of about 22 
years, it has also to be borne in mind that he had only 
moderately good instruments at his observatory, and no 
assistant^ and that a considerable part of his time had to 
be spent m earning the means of living and of working 

225 During the period under consideration Geirnany 
also produced one astionomer, primarily an observer, of 
great merit, Tobias Mayer (1723-1762) He was appointed 
professor of mathematics and political economy at Gottmgen 
in 1751, apparently on the understanding that he need not 
lecture on the latter subject, of which indeed he seems 
to have professed no knowledge , three years later he was 
put m charge of the observatory, which had been erected 
20 years before He had at least one fine instrument,* 
and following the example of Tycho, Flamsteed, and Bradley, 
he made a careful study of its defects, and carried further 
than any of his predecessors the theory of correcting 
observations for instrumental errors t 

He improved Lacaille's tables of the sun, and made a 
catalogue of 998 zodiacal stars, published posthumously m 
1775 > by a comparison of star places lecorded by Roemer 
(1706) with his own and Lacaille's observations he obtained 
evidence of a considerable number of proper motions 
( 20 3) 9 and he made a number of othei less interesting 
additions to astronomical knowledge 

226 But Mayer's most important woik was on the moon 
At the beginning of his career he made a careful study of 
the position of the craters and other markings, and was 
thereby able to get a complete geometrical explanation of 
the various librations of the moon (chapter vi , 133), and 
to fix with accuracy the position of the axis about which 
the moon rotates A map of the moon based on his 
observations was published with other posthumous works 
in 1775. 

* A mural quadrant 

f The ordinary approximate theory of the colhmation erroi. level 
erroi, and deviation error of a transit, as given m text-books of 
spherical and piactical astronomy, is substantially his. 

FIG 79 Tobias Ma>cfs map of the moon 

\TofaLCp 282 

> 225, 226] Tobias Mayer 283 

Much more important, however, were his lunar theory 
nd the tables based on it The intrinsic mathematical 
iteiest of the problem of the motion of the moon, and its 
ractical impoitance for the determination of longitude, had 
aused a great deal of attention to be given to the subject 
y the astronomers of the 1 8th century A further stimulus 
r as also furnished by the prizes offered by the British 
Government in 1713 foi a method of finding the longitude 
t sea, viz ^20,000 for a method reliable to within half 

degree, and smaller amounts for methods of less accuracy 

All the gieat mathematicians of the period made attempts 
t deducing the moon's motions from gravitational principles 
layer worked out a theory in accoi dance with methods 
sed by Euler (chapter xi , 233), but made a much more 
beral and also more skilful use of observations to determine 
anous numerical quantities, which pure theory gave either 
ot at all or with considerable uncertainty He accordingly 
icceeded in calculating tables of the moon (published with 
lose of the sun in 1753) which were a notable improve- 
lent on those of any earlier writer After making further 
nprovements, he sent them m 1755 to England Bradley, 
) whom the Admiralty submitted them for criticism, re- 
orted favourably of their accuracy 3 and a few years later, 
fter making some alterations in the tables on the basis of 
is own observations, he recommended to the Admiralty a 
mgitude method based on their use which he estimated 
) be m general capable of giving the longitude within 
bout half a degree 

Before anything definite was done, Mayer died at the 
irly age of 39, leaving behind him a new set of tables, 
hich were also sent to England Ultimately ^"3,000 was 
aid to his widow m 1765 , and both his Theory of the 
foon* and his improved Solar and Lunar Tables were 
ubhshed m 1770 at the expense of the Board of Longitude 
. later edition, improved by Bradley's former assistant 
"harks Mason (1730-1787), appeared in 1787 

A prize was also given to Euler for his theoretical work , 
hile ^3,000 and subsequently ^r 0,000 more were awarded 

> John Harrison for improvements in the chronometer, 

* The title-page is dated 1767, but it is known not to have been 
:tually published till three years later 

284 A Short History of Astronomy [Cn x 

which rendered practicable an entirely different method 
of finding the longitude (chapter vi , 127) 

227 The astronomers of the i8th century had two 
opportunities of utilising a transit of Venus for the deter- 
mination of the distance of the sun, as recommended bv 
Halley ( 202). J 

A passage or transit of Venus across the sun's disc is 
a phenomenon of the same nature as an eclipse of the 
sun by the moon, with the important difference that the 
apparent magnitude of the planet is too small to cause any 
serious diminution m the sun's light, and it merely appears 
as a small black dot on the bright surface of the sun 

If the path of Venus lay in the ecliptic, then at every 
inferior conjunction, occurring once in 584 days, she would 
necessarily pass between the sun and eaith and would 
appear to transit As, however, the paths of Venus and the 
earth are inclined to one another, at infenoi conjunction 
Venus is usually far enough "above" or "below" the 
ecliptic for no transit to occur With the present position 
of the two pathswhich planetary perturbations aie only 
very gradually changing tansits of Venus occur m pairs 
eight years apart, while between the latter of one pair and 
the earlier of the next pair elapse alternately intervals of 
105^ and of 124 years Thus transits have taken place in 
December 1631 and 1639, June 1761 and 1769, December 
1874 and 1882, and will occur again in 2004 and 2012 
2117 and 2125, and so on ' 

The method of getting the distance of the sun from a 
transit of Venus may be said not to differ essentially from 
that based on observations of Mars (chapter vin , 161) 

The observer's object m both cases is to obtain the 
difference m direction of the planet as seen from different 
places on the earth. Venus, however, when at all near 
the earth, is usually too neai the sun m the sky to be 
capable of minutely exact observation, but when a transit 
occurs the sun's disc serves as it were as a dial-plate on 
which the position of the planet can be noted. Moreover 
the measurement of minute angles, an art not yet carried 
to very great perfection m the i8th century, can be avoided 
by time-observations, as the difference m the times at 
which Venus enters (or leaves) the sun's disc as seen at 

227] Transits of Venus 285 

different stations, 01 the difference in the durations of the 
transit, can be without difficulty translated into difference 
of direction, and the distances of Venus and the sun can 
be deduced* 

Immense trouble was taken by Governments, Academies, 
and private persons in arranging for the observation of the 
transits of 1761 and 1769 For the former observing 
parties were sent as far as to Tobolsk, St Helena, the 
Cape of Good Hope, and India, while observations were 
also made by astronomers at Greenwich, Pans, Vienna, 
Upsala, and elsewhere in Europe The next transit was 
observed on an even larger scale, the stations selected 
ranging from Siberia to California, from the Varanger Fjord 
to Otaheiti (where no less famous a person than Captain 
Cook was placed), and from Hudson's Bay to Madras. 

The expeditions organised on this occasion by the 
American Philosophical Society may be regarded as the 
first of the contributions made by America to the science 
which has since owed so much to her , while the Empress 
Catherine bore witness to the newly acquired civilisation of 
her country by arranging a number of observing stations 
on Russian soil 

The results were far more in accordance with Lacaille's 
anticipations than with H alley's. A variety of causes pre- 
vented the moments of contact between the discs of Venus 
and the sun from being observed with the precision that 
had been hoped By selecting different sets of observations, 
and by making different allowances for the various probable 
sources of error, a number of discordant results were 
obtained by van oft s calculators. The values of the parallax 
(chapter vin , 161) of the sun deduced from the earlier 
of the two transits ranged between about 8" and io"_, while 
those obtained in 1769, though much more consistent, still 
varied between about 8" and 9", corresponding to a variation 
of about 10,000,000 miles in the distance of the sun 

The whole set of observations were subsequently very 
elaborately discussed in 1822-4 and again in 1835 by 
J'ohann Franz Encke (1791-1865), who deduced a parallax 
of 8"'57i, corresponding to a distance of 95,370,000 miles, 

* For a more detailed discussion of the transit of Venus, see Air/s 
Popular Astronomy and Newcomb's Popular Astronomy* 

286 A Short History of Astronomy [Cn x , 227 

a number which long remained classical The uncertainty 
of the data is, however, shewn by the fact that other equally 
competent astronomers have deduced from the observations 
of 1769 parallaxes of 8" 8 and 8" 9 

No account has yet been given of William Herschel, 
perhaps the most famous of all observers, whose career 
falls mainly into the last quarter of the i8th century and 
the earlier part of the ipth century. As, however, his 
work was essentially different from that of almost all the 
astronomers of the i8th century, and gave a powerful 
impulse to a department of astronomy hitherto almost 
ignored, it is convenient to postpone to a later chapter (xn ) 
the discussion of his work 



"Astronomy, considered in the most general way, is a great problem 
of mechanics, the arbitrary data of which are the elements of the 
celestial movements , its solution depends both on the accuracy of 
observations and on the perfection of analysis " 

LAPLACE, Preface to the Mecamque Celeste 

228 THE solar system, as it was known at the beginning 
of the 1 8th century, contained 18 recognised members, 
the sun, six planets, ten satellites (one belonging to the 
earth, four to Jupiter, and five to Saturn), and Saturn's 

Comets were known to have come on many occasions 
into the region of space occupied by the solar system, and 
there were reasons to believe that one of them at least 
(chapter x , 200) was a regular visitor , they were, how- 
ever, scarcely regarded as belonging to the solar system, 
and their action (if any) on its members was ignoied, a 
neglect which subsequent investigation has completely 
justified. Many thousands of fixed stars had also been 
observed, and their places on the celestial sphere determined , 
they were known to be at very great though unknown 
distances from the solar system, and their influence on it 
was regarded as insensible 

The motions of the 18 members of the solar system were 
tolerably well known , their actual distances from one 
another had been roughly estimated, while the proportions 
between most of the distances were known with considerable 
accuracy Apart from the entirely anomalous ring of 
Saturn, which may for the present be left out of considera- 
tion, most of the bodies of the system were known from 


288 A Short History of Astronomy [CH xi 

observation to be nearly spherical in form, and the rest were 
generally supposed to be so also 

Newton had shewn, with a considerable degree of proba- 
bility, that these bodies attracted one another according to 
the law of gravitation , and there was no leason to suppose 
that they exerted any other important influence on one 
another's motions * 

The problem which presented itself, and which may con- 
veniently be called Newton's problem, was therefore 

Given these 18 bodies, and their positions and ?notions 
at any time, to deduce from their mutual gravitation by 
a process of mathematical calculation their positions and 
motions at any other time , and to shew that these agree 
with those actually observed 

Such a calculation would necessarily involve, among other 
quantities, the masses of the several bodies ; it was evidently 
legitimate to assume these at will in such a way as to make 
the results of calculation agree with those of observation, 
If this were done successfully the masses would thereby be 
determined In the same way the commonly accepted 
estimates of the dimensions of the solar system and of the 
shapes of its members might be modified m any way not 
actually inconsistent with direct observation 

The general problem thus formulated can fortunately be 
reduced to somewhat simpler ones 

Newton had shewn (chapter ix., 182) that an ordinary 
sphere attracted other bodies and was attracted by them, 
as if its mass were concentrated at its centre , and that the 
effects of deviation from a spherical form became very 
small at a considerable distance from the body Hence, 
except in special cases, the bodies of the solar system coulcl 
be treated as spheres, which could again be regarded as 
concentrated at their respective centres. It will be con- 
venient for the sdke of brevity to assume for the future 
that all "bodies" referred to are of this sort, unless the 
contrary is stated or implied The effects of deviations 
from spherical form could then be treated separately 

* Some other influences are known eg. the sun's heat causes 
various motions of our air and water, and has a certain minute effect 
on the earth's rate of rotation, and presumably produces sumlai 
effects on other bodies 

* s] Newton's Problem the Problem of Three Bodies 289 

when required, as in the cases of precession and of 
other motions of a planet or satellite about its centre, and 
of the corresponding action of a non -spherical planet on its 
satellites , to this group of problems belongs also that of the 
tides and other cases of the motion of parts of a body of 
any form relative to the rest 

Again, the solar system happens to be so constituted that 
each body's motion can be treated as determined primarily 
by one other body only A planet, for example, moves 
nearly as if no other body but the sun existed, and the 
moon's motion relative to the earth is roughly the same as 
if the other bodies of the solar system were non-existent 

The problem of the motion of two mutually gravitating 
spheres was completely solved by Newton, and was 
shewn to lead to Kepler's first two laws Hence each 
body of the solar system could be regarded as moving 
nearly m an ellipse round some one body, but as slightly 
disturbed by the action of others Moreover, by a general 
mathematical pi maple applicable m problems of motion, 
the effect of a number of small disturbing causes acting 
conjointly is nearly the same as that which results from 
adding together their separate effects Hence each body 
could, without great error, be regarded as disturbed by one 
body at a time , the several disturbing effects could then 
be added together, and a fresh calculation could be made 
to further dimmish the error The kernel of Newton's 
problem is thus seen to be a special case of the so-called 
problem of three bodies, viz 

Given at any time the positions and motions of three 
mutually gravitating bodies, to determine their positions and 
motions at any other time 

Even this apparently simple problem in its general form 
entirely transcends the powers, not only of the mathe- 
matical methods of the eaily :8th century, but also of 
those that have been devised since Certain special cases 
have been solved, so that it has been shewn to be possible 
to suppose three bodies initially moving m such a way that 
their future motion can be completely determined But 
these cases do not occur m nature 

In the case of the solar system the problem is simplified 
not only by the consideration already mentioned that one 


290 A Short History of Astronomy [CH xi 

of the three bodies can always be regarded as exercising 
only a small influence on the relative motion of the other 
two, but also by the facts that the orbits of the planets 
and satellites do not differ much from circles, and that 
the planes of their orbits are in no case inclined at large 
angles to any one of them, such as the ecliptic , in other 
words, that the eccentucities and inclinations are small 

Thus simplified, the problem has been found to admit 
of solutions of considerable accuracy by methods of 
approximation * 

In the case of the system formed by the sun, eaith, 
and moon, the characteristic feature is the great distance 
of the sun, which is the disturbing body, from the other 
two bodies , in the case of the sun and two planets, the 
enormous mass of the sun as compared with the distuibmg 
planet is the important factor Hence the methods of 
treatment suitable for the two cases differ, and two sub- 
stantially distinct branches of the subject, lunar theory and 
planetary theory, have developed The problems presented 
by the motions of the satellites of Jupiter and Saturn, though 
allied to those of the lunar theory, differ m some important 
respects, and are usually treated separately 

229 As we have seen, Newton made a number of 
important steps towards the solution of his problem, but 
little was done by his successors in his own countiy On 
the Continent also progress was at first very slow The 
Pnncifia was read and admued by most of the leading 
mathematicians of the time, but its principles were not 
accepted, and Cartesianism remained the prevailing philo- 
sophy A foiward step is marked by the publication by 
the Pans Academy of Sciences in 1720 of a memoir written 
by the Chevaher de Louville (1671-1732) on the basis of 
Newton's principles^ ten years later the Academy awaicled 
a prize to an essay on the planetary motions wntten by 
John Bernomlh (1667-1748) on Cartesian principles, a 
Newtonian essay being put second. In i73 2 Maupcrtuis 
(chapter x., 221) published a treatise on the figure of the 

* The arithmetical processes of working out, figuie by figure, a 
non-terminating decimal or a square root are simple cases of successive 

$$ 229, 230] Development of Gravitational Astronomy 291 

earth on Newtonian lines, and the appearance six years later 
of Voltaire's extremely readable Ailments de la Philosofhie de 
Newton had a great effect in popularising the new ideas 
The last official recognition of Cartesianism m France 
seems to have been m 1740, when the prize offered by the 
Academy for an essay on the tides was shared between 
a Cartesian and three eminent Newtonians ( 230). 

The rapid development of gravitational astronomy that 
ensued between this time and the beginning of the 
1 9th century was almost entirely the work of five great 
Continental mathematicians, Euler, Clairaut, D'Alembert, 
Lagrange, and Laplace, of whom the eldest was born in 
1707 and the youngest died m 1827, within a month of the 
centenary of Newton's death. Euler was a Swiss, Lagrange 
was of Italian birth but French by extraction and to a great 
extent by adoption, and the other three were entirely 
French Fiance therefore during nearly the whole of the 
1 8th century reigned supreme in gravitational astronomy, 
and has not lost her supremacy even to-day, though during 
the present centuiy America, England, Germany, Italy, and 
other countues have all made substantial contributions to 
the subject 

It is convenient to consider first the work of the three 
first-named astronomers, and to treat latei Lagrange and 
Laplace, who carried gravitational astronomy to a decidedly 
higher stage of development than their predecessois 

230 Leonhard Euler was born at Basle m 1707, 14 years 
later than Biadley and six years earlier than Lacaille He 
was the son of a Protestant minister who had studied 
mathematics under James Bernouilh (1654-1705), the first of 
a famous family of mathematicians Leonhard Euler him- 
self was a favourite pupil of John Bernouilh (the younger 
brothei of James), and was an intimate friend of his two 
sons, one of whom, Daniel (1700-1782), was not only a dis- 
tinguished mathematician like his fathei and uncle, but was 
also the first important Newtonian outside Great Britain 
Like so many other astronomeis, Euler began by studying 
theology, but was induced both by his natural tastes and 
by the influence of the Bernouilhs to turn his attention to 
mathematics Thiough the influence of Daniel Bernouilh, 
who had recently been appointed to a professorship at 

292 A Short History of Astronomy CCn. XI 

St Petersburg, Euler received and accepted an invitation 
to join the newly created Academy of Sciences thcic (1727). 
This first appointment earned with it a stipend, and the 
duties were the general promotion of science , subsequently 
Euler undertook more definite professorial work, but most 
of his energy during the whole of his careei was 
devoted to writing mathematical papers, the majority of 
which were published by the St Petersbuig Academy 
Though he took no part in politics, Russian autocracy 
appears to have been oppiessive to him, ieaie<las he had 
been among Swiss and Protestant surioimdnigs ; and m 
1741 he accepted an invitation from Frederick the Great, 
a despot of a less pronounced type, to come to Beilm, and 
assist in reorganising the Academy of Sciences theie. ^ On 
being reproached one day by the Queen foi his taciturn 
and melancholy demeanour, he justified his silence on the 
ground that he had just come from a country where speech 
was liable to lead to hanging;* but notwithstanding this 
frank criticism he remained on good terms with the kussuui 
court, and continued to draw his stipend as a member 
of the St. Petersburg Academy and to contribute to its 
Transactions Moreover, after 25 years spent at Berlin, he 
accepted a pressing invitation from the Empress Catherine II. 
and returned to Russia (1766). 

He had lost the use of one eye in 1735, a disaster which 
called from him the remark that he would henoefoiward 
have less to distract him from his mathematics ; the second 
eye went soon after his return to Russia, and with the 
exception of a short time during which an operation restored 
the partial use of one eye he lemamed blind till the end 
of his life. But this disability made little difference to his 
astounding scientific activity , and it was only after nearly 
17 years of blindness that as a result of a fit of apoplexy 
"he ceased to live and to calculate" (1783)* 

Euler was probably the most versatile as well as the most 
prolific of mathematicians of all time. Theie is scarcely 
any branch of modern analysis to which he was not a large 
contributor, and his extraordinary powers of devising and 
applying methods of calculation were employed by him 
with great success m each of the existing branches of applied 
* "C'est que je viens d'un pays oil, quaiid on park, on eat pcttdu." 

231] Euler and Clairaut 293 

mathematics , problems of abstract dynamics, of optics, of 
the motion of fluids, and of astronomy were all m turn 
subjected to his analysis and solved The extent of his 
writings is shewn by the fact that, in addition to several 
books, he wrote about 800 papers on mathematical and 
physical subjects } it is estimated that a complete edition 
of his works would occupy 25 quarto volumes of about 
600 pages each 

Euler's first contribution to astronomy was an essay on 
the tides which obtained a share of the Academy prize for 
1740 ah eady referred to, Daniel Bernoulli! and Maclaunn 
(chapter x , 196) being the other two Newtonians The 
pioblem of the tides was, however, by no means solved by 
any of the three writers 

He gave two distinct solutions of the problem of three 
bodies in a form suitable for the lunar theory, and made 
a number of extremely important and suggestive though 
incomplete contributions to planetary theory. In both 
subjects his work was so closely connected with that of 
Clairaut and D'Alembert that it is more convenient to 
discuss it m connection with theirs 

231 Alexis Claude Clairaut \ born at Paris in 1713, 
belongs to the class of precocious geniuses He read the 
Infinitesimal Calculus and Conic Sections at the age of ten, 
presented a scientific memoir to the Academy of Sciences 
before he was 13, and published a book containing some 
important contributions to geometry when he was 18, 
thereby winning his admission to the Academy 

Shortly afterwards he took part in Maupertuis' expedition 
to Lapland (chaptei x, 221), and after publishing several 
papers of minor importance produced in 1743 his classical 
woik on the figure of the earth In this he discussed in 
a far more complete form than either Newton or Maclaunn 
the form which a rotating body like the earth assumes 
under the influence of the mutual gravitation of its parts, 
certain hypotheses of a very general nature being made as 
to the variations of density m the interior , and deduced 
formulae for the changes m different latitudes of the accelera- 
tion due to gravity, which are m satisfactoiy agreement with 
the results of pendulum experiments 

Although the subject has since been more elaborately 


A Short History of Astronomy 


and more generally treated by later writers, and a good 
many additions have been made, few if any results of 
fundamental importance have been added to those con- 
tamed in Clairaut's book 

He next turned his attention to the pioblem of three 
bodies, obtained a solution suitable for the moon, and made 
some progress in planetary theory 

Halley's comet (chapter x , 200) was " due " about 

FIG. 80, The path of Halley's comet 

1758; as the time approached Clairaut took up the task 
of computing the perturbations which it would probably have 
experienced since its last appearance, owing to the influence 
of the two great planets, Jupiter and Saturn, close to both 
of which it would have passed An extremely laborious 
calculation shewed that the comet would have been retarded 
about 100 days by Saturn and about 518 days by Jupiter, 
and he accordingly announced to the Academy towards the 
end of 1758 that the comet might be expected to pass its 

232] Hatters Comet D'Alembert 295 

perihelion (the point of its orbit nearest the sun, p in fig 80) 
about April i3th of the following year, though owing to 
various defects m his calculation there might be an error of 
a month either way The comet was anxiously watched for 
by the astronomical world, and was actually discovered by 
an amateur, George Pahtzsch (1723-1788) of Saxony, on 
Christmas Day, 1758 , it passed its perihelion just a month 
and a day before the time assigned by Clairaut 

Halley's bnlhant conjecture was thus justified , a new 
member was added to the solar system, and hopes were 
raised to be afterwards amply fulfilled that m other 
cases also the motions of comets might be reduced to 
rule, and calculated according to the same principles as 
those of less eriatic bodies The superstitions attached 
to comets were of course at the same time still further 

Clairaut appears to have had great personal charm and 
to have been a conspicuous figure m Pans society Un- 
fortunately his strength was not equal to the combined 
claims of social and scientific labours, and he died in 1765 
at an age when much might still have been hoped from his 
extraordinary abilities * 

232. Jean-le-Rond UAlenibert was found in 1717 as an 
infant on the steps of the church of St Jeaivle-Rond m 
Pans, but was afterwards recognised, and to some extent 
provided for, by his father, though his home was with his 
foster-parents After receiving a fair school education, 
he studied law and medicine, but then turned his attention 
to mathematics He first attracted notice in mathematical 
circles by a paper written in 1738, and was admitted to 
the Academy of Sciences two years afterwards His earliest 
important work was the Traite de Dynamique (1743), which 
contained, among other contributions to the subject, the 
first statement of a dynamical principle which bears his 
name, and which, though in one sense only a corollary 
from Newton's Third Law of Motion, has proved to be of 
immense service m nearly all general dynamical problems, 

* Longevity has been a remarkable characteristic of the gieat 
mathematical astronomers Newton died in his 85th year , Euler, 
Lagiange, and Laplace lived to be more than 75, and D'Alemberi 
was almost 66 at his death 

296 A Short History of Astronomy [Cn xi 

astronomical or otherwise During the next few yeais he 
made a number of contributions to mathematical physics, 
as well as to the problem of three bodies , and published 
in 1749 his work on precession and nutation, already 
referred to (chapter x, 215) From this time onwaidb 
he began to give an increasing part of his energies to work 
outside mathematics For some years he collaborated 
with Diderot in producing the famous French Encyclopaedia, 
which began to appear in 1751, and exercised so gieat 
an influence on contemporary political and philosophic 
thought D'Alembert wrote the introduction, which was 
read to the Academic Franfatse* in 1754 on the occasion 
of his admission to that distinguished body, as well as a 
variet> of scientific and othei ai tides In the later pait 
of his life, which ended in 1783, he wrote little on mathe- 
matics, but published a number of books on philosophical, 
literary, and political subjects , t as secretary of the 
Academy he also wrote obituary notices (kloges) of some 
70 of its membeis He was thus, in Carlyle's words, "of 
great faculty, especially of gieat clearness and method, 
famous m Mathematics , no less so, to the wonder of some, 
in the intellectual provinces of Literature." 

D'Alembert and Clairaut were great rivals, and almost 
every work of the latter was severely cutlassed by the 
former, while Clairaut retaliated though with " much less 
zeal and vehemence The great popular leputation acquired 
by Clairaut through his work on Halley's comet appears 
to have particularly excited D'Alembert's jealousy The 
rivalry, though not a pleasant spectacle, was, however, use- 
ful in leading to the detection and subsequent improvement 
of various weak points in the woik of each In other 
respects D'Alembert's personal characteristics appear to 
have been extremely pleasant He was always a poor 
man, but nevertheless declined magnificent offers made to 
him by both Catherine II of Russia and Fredenck the 

* This body, which is primarily literary, has to be distinguished 
from the much less famous Pans Academy of Sciences, constantly 
referred to (often simply as the Academy) m this chapter and the 

tEg Melanges de Philosophie, de PHtstotre, et de LttU'tature, 
Moments de Philosophie , Sur la Destruction d&s Jiswtes, 

2 33l UAkmbert Lunar Theory 297 

Great of Prussia, and preferied to keep his independence, 
though he retained the friendship of both sovereigns and 
accepted a small pension from the latter. He lived ex- 
tremely simply, and notwithstanding his poverty was very 
generous to his foster-mother, to vanous young students, 
and to many others with whom he came into contact 

233 Euler, Clauaut, and D'Alembert all succeeded in 
obtaining independently and nearly simultaneously solutions 
of the problem of three bodies in a form suitable for lunar 
theoiy Eulei published m 1746 some rather imperfect 
Tables of the Moon, which shewed that he must have 
already obtained his solution Both Clairaut and D'Alembert 
presented to the Academy in 1747 memons containing 
their respective solutions, with applications to the moon 
as well as to some planetary pioblems In each of these 
memoirs occurred the same difficulty which Newton had 
met with the calculated motion of the moon's apogee was 
only about half the observed lesult Clairaut at first met 
this difficulty by assuming an alteration m the law of gravi- 
tation, and got a result which seemed to him satisfactory 
by assuming gravitation to vary paitly as the inverse square 
and partly as the inverse cube of the distance * Euler also 
had doubts as to the correctness of the inverse square 
Two years later, however (1749), on going through his 
original calculation again, Clairaut discoveied that certain 
terms, which had appeared unimportant at the beginning of 
the calculation and had therefore been omitted, became 
important later on. When these weie taken into account, 
the motion of the apogee as deduced from theory agreed 
veiy nearly with that observed This was the first of several 
cases m which a serious discrepancy between theory and 
obseivation has at first disciedited the law of gravitation, 
but has subsequently been explained away, and has thereby 
given a new verification of its accmacy. When Clairaut 
had announced his discovery, Euler arrived by a fresh 
calculation at substantially the same result, while D'Alembert 
by carrying the approximation further obtained one that 
was slightly more accuiate A fresh calculation of the 
motion of the moon by Clairaut won the pnze on the 
subject offered by the St. Petersburg Academy, and was 

* I e he assumed a law of attraction lepresented by /-t/r 2 + v!r 3 . 

298 A Short History of Astronomy [Cn XI 

published in 1752, with the title Theone de la Lune Two 
years later he published a set of lunar tables, and just before 
his death (1765) he brought out a revised edition of the 
Theone de la Lune in which he embodied a new set of 

D'Alembert followed his paper of 1747 by a complete 
lunar theory (with a moderately good set of tables), which, 
though substantially finished in 1751, was only published 
in 1754 as the first volume of his Recherches sur differens 
points import ans du systems, du Monde In 1756 he pub- 
lished an improved set of tables, and a few months afterwaid 
a third volume of Recherches with some fresh developments 
of the theory The second volume of his Opuscules 
Mathematiques (1762) contained another memoir on the 
subject with a third set of tables, which were a slight 
improvement on the earlier ones 

Euler's first lunar theory (Theona Motuum Lunae) was 
published in 1753, though it had been sent to the St 
Petersburg Academy a year or two earlier In an appendix * 
he points out with characteristic frankness the defects from 
which his treatment seems to him to suffer, and suggests 
a new method of dealing with the subject It was on this 
theory that Tobias Mayer based his tables, referred to in 
the preceding chapter (226) Many yeais later Euler 
devised an entirely new way of attacking the subject, and 
after some preliminary papers dealing generally with the 
method and with special paits of the problem, he woiked 
out the lunar theory in great detail, with the help of one 
of his sons and two other assistants, and published the 
whole, together with tables, m 1772. He attempted, but 
without success, to deal in this theory with the secular 
acceleration of the mean motion which Halley had detected 
(chapter x, 201) 

In any mathematical treatment of an astronomical pioblem 
some data have to be borrowed from observation, and of 
the three astronomers Clairaut seems to have been the most 
skilful in utilising observations, many of which he obtained 
from Lacaille Hence his tables represented the actual 

* This appendix is memorable as giving foi the fiist lime the 
method of variation of parameters which Lagrarige afterwaith 
developed and used with such success 

234, ass] Lunar Theory 299 

motions of the moon far more accurately than those of 
D'Alembert, and were even superior in some points to those 
based on Euler's very much more elaborate second theory , 
Clairaut's last tables were seldom in error more than j|', 
and would hence serve to determine the longitude to 
within about | Clairaut's tables were, however, nevei 
much used, since Tobias Mayer's as improved by 
Bradley were found in practice to be a good deal more 
accuiate , but Mayer borrowed so extensively from observa- 
tion that his formulae cannot be regarded as true deductions 
from gravitation in the same sense in which Clairaut's were 
Mathematically Euler's second theory is the most interest- 
ing and was of the greatest importance as a basis for later 
developments The most modern lunar theory * is in 
some sense a return to Euler's methods 

234 Newton's lunar theory may be said to have given a 
qualitative account of the lunar inequalities known by 
observation at the time when the Pnnapia was published, 
and to have indicated others which had not yet been 
observed But his attempts to explain these irregularities 
quantitatively were only partially successful 

Euler, Clairaut, and D'Alembert threw the lunar theory 
into an entirely new form by using analytical methods 
instead of geometrical , one advantage of this was that by 
the expenditure of the necessary labour calculations could 
in general be carried fuither when required and lead to a 
higher degree of accuracy The result of their more 
elaborate development was that with one exception the 
inequalities known from observation were explained with a 
considerable degree of accuracy quantitatively as well as 
qualitatively ; and thus tables, such as those of Clairaut, 
based on theory, represented the lunar motions veiy closely 
The one exception was the secular acceleration we have 
just seen that Euler failed to explain it , D'Alembert was 
equally unsuccessful, and Clairaut does not appear to have 
considered the question 

235 The chief inequalities in planetary motion which 
observation had revealed up to Newton's time were the 
forward motion of the apses of the earth's orbit and a veiy 

* That of the distinguished American astionomer Dr, G, W Hill 
(chapter xm , 286) 

300 A Short History of Astronomy CCn xi 

slow diminution in the obliquity of the ecliptic. To these 
may be added the alterations in the rates of motion of 
Jupiter and Saturn discovered by Halley (chapter x , 204) 
Newton had shewn generally that the perturbing effect of 
another planet would cause displacements in the apses 
of any planetary orbit, and an alteration m the relative 
positions of the planes in which the disturbing and disturbed 
planet moved, but he had made no detailed calculations 
Some effects of this general nature, m addition to those 
already known, were, however, indicated with more or less 
distinctness as the result of observation in various planetary 
tables published between the date of the Principta and the 
middle of the i8th centuiy 

The irregularities in the motion of the earth, shewing 
themselves as irregulauties m the apparent motion of the 
sun, and those of Jupitei and Saturn, were the most 
interesting and important of the planetary inequalities, and 
prizes for essays on one or another subject were offered 
several times by the Pans Academy 

The perturbations of the moon necessarily involved by 
the principle of action and reaction -coi responding though 
smaller perturbations of the eaith; these were discussed on 
various occasions by Clairaut and Euler, and still more 
fully by D'Alembert 

In Clairaut's paper of 1747 ( 233) he made some 
attempt to apply his solution of the problem of thiee bodies 
to the case of the sun, earth, and Saturn, which on account 
of Saturn's great distance from the sun (nearly ten times 
that of the earth) is the planetary case most like that of the 
earth, moon, and sun (cf 228) 

Ten years later he discussed m some detail the perturba- 
tions of the earth due to Venus and to the moon This 
paper was remarkable as containing the first attempt to 
estimate masses of celestial bodies by obseivation of per- 
turbations due to them Clairaut applied this method to 
the moon and to Venus, by calculating perturbations m 
the earth's motion due to their action (which necessarily 
depended on their masses), and then compaimg the results 
with Lacaille's observations of the sun. The mass of the 
moon was thus found to be about / T and that of Venus 
-j that of the earth, the first result was a considerable 

23 6] Planetary Theory 3 01 

improvement on Newton's estimate from tides (chapter ix , 
> 189), and the second, which was entirely new, previous 
:stimates having been merely conjectuial, is m tolerable 
.greement with modern measurements * It is worth 
loticmg as a good illustration of the reciprocal influence 
>f obseivation and mathematical theory that, while Clairaut 
ised Lacaille's observations for his theory, Lacaille in turn 
ised Clairaut's calculations of the perturbations of the 
>arth to improve his tables of the sun published in 1758 

Clairaut's method of solving the problem of three bodies 
/vas also applied by Joseph Jkrdme Le Francois Lalande 
'1732-1807), who is chiefly known as an admirable popu- 
'ansei of astronomy but was also an indefatigable calculator 
ind observer, to the perturbations of Mars by Jupiter, of 
Venus by the eaith, and of the earth by Mars, but with 
:>nly moderate success 

D'Alembert made some progress with the general treat- 
ment of planetary perturbations in the second volume of 
bis Recherches, and applied his methods to Jupiter and 

236 Euler earned the general theory a good deal further 
in a series of papeis beginning in 1747 He made several 
attempts to explain the irregularities of Jupiter and Saturn, 
but never succeeded in representing the observations satis- 
factorily He shewed, however, that the perturbations due to 
the other planets would cause the earth's apse line to advance 
about 13" annually, and the obliquity of the ecliptic to 
dimmish by about 48" annually, both results being in fair 
accordance both with observations and with more elaborate 
calculations made subsequently He indicated also the 
existence of various other planetary 11 regularities, which for 
the most part had not previously been observed 

In an essay to which the Academy awarded a prize 
in 1756, but which was first published in 1771, he developed 
with some completeness a method of dealing with per- 
turbations which he had indicated in his lunai theory 
of 1753 As this method, known as that of the variation 
of the elements or parameters, played a very important part 

* They give about 78 for the mass of Venus compared to that oi 
the earth 

3 02 A Short History of Astronomy [Cn XL 

m subsequent researches, it may be worth while to attempt 
to give a sketch of it 

If perturbations are ignored, a planet can be regarded as 
moving in an ellipse with the sun m one focus The size and 
shape of the ellipse can be defined by the length of its axis 
and by the eccentricity ; the plane in which the ellipse is 
situated is determined by the position of the line, called the 
line of nodes, m which it cuts a fixed plane, usually taken 
to be the ecliptic, and by the inclination of the two planes 
When these four quantities are fixed, the ellipse may still 
turn about its focus in its own plane, but if the direction 
of the apse line is also fixed the ellipse is completely 
determined If, further, the position of the planet m its 
ellipse at any one time is known, the motion is completely 
determined and its position at any other time can be 
calculated, There are thus six quantities known as elements 
which completely determine the motion of a planet not 
subject to perturbation. 

When perturbations are taken into account, the path 
described by a planet m any one revolution is no longei 
an ellipse, though it differs very slightly from one , while in 
the case of the moon the deviations are a good deal greatei 
But if the motions of a planet at two widely different 
epochs are compared, though on each occasion the path 
described is \ery nearly an ellipse, the ellipses diffei m 
some respects For example, between the time of Ptolemy 
(A D 150) and that of Euler the direction of the apse line 
of the earth's orbit altered by about 5, and some of the 
other elements also varied slightly Hence m dealing with 
the motion of a planet through a long penod of time it is 
convenient to introduce the idea of an elliptic path which 
is gradually changing its position and possibly also its size 
and shape. One consequence is that the actual path 
described m the couise of a considerable number of 
revolutions is a curve no longer bearing much lesemblance 
to an ellipse If, foi example, the apse line turns round 
uniformly while the other elements remain unchanged the 
path described is like that shewn in the figure 

Euler extended this idea so as to represent any pei- 
turbation of a planet, whether experienced in the course 
of one revolution or in a longer time, by means of changes 

236] Variation of the Elements 303 

in an elliptic orbit For wherever a planet may be and 
whatever (within certain limits *) be its speed or direction 
of motion some ellipse can be found, having the sun m 
one focus, such that the planet can be regarded as moving 
in it for a short time Hence as the planet describes a 
perturbed orbit it can be regarded as moving at any instant 

FIG 8 1 A varying ellipse 

m an ellipse, which, however, is continually altering its 
position or other characteristics Thus the problem of 
discussing the planet's motion becomes that of determining 
the elements of the ellipse which represents its motion at 
any time Euler shewed further how, when the position 
of the peiturbmg planet was known, the corresponding 

* The orbit might be a parabola 01 hypeibola, though this does 
not occui m the case of any known planet 

304 A Short History of Astronomy [CH xi 

rates of change of the elements of the varying ellipse 
could be calculated, and made some progress towards 
deducing from these data the actual elements 3 but he 
found the mathematical difficulties too great to be over- 
come except in some of the simpler cases, and it was 
reserved for the next generation of mathematicians, notably 
Lagrange, to shew the full power of the method 

237 Joseph Louts Lagrange was born at Turin in 1736, 
when Clairaut was just starting for Lapland and D'Alembeit 
was still a child, he was descended from a French family 
three generations of which had lived in Italy He shewed 
extraordinary mathematical talent, and when still a mere 
boy was appointed professor at the Artillery School of his 
native town, his pupils being older than himself A few 
years afterwaids he was the chief mover in the foundation 
of a scientific society, afterwards the Turin Academy of 
Sciences, which published in 1759 its first volume of 
Transactions, containing several mathematical articles by 
Lagrange, which had been written during the last few 
years One of these* so impiessed Euler, who had made 
a special study of the subject dealt with, that he at once 
obtained for Lagrange the honour of admission to the 
Berlin Academy 

In 1764 Lagrange won the prize offered by the Pans 
Academy for an essay* on the hbration of the moon In 
this essay he not only gave the first satisfactory, though 
still incomplete, discussion of the librations (chapter vi , 
133) of the moon due to the non-spherical forms of both 
the earth and moon, but also introduced an extremely 
general method of treating dynamical problems,! which 
is the basis of nearly all the higher branches of dynamics 
which have been developed up to the present day 

Two years later (1766) Frederick II, at the suggestion 
of D'Alembert, asked Lagrange to succeed Euler (who 
had just returned to St Petersburg) as the head of the 
mathematical section of the Berlin Academy, giving as a 
reason that the greatest king in Europe wished to have 
the greatest mathematician m Europe at his court. 

* On the Calculus of Variations 

f The establishment of the general equations of motion by 
a combination of virtual velocities and U AUmberf s principle 


[To face p 305 

$ 237] Life of Lagrange 305 

Lagrange accepted this magnificently expressed invitation 
and spent the next 21 years at Berlin 

During this period he produced an extraordinary series 
of papers on astronomy, on general dynamics, and on a 
variety of subjects in pure mathematics Several of the 
most important of the astronomical papers were sent to 
Pans and obtained prizes offered by the Academy, most 
of the other papers about 60 in all were published by 
the Berlin Academy During this period he wrote also 
his great Mecanique Analytique^ one of the most beautiful 
of all mathematical books, in which he developed fully 
the general dynamical ideas contained in the earlier paper 
on hbration Curiously enough he had great difficulty in 
finding a publisher for his masterpiece, and it only appeared 
in 1788 in Pans. A year earlier he had left Berlin in 
consequence of the death of Frederick, and accepted an 
invitation from Louis XVI to join the Pans Academy 
About this time he suffered from one of the fits of melan- 
choly with which he was periodically seized and which are 
generally supposed to have been due to overwork during 
his career at Turin It is said that he never looked at 
the Mecantque Analytique for two yeais after its publication, 
and spent most of the time over chemistry and other 
branches of natural science as well as in non-scientific 
pursuits In 1790 he was made president of the Com- 
mission appointed to draw up a new system of weights 
and measures, which resulted in the establishment of the 
metric system , and the scientific work connected with this 
undertaking gradually lestored his interest m mathematics 
and astronomy He always avoided politics, and passed 
through the Revolution unmjuied, unlike his friend 
Lavoisier the great chemist and Bailly the histonan of 
astronomy, both of whom were guillotined during the Terror 
He was in fact held in great honour by the various govern- 
ments which ruled France up to the time of his death , 
in 1793 he was specially exempted from a decree of banish- 
ment directed against all foreigners , subsequently he was 
made professor of mathematics, first at the Ecole Normale 
(1795), and then at the 6cole Polylechmque (1797)* the 
last appointment being retained till his death in 1813 
During this period of his life he published, m addition 


306 A Short History of Astronomy [Cn XI 

to a large number of papeis on astionomy and mathematics, 
three important books on pure mathematics,* and at the 
time of his death had not quite finished a second edition 
of the Mtcanique Analytique^ the second volume appearing 

238 Pierre Simon Laplace^ the son of a small farmer, 
was born at Beaumont in Noimandy in 1749, being thus 
13 years younger than his great rival Lagrange Thanks 
to the help of well-to-do neighbours, he was first a pupil 
and afterwards a teacher at the Military School of his 
native town When he was 18 he went to Pans with a 
letter of introduction to D'Alembert, and, when no notice 
was taken of it, wrote him a letter on the principles of 
mechanics which impressed D'Alembert so much that he 
at once took interest in the young mathematician and 
procured him an appointment at the Military School at 
Pans From this time onwards Laplace lived continuously 
at Pans, holding various official positions. His first paper 
(on pure mathematics) was published in the Transactions 
of the Turin Academy for the years 1766-69, and from this 
time to the end of his life he produced an uninterrupted 
series of papers and books on astronomy and allied de- 
partments of mathematics 

Laplace's work on astronomy was to a great extent 
incorporated in his Mecanique Celeste, the five volumes 
of which appeared at intervals between 1799 an< ^ I ^ 2 5 
In this great treatise he aimed at summing up all that had 
been done in developing gravitational astronomy since the 
time of Newton. The only other astronomical book which 
he published was the Exposition du Systime du Monde 
(1796), one of the most perfect and chaimmgly written 
popular treatises on astronomy ever published, m which 
the great mathematician nevei uses either an algebraical 
formula or a geometrical diagram He published also m 
1812 an elaborate treatise on the theory of probability or 
chance, t on which nearly all later developments of the 
subject have been based, and m 1819 a more popular 
Essai Philosophique on the same subject 

, * Theone des Foncttons Analytiques (1797), Resolution dcs 
Equations Numettques (1798), Lefons sur k Calculates Foncttons 
( J 8o5) f Theone Analytiqw des Probabilite* 

I to l(Hi f) 407 

$ 238] Life of Laplace 307 

Laplace's personality seems to have been less attractive 
than that of Lagrange. He was vain of his reputation as 
a mathematician and not always generous to rival dis- 
coverers To Lagrange, however, he was always friendly, 
and he was also kind in helping young mathematicians of 
piomise While he was perfectly honest and courageous 
in upholding his scientific and philosophical opinions, his 
politics bore an undoubted resemblance to those of the 
Vicar of Bray, and were professed by him with great 
success He was appointed a member of the Commission 
foi Weights and Measures, and afterwaids of the Bureau des 
Longitudes, and was made professor at the Ecole Normale 
when it was founded When Napoleon became Fust 
Consul, Laplace asked for and obtained the post of Home 
Secietary, but fortunately for science was considered 
quite incompetent, and had to retire after six weeks 
(1799)*; as a compensation he was made a member of 
the newly created Senate The third volume of the 
Mecamque Celeste, published in 1802, contained a dedication 
to the "Heroic Pacificator of Europe," at whose hand he 
subsequently received various other distinctions, and by whom 
he was created a Count when the Empire was formed On 
the restoration of the Bourbons m 1814 he tendered his 
services to them, and was subsequently made a Marquis 
In 1 8 1 6 he also received a very unusual honour for a 
mathematician (shared, however, by D'Alembert) by being 
elected one of the Forty " Immortals " of the Acadbnie 
Franfaise , this distinction he seems to have owed in great 
part to the literary excellence of the Systime du Monde 

Notwithstanding these distractions he worked steadily 
at mathematics and astronomy, and even after the com- 
pletion of the Mecanigue Celeste wiote a supplement to it 
which was published after his death (1827) 

His last words, " Ce que nous connaissons est peu de chose^ 
ce que nous ignorons est immense? coming as they did from 
one who had added so much to knowledge, shew his 
character m a pleasanter aspect than it sometimes pre- 
sented during his career 

* The fact that the post was then given by Napoleon to his brother 
Lucien suggests some doubts as to the unprejudiced character of 
the verdict of incompetence pronounced by Napoleon against Laplace 

38 -A Short History of Astronomy [CH xi 

239 With the exception of Lagrange's paper on libration, 
nearly all his and Laplace's important contributions to 
astronomy were made when Clauaut's and D'Alembert's 
work was nearly finished, though Euler's activity con- 
tinued for nearly 20 years more Lagrange, howevei, 
survived him by 30 yeais and Laplace by more than 40, and 
together they carried astronomical science to a far higher 
stage of development than their three predecessors 

240 To the lunar theory Lagrange contributed com- 
paratively little except general methods, applicable to this 
as to other problems of astionomy , but Laplace devoted 
great attention to it Of his special discoveries in the 
subject the most notable was his explanation of the secular 
acceleration of the moon's mean motion (chapter x , 201), 
which had puzzled so many astronomers Lagrange had 
attempted to explain it (1774), and had failed so com- 
pletely that he was inclined to discredit the early observa- 
tions on which the existence of the phenomenon was 
based Laplace, after trying ordinary methods without 
success, attempted to explain it by supposing that gravita- 
tion was an effect not transmitted instantaneously, but 
that, like light, it took time to travel from the attracting 
body to the attracted one, but this also failed Finally 
he traced it (1787) to an indirect planetary effect For, as it 
happens, certain perturbations which the moon experiences 
owing to the action of the sun depend among other 
things on the eccentricity of the earth's orbit , this is one 
of the elements ( 236) which is being altered by the 
action of the planets, and has for many centuries been veiy 
slowly decreasing, the perturbation in question is there- 
fore being very slightly altered, and the moon's average 
rate of motion is m consequence very slowly increasing, or 
the length of the month decreasing The whole effect is 
excessively minute, and only becomes perceptible in the 
course of a long time Laplace's calculation shewed that 
the moon would, m the course of a century, or in about 
1,300 complete revolutions, gam about 10" (more exactly 
io"'2) owing to this cause, so that her place m the sky 
would differ by that amount from what it would be if this 
disturbing cause did not exist , m two centuries the angle 
gained would be 40", m three centuries 90", and so on 

239241] Lunar Theory 309 

This may be otherwise expressed by saying that the length 
of the month diminishes by about one-thirtieth of a second 
m the course of a century Moreover, as Laplace shewed 
( 2 4S)j ^e eccentncity of the earth's orbit will not go on 
diminishing indefinitely, but after an immense period to be 
reckoned m thousands of years will begin to increase, and 
the moon's motion will again become slower in consequence. 

Laplace's result agreed almost exactly with that indicated 
by observation , and thus the last known discrepancy of 
importance m the solar system between theory and observa- 
tion appeared to be explained away 3 and by a curious 
coincidence this was effected just a hundied years after the 
publication of the Pnnapia 

Many years afterwards, however, Laplace's explanation 
was shewn to be far less complete than it appeared at the 
time (chapter xin , 287) 

The same investigation revealed to Laplace the existence 
of alterations of a similar character, and due to the same 
cause,' of other elements in the moon's orbit, which, though 
not pieviously noticed, were found to be indicated by 
ancient eclipse observations 

241 The third volume of the M'ecamque C'eleste con- 
tains a general treatment of the lunar theory, based on a 
method entirely different from any that had been employed 
before, and worked out in great detail " My object," says 
Laplace, " m this book is to exhibit in the one law of 
univeisal gravitation the souice of all the inequalities of 
the motion of the moon, and then to employ this law as 
a means of discovery, to perfect the theory of this motion 
and to deduce from it several important elements m the 
system of the moon " Laplace himself calculated no lunar 
tables, but the Viennese astronomer John Tobias Burg 
(1766-1834) made considerable use of his foimulae, 
together with an immense number of Greenwich obseiva- 
tions, for the construction of lunar tables, which were sent 
to the Institute of France in 1801 (before the publication 
of Laplace's complete lunar theory), and published in a 
slightly amended form in 1806 A few years later (1812) 
John Charles Burckhardt (1773-1825), a German who had 
settled in Pans and worked under Laplace and Lalande, 
produced a new set of tables based directly on the formulae 

3io A Short History of Astronomy [CH XI 

of the Mecamque Celeste These were generally accepted 
in lieu of Burg's, which had been in their turn an im- 
provement on Mason's and Mayer's 

Later work on lunar theory may conveniently be regarded 
as belonging to a new period of astronomy (chapter XIIL, 

242 Observation had shewn the existence of inequali- 
ties in the planetary and lunar motions which seemed to 
belong to two different classes On the one hand were 
inequalities, such as most of those of the moon, which went 
through their cycle of changes in a single revolution or a 
few revolutions of the disturbing body , and on the other 
such inequalities as the secular acceleration of the moon's 
mean motion or the motion of the earth's apses, in which 
a continuous disturbance was observed always acting in the 
same direction, and shewing no signs of going through a 
periodic cycle of changes 

The mathematical treatment of perturbations soon shewed 
the desirability of adopting different methods of treatment 
for two classes of inequalities, which corresponded roughly, 
though not exactly, to those just mentioned, and to which 
the names of periodic and secular gradually came to be 
attached The distinction plays a considerable part in 
Euler's work ( 236), but it was Lagrange who first 
recognised its full importance, particularly for planetaiy 
theory, and who made a special study of seculai inequalities 

When the perturbations of one planet by anothei aie 
being studied, it becomes necessary to obtain a mathematical 
expression for the disturbing force which the second planet 
exerts This expression depends in general both on the 
elements of the two orbits, and on the positions of the 
planets at the time considered It can, howevei, be divided 
up into two parts, one of which depends on the positions of the 
planets (as well as on the elements), while the other depends 
only on the elements of the two orbits, and is independent of 
the positions in their paths which the planets may happen 
to be occupying at the time Since the positions of planets 
in their orbits change rapidly, the former part of the 
disturbing force changes rapidly, and produces m general, 
at short intervals of time, effects in opposite directions, fiist, 
for example, accelerating and then retarding the motion of 

24 2] Periodic and Secular Inequalities 311 

the disturbed planet , and the corresponding inequalities of 
motion are the periodic inequalities, which for the most part 
go through a complete cycle of changes in the course of a 
few revolutions of the planets, or even more rapidly The 
other part of the disturbing force remains nearly unchanged 
for a considerable period, and gives rise to changes in the 
elements which, though m general very small, remain for a 
long time without sensible alteration, and therefore continu- 
ally accumulate, becoming considerable with the lapse of 
time these are the secular inequalities 

Speaking generally, we may say that the periodical 
inequalities are temporary and the seculai inequalities 
permanent in their effects, or as Sir John Herschel 
expresses it 

" The secular inequalities are, in fact, nothing but what remains 
after the mutual destruction of a much larger amount (as it very 
often is) of periodical But these are in their nature transient and 
temporary , they disappear m short periods, and leave no trace 
The planet is temporarily withdrawn from its orbit (its slowly 
varying orbit), but forthwith returns to it, to deviate presently as 
much the other way, while the varied orbit accommodates and 
adjusts itself to the average of these excursions on either side 
of it " * 

" Tempoiary " and " short" aie, however, relative terms 
Some periodical inequalities, notably m the case of the 
moon, have periods of only a few days, and the majority 
which are of impoitance extend only over a few years , but 
some are known which last for centuries or even thousands 
of years, and can often be treated as secular when we only 
want to consider an interval of a few years On the other 
hand, most of the known secular inequalities are not really 
permanent, but fluctuate like the periodical ones, though 
only m the course of immense periods of time to be reckoned 
usually by tens of thousands of years 

One distinction between the lunar and planetary theories 
is that m the former periodic inequalities are comparatively 
large and, especially for practical purposes such as computing 
the position of the moon a few months hence, of great 

* Outlines of Astronomy, 656 

3 * 2 A Short History of Astronomy [Cn Xl 

importance , wheieas the periodic inequalities of the planets 
are generally small and the secular inequalities are the most 

The method of treating the elements of the elliptic orbits 
as variable is specially suitable for secular inequalities , but 
for periodic inequalities it is generally better to treat the 
body as being disturbed from an elliptic path, and to study 
these deviations 

" The simplest way of regarding these various perturbations 
consists m imagining a planet moving m accordance with the laws 
of elliptic motion, on an ellipse the elements of which vary by 
insensible degrees, and to conceive at the same time that the 
true planet oscillates round this fictitious planet m a very small 
orbit the nature of which depends on its periodic perturbations "* 

The former method, due as we have seen in great measure 
to Euler, was perfected and very generally used by Lagrange, 
and often bears his name 

243 It was at first naturally supposed that the slow 
alteration in the rates of the motions of Jupiter and Saturn 
( 2 35> 2 3 6 > and chapter x , 204) was a secular inequality , 
Lagrange in 1766 made an attempt to explain it on this 
basis which, though still unsuccessful, represented the 
observations better than Euler's work Laplace m his first 
paper on secular inequalities (1773) found by the use of 
a more complete analysis that the secular alteiations in 
the rates of motions of Jupiter and Saturn appeared to 
vanish entirely, and attempted to explain the motions by the 
hypothesis, so often used by astronomers when m difficulties, 
that a comet had been the cause 

In 1773 John Henry Lambert (1728-1777) discovered 
from a study of observations that, whereas Halley had found 
Saturn to be moving more slowly than m ancient times, it 
was now moving faster than m Halley's time a conclusion 
which pointed to a fluctuating or periodic cause of some 

Finally in 1784 Laplace arrived at the true explanation 
Lagrange had observed in 1776 that if the times of revo- 
lution of two planets are exactly proportional to two whole 

* Laplace, Systems du Monde 

243, 244] L n $ Inequalities 3 T 3 

numbers, then part of the periodic disturbing force produces 
a secular change in their motions, acting continually in the 
same direction,, though he pointed out that such a case 
did not occur in the solar system If moieover the times 
of revolution are nearly proportional to two whole numbers 
(neither of which is very laige), then part of the periodic 
disturbing force produces an irregularity that is not strictly 
secular, but has a very long period ; and a disturbing force 
so small as to be capable of being ordinarily overlooked 
may, if it is of this kind, be capable of producing a con- 
siderable effect * Now Jupiter and Saturn revolve round 
the sun in about 4,333 days and 10,759 days respectively , five 
times the former number is 21,665, and twice the latter is 
21,518, which is very little less Consequently the exceptional 
case occurs , and on working it out Laplace found an 
appreciable inequality with a period of about 900 years, 
which explained the observations satisfactory 

The inequalities of this class, of which several others have 
been discoveied, are known as long inequalities, and may 
be regarded as connecting links between secular inequalities 
and periodical inequalities of the usual kind 

244 The discovery that the observed inequality of 
Jupiter and Saturn was not secular may be regarded as 
the first step in a remarkable series of investigations on 
secular inequalities carried out by Lagiange and Laplace, 
for the most part between 1773 an d 1784, leading to some 
of the most interesting and general results in the whole of 
gravitational astronomy. The two astronomeis, though 
living lespectively in Berlin and Pans, were in constant 

* If , n' are the mean motions of the two planets, the expression 


for the disturbing force contains terms of the type = (n p& n r p') t, 

whcie/>,y are integers, and the coefficient is of the order p ^^ p' 
in the eccentricities and inclinations If now p and p' are such 
that np r^ n' p' is small, the corresponding inequality has a period 
2 TT/ (npr^n' p'\ and though its coefficient is of order/ r^p', it 
has the small factoi np /-w n' p' (or its square) in the denominator and 
may therefore be considerable In the case of Jupiter and Saturn, 
for example, n = 109,257 in seconds of arc per annum, n' = 43,996, 
5 n' 2 n = 1,466 , there is therefore an inequality of the third order, 

with a period (in years) = = 900 

3*4 A Short History of Astronomy [Cn XI, 

communication, and scarcely any important advance was 
made by the one which was not at once utilised and 
developed by the other 

The central problem was that of the secular alterations 
in the elements of a planet's orbit regarded as a varying 
ellipse Three of these elements, the axis of the ellipse, 
its eccentricity, and the inclination of its plane to a fixed 
plane (usually the ecliptic), are of much greater importance 
than the other three The first two are the elements on 
which the size and shape of the orbit depend, and the first 
also determines (by Kepler's Third Law) the period of 
revolution and average rate of motion of the planet , * the 
third has an important influence on the mutual relations of 
the two planets The other three elements are chiefly of 
importance for periodical inequalities 

It should be noted moreover that the eccentricities and 
inclinations were m all cases (except those specially men- 
tioned) considered as small quantities, and thus all the 
investigations were approximate, these quantities and the 
disturbing forces themselves being treated as small 

245 The basis of the whole series of investigations was a 
long paper published by Lagrange m 1766, in which he 
explained the method of variation of elements, and gave 
formulae connecting their rates of change with the disturbing 

In his paper of 1773 Laplace found that what was true of 
Jupiter and Saturn had a more general application, and 
proved that m the case of any planet, disturbed by any 
other, the axis was not only undergoing no secular change 
at the present time, but could not have altered appieciably 
since "the time when astronomy began to be cultivated " 

In the next year Lagrange obtained an expression for the 
secular change in the inclination, valid for all time When 
this was applied to the case of Jupiter and Saturn, which on 
account of their superiority in size and great distance fiom 
the other planets could be reasonably treated as foimmg 
with the sun a separate system, it appeared that the changes 
in the inclinations would always be of a periodic nature, so 

* This statement requires some qualification when perturbations 
are taken into account But the point is not very important, and 
is too technical to be discussed 

* 24s] Stability of the Solar System 315 

that they could never pass beyond certain fixed limits, not 
differing much from the existing values The like result 
held for the system formed by the sun, Venus, the earth, 
and Mars Lagrange noticed moreover that there were 
cases, which, as he said, fortunately did not appeal to exist 
in the system of the world, in which, on the contrary, the 
inclinations might increase indefinitely The distinction 
depended on the masses of the bodies m question ; and 
although all the planetary masses were somewhat uncertain, 
and those assumed by Lagrange for Venus and Mars almost 
wholly conjectural, it did not appear that any reasonable 
alteration in the estimated masses would affect the general 
conclusion arrived at 

Two years later (1775) Laplace, much struck by the 
method which Lagrange had used, applied it to the dis- 
cussion of the secular variations of the eccentricity, and 
found that these were also of a periodic nature, so that the 
eccentricity also could not increase or decrease indefinitely 

In the next year Lagrange, in a remarkable paper of 
only 14 pages, proved that whether the eccentricities and 
inclinations were treated as small or not, and whatevei the 
masses of the planets might be, the changes in the length of 
the axis of any planetary orbit were necessarily all periodic, 
so that for all time the length of the axis could only fluctu- 
ate between certain definite limits This result was, however, 
still based on the assumption that the dist tubing forces 
could be treated as small 

Next came a series of five papers published between 1781 
and 1784 m which Lagrange summed up his earlier work, 
revised and impioved his methods, and applied them to 
periodical inequalities and to various other problems 

Lastly in 1784 Laplace, in the same paper m which he 
explained the long inequality of Jupiter and Saturn, es- 
tablished by an extiemely simple method two lemarkable 
i elation s between the eccentricities and inclinations of the 
planets, or any similai set of bodies 

The fast relation is 

If the mass of each planet be multiplied by the square root 
of the axis of its orbit and by the square of the eccentricity r , 
then the sum of these products for all the planets is invariable 
save for periodical inequalities 

3 J 6 A Short History of Astronomy [CH xi 

The second is precisely similai, save that eccentricity is 
replaced by inclination * 

The first of these propositions establishes the existence 
of what may be called a stock or fund of eccentricity shared 
by the planets of the solar system If the eccentricity of 
any one orbit increases, that of some other orbit must 
undergo a corresponding decrease Also the fund can 
never be overdrawn Moieover observation shews that the 
eccentricities of all the planetaiy orbits are small , conse- 
quently the whole fund is small, and the share owned at 
any time by any one planet must be small t Consequently 
the eccentricity of the orbit of a planet of which the mass 
and distance from the sun are considerable can nevei 
increase much, and a similar conclusion holds foi the 
inclinations of the various orbits 

One lemarkable characteristic of the solar system is 
presupposed in these two propositions , namely, that all the 
planets revolve round the sun in the same direction, which 
to an observer supposed to be on the north side of the 
orbits appears to be contrary to that in which the hands 
of a clock move If any planet moved in the opposite 
direction, the corresponding parts of the eccentricity and 
inclination funds would have to be subtracted instead of 
being added , and there would be nothing to prevent the 
fund from being ovei drawn 

A somewhat similar restriction is involved in Laplace's 
eaiher results as to the impossibility of permanent changes 
m the eccentricities, though a system might exist in which 
his result would still be true if one or more of its members 
i evolved in a different direction from the rest, but in this 
case there would have to be certain restrictions on the 
proportions of the orbits not required in the other case 

* S #mVa = c, S tarftmVa = c f , where m is the mass of any 
pianet, , <?, z are the semi-major axis, eccentricity, and inclination 
ot the orbit The equation is true as far as squares of small 
quantities, and therefore it is indifferent whether or not tarn is 
replaced as m the text by i 

f Nearly the whole of the "eccentricity fund" and of the 

inclination fund of the solar system is shared between Jupiter 

and baturn If Jupiter were to absoib the whole of each fundfthe 

eccentricity of its orbit would only be increased by about 2< per 

cent , and the inclination to the ecliptic would not be doubled 

2 4S ] Stability of the Solar System 317 

Stated briefly, the lesults established by the two astro- 
nomers were that the changes m axis, eccentricity, and 
inclination of any planetary orbit are all permanently re- 
stricted within certain definite limits The perturbations 
caused by the planets make all these quantities undergo 
fluctuations of limited extent, some of which, caused by the 
periodic disturbing forces, go through their changes in 
comparatively short periods, while others, due to secular 
forces, require vast intervals of time for their completion 

It may thus be said that the stability of the solar system 
was established, as far as regards the paiticulai astionomical 
causes taken into account 

Moreover, if we take the case of the earth, as an in- 
habited planet, any large alteration in the axis, that is m 
the average distance from the sun, would pioduce a more 
than propoitional change in the amount of heat and light 
received fiom the sun ; any great increase in the eccentricity 
would increase largely that part (at present very small) of 
our seasonal variations of heat and cold which are due to 
varying distance from the sun , while any change m position 
of the ecliptic, which was unaccompanied by a conesponding 
change of the equator, and had the effect of increasing the 
angle between the two, would largely increase the variations of 
temperature in the course of the year The stability shewn 
to exist is theiefore a guarantee against certain kinds of 
great climatic alterations which might seriously affect the 
habitabihty of the earth. 

It is perhaps just worth while to point out that the 
results established by Lagrange and Laplace were mathe- 
matical consequences, obtained by processes involving the 
neglect of certain small quantities and therefoie not perfectly 
rigorous, of certain definite hypotheses to which the actual 
conditions of the solar system bear a tolerably close re- 
semblance Apart from causes at present unforeseen, it is 
therefore not umeasonable to expect that for a very con- 
siderable period of time the motions of the actual bodies 
forming the solar system may be very neaily in accordance 
with these results , but there is no valid reason why ceitain dis- 
tuibmg causes, ignored or rejected by Laplace and Lagrange 
on account of their insignificance, should not sooner or later 
produce quite appreciable effects (cf chapter xm , 293) 

318 A Short History of Astronomy [Cn XT 

246 A few of Laplace's numerical results as to the seculai 
variations of the elements may serve to give an idea of 
the magnitudes dealt with 

The line of apses of each planet moves in the same 
direction , the most rapid motion, occurring in the case of 
Saturn, amounted to about 15" per annum, 01 rather less 
than half a degree in a century If this motion were to 
continue uniformly, the line of apses would requne no less 
than 80,000 years to perform a complete circuit and return 
to its original position The motion of the line of nodes 
(or line in which the plane of the planet's orbit meets that 
of the ecliptic) was in general found to be rather more 
rapid The annual alteration in the inclination of any orbit 
to the ecliptic in no case exceeded a fraction of a second , 
while the change of eccentncity of Saturn's orbit, which 
was considerably the largest, would, if continued foi four 
centuries, have only amounted to j-fov 

247 The theory of the secular inequalities has been 
treated at some length on account of the general nature of 
the results obtained For the purpose of predicting the 
places of the planets at moderate distances of time the 
periodical inequalities are, however, of gi eater importance 
These were also discussed very fully both by Lagrange and 
Laplace, the detailed working out in a form suitable for 
numerical calculation being largely due to the latter Fiom 
the formulae given by Laplace and collected in the M'ecanique. 
Celeste several sets of solar and planetary tables were 
calculated, which were m general found to represent closely 
the observed motions, and which superseded the earlier 
tables based on less developed theories* 

248 In addition to the lunar and planetary theones 
nearly all the minor problems of gravitational astronomy 
were rediscussed by Laplace, m many cases with the aid 
of methods due to Lagrange, and their solution was in all 
cases advanced. 

The theory of Jupiter's satellites, which with Jupiter foim 

* Of tables based on Laplace's work and published up to the time 
of his death, the chief solar ones were those of von Zach (1804) and 
Delambre (1806) ; and the chief planetary ones were those of 
Lalande (1771), of Lmdenau for Venus, Mars, and Mercury (1810-13), 
and of Bouvard for Jupiter, Saturn, and Uranus (1808 and 1821), 

246249] Planetary Theory Minor Problems 319 

a sort of miniature solar system but with seveial character- 
istic peculiarities, was fully dealt with ; the other satellites 
received a less complete discussion Some progress was 
also made with the theory of Saturn's ring by shewing that 
it could not be a uniform solid body 

Precession and nutation were treated much more com- 
pletely than by D'Alembert ; and the allied problems of 
the irregularities in the rotation of the moon and of Saturn's 
ring were also dealt with 

The figure of the eaith was considered in a much more 
general way than by Clairaut, without, however, upsetting 
the substantial accuracy of his conclusions 3 and the theory 
of the tides was entirely reconstructed and greatly improved, 
though a considerable gap between theory and observation 
still remained 

The theory of perturbations was also modified so as to 
be applicable to cornets, and from observation of a comet 
(known as Lexell's) which had appeared m 1770 and was 
found to have passed close to Jupiter m 1767 it was inferred 
that its orbit had been completely changed by the attraction 
of Jupiter, but that, on the other hand, it was incapable of 
exercising any appreciable disturbing influence on Jupiter 
or its satellites 

As, on the one hand, the complete calculation of the 
perturbations of the various bodies of the solar system 
presupposes a knowledge of their masses, so reciprocally 
if the magnitudes of these disturbances can be obtained 
from observation they can be used to determine or to 
correct the values of the several masses In this way the 
masses of Mars and of Jupiter's satellites, as well as of 
Venus ( 235), were estimated, and those of the moon and 
the other planets revised In the case of Mercury, however, 
no perturbation of any other planet by it could be satis- 
factorily observed, and except that it was known to be small 
its mass remained for a long time a matter of conjecture 
It was only some years after Laplace's death that the effect 
produced by it on a comet enabled its mass to be estimated 
(1842), and the mass is even now very uncertain 

249 By the work of the great mathematical astronomers 
of the 1 8th century, the results of which were summarised 
m the Mecanique Celeste, it was shewn to be possible to 

320 A Short History of Astronomy [CH XI 

account for the observed motions of the bodies of the solar 
system with a tolerable degree of accuracy by means of the 
law of gravitation 

Newton's problem ( 228) was therefore approximately 
solved, and the agreement between theoiy and observation 
was in most cases close enough for the practical purpose 
of predicting for a moderate time the places of the various 
celestial bodies The outstanding discrepancies between 
theory and observation weie for the most part so small as 
compared with those that had already been removed as to 
leave an almost universal conviction that they were capable 
of explanation as due to errors of observation, to want 
of exactness in calculation, or to some similar cause 

250 Outside the circle of professed astronomers and 
mathematicians Laplace is best known, not as the author of 
the Mecamque Celeste, but as the inventor of the Nebular 

This famous speculation was published (in 1796) in his 
popular book the Systime du Monde already mentioned, 
and was almost certainly independent of a somewhat similai 
but less detailed theory which had been suggested by the 
philosopher Immanuel Kant in 1755 

Laplace was struck with ceitam remarkable charactenstics 
of the solar system The seven planets known to him when 
he wrote revolved round the sun m the same direction, the 
fourteen satellites revolved round their pnmaries still in 
the same direction,* and such motions of rotation of sun, 
planets, and satellites about then axes as were known 
followed the same law There were thus some 30 or 40 
motions all in the same direction If these motions of the 
several bodies were regarded as the result of chance and 
were independent of one another, this uniformity would be 
a coincidence of a most extiaordmary character, as unlikely 
as that a coin when tossed the like number of times should 
invariably come down with the same face uppermost 

These motions of rotation and revolution were moreover 
all in planes but slightly inclined to one another , and the 

* The motion of the satellites of Uranus (chapter xn , 253, 255) 
is in the opposite direction When Laplace first published his theory 
their motion was doubtful, and he does not appear to have thought 
it worth while to notice the exception in later editions of his book 

$ 2 soJ The Nebular Hypothesis 321 

eccentricities of all the orbits were quite small, so that 
they were nearly circular. 

Comets, on the other hand, presented none of these pecu- 
liarities , their paths were very eccentric, they were inclined 
at all angles to the ecliptic, and were described m either 

Moieover there were no known bodies foimmg a con- 
necting link m these respects between comets and planets 
or satellites * 

From these remarkable coincidences Laplace inferred 
that the various bodies of the solar system must have had 
some common origin. The hypothesis which he suggested 
was that they had condensed out of a body that might 
be regarded either as the sun with a vast atmosphere filling 
the space now occupied by the solar system, or as a fluid 
mass with a more or less condensed central part or nucleus ; 
while at an earlier stage the central condensation might have 
been almost non-existent 

Observations of Herschel's (chapter xn , 259-61) had 
recently revealed the existence of many hundreds of bodies 
known as nebulae, presenting very nearly such appearances 
as might have been expected from Laplace's primitive body. 
The differences m structure which they shewed, some being 
apparently almost structuieless masses of some extremely 
diffused substance, while others shewed decided signs of 
central condensation, and others again looked like ordinary 
stars with a slight atmospheie round them, were also 
strongly suggestive of successive stages m some process 
of condensation 

Laplace's suggestion then was that the solar system had 
been formed by condensation out of a nebula ; and a 
similar explanation would apply to the fixed stais, with the 
planets (if any) which surrounded them 

He then sketched, m a somewhat imaginative way, the 
process whereby a nebula, if once endowed with a lotatoiy 
motion, might, as it condensed, throw off a series of rings, 

* This statement again has to be modified m consequence of the 
discoveries, beginning on January 1st, 1801, of the minor planets 
(chapter xin , 294), many of which have orbits that are far more 
eccentric than those of the other planets and arc inclined to the 
ecliptic at considerable angles 


322 A Short History of Astronomy [Cn Xl,$aso 

and each of these might in turn condense into a planet with 
or without satellites , and gave on this hypothesis plausible 
reasons for many of the peculiarities of the solar system 

So little is, however, known of the behaviour of a body 
like Laplace's nebula when condensing and rotating that it 
is hardly worth while to consider the details of the scheme 

That Laplace himself, who has never been accused of 
underrating the importance of his own discoveries, did not 
take the details of his hypothesis neaily as seriously as 
many of its expounders, may be inferred both from the fact 
that he only published it in a popular book, and from his 
remarkable description of it as "these conjectures on the 
formation of the stars and of the solar system, conjectures 
which I present with all the distrust (defiance) which every- 
thing which is not a result of observation or of calculation 
ought to inspire " * 

* Systeme du Monde, Book V, chapter vi. 



"Coelorum perrupit claustra " 


251 Frederick William Herschel was born at Hanover on 
November 1 5th, 1738, two years after Lagrange and nine 
years before Laplace. His father was a musician in the 
Hanoverian army, and the son, who shewed a remarkable 
aptitude for music as well as a decided taste foi knowledge 
of various sorts, entered his father's profession as a boy (i 753) 
On the breaking out of the Seven Years' War he served 
during part of a campaign, but his health being delicate his 
parents " determined to remove him from the service a 
step attended by no small difficulties," and he was ac- 
coidingly sent to England (1757), to seek his fortune as a 

After some years spent in various parts of the country, he 
moved (1766) to Bath, then one of the great centres of 
fashion in England At first oboist m Lmley's orchestra, 
then organist of the Octagon Chapel, he rapidly rose to 
a position of gieat popularity and distinction, both as a 
musician and as a music-teacher He played, conducted, 
and composed, and his pnvate pupils increased so rapidly 
that the number of lessons which he gave was at one time 
35 a week But this activity by no means exhausted 
his extiaordmary energy ; he had never lost his taste for 
study, and, according to a contemporaiy biographer, " after 
a fatiguing day of 14 or 16 hours spent m his vocation, he 
would retire at night with the greatest avidity to unbend the 
mind, if it may be so called, with a few propositions in 
Maclaunn's Fluxions, or other books of that sort " His 


324 A Short History of Astronomy CCn, Xil. 

musical studies had long ago given him an interest in 
mathematics, and it seems likely that the study of Robert 
Smith's Harmonics 'led him to the Compleat System of Optus 
of the same author, and so to an interest in the construction 
and use of telescopes The astronomy that he read soon 
gave him a desire to see for himself what the books de- 
scribed 3 first he hired a small reflecting telescope, then 
thought of buying a larger mstiument, but found that the 
price was prohibitive. Thus he was gradually led to attempt 
the construction of his own telescopes (1773) His broth ei 
Alexander, for whom he had found musical work at Hath, 
and who seems to have had considerable mechanical talent 
but none of William's perseverance, helped him m thus 
undertaking, while his devoted sister Caroline (1750-1848)3 
who had been brought over to England by William in 
1772, not only kept house, but rendered a multitude of 
minor services The operation of grinding and polishing 
the mirror for a telescope was one of the greatest delicacy, 
and at a certain stage required continuous labour for 
several hours On one occasion HerschePs hand never left 
the polishing tool for 16 hours, so that "by way of keeping 
him alive " Caroline was " obliged to feed him by putting 
the victuals by bits into his mouth," and in less extreme 
cases she helped to make the operation less tedious by 
reading aloud it is with some feeling of relief that we hear 
that on these occasions the books read were not on mathe- 
matics, optics, or astronomy, but were such as JOon 
Quixote, the Arabian Nights, and the novels of Sterne and 

252 After an immense number of failuies Heischel 
succeeded m constructing a tolerable reflecting telescope- - 
soon to be followed by others of greater size and perfection 
and with this he made his fiist recoided obseivation of 
the Orion nebula, m March 1774. 

This observation, made when he was in his 36th year 
may be conveniently regarded as the beginning of 1m 
astronomical career, though for several yeais moie music 
remained his profession, and astronomy could only be 
cultivated in such leisure time as he could find or make 
for himself; his biographers give vivid pictuies of his 
extraordinary activity during this period, and of his zeal 

S 252, 253] HerschePs Early Life 325 

m using odd fragments of time, such as intervals between 
the acts at a theatre, for his beloved telescopes 

A letter written by him in 1783 gives a good account of 
the spirit m which he was at this time carrying out his 
astronomical work 

" I determined to accept nothing on faith, but to see with my 
own eyes what others had seen before me I finally suc- 

ceeded in completing a so-called Newtonian instrument, 7 feet 
in length From this I advanced to one of 10 feet, and at last 
to one of 20, for I had fully made up my mind to carry on 
the improvement of my telescopes as far as it could possibly be 
done When I had carefully and thoroughly perfected the great 
instrument in all its parts, I made systematic use of it m my 
observations of the heavens, first forming a determination never 
to pass by any, the smallest, portion of them without due 
investigation " 

In accordance with this last resolution he executed on 
four separate occasions, beginning in 1775, each time with 
an instrument of greater power than on the preceding, a 
leview of the whole heavens, m which everything that 
appeared m any way remarkable was noticed and if neces- 
sary more carefully studied He was thus applying to 
astronomy methods comparable with those of the naturalist 
who aims at drawing up a complete list of the flora or 
fauna of a country hitherto little known 

253 In the course of the second of these reviews, made 
with a telescope of the Newtonian type, 7 feet in length, 
he made the discovery (March i3th, 1781) which gave him 
a European reputation and enabled him to abandon music 
as a profession and to devote the whole of his energies 
to science 

" In examining the small stars in the neighbourhood of 
II Geminorum I perceived one that appeared visibly larger 
than the rest , being struck with its uncommon appearance I 
compared it to H Geminorum and the small star in the quartile 
between Aunga and Gemini^ and finding it so much larger than 
either of them, I suspected it to be a comet " 

If HerscheFs suspicion had been correct the discovery 
would have been of far less interest than it actually was, 
for when the new body was further observed and attempts 
were made to calculate its path, it was found that no 

326 A Short History of Astronomy [Cn xn 

ordinary cometary orbit would in any way fit its motion, 
and within three or four months of its disco veiy it was 
recognised first by Anders Johann Lexell (1740-1784) 
as being no comet but a new planet, revolving round the 
sun in a nearly circular path, at a distance about i 9 times 
that of the earth and nearly double that of Saturn 

No new planet had been discovered in historic times, and 
Herschel's achievement was therefore absolutely unique; 
even the discovery of satellites inaugurated by Galilei 
(chapter vi , 121) had come to a stop nearly a century 
before (1684), when Cassmi had detected his second pair 
of satellites of Saturn (chapter vm , 160). Hcischel 
wished to exercise the discoverer's right of christening by 
calling the new planet after his royalpation Georgium Sidus^ 
but though the name was used for some time in England, 
Continental astronomers never accepted it, and after an 
unsuccessful attempt to call the new body Herschel^ it was 
generally agreed to give a name similai to those of the 
other planets, and Uranus was proposed and accepted 

Although by this time Heischel had published two 01 
three scientific papers and was probably known to a slight 
extent in English scientific circles, the complete obscurity 
among Continental astronomers of the author of this memoi- 
able discovery is curiously illustiated by a discussion m 
the leading astronomical journal (Bode's Astronomisches 
Jahrbucti) as to the way to spell his name, Hertschel being 
perhaps the best and Mersthel the worst of seveial attempts 

254 This obscurity was naturally dissipated by the dis- 
covery of Uranus Distinguished visitors to Bath, among 
them the Astronomer Royal Maskelyne (chapter x., 219), 
sought his acquaintance ; before the end of the yeai he 
was elected a Fellow of the Royal Society, in addition to 
receiving one of its medals, and in the following spnng he 
was summoned to Court to exhibit himself, his telescopes, 
and his stars to George III and to various members of the 
royal family As the outcome of this visit he received 
from the King an appointment as royal astronomer, with 
a salary of ^200 a yeai 

With this appointment his caieer as a musician came 
to an end, and in August 1782 the brother and sister left 
Bath for good, and settled first m a dilapidated house at 


[To face p 32 

254, ass] The Discovery of Uranus Slough 327 

Datchet, then, after a few months (1785-6) spent at Clay 
Hall in Old Windsor, at Slough in a house now known 
as Observatory House and memorable in Arago's words as 
"le lieu du monde ou il a 6t6 fait le plus de decouvertes " 

255 Herschel's modest salary, though it would have 
sufficed for his own and his sister's peisonal wants, was of 
course insufficient to meet the various expenses involved m 
making and mounting telescopes The skill which he had 
now acquired in the art was, however, such that his telescopes 
were far superior to any others which were available, and, 
as his methods were his own, there was a consideiable 
demand for instruments made by him Even while at 
Bath he had made and sold a number, and foi years after 
moving to the neighbourhood of Windsor he derived a 
consideiable income from this source, the royal family and 
a number of distinguished British and foreign astronomers 
being among his customers 

The necessity for employing his valuable time in this 
way fortunately came to an end in 1788, when he married 
a lady with a considerable fortune ; Caroline lived hence- 
forward in lodgings close to her bi other, but worked for 
him with unabated zeal 

By the end of 1783 Herschel had finished a telescope 
20 feet m length with a great mirror 18 inches m diameter, 
and with this instrument most of his best work was done ; 
but he was not yet satisfied that he had reached the limit 
of what was possible During the last winter at Bath he 
and his bi other had spent a great deal of labour in an 
unsuccessful attempt to construct a 3o-foot telescope , the 
discovery of Uianus and its consequences prevented the 
renewal of the attempt for some time, but in 1785 he began 
a 4o-foot telescope with a muror four feet m diameter, the 
expenses of which were defrayed by a special grant from 
the King While it was being made Herschel tued a new 
form of construction of reflecting telescopes, suggested by 
Lemaire in 1732 but never used, by which a considerable 
gam of brilliancy was effected, but at the cost of some loss 
of distinctness This Herschelian or front-view construc- 
tion, as it is called, was first tried with the 2o-foot, and led 
to tbe discovery (January nth, 1787) of two satellites of 
Uranus, Oberon and Titama , it was henceforward regularly 

328 A Short History of Astronomy [Cn XI I 

employed After several mishaps the 4o-foot telescope 
(fig 82) was successfully constructed. On the first evening 
on which it was employed (August 28th, 1 789) a sixth satellite 
of Saturn (Enceladus) was detected, and on September iyth a 
much fainter seventh satellite (Mimas] Both satellites were 
found to be nearer to the planet than any of the five hitheito 
discovered, Mimas being the nearer of the two (cf fig 91) 

Although for the detection of extremely faint objects such 
as these satellites the great telescope was unequalled, foi 
many kinds of work and for all but the very clcaicst 
evenings a smaller instrument was as good, and being less 
unwieldy was much moie used The mirror of the great 
telescope deteriorated to some extent, and after 1811, 
Herschel's hand being then no longer equal to the delicate 
task of repolishing it, the telescope ceased to be used 
though it was left standing till 1839, when it was dismounted 
and closed up 

256 Fiom the time of his establishment at Slough till 
he began to lose his powers through old age the story of 
Herschel's life is little but a record of the woik he did It 
was his practice to employ m observing the whole of 
every suitable night , his daylight hours were devoted to 
interpreting his observations and to wilting the papers in 
which he embodied his results His sister was nearly 
always present as his assistant when he was observing, and 
also did a good deal of cataloguing, indexing, and similai 
work for him After leaving Bath she also did some 
observing on her own account, though only when hei 
brother was away or for some other reason did not require 
her services , she specialised on comets, and succeeded from 
first to last in discovering no less than eight To form any 
adequate idea of the discomfort and even danger attending 
the nights spent in observing, it is necessary to realise that 
the great telescopes used were erected m the open air, 
that for both the Newtonian and Herschelian forms of 
reflectors the observei has to be near the uppei end of the 
telescope, and therefore at a considerable height above 
the ground In the 40-foot, for example, ladders 50 feet 
in length were used to reach the platform on which the 
observer was stationed. Moreover from the nature of 
the case satisfactory observations could not be taken in the 


Life at Slough 


presence either of the moon or of artificial light It is 
not therefore surprising that Caiolme Herschel's journals 
contain a good many expressions of anxiety for her brother's 

FIG 82 Hcrschel's forty-foot telescope 

welfare on these occasions, and it is perhaps rather a matter 
of wonder that so few serious accidents occurred. 
Jn addition to doing his real work Heischd had to 

33 A Short History of Astronomy [CH xn 

receive a large number of visitors who came to Slough out 
of curiosity or genuine scientific interest to see the great 
man and his wonderful telescopes In 1801 he went to 
Pans, where he made Laplace's acquaintance and also saw 
Napoleon, whose astronomical knowledge he rated much 
below that of George III , while " his general air was 
something like affecting to know moie than he did know " 

In the spring of 1807 he had a serious illness , and from 
that time onwards his health remained delicate, and a 
larger proportion of his time was in consequence given to 
indoor work The last of the great series of papers 
presented to the Royal Society appeared m 1818, when he 
was almost 80, though three years later he communicated 
a list of double stars to the newly founded Royal Astro- 
nomical Society His last observation was taken almost at 
the same tune, and he died rather more than a yeai aftei- 
wards (August 2ist, 1822), when he was neaily 84 

He left one son, John, who became an astronomer only 
less distinguished than his father (chapter xm , 306-8) 
Caroline Herschel after her beloved brother's death leturned 
to Hanover, chiefly to be near other members of her family , 
here she executed one important piece of work by cataloguing 
in a convenient form her brother's lists of nebulae, and for 
the remaining 26 years of her long life her chief interest 
seems to have been m the prosperous astronomical career 
of her nephew John 

257 The incidental references to Herschel's woik that 
have been made m describing his career have shewn him 
chiefly as the constructor of giant telescopes far surpassing 
in power any that had hitherto been used, and as the 
diligent and careful observer of whatever could be seen 
with them in the skies Sun and moon, planets and fixed 
stars, were all passed in review, and their peculiarities noted 
and described But this merely descriptive work was m 
Herschel's eyes for the most part means to an end, for, as 
he said in 1811, "a knowledge of the construction of the 
heavens has always been the ultimate object of my 
observations " 

Astronomy had for many centuries been concerned almost 
wholly with the positions of the various heavenly bodies 
on the celestial sphere, that is with their directions, 

$257] HerscheVs Astronomical Programme 331 

Coppermcus and his successors had found that the apparent 
motions on the celestial sphere of the members of the solar 
system could only be satisfactorily explained by taking 
into account their actual motions in space, so that the 
solar system carne to be effectively regarded as consisting 
of bodies at different distances from the earth and sepaiated 
from one another by so many miles But with the fixed 
stais the case was quite different for, with the unimportant 
exception of the proper motions of a few stars (chapter x , 
203), all their known apparent motions were explicable as 
the result of the motion of the earth ; and the relative or actual 
distances of the stars scarcely entered into consideration. 
Although the belief m a real celestial sphere to which the 
stars were attached scarcely survived the onslaughts of 
Tycho Brahe and Galilei, and any astronomer of note 
m the latter part of the iyth or m the i8th century would, 
if asked, have unhesitatingly declared the stars to be at 
different distances from the earth, this was in effect a 
mere pious opinion which had no appieciable effect on 
astronomical woik 

The geometucal conception of the stars as represented 
by points on a celestial sphere was in fact sufficient for 
ordinary astronomical purposes, and the attention of great 
observing astronomers such as Flamsteed, Bradley, and 
Lacaille was directed almost entirely towards ascertaining 
the positions of these points with the utmost accuracy or 
towards obseivmg the motions of the solar system More- 
over the group of problems which Newton's work suggested 
naturally concentrated the attention of eighteenth-century 
astronomers on the solar system, though even from this 
point of view the construction of star catalogues had con- 
siderable value as providing reference points which could 
be used for fixing the positions of the members of the solar 

Almost the only exception to this general tendency 
consisted m the attempts hitherto unsuccessful to find 
the parallaxes and hence the distances of some of the 
fixed stars, a problem which, though ongmally suggested 
by the Coppermcan controversy, had been recognised as 
possessing great intrinsic interest 

Herschel therefore struck out an entirely new path when 

332 A Short History of Astronomy [CH XH 

he began to study the sidereal system per se and the 
mutual relations of its members From this point of view 
the sun, with its attendant planets, became one of an 
innumerable host of stars, which happened to have received 
a fictitious importance from the accident that we inhabited 
one member of its system 

258 A complete knowledge of the positions in space 
of the stars would of course follow from the measurement 
of the parallax (chaptei vi , 129 and chapter x , 207) of 
each The failure of such astronomers as Biadley to get the 
parallax of any one star was enough to shew the hopelessness 
of this general undertaking, and, although Heischel did make 
an attack on the parallax problem ( 263), he saw that the 
question of stellar distribution in space, if to be answeied 
at all, required some simpler if less reliable method capable 
of application on a large scale 

Accordingly he devised (1784) his method of star- 
gauging The most superficial view of the sky shews that 
the stars visible to the naked eye are very unequally dis- 
tributed on the celestial sphere, the same is true when 
the fainter stars visible in a telescope are taken into account 
If two portions of the sky of the same apparent or angular 
magnitude are compared, it may be found that the fust 
contains many times as many stars as the second. If we 
realise that the stars are not actually on a sphere but are 
scattered through space at diffeient distances from us, 
we can explain this inequality of distribution on the sky 
as due to either a real inequality of distribution m space^ 
or to a difference in the distance to which the sicleieal 
system extends in the directions in which the two sets of 
stars he The first region on the sky may coirespond to 
a region of space in which the stars are really clustered 
together, or may represent a direction in which the sidereal 
system extends to a greater distance, so that the accumula- 
tion of layer after layer of stars lying behind one another 
produces the apparent density of distribution In the same 
way, if we are standing in a wood and the wood appears 
less thick in one direction than in another, it may be 
because the trees are really more thinly planted there or 
because in that direction the edge of the wood is nearer. 
In the absence of any a priori knowledge of the actual 

$ 258] Star-gauging 333 

clustering of the stars in space, Herschel chose the former 
of these two hypotheses ; that is, he treated the apparent 
density of the stars on any particular part of the sky as 
a measure of the depth to which the sidereal systems 
extended in that direction, and interpreted from this point 
of view the results of a vast series of observations He 
used a so-foot telescope so arianged that he could see 
with it a circular portion of the sky 15' in diameter (one- 
quarter the area of the sun or full moon), turned the telescope 
to different parts of the sky, and counted the stais visible 
in each case. To avoid accidental irregularities he usually 
took the average of several neighbouring fields, and published 
in 1785 the results of gauges thus made in 683* regions, 

FIG, 83 Section of the sidereal system From Herschel's paper in 
the Philosophical Transactions. 

while he subsequently added 400 others which he did not 
think it necessary to publish Whereas m some parts of 
the sky he could see on an average only one star at a time, 
m others nearly 600 were visible, and he estimated that 
on one occasion about 116,000 stars passed through the 
field of view of his telescope m a quarter of an hour 
The general result was, as rough naked-eye observation 
suggests, that stars are most plentiful in and near the 
Milky Way and least so in the parts of the sky most remote 
from it Now the Milky Way forms on the sky an ill- 
defined band never deviating much from a great circle 
(sometimes called the galactic circle) , so that on HerschePs 
hypothesis the space occupied by the stars is shaped 
roughly like a disc or grindstone, of which according to 

* In his paper of 1817 Herschel gives the number as 863, but a 
reference to the original paper of 1785 shews that this must be a 
printer's error 

334 A Short History of Astronomy CCn XII. 

his figures the diameter is about five times the thickness 
Further, the Milky Way is during part of its length divided 
into two branches, the space between the two blanches 
being comparatively free of stars Coriespondmg to this 
subdivision there has thercfoie to be assumed a cleft in 
the " grindstone " 

This "grindstone" theoiy of the universe had been 
suggested in 1750 by Thomas Wright (1711 1786) in his 
Theory of the Universe, and again by Kant five ytvus latei ; 
but neither had attempted, like Herschel, to collect numencul 
data and to work out consistently and in detail the conse- 
quences of the fundamental hypothesis. 

That the assumption of umfoim distribution of stars in 
space could not be true m detail was evident to Hersehel 
from the beginning A stai clustei, for example, in which 
many thousands of faint stais aie collected together m a 
very small space on the sky, would have to be interpreted 
as representing a long projection or spike full of stars, 
extending far beyond the limits of the adjoining portions of 
the sideieal system, and pointing directly away from the 
position occupied by the solar system In the same way 
certain regions in the sky which aie found to be bare of 
stars would have to be regaided as tunnels through the 
stellar system That even one or two such spikes or tunnels 
should exist would be improbable enough, but as star 
clusters were known inconsiderable numbeis before Her- 
schel began his work, and weie discovered by him \\\ 
hundreds, it was impossible to explain their existence on 
this hypothesis, and it became necessary to assume that a 
star cluster occupied a region of space m winch stars were 
really closer together than elsewhere. 

Moreover further study of the anangcment of the stars, 
particularly of those in the Milky Way, led Herschel gradu- 
ally to the belief that his original assumption was a wider 
departure from the truth than he had at first supposed ; 
and m 1811, nearly 30 years after he had begun star- 
gauging, he admitted a definite change of opinion :~- 

" I must freely confess that by continuing my sweeps of the 
heavens my opinion of the arrangement oi the stars , , has 
undergone a gradual change For instance, an equal scattering 

$ * S 8] The Structure of the Sidereal System 335 

of the stars may be admitted m certain calculations , but when 
we examine the Milky Way, or the closely compressed clusters 
oi stars of which my catalogues have recorded so many instances 
this supposed equality of scattering must be given up." ' 

The method of star-gauging was intended primarily to give 

information as to the limits of the sidereal system or the 

visible portions of it Side by side with this method Herschel 
constantly made use of the brightness of a star as a probable 
test of nearness If two stars give out actually the same 
amount of light, then that one which is nearer to us will 
appear the brighter , and on the assumption that no light 
is absorbed or stopped m its passage through space, the 
apparent brightness of the two stars will be inversely as the 
square of their respective distances Hence, if we receive 
nine times as much light from one star as from another, 
and if it is assumed that this difference is merely due to 
difference of distance, then the first star is thiee times as 
far off as the second, and so on 

That the stars as a whole give out the same amount of 
light, so that the difference m their apparent brightness is 
due to distance only, is an assumption of the same general 
character as that of equal distribution There must neces- 
sarily be many exceptions, but, m default of more exact 
knowledge, it affords a rough-and-ready method of estimating 
with some degree of probability relative distances of stars 

To apply this method it was necessary to have some 
means of comparing the amount of light received from 
different stars This Herschel effected by using telescopes of 
different sizes If the same star is observed with two reflect- 
ing telescopes of the same construction but of different 
sizes, then the light transmitted by the telescope to the eye 
is proportional to the area of the mirror which collects the 
light, and hence to the square of the diameter of the mirror 
Hence the apparent brightness of a stai as viewed through 
a telescope is proportional on the one hand to the inverse 
square of the distance, and on the other to the square of 
the diameter of the mirror of the telescope , hence the 
distance of the star is, as it were, exactly counterbalanced by 
the diameter of the mirror of the telescope For example, 
if one stai viewed m a telescope with an eight-inch mirror 
and another viewed m the great telescope with a four-foot 

336 A Short History of Astronomy [Cn XII 

mirror appear equally bright, then the second star is on 
the fundamental assumption six times as fai off 

In the same way the size of the minor necessary to make 
a star just visible was used by Heischel as a measure of 
the distance of the star, and it was in this sense that he 
constantly referred to the " space-penetrating power " of his 
telescope On this assumption he estimated the faintest 
stars visible to the naked eye to be about twelve times as 
remote as one of the brightest stars, such as Arcturus, while 
Arcturus if removed to 900 tunes its present distance would 
just be visible in the 20-foot telescope which he commonly 
used, and the 4o-foot would penetrate about twice as far 
into space. 

Towards the end of his life (1817) Herschel made an 
attempt to compare statistically his two assumptions of 
uniform distribution in space and of uniform actual bright- 
ness, by counting the number of stars of each degree of 
apparent brightness and comparing them with the numbers 
that would result from uniform distribution in space if 
apparent brightness depended only on distance The 
inquiry only extended as far as stars visible to the naked 
eye and to the brighter of the telescopic stars, and indicated 
the existence of an excess of the fainter stars of these 
classes, so that either these stars are more closely packed 
in space than the brighter ones, or they are in reality smaller 
or less luminous than the others, but no definite con- 
clusions as to the arrangement of the stars were drawn. 

259 Intimately connected with the structure of the sidereal 
system was the question of the distribution and nature of 
nebulae (cf figs 100, 102, facing pp 397, 400) and star 
clusters (cf fig 104, facing p 405) When Herschel began 
his work rather more than 100 such bodies were known, 
which had been discovered for the most pait by the French 
observers Lacaille (chapter x., 223) and Charles Messier 
(1730-1817). Messier maybe said to have been a comet- 
hunter by profession, finding himself liable to mistake 
nebulae for comets, he put on record (1781) the positions 
of 103 of the former. Herschel's discoveries carried out 
much more systematically and with more powerful instru- 
mental appliances were on a far larger scale. In 1786 
he presented to the Royal Society a catalogue of 1,000 

$$ 2 S9 , 260] Nebulae and Star Clusters 337 

new nebulae and clusters, three years later a second cata- 
logue of the same extent, and in 1802 a third comprising 
500 Each nebula was carefully observed, its general 
appearance as well as its position being noted and described 
and to obtain a general idea of the distribution of nebulae 
on the sky the positions were marked on a star map 
Ihe differences in brightness and in apparent structure led 
to a division into eight classes , and at quite an eaily stage 
of his work (1786) he gave a graphic account of the extra- 
ordinary varieties in form which he had noted 

" I have seen double and treble nebulae, variously arranged 
large ones with small, seeming attendants, narrow but much 
extended, lucid nebulae or bright dashes , some of the shape 
ot a fan, resembling an electric brush, issuing from a lucid 
point, others of the cometic shape, with a seeming nucleus 
in the center, or like cloudy stars, surrounded with a nebulous 
atmosphere , a different sort again contain a nebulosity of the 
milky kind, like that wonderful inexplicable phenomenon about 
Orioms, while others shine with a fainter mottled kind 
of light, which denotes their being resolvable into stars " 

260 But much the most interesting problem m classifica- 
tion was that of the relation between nebulae and star clusters 
The Pleiades, for example, appear to ordinary eyes as a 
group of six stars close together, but many short-sighted 
people only see there a portion of the sky which is a little 
brighter than the adjacent region, again, the nebulous 
patch of light, as it appears to the ordinary eye, known as 
Praesepe (in the Crab), is resolved by the smallest telescope 
into a cluster of faint stars In the same way there are 
other objects which in a small telescope appear cloudy or 
nebulous, but viewed in an instrument of greater power are 
seen to be star clusters In particular Herschel found that 
many objects which to Messier were purely nebulous 
appeared in his own great telescopes to be undoubted 
clusters, though others still remained nebulous Thus in 
his own words : 

"Nebulae can be selected so that an insensible gradation 
shall take place from a coarse cluster like the Pleiades down 
to a milky nebulosity like that m Orion, every intermediate step 
being represented " 


338 A Short History of Astronomy [Cn. xii 

These facts suggested obviously the inference that the 
difference between nebulae and star clusters was merely a 
question of the power of the telescope employed, and accord- 
ingly Herschel's next sentence is 

11 This tends to confirm the hypothesis that all are composed 
of stars more or less remote " 

The idea was not new, having at any rate been suggested, 
rather on speculative than on scientific grounds, m 1755 
by Kant, who had further suggested that a single nebula 
or star cluster is an assemblage of stais comparable in 
magnitude and structure with the whole of those which 
constitute the Milky Way and the other separate stars which 
we see From this point of view the sun is one star m a 
cluster, and every nebula which we see is a system of the 
same order This " island universe " theory of nebulae, as 
it has been called, was also at first accepted by Herschel, 
so that he was able once to tell Miss Burney that he had 
discovered 1,500 new universes 

Herschel, however, was one of those investigators who 
hold theories lightly, and as early as 1791 fuither observa- 
tion had convinced him that these views were untenable, 
and that some nebulae at least were essentially distinct from 
star clusters The particular object which he quotes in 
support of his change of view was a certain nebulous star 
that is, a body resembling an oidmary star but surrounded 
by a circular halo gradually diminishing in brightness 

" Cast your eye," he says, " on this cloudy star, and the 
result will be no less decisive Your judgement, I may 

venture to say, will be, that the nebulosity about the star is not 
of a starry nature" 

If the nebulosity were due to an aggregate of stars so 
far off as to be separately indistinguishable, then the central 
body would have to be a star of almost incomparably greater 
dimensions than an ordinary star, if, on the other hand, 
the central body were of dimensions comparable with those 
of an ordinary star, the nebulosity must be due to some- 
thing other than a star cluster In either case the object 
presented features markedly different from those of a star 
cluster of the recognised kind , and of the two alternative 

2613 Nebulae and Star Clusters 339 

explanations Herschel chose the latter, considering the 
nebulosity to be " a shining fluid, of a nature totally un- 
known to us" One exception to his earlier views being 
thus admitted, others naturally followed by analogy, and 
henceforward he recognised nebulae of the " shining fluid " 
class as essentially different from star clusters, though it 
might be impossible in many cases to say to which class 
a particular body belonged 

The evidence accumulated by Herschel as to the distri- 
bution of nebulae also shewed that, whatever their nature, 
they could not be independent of the general sidereal 
system, as on the " island universe " theory In the first 
place observation soon shewed him that an individual nebula 
or clustei was usually surrounded by a region of the sky 
comparatively free from stars , this was so commonly the 
case that it became his habit while sweeping for nebulae, 
after such a bare region had passed through the field of 
his telescope, to warn his sister to be ready to take down 
observations of nebulae Moreover, as the position of a 
large number of nebulae came to be known and charted, 
it was seen that, whereas clusters were common near the 
Milky Way, nebulae which appeared incapable of resolution 
into clusters were scarce there, and shewed on the contrary 
a decided tendency to be crowded together in the regions 
of the sky most remote from the Milky Way that is, round 
the poles of the galactic circle ( 258) If nebulae were 
external systems, there would of course be no reason why 
their distribution on the sky should shew any connection 
either with the scarcity of stais generally or with the position 
of the Milky Way 

It is, however, rather remarkable that Herschel did not 
m this respect fully appreciate the consequences of his 
own observations, and up to the end of his life seems 
to have considered that some nebulae and clusters were 
external " universes," though many were part of our own 

261 As early as 1789 Herschel had thiown out the 
idea that the different kinds of nebulae and clusters were 
objects of the same kind at different stages of develop- 
ment, some " clustering power " being at work converting 
a diffused nebula into a brighter and more condensed 

340 A Short History of Astronomy [CH xn 

body, so that condensation could be regarded as a sign 
of " age " And he goes on 

" This method of viewing the heavens seems to throw them 
into a new kind of light They are now seen to resemble a luxu- 
riant garden, which contains the greatest variety of productions, in 
different flourishing beds , and one advantage we may at least 
reap from it is, that we can, as it were, extend the range of 
our experience to an immense duration For, to continue the 
simile I have borrowed from the vegetable kingdom, is it not 
almost the same thing, whether we live successively to witness 
the germination, blooming, foliage, fecundity, fading, withering 
and corruption of a plant, or whether a vast number of 
specimens, selected from every stage through which the plant 
passes in the course of its existence, be brought at once to 
our view?" 

His change of opinion in 1791 as to the nature of nebulae 
led to a corresponding modification of his views of this 
process of condensation Of the star already leferred to 
( 260) he remarked that its nebulous envelope " was more 
fit to produce a star by its condensation than to depend upon 
the star for its existence." In 1811 and 1814 he published 
a complete theory of a possible process whereby the shining 
fluid constituting a diffused nebula might gradually con- 
dense the denser portions of it being centres of attraction 
first into a denser nebula or compressed star cluster, then 
into one or more nebulous stars, lastly into a single star 
or group of stars. Every supposed stage m this piocess 
was abundantly illustrated from the records of actual nebulae 
and clusters which he had observed 

In the latter paper he also for the first time recognised 
that the clusters in and near the Milky Way really belonged 
to it, and were not independent systems that happened to 
lie in the same direction as seen by us 

262 On another allied point Herschel also changed his 
mind towards the end of his life When he first used his 
great 20-foot telescope to explore the Milky Way, he thought 
that he had succeeded in completely resolving its faint 
cloudy light into component stars, and had thus penetrated 
to the end of the Milky Way , but afterwards he was con- 
vinced that this was not the case, but that there remained 
cloudy portions which whether on account of their remote- 

$$ 26a, 263] Condensation of Nebulae Double Stars 341 

ness or for other reasons his telescopes were unable to 
resolve into stars (cf fig 104, facing p 405) 

In both these respects therefore the structure of the 
Milky Way appeared to him finally less simple than at 

263 One of the most notable of Herschel's discoveries 
was a bye-product of an inquiry of an entirely different 
character. Just as Bradley m trying to find the parallax of 
a star discovered aberration and nutation (chapter x , 207), 
so also the same problem in HerschePs hands led to the 
discovery of double stars. He pioposed to employ Galilei's 
differential 01 double-star method (chapter vi , 129), in 
which the minute shift of a star's position, due to the earth's 
motion round the sun, is to be detected not by measuring 
its angular distance from standard points on the celestial 
sphere such as the pole or the zenith, but by observing the 
variations in its distance from some star close to it, which 
from its famtness or for some other reason might be 
supposed much further off and therefore less affected by 
the eaith's motion 

With this object in view Herschel set to work to find 
pairs of stars close enough together to be suitable for his 
purpose, and, with his usual eagerness to see and to record 
all that could be seen, gathered in an extensive harvest 
of such objects The limit of distance between the two 
members of a pair beyond which he did not think it worth 
while to go was 2', an interval imperceptible to the naked 
eye except in cases of quite abnormally acute sight. In 
other woids, the two stars even if blight enough to be 
visible would always appear as one to the oidinary eye, 
A first catalogue of such pairs, each forming what may 
be called a double star, was published early in 1782 and 
contained 269, of which 227 were new discoveries; a second 
catalogue of 434 was presented to the Royal Society at the 
end of 1784, and his last paper, sent to the Royal Astio- 
nomical Society m 1821 and published in the first volume 
of its memoirs, contained a list of 145 more. In addition to 
the position of each double star the angular distance between 
the two membeis, the direction of the line joining them, 
and the brightness of each were noted In some cases also 
curious contrasts in the colour of the two components were 

342 A Short History of Astronomy [CH xn 

observed There were also not a few cases in which not 
merely two, but three, four, or more stars were found close 
enough to one another to be reckoned as forming a multiple 

Herschel had begun with the idea that a double star 
was due to a merely accidental coincidence in the direction 
of two stars which had no connection with one another and 
one of which might be many times as remote as the other 
It had, however, been pointed out by Michell (chapter x , 
219), as early as 1767, that even the few double stars 
then known afforded examples of coincidences which were 
very improbable as the result of mere random distribution 
of stars A special case may be taken to make the argu- 
ment clearer, though Michell's actual reasoning was not 
put into a numerical form The bnght star Castor (in the 
Twins) had for some time been known to consist of two 
stars, a and /3, rather less than 5" apart Altogether there 
are about 50 stars of the same order of brightness as a, and 
400 like /3 Neither set of stars shews any particular 
tendency to be distributed in any special way over the 
celestial sphere So that the question of probabilities 
becomes if there are 50 stars of one sort and 400 of another 
distributed at random over the whole celestial sphere, the 
two distributions having no connection with one another, 
what is the chance that one of the first set of stars should 
be within 5" of one of the second set? The chance is 
about the same as that, if 50 grams of wheat and 400 of 
barley are scattered at random in a field of 100 acres, one 
gram of wheat should be found within half an inch of a 
gram of barley The odds against such a possibility are 
clearly very great and can be shewn to be more than 
300,000 to one These are the odds against the existence 
without some real connection between the members- of 
a single double star like Castor ; but when Herschel began 
to discover double stars by the hundred the improbability 
was enormously increased In his first paper Herschel 
gave as his opinion that " it is much too soon to form any 
theories of small stars revolving round large ones," a remark 
shewing that the idea had been considered, and in 1784 
Michell returned to the subject, and expressed the opinion 
that the odds in favour of a physical relation between the 

264] Double Stars 343 

members of Herschel's newly discovered double stars were 
" beyond arithmetic " 

264 Twenty years after the publication of his first 
catalogue Herschel was of Michell's opinion, but was 
now able to support it by evidence of an entirely novel 
and much more direct character A series of observations 
of Castor, presented in two papers published in the Philo- 
sophical Transactions m 1803 and 1804, which were fortu- 
nately supplemented by an observation of Bradley's in 
1759, had shewn a progiessive alteration in the direction 
of the line joining its two components, of such a character 
as to leave no doubt that the two stars were revolving 
round one another; and there were five other cases in 
which a similar motion was observed In these six cases 
it was thus shewn that the double star was really formed by 
a connected pair of stars near enough to influence one 
another's motion. A double star of this kind is called a 
binary star or a physical double star, as distinguished from 
a merely optical double star, the two members of which have 
no connection with one another In three cases, including 
Castor, the observations were enough to enable the period 
of a complete revolution of one star round another, assumed 
to go on at a uniform rate, to be at any rate roughly 
estimated, the results given by Herschel being 342 years 
for Castor,* 375 and 1,200 years for the other two. It was 
an obvious inference that the motion of revolution observed 
in a binary star was due to the mutual gravitation of its 
members, though Herschel's data were not enough to 
determine with any precision the law of the motion, and 
it was not till five years after his death that the first attempt 
was made to shew that the orbit of a binary star was such 
as would follow from, or at any rate would be consistent 
with, the mutual gravitation of its membeis (chapter xin , 
309 cf also fig 101). This may be regarded as the first 
dnect evidence of the extension of the law of gravitation to 
regions outside the solar system 

Although only a few double stars were thus definitely 
shewn to be binaiy, there was no reason why many others 

* The motion of Castor has become slower since Herschel's time, 
and the piesent estimate of the period is about 1,000 years, but it 
is by no means certain 

344 A Short History of Astronomy [CH xn 

should not be so also, their motion not having been rapid 
enough to be clearly noticeable during the quarter of a 
century or so over which Herschel's observations extended , 
and this probability entirely destroyed the utility of double 
stars for the particular purpose for which Herschel had 
originally sought them. For if a double star is binary, 
then the two members are approximately at the same 
distance from the earth and therefore equally affected by 
the earth's motion, whereas for the purpose of finding the 
parallax it is essential that one should be much more 
remote than the other. But the discovery which he had 
made appeared to him far more interesting than that which 
he had attempted but failed to make , in his own picturesque 
language, he had, like Saul, gone out to seek his father's 
asses and had found a kingdom 

265 It had been known since Halley's time (chapter x , 
203) that certain stars had proper motions on the celestial 
sphere, relative to the general body of stars The conviction, 
that had been gradually strengthening among astronomers, 
that the sun is only one of the fixed stars, suggested the 
possibility that the sun, like other stars, might have a 
motion in space Thomas Wright, Lambert, and others 
had speculated on the subject, and Tobias Mayer (chapter x , 
225-6) had shewn how to look for such a motion 

If a single star appears to move, then by the principle of 
relative motion (chapter iv, 77) this may be explained 
equally well by a motion of the star or by a motion of the 
observer, or by a combination of the two , and since in this 
problem the internal motions of the solar system may be 
ignored, this motion of the observer may be identified with 
that of the sun When the proper motions of several stars 
are observed, a motion of the sun only is in general inade- 
quate to explain them, but they may be regarded as due 
either solely to the motions m space of the stars or to 
combinations of these with some motion of the sun. If 
now the stars be regarded as motionless and the sun be 
moving towards a particular point on the celestial sphere, 
then by an obvious effect of perspective the stars near 
that point will appear to recede from it and one another 
on t the celestial sphere, while those in the opposite region 
will approach one another, the magnitude of these changes 

26 S ] 

Motion of the Sun in Space 


depending on the rapidity of the sun's motion and on 
the nearness of the stars in question. The effect is exactly 
of the same nature as that produced when, on looking 
along a street at night, two lamps on opposite sides of the 
street at some distance from us appear close together, but 
as we walk down the street towards them they appear to 
become more and more separated from one another In 
the figure, for example, L and L' as seen from B appear 
farther apait than when seen from A 

FIG. 84 Illustrating the effect of the sun's motion m space 

If the observed proper motions of stars examined are not 
of this character, they cannot be explained as due merely to 
the motion of the sun ; but if they shew some tendency 
to move in this way, then the observations can be most 
simply explained by regaidmg the sun as in motion, and 
by assuming that the discrepancies between the effects 
resulting from the assumed motion of the sun and the 
observed proper motions are due to the motions in space 
of the* several stars. 

From the few proper motions which Mayer had at his 
command he was, however, unable to derive any indication 
of a motion of the sun 

Herschel used the proper motions, published by Maskelyne 
and Lalande, of 14 stars (13 if the double star Castor be 
counted as only one), and with extraordinary insight detected 
in them a certain uniformity of motion of the kind already 
described, such as would result from a motion of the sun 
The point on the celestial sphere towards which the sun 
was assumed to be moving, the apex as he called it, was 
taken to be the point marked by the star X in the constella- 

346 A Short History of Astronomy [Cn xn 

tion Hercules A motion of the sun in this direction 
would, he found, produce in the 14 stars apparent motions 
which were in the majority of cases in general agreement 
with those observed* This result was published in 1783, 
and a few months later Pierre Pr'evost (1751-1839) deduced 
a very similar result from Tobias Mayer's collection of 
proper motions More than 20 years later (1805) Herschel 
took up the question again, using six of the brightest stars 
in a collection of the proper motions of 36 published by 
Maskelyne in 1790, which were much more reliable than 
any earlier ones, and employing more elaborate processes 
of calculation ; again the apex was placed in the constellation 
Hercules, though at a distance of nearly 30 from the 
position given in 1783 Herschel's results were avowedly 
to a large extent speculative, and were received by con- 
temporary astronomers with a large measure of distrust , 
but a number of far more elaborate modern investigations 
of the same subject have confirmed the general correctness 
of his work, the earlier of his two estimates appearing, 
however, to be the more accurate He also made some 
attempts in the same papers and in a third (published m 
1806) to estimate the speed as well as the direction of the 
sun's motion , but the work necessarily involved so many 
assumptions as to the probable distances of the stais 
which were quite unknown that it is not worth while to 
quote icsults more definite than the statement made m 
the paper of 1783, that " We may in a general way estimate 
that the solar motion can certainly not be less than that 
which the earth has in her annual orbit " 

266 The question of the comparative brightness of stars 
was, as we have seen ( 258), of importance in connection 
with HerschePs attempts to estimate their relative distances 
from the earth and their arrangement in space ; it also 
presented itself in connection with inquiries into the vari- 
ability of the light of stars Two remarkable cases of 
variability had been for some time known A star in the 
Whale (o Ceti or Mira) had been found to be at times 

* More precisely, counting motions m right ascension and in 
decimation separately, he had 27 observed motions to deal with (one 
of the stars having no motion m declination) , 22 agreed m sign with 
those which would result from the assumed motion of the sun 

266] Variable Stars 347 

invisible to the naked eye and at other times to be con- 
spicuous , a Dutch astronomer, Phocyhdes Holwarda (1618- 
1651), first cleaily recognised its variable character (1639), 
and Ismael Boulhau or Bulhaldus (1605-1694) in 1667 fixed 
its period at about eleven months, though it was found that 
its fluctuations were irregular both in amount and in period 
Its variations formed the subject of the first paper published 
by Herschel in the Philosophical Transactions (1780) An 
equally remarkable variable star is that known as Algol 
(or ft Persei ), the fluctuations of which were found to be 
performed with almost absolute regularity Its variability 
had been noted by Gemimano Montanari (1632-1687) in 
1669, but the regularity of its changes was first detected 
in 1783 by John Goodncke (1764-1786), who was soon 
able to fix its period at very nearly 2 days 20 hours 49 
minutes Algol, when faintest, gives about one-quarter as 
much light as when brightest, the change from the first 
state to the second being effected in about ten hours , 
whereas Mira vanes its light several hundredfold, but 
accomplishes its changes much more slowly 

At the beginning of Herschel's career these and three or 
four others of less interest were the only stars definitely 
recognised as variable, though a few others were added soon 
afterwards Several records also existed of so-called " new " 
stars, which had suddenly been noticed m places where no 
star had previously been observed, and which foi the most 
part rapidly became inconspicuous again (cf chapter 11 , 42 , 
chapter v , 100 , chapter vn , 138) , such stars might 
evidently be regarded as variable stars, the times of greatest 
brightness occunmg quite irregularly or at long intervals 
Moreover various records of the brightness of stars by earlier 
astronomers left little doubt that a good many must have 
varied sensibly in brightness For example, a small star in 
the Great Bear (close to the middle star of the " tail ") was 
among the Arabs a noted test of keen sight, but is perfectly 
visible even in our duller climate to persons with ordinary 
eyesight , and Castor, which appeared the brighter of the 
two Twins to Bayer when he published his Atlas (1603), 
was in the i8th century (as now) less bright than Pollux 

Herschel made a good many definite measurements of 
the amounts of light emitted by stars of various magnitudes, 

34& A Short History of Astronomy [Cn XI I 

but was not able to carry out any extensive or systematic 
measurements on this plan. With a view to the future 
detection of such changes of brightness as have just been 
mentioned, he devised and carried out on a large scale 
the extremely simple method of sequences If a group of 
stars are observed and their order of brightness noted at 
two different times, then any alteration in the order will 
shew that the brightness of one or more has changed So 
that if a number of stars are observed in sets m such a way 
that each star is recorded as being less bright than certain 
stars near it and brighter than certain other stais, materials 
are thereby provided for detecting at any future time any 
marked amount of variation of brightness Herschel pre- 
pared on this plan, at various times between 1796 and 1799, 
four catalogues of comparative brightness based on naked- 
eye observations and comprising altogether about 3,000 
stars In the course of the work a good many cases of 
slight variability were noticed , but the most interesting 
discovery of this kind was that of the variability of the 
well-known star a Hercuhs, announced in 1796 The period 
was estimated at 60 days, and the star thus seemed to form 
a connecting link between the known variables which like 
Algol had periods of a very few days and those (of which 
Mira was the best known) with periods of some hundreds 
of days As usual, Herschel was not content with a mere 
record of observations, but attempted to explain the observed 
facts by the supposition that a variable star had a rotation 
and that its surface was of unequal brightness 

267 The novelty of HerschePs work on the fixed stars, 
and the very general character of the results obtained, have 
caused this part of his researches to overshadow m some 
respects his other contributions to astronomy 

Though it was no part of his plan to contribute to that 
precise knowledge of the motions of the bodies of the solar 
system which absorbed the best energies of most of the 
astronomers of the i8th century whether they were 
observers or mathematicians he was a careful and success- 
ful observer of the bodies themselves 

His discoveries of Uranus, of two of its satellites, and of 
two new satellites of Saturn have been already mentioned 
in connection with his life ( 253, 255). He believed 

$ 267] JBnghtness of Stars Planetary Observations 349 

himself to have seen also (1798) four other satellites of 
Uranus, but their existence was never satisfactorily verified , 
and the second pair of satellites now known to belong to 
Uranus, which weie discovered by Lassell m 1847 (chap- 
ter xin , 295), do not agree in position and motion with 
any of HerschePs foui It is therefoie highly probable that 
they were mere optical illusions due to defects of his mirror, 
though it is not impossible that he may have caught glimpses 
of one or other of LasselPs satellites and misinterpreted the 

Saturn was a favourite object of study with Herschel from 
the very beginning of his astronomical career, and seven 
papers on the subject were published by him between 1790 
and 1806 He noticed and measuied the deviation of the 
planet's form from a sphere (1790),, he observed various 
markings on the surface of the planet itself, and seems to 
have seen the inner ring, now known from its appearance 
as the crape ring (chapter xui , 295), though he did not 
recognise its nature By observations of some markings at 
some distance from the equator he discovered (1790) that 
Saturn rotated on an axis, and fixed the period of rotation 
at about ich i6m (a period differing only by about 2 
minutes from modern estimates), and by similar observations 
of the ring (1790) concluded that it lotated in about joj 
hours, the axis of rotation being in each case perpendicular 
to the plane of the ring The satellite Japetus, discovered 
by Cassini in 1671 (chapter vni , 160), had long been 
recognised as variable m brightness, the light emitted being 
several times as much at one time as at another Heischel 
found that these variations were not only perfectly regular, 
but recurred at an interval equal to that of the satellite's 
period of rotation round its primary (1792), a conclusion 
which Cassini had thought of but i ejected as inconsistent 
with his observations This peculiarity was obviously capable 
of being explained by supposing that different portions of 
Japetus had unequal power of reflecting light, and that like our 
moon it turned on its axis once m eveiy revolution, m such 
a way as always to present the same face towards its 
primary, and in consequence each face in turn to an 
observer on the earth It was natural to conjecture that 
such an arrangement was general among satellites, and 

350 A Short History of Astronomy [Cn xn 

Herschel obtained (1797) some evidence of variability in 
the satellites of Jupiter, which appeared to him to support 
this hypothesis 

HerschePs observations of other planets were less 
numerous and important He rightly rejected the supposed 
observations by Schroeter (271) of vast mountains on 
Venus, and was only able to detect some indistinct mai kings 
from which the planet's rotation on an axis could be 
somewhat doubtfully inferred He frequently observed the 
familiar bright bands on Jupiter commonly called belts, 
which he was the first to interpret (1793) as bands of 
cloud On Mars he noted the periodic diminution of the 
white caps on the two poles, and obseived how in these 
and other respects Mars was of all planets trie one most 
like the earth. 

268 Herschel made also a numbei of careful obseiva- 
tions on the sun, and based on them a famous theoiy of its 
structure He confirmed the existence of various features 
of the solar surface which had been noted by the earlier 
telescopists such as Galilei, Schemer, and Hevel, and 
added to them in some points of detail Since Galilei's 
time a good many suggestions as to the nature of spots had 
been thrown out by various observeis, such as that they 
were clouds, mountain-tops, volcanic products, etc , but 
none of these had been supported by any serious evidence 
Herschel's observations of the appeaiances of spots suggested 
to him that they were depressions in the surface of the sun, 
a view which derived support from occasional observations 
of a spot when passing over the edge of the sun as a 
distinct depression or notch there Upon this somewhat 
slender basis of fact he constructed (1795) an elaboiate 
theory of the nature of the sun, which atti acted very general 
notice by its ingenuity and picturesqueness and commanded 
general assent in the astronomical world for more than half 
a century The interior of the sun was supposed to be a 
cold dark solid body, surrounded by two cloud-layers, of 
which the outei was the photosphere or ordinary surface of 
the sun, intensely hot and luminous, and the inner served as 
a fire-screen to protect the interior The umbra (chapter vi , 
124) of a spot was the dark interior seen through an 
opening in the clouds, and the penumbra corresponded 

268,269] HerscheVs Theory of the Sun 351 

to the inner cloud-layer rendered luminous by light from 

"The sun viewed in this light appears to be nothing else 
than a very eminent, large, and lucid planet, evidently the first 
or, in strictness of speaking, the only primary one of our 
system , it is most probably also inhabited, like the rest 

of the planets, by beings whose organs are adapted to the 
peculiar circumstances of that vast globe " 

That spots were depressions had been suggested moie 
than twenty years before (1774) by Alexander Wilson of 
Glasgow (1714-1786), and supported by evidence different 
from any adduced by Herschel and in some ways more 
conclusive Wilson noticed, first in the case of a large 
spot seen in 1769, and afterwards in other cases, that as 
the sun's rotation carries a spot across its disc from one 
edge to another, its appearance changes exactly as it would 
do in accordance with ordinary laws of perspective if the 
spot were a saucer-shaped depression, of which the bottom 
formed the umbra and the sloping sides the penumbra, 
since the penumbra appears narrowest on the side nearest 
the centre of the sun and widest on the side nearest the 
edge Hence Wilson inferred, like Herschel, but with 
less confidence, that the body of the sun is dark In 
the paper referred to Herschel shews no signs of being 
acquainted with Wilson's work, but in a second paper 
(1801), which contained also a valuable series of observa- 
tions of the detailed markings on the solar surface, he 
refers to Wilson's "geometrical proof" of the depression 
of the umbra of a spot 

Although it is easy to see now that HerschePs theory was 
a rash generalisation from slight data, it nevertheless ex- 
plained with fair success most of the observations made 
up to that time 

Modern knowledge of heat, which was not accessible 
to Herschel, shews us the fundamental impossibility of 
the continued existence of a body with a cold interior and 
merely a shallow ring of hot and luminous material round 
it , and the theory in this form is therefore purely of 
historic interest (cf also chapter xin , 298, 303) 

269. Another suggestive idea of Herschel's was the 
analogy between the sun and a variable star, the known 

352 A Short History of Astronomy [Cn xn 

variation in the number of spots and possibly of other 
markings on the sun suggesting to him the probability 
of a certain variability in the total amount of solar light 
and heat emitted, The terrestrial influence of this he 
tried to measure in the absence of precise meteoro- 
logical data with characteristic ingenuity by the price of 
wheat, and some evidence was adduced to shew that at 
times when sun-spots had been noted to be scarce 
corresponding according to HerschePs view to periods 
of diminished solar activity wheat had been dear and 
the weather presumably colder In reality, however, 
the data were insufficient to establish any definite con- 

270 In addition to carrying out the astronomical re- 
searches already sketched, and a few others of less import- 
ance, Herschel spent some time, chiefly towards the end of 
his life, in working at light and heat , but the results obtained, 
though of considerable value, belong rather to physics than 
to astronomy, and need not be dealt with here 

271. It is natural to associate HerschePs wonderful series 
of discoveries with his possession of telescopes of unusual 
power and with his formulation of a new programme of 
astronomical inquiry , and these were certainly essential 
elements It is, however, significant, as shewing how im- 
portant other considerations were, that though a great 
number of his telescopes were supplied to other astro- 
nomers, and though his astronomical programme when 
once suggested was open to all the world to adopt, hardly 
any of his contemporaries executed any considerable 
amount of work comparable in scope to his own. 

Almost the only astronomer of the period whose work 
deserves mention beside Herschel's, though very inferior to 
it both in extent and in originality, was Johann Jffieronymus 
Schroeter (1745-1816) 

Holding an official position at Lihenthal, near Bremen, 
he devoted his leisure during some thirty years to a scrutiny 
of the planets and of the moon, and to a lesser extent of 
other bodies 

As has been seen in the case of Venus ( 267), his results 
were not always reliable, but notwithstanding some errors 
he added considerably to our knowledge of the appearances 

$ 2 7 o, 271] Herschel and Schroeter 353 

presented by the various planets, and m particular studied 
the visible features of the moon with a minuteness and 
accuracy far exceeding that of any of his predecessors, and 
made some attempt to deduce from his observations data 
as to its physical condition. His two volumes on the 
moon (Selenotopographische Fragmente, 1791 and 1802), and 
other minor writings, are a storehouse of valuable detail, 
to which later workers have been largely indebted 



"The greater the sphere of oui knowledge, the larger is the 
surface of its contact with the infinity of our ignorance " 

272 THE last three chapters have contained some account 
of progress made m three branches of astronomy which, 
though they overlap and exercise an important influence on 
one another, are to a laige extent studied by different men 
and by different methods, and have different aims The 
difference is perhaps best realised by thinking of the work 
of a great master m each department, Bradley, Laplace, 
and Herschel So great is the difference that Delambie 
m his standard history of astronomy all but ignores the 
work of the great school of mathematical astronomers who 
were his contemporaries and immediate predecessors, not 
from any want of appreciation of their impoitance, but 
because he legards their work as belonging rather to mathe- 
matics than to astronomy 3 while Bessel ( 277), m saying 
that the function of astronomy is " to assign the places on 
the sky where sun, moon, planets, comets, and stars have 
been, are, and will be," excludes from its scope nearly 
everything towards which HerschePs energies were directed 

Current modern practice is, however, more liberal in its 
use of language than either Delambre or Bessel, and finds it 
convenient to recognise all three of the subjects or groups 
of subjects referred to as integral parts of one science. 

The mutual relation of gravitational astronomy and what 
has been for convenience called observational astronomy 
has been already referred to (chapter x , 196) It should, 
however, be noticed that the latter term has m this book 
hitherto been used chiefly for only one pait of the astrono- 


CH xiii , $ 272, 273] Descriptive Astronomy 355 

mical work which concerns itself primarily with obsei vation 
Observing played at least as large a part m Herschel's 
work as in Bradley's, but the aims of the two men were 
m many ways different Bradley was interested chiefly in 
ascertaining as accurately as possible the apparent positions 
of the fixed stars on the celestial sphere, and the positions 
and motions of the bodies of the solar system, the former 
undertaking being m great part subsidiary to the latter 
Herschel, on the other hand, though certain of his re- 
searches, e g into the parallax of the fixed stars and into 
the motions of the satellites of Uranus, were precisely like 
some of Bradley 's, was far more concerned with questions 
of the appearances, mutual relations, and structure of the 
celestial bodies in themselves This latter branch of 
astronomy may conveniently be called descriptive astronomy, 
though the name is not altogether appropriate to inquiries 
into the physical structure and chemical constitution of 
celestial bodies which are often put under this head, and 
which play an important part in the astronomy of the 
present day 

273 Gravitational astronomy and exact observational 
astronomy have made steady progress during the nineteenth 
century, but neither has been revolutionised, and the 
advances made have been to a great extent of such a 
nature as to be barely intelligible, still less interesting, to 
those who are not experts The account of them to be 
given in this chapter must therefore necessarily be of the 
slightest character, and deal either with general tendencies or 
with isolated results of a less technical character than the rest 

Descriptive astronomy, on the other hand, which can be 
regarded as being almost as much the cieation of Herschel 
as gravitational astronomy is of Newton, has not only been 
greatly developed on the lines laid down by its founder, but 
has received chiefly through the invention of spectrum 
analysis ( 299) extensions into regions not only unthought 
of but barely imaginable a century ago Most of the ^ 
results of descriptive astronomy unlike those of the oldei 
branches of the subject are readily intelligible and fairly 
interesting to those who have but little knowledge of the 
subject, m particular they are as yet to a considerable 
extent independent of the mathematical ideas and language 

356 A Short History of Asfrono7ny [CH XIIL 

which dominate so much of astronomy and render it 
unattractive or inaccessible to many Moreover, not only 
can descriptive astronomy be appreciated and studied, but 
its progress can materially be assisted, by obseivers who 
have neither knowledge of higher mathematics nor any 
elaborate instrumental equipment . 

Accordingly, while the successors of Laplace and Eradley 
have been for the most part astionomers by profession, 
attached to public observatories or to universities, an 
immense mass of valuable descriptive work has been done 
by amateurs who, like Herschel in the earlier part of his 
career, have had to devote a large part of their energies to 
professional work of other kinds, and who, though m some 
cases provided with the best of instruments, have in many 
others been furnished with only a slender instrumental 
outfit Tor these and other reasons one of the most 
notable features of nineteenth century astronomy has been 
a great development, particularly m this country and in the 
United States, of general interest in the subject, and the 
establishment of a large number of private observatories 
devoted almost entirely to the study of special branches of 
descriptive astronomy. te ' ^he nineteenth centuiy has ac- 
cordingly witnessed the acquisition of an unprecedented 
amount of detailed astronomical knowledge But the 
wealth of material thus accumulated has outrun our powers 
of interpretation, and m a number of cases our knowledge 
of some particular department of descriptive astronomy 
consists, on the one hand of an immense senes of careful 
observations, and on the other of one or more highly 
speculative theories, seldom capable of explaining more 
than a small portion of the observed facts / 

In dealing with the progress of modern descriptive 
astronomy the proverbial difficulty of seeing the wood on 
account of the trees is therefore unusually great To give 
an account within the limits of a single chapter of even the 
most important facts added to our knowledge would be a 
hopeless endeavour ; fortunately it would also be superfluous 
as they are to be found m many easily accessible textbooks 
on astronomy or m treatises on special parts of the subject 
All that can be attempted is to give some account of the 
chief lines on which progress has been made, and to 

274,275] Descriptive Astronomy Theory of Errors 357 

indicate some general conclusions which seem to be 
established on a tolerably secure basis 

274 The progress of exact observation has of course 
been based very largely on instrumental advances Not 
only have great improvements been made in the extremely 
delicate work of making large lenses, but the graduated 
circles and other parts of the mounting of a telescope 
upon which accuracy of measurement depends can also be 
constructed with far greater exactitude and certainty than 
at the beginning of the century New methods of mounting 
telescopes and of making and recording observations have 
also been introduced, all contributing to greatei accuracy 
For certain special problems photography is found to 
present gieat advantages as compared with eye- observations, 
though its most important applications have so far been to 
descriptive astronomy J 

275 The necessity for making allowance for various 
known sources of errors in observation, and for diminishing 
as far as possible the effect of errors due to unknown causes, 
had been recognised even by Tycho Brahe (chapter v., 
no), and had played an important part in the work 
of Flamsteed and Bradley (chapter x, 198, 218) 
Some fuither important steps in this direction were taken 
in the earlier part of this centuiy The method of 
Jleast sguareSj established independently by two great 
mathematicians, Adnen Mane Legendre (1752-1833) of 
Pans and Carl Fnednch Gauss (1777-1855) of Gottmgen,* 
was a systematic method of combining obseivations, 
which gave slightly different results, in such a way 
as to be as near the truth as possible Any oidmary 
physical measurement, eg of a length, however carefully 
executed, is necessarily imperfect , if the same measurement 
is made several times, even under almost identical condi- 
tions, the results will m general differ slightly , and the 
question arises of combining these so as to get the most 
satisfactory result The common practice in this simple 
case has long been to take the anthmetical mean or average 
of the diffeient results But astronomeis have constantly 

* The method was published by Legcndre in 1806 and by Gauss 
in 1809, but it was invented and used by the latter more than 20 
yeais earhei 

35 8 A Short History of Astronomy [CH xni 

to deal with more complicated cases in which two or more 
unknown quantities have to be determined from observa- 
tions of different quantities, as, for example, when the 
elements of the orbit of a planet (chapter xi , 236) have 
to be found from observations of the planet's position at 
different times The method of least squaies gives a rule 
for dealing with such cases, which was a generalisation 
of the ordinary mle of averages for the case of a single 
unknown quantity, and it was elaborated m such a way 
as to provide for combining observations of different value, 
such as observations taken by observers of unequal skill 
or with different instruments, or under more 01 less favour- 
able conditions as to weather, etc It also gives a simple 
means of testing, by means of their mutual consistency, 
the value of a series of obseivations, and comparing their 
probable accuracy with that of some othei series executed 
under different conditions The method of least squares 
and the special case of the "average" can be deduced 
from a certain assumption as to the general charactei of 
the causes which produce the error m question, but the 
assumption itself cannot be justified a priori , on the other 
hand, the satisfactory results obtained from the application 
of the rule to a great variety of problems in astronomy 
and in physics has shewn that m a large number of cases 
unknown causes of error must be approximately of the 
type considered The method is theiefore very widely 
used in astronomy and physics wherever it is worth/ 
while to take trouble to secuie the utmost attainable ^ 

276 Legendre's other contributions to science were 
almost entirely to branches of mathematics scarcely affect- 
ing astronomy Gauss, on the other hand, was for nearly 
half a century head of the observatory of Gottmgen, and 
though his most brilliant and important work was m pure 
mathematics, while he carried out some reseaiches of first- 
rate importance m magnetism and other branches of physics, 
he also made some further contributions of importance to 
astronomy These were foi the most part processes of 
calculation of various kinds required for utilising astrono- 
mical observations, the best known being a method of 
calculating the orbit of a planet from three complete 

276, 277 Legendre and Gauss 359 

observations of its position, which was published m his < 
Theona Motus (1809). As we have seen (chapter xi , ^/ 
236), the complete determination of a planet's orbit 
depends on six independent elements any complete ob- 
servation of the planet's position in the sky, at any time, 
gives two quantities, eg the light ascension and declination 
(chapter n , 33) , hence three complete observations 
give six equations and are theoretically adequate to de- 
termine the elements of the orbit , but it had not hitherto 
been found necessary to deal with the problem in this 
form The orbits of all the planets but Uranus had been 
worked out gradually by the use of a series of observations 
extending over centuries ; and it was feasible to use ob- 
seivations taken at paiticular times so chosen that certain 
elements could be determined without any accurate know- 
ledge of the others y even Uranus had been under observa- 
tion for a considerable time before its path was determined 
with anything like accuracy , and m the case of comets 
not only was a considerable series of obseivations generally 
available, but the problem was simplified by the fact that 
the 01 bit could be taken to be nearly or quite a parabola 
instead of an ellipse (chapter ix , 190) The discovery 
of the new planet Ceres on January ist, 1801 ( 294), and 
its loss when it had only been observed for a few weeks, 
presented virtually a new problem in the calculation of an 
orbit Gauss applied his new methods including that 
of least squares to the observations available, and with 
complete success, the planet being rediscovered at the 
end of the year nearly in the position indicated by his 

27y f YThe theory of the "reduction" of observations 
(chapter x, 218) was first systematised and very much 
improved by Fnednch Wilhelm JBessel (1784-1846), who 
was for more than thirty years the director of the new 
Prussian observatory at Komgsberg His first great work 
was the reduction and publication of Bradley's Greenwich 
observations (chapter x., 218) This undertaking involved 
an elaborate study of such disturbing causes as precession, 
aberration, and refraction, as well as of the eirors of Bradley's 
instruments. Allowance was made for these on a uniform and 
systematic plan, and the result was the publication m 1818, 

360 A Short History of Astronomy [CH xin 

under the title Fundamenta Astronomiae^ of a Catalogue of 
the places of 3,222 stars as they were in 1755 /A special 
problem dealt with in the course of the work was that of 
refraction Although the complete theoretical solution 
was then as now unattainable, Bessel succeeded m con- 
structing a table of refractions which agreed very closely 
with observation and was presented in such a form that 
the necessary correction for a star m almost any position 
could be obtained with very little trouble His general 
methods of reduction published finally m his Tabulae 
Xegiomontanae (1830) also had the great advantage of 
arranging the necessary calculations m such a way that 
they could be performed with very little labour and by an 
almost mechanical process, such as could easily be carried 
out by a moderately skilled assistant In addition to 
editing Bradley's observations, Bessel undertook a fresh 
series of observations of his own, executed between the 
years 1821 and 1833, upon which were based two new 
catalogues, containing about 62,000 stars, which appeared 
after his death v * 

278 The most memorable of Bessel's special pieces of 

FIG 85. 61 Cygm and the two neighbouring stars used by Bessel 

WaS Jrr fos i defimte detectl n of the parallax of a 
fixed star.^He abandoned the test of brightness as an 

2 7 8] 

The Parallax of 61 Cygnt 


indication of nearness, and selected a star (61 Cveni) 
which was barely visible to the naked eye but was re- 
markable for its large proper motion (about 5" per annum) , 
evidently if a star is moving at an assigned rate (in miles 
per hour) through space, the nearer to the observer it is the 
more rapid does its motion appear to be, so that apparent 
rapidity of motion, like brightness, is a 
probable but by no means infallible 
indication of nearness A modification 
of Galilei's differential method (chap- 
ter vi , 129, and chapter xn , 263) 
being adopted, the angular distance 
of 6 1 Cygni from two neighbouring 
stais, the famtness and immovability 
of which suggested their great distance 
m space, was measured at frequent 
mteivals during a year From the 
changes in these distances cr a, o- b 
(in fig 85), the size of the small ellipse 
described by a- could be calculated 
The result, announced at the end of 
1838, was that the star had an annual 
paiallax of about $* (chapter vm , 
161), te that the star was at such 
distance that the greatest angular dis- 
tance of the earth from the sun viewed 
from the star (the angle s <rE in fig 86, 
where s is the sun and E the earth) 
was this insignificant angle * The 
result was confirmed, with slight altera- 
tions, by a fresh investigation of 

Bessel's in 1839-40, but later work FIG 86 The parallax 
seems to shew that the parallax is a of6t Qv# 
little less than j"t With this latter 
estimate, the apparent size of the earth's path round the 
sun as seen fiom the star is the same as that of a halfpenny 

* The figure has to be enormously exaggerated, the angle s cr E as 
shewn there being about 10, and therefoie about 100,000 times too 

f Sir R S Ball and the late Piofessor Pntchard ( 279) have 
obtained respectively 47" and '43" , the mean of these, 45", may be 
provisionally accepted as not very far fiom the truth 

362 A Short History of Astronomy [Cn xii 

at a distance of rather more than three miles In other 
words, the distance of the star is about 400,000 times the 
distance of the sun, which is itself about 93,000,000 miles 
A mile is evidently a very small unit by which to measure 
such a vast distance, and the practice of expiessmg such 
distances by means of the time required by light to perform 
the journey is often convenient Travelling at the rate of 
186,000 miles per second ( 283), light %ik6s rather more 
than six years to reach us from 61 Cygm - v 

279 Bessel's solution of the great problem which had 
baffled astronomers ever since the time of Coppeimcus was 
immediately followed by two others Early in 1839 Thomas 

Henderson (1798-1844) announced a parallax of nearly i" 
for the bright star a Centaun which he had observed at the 
Cape, and in the following year Friednch Georg Wtlhelm 
Struve (1793-1864) obtained from observations made at 
Pulkowa a parallax of |'' for Vega ) later woik has reduced 
these numbers to f " and T y respectively 

A number of other . parallax determinations have subse- 
quently been made r mn interesting vanation in method was 
made by the late Professor Charles Pritchard (I%Q%-I%<)'$) 
of Oxford by photographing the star to be examined and its 
companions, and subsequently measuring the distances on 
the photograph, instead of measuring the angular distances 
dijectly with a micrometer V 

""/At the present time some 50 stars have been ascertained 
with some leasonable degree of probability to have measui- 
able, if rathei uncertain, parallaxes } a Centaun still holds 
its own as the nearest star, the light-journey from it being 
about four years J/A considerable number of other stais 
have been examined with negative or highly uncertain 
results, indicating that their parallaxes are too small to be 
measured with our present means, and that their distances 
are correspondingly great 

280 A number of star catalogues and star maps too 
numerous to mention separately have been constructed 
during this century, marking steady progress m our know- 
ledge of the position of the stars, and providing fiesh 
materials for ascertaining, by comparison of the state of 
the sky at different epochs, such quantities as the proper 
motions of the stars and the amount of precession Among 

$ 279281] Parallax Star Catalogues 363 

the most important is the great catalogue of 324,198 stars 
in the northern hemisphere known as the Bonn Durch- 
musterung) published in 1859-62 by Bessel's pupil Friednch 
Wilhelm August Arge lander (1799-1875),, this was extended 
(1875-85) so as to include 133,659 stars in a portion of 
the southern hemisphere by Eduard ^0^/^(1828-1891) , 
and more recently Dr Gill has executed at the Cape 
photogiaphic observations of the lemamder of the southern 
hemisphere, the reduction to the form of a catalogue (the 
first instalment of which was published in 1896) having 
been performed by Piofessor Kapteyn of Gromngen The 
star places determined in these catalogues do not profess 
to be the most accuiate attainable, and for many purposes 
it is important to know with the utmost accuracy the 
positions of a smaller number of stars ^he greatest 
undertaking of this kind, set on foot by the German 
Astronomical Society in 1867, aims at the construction, by 
the co-operation of a number of observatories, of catalogues 
of about 130,000 of the stars contained in the "approximate " 
catalogues of Aigelander and Scfronfeld , nearly half of the 
work has now been published / 

\The greatest scheme for a suivey of the sky yet attempted 
is the photographic chart, together with a less extensive 
catalogue to be based on it, the construction of which was 
decided on at an international congress held at Pans 
in 1887 The whole sky has been divided between 18 
observatories in all parts of the world, from Helsmgfors in 
the north to Melbourne m the south, and each of these is 
now taking photographs with virtually identical instruments 
It is estimated that the complete chart, which is intended 
to include stars of the i4th magnitude,* will contain about 
20,000,000 stars, 2,000,000 of which will be catalogued 
also iy J 

281. One other great problem -that of the distance of 
the sun may conveniently be discussed under the head 
of obseivational astronomy **"""' 

%/The transits of Venus (chapter x, 202, 227) which 
occurred m 1874 and 1882 were both extensively observed, 

* An average star of the I4th magnitude is 10,000 times fainter 
than one of the 4th magnitude, which again is about 150 times less 
bright than Sinus. See 316 

364 A Short History of Astronomy [CH xill 

the old methods of time-observation being supplemented 
by photography and by direct micrometrjc measurements 
of/the positions of Venus while transiting ? 
yThe method of finding the distance of the sun by means 
of observation of Mars in opposition (chapter vin , 161) 
has been employed on several occasions with considerable 
success, notably by Dr Gill at Ascension m 1877 A 
method originally used by Flamsteed, but revived in 1857 
by Szr George Bidddl Airy (1801-1892), the late Astronomer 
Royal, was adopted on this occasion For the deteimmation 
of the parallax of a planet observations have to be made from 
two different positions at a known distance apart ; commonly 
these are taken to be at two different observatories, as 
far as possible removed from one another in latitude 
Airy pointed out that the same object could be attained if 
only one observatory were used, but observations taken at 
an interval of some hours, as the rotation of the eaith on 
its axis would in that time produce a known displacement 
of the observer's position and so provide the necessary 
base line The apparent shift of the planet's position 
could be most easily ascertained by measuring (with the 
micrometer) its distances from neighbouring fixed stars 
This method (known as the diurnal method) has the great 
advantage, among others, of being simple in application, jx 
single observer and instrument being all that is needed, i ' 

The diurnal method has also been applied with great 
success to certain of the minor planets ( 294) Revolving 
as they do between Mars and Jupiter, they are all farther 
off from us than the former , but there is the compensating 
advantage that as a minor planet, unlike Mars, is, as a 
rule, too small to shew any appreciable disc, its angular 
distance from a neighbouring star is more easily measured 
The employment of the minor planets in this way was first 
suggested by Professor Galle of Berlin m 1872, and recent 
observations of the minor planets Victoria^ Saffho, and Iris 
m 1888-89, made at a number of observatories under the 
general direction of Dr Gill, have led to some of the most 
satisfactory determinations of the sun's distance 

282 It was known to the mathematical astronomers of 
the 1 8th century that the distance of the sun could be 
obtained from a knowledge of various perturbations of 

282, 283] The Distance of the Sun 365 

members of the solar system 3 and Laplace had deduced 
a value of the solar parallax from lunar theory Improve- 
ments in gravitational astronomy and in observation of the 
planets and moon during the present century have added 
considerably to the value of these methods ' ;A certain 
irregularity in the moon's motion known as the parallactic 
inequality, and another in the motion of the sun, called 
the lunar equation, due to the displacement of the earth 
by the attraction of the moon, alike depend on the ratio 
of the distances of the sun and moon from the earth } if 
the amount of either of these inequalities can be observed, 
the distance of the sun can theiefore be deduced, that of 
the moon being known with great accuracy l/lt was by a 
virtual application of the first of these methods that Hansen 
( 286) m 1854, in the course of an elaborate investigation 
of the lunar theory, ascertained that the current value of 
the sun's distance was decidedly too large, and Leverner * 
( 288) confirmed the correction by the second method in 

gam, certain changes m the orbits of ourjwo^ rjeigh- 
boursj Venus and Mars, are known to depend upon the 
ratio of the masses of the sun and earth, and can hence 
be connected, by gravitational principles, with the quantity 
sought Leverner pointed out m 1861 that the motions 
of Venus and of Mars, like that of the moon, were incon- 
sistent with the received estimate of the sun's distance, and 
he subsequently worked out the method more completely 
and deduced (1872) values of the parallax The displace- 
ments to be observed are very minute, and their accuiate 
determination is by no means easy, but they are both 
secular (chapter xi , 242), so that in the course of time 
they will be capable of very exact measurement Leverner's 
method, which is even now a valuable one, must therefore 
almost inevitably outstrip all the others which are at present 
known ; it is difficult to imagine, for example, that the 
transits of Venus due in 2004 and 2012 will have any 
value for the, purpose of the determination of the sun's 
distance f 

283 One other method, in two slightly different forms, 
has become available dmmg this centuiy The displace- 
ment of a star by aberration (chapter x, 210) depends 

366 A Short History of Astronomy [CH xin 


upon the ratio of the velocity of light to that of the earth 

in its orbit round the sun , and observations of Jupiter's 
satellites after the manner of Roemer (chaptei vin , 162) 
give the light-equation, or time occupied by light in 
travelling from the sun to the earth Either of these 
astronomical quantities of which aberration is the more 
accurately known can be used to determine the velocity 
of light when the dimensions of the solar system are known, 
or mce versa No independent method of determining the 
velocity of light was known until 1849, when Hifpolyte 
JFtzeau (1819-1896) inyented and successfully carried out 
a laboratory method ^ 

%/ New methods have been devised since, and three com- 
paiatively recent series of experiments, by M Cornu in 
France (1874 and 1876) and by Dr Michelson (1879) 
and Professor New comb (1880-82) in the United States, 
agreeing closely with one another, combine to fix the velocity 
of light at very nearly 186,300 miles (299,800 kilometres) 
per second , the solar parallax resulting from this by means 
of aberration is very nearly 8" 8 * r 

284 Encke's value of the sun's parallax, S" 571, deduced 
from the transits of Venus (chapter x , 227) in 1761 and 
17695 and published in 1835, corresponding to a distance 
of about 95,000,000 miles, was generally accepted till past 
the middle of the century. Then the gravitational methods 
of Hansen and Leverner, the earlier determinations of the 
velocity of light, and the observations made at the opposition 
of Mars in 1862, all pointed to a considerably larger value 
of the parallax 3 a fresh examination of the i8th century 
observations shewed that larger values than Encke's could 
easily be deduced from them, and for some time from 
about 1860 onwards a parallax of nearly 8" 95, correspond- 
ing to a distance of rather more than 91,000,000 miles, was 
in common use Various small errors in the new methods 
were, however, detected, and the most probable value of the 
parallax has again increased Three of the most reliable 
methods, the diurnal method as applied to Mars in 1877, 
the same applied to the minor planets in 1888-89, anc * 

* Newcomb's velocity of light and Nyren's constant of aberration 
(20" 4921) give 8" 794, Struve's constant of aberration (20" 445). 
Loewy's (20*447), and Hall's (20*454) each give 8"8i 

$ 284286] Solar Parallax Variation of Latitude 367 

abeiration, unite in giving values not differing from 8" 80 
by more than two or three hundredths of a second The 
results of the last transits of Venus, the publication and 
discussion of which have been spread over a good many 
years, point to a somewhat larger value of the parallax. 
JMost astionomers appear to agree that a paiallax of 8" 8, 
corresponding to a distance of rather less thaja 93,000,000 
miles, represents fairly the available data \s* 

2 85.V ; The minute accuracy of modern observations is 
well illustrated by the recent discovery of a variation in 
the latitude of several observatories ^Observations taken at 
Berlin in 1884-85 indicated a minute variation m the latitude, 
special senes of observations to verify this were set on 
foot in several European observatories, and subsequently at 
Honolulu and at Cordoba A periodic alteration in latitude 
amounting to about %' emerged as the result Latitude 
being defined (chapter x, 221) as the angle whicb the 
vertical at any place makes with the equator, which is 
the same as the elevation of the pole above the horizon, 
is consequently altered by any change in the equator, and 
therefore by an alteration in the position of the, earth's poles 
01 ,the ends of the axis about which it rotates. ^ 
XDr S C Chandler succeeded (1891 and subsequently) 
m shewing that the observations in question could be in 
gieat part explained by supposing the earth's axis to undergo 
a minute change of position in such a way that either pole 
of the earth describes a circuit round its mean position in 
about 427 days, never deviating more than some 30 feet 
from it It is well known from dynamical theory that a 
rotating body such as the earth can be displaced m this 
manner, but that if the earth were perfectly iigid the period 
should be 306 days instead of 427. The disciepancy 
between the two numbers has been ingeniously used as a 
test of the extent to which the earth is capable of yielding . j 
like an clastic solid to the various forces which tend to r 
strain it 

286. All the great problems of gravitational astronomy 
have been rediscussed since Laplace's time, and further 
steps taken towards their solution 

Laplace's treatment of the lunar theory was first developed 
by Mane Charles Theodore Damomau (1768-1846), whose 

368 A Short History of Astronomy CCH xiu 

Tables de la Lune (1824 and 1828) were for some time in 
general use 

Some special problems of both lunar and planetary theory 
were dealt with by Simeon Denis Poisson (1781-1840), who 
is, however, better known as a writer on other branches of 
mathematical physics than as an astronomer A very 
elaborate and detailed theory of the moon, investigated by 
the general methods of Laplace, was published by Giovanni 
Antonio Amadeo Plana (1781-1869) in 1832, but unac- 
companied by tables A general treatment of both lunar 
and planetary theories, the most complete that had appeared 
up to that time, by Philippe Gustave Doulcet de Pontecoitlant 
(1795-1874), appeared in 1846, with the title TMorie 
Analytique du Syst&me du Monde 9 and an incomplete 
lunar theory similar to his was published \>y John William 
Lubbock (1803-1865) in 1830-34 

A great advance in lunar theory was made by Peter 
Andreas Hansen (1795-1874) of Gotha, who published in 
1838 and 1862-64 the treatises commonly known respectively 
as the Fundamenta * and the Darlegung^ and produced 
in 1857 tables of the moon's motion of such accuracy that 
the discrepancies between the tables and observations in 
the century 1750-1850 were never greater than i" 01 2". 
These tables were at once used for the calculation of the 
Nautical Almanac and other periodicals of the same kind, 
and with some modifications have remained in use up to 
the present day 

A completely new lunar theory of great mathematical 
interest and of equal complexity was published by Charles 
Delaunay (1816-1872) m 1860 and 1867 Unfortunately 
the author died before he was able to woik out the 
corresponding tables 

Professor Newcomb of Washington ( 283) has rendered 
valuable services to lunar theory as to other branches of 
astronomy by a number of delicate and intricate calcula- 
tions, the best known being his comparison of Hansen's tables 
with observation and consequent corrections of the tables. 

* Fundamenta Nova Investtgattoms Orbitae Verae quam Luna. 

f Darlegung der theoretischen Berechnung der in den Mondtafaln 
angewandten Storungen. 

287] Lunar Theory 369 

New methods of dealing with lunar theory were devised 
by the late Professor John Couch Adams of Cambridge 
(1819-1892), and similar methods have been developed by 
Dr G W Hill of Washington , so fai they have not been 
worked out in detail in such a way as to be available for 
the calculation of tables, and their interest seems to be 
at present mathematical rather than practical,, but the 
necessary detailed work is now in progress, and these and 
allied methods may be expected to lead to a considerable 
diminution of the present excessive intricacy of lunar 

287 One sjjecial point in lunar theory may be worth 
mentioning %The secular acceleration of the moon's mean 
motion which had perplexed astronomers since its first 
discoveiy by Halley (chapter x , 201) had, as we have 
seen (chapter xi , 240), received an explanation in 1787 
at the hands of Laplace Adams, on going through the 
calculation, found that some quantities omitted by Laplace 
as unimportant had in reality a very sensible effect on the 
result, so that a ceitain quantity expressing the rate of 
increase of the moon's motion came out to be between 
5'' and 6", instead of being about 10", as Laplace had found 
and as observation required The coriection was disputed 
at first by several of the leading experts, but was confirmed 
independently by Delaunay and is now accepted The 
moon appears m consequence to have a certain very minute 
increase m speed for which the theory of gravitation affords 
no explanation An ingenious though by no means certain 
explanation was suggested by Delaunay in 1865 It had 
been noticed by Kant that tL^aL^dtLQTi that is, the friction 
set up between the solid earth and the ocean as the result 
of the tidal motion of the latter would have the effect of 
checking to some extent the rotation of the earth , but as 
the effect seemed to be excessively minute and incapable 
of piecise calculation it was generally ignored An attempt 
to calculate its amount was, however, made in 1853 by 
IVilham Ferrel, who also pointed out that, as the period 
of the earth's rotation the day is our fundamental unit 
of time, a reduction of the eaith's rate of rotation involves 
the lengthening of oui unit of time, and consequently pro- 
duces an appaient increase of speed in all other motions 


370 A Short History of Astronomy [CH 

measuied m terms of this unit Delaunay, working inde- 
pendently, arrived at like conclusions, and shewed that tidal 
friction might thus be capable of producing just such an 
alteration in the moon's motion as had to be explained , if 
this explanation were accepted the observed motion of the 
moon would give a measure of the effect of tidal friction. 
The minuteness of the quantities involved is shewn by 
the fact that an alteration m the eaith's rotation equivalent 
to the lengthening of the day by T \- second in 10,000 years 
is sufficient to explain the acceleration m question More- 
over it is by no means certain that the usual estimate of 
the amount of this acceleration based as it is in part on 
ancient eclipse observations is correct, and even then a 
part of it may conceivably be due to some indirect effect 
of gravitation even more obscure than that detected^by 
Laplace, or to some other cause hitherto unsuspected ^ 

288. Most of the writers on lunar theory alieady men- 
tioned have also made contributions to various parts of 
planetary theory, but some of the most impoitant advances 
in planetary theory made since the death of Laplace have 
been due to the French mathematician Urbain Jean Joseph 
Leverner (1811-1877), whose methods of determining the 
distance of the sun have been already refeired to ( 282). 
His first important astronomical paper (1839) was a dis- 
cussion of the stability (chapter xi , 245) of the system 
formed by the sun and the three largest and most distant 
planets then known, Jupiter, Saturn, and Uranus Subse- 
quently he worked out afresh the theory of the motion of 
the sun and of each of the principal planets, and constructed 
tables of them, which at once superseded earlier ones, and 
are now used as the basis of the chief planetary calculations 
m the Nautical Almanac and most other astronomical 
almanacs. Leverner failed to obtain a satisfactory agree- 
ment between observation and theory in the case of 
Mercury, a planet which has always given great trouble to 
astronomers, and was inclined to explain the discrepancies 
as due to the influence either of a planet revolving between 
Mercury and the sun or of a number of smaller bodies 
analogous to the minor planets ( 294). 

Researches of a more abstract character, connecting 
planetary theory with some of the most recent advances 

** 288 28 9l Planetary Theory 37! 

m pure mathematics, have been carried out by Hugo Gyld'en 
(1841-1896), while one of the most eminent pure mathe- 
maticians of the day, M Henri Poincare of Pans, has 
recently turned his attention to astronomy, and is engaged 
m investigations which, though they have at present but 
little bearing on practical astronomy, seem likely to throw 
important light on some of the general problems of celestial 

289 One memoiable triumph of gravitational astronomy, 
the discovery of Neptune, has been described so often and 
S ful i "^ elsewliere * that a ver 7 brief account will suffice 
here VSoon after the discovery of Uranus (chapter xn , 
253) it was found that the planet had evidently been 
observed, though not recognised as a planet, as early as 
*6c)o, and on several occasions afterwards 
^when the first attempts were made to compute its orbit 
carefully, it was found impossible satisfactorily to reconcile 
the earlier with the later obseivations, and in Bouvard's 
tables (chaptei xi , 247, note) published in 1821 the 
earlier observations were rejected But even this drastic 
measure did not cure the evil ; discrepancies between the 
obseived and calculated places soon appeared and increased 
year by year Several explanations were proposed, and 
more than one astronomer threw out the suggestion that 
the irregularities might be due tp the attraction of a hitherto 
unknown planet The first serious attempt to deduce from 
the irregularities m the motion of Uranus the position of 
this hypothetical body was made by Adams immediately 
after taking his degree (1843) By October 1845 he had 
succeeded m constructing an orbit for the new planet, and 
m assigning for it a position differing (as we now know) by 
less than 2 (four times the diameter of the full moon) from 
its actual position No telescopic search for it was, how- 
ever, undertaken. Meanwhile, Leverner had independently 
taken up the inquiry, and by August 3ist, 1846, he, like 
Adams, had succeeded in detei mining the orbit and"* the 
position of the disturbing body. On the 23rd of the follow- 

* JSg in Grant's History of Physical Astronomy, Herschel's Out- 
lines of Astronomy, Miss Cleike's History of Astronomy in the 
Nineteenth Century, and the memoir by Dr Glaisher prefixed to the 
first volume of Adams's Collected Papers 

372 A Short History of Astronomy [CH xin 

ing month Dr Galle of the Berlin Observatory received 
from Leverner a request to search for it, and on the same 
evening found close to the position given by Leverner a 
strange body shewing a small planetary disc, which was 
soon recognised as a new planet, known now as Neptune 

It may be worth while noticing that the error m the 
motion of Uranus which led to this remarkable discovery 
never exceeded 2', a quantity imperceptible to the ordinary 
eye , so that if two stars were side by side m the sky, one 
m the true position of Uranus and one in the calculated 
position as given by Bouvard's tables, an ? observer of 
ordinary eyesight \\ould see one star only * 

290 The lunar tables of Hansen and Professor Newcomb, 
and the planetary and solar tables of Leverner, Pro- 
fessor Newcomb, and Dr. Hill, represent the motions of 
the bodies dealt with much more accurately than the corre- 
sponding tables based on Laplace's work, just as these were 
m turn much more accurate than those of Euler, Clairaut, 
and Halley But the agreement between theory and obser- 
vation is by no means perfect, and the discrepancies are m 
many cases greater than can be explained as being due to 
the necessary imperfections in our observations 

The two most striking cases are perhaps those of Mercury 
and the moon. Leverner's explanation of the irregularities 
of the former ( 288) has^ never been fully justified or 
generally accepted , and the" position of the moon as given 
m the Nautical Almanac and in similar publications is 
calculated by means of certain corrections to Hansen's 
tables which were deduced by Professor Newcomb from 
observation and have no justification m the theory of 

29i!/rhe calculation of the paths of comets has be- 
come of some importance during this century owing to 
the discovery of a number of comets revolving round the 
sun in comparatively short periods Halley's comet 
(chapter xi , 231) reappeared duly m 1835, passing through 
its perihelion within a few days of the times predicted by 
three independent calculators, and it may be confidently 
expected again about 1910 Four other comets are now 
known which, like Halley's, revolve m elongated elliptic 
orbits, completing a revolution in between 70 and 80 yeais , 

) 2QO 2Q2 

Orbits of Comets 


two of these have been seen at two returns, that known as 
Olbers's comet m 1815 and 1887, and the Pons-Brooks 
comet in 181 2 and 1884 Fourteen other comets with periods 
varying between 3^ years (Encke's) and 14 years (Turtle's), 
have been seen at more than one return } about a dozen 
more have periods estimated at less than a century, and 
20 or 30 otheis move in orbits that are decidedly elliptic, 
though their periods are longer and consequently not known 

FIG. 87 The path of Halley's comet 

with much certainty. Altogether the paths of about 230 
or 240 comets hajpe been computed, though many are 
highly uncertain r 

292 In the theory of the tides the fiisl important advance 
made after the publication of the M'ecanique Celeste was 
the collection of actual tidal observations on a large scale, 
their interpretation, and their companson with the results 
of theory. The pioneers in this direction weie Lubbock 
( 286), who presented a series of papers on the subject 

374 -^ Short History of Astronomy [CH xni 

to the Royal Society in 1830-37, and William Whewell 
(1794-1866), whose papers on the subject appeared between 
1833 an d l8 5* Airy ( 28l )> then Astionomer Royal, 
also published in 1845 an important treatise dealing with 
the whole subject, and discussing m detail the theoiy of 
tides in bodies of water of limited extent and special form. 
The analysis of tidal observations, a large number of which 
taken from all parts of the world are now available, has 
subsequently been carried much further by new methods 
due to Lord Kelvin and Professor G H Darwin A 
large quantity of information is thus available as to the 
way m which tides actually vary in different places and 
according to different positions of the sun and moon 
VOf late years a good deal of attention has been paid to 
the effect of the attraction of the sun and moon in pioducmg 
alterations analogous to oceanic tides m the earth itself. 
No body is perfectly rigid, and the forces in question must 
therefore produce some tidal effect The problem was first 
investigated by Lord Kelvin m 1863, subsequently by 
Professor Darwin and others Although definite numerical 
results are hardly attainable as yet, the work so far earned 
out points to the comparative smallness of these bodily 
tides and the consequent great rigidity of the earth, a result 
of interest m connection with geological inquiries into the 
nature of the interior of the earth 

Some speculations connected with tidal friction aie 
referred to elsewhere (320) 

293 The series of propositions as to the stability of 
the solar system established by Lagrange and Laplace 
(chapter xi , 244, 245), regarded as abstract propositions 
mathematically deducible from certain definite assumptions, 
have been confirmed and extended by later mathematicians 
such as Poisson and Levernei , but their claim to give 
information as to the condition of the actual solar system 
at an indefinitely distant future time receives much less 
assent now than formerly The general trend of scientific 
thought has been towards the fuller recognition of the 
merely approximate and probable character of even the best 
ascertained portions of our knowledge , " exact," " always," 
and "certain" are words which are disappearing from the 
scientific vocabulary, except as convenient abbreviations, 

$ 293] Tides the Stability of the Solar System 375 

Propositions which profess to be or are commonly inter- 
preted as being " exact" and valid throughout all future 
time are consequently regarded with considerable distrust, 
unless they are clearly mere abstractions 

In the case of the paiticular propositions in question the 
progress of astronomy and physics has thrown a good deal 
of emphasis on some of the points in which the assumptions 
requned by Lagrange and Laplace are not satisfied by the 
actual solar system 

It was assumed for the purposes of the stability theorems 
that the bodies of the solar system are perfectly rigid , m 
other words, the motions relative to one another of the parts 
of any one body were ignored Both the ordinary tides of 
the ocean and the bodily tides to which modern lesearch 
has called attention were therefore left out of account 
Tidal friction, though at present very minute m amount 
( 287), differs essentially from the perturbations which 
form the mam subject-matter of gravitational astronomy, 
inasmuch as its action is irreversible The stability theorems 
shewed in effect that the ordinary perturbations produced 
effects which sooner or later compensated one another, so 
that if a particular motion was accelerated at one time it 
would be retarded at another , but this is not the case with 
tidal friction /Tidal action between the earth and the 
moon, for example, gradually lengthens both the day and the 
month, and increases the distance between the earth and 
the moon Solar tidal action has a similar though smaller 
effect on the sun and earth. The effect in each case as 
far as we can measure it at all seems to be minute almost 
beyond imagination, but there is no compensating action 
tending at any time to leverse the process U^tnd on the 
^vhole the energy of the bodies concerned is thereby lessened 
'/Again, modern theories of light and electricity require space 
to be filled with an "ether" capable of transmitting certain 
waves , and although there is no direct evidence that it in 
any way affects the motions of earth or planets, it is difficult 
to imagine a medium so different from all known foims of 
oidmaiy matter as to offer no lesistance to a body moving 
through it Such resistance would have the effect of slowly 
bringing the members of the solar system nearer to the sun, 
and gradually diminishing their times of Devolution round 

3?6 A Short History of Astronomy [CH xin 

it This is again an irreversible tendency for which we 
know of no compensation & 

In fact, from the point of view which Lagrange and 
Laplace occupied, the solar system appeared like a clock 
which, though not going quite regularly, but occasionally 
gaming and occasionally losing, nevertheless lequired no 
winding up, whereas modern research emphasises the 
analogy to a clock which after all is running down, though 
at an excessively slow rate Modern study of the sun's 
heat (319) also indicates an irreversible tendency towards 
the " running down " of the solar system m another way 

294. Our account of modem descriptive astronomy may 
conveniently begin with planetary discoveries 
\/ Tn e first day of the ipth century was marked by the 
discovery of a new planet, known as Ceres It was seen 
by Giusepfe Piazzi (1746-1826) as a strange star m a 
region of the sky which he was engaged in mapping, and 
soon recognised by its motion as a planet Its orbit- 
first calculated by Gauss ( 276) shewed it to belong 
to the space between Mars and Jupiter, which had been 
noted since the time of Kepler as abnormally large That 
a planet should be found m this region was therefore 
no great surprise , but the discovery by Heinnch Olbers 
(1758-1840), scarcely a year later (March 1802), of a second 
body (Pallas), revolving at nearly the same distance from 
the sun, was wholly unexpected, and revealed an entirely 
new planetary arrangement It was an obvious con- 
jecture that if there was room for two planets there was 
room for more, and two fresh discoveries (Juno in 1804, 
Vesta in 1807) soon followed. 

The new bodies were very much smaller than any of 
the other planets, and, so far from readily shewing a 
planetary disc like their neighbours Mars and Jupiter, 
were barely distinguishable in appearance from fixed stars, 
except m the most powerful telescopes of the time , hence 
the name asteroid (suggested by William Herschel) or 
minor planet has been generally employed to distinguish 
them from the other planets Herschel attempted to 
measure their size, and estimated the diameter of the largest 
at under 200 miles (that of Mercury, the smallest of the 
ordinary planets, being 3000), but the problem was m reality 

FIG 88 Photographic trail of a minor planel . 

2 94l The Minor Planets 377 

too difficult even for his unrivalled powers of observation 
The minor planets were also found to be remarkable for 
the great inclination and eccentricity of some of the orbits , 
the path of Pallas, for example, makes an angle of 35 with 
the ecliptic, and its eccentricity is |, so that its least dis- 
tance fiom the sun is not much more than half its greatest 
distance These chaiactenstics suggested to Olbers that 
the minor planets were in reality fragments of a primeval 
planet of moderate dimensions which had been blown 
to pieces, and the theory, which fitted most of the facts 
then known, was received with great favoui in an age 
when "catastrophes" were still in fashion as scientific 

The four minor planets named were for nearly 40 years 
the only ones known; then a fifth was discovered in 
1845 by Karl Ludwtg Hencke (1793-1866) after 15 years 
of search Two more were found in 1847, another m 
1848, and the number has gone on steadily increasing 
ever since The process of discovery has been very much 
facilitated by improvements in star maps, and latterly by 
the introduction of photography In this last method, 
first used by Di Max Wolf of Heidelberg in 1891, a 
photographic plate is exposed for some hours , any planet 
present in the legion of the sky photographed, having 
moved sensibly relatively to the stars m this period, is thus 
detected by the trail which its image leaves on the plate 
The annexed figure shews (near the centre) the trail of the 
minor planet Svea, discovered by Dr Wolf on March 
2ist, 1892 

At the end of 1897 no less than 432 minor planets were 
known, of which 92 had been discovered by a single 
observer, M Chariots of Nice, and only nine less by 
Professor Pahsa of Vienna 

The paths of the minor planets practically occupy the 
whole region between the paths of Mars and Jupitei, 
though few aie near the boundaries ; no orbit is more 
inclined to the ecliptic than that of Pallas, and t 
eccentricities range from almost zero up to about ] 

Fig 89 shews the orbits of the first two minor planets 
discovered, as well as of No 323 (Brucia), which comes 
nearest to the sun, and gf No 361 (not yet named), 

378 A Short History of Astronomy [Cn xin 

which goes farthest from it. ^.11 the orbits are described 
m the standard, or west to east, dnection. The most 
interesting characteristic in the distribution of the minor 
planets, first no ted in 1866 by JDamd jKir^wood(ji^>i^i^>g^)j 
is the existence of comparatively clear spaces in the regions 
where the disturbing action of Jupiter would by Lagiange's 

FIG 89 Paths of minor planets 

principle (chapter xi , 243) be most effective for instance, 
at a distance from the sun about five-eighths that of Jupiter, 
a planet would by Kepler's law revolve exactly twice as fast 
as Jupiter ; and accordingly there is a gap among the minor 
planets at about this distance, 

Estimates of the sizes and masses of the minor planets 
are still very uncertain. The first direct measiuemcnts 

* 2 94] 

The Minor Planets 


of any of the discs which seem reliable are those of 
Professor E E Barnard, made at the Lick Observatory 
m 1894 and 1895 9 according to these the three largest 
minor planets, Ceres, Pallas, and Vesta, have diameters 
of nearly 500 miles, about 300 and about 250 miles 
respectively Their sizes compared with the moon aie 
shewn on the diagram (fig 90) An alternative method 
the only one available except for a few of the very largest 

90 Comparative sizes of three minor planets and the moon, 

of the minor planets is to measure the amount of light re- 
ceived, and hence to deduce the size, on the assumption that 
the reflective power is the same as that of some known planet 
This method gives diameters of about 300 miles for the 
brightest and of about a dozen miles for the faintest known 
Leverner calculated from the perturbations of Mars that 
the total mass of all known or unknown bodies between 
Mais and Jupiter could not exceed a fouith that of the earth , 
but such knowledge of the sixes as we can derive from 

380 A Short History of Astronomy [dr. XIII 

light-observations seems to indicate that the total mass of 
those at present known is many hundred times less than 
this limit y 

\/295 Neptune and the minor planets are the only planets 
which have been discovered during this century, but several 
satellites have been added to our system 

Barely a fortnight after the discovery of Neptune (1846) 


FIG 91. Saturn and its system. 

a satellite was detected by William Lassell o 

at Liverpool Like the satellites of Uianus, this revolves 
round its primary from east to west that is, in the direction 
contrary to that of all the other known motions of the solar 
system (certain long-period comets not being counted) 

Two years later (September i6th, 1848) William Cranch 
hond (1789-1859) discovered, at the Harvard College 

2 9s] New Satellites 381 

Jbservatory, an eighth satellite of Saturn, called Hyperion, 
r hich was detected independently by Lassell two days 
fterwards In the following year Bond discovered that 
aturn was accompanied by a third comparatively dark ring 
-now commonly known as the crape ring lying imme- 
lately inside the bright rings (see fig 95), and the 
iscovery was made independently a fortnight later by 


/' MARS "\ 



FIG. 92. Mars and its satellites 

Vilham Rutter Daives (1799-1868) in England Lassell 
iscovered in 1851 two new satellites of Uranus, making 
total of four belonging to that planet The next dis- 
ovenes were those of two satellites of Mars, known as 
leimos and P/iobos, by Professor Asaph Hall of Washington 
n August nth and i;th, 1877. These are remarkable 
hiefly for their close proximity to Mars and their extremely 
ipid motion, the nearer one revolving more rapidly than 

32 A Short History of Astronomy [CH XIII 


FlG 93 Jupiter and its satellites 

con^nel ^ ^^ * phyS1Cal C0ndltion f 'he bod i' 
Astronomers are naturally most famihai with the surface 


296, 297] Satellites of Jupiter the Moon Mars 383 

of our nearest neighbour, the moon The visible half has 
been elaborately mapped, and the heights of the chief 
mountain ranges measured by means of their shadows 
Modern knowledge has done much to dispel the view, held 
by the earlier telescopists and shared to some extent even 
by Herschel, that the moon closely resembles the earth and 
is suitable for inhabitants like ourselves The dark spaces 
which were once taken to be seas and still bear that name 
are evidently covered with dry rock , and the craters with 
which the moon is covered are all with one or two doubt- 
ful exceptions extinct , the long dark lines known as 
rills and formerly taken for river-beds have clearly no 
watei in them The question of a lunar atmosphere is 
more difficult if there is an its density must be very small, 
some hundredfold less than that of our atmosphere at the 
surface of the earth , but with this restriction there seems 
to be no bar to the existence of a lunar atmosphere of 
considerable extent, and it is difficult to explain certain 
obseivations without assuming the existence of some atmo- 
spheie f^ 

297. Mars, being the nearest of the superior planets, is 
the most favourably situated for observation The chief 
markings on its surface provisionally interpreted as being 
land and water are fairly peimanent and therefore 
recognisable , several tolerably consistent maps of the 
surface have been constructed, and by observation of 
certain striking features the rotation period has been 
determined to a fraction of a second N/Signor Schiaparelli 
of Milan detected at the opposition of 1877 a number of 
mteisecting dark lines generally known as canals, and as 
the result of observations made during the opposition of 
1881-82 announced that certain of them appeared doubled, 
two nearly parallel lines being then seen instead of one 
These remarkable observations have been to a great extent 
confirmed by other observers, but remain unexplained t~ 

The visible surfaces of Jupiter and Saturn appear to be 
layers of clouds , the low density of each planet ( i 3 and 
7 respectively, that of water being i and of the earth 5*5), 
the lapid changes on the surface, and other facts indicate 
that these planets aie to a great extent in a fluid condition, 
and have a high temperature at a veiy modeiate distance 

384 A Short History of Astronomy fdr xin, 

below the visible surface The surface maikmgs are m each 
case definite enough for the rotation periods to be fixed with 
some accuracy , though it is clear in the case of Jupitei, 
and probably also in that of Saturn, that as with the sun 
( 298) different parts of the surface move at different rates 

Laplace had shewn that Saturn's nng (01 rings) could not 
be, as it appeared, a uniform solid body , he lashly inferred 
without any complete investigation that it might be 
an irregularly weighted solid body The fust important 
advance was made by James Clerk Maxwell (1831 1879), 
best known as a writer on electricity and othei branches 
of physics VMaxwell shewed (1857) that the rings could 
neither be continuous solid bodies nor liquid, but that 
all the impoitant dynamical conditions would be satisfied 
if they were made up of a very large number of small 
solid bodies revolving independently round the sun * The 
theory thus suggested on mathematical grounds has le- 
ceived a good deal of support from telescopic evidence 
The rings thus bear to Saturn a relation having some 
analogy to that which the minor planets beat to the sun , 
and Kirkwood pointed out m 1867 that Cassim's division 
between the two mam rings can be explained by the 
perturbations due to certain of the satellites, just as the 
corresponding gaps in the minor planets can be explained 
by the action of Jupiter ( 294) /^ 

The great distance of Uranus and Neptune naturally 
makes the study of them difficult, and next to nothing us 
known of the appearance 01 constitution of either , their 
mtation periods are wholly uncertain 
v Mercury and Venus, being infenoi planets, are never very 
far from the sun in the sky, and therefore also extremely 
difficult to observe satisfactorily Various bright and dark 
markings on their surfaces have been iecorded, but different 
observers give very different accounts of them The i otation 
periods are also very uncertain, though a good many astrono- 
mers support the view put forward by Sig, Schiaparelh, in 
1882 and 1890 for Mercury and Venus respectively, that 
each rotates m a time equal to its period of revolution round 
the sun, and thus always turns the same face towards the 
sun Such a motion which is analogous to that of the 
* This had been suggested as a possibility by several eaihci wntois 




* 398] Planetary Observations Sun-spots 385 

moon round the earth and of Japetus round Saturn 
(chapter xn , 267) -could be easily explained as the 
result of tidal action at some past time when the planets 
were to a great extent fluid. ^ 

298 Telescopic study of the surface of the sun during 
the century has resulted in an immense accumulation of 
detailed knowledge of peculiarities of the various markings 
on the surface The most interesting results of a general 
nature are connected with the distribution and periodicity 
of sun-spots The earliest telescopists had noticed that the 
number of spots visible on the sun varied from time to time 
but no law of variation was established till 1851, when Hem- 
rich ^toa^of Dessau(i78 9 -i87s) published m Humboldt's 
Cosmos the results of observations of sun-spots earned out 
during the piecedmg quarter of a century, shewing that the 
number of spots visible increased and decreased in a 
tolerably regular way in a period of about ten years 

Earlier records and later observations have confirmed 
the general result, the period being now estimated as 
slightly over ii years on the average, though subject to 
considerable fluctuations. A year later (1852) three inde- 
pendent investigators, Sir Edward Salnne (1788-1881) in 
England, Rudolf Wolf (1816-1893) and Alfred Gautier 
(1793-1881) m Switzerland, called attention to the remark- ^ 
able similarity between the periodic vacations of sun-spots 
and of various magnetic disturbances on the earth Not 
only is the period the same, but it almost invariably happens 
that when spots are most numeious on the sun magnetic 
disturbances are most noticeable on the earth, and that 
similarly the times of scarcity of the two sets of phenomena 
coincide This wholly unexpected and hitherto quite un- 
explained relationship has beenconfiimed by the occurrence 
on seveial occasions of decided magnetic disturbances 
simultaneously with rapid changes on the surface of the sun 
A long series of observations of the position of spots on 
the sun undertaken by Richard Christopher Carrmgton 
(1826-1875) led to the first clear recognition of the differ- 
, ence m the rate of rotation of the different parts of the 
/surface of the sun, the period of rotation being fixed (18*0) 
at about 25 days at the equator, and two and a half days I 
longer half-way between the equator and the poles ; while 

2 5 

3 86 A Short History of Astronomy CCH xin 

m addition spots were seen to have also independent 
"proper motions " Camngton also established (1858) the 
scarcity of spots in the immediate neighbourhood of the 
equator, and confirmed statistically their prevalence in 
the adjacent regions, and their great scarcity more than 
about 35 from the equator, and noticed further certain 
regular changes in the distribution of spots on the sun in 
the course of the i i-year cycle 

Wilson's theory (chapter xn , 268) that spots are de- 
pressions was confirmed by an extensive series of photogiaphs 
taken at Kew in 1858-72, shewing a large preponderance 
of cases of the perspective effect noticed by him , but, on 
the other hand, Mr F Howktt, who has watched the sun 
for some 35 years and made several thousand drawings of 
spots, considers (1894) that his observations are decidedly 
against Wilson's theory Other observers are divided in 

299 Spectrum analysis, which has played such an im- 
portant part in recent astronomical work, is essentially a 
method of ascertaining the nature of a body by a process 
of sifting or analysing into different components the light 
received from it 

It was first clearly established by Newton, m 1665-06 
(chapter ix , 168), that ordinary white light, such as sun- 
light, is composite, and that by passing a beam of sunlight 
with proper precautions through a glass prism it can be 
decomposed into light of different colours , if the beam so 
decomposed is received on a screen, it produces a band of 
colours known as a spectrum, red being at one end and 
violet at the other. 

Now according to modern theories light consists essen- 
tially of a series of disturbances or waves transmitted at 
extremely short but regular intervals from the luminous 
object to the eye, the medium through which the disturb- 
ances travel being called ether The most important 
characteristic distinguishing different kinds of light is the 
interval of time or space between one wave and the next, 
which is generally expressed by means of wave-length, or 
the distance between any point of one wave and the corre- 
sponding point of the next Differences m wave-length 
shew themselves most readily as differences of colour ; so 

bO -ft, 

C 8 



* 299] Spectrum Analysts 3 g 7 

that light of a particular colour found at a particular cart of 

about twice as great, fiom which it follows (28? from 
the known velocity of light, that when we look at the red en^ 
of a spectrum about 400 billion waves of light enter the eve 
otLT; I ' M nd 'T 6 that number ^ we looVat the 

mcombmation with one or more prisms o a gratmV and 
the arrangement is such that the spectrum /no fhrown 
on to a screen, but either viewed directly by the eye or 
photographed The whole apparatus is knL/as a s^ectro* 

>lar spectrum appeared to Newton as a continuous 
colours , but in 1802 Wzlham Hyde w~n~. 

f ** oo,' 2 am yde Vtoln 


I certain letters of the alphabet to a few of the most 

S'ofT ' ^ ieSt "? no W^y ^own by the wave- 
length of the corresponding kind of light 

It was also gradually discovered that dark bands could 
oe produced artificially in spectra by passing lieht throntrh 
various coloured substances , and that, on the other haSd "he 
spectra of certain flames were crossed by various 3nes 

Several attempts were made to explain and to connect 
these various observations, but the first satisfactory and 
tolerably complete explanation was given m 1859 by Lstev 

388 A Short History of Astronomy [Cn xin. 

Robert Kirchhoff (1824-1887) of Heidelberg, \\ho at first 
worked in co-operation with the chemist Bunsen 

Kirchhoff shewed that a luminous solid or liquid or, 
as we now know, a highly compressed gas gives a con- 
tinuous spectrum , whereas a substance m the gaseous 
state gives a spectrum consisting of bright lines (with or 
without a faint continuous spectrum), and these bright 
lines depend on the particular substance and are charac- 
teristic of It Consequently the presence of a particular 
substance in the form of gas m a hot body can be inferred 
from the presence of its characteristic Imes in the spectrum 
of the light The dark lines in the solar spectrum were 
explained by the fundamental principle often known as 
Kirchhoff's law that a body's capacity for stopping or 
absorbing light of a particular wave-length is proportional 
to its power, under like conditions, of giving out the 
same light If, in particular, light from a luminous solid 
or liquid body, giving a continuous spectrum, passes through 
a gas, the gas absorbs light of the same wave-length as that 
which it itself gives out if the gas gives out more light 
of these particular wave-lengths than it absorbs, then the 
spectrum is crossed by the corresponding bright lines , 
but if it absorbs more than it gives out, then there is a 
deficiency of light of these wave-lengths and the corre- 
sponding parts of the spectrum appear dark that is, the 
spectrum is crossed by dark lines m the same position as 
the bright lines m the spectrum of the gas alone Whether 
the gas absorbs more or less than it gives out is essentially 
a question of temperature, so that if light from a hot solid 
or liquid passes through a gas at a higher temperature a 
spectrum crossed by bright lines is the result, whereas if 
the gas is cooler than the body behind it dark lines are 
seen in the spectrum 

300 The presence of the Fraunhofer lines in the 
spectrum of the sun shews that sunlight comes from a 
hot solid or liquid body (or from a highly compressed gas), 
and that it has passed through cooler gases which have 
absorbed light of the wave-lengths corresponding to the 
dark lines These gases must be either round the sun 01 
in our atmosphere , and it is not difficult tQ shew that, 
although some of the Fraunhofer lines are due to our 

* 300, soi] Spectrum Analysts 389 

trnosphere, the majority cannot be, and are therefore 
a-used by gases m the atmosphere of the sun 

For example, the metal sodium when vaporised gives a 
^ectrum characterised by two nearly coincident bright 
ties in the yellow part of the spectrum , these agree in 
Dsition with a pair of dark lines (known as D) in the 
>ectrum of the sun (see fig. 97); KirchhorT inferred there- 
>re that the atmosphere of the sun contains sodium By 
^rapanson of the dark lines in the spectmm of the sun 
ith the bright lines in the spectra of metals and other sub- 
ances, their presence or absence in the solar atmosphere 
in accordingly be ascertained In the case of iron which 
is an extremely complicated spectrum Kirchhoff suc- 
ieded m identifying 60 lines (since increased to more 
tan 2,000) m its spectrum with dark lines in the spectrum 
: the sun Some half-dozen other known elements were 
so identified by KirchhorT in the sun. 

The inquiry into solar chemistry thus started has since 
sen piosecuted with great zeal Improved methods and 
creased care have led to the construction of a series of 
aps of the solar spectrum, beginning with KirchhofFs own, 
iblished in 1861-62, of constantly increasing complexity 
id accuracy. Knowledge of the spectra of the metals has 
so been greatly extended At the present time between 
> and 40 elements have been identified m the sun, the 
ost interesting besides those already mentioned being 
rdrogen, calcium, magnesium, and carbon 
The first spectroscopic work on the sun dealt only with 
e light received from the sun as a whole, but it was soon 
en that by throwing an image of the sun on to the slit 

the spectroscope by means of a telescope the spectrum 

a particular part of the sun's surface, such as a spot or 
facula, could be obtained 3 and an immense number of 
iservations of this character have been made 
301 Observations of total eclipses of the sun have shewn 
it the bright surface of the sun as we ordinarily see it 
not the whole, but that outside this there is an envelope 
^sorne kind too faint to be seen ordinarily but becoming 
iible when the intense light of the sun itself is cut off 

the moon A white halo of considerable extent round 
^ eclipsed sun, now called the coroiia, is leferred to by 

39 A Short History of Astronomy [CH xill 

Plutarch, and discussed by Keplei (chapter vn., 145) 
Several i8th century astronomers noticed a red streak along 
some portion of the common edge of the sun and moon, 
and red spots or clouds here and there (cf chapter x , 205) 
But little serious attention was given to the subject till after 
the total solar eclipse of 1842 Observations made then 
and at the two following eclipses of 1851 and 1860, in the 
latter of which years photography was for the first time 
effectively employed, made it evident that the red streak 
represented a continuous envelope of some kind sunounding 
the sun, to which the name of chromosphere has been given, 
and that the red objects, generally known as prominences, 
were in general projecting parts of the chromosphere, though 
sometimes detached from it At the eclipse of 1868 the 
spectrum of the prominences and the chromospheie was 
obtained, and found to be one of bright lines, shewing that 
they consisted of gas Immediately afterwards M Janssen, 
who was one of the observers of the eclipse, and Sir 
J. Norman Lockyer independently devised a method 
whereby it was possible to get the spectrum of a prominence 
at the edge of the sun's disc m ordinary daylight, without 
waiting for an eclipse, and a modification introduced by 
Sir William ffuggins in the following year (1869) enabled 
the form of a prominence to be observed spectioscopically. 
Recently (1892) Professor G E Hah of Chicago has 
succeeded in obtaining by a photographic process a repre- 
sentation of the whole of the chromosphere and prominences, 
while the same method gives also photographs of faculae 
(chapter vni , 153) on the visible surface of the sun 

The most important lines ordinarily present m the 
spectrum of the chromosphere aie those of hydrogen, two 
lines (H and K) which have been identified with some 
difficulty as belonging to calcium, and a yellow line the 
substance producing which, known as helium, has only 
recently (1895) been discovered on the earth But the 
chromosphere when disturbed and many of the prominences 
give spectra containing a number of other lines 

The corona was for some time regarded as of the nature 
of an optical illusion produced in the atmospheie That it 
is, at any rate in great part, an actual appendage of the sun 
was first established in j86 9 by the American astronomers 


8 Ihc total solai eclipse of August 291*1, 1886 Flora a drawing 
based on photogiaphs by Dr Schuster and Mr Maunder 

[Tofaccp 390 

io2] Solar Spectroscopy Doppler's Principle 391 

ofessor Harkness and Professor C A Young, who dis- 
>vered a bright lineof unknown origin * m its spectrum, 
us shewing that it consists in part of glowing gas 
ibsequent spectroscopic work shews that its light is partly 
fleeted sunlight 

The coiona has been carefully studied at every solai 
hpse during the last 30 years, both with the spectroscope 
.d with the telescope, supplemented by photography, and 
number of ingenious theories of its constitution have been 
opounded , but our present knowledge of its nature hardly 
es beyond Professor Young's description of it as "an 
conceivably attenuated cloud of gas, fog, and dust, sur- 
undmg the sun, formed and shaped by solar forces " 
302 The spectroscope also gives information as to certain 
otions taking place on the sun It was pointed out in 1842 
' Christian Doppler (1803-1853), though in an imperfect 
.d partly erroneous way, that if a luminous body is 
preaching the observer, or vice versa, the waves of light 
s as it were crowded together and reach the eye at shorter 
tervals than if the body were at rest, and that the character 
the light is thereby changed The colour and the position 
the spectium both depend on the interval between one 
ive and the next, so that if a body giving out light of a 
rticular wave-length, eg. the blue light corresponding to 
e F line of hydrogen, is approaching the observer rapidly, 
e line m the spectrum appears slightly on one side of its 
ual position, being displaced towards the violet end of 
e spectrum, whereas if the body is receding the line 

in the same way, displaced in the opposite direction 
us result is usually known as Doppler's principle. The 
ect produced can easily be expressed numerically If, 
r example, the body is approaching with a speed equal 
TB^ that of light, then 1001 waves entei the eye or the 
ectroscope in the same time m which there would other- 
se only be 1000 ,, and there is m consequence a virtual 
ortening of the wave-length in the ratio of 1001 to 
oo. So that if it is found that a line m the spectrum 

a body is displaced from its ordinary position m such 

* The discovery of a terrestrial substance with this line in its 
sctrum has been announced while this book has been passing 
rough the press. 

39 2 A Short History of Astronomy [CH xni. 

a ^way that its wave-length is apparently decreased by 
TOftr part, it may be inferred that the body is approach- 
ing with the speed just named, or about 186 miles per 
second, and if the wave-length appears increased by the 
same amount (the line being displaced towards the red end 
of the spectrum) the body is receding at the same rate 

Some of the earliest observations of the prominences by 
bir J N Lockyer (1868), and of spots and other features 
of the sun by the same and othei observers, shewed dis- 
placements and distortions of the lines in the spectrum 
which were soon seen to be capable of interpretation by 
this method, and pointed to the existence of violent dis- 
turbances m the atmosphere of the sun, velocities as 
great as 300 miles per second being not unknown The 
method has received an interesting confirmation from obser- 
vations of the spectrum of opposite edges of the sun's disc, 
of which one is approaching and the other leceding; owing 
to the rotation of the sun Professor Duner of Upsala has 
by this process ascertained (1887-89) the rate of rotation 
of the surface of the sun beyond the regions where spots 
exist, and therefore outside the limits of observations such 
as Camngton's ( 2198). 

303 The spectroscope tells us that the atmosphere of 
the sun contains iron and other metals in the form of 
vapour , and the photosphere, which gives the continuous 
part of the solar spectrum, is certainly hotter Moreover 
eveiything that we know of the way m winch heat is com- 
municated from one part of a body to another shews that 
the outer regions of the sun, from which heat and light are 
radiating on a very large scale, must be the coolest parts, 
and that the temperature m all probability rises very rapidly 
towards the interior These facts, coupled with the low 
density of the sun (about a fourth that of the earth) and 
he vio ently disturbed condition of the surface, indicate that 
the bulk of the interior of the sun is an intensely hot and 
highly compressed mass of gas Outside this come in order 
their respective boundaries and mutual relations bemR how- 
ever, very uncertain, first the photosphere, generally regarded 
as a cloud-layer, then the reversing stratum which produces 
most of the Fraunhofer lines, then the chromosphere and 
prominences, and finally the corona, Sun-spots, faculae, and 

FIG 99 The great comet of 1882 (n) on Novcmbci 7th Fro 
a photograph by Di Gil] [7o/acc/> 


303, 304] Structure of the Sun Comets MA 

prominences have been explained in a variety of different 
ways as joint results of solar disturbances of vuimus 
kinds, but no detailed theory that has been given explains 
satisfactory more than a fraction of the observed fats 
or commands rnoie than a very limited amount of assent 
among astronomical experts 

304 More than 200 comets have been seen during t re- 
present century , not only have the motions of most of them 
been observed and their 01 bits computed (291), but in a large 
number of cases the appearance and structure of the romt*t 
have been carefully observed telescopically, while latterly 
spectrum analysis and photography have also been employed. 

Independent lines of inquiry point to the extremely un- 
substantial chaiacter of a comet, with the possible exreptuw 
of the bright cential part or nucleus, which is nearly *ilwn>s 
present More than once, as in 1767 (chapter XI,, 34#), a 
comet has passed close to some member of the solar sy.sUm, 
and has never been ascertained to affect its motion, Thr 
mass of a comet is therefore very small, but itH bulk or 
volume, on the othei hand, is in general very great, th<! tail 
often being millions of miles in length ; so that the density 
must be extremely small Again, stars have often been ol> 
served shining through a comet's tail (as shewn in fig, <>;), 
and even through the head at no great distance fiom the 
nucleus, their brightness being only slightly, if at all, affertrct 
Twice at least (1819, 1861) the earth has passed through a 
comet's tail, but we were so little affected that the* isiel was 
only discovered by calculations made after the event, Thr 
early obseivation (chapter in , 69) that a cometAs tail points 
away fiom the sun has been abundantly verified ; anil from 
this it follows that very rapid changes m the position of 4 the 
tail must occur in some cases For example, the eomet of 
1843 passed very close to the sun at such a rale that tit 
about two hours it had passed from one side of the tm to 
the opposite , it was then much too near the sun to IK* sc*ai f 
but if it followed the ordinary law its tail, which was umifuutlly 
long, must have entirely reversed its direction within this 
short time It is difficult to avoid the inference that tin* 
tail is not a permanent part of the comet, but IK a wtrvum 
3f matter driven off from it in some way by the action of 
;he sun, and in this respect comparable with the 

394 <d Short History of Astronomy [CH xin 

issuing from a chimney This view is confirmed by the 
fact that the tail is only developed when the comet 
approaches the sun, a comet when at a great distance from 
the sun appearing usually as an indistinct patch of nebulous 
light, with perhaps a brighter spot representing the nucleus 
Again, if the tail be formed by an outpouring of matter from 
the comet, which only takes place when the comet is near 
the sun, the more often a comet approaches the sun the 
more must it waste away , and we find accordingly that the 
short-period comets, which return to the neighbourhood of 
the sun at frequent intervals ( 291), are inconspicuous 
bodies The same theory is supported by the shape of the 
tail In some cases it is straight, but more commonly it is 
curved to some extent, and the curvature is then always 
backwards in i elation to the comet's motion Now by 
ordinary dynamical principles matter shot off from the head 
of the comet while it is revolving round the sun would 
tend, as it weie, to lag behind moie and more the farther 
it receded from the head, and an apparent backwaid 
curvature of the tail less or greater according to the speed 
with which the particles forming the tail were lepelled 
would be the result Variations in curvature of the tails 
of different comets, and the existence of two or more 
differently curved tails of the same comet, are thus readily 
explained by supposing them made of different matenals, 
repelled from the comet's head at diffeient speeds 

The first application of the spectroscope to the study of 
comets was made in 1864 by Giambattista Donati (1826- 
1873), best known as the discoverer of the magnificent 
cornet of 1858 A spectrum of three bught bands, widei 
than the ordinary " lines," was obtained, but they weie 
not then identified Four years later Sir William Huggms 
obtained a similar spectrum, and identified it with that 
of a compound of carbon and hydrogen Nearly every 
comet examined since then has shewn in its spectrum 
bught bands indicating the presence of the same or some 
other hydrocaibon, but in a few cases other substances 
have also been detected A comet is therefore in pait 
at least self-luminous, and some of the light which it sends 
us is that of a glowing gas. It also shines to a consideiable 
extent by reflected sunlight , there is nearly always a con- 

3s3 Comets and Meteors 395 

inuous spectium, and in a few cases fiist m 1881 the 
pectrum has been distinct enough to shew the Fraunhofer 
mes crossing it But the continuous spectrum seems also 

be due m pait to solid or liquid matter m the comet itself, 
mich is hot enough to be self-luminous 

SosVThe work of the last 30 or 40 years has established / 
. remarkable relation between comets and the minute bodies 
vhich are seen m the form of meteors or shooting stars. 
)nly a few of the more important links in the chain of 
vidence can, however, be mentioned Showers of shooting 
tars, the occuirence of which has been known from quite 
arly times, have been shewn to be due to the passage of 
be eaith through a swarm of bodies revolving m elliptic 
rbits round the sun The paths of four such swarms 
fere ascertained with some precision m 1866-67, and found 

1 each case to agree closely with the paths of known 
omets And since then a consideiable number of other 
ases of resemblance or identity between the paths of 
aeteor swarms and of comets have been detected One 
f the four comets just referred to, known as Biela's, with 

period of between six and seven years, was duly seen on 
everal successive returns, but m 1845-46 was observed 
.rst to become somewhat distorted in shape, and afterwards 
3 have divided into two distinct comets , at the next return 
1852) the pair were again seen, but since then nothing 
as been seen of either portion. At the end of November m 
ach year the earth almost crosses the path of this comet, and 
n two occasions (1872, and 1885) it did so nearly at the time 
r hen the comet was due at the same spot , if, as seemed 
kely, the comet had gone to pieces since its last appearance, 
lere seemed a good chance of falling m with some of its 
imams, and this expectation was fulfilled by the occurrence 
n both occasions of a meteor shower much more brilliant 
lan that usually observed at the same date ^ 

Biela's comet is not the only comet which has shewn 
gns of breaking up , Biooks's comet of 1889, which is 
robably identical with Lexell's (chapter xi , 248), was 
mnd to be accompanied by three smaller companions , 
3 this comet has more than once passed extremely close 
) Jupiter, a plausible explanation of its breaking up is at 
nee given m the attractive force of the planet Moieover 

39^ A Short History of Astronomy [CH xin 

certain systems of comets, the members of which revolve 
in the same orbit but separated by considerable intervals 
of time, have also been discovered Tebbutt's comet of 
1 88 1 moves in practically the same path as one seen in 
1807, and the great comet of 1880, the great comet of 1882 
(shewn in fig 99), and a third which appeared in 1887, 
all move in paths closely resembling that of the comet of 
1843, while that of 1668 is more doubtfully connected 
with the same system And it is difficult to avoid regarding 
the members of a system as fragments of an earlier comet, 
which has passed thiough the stages in which we have 
actually seen the cornets of Biela and Brooks 

Evidence of such different kinds points to an intimate 
connection between comets and meteors, though it is 
perhaps still premature to state confidently that meteors 
are fragments of decayed comets, or that conversely comets 
are swarms of meteors r 

306 Each of the great problems of sidereal astronomy 
which Herschel formulated and attempted to solve has 
been elaborately studied by the astronomers of the ipth 
century Vine multiplication of observatories, improve- 
ments in telescopes, and the introduction of photography to 
mention only three obvious factois of progress have added 
enoimously to the extent and accuracy of oui knowledge of 
the stars, while the invention of spectrum analysis has thrown 
an entnely new light on seveial important pioblems. ^ 

William Herschel's most direct successoi was his son 
John Frederick William (1792-1871), who was not only an 
astronomer, but also made contributions of importance to 
pure mathematics, to physics, to the nascent art of photo- 
graphy, and to the philosophy of scientific discovery He 
began his astronomical caieer about 1816 by le-measurmg, 
first alone, then in conjunction with James South (1785- 
1867), a number of his father's double stais The first 
lesult of this work was a catalogue, with detailed measure- 
ments, of some hundred double and multiple stais (published 
m 1824), which formed a valuable third term of comparison 
with his fathers observations of 1781-82 and 1802-03, an d 
contained m several cases the slow motions of revolution 
the beginnings of which had been observed before. A 
great survey of nebulae followed, resulting m a catalogue 

' so6, 307 John Herschel 


(1833) of about 2500, of which some 500 were new and 
2000 were his father's, a few being due to other observers , 
incidentally moie than 3000 pairs of stars close enough 
together to be worth recording as double stars were observed 

307 Then followed his well-known expedition to the 
Cape of Good Hope (1833-1838), where he "swept" the 
southern skies in very much the same way in which his 
father had explored the regions visible in our latitude 
Some 1200 double and multiple stars, and a rather larger 
number of new nebulae, were discovered and studied, while 
about 500 known nebulae were re-observed , star-gauging on 
William HerschePs lines was also carried out on an extensive 
scale A number of special observations of interest were 
made almost incidentally during this survey the remarkable 
variable stai t] Argus and the nebula surrounding it (a 
modern photograph of which is reproduced m fig 100), the 
wonderful collections of nebulae clusters and stars, known 
as the Nubeculae 01 Magellamc Clouds, and Halley's comet 
were studied in turn, and the two faintest satellites of 
Saturn then known (chapter xn , 255) were seen again 
for the first time since the death of their discoverer 

An important investigation of a somewhat diiferent 
character "that of the amount of heat leceived from the 
sun-Mvas also carried out (1837) dm ing Herschel's residence 
at the Cape , and the result agreed satisfactorily with that 
of an independent inquiry made at the same tune in France 
by Claude Servais Mathias Pomllet (1791-1868) In both 
cases the heat leceived on a given aiea of the earth in a 
given time from direct sunshine was measured 9 and allow- 
ance being made for the heat stopped in the atmosphere 
as the sun's rays passed through it, an estimate was formed 
of the total amount of heat received annually by the earth 
from the sun, and hence of the total amount radiated by 
the sun m all directions, an insignificant fraction of which 
(one part in 2,000,000,000) is alone intercepted by the 
earth But the allowance for the heat intercepted m our 
atmospheie was necessarily uncertain, and latei work, m 
particular that of Dr S, P Langley in 1 880-81, shews that 
it was very much under-estimated by both Herschel and 
Pomllet. According to HerscheFs lesults, the heat received 
annually from the sun including that intercepted m the 

39 8 A Short History of Astronomy [Cn xui 

atmospherewould be sufficient to melt a shell of ice 
120 feet thick covering the whole earth , accoidmg to 
Dr. Langley, the thickness would be about 160 feet* ^ 

308 With his return to England in 1838 Herschel's 
career as an observer came to an end , but the working out 
of the results of his Cape observations, the arrangement 
and cataloguing of his own and his father's discoveries, 
provided occupation for many years A magnificent volume 
on the Results of Astronomical Observations made during the 
years 1834-8 at the Cape of Good Hope appeared in 1847 , 
and a catalogue of all known nebulae and clusters, amount- 
ing to 5,079, was presented to the Royal Society in 1864, 
while a corresponding catalogue of moie than 10,000 double 
and multiple stars was never finished, though the matenals 
collected for it were published posthumously in 1879 J onn 

-HerscheFs great catalogue of nebulae has since been revised 
and enlarged by Dr Dreyer y the result being a list of 7,840 
nebulae and clusters known up to the end of 1887 , and 
a supplementary list of discoveries made in 1888-94 
published by the same writer contains 1,529 entnes, so that 
the total number now known is between 9,000 and 10,000, 
of which more than half have been discovered by the two 
Herschels t*^~ 

309 Double stars have been discovered and studied by 
a number of astronomers besides the Herschels. One of 
the most indefatigable workers at this subject was the elder 
Struve ( 279), who was successively dnector of the two 
Russian observatories of Dorpat and Pulkowa He 
observed altogether some 2,640 double and multiple stars, 
measuring m each case with caie the length and direction 
of the line joining the two components, and noting othei 
peculiarities, such as contrasts in colour between the 
members of a pair. He paid attention only to double stars 
the two components of which were not more than 32" apart, 
thus rejecting a good many which William Herschel would 
have noticed , as the number of known doubles rapidly 
increased, it was clearly necessary to concentrate attention 
on those which might with some reasonable degree of 

* Observations made on Mont Blanc under the direction of 
M Janssen in 1897 indicate a slightly larger number than Dr 

38, 309] 

Double Stars 


>robabihty turn out to be genuine binaries (chapter xn , 
> 264) 

In addition to a number of minor papers Stmve published 
hiee separate books on the subject m 1827, 1837, and 1852 * 
^. comparison of his own earlier and later observations, and 
>f both with HerschePs earlier ones, shewed about 100 cases 
if change of relative positions of two members of a pair, 
duch indicated more or less clearly a motion of revolution, 
nd further results of a like character have been obtained 


IG. ioi The orbit of Ursae, shewing the relative positions of 
the two components at various times between 1781 and 1897 
(The observations of 1781 and 1802 were only enough to 
determine the dnection of the line joining the two components 
not its length.) ' 

om a comparison of Struve's observations with those of 
.ter observers 

William HerschePs observations of binaiy systems 
chapter xn , 264) only sufficed to shew that a motion of 
evolution of some kind appeared to be taking place,, it 
as an obvious conjecture that the two members of a pair 

* Catahgus novus stdlarum duphcium, Stellarum duphcium et 
ultiphcmm mensurac micrometncae, and Stellarnm fixai um imprimis 
tphcmm et muUtphcium positiones mediae pro epocha 1830 

400 A Short History of Astronomy [Cn xm 

attracted one another according to the law of gravitation, 
so that the motion of revolution was to some extent 
analogous to that of a planet round the sun ; if this were 
the case, then each star of a pair should describe an ellipse 
(or conceivably some other come) round the othei, or each 
round the common centre of gravity, in accordance with 
Kepler's laws, and the appaient path as seen on the sky 
should be of this nature but in geneial foreshortened by 
being projected on to the celestial sphere The first attempt 
to shew that this was actually the case was made by Felix 
Savary (1797-1841) in 1827, the star being f Ursae, which 
was found to be revolving in a period of about 60 years 

Many thousand double stars have been discovered by 
the Herschels, Struve, and a number of other observers, 
including several living astionomers, among whom Pro- 
fessor S W Burnham of Chicago, who has discovered 
some 1300, holds a leading place/ Among these stars there 
aie about 300 which we have fair leason to regard as 
bmaiy, but not more than 40 or 50 of the oibits can be 
regarded as at all satisfactorily known ^ One of the most 
satisfactory is that of Savary's star Ursae, which is shewn 
in fig 10 1 Apart from the binaries discovered by the 
spectroscopic method ( 314), which foim to some extent 
a distinct class, the periods of revolution which have been 
computed range between about ten years and several 
centuries, the longer periods being for the most part 
decidedly uncertain 

3io"^Wilham HerschePs telescopes represented for some 
time the utmost that could be done m the construction of 
reflectors ; the fast advance was made by Lord Rosse 
(1800-1867), who after a numbei of less successful ex- 
periments finally constructed (1845), at Parsonstown in 
Ireland, a reflecting telescope nearly 60 feet m length, with 
a mirror which was six feet across, and had consequently a 
"light-grasp " more than double that of Herschel's gieatest 
telescope Lord Rosse used the new mstiument in the fiist 
instance to re-examine a number of known nebulae, and in 
the course of the next few years discovered a vanety of new 
features, notably the spiral form of certain nebulae (fig 102), 
and the resolution into apparent star clusters of a number 
of nebulae which Herschel had been unable to resolve 

FIG 102 Spiral nebulae From drawings by Lord Rossc 

[To taw p 400 

W 310-313] D ou bi e stars and Nebulae 4OI 

and had accordingly put into " the shining fluid " class 
(chapter xn, 2 6o). Th.s last discovery, being exact y 
analogous to Herschel's experience when he first legan to 
examine nebulae hitherto only observed with infeno? tele- 
scopes naturally led to a revival of the view that nebulae 
are indistinguishable from clusters of stars, though many 
of the arguments from piobability uiged by Herschel and 
otheis were m reality unaffected by thl new discoveries 

form , qUeSt "f f th , 6 Status of nebulae m lts simplest 
form may be said to have been settled by the first 
application of spectrum analysis Fraunhofer ( 2 oo) had 

thatof y t h S l23 ' at , st r S , had S P 6Ctra charanse 
that of the sun by dark lines, and more complete 

S m ' 


aer Kirchhoff ' s d,scove by 

several astronomers, m particular by Sir Wilham Huggms 


i T, 
stars ord C nfirmed *"" "^ U '^nearly all 

fi i St s P ectrum of a nebula was obtained by Sir 
Huggms m 1864, and was seen to consist of Lee 
bnght hnes by x868 he had examined 70, and found m 
abou one-durd of the cases, including that of the Orton 

J 6 2 ' a r 1 ' ^ SpeCtmm f b "S ht lmes ^ these cases 
therefore the luminous part of the nebula is gaseous and 
Herschel's suggestion of a "shining fluid" wa g s confirmed 
in the most satisfactory way In nearly all cases three 

th her K 

! fr f ^ K aV t n0t b t en ldentlfie d> id in the case of 
a few of the brighter nebulae some other lines have also 
been seen. On the other hand, a considerable number of 
nebulae, including many of those which appear capable o 
telescopic resolution into star clusters, grve a continuous 
spectrum, so that there is no clear spectroscope eSdence 
to distinguish them from clusters of stars, since the dark 
lines seen usually m the spectra of the latter could hard y 


e aer cou 
as ne X b P uTae ? m the aSe f Such famt 

312 Stars have been classified, first by Secchi (1863), 
afterwards m shghtly different ways by others, according to 
the general arrangement of the dark lines in their spectra- 
and some attempts have been made to base on these 

402 A Short History of Astronomy [Cn xin 

differences inferences as to the relative " ages," or at any 
rate the stages of development, of different stars 

Many of the dark lines in the spectra of stars have been 
identified, first by Sir William Huggms in 1864, with the 
lines of known terrestrial elements, such as hydrogen, iron, 
sodium, calcium 3 so^that a certain identity between the 
materials of which our own earth is made and that of 
bodies so remote as the fixed stars is thus established 

In addition to the classes of stars already mentioned, the 
spectioscope has shewn the existence of an extiemely in- 
teresting if rather peiplexing class of stars, falling into 
several subdivisions, which seem to form a connecting 
link between ordinary stars and nebulae, for, though in- 
distinguishable telescopically from ordinary stars, their 
s^ctra-^esc- -$$ lines eithej M periodically or regularly 
A good many stars of this class are variable, and several 
" new " stars which have appeared and faded away of late 
years have shewn similar characteristics 

313 The first application to the fixed stars of the spectro- 
scopic method ( 302) of determining motion towards or away 
from the observer was made by Sir William Huggms m 1868 
A minute displacement from its usual position of a dark 
hydrogen line (F) in the spectrum of Sinus was detected, 
and interpreted as shewing that the star was receding from 
the solar system at a considerable speed A number of 
other stars were similarly observed in the following year, 
and the work has been taken up since by a number of 
other observers, notably at Potsdam under the direction 
of Professor H C. Vogel^ and at Greenwich 

314 A veiy remarkable application of this method to 
binary stars has recently been made If two stars are 
revolving round one another, their motions towards and 
away from the earth are changing legularly and are differ- 
ent , hence, if the light from both stars is received m the 
spectroscope, two spectra aie formed one for each star 

, the lines of which shift regularly relatively to one another. 

\If a particular line, say the F line, common to the spectra 
of both stars, is observed when both stars are moving 
towards (or a\\ay from) the earth at the same rate which 
happens twice in each revolution only one line is seen , 
but when they are moving differently, if the spectroscope 

$$ 313316] Stellar Spectroscopy 403 

be powerful enough to detect the minute quantity involved, 
the line will appear doubled, one component being due to 
one star and one to the other /*& periodic doubling of 
this kind was detected at the end of 1889 by Professor 
E C Pickering of Harvard in the case of Ursae, which 
was thus for the first time shewn to be binary, and found 
to have the remarkably short period of only 104 days 
This discovery was followed almost immediately by Pro- 
fessor Vogel's detection of a periodical shift m the position 
of the dark lines in the spectrum of the variable star Algol 
(chapter xn , 266) , but as in this case no doubling of the 
lines can be seen, the inference is that the companion star 
is nearly or quite dark, so that as the two revolve round 
one anothex the spectrum of the bright star shifts in the 
manner observed , ^Thus_jthe eclipse-theory of Algol's 
variability^ received a^strflong verification 

A number of other cases of both classes of spectroscopic 
binary stars (as they may conveniently be called) have 
since been discovered The upper part of fig 103 shews 
the doubling of one of the lines in the spectrum of the 
double star ft Aungae , and the lower part shews the 
corresponding part of the spectrum at a time when the line 
appeared single 

315 Variable stars of different kinds have received a 
good deal of attention during this century, particularly 
during the last few years About ^400 stars, are now clearly 
recognised as variable, while in a large number of other 
cases variability of light has been suspected , except, how- 
ever, in a few cases, like that of Algol, the causes of 
variability are still extremely obscure 

316 The study of the relative brightness of stars a 
branch of astronomy now generally known as stellar photo- 
metry has also been carried on extensively during the 
century and has now been put on a scientific basis The 
traditional classification of stars into magnitudes, according 
to their brightness, was almost wholly arbitrary, and 
decidedly uncertain As soon as exact quantitative com- 
parisons of stars of different brightness began to be carried 
out on a considerable scale, the need of a more precise 
system of classification became felt John Herschel was 
one of the pioneers in this direction , he suggested a scale 

404 A Short History of Astronomy [CH xm 

capable of precise expression, and agreeing loughly, at 
any rate as far as naked-eye stars are concerned, with the 
current usages, while at the Cape he measured carefully 
the light of a large nurnfoer of bright stars and classified 
them on this principle '/According to the scale now gener- 
ally adopted, first suggested in 1856 by Norman Robert 
Pogson (1829-1891), the light of a star of any magnitude 
bears a fixed ratio (which is taken to be 2 512 ) to that 
of a star of the next magnitude /"The number is so chosen 
that a star of the sixth magnitude thus defined is 109 
times fainter than one of the first magnitude* Stars of 
intermediate brightness have magnitudes expressed by 
fractions which can be at once calculated (according to 
a simple mathematical rule) when the ratio of the light 
received from the star to that received from a standard star 
has been observed t 

Most of the great star catalogues ( 280) have included 
estimates of the magnitudes of stars The most extensive 
and accurate series of measurements of star brightness have 
been those executed at Harvard and at Oxford under the 
superintendence of Professor E C Pickering and the late 
Professor Pntchard respectively Both catalogues deal with 
stars visible to the naked eye , the Harvard catalogue 
(published in 1884) comprises 4,260 stars between the 
North Pole and 30 southern declination, and the Urano- 
metna Nova Oxoniensis (1885), as it is called, only goes 
10 south of the equator and includes 2,784 stars Portions 
of more extensive catalogues dealing with fainter stars, in 
progress at Harvard and at Potsdam, have also been 

* I e 2 512 is chosen as being the number the logarithm of which 
is 4, so that (2 512 ) 5 ^ = 10 

f If L be the ratio of the light received from a star to that received 
from a standard first magnitude star, such as Aldebaran or Altai r, 
then its magnitude m is given by the formula 

L /1_\ - l _ (J-Y^, whence m - i - - 1 log L 

\2$I2j \lQOj ' 2 

A star brighter than Aldebaran has a magnitude less than I, while 
the magnitude of Sinus, which is about nine times as bright as 
Aldebaran, is a negative quantity, I 4, according to the Harvard 

FIG 104- 

-The Milky Way near the cluster in Perseus, 
by Professor Barnard 

From a photograph 

[Tofacep 405 

$ 317] Photometry the Sidereal System 405 

317 The great pioblem to which Herschel gave so 
much attention, that of the general arrangement of the 
stars and the structure of the system, if any, formed 
by them and the nebulae, has been affected in a variety 
of ways by the additions which have been made to our 
knowledge of the stars But so far are we from any 
satisfactory solution of the problem that no modern theory 
can fairly claim to represent the facts now known to us as well 
as Herschel's earlier theory fitted the much scantier stock 
which he had at his command In this as in so many 
cases an increase of knowledge has shewn the insufficiency 
of a previously accepted theory, but has not provided a 
successoi. Detailed study of the form of the Milky Way 
(cf fig 104) and of its relation to the general body of stars 
has shewn the inadequacy of any simple arrangement of 
stars to represent its appearance ; William HerschePs cloven 
grindstone, the ring which his son was inclined to substitute 
for it as the result of his Cape studies, and the more 
complicated forms which later writers have suggested, alike 
fail to account for its peculiarities. Again, such evidence 
as we have of the distance of the stars, when compared 
with their brightness, shews that there are large variations 
in their actual sizes as well as in their apparent sizes, and 
thus tells against the assumption of a certain uniformity 
which underlay much of Herschel's work The "island 
universe" theory of nebulae, partially abandoned by 
Herschel after 1791 (chapter xn , 260), but brought into 
credit again by Lord Rosse's discoveries ( 310), scarcely 
survived the spectroscopic proof of the gaseous character 
of certain nebulae. Other evidence has pointed clearly to 
intimate relations between nebulae and stars generally , 
NHerschel's obseivation that nebulae are densest in regions 
farthest from the Milky Way has been abundantly verified 
as far as irresoluble nebulae are concerned while 
obvious star clusters shew an equally clear preference for 
the neighbourhood of the Milky Way ^ln many cases again 
individual stars or gioups seen on the sky in or neai a 
nebula have been clearly shewn, either by their arrangement 
or in some cases by peculiarities of their spectra, to be really 
connected with the nebula, and not merely to be accident- 
ally m the same direction Stars which have bright lines 

46 A Short History of Astronomy [CH xm 

in their spectra (312) form anothei link connecting 
nebulae with stars 

A good many converging lines of evidence thus point 
to a greater vanety m the arrangement, size, and structure 
of the bodies with which the telescope makes us acquainted 
than seemed probable when sidereal astionomy was first 
seriously studied , they also indicate the probability that 
these bodies should be regarded as belonging to a 
single system, even if it be of almost inconceivable 
complexity, rather than to a number of perfectly distinct 
systems of a simpler type 

31 8 -Laplace's nebular hypothesis (chaptei xi , 250) 
was published a little more than a century ago (1796), and 
has been greatly affected by progress in various depart- 
ments of astronomical knowledge Subsequent discoveries 
of planets and satellites ( 294, 295) have marred to some 
extent the uniformity and symmetry of the motions of the 
solar system on which Laplace laid so much stress , but it 
is not impossible to give reasonable explanations of the 
backwaid motions of the satellites of the two most distant 
planets, and of the large eccentricity and inclination of the 
paths of some of the minor planets, while apart from these 
exceptions the number of bodies the motions of which 
have the characteristics which Laplace pointed out has 
been considerably increased The case for some sort of 
common origin of the bodies of the solar system has per- 
haps in this way gamed as much as it has lost Again, the 
telescopic evidence which Herschel adduced (chapter xn , 
261) in favour of the existence of certain processes of 
condensation in nebulae has been strengthened by later 
evidence of a similar character, and by the various pieces 
of evidence already referred to which connect nebulae with 
single stars and with clusters The differences in the 
spectra of stars also receive their most satisfactory explana- 
tion as representing different stages of j^ondensation of 
bodies of the same general chaiacter. v^ 

319 An entirely new contribution to the problem has 
resulted from certain discoveries as to the nature of heat, 
culminating in the recognition (about 1840-50) of JbuaaJLj-s 
only^ one form of what physicists now call energy, which 
manifests itself also in ttie motion "of bodies", 1 in the 

tt 3*8, ,x 9 ] The Evolution of the Solar System 407 

separation of bodies which attract one another, as well as 
m various electrical, chemical, and other ways With this 
discovery was closely connected the general theory known 
as the conservation of energy, according to which energy, 
though capable of many transformations, can neither be 
mci eased nor decreased m quantity A body which, like 
the sun, is giving out heat and light is accordingly thereby 
losing energy, and is like a machine doing work , either 
then it is receiving energy fiom some other source to 
compensate this loss or its store of energy is diminishing 
But a body which goes on indefinitely giving out heat and 
light without having its store of energy replenished is 
exactly analogous to a machine which goes on working 
indefinitely without any motive power to drive it , and both 
are alike impossible 

The results obtained by John Heischel and Pouillet m 
l8 36 ( 307) called attention to the enormous expenditure 
of the sun m the form of heat, and astronomers thus had to 
face the problem of explaining how the sun was able to go 
on radiating heat and light in this way Neither in the 
few thousand years of the past covered by historic recoids, 
nor m the enormously great periods of which geologists 
and biologists take account, is theie any evidence of any 
important permanent alteration in the amount of heat and 
light received annually by the earth from the sun Any 
theory of the sun's heat must therefore be able to account 
for the continual expenditure of heat at something like the 
present rate for an immense period of time The obvious 
explanation of the sun as a furnace deriving its heat from 
combustion is found to be totally inadequate when put to 
the test of figures, as the sun could in this way be kept 
going at most for a few thousand years The explanation 
now generally accepted was first given by the great German 
physicist Hermann von ffelmholtz (1821-1894) in a popular 
lecture m 1854 The sun possesses an immense store of 
energy in the foim of the mutual gravitation of its parts , 
if from any cause it shrinks, a certain amount of gravita- 
tional energy is necessarily lost and takes some other form. 
In the shrinkage of the sun we have therefore a possible 
source of energy The precise amount of energy libeiated 
by a definite amount of shrinkage of the sun depends upon 

408 A Short History of Astronomy [Cn xm. 

the internal distribution of density m the sun, which is 
uncertain, but making any reasonable assumption as to this 
we find that the amount i of shrinking required to supply 
the sun's expenditure of heat would only dimmish the 
diameter by a few hundred feet annually, and would 
therefore be imperceptible with our present telescopic 
power for centuries, while no earlier records of the sun's 
size are accurate enough to shew it. It is easy to calculate 
on the same pi maples the amount of energy liberated by a 
body like the sun m shrinking from an indefinitely diffused 
condition to its present state, and from its present state to 
one of assigned greater density ; the result being that we 
can in this way account for an expenditure of sun-heat at 
the present rate for a period to be counted m millions of 
years m either past or future time, while if the rate of 
expenditure was less m the remote past or becomes less 
in the future the time is extended to a corresponding 

No other cause that has been suggested is competent 
to account for more than a small fraction of the actual 
heat-expenditure of the sun , the gravitational theory 
satisfies all the requirements of astronomy proper, and goes 
at any rate some way towards meeting the demands of 
biology and geology 

If then we accept it as piovisionally established, we 
are led to the conclusion that the sun was m the past 
larger and less condensed than now, and by going sufift- 
ciently far back into the past we find it in a condition not 
unlike the primitive nebula which Laplace presupposed, 
with the exception that it need not have been hot 

320 A new light has been thrown on the possible 
development of the earth and moon by Professor G H 
Darwin's study of the effects of tidal friction (cf 287 and 
292, 293). Since the tides increase the length of the 
day and month and gradually repel the moon from the 
earth, it follows that in the past the moon was nearer to 
the earth than now, and that tidal action was consequently 
much greater Following out this clue, Professor Darwin 
found, by a series of elaborate calculations published in 
1879-81, strong evidence of a past time when the moon 
was close to the earth, revolving round it m the same time 

* 3=0] The Evolution of the Solar System 409 

m which the earth rotated on its ax,s, which was then a 
httle over two hours The two bodies, m fact, were moving 

hi * 7 ere COI J nected > * w difficult to avoid the 
probable inference that at an earlier stage the two really 

!3,T' I/ the T n 1S m reallt y a fa g ment of the 

SS, t m oth e rte r0m " * ** t0 - raptd * f the 

Professor Darwin has also examined the possibility of 

expammg m a similar way the formation of the satellites 

the ^ h S !: ,S etS and f the P lanets themselves from 
I '* * u circumsta nces of the moon-eaith system 
turn out to be exceptional, and tidal influence has been 

Shft % m ! : 6r CaSeS) th Ugh rt S' ves a satisfactoiy 
S,f M ertam P ecul ! ante of the planets and their 

SS H% T f 0ently (l892 ^ Dr &fi has a PP^d a 
somewhat sirndar Ime of reasonmg to explarn by means 

elr^rLl , n thC f evel P ment of double stars from an 
earlier nebulous condition 

Speaking generally, we may say that the outcome of the 
i9th century study of the problem of the early history 
fj, , S ! ar s ^ tem has been to discredit the details of 
Laplace s hypothesis in a variety of ways, but to establish 
on a firmer basis the general view that the solar system 
has been formed by some process of condensation out of 
an earlier very diffused mass bearing a general resemblance 
to one of the nebulae which the telescope shews us, and 
that stars other than the sun are not unlikely to have been 
formed in a somewhat similar way, and, further, the theory 
of t!dal faction supplements this geneial but vague theory, 
by giving a rational account of a process which seems to 
have been the predominant factor m the development of 
the system formed by our own earth and moon, and to have 
had at any rate an important influence in a number of 

OtJQGr C3.S6S 



I HAVE made great use throughout of R Wolf's Geschichte der 
Astronomte, and of the six volumes of Delambre's Histotre 
de V Astronomie (Ancienne, 2 vols , du Moyen Age, I vol 
Moderne, 2 vols , du Dixhmtieme Siecle^ i vol ) I shall subse- 
quently refer to these books simply as Wolf and Delambre 
respectively I have used less often the astronomical sections 
of Whewell's History of the Ind^ict^ve Sciences (referred to as 
Whewell}, and I am indebted chiefly for dates and references 
to the histories of mathematics written respectively by Mane, 
W. W R Ball, and Cajon, to Poggendorffs Handworterbuch 
der Exacten Wissenschaften, and to articles in various bio- 
graphical dictionaries, encyclopaedias, and scientific journals 
Of general treatises on astronomy Newcomb's Popular Astro- 
nomy, Young's General Astronomy, and Proctor's Old and New 
Astronomy have been the most useful for my purposes 

It is difficult to make a selection among the very large number 
of books on astronomy which are adapted to the general reader 
For students who wish for an introductory account of astronomy 
the Astronomer Royal's Primer of Astronomy may be recom- 
mended , Young's Elements of Astronomyvs a little more advanced, 
and Sir R S Ball's Story of the Heavens, Newcomb's Popular 
Astronomy, and Proctor's Old and New Astronomy enter into 
the subject m much greater detail Young's General Astronomy 
may also be recommended to those who are not afraid of a 
little mathematics There are also three modern English books 
dealing generally with the history of astronomy, in all of which 
the biographical element is much more prominent than in this 
book viz Sir R. S Ball's Great Astronomers, Lodge's Pioneers 
of Science, and Morton's Heroes of Science Astronomers, 


412 Authorities and Books for Students 


Chapters 1 and II In addition to the general histories quoted 
above especially Wolf I have made most use of Tannery's 
Recherches sur IHistoire de VAstronomie Ancienne and of several 
biographical articles (chiefly by De Morgan) in Smith's Dictionary 
of Classical Biography and Mythology Ideler's Chronologische 
Unter suckling en, Hankel's Geschichte der Mathematik im Alter- 
thum und Mittelalter, G C Lewis's Astronomy of the Ancients, 
and Epping & Strassmaier's Astronomisches aus Babylon have 
also been used to some extent Unfortunately my attention was 
only called to Susemihl's Geschichte der Gnechischen Littetatur 
in der Alexandrmer Zett when most of my book was in proof, 
and I have consequently been able to make but little use of it 

I have in general made no attempt to consult the original 
Greek authorities, but I have made some use of translations 
of Anstarchus, of the Almagest, and of the astronomical writings 
of Plato and Aristotle 

Chapter III The account of Eastern astronomy is based 
chiefly on Delambre, and on Hankels Geschichte der Mathematik 
im Alterthum und Mzttelalter , to a less extent on Whewell 
For the West I have made more use of Whewell, and have 
borrowed biographical material for the English writers from the 
Dictionary of National Biography I have also consulted a good 
many of the original astronomical books referred to m the latter 
part of the chapter 

I know of no accessible book in English to which to refer 
students except Whewell 

Chapter IV For biographical material, for information as to 
the minor writings, and as to the history of the publication of 
the De Revolntionibus I have used little but Prowe's elaborate 
Nicolaus CoppemicuS) and the documents printed in it My 
account of the De Revolutwmbus is taken from the book itself 
The portrait is taken from Dandeleau's engraving of a picture m 
Lalande's possession I have not been able to discover any 
portrait which was clearly made during Coppermcus's lifetime, 
but the close resemblance between several portraits dating from 
the 1 7th century and Dandeleau's seems to shew that the latter 
is substantially authentic 

There is a readable account of Coppernicus, as well as of several 
other astronomers, m Bertrand's Fondateurs de VAstronomie 
Moderne , but I have not used the book as an authority 

Chapter V For the life of Tycho I have relied chiefly on 
Dreyer's Tycho Brahe, which has also been used as a guide to 
his scientific work , but I have made constant reference to the 
original writings I have also made some use of Gassendi's Vita 

Authorities and Books for Students 413 

Tychoms Brake The portrait is a reproduction of a picture m 
the possession of Dr Crompton of Manchester, described by him 
m the Memoirs of the Manchester Literary and Philosophical 
Society, Vol VI , Ser III For minor Continental writers I have 
used chiefly Wolf and Delambre, and for English writers 
Whewell, various articles by De Morgan quoted by him and 
articles m the Dictionary of National Biography 

Students will rind m Dreyer's book all that they are likely to 
want to know about Tycho 

Chapter F/ For Galilei's lite I have used chiefly Karl von 
Gebler's Galilei und die Romische Curie, partly in the original 
German form and partly m the later English edition (translated 
by Mrs Sturge) For the disputed questions connected with the 
trial I have relied as far as possible on the original documents 
preserved m the Vatican, which have been published by von 
Gebler and independently by L'Epmois in Les Pieces du Proces 
de Galilee m the latter book some of the most important docu- 
ments are reproduced m facsimile For personal characteristics 
I have used the charming Private Life of Galileo, compiled 
chiefly from his correspondence and that of his daughter Mane 
Celeste I have also read with great interest the estimate of 
Galilei's work contained in H Martin's Galilee, and have probably 
borrowed from it to some extent What I have said about 
Galilei's scientific work has been based almost entirely on study 
of his own books, either in the original or m translation I have 
used freely the translations of the Dialogue on the Two Chief 
Systems of the World and of the Letter to the Grand Duchess 
Christine by Salusbury, that of the Two New Sciences by 
Weston (as well as that by Salusbury), and that of the Sidereal 
Messenger by Carlos I have also made some use of various 
controversial tiacts written by enemies of Galilei, which are to be 
found (together with his comments on them) in the magnificent 
national edition of his works now m course of publication, and 
of the critical account of Galilei's contributions to dynamics 
contained in Mach's Geschichte der Mechamk 

Wolf and Delambre have only been used to a very small 
extent m this chapter, chiefly for the minor writers who are 
referred to 

The portrait is a reproduction of one by Susterrnans m the 
Uffizi Gallery 

There is an excellent popular account of Galilei's life and 
work m the Lives of Eminent Persons published by the Society 
for the Diffusion of Useful Knowledge, students who want 
fuller accounts of Galilei's life should read Gebler's book and 
the Private Life, which have been aheady quoted, and are 
strongly recommended to read at any rate parts of the Dialogue 

414 Authorities and Books for Students 

on the Two Chief Systems of the World, either in the original or 
in the picturesque old translation by Salusbury there is also a 
modern German version of this book, as well as of the Two New 
Sciences, m Ostwald's series of Klassiker der exakten Wissen- 

Chapter VII For Kepler's life I have used chiefly Wolf 
and the life or rather biographical material given by Fnsch 
in the last volume of his edition of Kepler s works, also to a 
small extent Breitschwerdt's Johann Keppler For Kepler's 
scientific discoveries I have used chiefly his own writings, but 1 
am indebted to some extent to Wolf and Delambre, especially 
for information with regard to his minor works The portrait 
is a reproduction of one by Nordhng given m Fnsch's edition 

TheZz^w of Eminent Persons, already referred to, also contains 
an excellent popular account of Kepler's life and work 

Chapter VIII I have used chiefly Wolf and Delambre , 
for the English writers Gascoigne and Horrocks I have used 
Whewell and articles in the Diet Nat Biog What I have 
said about the work of Huygens is taken directly from the books 
of his which are quoted in the text, and for special points I 
have consulted the Prmcipia of Descartes, and a very few of 
Cassmi's extensive writings 

There is no obvious book to recommend to students 

Chapter IX For the external events of Newton's life I have 
relied chiefly on Brewster's Memoirs of Sir Isaac Newton , and 
for the history of the growth of his ideas on the subject of 
gravitation I have made extensive use of W W R Ball's Essay 
on Newton's Pnncipia, and of the original documents contained 
m it 1 have also made some use of the articles on Newton in 
the Encyclopaedia Bntanmca and the Dictionary of National 
Biography , as well as of Rigaud's Correspondence of Scientific 
Men of the Seventeenth Century, of Edleston's Correspondence 
of Sir Isaac Newton and Prof Cotes, and of Baily's Account of 
the Rev d John Flamsteed The portrait is a reproduction of one 
by Kneller 

Students are recommended to read Brewster's book, quoted 
above, or the abridged Life of Sir Isaac Newton by the same 
author The Laws of Motion are discussed in most modern 
text-books of dynamics , the best treatment that I am acquainted 
with of the various difficulties connected with them is in an 
article by W H Macaulay m the Bulletin of the American 
Mathematical Society -, Ser II, Vol III , No 10, July 1897 

Chapter X For Flamsteed I have used chiefly Baily's 
Account of the Rev* John Flamsteed , for Bradley little but the 
Miscellaneous Works and Correspondence of the Rev, fames 

Authorities and Books for Students 

extent on 

information about him m 

a , eonsi ^rable 
i ^ deal f bl graphical 


and lor 

the ongmal wnt ng 7 1 have ' reerre to 

of those of Lagiange and Claira?it h f f her wntln gs and 
study of them Uairaut , but have made no systematic 


from Mi SS AM 
from the /V/r 
Century by the 

4 i 6 Authorities and. Books for Students 

writings I have made also some little use of Grant's History 
(already quoted), of Wolf, and of Miss Clerke's System of the 

Students are recommended to read any or all of the first four 
books named above, the Memoir gives a charming Picture of 
Herschel's personal life and especially of his relations with his 
sister There is also a good critical account of Heischel s work 
on sidereal astronomy in Proctor's Old and New Astronomy 

Chapter XIII Except in the articles dealing with gravita- 
tional astronomy I have constantly used Miss Clerke's History 
(already quoted), a book which students are strongly recom- 
mended to read and m dealing with the first half of the century 
I have been helped a good deal by Grant's History But for 
the most part the materials for the chapter have been drawn 
from a great number of sources-consisting very largely of the 
original writings of the astronomers referred to which it would 
be difficult and hardly worth while to enumerate, for the lives 
of astronomers (especially of English ones), as well as for recent 
astronomical history generally, I have been much helped by the 
obituary notices and the reports on the progress of astronomy 
which appear annually in the Monthly Notices of the Royal 
Astronomical Society 

I add the names of a few books which deal with special parts 
of modern astronomy in a non-technical way 

The Sun, C A Young, The Sun, R A Proctor The Story 
of the Sun, R S Ball , The Sun's Place in Nature, J N 

The Moon, 'E Neison, The Moon, T G Elger 
Saturn and its System, R A. Proctor 
Mars, Percival Lowell 

The World of Comets, A Guillemm (a well-illustrated but 
uncritical book, now rather out of date) , Remarkable 
Comets, W T Lynn (a very small book full of useful in- 
formation) , The Great Meteoritic Shower of November, 

W F. Denning ,0,0, r u 

The Tides and Kindred Phenomena in the Solar System, (j tt 

Darwin _ 

Remarkable Eclipses, W T. Lynn (of the same character as 

his book on Comets ) 
The System of the Stars, A. M, Clerke 
Spectrum Analysts, H Schellen, Speetrum Analysis, H E. 



Roman figwes tefer to the chapters, Arabic to the articles The 
numbers given in brackets after the name of an astronomer are 
the dates of birth and death All dates are A D unless otherwise 
stated In cases in which an author's name occurs in several 
articles, the numbers of the articles in which the principal account of 
him or of his wot k is given are printed tn clarendon type thus . 286 
The names of living astronomers are italicised 

Abul Wafa See Wafa 
Adams (1819-1892), xm 286, 

287, 289 

Adelard See Athelard 
Airy (1801-1892), x 227 , 

xm 281, 292 
Albategmus ( ? -929), n 53 , m 

59, 66, 68 n , iv 84, 85 
Albert (of Prussia), v 94 
Albertus Magnus (i3th cent), 

iir 67 

Alcuin (735-804), in 65 
Alembert, d' See D'Alembert 
Alexander, n 31 
Alfonso X (1223-1284), in 66, 

68 , v 94 

Al Mamun, m 57, 69 
Al Mansur, in 56 
Al Rasid, in 56 
Alva, vn 135 
Anaxagoras (499 B.C ?-427 

B c ?), i 17 
Anaxirnander (610 30-546 

B c ?), I ii 
Apian (I495-I55 2 X ni. 69, v 

97 , vu 146 


Apollonms (latter half of 3rd 

cent BC), n. 38, 39> 45, 51, 

52 n , x 205 
Arago, xii 254 
Archimedes, n 52 n , m 62 
Argelander (1799-1875), xin. 

Anstarchus (earlier part of 3rd 

cent BC), n 24,32,41, 42, 

54, xv 75 
Aristophanes, n 19 
Aristotle (384 B c -322 B c ), 

n 24 27-30,31, 47, 51,52, 

in, 56, 66, 67, 68 , iv 70, 77 , 

v 100, vi 116, 121, 125, 

134, vin 163 
Anstyllus (earlier part of 3rd 

cent. B c,), n 32, 42 
Arzachel (fl 1080), in 61, 

d'Ascoli, Cecco (i3th cent), 

in 67 
Athelard (beginning of I2th 

cent.), in. 66 
Auzout (7-1691), vni. 155, 

1 60, x 198 


Index of Names 
\Roman figures refer to the chapteis, Aiabic to the articles ] 

Bacon, Francis (1561-1627), 

vi 134, vin 163 
Bacon, Roger (1214^-1294), 

in 67, vi 118 
Bailly, xi 237 
JBall, xni 278 n 
Bar, Reymers (Ursus) ( ? -i6oo), 

v 105 
Barbenm (Urban VIII), vr 

125, 127, 131, 132 
Barnard, xni 294, 295 
Baronius, vi 125 
Barrow, Isaac, ix 166 
Bayer, xn 266 
Bede, m 65 

Begh, Ulugh See Ulugh Begh 
Bellarmme, vi 126 
Bentley, ix 191 
Berenice, I 12 
Bernomlli, Daniel (1700-1782), 

xi 230 
Bernoulli!, James (1654-1705), 

xi 230 
Bernomlli, John (1667-1748), 

xi 229, 230 
Bessel (1784-1846), x 198 n, 

218, xni 272, 277-278, 279, 


Bille, v. 99 

Bliss (1700-1764), x 219 
Bond, William Cranch (1789- 

1859), xm 295 
Borelh (1608-1679), ix 170 
Bouguer (1698-1758), x 219, 


Boulliau See Bulhaldus 
Bouvard, XL 247 n , xni 289 
Bradley (1693-1762), x 198, 

206-218, 219, 222-226, xi 

233, xii 257, 258, 263, 264, 

xni 272, 273, 275, 277 
Brahe, Tycho (1546-1601), m 

60, 62 , v 97, 98 , 99-112 , 

vi 113, 117, 127, vu 136- 

139,141^142,145, 146,148, 

vin 152, 153, 162, ix 190, 

x 198, 203, 225 , xn 257 , 

xm 275 

Brudzewski, iv 71 
Bruno, vi 132 

Bulhaldus ( 1 605-1 694), xn 266 
Bunsen, xm 299 
Burckhardt (1773-1825), xi 


Burg (1766-1834), xi 241 
Burgi (1552-1632), v 97, 98 , 

vni 157 

Burney, Miss, xn 260 
Bumham, xm 309 

Caccim, vi 125 
Caesar, n 21 , in 67 
Calhppus (4th cent B c ), II 

20, 26, 27 
Capella, Martianus (5th or 6th 

cent AD), iv 75 
Carlyle, xi 232 
Carnngton (1826-1875), xni 

298, 302 

Cartesms See Descartes 
Cassim, Count (1748-1845), x 

Cassim, Giovanni Domenico 

(1625-1712), vni 160, 161, 

ix 187, x 216, 220, 221, 

223 , xii 253, 267 , xni 297 
Cassim, Jacques (1677-1756), 

x 220, 221, 222 
Cassim de Thury (1714-1784), 

x 220 

Castelh, vi 125 
Catherine II , x 227 , xi 230, 


Cavendish (1731-1810), x 219 
Cecco d'Ascoh (1257 ?-i 327), 

in 67 

Chandler, xni 285 
Charlemagne, in 65 
Charles II , x 197, 223 
Chariots, xni 294 

Index of 'Names 
[Roman figures refer to the chapter, Arabic to the cuticles ] 


Christian (of Denmark), v 106 
Christine (the Grand Duchess) 

vi 125 

Clairaut (1713-1765), xi 220 
230, 231, 232, 233-235, 237, 
239, 248 , xin 290 
Clement VII , iv 73 
Clerke, xm 289 n 
Clifford, ix 173 n 
Colombe, Ludovico delle, vi 

119 n 

Columbus, in 68 
La Condamme (1701-1774) x 

219, 221 ' 

Conti, vi 125 
Cook, x 227 

Coppernicus (1473-1 543), n 
24,41 , 54, in 55, 62,69, 
IV passim, v 93-97, IO o, 
105, no, in , vi 117, 126, 
127, 129, vn 139, 150, ix 
1 86, 194, xii 257, xui 279 
Cornu, xni 283 
Cosmo de Medici, vi 121 
Cotes (1682-1716), ix 192 
Crosthwait, x 198 
Cusa, Nicholas of (1401-1464) 
iv 75 

D'Alembert (1717-1783), x 215, 

xi 229, 230, 23i, 232-235, 

237-239, 248 
Damoiseau (1768-1846), xm 


Dante, in 67, vi 119 n 
Darwin^ xm 292, 320 
Da Vmci See Vinci 
Dawes (1799-1868), xm 295 
Delambre, n 44, x 218, xi 

247 n , xm 272 
Delaunay (1816-1872), xm 

286, 287 

De Morgan, n 52 n 
Descartes (1596-1650), vm 163 
Diderot, xi 232 

Digges, Leonard (^-1571 ?), vi 

1 1 8 

Digges, Thomas ( ? -i595), v 95 
Donati (1826-1873), xm 304 
Doppler (1803-1853), xm 302 
Dreyet, xm 308 
Duner, xm 302 

Ecphantus (5th or 6th cent 

B c ), n 24 
Eddm, Nassir (1201-1273), in 

62, 68 , iv 73 J; 

Encke (1791-1865), x 227, 

xm 284 
Eratosthenes (276 60-195 or 

196 BC), ii 36, 45, 54, x 


Euclid (fl 300 B c ), n 33, 52 
n , m 62, 66, vi 115 , ix 

Eudoxus (409 B c ?~356 B c ?), 
n 26,27,38,42,51 

Euler (1707-1783), x 215,226, 
xi 229, 230, 231 n, 233-236, 
237, 239, 242, 243 , xm 290 

Fabncius, John (1587-1615?), 

vi 124 
Ferdinand (the Emperor), vn 

137, 147 

Fernel (1497-1558), ni 69 
Ferrel, xm 287 

P)eld (*525 ? -iS87), v 95 
Fizeau (1819-1896), xm 283 
Flamsteed(i646-i72o), ix 192, 
x 197, 198, 199, 204, 207 , 
218, 225, xn 257, xm 275, 

Fracastor (1483-1553), ni 69, 

TV 89, vii 146 
Fraunhofer (1787-1826), xm 

Frederick II (of Denmark), v. 

101, 102, IOO 


Index of Names 

[Roman figures refer to the chapters, Aiabic to the articles ] 

Frederick II (the Emperor), 

in 66 
Frederick II (of Prussia), xi 

230, 232, 237 

Galen, ii 20, m 56 , vi 116 

Galilei, Galileo (1504-1642), n 
30 n, 47 , iv 73 , v 96, 98 n , 
VI. passim, vn 135, 136, 
138, 145, 151, vm 152-154, 
157, 163, ix 165, 168, 170, 
171, 173. I79> 180, 186, 190, 
195, x 216, xii 253, 257, 
263, 268 , xni 278, 295 

Galilei, Vmcenzo, vi. 113 

Galley xin 281, 289 

Gascoigne (1612 ^-1644), vm 
155, 156, x 198 

Gauss (1777-1855), xin 275, 
276, 294 

Gautier (i 793-1881), xm 298 

Genghis Khan, in 62 

George III , xii 254-256 

Gerbert (?-ioos), in 66 

Gherardo of Cremona (1114- 
1187), ni 66 

Gibbon, n 53 n 

Giese, iv 74 

Gilbert (1540-1603), vn 150 

Gill, xui 280, 281 

Glaisher, xm 289 n 

Godm (1704-1760), x 221 

Goodncke (1764-1786), xn 

Grant, xm 289 n 

Grassi, vi 127 

Gregory, James (1638-1675), 
ix 168, 169 , x. 202 

Gregory XIII ,, 11 22 

Gylden (1841-1896), xm 288 

Hamzel, v 99 
Hale, xm. 301 
Halifax, John, See Sacrobosco 

Halifax (Marquis of), ix. 191 

Hall, xni 283 n, 295 

Halley (1656-1742), vm. 156 , 
ix 176, 177, 192 , x 198, 
199-205, 206, 216, 223, 224, 
227, xi 231, 233, 235, 243, 
xn 265 , xm 287, 290 

Hansen (1795-1874), xm 282, 
284, 286, 290 

Harkness, xm 301 

Harriot (1560-1621), vi 118, 

Harrison, x 226 

Harun al Rasid, m 56 

Helmholtz (1821-1894), xm. 


Hencke (1793-1866), xm 294 

Henderson (1798-1844), xm 

Herachtus (5th cent B c ), n 

Herschel, Alexander, xn. 25 1 

Herschel, Caroline ( 1750- 1 848), 
xn 251, 254-256, 260 

Herschel, John (1792-1871), 
I 12 , x 221 , xi 242, xn 
256, xm 289 n, 306-308, 
309, 316, 317, 310 

Herschel, William (1738-1822), 
ix 168, x 223, 227, xi 250, 
XII. passim , xm 272, 273, 
294,296, 306-311, 317, 318 

Hesiod, ii 19, 20 

Hevel (1611-1687), vm 153, 
x 198, xn 268 

Hicetas (6th or 5th cent B c ), 
ii 24, iv 75 

Hill, xi 233 n , xm 286, 290 

Hipparchus (2nd cent B c ), i 
13, n 25, 27, 31, 32, 37-44, 
45> 47-52, 54, m 63, 68, 
iv 73, 84, v in , vii 145 

Hippocrates, in 56 

Holwarda (1618-165 1), xn 266 

Holywood See Sacrobosco 

Index of Names 421 

[Roman figures refer to the chapters, Atabic to the articles ] 

Honem ben Ishak (?-8;3), in 

Hooke (1635-1703), ix 174, 

176, X 2O7, 212 

Horky, vi 121 

Horrocks (1617 ?-i64i), vin 

156, ix 183, x 204 
Hewlett, xni 298 
Huggtns, xni 301, 304, 311- 


Hulagu Khan, in 62 
Huniboldt, xni 298 
Hutton (1737-1823), x 219 
Huygens (1629-1695), v 98 n , 

vi 123 , vni 154, 155, 157, 

158; ix 170-172, 191 
Hypatia (^-415), n 53 

Ibn Yunos See Yunos 
Ishak ben Honem (?~9io or 
9 I] Oi I" 56 

James I , v 102 , vn 147 
James II , ix 192 
JansseH) xni 301, 307 n 
Joachim See Rheticus 

Kaas, v 106 

Kant, xi 250, xn 258, 260, 
xni 287 

Kapteyn^ xui. 280 

Kelvin^ xin 292 

Kepler (157 1-1630), n 23,5172, 
54, iv 91, v 94, ioo, 104, 
108-110, vi 113, 121, 130, 
132 , VII. passim , vm 152, 
156, 160, ix 168-170, 172, 
175, 176, 190, 194, 195 , x 

202, 205, 220, XI 228, 244, 

xm 294,301,309 
Kirchhoff (1824-1887), xm 

Kirkwood (1815-1895), xin 

294, 297 

Koppermgk, iv 71 

Korra, Tabit ben See Tabit 

Lacaille (1713-1762), x 222- 

224, 225, 227 , xi 230, 233, 

235 , xii 257, 259 
La Condamme (1701-1774) x 

219, 221 
Lagrange (1736-1813), ix 193 , 

xi 229, 231 n, 233 n, 236, 

237, 238-240, 242-245, 247, 

248, xii 251, xm 293, 294 
Lalande (1732-1807), xi 235, 

241, 247 n , xii 265 
Lambert (1728-1777), xi 243, 

xn 265 

Lami, ix 1 80 n 
Landgrave of Hesse See 

William IV 
Lang ley t xin 307 
Lansberg (1561-1632), vm 156 
Laplace (1749-1827), xi 229, 

231 n, 238-248, 250, xn 

251,256, xm 272, 273, 282, 

266-288,290, 293, 297,318- 

Lassell (1799-1880), xn. 267 , 

xm 295 

Lavoisier, xi 237 
Legendre (1752-1833), xin 

275, 276 

Leibniz, ix 191, 193 
Lemaire, xn 255 
Leverner(i8ir-i877),xm 282, 

284, 288, 289, 290, 293, 294 
Lexell (1740-1784), xn. 253 
Lmdenau, xi 247 n 
Lionardo da Vmci See Vmci 
Lippersheim (7-1619), VI n 8 
Locke, ix 191 
Lockyer, xm 301, 302 
Loewy, xni 283 n 
Louis XIV , vm 160 
Louis XVI , xi, 237 
Louville (1671-1732), xi 229 

422 Index of Names 

[Roman figures tefet to the chapters, Aiahc to the articles ] 

Lubbock( 1 803-1 865), xni 286, 

Luther, iv 73 , v 93 

Machm ( ? -i75i), x 214 
Maclaurm (1698-1746), x 196 , 

xi 230, 231 , xn 251 
Maestlm, vn 135 
Maraldi, x 220 
Harms (1570-1624), vi 118, 

vu 145 



Capella See 

Maskelyne(i732-i8n),x 219, 
xn 254, 265 

Mason (1730-1787), x 226, 

xi 241 
Matthias (the Emperor), vn 

143, 147 
Maupertms( 1698-1759), x 213, 

221, xi 229, 231 
Maxwell (1831-1879), xui 297 
Mayer, Tobias (1723-1762), x 

217,225,226, xi 233, 241, 

xn 265 

Melanchthon, iv 73, 74 , v 93 
Messier (1730-1817), xn 259, 


Meton (460 B c ?-?), n 20 
Michel Angelo, vi 113 
Michell, John (1724-1793), x 

219, xii 263, 264 
) xni 283 


Molyneux (1689-1728), x 207 
Montanan (1632-1687), xn 266 
Muller See Regiomontanus 

Napier, v 97 n 
Napoleon I , xi 238 , xii 256 
Napoleon, Lucien, xi. 238 n 
Nassir Eddin See Eddm, 

Newcomb, x 227 n , xni. 283 

286, 290 ' 

Newton (1643-1727), n 54, 
iv 75, vi. 130, 133, 134, 
vii 144, 150, vin 152, IX, 
passim, x 196-200, 211, 
213, 215-217, 219, 221, xi 
228, 229, 231-235, 238, 249, 
xn 257, xin 273, 299 

Niccolmi, vi 132 

Nicholas of Cusa (1401-1464) 
iv 75 

Nonius (1492-1577), in 69 

Norwood (1590 ?-i 675), vin 
159 , ix 173 

Numa, ii 21 

Nunez See Nonius 

Nyren, xui 283 n 

Gibers (1758-1840), xni 294 
Orange, Prince of, v 107 
Osiander, iv 74 , v 93 

Pahsa, xni 294 

Pahtesch (1723-1788), xi 231 

Pemberton, ix 192 

Philolaus (5th cent B c ), n 

24:, iv 75 Ji 

Piazzi (1746-1826), xm 294 
Picard (1620-1682), vm 155, 

157,159-161, 162, ix i 74 ; 

X 196, 198, 221 

Pzckenng, xni 314,316 
Plana (1781-1869), xni 286 
Plato (428 B c ?-347 B c ?), n 

24, 25, 26, 51 , iv 70 
Plato of Tivoh (Ji 1116), in 


Pliny (23 A D -79 A D ), n 45 
Plutarch, n 24 , xni 301 
Pogson (1829-1 891), xm 316 
Pomcare, xm 288 
Poisson (1781-1840), xm 286, 

Poutecoulant (1795-1874), xni 

Porta, vi 118 

Index of Names 4 2 3 

\_Rcman figures refer to the chapters, Arabic to the articles ] 

Posidonius (i 35 B c ?-5 1 B c ?), 

ii 45 47 
Poiullet (1791-1868), xni. 307, 

3 J 9 

Pound, x 206, 216 

Provost (1751-1839), xn 265 

Pritchard (i 808-1 893), xni 
278 rc,279, 316 

Ptolemy, Claudius (Jl 140 AD), 
ii 25, 27, 32, 37, 46-52, 53, 
54, m 55, 57, 59- 6 3, 68, 
iv 70, 76, 80, 83-87, 89, 91 , 
v 94, 105, vi 121, 129,134, 
vn 145 , vm 161 , ix 194, 
x 205 , xi 236 

Ptolemy Philadelphia, n 3 1 

Purbach (1423-1461), in 68, 
iv 71 

Pythagoras (6th cent B c ), I 
ii, 14, n 23, 28, 47, 51, 54 

Recorde(i5io-i558), v. 95 
Regiomontanus (1436-1476), 

in 68, 69, iv 70, 71 , v 97, 


Reirnarus See Bar 
Remhold (1511-1553), v 93- 

96, vii 139 
Reymers See Bar 
Rheticus (1514-1576), iv 73, 

74, v 93, 94,96 
Ricardo, ii 47 n 
Riccioh (1598-1671), vm 153 
Richer (^1696), vm 161, IX. 

1 80, 187 , x 199, 221 
Rigaud, x 206 11 
Roemer (1644-1710), vm 162 ; 

x. 198, 210, 216, 220, 225 ; 

xni 283 
Rosse (1800-1867), xni. 310, 

Rotlimann (Jl 1580), v 97, 

98, 1 06 
Rudolph II. (the Emperor), v 

106-108, vii 138, 142, 143 

Sabine (1788-1883), xni. 298 
Sacrobosco (7-1256?), in 67, 


St. Pierre, x 197 
Savary (1797-1841), xni 309 
Schemer (1575-1650), vi 124, 

125 , vii 138, vm 153, 

xii 268 

Schiajbarelh) xin 297 
Schomberg, iv. 73 
Schoner, iv 74 
Schonfeld (1828-1891), XIII. 

Schroeter (1745-1816), xii 267, 


Schwabe (1789-1875), xni 298 
Secchi (1818-1878), xin 311, 


See, xni 320 

Seleucus (2nd cent B.c ), n 24 
Shakespeare, vi. 1 13 
Sharp (1651-1742), x. 198 
Slusms, ix 169 
Smith, xii 251 
Snell (1591-1626), vin 159, 

ix 173 

Sosigenes (fl 45 B c ), ii 21 
South (1785-1867), xni 306 
Stmve, F G W (1793-1864), 

xni 279, 309 
Stnme, O , xni 283 n 
Svanberg (1771-1851), X 221 
Sylvester II. See Gerbert 

Tabit ben Korra (836-901), in 

56, 58, 68 , iv 84 
Tamerlane, in 63 
Tannery, ii 36 n 
Tliales (640 B c 7-546 B c ?), 

n 23, in. 55 

Theon (Jl 365 AD), ii 53 
Theophrastus, II 24 
Theopbylactus, iv 72 
Thomson, T , x 208 n 
Thomson, William Sec Kelvin 

Index of Names 
\Rcmanjigwes refer to the chapters, Arabic to the articles ] 

Thury, Cassmi de. See Cassmi 

de Thury 
Timocharis (beginning of 3rd 

cent BC) ii 32, 42, iv. 84 
Tycho Brahe See Brahe 

Ulugh Begh (1394-1449), in 

63, 68 , iv 73 
Urban VIII (Barberim), vi. 

125, 127,131, 132 
Ursus See Bar 

Varignon, ix 180 n 

Vinci, Lionardo da (1452-1 ;IQ). 

in 69 

Voge^xm 313, 314. 
Voltaire, n 21 , xi 229 

Wafa, Abul (939 or 940-998), 
ni 60,68 , iv 85, v in 

Wallen stein, vn. 149 
Walther (1430-1504), in 68, 
v 97 

Wargentin (1717-1783), x 216 

Watzelrode, iv 71 

Wefa See Wafa 

Welser, vi 1 24 

Whewell (1794-1866), xin 292 

William IV (Landgrave of 

Hesse) (1532-1592), v 97, 

98, 100, 105, 1 06, no 
Wilson (1714-1786), xii 268, 

xni 298 

Wolf, Mar, xin. 294 
Wolf, Rudolf (1816-1893), xin 

Wollaston (1766-1828), xin 


Wren (1632-1723), ix 174, 176 
Wright, Thomas (1711-1786), 

xii 258, 265 

Young, xin 301 
Yunos, Ibn (?-ioo8), in 60 
62, 68 n 

\on Zacb, xi 247 n 


the , cha P Un < A rafa to the articles When swerat 
ne hta * m g t >* numbers of the most important 

a tyfe < thui 207 T <" 

Serration, x 206, 207-211, 212 
213, 216, 218, xn 263. xm 
277, 283, 284 

.cademie Franchise, xi 232, 238 
.cademy of Berlin, xi 230, 237 
.cademy of St Petersburg, xi, 
2 30 } 233 
cademy oi Sciences (of Pans), 

X 221, 223, XI 229-233, 

cademy of Turin, xi 237, 238 
cceleration, vi. 133, ix 171 
172, 173, 179, iSo, 185, 195! 
x 223 

d ViUlhonem Parahpomena (of 

Kepler), vn 138 

laesive Scalae (of Digges), v 95 

xlebaran, m 64, xm 316 n 

Lexandi me school, ii 21 ^i-^?? 

36-38, 45, 53 ' 

Ifonsim Tables, in 68. 68 v 

94, 96, 99 

gol, xn 266, xm 314, 315 

Images* (of Ptolemy), n 46-52 

111 55, 56, 58, 6o ; 62, 66,68, 

iv- 75, 76, 83 

magest (of Abul Wafa), in 60 

'magest, New (of Kepler), vii 


magest, Nezv (of RicciolO, VIH 



Almanac, Nautical^ x. 218; xm 

286, 288, 290 
Almanacks, i i8?z, n 20, 38, in 

64, 68, v 94, 95, ioo ; vii, 

136; x 218, 224, xm 286, 

288, 290 

Altair, in 64, xm 316 n 
Analysis, analytical methods, x 

196 , xi 234 

Angles, rneasuiement of, i 7 
Annual equation, v 111 , vn 145 
Annual motion of the earth See 

Earth, revolution of 
Annual motion of the sun See 

Sun, motion of 
Annual parallax See Parallax, 


Annular eclipse, n. 43 , vn 145 
Anomalistic month, n 40 
'A.VTixQdv, ii 24 
Apex of solar motion, xn 265 
Aphelion, iv 85 
Apogee, ii 39, 40, 48, in 58,59, 

iv 85; v. in, ix. 184, xi, 

2 33 

Apparent distance, i 7 
Apple, Newton's, ix 170 
Apse, apse-line, n 39, 40, 48 , iv. 

85 ix 183, xi 235, 236, 242, 

Arabic numerals, in 64, v 96 


General I?idex 

\Romanfigures refer to the chapters, Arabic to the articles ] 

De Motu (of Newton), ix 177, 

De Mundi aetherei (of Tycho), 

v 104 

De Nova Stella (of Tycho), v. 100 
De Revoluhombus (of Copperm- 

cus), ii 41 n , iv 74-92 , v 93, 

94, vi 126 
De Satitrni Lima (of Huygens), 

vin 154 
Descriptive astronomy, xin 272, 

273. 294 

Deviation error, x 225 n 
Dialogue on the Two Chief Sys- 
tems (of Galilei), vi 124 n, 

128-132, 133 
Differential method of parallax, 

vi 129, xn 263, xm 278 
Diffraction-grating, xm 299 
Dione, vni 160 
Dtoptnce (of Kepler), vn 138 
Direct motion, i 14 
Disturbing force See Perturba- 
Diurnal method of parallax, xm 

281, 284 
Doctrine of the spheie See 

Doppler's principle, xm 302, 

313, 3'4 

Double hour, i 16 
Double-star method of parallax 

See Differential method of 

Double stars See Stais, double 

and multiple 

Dracomtic month, 11 40, 43 
Durchmustet ung l xm 280 
Dynamics, vi 133, 134, ix 179, 

180, xr 230, 232, 237 
Dynamique, ftaitede (of D'Alem- 

bert), xi 232 

Earth, i i, 15, 17, n 28, 29, 32, 

39, 4i, 43, 47, 49, 5 1 > i" 66, 
69, iv 80, 86 , vi 117, i2i, 
133, vii 136 n, 144, 145, 150, 
vni 153, 154, ix 173, 174, 179- 

182, 184, 1 86, 195 , xi 228, 

245 , xm. 285, 287, 292, 293, 
297, 320. See also the following 

Earth, density, mass of, ix, 180, 
185, 189, x 219, xi 235, 
xni 282, 294 

Earth, motion of, 11, 24, 32, 47 , 
iv 73, 76, 77, v 96, 97, 105, 
vi 121, 125-127,129-132, vm 
161, 162, ix 186, iQ4,xn 257 
See also Earth, revolution of and 
rotation of 

Earth, revolution of,annual motion 
of, n 23, 24, 28 n, 30, 47 , iv 75, 
77, 79-82, 85-88, 89, 90, 92, v 
1 1 1, vi 119,126,129,131,133, 
vii 139, 142, 146 , vin 161 ; ix 
172, 183, x 207-210,212,227, 
xi 235, 236, 240 j xn 263 , xm 
278, 282, 283 

Earth, rigidity of, xm 285, 292 

Earth, rotation of, daily motion 
of, ii 23, 24, 28 n , iv 75, 78, 
79 n, 80, 84, v 105; vi 124, 
126, 129, 130, ix 174, 194, 
x 206, 207, 213 1 xm 281, 285, 
287, 320 

Earth, shape of, n 23, 29, 35, 
45, 47, 54, iv 76, vin 161, 
ix 187, 188, x 196, 213, 215, 

220, 221, 222, 223 , xi. 229, 231, 
237, 248 

Earth, size of, ii 36, 41, 45, 47, 
49, m 57,69, iv 85, vn 145, 
vni 159, 161 , ix 173, 174, x. 

221, 222, 223 

Earth, zones of, ii 35, 47 
Earthshmc, in 69 
Easter, lule for fixing, n 20 
Eccentric, ii 37, 39, 40, 41 1 48, 
51, m 59, iv 85, 89-91 ,' vn. 

139, ISO 

Eccentricity, ii 39, iv 85, vii 
140 n , xi 228, 236, 240, 244- 

246, 250, xm 294, 318 
Eccentricity fund, xi 245 
Eclipses, i ii, 15, 17, n, 29, 32, 

General Index 
[Roman figures tefer to the chapters, Atabc to the articles ] 


40-42, 43 ,47-49, 54, m 57, 
68, iv 76,85, v no, vi 127, 
vii 145, 148, viii 162, x 201, 

205, 210, 2l6, 227, XI 240; 

xm 287, 301 

Eclipses, annular, n 43 , vii 145 
Eclipses, partial, u 43 
Eclipses, total, n 43 , vii 145 

x 205 , xm 301 
Ecliptic, i 11, 13, 14, n 26, 33, 

35, S^, 38, 40, 42, 5i , m 58, 

59, 68 , iv 80, 82-84, 87, 89 , 

v in, vni 154, x 203,209, 

213,214,227, xi 235,236,244, 

246, 250 
Ecliptic, obliquity of, i 11, n 

35, 36,42, m 59,68, iv, 83, 

64 , xi. 235, 236 
Ecole Noimale, xi 237, 238 
Ecole Poly technique, xi 237 
Egyptians, Egyptian astronomy, 

i 6, II, 12, 16, n 23, 26. m 

45 , iv. 75 
Elements (of Euclid), in 62. 66 

ix 165 
Elements (of an orbit), xi 236, 

240, 242, 244, 246, xm 275, 

Elements, variation of. See 

Variation of elements 
Ellipse, ii 51 n , m 66 , vn. 140, 

141; IX 175, 176, 190, 194, X 
200, 209, 214 , XI. 228, 236, 242, 

244 , xm 276, 278, 309 
Ellipticity, x 221 
Empty month, n 19, 20 
Empyrean, HI 68 
Enceladus, xn 255 
Encke's comet, xm. 291 
Encyclopaedia, the French, xi. 232 
Energy, xm 319 
Ephemendes See Almanacks 
Ephemendes (of Regiomontanus), 

in 68 
Epicycle, n 37, 39, 41, 5, 48, 

51, 54 , m 68 , iv 85-87, 89- 

91, vn 139,150, vni 163, ix. 

170, 194 

Epitome (of Kepler), vr 132 , vii 

144, 145 

Epitome (of Purbach), in 68 
Equant, n 51 , in 62 , iv 85, 89, 

91 , vii. 139, 150 
Equation of the centre, n 39, 48 ; 

in 60, v m 

Equator, i 9, 10, n , n. 33, 35, 
39, 42 , iv 82, 84 , v 98 , vi. 
I2 9> 133; ix 187 , x. 207, 220, 
221 ; xm 285 

Equator, motion of See Preces- 
Equinoctial points, i 11, 13 , n 

42 See also Aries, first point of 
Equinoxes, i 11 , n 39, 42 
Equinoxes, precession of See 

Essai philosophtque (of Laplace). 

xi. 238 

Ether, XHI 293, 299 
Evection, n 48, 52, m 60, iv 

85 , v. r n , vn. 145 
Evening stai, i 14 See also 


Exposition du Syste-me du Monde 
(of Laplace), xi 238, 242 , 250 

Faculae, vni 153, xm 300,301. 

Figure of the eaith See Earth, 

shape of 

Firmament, in. 68 
First point of Aries, Libia See 

Aries, Libra, first point of 
Fixed stars, i 14 See Stars 
Fluxions, ix 169, 191, x 196 
Fluxions (of Maclaurm), xn 251 
Focus, vn 140, 141, ix 175, xi 


Force, vi. 130, ix 180, 181 
Fraunhofer lines, xm. 299, 300, 

303, 304 
Front-view con sti action See 

Herschelian telescopes 
Full month, n 19, 20 
Full moon See Moon, phases of 
iii 286 


General Index 

[Roman figwes refer to the chapters, Arabic to the cuticles ] 

Fundamenta Astronomiae 
Bessel),x 218, xm 277 

Funds of eccentricity, inclination, 
xi 245 

Galactic circle, xn 258, 260 
Galaxy See Milky Way 
Gauges, gauging See Star- 

Georgmm Sidus See Uranus 

Gravitation, gravity, n 38 n , vn 

150, vm 158, 161 ; IX passim , 

x 196, 201, 213, 215, 219, 220, 

223, 226 , XI passim , xn 264 , 

xm 282, 284, 286-293, 309, 319 

Gravitational astronomy, x 196, 

xni 272, 273, 286 
Gravity, variation of, vm 161 , 
ix 180, x 199, 217, 221, 223, 
xi 231 

Great Bear, i 12, xn 266 
Great circle, i 11 , n 33, 42 , iv 

82, 84 

Gregorian Calendar See Cal- 
endar, Gregorian 
Grindstone theory, xn. 258 , xm 

Hakemite Tables, in 60, 62 
Halley's comet, vn 146 , x 200, 

205 , xi 231, 232 , xm 291, 


Harmonics (of Smith), xn 25 1 
Harmony of the Woiid (of Kepler), 

vn 144 

Helium, XHI 301 
Herschelian telescope, xn 255, 

Histona Coelestts (of Flam steed), 

x 198 

Holy Office See Inquisition 
Horizon, i 3, 9, n 29,88, 35, 39, 

46, vm 161 , xm 285 
Horoscopes, v 99 
Hour, i 1 6 

Hydrostatic balance, vi 115 n 
Hyperbola, ix 190, xi 236 n 
Hyperion, xm 295 

Ilkhamc Tables, in 62 

II Saggtatot? (of Galilei), vi 127 

Inclination, in 58 ; iv 89 , xi 

228, 244, 245, 246, 250, :mi 

294, 3i8 

Inclination fund, xi 245 
Index of Prohibited Books, vi 126, 

132 , vii 145 
Indians, Indian astronomy, i 6, 

in 56, 64 

Induction, complete, i\ 195 
Inequalities, long, xi 243 
Inequalities, periodic, xi 242, 

243, 245, 247 
Inequalities, seculai, xi 242, 

243-247 , xm 282 Sec afao 


Inequality, parallactic, xni 282 
Inferior planets, i 15 ; iv 87, 88 

See also Meictuy, Venus 
Inquisition (Holy Omce), vi 126, 

I3 2 > 133 

Institute of France, xi 241 
Inverse deductive method, ix 195 
Inverse squaic, JAW of, ix 172 

176, 181, 195 , xi 233, See CI!$Q 

Ionian school, n 23 
Ins, xm 281 
Irradiation, vi 129 
Island umveise theory, xir 260, 

xm 317 

Japetus, vm t6o, xn 267, xin 

Julian Calcndai See Cakmlai, 

Juno, xm 294 

Jupiter, i 14-16, n 25, 51, iv 
81, 87, 88, v 98, 99, vi. 121, 
127 , vii 136 , 142, 144, 145, 
150, vm 154, 156, 162, ix 
172, 181, 183, 185-187, x 204, 
216; xi 228, 231, 235, 236, 
243-245, 248 , xn 267 , xni, 
281, 288, 294, 297, 305 See 
also the following 1 headings 

Jupiter, belts of, xn 267 

General Index 
[Roman figures refer to the chapters, Arabic to the articles ] 

43 1 

Jupiter, mass of, ix 183, 185 
Jupiter, rotation of, vm 160 

ix 187, xm 297 
Jupiter, satellites of, u 43 , vi 

121, 127, 129, 133, vii 145, 

150, vm 1 60, 162, ix 170, 
184, 185, x 210, 216 , xi 228, 
248 , xri 267, xm 283, 295, 

Jupiter's satellites, mass of, xi 

Keplei's Laws, vii 141, 144, 145, 

151, vm 152, ix 169, 172, 
175, 176, 1 86, 194, 195, x 220, 
xi 244 , xm 294, 309 

Latitude (celestial), n 33, 42, 

43; ni 63, iv 89 
Latitude (tenestnal), in 68, 69, 

iv 73, x 221, xm 285 
Latitude, vaiiation of, xm 285 
Law of gravitation See Gravi- 

Laws of motion, vi 130, 133 , 
vm 152, 163, ix 171, 179- 
181, 183, 186,194, 195, xi 232 
Leap-year, i 17, n 21, 22 
Least squares, xm 275, 276 
Letter to the Grand Duchess (of 

Galilei), vi 125 
Level error, x 225 n 
Lexell's comet, xi 248 ; xm 305 
Libra, fhst point of (==), T 13 ; n 

Librations of the moon, vi 133 , 

x 226, xi 237, 239 
Libros del Saber, m 66 
Light-equation, xm 283 
Light, motion of, velocity of, 
vm. 162, x 208-211, 216, 220, 
xm 278, 279, 283, 302 See 
also Aberration 
Logarithms, v 96, 97 n 
Long inequalities, xi 243 
Longitude (celestial), n 33, 39, 
42, 43 ; ni 63 ; iv 87 , vii, 139 

Longitude (terrestrial), in 68; 

IiM 7 2 'e I33 ' VI1 1S ' X ' 97 ' 

Longitudes, Bureau cles. xi 


Lunar distances, m 68 n 
Lunar eclipses See Eclipses 
Lunai equation, xm 282 
Lunar theory, n 48, 51 , v m , 
vii 145, vm 156, ix 184,192, 
x 226, xi 228, 230, 231, 233, 
234, 240, 241, 242, 248, xm 
282, 286, 287, 288, 290 See 
aho Moon, motion of 
Lunation, n 40 See also Month, 

Macchie Solan (of Galilei), vi 124. 

Magellanic clouds, xm 307 

Magnetism, vn 150, xni* 276, 298 

Magnitudes and Distances of the 
SimandMoon (of Anstarclius), 
IT 32 

Magnitudes of stars, n 42, xii 
266, xii 280, 316 See also 
Stars, biififhtness of 

Mars, i 14-16, n 25, 26, 30, 51 , 
ni 68, iv 81, 87, v 108, 
vi 129, vn 136 n, 139-142, 144, 
145 / vm 154, 161 , ix 181, 
183, 185, x 223, 227, xi 235, 
245, xn 267, xm 281, 282, 
284, 294, 295, 297 Sre also 
the following- headings 

Mars, canals of, xm 297 

Mars, mass of, xi 248 

Mars, opposition of, vm 161: xnr. 
281, 284, 297 

Mais, rotation of, vin 160, xni 
295, 297 

Mai s, satellites of, xm 295 

Mass, ix 180, 18 1, 185 

Mass of the earth, sun, Venus 
See Earth, Sun, Venus . , mass 

Mecamqm Anatyttque (of La- 
grange), XT 237 

43 2 

General Index 
[Roman figures refer to the chapters, Arabic to the articles ] 

Mecamque Celeste (of Laplace), 

xi 238, 241, 247, 249, 25o ; 

xni 292 
Medicean Planets. See Jupiter, 

satellites of 
Meraga, m 62 
Mercury, i 14-16 , n 25, 26, 45, 

47,51, ui 66, iv 73, 75, 81, 

86-89, VI 121, 124, VII 136 , 

139, 142, 144 , ix 185 , xm 288, 

290, 294, 297 See also the 

following headings 
Mercury, mass of, xi 248 
Mercury, phases of, vi 129 
Mercury, rotation of, xm, 297 
Mercury, transit of, x 199 
Meridian, n 33, 39, m 57, vi 

127, vin 157, x 207,218, 221 
Meteorologica (of Aristotle), n 27 
Meteors, xm 305 
Meton's cycle, n 20 
Metric system, xi 237 
Micrometer, vm 155, xm 279, 

Milky Way, n 30, 33, vi 120, 

xii 258, 260-262, xm 317 
Mimas, xii 255 
Minor planets, xi 250 n , xm 

276, 281, 284, 288, 294, 295, 

297, 318 

Minor planets, mass of, xm 294 
Minute (angle), I 7 
Mira, xii. 266 
Mongols, Mongol astronomy, m 

Month, i 4, 1 6, n 19-21,40,48, 

ix 173; xi 240, xm 293,320 

See also the following headings 
Month, anomalistic, n 40 
Month, dracomtic, n 40, 43 
Month, empty, n 19, 20 
Month, full, ii 19, 20 
Month, lunar, i 16, n 19, 20, 40 
Month, sidereal, 11 40 
Month, synodic, 11 40, 43 
Moon, i i, 4, 5, n, 13-16, n. 

19-21, 25, 28, 30, 32, 39, 43 , 

in 68, 69 , iv 81, 86 , v 104, 

105 , vi 119, 121, 123, 129, 

W *33> VI1 H5* I5 vni - 
153, ix 169, 180, 181, 1 88, 189, 
x 198, 204, 213, 215, 226, xi 
228, 235 , xii 256, 257, 271 , 
xm 272, 292, 293, 296, 297, 
301 , 320 See also the following 

Moon angular or apparent size of, 
n 32, 41, 43, 46 n, 48 , iv 73, 
85, 90 , v 105 n 

Moon, apparent flattening of, 11 

Moon, atmosphere of, xin. 296 

Moon, distance of, i 15 ; n 24, 

25,30,82,41,43, 45i 4-8, 48, 51; 
iv 85, 90, v ioo, 103, ix 173 
185, x 223, xm 293, 320 

Moon, eclipses of See Eclipses 

Moon, librations of, vi 133, x 
226, xi 237, 239 

Moon, map of, x 226 , xin 

Moon, mass of, ix. 1 88, 189 
xi 235 

Moon, motion of, i 4, 8, 13, 15, 
17, n 20, 24-26, 28, 37, 39, 
40, 43, 47, 48, 51, in 60, iv 
73, Si, 85, 89, 90, v in, vi 
133, vii 145, 150, vm 156, 
ix 169, 173, 174, 179, 184, 185, 
189, 194, 195, x. 201, 204,213, 
226, xi 235, 237,248, xni 287, 
290, 297, 320 See also Lunar 

Moon, origin of, xni 320 

Moon, parallax of, 11 43, 49 , iv 
85 Cf also Moon, distance of 

Moon, phases of, i 4, 16, 17, n 
19, 20, 23, 28, 43, 48 , m. 68, 
69, vi 123 

Moon, rotation of, x 226 ; xi 248 ; 
xn 267, xm 297 

Moon, shape of, n. 23, 28, 46 , 
vi. 119, xi 237 

Moon, size of, n 32, 41 , iv 85 

Moon, tables of See Tables, 

General Index 

[Roman figures" refer g to the chapters, Arabic^ the articles} 


Moons See Satellites 

Morning star, i 14 See also 


Morocco, in 6 1 
Motion, laws of See Laws of 

Multiple stars See Stars, double 

and multiple 

Mural quadrant, x 218, 225 ;/ 
Music of the spheres, n 23 vn 

144 ' 

Mystermm Cosniographicum (of 
Keplei), v 108, vii. 136, 144 

Nadir, ni 64 

Nautical Almanac See Almanac, 


Nebula m Argus, xm 307 
Nebula in Orion, xn 252, 259 

260, xni 311 
Nebulae, x 223, xi 250. xn 

252, 256, 259-261, xni 306- 

308 ;, 310, 311, 317, 318, 3 19, 320 
Nebulae, spiral, xni 310 
Nebular hypothesis, xi.250. xin 

Nebulous stars, x 223 , xn 260 


Neptune, xni 289, 295, 297 
Neptune, satellite of, xm 295 
New Almagest (of Kepler), vn 

New Almagest (of Riccioh), vin 

XT I53 

New moon See Moon, phases of 
New stars, See Stars, new 
New Style (N S ), n 22 Sec 

also Calendar, Gregorian 
Newton's problem, xi 228, 220 

Newtonian telescope, ix 168 

XT*? ;*2,253,256 
Night-hour, i 16 

Node, n 40, 43, v. m, ix 184, 

x 213, 214, xi 286,246 
Nubeculae, xm. 307 
Nucleus (of a comet), xni 304 
Ntirnberg school, in 68, iv. 73 

Nutation, x, 206, 207, 213-215 
216 218, xi 232, 248, xn 263 
i i6n 

Oberon, xn 255 

Obliquity of the ecliptic See 

Ecliptic, obliquity of 
Observational astronomy, xni 

272, 273 

Occupations, i 15 , n 30 
Octaetens, n 19 
Olbers's comet, xm. 291 
Old Moore's Almanack, i 18 n 
Old Style (O S ) See Calendar, 


Opposition, n. 43, 48 n , in. 60 
iv 87, 88, v in, viii. 161' 
xm 281, 284, 297 
Opposition of Mars, vin 161 

xm 281, 284, 297 ' 

Optical double stars, xii 264 
Optics (of Gregory), x 202 
Optics (of Newton), ix 192 
Optics (of Ptolemy), n 46 
Optics (of Smith), xii 251 
Opus Majus, Mtmts, Tcrtwm 

(of Bacon), m. 67 
Opuscules Mathcmatiqttes (of 

D'Alcmbert), xi 233 
Orion, nebula m, xii 252, 259, 

260, xm 311 

Osallatonum Ho? ologium (of 
Huygens), vm. 158 , ix 171 

Pallas, xm. 294 

Parabola, ix. 190 , xi. 2^6 n 
xm 276 ' 

Parallactic inequality, xm 282 

Parallax, n 43, 49, iv. 85, 92- 
v 98, ioo, no, vi 129, vn 
145. vm 161; x 207, 212, 
223, 227, xii 257, 258, 263, 
264; xm 272, 278, 279,281- 
Parallax, annual, vm. 161 See 

also Parallax, stellar 
Paiallax, horizontal, vm, 161 



General Inde& 

[Roman figut es refer to the chapters, Arabic to the articles ] 

Parallax of the moon. See Moon, 
parallax of 

Parallax of the sun See Sun, 
parallax of 

Parallax, stellar, iv 92 , v 100 , 
vi 129, vin 161, x 207, 212, 
xii 257, 258, 263, 264, xin 
272, 278, 279 

Parallelogram offerees, ix 1 80 n 

Parameters, variation of, xi.233 n 
See also Variation of elements 

JlapaTT^y^ara, n 20 

Partial eclipses, n 43 

Pendulum, pendulum clock, v. 
98, vi 114, vm 157, 158, 
161 , ix 180, 187, x 199, 217, 
221, 223, xi. 231 See also 
Gravity, variation of 

Pendulum Clock (of Huyg-ens), 
vm. 158, ix 171 

Penumbra (of a sun-spot), vi. 
124 , xn 268 

Perigee, n 39, 40, 48; iv. 85 
See also Apse, apse-line 

Perihelion, iv 85 , xi 231 See 
also Apse, apse-line 

Periodic inequalities See In- 
equalities, periodic 

Perturbations, vm 156, ix 183, 
184 , x. 200, 204, 224, 227 , XI 
passim, xni 282, 293, 294, 297 

Phases of the moon See Moon, 
phases of 

Phenomena (of Euclid), 11 33 

Phobos, xiu 295 

Photography, xni. 274, 279-281, 
294, 298, 299, 301, 306 

Photometry, xm, 316 See also 
Stars, brightness of 

Photosphere, xii, 268 , xni 303 

Physical double stars, xii 264 
See also Stars, double and mul- 

Planetary tables See Tables, 

Planetary theory, u 51, 52, 54, 
in 68 , iv. 86-90 , xi. 228, 230, 
231, 233, 235, 236, 242-247, 

248, xni 286, 288-290, 293. 
See also Planets, motion of 
Planets, i 13, 14, 15, 1 6 , n 23- 
27, 30, 3 3 > 51, "i 68, iv 81, 

V 10^, IOS, IIO, 112, VI 119, 

121, vii. 136, 144, vm 154, 

155, X 200, XI 228, 250, XII, 

253, 255, 257, 267, 271, xm 
272, 275, 276, 281, 282, 294- 
296, 297, 318, 320 See also 
the followiDg headings, and the 
several planets Mercury, Venus, 

Planets, discoveries of, xii 253, 
2 54 255, 267, xm 289, 294, 
295, 318 

Planets, distances of, i. 1 5 , n 30, 
51 , iv 81, 86, 87, vi 117, 
vn 136, 144; ix 169, 172, 173 

Planets, inferior, i 15 , iv 87, 88 
See also Mercury, Venus 

Planets, masses of, ix. 185 , xi. 
245, 248 , xm 294 See also 
under the several planets 

Planets, mmoi See Minor planets 

Planets, motion of, i 13, 14, 15 , 
ii 23-25, 26, 27, 30, 41, 45, 47, 
51, 52 , ni 62, 68 , iv. 81, 86- 
90, 92, v 100, 104, 105, 112, 
vi 119, 121, 129, vn 139-142, 
144, 145, 150, 151, vni 152, 

156, ix. 169, 170, 172-177, 181, 
183, 194, x 199, 204, xi 228, 
229, 245, 250, xm 275, 276, 
282, 294 See also Planetary 

Planets, rotation of, vm 160 , ix. 

187, xi 228, 250, xn. 267, 

xm 297 
Planets, satellites of See 

Planets, stationary points of, i. 

14 , n 5 1 , iv 88 
Planets, superior, 1. 15 , iv 87, 88 

See also Mars, Jupiter, etc, 
Pleiades, vi. 120 , xn 260 
Poles (of a great circle), n. 


General Index 
{Roman figures refer to the chapters, Atabic to the articles ] 


Poles (of the celestial sphere), i. 
8, 9, 10 , ii 33, 35 , lv 78 , vi. 
129, x 207, 214, xni 285 
Poles (of the earth), iv 82 , ix 

187, x 220,221, xm 285 
Pole-star, i. 8, 9 
Pollux, xn 266 
Pons-B rooks comet, xm 291 
Postulates (of Ptolemy), n 47 
Postulates (of Coppermcus), iv 


Praesepe, xn. 260 
Precession (of the equinoxes), 
n 42, 50 , ni 58, 59, 62, 68 , 
Iv - 73,83,84, 85, v, 104, 112, 
vi. 129; ix 188, 192, x 213- 
215, 218, 221, xi. 228, 232, 
248, xm 277, 280 
Pnma Narratio (of Rheticus), 

iv. 74, v 94 
Pnmum Mobile, in 68 
Prmcipia (of Descartes), vm 163 
Principia (of Newton), iv 75 , vm 
152, ix 164, 177-192, 195; x 
*96, 199, 200, 213, xi. 229, 234, 
235, 240 
Principles of Philosophy (of 

Descartes), vm, 163 
Probability Theone Analytiqw 

des (of Laplace), xi 238 
Problem of three bodies Sec 

Three bodies, problem of 
Prodromes Cometicus (of Hevel), 

vni 153 

Prominences, xm 301, 302, 303 
Proper motion (of stars), x 203, 
225 , xn 257, 265 , xm 278, 280 
Piosneusis, n 48, in 60, iv 85 
Prussian Tables, v 94, 96, 97, 

99, vn. 139 
Pythagoreans, n 24 , iv 75 

Quadrant, v 99 , x 218, 225 n 
Quadrature, ii 48, in 60, v in 
Quadnvium, in 65 

Recherches sur differ ens points (of 
D'Alembert), xi. 233, 235 

Recherches sur la precession (of 

D'Alembert), xi 215 
Reduction of observations, x. 

198, 218 , xm. 277 
Reflecting telescopes, ix 168 

xn 251-255 
Refracting telescopes, ix 168 

See also Telescopes 
Refraction, 11. 46 , in 68 , v gV 

110, vn 138; vm 159, 160; 

x 217, 218, 223 , xm. 277 
Relative motion, principle of, 

iv 77, IX iS6n 
Renaissance, iv 70 
Results of Astronomical Observa- 
tions (of John Herschel), xm. 

308 ' 

Retrograde motion, i 14 
Reversing stratum, xm. 303 
Reviews of the heavens, xn 2*2, 


Revival of Learning, iv 70 
Rhea, vm 160 
Rigel, in 64 
Right ascension, n 33, 39, x 

198, 218 , xm. 276 
Rills, xm 296 
Rings of Saturn See Saturn, 

rings of 
Rotation of the celestial sphere 

See Daily motion 
Rotation of the earth, sun, Mars, 

etc See Earth, Sun, Mais, 

etc, rotation of 
Royal Astronomical Society. See 

Astronomical Society, Royal 
Royal Society, ix 166, 174, 177, 

191, 192 ; x 201, 202, 206, 208 , 

xn 254, 256, 259, 263. xm 

292, 308 
Rudolphme Tables, v 94, vn 

148, 151 , vm 156 
Ruler, i 16 
Running down of the solar 

system, xm. 293, 319 

Saggtatore (of Galilei), vi 127 
Sappho, xm. 281 

General Index 

\Romanfigures refer to the chapters Arabic to the articles] 

Saros, i 17 , ii 43 

Satellites, vi 121, 127, 129, 133 ; 
vii. 145, 150, vin 154, 160, 
162, ix 170, 183-185, x 210, 

216 , XI 228, 248. XII 2*7 

255, 267, xm 272,' 283, 295 
2 96, 297, 318, 320. See also 
Jupiter, Saturn, etc, satellites 

Satellites, direction of revolution 
of'* 1 ' 2 * ' xin. 295, 318 
Satellites, rotation of, xi 250 

xii. 267 , xin 297 
Saturn, i. 14-16, 11 25, 51; IV 
oi, 87, v 99, vi 123 , vii. 
136 n, 142, 144; vin 154, ie6, 
*x 183, 185, 186, x 204, xi 
228, 231, 235, 236, 243-246, 
xn 253, 267 , xni 288, 297 
See also the following headings 
Saturn, mass of, ix 185 
Saturn, imgs of, vi 123, vin 
154, 160 , xi. 228. 248 ; xii. 267 
xm 295, 297 
Saturn, rotation of, xn 267 . xm 


Saturn, satellites of, vm 154 
160, ix 184, xi. 228; xn 253' 
255, 267 ; xm 295, 297, 307 
Scientific method, 11 54 ; vi 134 
ix 195 ; 

Seas (on the moon), vi 119 ; vm 

153, xm 296 
Seasons, i 3, n 35, 39, iv 82, 

xi 245 

Second (angle), i 7 
Secular acceleration of the moon's 
mean motion, x 201 : xi. 233 
2 34 ,240,2 4 2, xin 287 
Secular inequalities See In- 
equalities, secular 
Selenographia (of Hevel), vin. 

Selenotopographische Ft agnwnte 

(of Schroeter), xii 271 
Sequences, method of, xn 266 
Shadow of earth, moon. See 

" Shining-fluid " theory, xii. 260 

xm 310, 311 

bhootmg stars See Meteors 
Short-period comets, xm. 291 
Sidereal month, n 40 
Sidereal period, iv 86, 87 
Sidereal system, structure of, xn 

257, 258, 259-262, xni 317 
Sidereal year, 11 42 
Sidereus Nuncius (of Galilei), vi 

"Sights, 9 v no, vm 155 x. 


Signs of the zodiac, i 13 
Sine, n 47 n ; in. 59 , 68 n 
Sinus, xin 31 6 n 
Solar eclipse See Eclipse 
Solar system, stability of, xi 24 q 

xm 288, 293 ' 4i ' 

Solstices, i 11, u 36,39,42 
oolstitial points, i n 
Space-penetrating power, xn 


Spanish astronomy, in 6 1, 66 
Spectroscope, xin 299 See also 

Spectrum analysis 
Spectrum, spectrum analysis, ix 

iS' xm 273 > s "- 3 2i 303, 

el 04 ' 3 ^ 3 9 ' 311-314,3i 7 , 3/8 
Sphaera Mundi (of Sacrobosco) 

m. 67 " 

Sphere, attraction of, ix m 

182; xi 228 ^ 

Sphere, celestial See Celestial 

Sphere, doctrine of the See 

Spheres, celestial, crystal See 

Celestial spheres 
Spheres, music of the, n. 23 , vii 

Spherical form of the earth, moon 

See Earth, Moon, shape of 
Spherics, n 33, 34 
Spica, n. 42 

Spiral nebulae, xni 310 
Stability of the solar system, xi, 

245 ; xni 288, 293 

General Index 
[Roman fgui es refer to the chapters, Arabic to the articles ] 


Stadium, n 36, 45, 47 
btar-atlases, star-maps, i 12 n 
x. 198, 223 , xn 259, 266 , xm 
280, 294 

Star-catalogues, n 33, 42, 50 , 
in 62, 63 , iv 83 , v 98, 107, 
1 10, 112, vm 153, x 198,199 
205, 218, 223-225, xii. 257 
xm 277, 280, 316 
Star-clusters, vi 120, \ 223, 
xii 258, 259, 260, 261 , xm 
o 307, 38, 310, 3"i 318 
star-gauging, xn 258, xm 307 
Star-groups See Constellations 
Stars, i 1,5, 7-10, 12-15, 18 , n. 
42, 45-47, 5o, in 56, 57, 62, 
68 > lv 73, 78, So, 86, 89, 92 , 

V 90-100, 104, 105, 1 10, VI 120, 
121 129, VIII 155, 157, !6i , 

ix 1 86 n t x 198, 199, 203, 207- 
214, 218, 223, xi 228, xn 25-5, 
257-266, 267 , xm 272, 277- 
280, 283, 304, 306-318, 320 
See also the preceding and fol- 
lowing headings 

Stars, binary See Stars, double 
and multiple 

Stars, brightness of, n 42 , xn 
258, 266 , xm 278, 280, 316, 
317 See also Stars, variable 

Stars, circumpolar, i 9 , n 35 

Stars, colours of, xn. 263 , xni 

Stars, distances of, i 7 ; n 30, 32, 
45, 47; iv 80, 92, v 100, vi. 
117, 129, xi 228, xn. 257, 
258, 265, 266 , xm 278, 279, 
317 See also Parallax, stellar 

Stais, distribution of, xii. 257, 
258. See also Sidereal system, 
structure of 

Stars, double and multiple, xii 
256, 263, 264; xm. 306-308, 
309, 314, 320 * ' 

Stars, magnitudes of, n 42 , xii. 
266, xm 280, 316 See also 
Stars, brightness of 

Stars, motion of. See Stars, 

proper motion of, and Daily 

motion (of the celestial sphere) 

Stars, names of, i 12, 13 ; ni 64 

Stars, nebulous, x 223 , xn 260. 


Stars, new, n 42 ; v 100, 104 , 
vi 117, 129, vn 138, xii 266, 
xm 312 

Stars, number of, i. 7 n , xm. 280 
Stars, parallax of See Parallax, 


Stars, proper motion of, x 203, 
225, xn 257, 265, xm 278, 

Stars, rotation of, xn 266 
Stars, spectra of, xm 311-314, 

Stars, system of See Sideieal 

system, structuie of 
Stars, variable, xii 266, 269, 

xm 307, 312, 314, 315 
Stationaiy points, i. 14, n ci 

iv 88 

Stjerneborg, v 101 
Summer solstice, i 1 1 . See also 


Sun, i i, 4f 10, 13, 14, i6,n 21, 
23-26, 28-30, 32, 35, 36, 40, 
43. 45, 48, 51 ; ni 68, 69, iv 
73> 75. 77, 79~82, 85-90, 92. 
v 98, 103, 105, no, rn, vi 
119, 121, 123, 124, 126, 127, 
129, 132, vn 136, 139-141, 
144-1461 150, vm 153, 154, 
*5; ix 170, 172-17?, ii, 
183-186,188-190, 194 , x 198, 

200, 202, 205, 210, 213, 223, 

227, xi. 228,235,236,240,243, 
2 45, 250, xn 257, 265, 268. 269 , 
xm 272, 278, 283, 288, 292- 
294, 297, 298-303, 304, 305, 
307, 319, 320. See also the 
following headings 

Sun, angular or apparent size 
of, n. 32, 38, 39, 41, 43, 4 6 n , 
48; iv. 73, 90, v. 105 n 

un, apparent flattening of, n, 46 


General Index 

[Roman figures refer to the chapters, Arabic to the articles ] 

Sun, distance of, i 15 ; n. 24, 25 
30,32,38 ,41,43,45,48,49,51, 
iv. 81, 85, 86, 87, 90, 92, v 
ill , vii 144, 145 , viii 156, 
161, ix 185, 188, x 202, 205, 

m-m |XI 235; xm 278 ' 

Sun, eclipses of See Eclipses 

Sun, heat of, xn 268, 269 . xui. 
303, 307, 319 

Sun, mass of, ix 183, 184, 185, 
189, xi 228, xm 282 

Sun, motion of, i 3, 5, 8, 10, 11, 
r 3 iS-17, n 20, 21, 24-26, 35, 
in 59; iv 73, 77,79,85,86,87, 

92, V. 104, 105, III; vi 121, 

126, 127, 132, vra, 160, ix. 

186 ,x 223; xi 235, xn 265; 

xm 288 
Sun, parallax of, n 43, v 98, 

i' VI1 H5, viii. 161, x. 223, 

227, xm 281-284. See also 

Sun, distance of 
Sun, rotation of, vi 124, vn, 

150 , xi 250 , xm 297, 298, 302 
Sun, size of, n 32 , iv 85 , vn 

145 ,ix. 173, xin 319 
Sun, tables of See Tables, solar 
Sun-dials, n 34 
Sun-spots, vi 124, 125 , vm 153 

xn 268, 269 , xm 298, 300, 
302, 303 

Superior planets, i. 15 ; iv 87, 
88 See also Mars, Jupiter, etc. 
Svea, xra 294 
Synodic month, 11 40, 43 
Synodic period, iv 86, 87 
Synopsis of Cometary Astronomy 

(ofHalley), x 200 
Sy sterna Satut mum (of Huygens), 

vm 154 
Systeme du Monde (of Laplace), 

xi 238, 242^,250 
Systeme du Monde (of Ponte- 
coulant), xm 286 

Table Talk (of Luther), iv, 73 

Tables, astronomical, in 58, 60- 
63, 66, 68, iv 70, v 94, 96, 
97, 99, 1 10 , vn 139, 148 , vm 
156, 160, x 216, 217, xm 277 
See also the following headings 

Tables, lunar, 11 48 , m 59 , x 
204, 216, 217, 226 , xi 233, 234, 
241 , xm 286, 290 

Tables, planetary, m 63 , v 108, 
1 12, vii. 142, 143, x 204,216, 
xi 235, 247, xm 288, 289, 290 

Tables, solar, m 59, iv 85, 
v in , vm 153, x 224,225, 
226, xi 235, 247, xm 290 

Tables, Alfonsme, in 66, 68, 
v 94, 96, 99 

Tables, Hakemite, m 60, 62 

Tables, Ilkhanic, m 62 

Tables, Prussian, v 94, 96, 97, 
99 , vii 139 

Tables, Rudolphine, v 94 , vii 
148, 151, vm 156 

Tables, Toletan, in 61, 66 

Tables de laLum (of Damoiseau) 
xin 286 

Tabulae Regiomontanae (of Bes- 
sel), xin 277 

Tangent, m 59 n, 68 n 

Tartars, Tartar astronomy, m 63 

Tebbutt's comet, xm 305 

Telescope, m. 67, vi 118-124, 
134, vn. 138, vm. 152-155, 
ix 168, x 207, 213, 218, xn 
251, 252-258, 260, 262, 271, 
xm. 274, 300, 301, 306, 310, 

Theona Motus (of Gauss), xm 

Theona MotuumLunae(ofEu\er\ 

xi 233 ' 

Theone de la Lune (of Clairaut), 

xi 233 
Theone des Probabihtes (of 

Laplace), xi 238 
Theone . du Systeme du Monde 

(of Pont6coulant), xm 286 
Theory of the Moon (of Mayer), 

x 226 

General Index 


[Roman Jigmes refer to the chapters, Atabic to the articles ] 

Theory of the Universe (of Wright), 

xii 258 ' 

Thetis, vin 1 60 
Three bodies, problem of. xi 228, 

230-233, 235 
Tidal friction, xm 287, 292, 203 

320 * 

Tides, vi 130, vn 150, ix 189, 

xi 228-230,235,248, xm 287, 

292, 293, 297, 320 
Time, measurement of, i 4, 5, 16 

See also Calendar, Day, Hour, 

Month, Week, Year 
Titan, vin 154 
Titania, xii 255 
Toktan Tables, m 61, 66 
Torrid zones, n 35 
Total eclipse, n 43 , vn 145 f 

x 205, xni. 301 See also 


Transit instrument, x 218, 225 
Transit of Mercuiy, x 199 
Transit of Venus, vm 156, x 

202, 205, 224, 227, xm 281, 

282, 284 
Translations, in 56, 58, 60, 62, 

66, 68 

Transversals, v non 
Trepidation, in, 58, 62, 68, iv 

84, v 112 
Trigonometry, n 37 n, 47 n ; in 

59 n, 64 n } 68 n , iv 74 
Trivmm, m 65 
Tropical year, 11 42 
Tuttle's comet, xm. 291 
Twilight, in 69 
Twinkling of stars, n 30 
Two New Sciences (of Galilei), 

vi. 133, 134*2, vin 152 
Tychonic system, v. 106; vi 127 

Umbra (pi sun-spots), vi 124, 

xii. 268 
Uniform acceleration, vi 133 

See also Acceleration 
Uraniborg, v 101 
Uranometna Nova Oxomensts, 

xm 316 

Uranus, xn 253, 254, 255, 267 , 

xm 276, 288, 289, 297 
Uranus, rotation of, xm. 297 
Uranus, satellites of, xi 250 n , 

xu. 255, 267 , xm. 272, 295 

Variable stars See Stars, vari- 

Variation (of the moon), m 60 ; 
v 111 , vii 145 

Variation of elements or para- 
meters, xi 233 , 236, 245 

Variations, calculus of, xi. 237 n 

Vega, m 64 

Venus, i. 14-16, n. 25, 26, 45, 
47, 5i, ni 68, iv 75, 81, 86, 
87, v 98, 100, 103, vi 121, 

I2 3' Y?- '36 , 139, 142, 144, 
vm 154, ix. 181, 185, x. 223, 
227; xi. 235, 245, xii 267, 
271, xm 282, 297 See also 
the following headings 

Venus, mass of, xi 235, 248 

Venus, phases of, vi 123, 129 

Venus, rotation of, vm. 160, xn 
267 , xm 297 

Venus, transits of See Transits 
of Venus 

Vernal equinox, i n Sec also 

Vernier, m. 69 n 

Vertical, n 33, x 221, xm 
2 ^5 

Vesta, xm 294 

Victoria, xm 281 

Virtual velocities, xi 237 n 

Vortices, vm 163, ix. 178, 

Wave, wave-length (of light), 
xm 299, 300, 302 

Weather, prediction of, n. 20, 
vii 136 

Week, i. 16 

Weight, vi 116, 130, ix 180 

Weights and Measures, Com- 
mission on, xi, 237, 238 

440 General Index 

[Roman figures refer to the chapter, Arabic to the articles ] 

Whetstone of Witte (of Recorde), 
v 95 

Winter solstice, i n See also 

Year, I, 3, 4, 16, n 19-22, 42, 

47, in 66, v in 
Year, sidereal, n 42 
Year, tropical, n 42 

ZadkieVs Almanack, i 18 n 
Zenith, n 88,35,36,46, in 

X 221 

Zenith-sector, x 206 
Zodiac, i 13 , x 224 
Zodiac, signs of the, i 13 
Zodiacal constellations, i 13 
Zones of the earth, n 35, 47 


Prmted by Hazell, Watson, & Vmey, Ld , London and Aylesbury