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Full text of "Transits of Venus : a popular account of past and coming transits from the first observed by Horrocks A.D. 1639 to the transit of A.D. 2012. Also an account of the successes achieved in December 1874 and suggestions respecting the transit of 1882"

TEANSITS OF VENUS. 



LONDON : PRINTED JiV 

8PSTTISWOODB AND CO., XKW-STIIKET BQL'AKE 

AND rAULI-fSlKXT STREET 



PLATE I. 



PATHS OF VENUS 

(MOST NORTHERLY, CENTRAL, AND MOST SOUTHERLY) 

ACROSS THE SUN'S FACE 




R. A. Proctor atl. 

DURING THE TRANSITS OF 

A.D. 1631, 1639, 1761, 1769, 1874, 1882, 2004, AND 2012. 

(The regions where the ingress t, the egress «, or the whole transit could be seen, are 
shown in the eight coloured plates II.— IX.) 



fts- 



TRANSITS OF VENUS 

A POPULAR ACCOUNT 

OF 

PAST AND COMING TRANSITS 

FROM THE FIRST OBSERVED BY HORROCKS A.D. 1639 
TO THE TRANSIT OF A.D. 2012. 

RICHARD A. PROCTOR, 
in 

AUTHOR OF 'SATURN' ' THE SUN' 'THE MOON' 'OTHER WORLDS THAN OUItS' 

'THE UNIVERSE' ETC. 



A spot like which 
Astronomer in the Sun's lucent orb 
Through his glazed optic tube yet never saw — Mir.TON. 

Et vera incessu patuit Dea— Virgil. 



WITH 20 PLATES (12 COLOURED) AND 38 WOODCUTS, 

ALSO AN ACCOUNT OF THE SUCCESSES ACHIEVED IN DECEMBER 1874 

AND SUGGESTIONS RESPECTING THE TRANSIT OF 188?. 1*5 

FOURTH ED1TIOX 



LONDON : 
LONG M A N S, GREE N, A N I) C 0. 

1882. 

All iig!ilt ies(it!id. 







.3 
50 q 

?2 



5L' 



/3 



^3 



<?2- 



PBEFACE 

TO 

THE FOURTH EDITION 



The approach of the transit of Venus on December 6 
(partly visible in this country), and very favourably 
visible throughout its entire duration in the United 
States, renders necessary a new edition of this work. 
Very few changes have been made, as the second and 
third editions both followed the transit of 1874, and 
very little has been done in the interval which renders 
change necessary or desirable. The estimates now 
regarded as probably nearest the truth assign to the 
sun a distance of about 92,885,000 miles, correspond- 
ing to a mean equatorial long horizontal solar parallax 
of 8"80. It remains to be seen whether observations 
made on the approaching transit will modify this 
value* 

Richard A. Pkoctok 

London: June 1882. 



PEEFACE 



TO 



THE SECOND EDITION 



Though I have had good reason for believing that 
during the last few years there has been a remarkable 
increase of interest in scientific subjects, I do not 
know that any circumstance has tended more directly 
to convince me of this than the welcome extended to 
the present volume. It was justly remarked, in a 
review which appeared in the ' Quarterly Journal of 
Science,' that ' the work ' could hardly appeal to so 
large a section of the public as the ' Sun,' 'Moon,' &c, 
' for the subject is one that rather concerns the astro- 
nomer than the general public ; the objects at issue do 
not bear so distinctly upon every-day life ; and if a 
man has never seen Venus, and has no chance of ever 
seeing a transit, and does not easily comprehend how 
his race can be benefited by an exact determination 
of the sun's distance, he is not likely to trouble him- 



mu PREFACE TO THE SECOND EDITION. 

self about the subject at all.' The sale of 1500 copies 
of the present work in six months shows that many 
besides astronomers have taken interest in the efforts 
made during the recent transit to improve our know- 
ledge of the dimensions of the solar system. 

In the present edition I have given a general ac- 
count of the successes achieved last December. 1 
have also directed special attention to the advantages 
which may attend the use of the mid-transit method in 
] 882. See pp. 226-229. Fig. 44, p. 228, shows what 
regions would require to be occupied for this purpose. 
. A few passages in the former edition, correcting 
statements in which the controversy pending the late 
transit had been erroneously described, have been re- 
moved. I am glad to be able to say that since the 
present work appeared matters have been in general 
very fairly represented ; and it may well be hoped 
that any soreness still remaining in certain quarters 
vvill before long disappear altogether. 

Richard A. Proctor. 

Lokdon : May 1875. 



PKEFACE 



TO 



THE FIRST EDITION 



This work is intended to be partly historical and 
partly explanatory. So far as I know, no book has 
hitherto been published in England giving a com- 
plete account of the transits of 1639, 1761, and 1769, 
and of the various interesting circumstances connected 
Avith them. This want I have endeavoured here to 
meet, illustrating by maps the conditions under which 
those transits were observed. In the chapters re- 
lating: to the transits of 1761 and 1769, I sketch 
the causes of the partial failure of the observations 
then made, and give an account of the attempts made 
in recent years to reconcile those observations with 
the present estimate of the sun's distance. It will be 
observed that in dealing with the latest of these at- 
tempts I adopt the opinion of Continental and American 
astronomers, no longer regarding that attempt as in 
any sense removing the difficulties recognised before 
it was made. 



x riiEFACE TO THE FIRST EDITION. 

In Chapter IV. I have given a simple account of 
the principles on which the recurrence and observa- 
tion of transits depend. 

In the last chapter I carry on the history of the 
subject to the present time. It would be impossible, 
as Sir Edmund Beckett points out in the latest edition 
of his fine work ' Astronomy without Mathematics,' to 
present the subject adequately without a short account 
of the occurrences of 1869 and 1873 — now belonging 
to the history of transits, and instructive in many 
respects. It has seemed to me best to quote the 
original papers of 1868 and 1869, and then briefly 
sketch the progress of events which led to the arrange- 
ments finally adopted. 

A brief account is given at the end of Chapter V. 
of the conditions of the transits of 2004 and 2012. 

Richard A. Proctor. 

Londox : October 1874. 



For the use of Plates X., XL, XII., XIIL, and 
XIV., I have to thank the Editor of the ' Astro- 
nomical Register,' Rev. S. J. Jackson. These pic- 
tures originally appeared in the ' Illustrated London 
News,' for which journal I drew them. Electros 
were supplied to Mr. Jackson for use in the ' Re- 
gister,' and were lent to me by him. These plates 
have also appeared, slightly reduced by some process 
unknown to me, in the New York ' Daily Graphic' 



CONTENTS. 



CHAPTER FAUK 

I. Transits of the Seventeenth Century ... 1 

II. The Transit of 1761 • .27 

III. The Transit of 1769 . . . . . . . 67 

IV. Of Transits and their Conditions .... 93 
V. The Transits of 187-1 and 1882 156 



TABLE 

I. Transit of 1874. Places for observing early be- 
ginning 233 

II. Transit of 1874. Places for observing late be- 
ginning ib. 

III. Transit of 1874. Places for observing early ending 234 

IV. Transit of 1874. Places for observing late ending, ib. 



ILLUSTRATIONS. 



PLATES. 

PLATE 

I. Clnrds of transit in 1631, 1639, 1761, 1769, 1874. 1882, 

2004, and 2012 Frontispiece 

PAGE 

II. 1 Chart of the transit of 1631 -» To face each other f 12 
III. „ ,. 1639 / between -pages \ 13 



IV- „ „ 1761 1 f 46 

V. „ „ 1769 J I 47 



VI. ., „ 1874 \ f 92 

VII. „ ,, 1882 J I 93 



1761 


1 


1769 


J 


1874 


\ 


1882 


J 


2004 


} 


2012 



{ 

f 92 

{ 



VIII. ,. „ 2004 "1 ' 92 

IX. „ „ 2012 J 

X. Illustrating passage of Venus's shadow-cone over Earth 

in 1631, 1639, 1874, and 1882. . To face page 119 

XI. Transit-chords, &c, in 1874 and 1882 . . „ 12") 



» Hates II.— IX., and Plates XVII., XVIII., are to be arranged 
so that ivll the titles, TRANSIT OF 1631,' 1639, &c, lie towards 
tke l>ft when the book is opened between any pair of plates and held 
in the usual manner. Plate XX. is to read the other way ; that is, 
in is So hare its title, Plate XX., towards the right. 



xiv ILL USTRA TIONS. 



PLATE J"AGK 

XII. Sun-view of the Earth at beginning^ 

of transit of 1874 
XIII. Sun-view of the Earth at end of 

transit, of 1874 J 



„ To face each other f 1 26 
between pages 1 1 2 7 



XIV. Sun-view of the Earth at beginning 

. of transit of 1882 

XV. Sun-view of the Earth at end of 

transit of 1882 ) 



f 126 

1 127 



XVI. The Earth's passage through Venus's shadow-cone during 

the transit of 1874 .... To face page J4o 

XVII. The transit of 1874, beginning . -| To face each othir rl46 

XVIII. „ „ end . . / between -pages \ 147 

XIX. Paths of Venus's centre across Sun's disc, as seen from 

twelve stations, in 1874 . . . To face page lol 

XX. The same in miniature, shown on the Sun's disc . .152 



WOODCUTS IN THE TEXT. 

riG. VAGM 

1. Paths of Venus and the Earth 2 

2. Transit of 1639, as observed by Horroeks . . . . 21 

3. „ 1 761. as computed by Halley, and as observed . 37 

4. Illustrating conditions of same, as computed by Halley . . 38 

5. Projection of same on Halley's mistaken assumption . ai 

6. Three views of ' black drop ' , 57 



ILL VSTBA Tl OXS. x V 

FIG. PAGE 

61 



7. Venus distorted (Mayer) . 

8. The ' black drop ' as seen by Bayley 

■* 9. „ „ Hirst .... 

10. „ ,, Bevis 

] 1 and 12. Explaining formation of ' black drop ' 

13. Illustrating determination of Sun's distance by transit obser 

vations 

14. Illustrating effects of Earth's rotation on Venus in transit 

15. Conjunctions of the Earth and Venus .... 

16. Showing transit-regions of the Earth's orbit 

17. Illustrating occurrence of transits . .... 

18. Regression of conjunction-lines over transit-regions . 

19. Position of conjunction-lines in years 1870, 1871, 1873, 1874 

and 1876 

20. Venus's shadow-cone ....... 



G2 

63 
63 
64 

94 
98 
102 
106 
107 
ilO 

115 

118 



21, 22. 23, 24, 25, and 26 fall in Plate X. . . . facing 119 

27, 28, 29, 30, and 31. Illustrating passage of Venus's shadow-cone 

over Earth in 1761, 1769. 2004, and 2012 . . .124 

32. Showing Halleyan poles midway between Delislean poles . . 131 

33. Illustrating case unfavourable for Halley's method . .135 

34. „ internal and external shadow-cones . . . 140 

35. Internal and external shadow-cones 142 

36. Explaining Plate XVI 145 

37. Illustrating construction of Plate XIX 148 

38. Transit of 1832, ingress . 154 



xvi ILLVSTHATIONS. 

FIG. PAG.E 

39. Transit of 1882, egress 155 

40. Effect of Earth's rotation on progress of a transit . . . 158 

41. „ position of transit chords 159 

42. Illustrating the photographic and direct methods . . . 197 

43. ,. „ „ 198 

44. Illustrating the mid-transit method (transit of 1882) . . 228 



TEANSITS OF VENUS. 



CHAPTER I. 

TRANSITS OF THE SEVENTEENTH CENTURY. 

As soon as the Copernican theory of the solar system 
was established, astronomers perceived that the inferior 
planets, Mercury and Venus, must from time to time 
appear to cross the face of the sun. For although on 
most of these occasions when either planet passes 
between the sun and the earth, no transit was to be 
expected, the planet either passing above or below the 
face of the sun, yet it could not but happen that, in 
the course of many such conjunctions, the planet 
would make a passage at so small a distance north or 
south of the sun's centre as to appear for a time to be 
upon the sun's disc. To make this clear, without- 
entering into any nice details at this stage, let E e and 
V v (fig. 1 ) be the paths of the Earth and Venus, 

B 



2 TRANSITS OF VENUS. 

respectively, around the Sun, s. 1 Then if we suppose, 
the path e e to lie in the level of the paper, we must 
imagine one-half of the path v v — the half v' vv' — to 
lie above the level of the paper, the other half, v v v', 
lying below that level — not greatly above or below ; 
in fact, the short white lines near v and V show how 
much these parts of the path of Venus are to be 
supposed respectively above and below the level of 
the paper. fetill, it will be clear that when Venus is, 




Fig. 1 . — Showing the paths of Venus and the Earth, and indicating 
their inclination and the line of intersection of their planes. 

as at v, between the Sun and the Earth at s and e, she 
is not really on the line s e, but considerably below 
it ; and, as supposed to be seen from the Earth, she 
passes below the Sun. When in conjunction on the 
other side of v' v' , Venus passes above the Sun. Only 
when she is in conjunction nearly at v' (the Earth 
near e'), or nearly at v' (the Earth near e'), will she 

' e is supposed to be the place occupied by the earth at the time of 
the autumnal equinox. 



TRANSITS OF THE SEVENTEENTH CENTURY. 3 

appear to cross the face of the Sun. But in the course 
of many conjunctions there must be some which take 
place when the two planets are thus placed; that is, 
eithej near v' and e', or near v' and e'. Similar 
remarks apply to the case of Mercury. 

This was early perceived by the followers of 
Copernicus. The Ptolemaic system did not. indeed, 
preclude the possibility of such phenomena as transits ; 
but since the older astronomers regarded the planets as 
shining by their own inherent lustre, it was not to be 
expected that, even if a transit occurred, the planet 
would be discernible while crossing the sun's face. 
And as in reality the Ptolemaic system gave no means 
of inferring the relative distances of the several planets 
(including the sun 1 ), there could not even be any 
certain assurance that Venus or Mercury ever came 
between the earth and the sun. It was only by a 
mere assumption that the old astronomy assigned to 
the sun a sphere outside the spheres of Mercury and 
Venus. 

Still we find that, even so far back as the ninth 
century, Mercury was supposed to have been seen as 
a dark spot on the face of the sun. Doubtless one of 
those large sun-spots, which from time to time arc 
visible to the naked eye, had attracted attention, and 
was regarded by the ignorant as caused by the passage 
of one or other of the planets, Mercury or Venus, 
between the earth and the sun. Venus being probably 

1 The sun and moon were 'planets' in the old astronomy; and we 
still find traces of the usage in some modern expressions. 

ai 2 



4 TRANSITS OF VENUS. 

conspicuous at the time, either as a morning or evening 
star, the less familiar planet Mercury afforded a con- 
venient explanation of the dark spot. The account 
of the phenomenon accords well with the belief that a 
solar spot was seen, for we are told by the author of 
the *' Life of Charlemagne ' that Mercury Avas visible 
as a black spot upon the sun for eight consecutive 
days in April of the year 807. Kepler, who Avas 
perfectly Avell aAvare that Mercury moves too rapidly 
to remain even for as many hours on the sun's disc, 
endeavoured to sIioav that the expression originally 
used in the manuscript had not been octo dies, but 
octutles, a barbaric form of octies, for 'eight times.' 

It is iioav Avell knoAvn that Mercury is far too 
small to be seen by the naked eye Avhen crossing the 
sun's disc. And this fact disposes of the statement 
made by the famous physician Ebn Roschd (commonly 
called Averroes), in his Ptolemaic Paraphrase, to the 
effect that he saw the planet on the sun in the year 
1161, at a time Avhen Mercury really Avas in inferior 
conjunction. "We need not, hoAvever, question the 
veracity of the learned doctor, seeing that Kepler him- 
self supposed he had seen the planet upon the sun on 
one occasion. When, a few years later, the existence 
of sun-spots Avas detected by the telescope, Kepler 
admitted that in all probability he had seen such a 
spot, and not the planet Mercury. 

After Kepler had completed his Rudolphine tables 
ot the planetary motions he Avas able to arrive at 
tolerably accurate results as to the epochs of the 



TRANSITS OF THE SEVENTEENTH CENTURY. 5 

transits of Mercury and Venus over the solar disc. 
In fact, he announced, in 1627, that in the year 1631 
both Mercury and Venus would pass over the sun's 
face — Mercury on November 7, and Venus on De- 
cember 6 ; and that in 1761 Venus would again pass 
across the face of the sun. 

As the first occasion on which the transit of an 
inferior planet was ever witnessed, the transit of 
Mercury in 1631 has an interest resembling that which 
attaches to the first observation of a transit of Venus, 
eight years later. Therefore I think the reader will 
be interested to hear how Gassencli succeeded in ob- 
serving Mercury in transit. 

Gassendi made preparations for the observation of 
the transit at Paris. The manner in which he ob- 
served the phenomenon was somewhat remarkable. 
Through a small aperture in a shutter the solar light 
was admitted into a darkened room, and an image of 
the sun, some nine or ten inches in diameter, was 
formed upon a white screen. A carefully divided 
circle was traced upon this screen, and the whole was 
so arranged that the image of the sun could be made 
to coincide exactly with the circle. As Gassendi was 
anxious to ascertain the exact moment of the ingress 
of the planet upon the sun's disc, or — supposing he 
should fail in that respect — at least to determine the 
moment of egress, and as he had no trustworthy clock, 
he determined that the altitude of the sun should be 
carefully estimated several times during the progress 
of the transit, and particularly at the moment of 



6 TRANSITS OF VENUS. 

egress. It was necessary, therefore, that he should 
have an assistant, and, further, that his assistant should 
work in another room ; for from the room in which 
Gassendi was working the sun's light, as I have said, 
had been carefully excluded, save at the minute 
aperture in the window-shutter. Accordingly, Gassendi 
placed his assistant in a room above him, with a large 
quadrant for taking altitudes, instructing him to ob- 
serve the height of the sun as soon as he heard 
Gassendi stamp upon the floor of the room beneath. 
A clumsy arrangement, truly, when compared with 
the subtle devices of modern astronomers — with the 
aid which they derive from powerful telescopes, all but 
perfect clocks, and, where need arises for communi- 
cating with one another from distant stations, the 
instantaneous indications of telegraphy. Yet we can- 
not but admire the spirit in which Gassendi worked, 
the readiness with which, for want of more perfect 
instruments, he set himself to invent arrangements 
which suited his requirements, and the skill with 
which he availed himself of those imperfect adap- 
tations. 

And if we admire these qualities in Gassendi, still 
more must we admire the patience with which he 
waited for the commencement of the phenomenon. 
Modern astronomy is able to announce, within three 
or four minutes, the instant at which a transit will 
commence at any given spot upon the earth's surface. 
But Kepler's prediction respecting Mercury's motions 
did not lay claim to any accuracy of this sort. So 



TRANSITS OF THE SEVENTEENTH CENTUR1. 7 

uncertain did the epoch of the occurrence appear to 
be, that Gassendi began to watch for the transit 
two days before the date assigned by Kepler for its 
occurrence. 

The 5th of November proved unfavourable for 
observation, the day being rainy. The next day was 
also unsuitable, clouds having overspread the sky 
during nearly the whole day. The morning of the 7th, 
the day appointed by Kepler for the transit, was also 
cloudy. Thus Gassendi began his watch on that day 
with the uncomfortable feeling that during some part 
of the two preceding days the planet might already 
have passed over the sun's disc, — perhaps that the 
transit had been completed but a few minutes before 
the clouds broke up on the morning of the 7th. 

A little before eight the sun shone for a few 
minutes through the openings between the clouds, but 
there still remained enough mist to prevent Gassendi 
from being able to determine Avhether any spot existed 
upon the image of the sun in his observing-room. 
Nearly an hour passed before the sun was sufficiently 
clear of clouds to enable Gassendi to make any satis- 
factory observations. Towards nine, however, the 
sun became distinctly visible, and turning to the image 
on the screen, the astronomer perceived upon it a 
small black spot. He could not believe, however, that 
this was Mercury, as the received estimate of the 
planet's dimensions had led him to look for a spot 
nearly twice as large. As he was familiar with the 
nature of solar spots, and the rapid manner in which 



8 TRANSITS OF VENUS. 

they for n. lie concluded that one had made its appear- 
ance on the sun's surface since the preceding day. 
At nine o'clock he had another opportunity of observ- 
ing; the spot, and he carefully estimated its position, 
intending to make use of it as a point of reference for 
determining the path of the planet in transit, if 
he should I e fortunate enough to witness that phe- 
nomenon. Soon after, he had another view of the 
spot, and was surprised to find that it had moved away 
considerably from its former position. He felt assured 
that no ordinary solar spot could have moved so 
rapidly ; but still he could not persuade himself that 
he was looking at Mercury in transit, having so fully 
satisfied his mind respecting the dimensions which the 
planet would exhibit. Besides, the hour had not yet 
arrived at which Kepler had predicted that the transit 
would begin. 

Gassendi was still in doubt, and endeavouring to 
recall the circumstances of his former measurement, 
in order to convince himself that he had made no 
mistake, when the sun again made his appearance 
through the clouds, and it was apparent that the spot 
had moved yet farther from its original place. No 
room now remained for doubt. It was clear that the 
phenomenon which had been so long and so anxiously 
awaited by the astronomer Avas already in progress. 
He immediately stamped upon the floor to attract the 
notice of his assistant. But this person, whose name 
lias not reached us, was possessed of less patience than 
Gassendi. He probably felt much less interest in the 



TRANSITS OF THE SEVENTEENTH CENTURY. 9 

phenomenon ; possibly, he placed very little faith in 
the calculations of Kepler. Whatever was the reason, 
he had grown weary of watching, and had left his 
post/ Gassendi had to continue his observations 
alone, hoping that at least his assistant would re- 
turn before the planet had passed completely off the 
sun's face. Fortunately this happened ; the requisite 
observations were made for determining the time of 
egress ; and thus an important addition was made to 
our knowledge of the motions of the innermost planet 
of the solar system. 

Gassendi sent an amusing account of his observa- 
tions to Professor Shickhard, of the University of 
Tubingen. ' The crafty god,' he wrote, ' had sought 
to deceive astronomers by passing over the sun a little 
earlier than was exp?cted, and had drawn a veil of 
dark clouds over the earth in order to make his escape 
more effectual. But Apollo, acquainted with his 
knavish tricks from his infancy, would not allow him 
to pass altogether unnoticed. To be brief, I have 
been more fortunate than those hunters after Mercury 
who sought the cunning god in the sun. I found him 
out, and saw him where no one else had hitherto seen 
him.' He states that the planet, as seen projected on 
the image of the sun, did not appear altogether black, 
but was greyish, and somewhat ruddy round the 
margin. Doubtless these peculiarities were due to the 
method of observation employed by the astronomer. 
He estimated the apparent diameter of the spot at 
about one-ninetieth part of the sun's apparent diameter, 



IO TSAXSITS OF VENUS. 

an estimate considerably exceeding the true dimen- 
sions, but still more considerably beloAv the dimensions 
which astronomers had been disposed to assign to the 
planet. 

Gassendi, although he did not observe the com- 
mencement of the transit, Avas yet able to compute 
the time of its occurrence. He found that the transit 
had begun nearly five hours before the time assigned 
by Kepler. 1 

I have mentioned that Kepler had predicted that 
a transit of Venus would take place on December 6, 
1631. It need hardly be said that Gassendi, after his 

1 The second observed transit of Mercury took place on November 3, 
1651. The observations of Gassendi had enabled astronomers to esti- 
mate the epoch of the transit much more exactly than in the former 
instance. It resulted from their cakmlations that the phenomenon 
would not be visible in England, or indeed in Europe ; but would be 
well seen over a large part of Asia. Accordingly a young Englishman, 
Jeremiah Shakerley, went to Surat. in India, for the purpose of witness- 
ing the phenomenon. Such a journey undertaken for such a purpose in 
an age when sea-voyages were not only much more protracted, but also far 
more dangerous than in the present day, must be looked upon as a re- 
markable and commendable instance of devotion to scientific pursuits. 
It is pleasing to be able to record that the energy of the young English- 
man was rewarded by complete success. 

The third observed transit took place on May 3, 1661. It was 
observed by Hevelius at Dantzic, and at London by Huyghens, Street, 
and Mercator. Hevelius was surprised to find that the diameter of the 
planet was A'ery much smaller than he had been led to expect. He 
found on measurement that Gassendi's estimate was nearly twice as 
great as the true diameter of the planet. 

The fourth transit of Mercury was observed by Halley at St. Helena 
on November 7, 1677. He was the first astronomer who had ever 
observed the complete passage of the planet across the solar disc. 

Later transits of Mercury have no special historical interest, though 
observations of considerable importance were made during the transits 
of 1736, 1799, and 1868. 



TRANSITS OF THE SEVENTEENTH CENTURY. II 

success in observing the transit of Mercury, had 
good hopes of observing Venus to even greater ad- 
vantage. It is true that, according to Kepler's calcu- 
lation, the transit might be expected to begin only 
towards sunset, and it was therefore possible that the 
phenomenon would not be visible at all in Europe. 
But it was equally possible that any error in the 
calculation might lie in the other direction, and so 
the whole transit be favourably seen before sunset. 
Gassendi took the same measures for observing the 
transit as in the case of Mercury. He had proposed 
to observe the sun on December 4 and 5, but ' an 
impetuous storm of wind and rain rendered the face of 
the heavens invisible on both those days. On the 6th 
he continued to obtain occasional glimpses of the sun 
till a little past three o'clock in the afternoon, but no 
indication of the planet could be discerned upon the 
sun's disc as depicted upon the white circle. On the 
7th he saw the sun during the whole forenoon, but he 
looked in vain for any trace of the planet.' ' It is 
now well known,' proceeds Prof. Grant, from whose 
account I have just quoted, ' that the transit of the 
planet took place during the night between December 
6 and 7.' I do not know where any calculation of the 
circumstances of the transit can be found ; but an 
investigation of my own (sufficiently accurate for a 
past and unseen phenomenon) shows that in the South- 
eastern parts of Europe the egress might have been 
observed, occurring for those parts after sunrise on the 



12 TRANSITS OF VENUS. 

morning of December 7. 1 Plate II. shows the parts 
of the earth whence the transit might have been seen 
wholly or in part. The position of the line C d, which, 
according to my calculation, marks the boundary be- 
tween the places where day and night were in progress 
in the Northern hemisphere at egress, shows the parts 
of Europe whence the end of the transit might have 
been observed. 

Kepler had stated that after the transit of 1631 
there would be none till the year 1761. According 
to his calculations, Venus, when in her inferior con- 
junction on December 4, 1639, would pass very near 
to the sun's centre, but not quite near enough for a 
transit to occur, the planet passing below — that is, 
south of the sun. On the other hand, the tables of 
Lansberg, a Belgian astronomer, who followed the old 
system of computation, seemed to show that Venus 
would on this occasion transit the upper or northern 
part of the sun's face. Horrocks, a young and then 
unknown astronomer, having been led to examine the 
tables of Venus, found that though Kepler's were much 
more exact than Lansberg's, a transit would really 
occur, Venus passing below the centre of the sun, as 
Kepler had predicted, but not so low as to miss the 

1 M. Dubois, in his admirable work, ' Les Passages de Venus,' gives 
the following humorous explanation of Gassendi's failure : — ' Le Pas- 
sage de Venus, qui sans doute n'etait pas predit avec une precision 
suffisante, ne fut pas observe — cTabord parce que Gassendi, qui s'appretait 
a I'observation, en fut empecbJ par li pluie, mais surtout parce que le 
passage eut lieu pendant la nuit pour les observatuurs europeens.' [The 
it ilics are mine.] 



63 



ft. 







^ -V 



CO o» 




TRANSITS OF THE SEVENTEENTH CENTURY. I 3 

sun's disc altogether. The circumstances under which 
Horrocks made this discovery possess considerable 
interest, and I propose to devote some space to his 
account of them. 

While preparing himself for practical observation, 
Horrocks undertook (apparently from sheer love of 
science) the computation of Venus's motions from the 
tables of Lansberg. These tables were so highly 
valued by their author that he had spoken of them 
as superior to all others, quantum lenta solent inter 
viburna cupressi. But Horrocks recognised many im- 
perfections in them, and at length, as he says, ' broke 
off the useless computation, resolved for the future 
with his own eyes to observe the positions of the stars 
in the heavens ; but, lest so many hours should be 
entirely thrown away,' he made use of his results to 
predict the positions of the planets. ' While thus 
engaged, I received,' he proceeds, ' my first intimation 
of the remarkable conjunction of Venus and the sun ; 
and I regard it as a very fortunate occurrence, inasmuch 
as about the beginning of October it induced me, in 
expectation of so grand a spectacle, to observe with 
increased attention.' Xevei'theless, his heart was 
wroth within him against Lansberg, insomuch that he 
could not refrain from the extreme step of ' forgiving ' 
him in the following agreeable terms: 'I pardon, in 
the meantime, the miserable arrogance of the Belgian 
astronomer who has overloaded his useless tables with 
such unmerited praise, and cease to lament the mis- 
application of my own time, deeming it a sufficient 



14 TRANSITS OF VENUS. 

reward that I was thereby led to consider and to fore- 
see the appearance of Venus in the sun. But, on the 
other haud, may Lansberg forgive me' (this is charming) 
' that I hesitated to trust him in an observation of such 
importance, and from having been so often deceived by 
his pretensions to universal accuracy that I disregarded 
the general reception of his tables.' ' Lest a vain 
exultation should deceive me,' he proceeds, ' and to 
prevent the chance of disappointment, I not only de- 
termined diligently to watch the important spectacle 
myself, but exhorted others whom I knew to be fond 
of astronomy to follow my example; in order that the 
testimony of several persons, if it should so happen, 
might the more effectually promote the attainment of 
truth, and because by observing in different places our 
purpose would be less likely to be defeated by the 
accidental interposition of clouds, or any fortuitous 
impediment.' He was particulai'ly anxious, because 
Jupiter and Mercury seemed by their positions to 
threaten bad weather. ' For,' says he, ' in such ap- 
prehension I coincide with the opinion of the astrologers, 
because it is confirmed by experience ; but in other 
respects I cannot help despising their puerile vanities.' 
Among the astronomers to whom he wrote was his 
friend Crabtree. 1 

1 Both these ardent students of astronomy died young. Horrox 
(or Horrocks, as his name is now more commonly spelt) was but twenty 
years old when he calculated the transit, so that his feat may not in- 
aptly bo compared to that of Adams in calculating the place of the 
unknown planet Neptune within a few months of taking his degree. 
Each instance of an early nv.stery of difficult problems was fated to 



TRANSITS OF THE SEVENTEENTH CENTURY. I 5 

In what follows I quote the account given by 
Horrocks himself of the observations made upon this 
occasion, using the translation given by the Rev. Mr. 
Wharton. 1 

'Following the example of Gassendi,' says Horrocks, 
' I have drawn up an account of this extraordinary 
sight, trusting that it will not prove less pleasing to 
astronomers to contemplate Venus than Mercury, 
though she be wrapt in the close embraces of the sun : 

Vinclisque nova ratione paratis 
Admisisse Deos. 

Hail ! then, ye eyes that penetrate the inmost rpcesses 
of the heavens, and, gazing upon the bosom of the sun 
with your sight-assisting tube, have dared to point out 
the spots on that eternal luminary ! And thou, too, 
illustrious Gassendi above all others, hail ! thou who, 
first and only, didst depict Hermes' changeful orb in 
hidden congress with the sun. Well hast thou re- 
stored the fallen credit of our ancestors, and triumphed 
o'er the inconstant wanderer. Behold thyself, thrice 
celebrated man! associated with me, if I may venture 
so to speak, in a like good fortune. Contemplate, I 
repeat, this most extraordinary phenomenon, never in 



meet with neglect ; but Horrocks died before justice had been done him. 
Adams was quickly able to prove that his work was sound, notwith- 
standing the coolness with which it had been received by official 
astronomers. Horrocks died in 1641, in his twenty-second year. Crab- 
tree is supposed to have been killed at the battle of Naseby Field. 

1 The memoir Accompanying Mr. Whatton's translation will be 
found full of interest. The complete work is published by Macintosh, 
21 Paternoster Row. 



1 6 TRANSITS OF VENUS. 

our time to be seen again ! the planet Venus, drawn 
from her seclusion, modestly delineating on the sun, 
without disguise, her real magnitude, whilst her disc, 
at other times so lovely, is here obscured in melancholy 
gloom ; in short, constrained to reveal to us those 
important truths, which Mercury on a former occasion 
confided to thee. 

* How admirably are the destinies appointed ! 
How wisely have the decrees of Providence ordered 
the several purposes of their creation ! Thou, a 
profound divine, hast honoured the patron of wisdom 
and learning ; whilst I, whose youthful days are scarce 
complete, have chosen for my theme the queen of love, 
veiled by the shade of Phoebus' light. 

' Whilst I was meditating in what manner I should 
commence my observation of the planet Venus, so 
as effectually to realise my expectations, the recent 
and admirable invention of the telescope afforded me 
the greatest delight, on account of its singular ex- 
cellence and superior accuracy above all other instru- 
ments. For although the method which Kepler 
recommends in his treatise on Optics, of observing 
the diameter and eclipse of the sun through a plain 
aperture without the aid of glasses, is very ingenious, 
and in his opinion, on account of its freedom from 
refraction, preferable to the telescope; yet I was un- 
able to make use of it, even if I had wished to do so, 
inasmuch as it does not show the sun's image exactly, 
nor with sufficient distinctness, unless the distance 
from the aperture be very great, which <he smallness 



TRANSITS OF THE SEVENTEENTH CENTURY. 1 7 

of my apartment would not allow. Moreover, I was 
afraid to risk the chance of losing; the observation : 
a misfortune which happened to Schickard and 
Mostling, the astronomer to the Prince of Hesse, as 
Gassendi tells us in his " Mercury : " for they, expect- 
ing to find the diameter of Mercury greater than it 
was reasonable to anticipate, made use of so large an 
aperture that it was impossible to distinguish the 
planet at all, as Schickard himself has clearly proved ; 
and even though Venus gave promise of a larger 
diameter, and thereby in some measure lessened this 
apprehension, and I was able to adapt the aperture to 
my own convenience, yet in an observation that could 
never be repeated I preferred encountering groundless 
fears to the certainty of disappointment. Besides, I 
possessed a telescope of my own, of such power as to 
show even the smallest spots upon the sun, and to 
enable me to make the most accurate division of his 
disc; one which, in all my observations, I have found 
to represent objects with the greatest truth. 

' This kind of instrument, therefore, I consider 
ought always to be preferred in such experiments. 

' Having attentively examined Venus with my 
instrument, I described on a sheet of paper a circle 
whose diameter was nearly equal to six inches, 
the narrowness of the apartment not permitting me 
conveniently to use a larger size. This, however, 
admitted of a sufficiently accurate division ; nor could 
the arc of a quadrant be apportioned more exactly, 
even with a radius of fifty feet, which is as great a 

C 



J 8 TRANSITS OF VENUS. 

one as any astronomer has divided ; and it is in my 
opinion far more convenient than a larger, for although 
it represents the sun's image less, yet it depicts it more 
clearly and steadily. I divided the circumference of 
this circle into 360° in the usual manner, and its 
diameter into thirty equal parts, which gives about as 
many minutes as are equivalent to the sun's apparent 
diameter ; each of these thirty parts was again divided 
into four equal portions, making in all 120; and these, 
if necessary, may be more minutely subdivided ; the 
rest I left to ocular computation, whioh, in such small 
sections, is quite as certain as any mechanical division. 
Suppose, then, each of these thirty parts to be divided 
into 60", according to the practice of astronomers. 
When the time of the observation approached I re- 
tired to my apartment, and having closed the windows 
against the light, I directed my telescope, previously 
adjusted to a focus, through the aperture towards the 
sun and received his rays at right angles upon the 
paper already mentioned. The sun's image exactly 
filled the circle, and I watched carefully and unceasingly 
for any dark body that might enter upon the disc of 
light. 

' Although the corrected computation of Venus's 
motions which I had before prepared, and on the 
accuracy of which I implicitly relied, forbade me to 
expect anything before three o'clock in the afternoon 
of the 24th ; yet since, according to the calculations of 
most astronomers, the conjunction should take place 
sooner — by some even on the 23rd — I was unwilling to 



TRANSITS OF THE SEVENTEENTH CENT 'I'll Y. 1 9 

depend entirely on my own opinion, which was not suffi- 
ciently confirmed, lest by too much self-confidence I 
might endanger the observation. Anxiously intent, 
therefore, on the undertaking through the greater part 
of the 23rd, and the whole of the 24th, I omitted no 
available opportunity of observing her ingress. I 
watched carefully on the 24th from sunrise to nine 
o'clock, and from a little before ten until noon, and at 
one in the afternoon, — being called away in the in- 
tervals by business of the highest importance, which for 
these ornamental pursuits I could not with propriety 
neglect. 1 But during all this time I saw nothing in the 
sun except a small and common spot, consisting as it 
were of three points at a distance from the centre 
towards the left, which I noticed on the preceding and 
following days. This evidently had nothing to do 
with Venus. About fifteen minutes past three in the 
afternoon, when I was again at liberty to continue my 
labours, the clouds, as if bv Divine interposition, were 
entirely dispersed, and I was once more invited to the 



1 Presumably, as Mr. Whatton points out, 'the business of the 
highest importance' here referred to was the duty of conducting divine 
service, as November 24, Old Style, was a. Sunday. Mr. Whatton quotes 
the following passage from one of Thomas Hearne's pocket-books, dated 
February 8. 1723: 'Mr. Horrox, a young man, minister of Hople, a. 
very poor pittance, within four miles of Preston, in Lancashire, was a 
prodigy for his skill in astronomy, and had lie Lived, in all probability 
lie would have proved the greatest man in the whole world in his 
profession. He had a very strange unaccountable genius, and he is 
mentioned with great honour by Hevelius upon account of his discovery 
of Venus in the sun, upon a Sunday; but being called away to his 
devotions and duty at church, he could not make such observations as 
otherwise he would have don'. j .' 



20 TRANSITS OF VEX VS. 

grateful task of repeating my observations. I then 
beheld a most agreeable spectacle, the object of my 
sanguine wishes, a spot of unusual magnitude and 
of a perfectly circular shape, which had already fully 
entered upon the sun's disc on the left, so that the 
limbs of the sun and Venus precisely coincided, 
forming an angle of contact. Not doubting that this 
was really the shadow of the planet, I immediately 
applied myself sedulously to observe it. 

' In the first place, with respect to the inclination, 
the line of the diameter of the circle being perpen- 
dicular to the horizon, although its plane was somewhat 
inclined on account of the sun's altitude, I found that 
the shadow of Venus at the aforesaid hour — namely, 
fifteen minutes past three — had entered the sun's disc 
about 62° 30', certainly between 60° and 63°, from 
the top towards the right. This w r as the appearance 
in the dark apartment ; therefore out of doors beneath 
the open sky, according to the laws of optics, the 
contrary would be the case, and Venus would be below 
the centre of the sun, distant 62° 30' from the lower 
limb, — or the nadir, as the Arabians term it. The in- 
clination remained to all appearance the same until 
sunset, when the observation was concluded. 1 

' In the second place, the distance between the 
centres of Venus and the sun, I found by three ob- 
servations, to be as follows : — 



1 Horrocks observed Venus close by the place marked i, in Plate I. 
She had barely completed ingress when he first saw her, and when his 
observations closed she had advanced nearly two diameters of herself 



TRANSITS OF THE SEVENTEENTH CENTURY. 21 



The Hour 
At 3.15 by the clock 
„ 3.3o „ 

„ 3.45 

,, 3.50 the apparent sunset. 



Distance 
of the Centres 

. 14' 24" 

. 13' 30'' 

. 13' 0" 



The true setting being 3.45, and the apparent about 
five minutes later, the difference being caused by 
refraction. The clock, therefore, was sufficiently 
correct. 

' In the third place, I found, after careful and 
repeated observation, that the diameter of Venus, as 
her shadow was depicted on the paper, was larger, 
indeed, than the thirtieth part of the solar diameter, 
though not more so than the sixth, or at the utmost 

along the line of transit from the place just noted. His picture is too 
elaborate to be given in full, but the accompanying drawing (fig. 2 J 




Fig. 2.— The Transit of 1639, as observed by Hotrocks. 

serves sufficiently to show what lie observed — v being the position of 
Venus when first observed, v' the position she had reached when the 
sun was about to set. 



22 TEANSITS OF VENUS. 

the fifth of such a part. Therefore, let the diameter 
of the sun be to the diameter of Venus as 30' to 1' \'2" . 
Certainly her diameter never equalled 1' 30", scarcely 
perhaps V 20" ', and this was evident as well when the 
planet was near the sun's limbs as when far distant 
from it. 

' This observation was made in an obscure village, 
where I have loner been in the habit of observing, 
about fifteen miles to the north of Liverpool, the 
latitude of which I believe to be 52° 20', although by 
the common maps it is stated to be 54° 12'; therefore 
the latitude of the village will be 53° 35', and the 
longitude of both 22° 30' from the Fortunate Islands, 
now railed the Canaries. This is 14° 15' to the west 
of Urasuburg. in Denmark, the longitude of which is 
stated by Brahe, a native of the place, to be 36° 45' 
from these islands. 

' This is all I could observe respecting this cele- 
brated conjunction during the short time the sun 
remained in the horizon: for although Venus continued 
on his disc for several hours, she was not visible to me 
for longer than half an hour, on account of his so 
quickly setting. Nevertheless, all the observations 
which could possibly be made in so short a time I 
was enabled by Divine Providence to complete so 
effectually that I could scarcely have wished for a 
more extended period. The inclination was the only 
point upon which I failed to attain the utmost pre- 
cision ; for, owing to the rapid motion of the sun, it 
was difficult to observe with certainty to a single 



TRANSITS OF THE SEVENTEENTH CENTURY. 23 

deo-ree; and I frankly confess that I neither did nor 
could ascertain it. But all the rest is sufficiently 
accurate, and as exact as I could desire.' 

Horrocks was not the only observer of the transit 
of 1639. 'I had written,' he says, 'to my most 
esteemed friend William Crab tree, a person who has 
few superiors in mathematical learning, inviting him 
to be present at this Uranian banquet, if the weather 
permitted ; and my letter, which arrived in good time, 
found him ready to oblige me. He therefore carefully 
prepared for the observation, in a manner similar to 
that which has been before mentioned. But the sky 
was very unfavourable, being obscured during the 
greater part of the day with thick clouds ; and as he 
was unable to obtain a view of the sun, he despaired 
of making an observation, and resolved to take no 
further trouble in the matter. But a little before 
sunset — namely, about thirty-five minutes past three 
— the sun bursting forth from behind the clouds, he 
at once began to observe, and was gratified by behold- 
ing the pleasing spectacle of Venus upon the sun's 
disc. Rapt in contemplation, he stood for some time 
motionless, scarcely trusting his own senses, through 
excess of joy ; for we astronomers have, as it were, a 
womanish disposition, and are overjoyed with trifles, 
and such small matters as scarcely make an impres- 
sion upon others; a susceptibility which those who 
will may deride with impunity, even in my own 
presence ; and if it gratify them, I too will join in the 
merriment. One thing I request : let no severe Cato 



24 



TRANSITS OF VENUS. 



be seriously offended with our follies ; for, to speak 
poetically, what young man on earth would not, like 
ourselves, fondly admire Venus in conjunction with 
the sun, pulchritudinem divitiis conjunctam ? 

' But to return, he from his ecstasy and I from 
my digression. In a little while the clouds again 
obscured the face of the sun, so that he could observe 
nothing more than that Venus was certainly on the 
disc at the time. What he actually saw in so short 
a space was as follows: In ihe apartment Venus 
occupied the right side of the sun, being higher than its 
centre, and therefore in the heavens lower, and on the 
left. She was distant at the aforesaid hour — namely, 
thirty-five minutes past three — a sufficiently appre- 
ciable space from the sun's left limb, but Crabtree's 
opportunity was so limited that he was not able to 
observe very minutely either the distance itself or the. 
inclination of the planet. As well as he could guess by 
his eye, and to the best of his recollection, he drew 
upon the paper the situation of Venus, which I found 
to differ little or nothing from my own observation ; 
nor indeed did he err more than Apelles himself 
might have done in so rapid a sketch. He found 
the diameter of Venus to be seven parts, that of the 
sun being 200, which, according to my calculations, 
gives about 1/ 3". 

' This observation was made near Manchester, 
called by Antoninus, Mancunium, or Manucium, the 
latitude of which Mr. Crabtree makes 52° 24' ; and 
the common tables 54° 15'; the longitude 23° 15'; or 



TRANSITS OF THE SEVENTEENTH CENTURY. 2$ 

three minutes of time to the east of Liverpool, from 
which it is distant twenty-four miles. 

' I wrote also of the expected transit to my younger 
brother, who then resided at Liverpool, hoping that 
he would exert himself on the occasion. This indeed 
he did, but it was in vain ; for on the 24th the sky 
was overcast, and he was unable to see anything, 
although he watched very carefully. He examined 
the sun again on the following day, which was some- 
what clearer, but with no better success, Venus having 
already completed her transit. 

' I hope to be excused for not informing other of 
my friends of the expected phenomenon ; but most of 
them care little for trifles of this kind, preferring rather 
their hawks and hounds, to say no worse ; and although 
England is not without votaries of astronomy, with 
some of whom I am acquainted, I was unable to con- 
vey to them the agreeable tidings, having myself had 
so little notice. If others, without being warned by 
me, have witnessed the transit, I shall not envy their 
good fortune but rather rejoice, and congratulate them 
on their diligence. Nor will I withhold my praise from 
anyone who may hereafter confirm my observations 
by their own, or correct them by anything more exact. 

' Venus was visible in the sun throughout nearly 
the whole of Italy, France, and Spain ; but in none 
of those countries during the entire continuance of the 
transit. 

'But America! 

fortunatos nimium, bona si sua norint. 



26 TRANSITS OF VENUS. 

Venus ! what riches dost thou squander on unworthy 
regions which attempt to repay such favours with gold, 
the paltry product of their mines. Let these bar- 
barians keep their precious metals to themselves, the 
incentives to evil which we are content to do without. 
These rude people would indeed ask from us too much 
should they deprive us of all those celestial riches, the 
use of which they are not able to comprehend. But 
let us cease this complaint, O Venus ! and attend to 
thee ere thou dost depart.' 

On which Horrocks bursts into strains of poetry, 
imploring Venus not to seek those barbarous regions 
for which, even as his eyes were gazing upon her, she 
Avas hastening. ' But ah ! ' he sighs, ' thou fliest, 

And torn from civil life, 
The savage grasp of wild untutored man 
Holds thee imprisoned in its rude eml>race. 
Thou fliest, and we shall never see thee more ; 
While heaven, unpitying, scarcely would permit 
The rich enjoyment of thy parting smile. 
Oh ! then farewell, thou beauteous queen ! thy sway 
May soften natures yet untamed, whose breasts, 
Bereft of native fury, then shall learn 
The milder virtues. We, with anxious mind, 
Follow thy latest footsteps here, and far 
As thought can carry us ; my labours now 
Bedeck the monument for future times 
Which thou at parting left us. Thy return 
Posterity shall witness ; years must roll 
Away, but then at length the splendid sight 
Again shall greet our distant children's eyes.' 



[' THE TRANSIT OF 1701. 2 J 



CHAPTER IT. 

THE TRANSIT OF 1761. 

From the way in which Horrocks showed how the 
apparent place of Venus on the sun's face must be 
affected by the observer's position, it is tolerably clear 
that he would have been led to perceive how obser- 
vations made from different places could be used to 
determine the sun's distance, had time permitted him 
to correspond with other astronomers. For at the 
beginning of Chapter VI. he says : ' I beheld Venus 
during the transit, not from the centre, but from the 
surface of the earth, therefore I observed her apparent 
and not her true situation. Her true situation, which 
chiefly concerns us, is only to be obtained by the 
correction of the parallaxes, into which subject I now 
proceed to inquire. The hypotheses of all astronomers 
make the parallax of Venus in so near an approach to 
the earth sufficiently apparent ; but this I shall leave 
to be further considered in a separate treatise.' He 
then shows how the sun's distance enters into the 
determination of the true from the apparent position. 
xVt the end of the work he speaks again of the pro- 
posed treatise. ' T had intended,' he says, ' to offer 
a more extended treatise on the sun's parallax ; but as 



28 TRANSITS OF VENUS. 

the subject appears foreign to our present purpose, 
and cannot be dismissed with a few incomplete ai'gu- 
ments, I prefer discussing it in a separate treatise — 
" De syderum dimensione " — which I have in hand. 
In this work I examine the opinions and views of 
others ; I fully explain the diagram of Hipparchus, 
by which the sun's parallax is usually demonstrated, 
and I subjoin sundry new speculations. I also show 
that the hypotheses of no astronomer (Ptolemy not 
excepted — nor even Lansberg, who boasts so loudly 
of his knowledge of this subject) answer to that 
diagram, but that Kepler alone properly understood it. 
I show, in fact, that the hypotheses of all astronomers 
make the sun's parallax either absolutely nothing or 
so small that it is quite imperceptible, whereas they 
themselves, not understanding what they are about, 
come to an entirely opposite conclusion, a paradox of 
which Lansberg affords an apt illustration. Lastly, 
I show the insufficiency and uselessness of the common 
mode of demonstration from eclipses. I give many 
other certain and easy methods of proving the distance 
and magnitude of the sun, and I do the same with 
regard to the moon and the rest of the planets, adducing 
several new observations.' 

There cannot be a doubt, I think, that had Hor- 
rocks lived to complete this treatise, the methods 
subsequently devised by Halley and Delisle would 
have been found included among the ' certain and 
easy methods of proving the sun's distance and mag- 
nitude.' They are so obvious, when once the connec- 



THE TRANSIT OF 1761. 29 

tion betAveen transits and the solar parallax has been 
noticed, that they could not possibly have escaped the 
keen insight of the young astronomer, especially as he 
had actually observed Venus in transit. 

Passing, however, from what might have happened, 
let us consider how, during the interval between 
Horrocks's transit and the next, the idea of utilising 
transits for the determination of the sun's distance 
presented itself to astronomers. 

Priority in this matter has been claimed for James 
Gregory ; but, as Sir Edmund Beckett points out in 
the last edition of his ' Astronomy without Mathe- 
matics,' on insufficient grounds. In a scholium to the 
87th problem of his Optica JPromuta, Gregory says 
that ' the problem has a very beautiful application, 
although perhaps laborious, in observations of Venus 
or Mercury when they obscure a small portion of the 
sun ; for by means of such observations the parallax 
of the sun may be investigated.' But the method 
described in the problem, the object of which is to 
determine the parallaxes of two planets by observations 
of their conjunctions, has no practical value. I can- 
not understand on what grounds Prof. Grant, in his 
' Physical Astronomy,' claims for Gregory the credit 
usually attributed to Halley. For if the mere mention 
of the connection between the phenomena of a transit 
and the solar parallax be the point insisted upon, 
Horrocks seems clearly to have anticipated Gregory ; 
if the method described by Gregory be insisted upon, 
then, since that method never has been and never 



30 TRANSITS OF VRAUS. 

could be applied successfully, Gregory cannot be 
regarded as having anticipated Halley, the inventor 
of a practicable method. The very fact that Mercury 
is associated with Venus, in the sentence quoted from 
Gregory's work, shows how little he had grasped the 
idea of Halley's problem, in the solution of which 
transits of Mercury are useless. It is not because of 
the intrinsic importance of the invention that I discuss 
the rival claims ; for I think that the approach of the 
transits of 1761 and 1769 would probably have forced 
the attention of astronomers to the very simple con- 
siderations on which the matter depends. But. as 
Halley had in all probability read the Optica Promota 
(Admiral Smyth thinks Halley had certainly done so 1 ), 
the much more important question whether Halley 
treated Gregory with fairness is really involved. As 
Gregory died in 1675, only four years before Halley 
mentioned the utility of observations of Venus in 
transit, it would seriously affect our estimate of Halley's 
character if we adopted Prof. Grant's conclusion. I 
think, however, there can be very little question, when 
Gregory's remarks have been carefully studied, that 
Halley must be acquitted of all unfairness. 

On November 7, 1677, Halley, stationed at St. 
Helena, witnessed a transit of Mercury. He noticed 
that the duration of the transit could be observed very 
exactly, and was thus led to believe that the apparent 

1 Nevertheless, this may lie doubted, as Halley was but twenty-one 
years old when the idea of utilising transits first occurred to him; and 
it. was only two years later that he announced the idea. 



THE TRANSIT OF 1761. 3 1 

position of the path of transit of Mercury or Venus 
could be very accurately determined. In 1679, in the 
Catalogus Stellarum Australhun, Ave find his first 
public mention of the idea. Later, he gave it closer 
attention, and at last, in 1716 (three years before he 
became Astronomer Royal), he contributed to the 
Proceedings of the Royal Society the following paper ' 
(I quote Ferguson's translation): — 

' There are many things exceedingly paradoxical, 
and that seem quite incredible to the illiterate, which 
yet, by means of mathematical principles, may be 
easily solved. Scarce any problem will appear more 
hard or difficult than that of determining the distance 
of the sun from the earth, very near the truth ; but 
even this, when we are made acquainted with some 
exact observations, taken at places fixed upon and 
chosen beforehand, will, without much labour, be 
effected. And this is what I am now desirous to lay 
before this illustrious Society (which I foretell will 
continue for ages), that I may explain beforehaud to 
young astronomers, who may perhaps live to observe 
these things, a method by which the immense distance 

1 'It must he admitted,' says Grant of this essay, 'that the ability 
with which Halley expounded the peculiar advantages attending the 
determination of the solar parallax by observations of the transits of 
Venus, the earnestness with which he recommended the practical ap- 
plication of the method, and the weight of his authority on questions 
relating to astronomical science, were mainly instrumental in inducing 
the different Governments of Europe to adopt those liberal proceedings 
for observing the transits of 17'il and 17(>D which have led to a more 
accurate knowledge of the dimensions of the solar system than could 
otherwise he hoped for. 



32 THAXSITS OF VENUS. 

of the sum may be truly obtained to within a five- 
hundredth part of what it really is. 

* It is well known that the distance of the sun 
from the earth is by different astronomers supposed 
different ; according to what was judged most probable 
from the best conjecture that each could form. 
Ptolemy and his followers, as also Copernicus and 
Tycho Brahe, thought it to be 1,200 semidiameters 
of the earth ; Kepler, 3,500, nearly ; Ricciolus doubles 
the distance mentioned by Kepler, and Hevelius only 
increases it by one-half. But the planets Venus and 
Mercury, having, by the assistance of the telescope, 
been seen in the disc of the sun, deprived of their 
borrowed brightness, it is at length found that the 
apparent diameters of the planets are much less than 
they were formerly supposed ; and that the semi- 
diameter of Venus, seen from the sun, subtends no 
more than a fourth part of a minute, or fifteen seconds, 
while the semidiameter of Mercury, at its mean dis- 
tance from the sun, is seen under an angle only of ten 
seconds ; that the semidiameter of Saturn, seen from 
the sun, appears under the same angle ; and that the 
semidiameter of Jupiter, the largest of all the planets, 
subtends an angle of no more than a third part of a 
minute in the sun. Whence, trying the proportions, 
some modern astronomers have thought that the semi- 
diameter of the earth, seen from the sun, would sub- 
tend a mean angle between that larger one subtended 
by Jupiter and that smaller one subtended by Saturn 
and Mercury ; and equal to that subtended by Venus 



THE TRANSIT OF 1761. 33 

— namely, fifteen seconds — and have thence concluded 
that the sun is distant from the earth almost 1,400 of 
the earth's semidiameters. But the same authors have, 
on another account, somewhat increased this distance ; 
for inasmuch as the moon's diameter is a little more 
than a fourth part of the diameter of the earth, if the 
sun's parallax should be supposed fifteen seconds, it 
would follow that the body of the moon is larger than 
that of Mercury ; that is, that a secondary planet 
would be greater than a primary, which would seem 
inconsistent Avith the uniformity of the mundane 
system. And, on the contrary, the same regularity 
and uniformity seems scarcely to admit that Venus, 
an inferior planet, that has no satellite, should be 
greater than our earth, which stands higher in the 
system, and has such a splendid attendant. There- 
fore, to observe a mean, let us suppose the semi- 
diameter of the earth seen from the sun, or, which is 
the same thing, the sun's horizontal parallax, to be 
twelve seconds and a half — according to which the 
moon will be less than Mercury, and the earth larger 
than Venus — and the sun's distance from the earth 
will come out nearly 16,500 of the earth's semi- 
diameters. This distance I assent to at present as the 
true one, till it shall become certain what it is by the 
experiment which I propose. Nor am I induced to 
alter my opinion by the authority of those (however 
weighty it may be) who are for placing the sun at an 
immense distance beyond the bounds here assigned, 
relying on observations made upon the vibrations of a 

D 



34 TRANSITS OF VENUS. 

pendulum, in order to determine those exceeding small 
angles ; but which, as it seems, are not sufficient to be 
depended upon ; at least, by this method of investigating 
the parallax, it will come out sometimes nothing, or 
even negative — that is, the distance would either 
become infinite, or greater than infinite, which is 
absurd. And indeed, to confess the truth, it is hardly 
possible for a man to distinguish, with any degree of 
certainty, seconds, or even ten seconds, with instru- 
ments, let them be ever so skilfully made. Therefore 
it is not at all to be wondered at that the excessive 
nicety of this matter has eluded the many and in- 
genious endeavours of such skilful operators. 

' About forty years ago, when I was in the island 
of St. Helena, observing the stars about the south pole, 
I had an opportunity of observing, with the greatest 
diligence, Mercury passing over the disc of the sun ; 
and (which succeeded better than I could have hoped 
for) I observed, with the grpatest degree of accuracy, 
by means of a telescope twenty-four feet long, the 
very moment when Mercury, entering upon the sun, 
seemed to touch its limb within, and also the moment 
when going off it struck the limb of the sun's disc, 
forming the an^le of interior contact; whence I found 
the interval of time, during which Mercury then ap- 
peared within the sun's disc, even without an error of 
one second of time. For the lucid line intercepted 
between the dark limb of the planet and the bright 
limb of the sun, although exceedingly fine, is seen by 
the eye, and the little dent made on the sun's limb, 



THE TRANSIT OF 1761. 35 

by Mercury's entering the disc, appears to vanish in a 
moment ; and also that made by Mercury leavino- the 
disc seems to begin in an instant. When I perceived 
this it immediately came into my mind that the sun's 
parallax might be accurately determined by such kinds 
of observations as these, provided Mercury were but 
nearer to the earth, and had a greater parallax from the 
sun ; but the difference of these parallaxes is so little 
as always to be less than the solar parallax which we 
seek, and therefore Mercury, though frequently to be 
seen on the sun, is not to be looked upon as fit for our 
purpose. 

' There remains, then, the transit of Venus over 
the sun's disc ; whose parallax, being almost as crreat 
as the solar parallax, will cause very sensible differ- 
ences between the times in which Venus will seem 
to be passing over the sun at different parts of the 
earth. And from these differences, if they be ob- 
served as they ought, the sun's parallax may be 
determined even to a small part of a second. Nor do 
we require any other instruments for this purpose 
than common telescopes and clocks, only good of their 
kind : and in the observers nothing more is needful 
than fidelity, diligence, and a moderate skill in as- 
tronomy. For there is no need that the latitude 
of the place should be scrupulously observed, nor 
that the hours themselves should be accurately deter- 
mined with respect to the meridian; it is sufficient 
that the clocks be regulated according to the motion 
of the heavens, if the times be well reckoned from 



u 2 



36 TRANSITS OF VENUS. 

the total ingress of Venus into the sun's disc to the 
beginning; of her egress from it ; that is, "when the dark 
globe of Venus first begins to touch the brig-lit limb 
of the sun within ; which moments I know, by my 
own experience, may be observed within a second of 
time. 

' But, on account of the very strict laws by which 
the motions of the planets are regulated, Venus is 
seldom seen within the sun's disc ; and during the 
course of 120 years it could not be seen once — namely, 
from the year 1639 (when this most pleasing sight 
happened to that excellent youth Horrocks, our 
countryman, and to him only since the Creation) to 
the year 1761, in which year, according to the theories 
which we have hitherto found agreeable to the celestial 

© 

motions, Venus will again pass over the sun on May 
26, x in the morning ; so that at London about five 
o'clock in the morning we may expect to see it near 
the middle of the sun's disc, and not above four minutes 
of a degree south of the sun's centre. 2 But the dura- 

1 June 6, according to new style. 

2 The true time of mid-transit was almost twenty-three minutes past 
five, and Venus, instead of being only 4 south of the sun's centre at 
mid-transit, passed more than 9^' below that point. The difference in 
the latter respect was much the more important. Halley was not un- 
aware of the possibility of error in his computation, since the error 
arose from his neglecting the shifting of the nodes of Venus, described 
farther on (p. 108) ; and he notes that possibly the nodes may shift. 

Any exact discussion of the phenomena which the transit would have 
presented if ilalley's computations had been correct would, of course, 
l>e idle ; but it may be as well roughly to indicate the actual difference 
between the transit as it occurred and as Halley computed it. 

In fig. 3, c is the centre of the sun's disc, is; i e is the pnth of 



THE TRANSIT OF 1761. 37 

tion of this transit will be almost eight hours — namely, 
from two o'clock in the morning till almost ten. Hence 

Venus, as computed by Halley ; i e is the path she actually traversed. 
The time occupied in traversing i e was about 6j hours, whereas the 




Fig. 3. — Illustrating the Transit of Venus in 1761, as it actually 
occurred, and as Halley computed it. 

time which would have been occupied in traversing i e amounts to close 
upon eight hours, being very little less than that occupied in a central 
transit. It is manifest, at once, that the chords of transit i e are much 
more nearly equal than the chords, i e, so that as far as mere length of 
transit chord is concerned it would be useless to set the observers far 
apart in a northern and southern direction. But what Halley hoped to 
do was this : — 

Let p, fig. 4, be the North pole of the earth, travelling in the direction 
indicated by the arrow, p being in sunlight, as the date is June 6. The 
equator is represented by e' v. c. Now, supjxi.se for a moment that an 
observer at e sees Venus in the direction e v (Venus herself being sup- 
posed to lie far beyond the picture on the right, and above the level of 
the paper, to correspond to the shape given to the terminator between 
light and darkness on the earth). Then, at this moment an observer 
at a sees Venus in direct ion a v, or apparently not so far advanced (sine, 
she comes between the earth and sun, moving in the same direction as 
the earth around the sun, and with a greater velocity). On the other 
hand, the observer at a' sees her in direction a' v', or apparently farther 



3§ TJiAXSITS OF J 'EX US. 

the ingress will not be visible in England ; but as the 
sun will at that time be in the sixteenth decree of 

advanced. Hence the effect of being carried from a to a' i.s fib throw 
Venus forward on her pith. But an observer at a, when transit began, 



Fig. 4. — Illustrating the Conditions of the Transit of 17(31, 
as computed 1 y Halley. 

would be carried by the earth's rotation, during the transit (lasting 
nearly eight hours) to the position a' ; to him, therefore, the dura- 
tion of the transit would be shortened by the earth's rotation. But 
next consider three observers in the latitude parallel a b a, near to the 
pole. The observer at h sees Venus in direction b v ; from a she is seen 
towards w, or thrown forwards; from a' she is seen towards w', or 
thrown backwards. The effect of being cariied from a to a is, then, to 
throw Venus back, or lengthen the duration of her transit. Now, if we 
set an observer so that at the beginning of the transit he is at «, he will 
be carried to the position a at the end of the transit, it' only we so select 
the latitude parallel a a' that the part in the darkened hemisphere cor- 
responds to rather less than eight hours' rotation; in other words, take a 
latitude where, on June 6, or 15 days before midsummer, the night las's 
less than eight hours. We find latitude 56° North suitable. This would 
give the beginning of the transit at sunset and the end at sunrise ; and 
the whole of the transit, between the contacts invisil le. But as the sun 
must not be exactly on the horizon at the critical moments, we must, 
take a place in somewhat higher latitude than 56° ; and of course, the 



THE TRANSIT OF 1761. 



39 



Gemini, having almost twenty-three degrees north 
declination, it will be seen without setting at all, 

longitude of a, as of a, would depend on the time at which transit 
began, since we must have the station which is at a at the beginning 
carried to the position E, at the middle. According to Halley's computa- 
tion the middle of the transit would occur at about 5 in the evening, or 
B must be in seven hours east longitude at mid-transit. This, then, is the 
longitude of the equatorial station ; and the longitude of the northern 
station is therefore to be in five hours west longitude. 

Plate IV. would have to be thus altered to illustrate the circum- 
stances of the transit as computed by Halley : — The two projections, 
instead of touching in Sumatra, should touch about a third of an hour 
farther east ; since c a corresponds to the length of transit, the points 
a and d should be brought nearly two hours in longitude nearer together ; 
and of course a' and d' should be shifted to correspond. The point 
i would move to a place near the new position of a', i' to a point near 
the new position of b, e near to the new position of d, and e' near the 
new position of c'. Thus, h, which is the middle of the arc e i, would 
come close to Sumatra, and h' would be near the Galapagos Islands. 
It would have been easy to find a number of stations near H in its new 
position ; but the region e on i, much increased by the shifting of a b 




Fig. 5. — Illustrating the changes to be made in Plate IV. in order that 
it may correspond to the transit of 1761, as computed by Halley. 

and C n, would be the best part, so far as approach to the new position 
of h' was concerned. It will he seen that, under the actual conditions 
of the transit, the region i >/t ». was cjuitj unsuited for the purpose which 



40 TRANSITS OF VEX US. 

in almost all parts of the north frigid zone ; and there- 
fore the inhabitants of the north coast of Norway, 
beyond the city of Nidrosia, which is called Drontheira, 
as far as the North Cape, will be able to observe Venus 
entering the sun's disc ; and perhaps the ingress of 
Venus upon the sun when rising will be seen by the 
Scotch, in the northern parts of the kingdom, and by 
the inhabitants of the Shetland Isles, commonly called 
Thule. But at the time when Venus will be nearest 
the sun's centre the sun will be vertical to the northern 
shores of the Bay of Bengal, or rather over the kingdom 
of Pegu ; and therefore in the adjacent regions, as the 
sun, when Venus enters his disc, will be almost four 
hours towards the east, and as many towards the west 
at the time of her egress, the apparent motion of Venus 
on the sun will be accelerated by almost double the 
horizontal parallax of Venus from the sun ; because 
Venus at that time is carried with a retrograde motion 
from east to west, while an eye placed upon the earth's 
surface is whirled the contrary way, from east to west. 
Supposing the sun's parallax (as we have said) to be 
12|", the parallax of Venus will be 43" ; from which, 
subtracting the parallax of the sun, there will remain 
30" at least for the horizontal parallax of Venus from 
the sun ; and therefore the motion of Venus will be 
increased 45" at least by that parallax, while she passes 
over the sun's disc in those elevations of the pole 

had led Halley to indicate it for occupation ; and the nearest approach 
to h' was within the space d' m! a', near m'. Fig. 5 illustrates the con- 
ditions of transit as computed by Halley. 



THE TRANSIT OF 1761. 41 

which are in places near the tropic, and yet more in 
the neighbourhood of the equator. Now, Venus at 
that time will move on the sun's disc very nearly at 
the rate of four minutes of a degree in an hour ; and 
therefore eleven minutes of time at least are to be 
allowed for 45" ', or three-fourths of a minute of a 
degree ; and by this space of time the duration of this 
eclipse caused by Venus will, on account of the parallax, 
be shortened. And from this shortening of the time 
only we might safely enough draw a conclusion con- 
cerning the parallax which we are in search of, pro- 
vided the diameter of the sun and the latitude of 
Venus were accurately known. But we cannot expect 
an exact computation in a matter of such subtility. • 

' We must endeavour, therefore, to obtain if possible 
another observation, to be taken in those places where 
Venus will be in the middle of the sun's disc at mid- 
night ; that is, in places under the opposite meridian 
to the former, or about six hours or ninety degrees 
west of London, and where Venus enters upon the 
sun a little before its setting, and goes off a little after 
its rising. And this will happen under the above- 
mentioned meridian, and where the elevation of the 
north pole is about fifty-six degrees ; that is, in a part 
of Hudson's Bay near a place calied Port Nelson. 
For, in this and the adjacent places, the parallax of 
Venus Avill increase the duration of the transit by at 
least six minutes of time ; because while the sun from 
its setting and rising seems to pass under the pole, 
those places on the earth's disc will be carried with a 



42 TRANSITS OF VENUS. 

motion from east to west contrary to the motion of the 
Ganges ; that is, with a motion conspiring with the 
motion of Venus; and therefore Venus will seem to 
move more slowly on the sun, and to be longer in 
passing over its disc. 

' If therefore it should happen that this transit should 
be properly observed by skilful persons at both these 
] daces, it is clear that its duration will be seventeen 
minutes longer as seen from Port Nelson, than as 
seen from the East Indies. Nor is it of much con- 
sequence (if the English shall at that time give any 
attention to this affair) whether the observation be 
made at Fort George, commonly called Madras, or 
at Bencoolen, on the western shore of the island of 
Sumatra, near the equator. But if the French should 
be disposed to take any pains herein, an observer may 
station himself conveniently enough at Pondicherry, 
on the west shore of the Bay of Bengal, where the 
altitude of the pole is about twelve degrees. As to 
the Dutch, their celebrated mart at Batavia will afford 
them a place of observation fit enough for the purpose, 
provided they also have but a disposition to assist in 
advancing, in this particular, the knowledge of the 
heavens. And indeed I could wish that many obser- 
vations of this famed phenomenon might be taken by 
different persons at separate places, both that we 
might arrive at a greater degree of certainty by their 
agreement, and also lest any single observer should 
be deprived by the intervention of clouds of a sight 
which I know not whether any man living in this or 



THE TRANSIT OF 1761. 43 

the next age will ever see again ; and on which depends 
the certain and adequate solution of a problem the 
most noble, and at any other time not to be attained 
to. 1 recommend it therefore again and again to those 
curious astronomers who (when I am dead) will have 
an opportunity of observing these things, that they 
would remember this my admonition, and diligently 
apply themselves with all their might in making this 
observation, and I earnestly wish them all imaginable 
success : in the first place, that they may not by the 
unseasonable obscurity of a cloudy sky be deprived of 
this most desirable sight, and then, that having ascer- 
tained with more exactness the magnitudes of the 
planetary orbits, it may redound to their immortal 
fame and glory. 

' AVe have now shown that by this method the 
sun's parallax may be investigated to within its 500th 
part, which doubtless will appear wonderful to some. 
But if an accurate observation be made in each of 
the places above marked out, we have already demon- 
strated that the durations of this eclipse made by 
Venus will differ from each other by 17 m. of time; 
that is, upon a supposition that the sun's parallax is 
J2V'. But if the difference shall be found by obser- 
vation to be greater or less, the sun's parallax will be 
greater or less nearly in the same proportion. And 
since 17 in. of time are answerabb to 12^" of solar 
parallax, for every second of parallax there will arise 
a difference of more than 80 s. of time ; whence if we 
have this difference true to two seconds it will be certain 



44 TRANSITS OF VENUS. 

what the sun's parallax is to within a 40th part of 1" ; 
therefore his distance will be determined to within its 
500th part at least, if the parallax be not found less than 
what we have supposed : for 40 times 12^ make 500. 

'And now I think that I have explained this 
matter fully, and even more than I needed to have 
done to those who understand astronomy ; and I would 
have them take notice that on this occasion I have 
had no regard to the latitude of Venus, both to avoid 
the inconvenience of a more intricate calculation, 
which would render the conclusion less evident, and 
also because the motion of the nodes of Venus is not 
yet discovered, nor can be determined but by such 
conjunctions of the planet with the sun as this is. 
For we conclude that Venus will pass four minutes 
bdlow the sun's centre, only in consequence of the 
supposition that the plane of Venus's orbit is im- 
movable in the sphere of the fixed stars, and that its 
nodes remain in the same places where they were 
found in the year 1639. But if Venus in the year 
1761 should move over the sun in a path more to the 
south, it will be manifest that her nodes have moved 
backwards among the fixed stars ; and if more to the 
north, that they have moved forwai-ds ; and that at 
the rate of 5h' of a degree in 100 Julian years, for 
every minute that Venus's path shall be more or less 
distant than the above-said 4' of the sun's centre. 
And the difference between the duration of these 
eclipses will be somewhat less than 17 in. of time, on 
account of Venus's south latitude ; but greater if by 



THE TRANSIT OF 17G1. 45 

the motion of the nodes forwards she should pass on 
the north of the sun's centre.' 

The rest of Halley's dissertation I omit, because 
it relates to the details of the transit as incorrectly 
computed by him, and therefore possesses no present 
interest. 

As I have said it was not until three years after 
his essay appeared that Halley became Astronomer 
Royal. It does not appear that during the remaining 
years of his life he made any farther contribution to 
the subject. He died on January 14, 1742, more 
than nineteen years before the transit occurred. 

As the time for the transit drew near astronomers 
began to examine carefully the motions of Venus, in 
order to ascertain how far the conditions on which 
Halley's computation had been based were really 
fulfilled. Passing over, however, a paper by Tre- 
buchet, pointing out inaccuracies in Halley's disser- 
tation, it was not until August 1760, or less than a 
year before the transit took place, that the conditions 
on which successful observation depended were pointed 
out by Delisle. He published a chart of the earth 
on an ecpjatorial projection, showing the hour at which 
the transit would begin or end. The chart corresponded, 
in fact, to Plate IV., meridional projections being sub- 
stituted for the equatorial projections there used. It 
will be understood, however, that Delisle did not claim 
for his chart the degree of accuracy aimed at in 
Plate IV. He showed that the stations selected by 
Halley were not suited to the actual conditions of the 



46 TRANSITS OF VENUS. 

transit, and that in fact the transit could not be well 
observed by the method of durations. He showed 
how, at suitably selected stations, whose longitude had 
been accurately determined, the single observation of 
a contact, whether at ingress or egress, would supply 
the means of determining the solar parallax. For 
the description of his method the reader is referred to 
Chapter IV. 

Ferguson, in England, seems to have independentlv 
arrived at the same conclusion, not long after ; at least 
his treatise on the subject suggests the impression that 
he had selected his own method of dealing with it, and 
had carried his analysis nearly to its completion when 
Delisle's paper and map reached him. He found that 
* instead of passing only four minutes of a degree below 
the sun's centre, Venus will pass almost ten minutes of 
a degree below it, on which account the line of the 
transit will be so much shortened as will make her 
passage over the sun's disc about an hour and twenty 
minutes less than if she passed only four minutes below 
the sun's centre at the middle of her transit ; and 
therefore her parallax from the sun will be so much 
diminished, both at the beginning and end of her transit, 
and at all places from which the whole of it will be 
seen, that the difference of its duration, as seen from 
them, and as supposed to be seen from the earth's 
centre, will not amount to eleven minutes of time. But 
this is not all; for although the transit will begin 
before the sun sets to Port Nelson, it will be quite 
over before he rises to that place next morning, on 



L« 



THE TRANSIT OF 1761. 47 

account of its ending so much sooner than as given by 
the tables to which Dr. Halley was obliged to trust. 
80 that we are quite deprived of the advantage that 
otherwise would have arisen from observations made at 
Port Nelson.' 

Ferguson gave a chart of the transit on the same 
plan as I have used in Plates II.-IX. The chart 
was taken directly from Delisle, however, as Fergu- 
son tells us, only * I have changed,' he says, ' his 
meridional projections into that of the equatorial ; by 
which I apprehend that the curved lines showing at 
what places the transit begins or ends with the rising 
or setting sun appear more natural to the eye and 
are more fully seen at once than in the map from 
which I copied ; for in that map the lines are inter- 
rupted and broken in the meridian that divides the hemi- 
sphere, and the places where they should join cannot be 
perceived so readily by those who are not well skilled 
in the nature of the stereographical projections.' It 
shows how clear an insight Ferguson had obtained into 
the conditions of the transit, that, commenting on his 
charts, in which the line, b a of Plate IV., passes down 
the eastern shore of the Red Sea, while a' b' crosses 
Madagascar, he says : ' I question much whether the 
transit will begin at sunrise to any place in Africa that 
is west of the Red Sea, and am pretty certain that the 
sun will not be risen to the northernmost part of Mada- 
gascar when the transit begins, so that the line,' corre- 
sponding to a b, a' b' of Plate IV., * seems to be a little 
too far west in the map at all places which are south 



48 TRANSITS OF VENUS. 

of Asia Minor ; but in Europe I think it is very 
well.' 

The actual circumstances of the transit of 1761 in 
different parts of the earth can be inferred with suffi- 
cient accuracy from what is shown in Plate IV. Here 
the arcs A I B and a' \' b' separate the dark and light 
hemispheres of the earth at the beginning of the transit, 
while the arcs C £ D and c' e' d' separate the dark and 
light hemispheres at the end of the transit. Thus the 
beginning of transit was visible at all places on the 
hemisphere formed by combining the sections aibd and 
a! i' b' d', and the end of the transit was visible at all 
places on the hemisphere formed by combining the 
sections ceda and c' e' d' a'. The whole of the 
transit was visible over the spaces D e i a and d' m' A.' ; 
but in the space i m e, though the beginning and end 
of the transit were seen, the progress of the transit 
was not wholly visible. No part of the transit was 
visible over the spaces B m C and b' i' e c' ; but in 
the space i' in' e' , though neither the beginning nor 
the end were visible, the progress of the transit was 
partially visible. At all points of the arcs aib and 
a' i' b' the ingress occurred with the sun on the horizon ; 
but whereas the sun was rising for the arcs A i and a' i' , 
he was setting for the arcs B i and b' i : at all points 
of the arcs CED and c' e' d' the egress occurred with 
the sun on the horizon ; but whereas the sun was 
rising for the arcs C e and c' e' , he was setting for the 
arcs d e and d' e'. At the points m and m' the sun 
was on the horizon both at ingress and at egress ; but 



THE TRANSIT OF 1761. 4? 

whereas the progress of the whole transit, except ingress 
and egress, took place during the night at m, it took 
place during the day at m . In all that has here been 
said, the passage of Venus's centre has been alone con- 
sidered. 

The point i' was that where ingress occurred 
earliest, the point I being that where ingress occurred 
latest. It was around these points, then, that observers 
of ingress by Delisle's method were to be placed, keep- 
ing, of course, to that side of the arcs a' b' and A v, 
on which the sun would be above the horizon at the 
time of ingress. We see that several islands were con- 
veniently placed near \' for showing accelerated ingress, 
though they were not very well known in those days. 
The eastern parts of Arabia and parts of India 
afforded convenient stations near I for observing re- 
tarded ingress. 

The point E was that where egress occurred earliest, 
e' being that where egress occurred latest. Karns- 
chatka, Japan, and Manchooria afforded convenient 
stations for observing accelerated egress, while the Cape 
of Good Hope was well placed fur observing retarded 
egress. 1 

As regarded the application of Halley's method — 
that is, the observation of duration where greatest and 
least — the transit was not a favourable one. h was the 



1 Eneke, in 1 822, found the following elements for the transit of 
1761. I quote them from the excellent little treatise, 'Lea Passages de 
Venus sur le disque Solaire,' by M. Dubois. Naval Examiner in Hydro- 
graphy for France, substituting Greenwich for Paris time and longitude, 

E 



50 



TSAXSITS OF VENUS. 



place where transit had the shortest duration, h' being 
the place where, if the transit had been visible, its 
duration would have been least. Stations near h 
could of course be occupied, as here the summer of 
Siberia was in progress. But we see that there was 
no station at all near to h' Avhence the whole transit 
could be seen. The point m' w r as geometrically the 
most advantageous, but there the sun was upon the 
horizon. The south-western extremity of Australia or 
the island of St. Paul were the only regions available, 
and they were almost as far from h' as from h. In 
point of fact, Halley's method failed totally on this 
occasion. It commonly fails at the earlier transit of a 
pair separated by eight years, as will be shown in the 
next chapter ; but it is worthy of notice that the 
circumstances of the transit of 1761 in this respect 
were very much like those of the coming transit of 
1882. Although the transit of 1882 will be the 



and correcting a misprint, by which in one place north and south lati- 
tudes are interchanged : — 





h. 


m. 


s. 






Ingress of Venus's centre 


. 14 


12 


48-5 


•J Gr 

f al 
1 sol 


eenwich 


Middle of the transit 


• 17 


23 


00 


>parent 


Egress of the centre 


. 20 


29 


13o 


ar time. 


Duration of the transit . 


. 6 


16 


250 






Least distance of centres . 





9 


342 








Latitude 




Longitude 


Pole of accelerated ingress 




. 20 


56 S 




o 

132 


28 W 


,, ,, retarded ,. . 


. 20 


56 N 




47 


32 E 


,, „ accelerated egress 


. 46 


47 N 




167 


59 E 


,, „ retarded 


. 46 


47 S 




12 


nv 


,, shortened durations 


. 52 


31 N 




92 


42 E 


„ „ lengthened 


. 62 


31 S 




87 


18 W 



THE TRAXSIT OF 1761. 5 I 

second transit of a pair, its geometrical superiority is 
counterbalanced by the inaccessibility of the antarctic 
as compared with the arctic regions. 

I do not know that any useful purpose could be 
served by inserting here an account of the various 
observations of the transit of 1761 made by the persons, 
176 in number, who took a more or less important share 
in the work at no less than 117 stations. Presently 
the peculiar phenomena which rendered the observation 
of internal contact uncertain will be described ; but 
the mere records of time observations have no special 
interest. A few examples may suffice to show this. 

We see from Plate IV. that the beginning of the 
transit was invisible in the western parts of Europe, 
but the latter half was visible there, though not under 
specially advantageous circumstances. We have the 
following particulars respecting the observations in 
London at Greenwich : ' Earlv in the morning, when 
every astronomer was preparing for observing the 
transit, it unluckily happened that, both at London and 
the Royal Observatory at Greenwich, the sky was so 
overcast with clouds as to render it doubtful whether 
any part of the transit would be seen, and it was 38 m. 
21 s. past 7 o'clock, apparent time, at Greenwich when 
the Rev. Mr. Bliss, our Astronomer Royal, first saAv 
Venus on the sun. . . From that time to the beginning 
of egress the Doctor made several observations, both of 
the difference of right ascension and declination of the 
centres of the sun and Venus, and at last found the 
beginning of egress, or instant of the internal contact 

E 2 



52 TBANSITS OF VENUS. 

of Venus with the sun's limb, to be at 8 hours 1 9 minutes 
seconds apparent time. . . . By the means of three 
good observations the diameter of Venus on the sun 
was 58 seconds of a decree.' ' Mr. Short made his 
observations at Savile House, in London, 30 seconds 
in time west of Greenwich, in presence of His Royal 
Highness the Duke of York, accompanied by Their 
lioyal Highnesses Prince William, Prince Henry, and 
Prince Frederick.' So the account runs. We are not 
told whether the Duke of York actually honoured 
Venus by directing His Royal gaze upon her during her 
transit, or whether Their Other Royal Highnesses made 
any observations ; but as Venus was under observation 
for about 3^ hours, we may suppose that these exalted 
persons did not lose the opportunity of witnessing a 
phenomenon so seldom seen. Venus, all unconscious of 
the honour, moved onwards to egress, contact occurring 
at 8 h. 18 m. 15| s. apparent Greenwich time, or 
8^ s. sooner than at Greenwich. At Stockholm the 
whole transit was observed by Wargentin, the whole 
duration (between the internal contacts) being 5 h. 
50 m. 45 s.j corresponding to a little over six hours 
for the passage of the centres. At Stockholm, as we 
see from Plate IV., the transit was shortened as com- 
pared with the mean duration. 

Chappe d'Auteroche was stationed at Tobolsk, in 
Siberia — an important station for the Halleyan method 
(see Plate IV.), if any stations had been available 
for observing lengthened durations. The transit, as 
observed by him, lasted 5 h. 4S m. 32^ s., or nearly 



THE TRANSIT OF 1761. 53 

m. less than at Stockholm. Chappe had some 
xmble in reaching Tobolsk in time for his observations. 
[e started at the end of November 1760, and reached 
t. Petersburg readily enough ; but the journey 
lence to Tobolsk was not completed without incon- 
enience and even serious dangers. He reached 
'obolsk on April 10, 1761, the voyage having lasted 
ve months. 

England sent out an expedition intended for Ben- 
aolen, in Sumatra, apparently because that station had 
een mentioned in Halley's dissertation ; for Sumatra, 
lmost midway between h and rri (Plate IV.), offered 
o advantages for the observation of durations, and was 
Itoo-ether too far removed both from I and e to be of 
he least service as a Delislean station. Fortunately the 
bip was attacked by a Spanish war-ship on the road, 
nd had to put in at the Cape, where very useful obser- 
ations of the retarded egress were made. Another 
inglish expedition was sent to St. Helena, a station 
:here retarded egress was observable, but by no 
leans advantageously. At Madras, Mr. Hirst, and 
t Calcutta, Mr. Magee (whom M. Dubois converts 
ito Magec) observed the duration of transit, obtain- 
ig respectively the periods 5 h. 51 m. 43 s., and 5 h. 
m. 36 s., values which differ much more from each 
ther than parallax will account for. As Ferguson well 
emarks of the whole series of observations : ' Whoever 
ompares the times of the internal contacts, as given 
y different observers, will find such difference among 
hem, even those which were taken from the same spot, 



54 TRANSITS OF VENUS. 

as will show that the instant of either contact could 
not be so accurately perceived by the observers as 
Dr. Halley thought it could, which probably arises 
from the difference of people's eyes and the different 
magnifying powers of those telescopes through Avhich 
the contacts were seen. If all the observers had made 
use of equal magnifying powers there can be no doubt 
that the times would have more nearly coincided, since 
it is plain that, supposing all their eyes to be equally 
quick and good, they whose telescopes magnified most 
could perceive the point of internal contact soonest 
and of the total exit latest.' 

Le Gentil, who had been appointed to observe at 
Pondicherry, was very unfortunate. The following 
account is taken from M. Dubois' admirable work 
already referred to : ' On account of the distance of 
the station where he was to observe the transit, Le 
Gentil set out from France on March 26, 1760. The 
observation he hoped to make at Pondicherry was 
curious and interesting, says J. D. Cassini; in fact, he 
would have seen the whole transit, and the middle 
would have occurred when the sun was nearly on the 
meridian at about ten degrees from the zenith. Le 
Gentil arrived at the Isle of France on July 10, 1760, 
that is to say, nearly a year before the expected 
transit ; but the war which arose at that epoch between 
France and England rendered it no longer possible 
for him to go to Pondicherry. He resolved to betake 
himself to Rodriguez, awaiting meanwhile the pro- 
gress of events. He was just setting off for this new 



THE TRANSIT OF 1701. 55 

station, where also De Pingre was to observe, when he 
learned that a French frigate was about to leave the 
Isle of France for the coast of Coromandel. Le Gentil 
resolved to avail himself of this opportunity to go to 
the place selected by the Academy of Sciences ; but 
he was not able to leave the Isle of France on board 

* 

this frigate till about the middle of March 1761. It 
was already very late. The frigate carrying the 
French astronomer experienced at first long-continued 
calms, which were enough to cause Le Gentil to 
despair, and which did not permit him to reach the 
coast of Malabar before May 24. To increase his rll- 
fortune, the commander of the frigate learned that the 
English were masters of Mahe and Pondicherry. The 
frio-ate had no other resource but to take flight without 
delay. This she did ; and, to the utter despair of Le 
Gentil, she retook her way towards the Isle of France. 
The 6th of June arrived! The frigate was in 87° 
East longitude (from Paris), and 5° 45' South latitude. 
The sky was clear, the sun splendid I The unfortunate 
Le Gentil, unwilling to be altogether idle, observed 
the transit on board the ship, taking all possible care. 
He noted the times of ingress and egress ; but with 
what degree of approximation were those times ob- 
tained, even admitting that those he noted coincided 
exactly with the instant of the contacts ? The voyage 
of the French Academician ended thus in failure. 
Le Gentil then experienced one of those mishaps which 
assume to the man of science all the proportions of a 
real misfortune— to have traversed so large a portion of 



56 TRANSITS OF VENUS. 

the globe, to have endured all the weariness, all the 
privations, all the perils of a long sea-voyage, and to 
effect nothing: ! This was enoug;h to have disg-usted 
anyone with scientific observation, or at least with 
1 1 alley's method. We shall presently see, however, 
when dealing with the transit of 1769, that Le Gentil, 
so far as that method was concerned, had not yet seen 
the last of his troubles.' 

De Pingre reached Rodriguez in May 1761 ; and 
although he had to observe in the open air, and could 
scarcely find a place where to keep his clock out of the 
wind, his observations were among the best of those 
effected during the transit of 1761. 

The results of the observations were far from 
satisfactory, the values of the solar parallax deduced 
by mathematicians ranging between 8" # 5 and 10 //# 5, 
corresponding to a distance of the sun ranging from 
96,162,840 miles to 77,846,110 miles. From a com- 
parison of a great number of observations made by 
Short the parallax 8"'5 was deduced for the day of 
the transit, corresponding to 8"*65 for the earth's 
mean parallax, or a distance of 94,498,420 miles. In 
1822, Encke, then sub-director at Seeberg, deduced 
from the observations made in 1761 a parallax lying 
between the extreme limits 8" -4298 13 and 8" '551237, 
corresponding to the distances 97,000,000 miles and 
95,600,000 miles. 

These discrepancies were no doubt due to two 
chief causes. In the first place, the observations Avere 
mostly Delislean, and in the last century means did 



THE TRANSIT OF 1761. 57 

not exist for the determination of the longitude with 
the degree of accuracy Avhich was required. Secondly, 
it was found that the phenomena attending the ingress 
and egress of Venus are not so simple as Halley had 
supposed, when he stated that the time of internal con- 
tacts can be determined within a single second of time. 
Halley had reckoned on the appearances presented 
during a transit such as he had observed at St. 
Helena, when the sun was high above the horizon, 
and the small disc of Mercury was little disturbed by 
atmospheric effects. But at most of the stations 
for effectively observing the transit of Venus in 1761, 
and at all those best suited for applying Delisle's 
method, the sun was not far from the horizon, and the 
outline of Venus was seriously affected by atmospheric 
undulations. Moreover, an optical phenomenon which 
had not attracted Halley's attention was presented 
during the transit of 1761, and caused the observations 
to be much less reliable than they would otherwise 
have been. The disc of Venus was found to assume 
near the time of internal contact a distorted form. In 
some cases she seemed to be attached to the edge of 

W F W 

Fig. 6.— Illustrating the ' Black Drop.' 

the sun by a dark ligament of greater or less breadth, 
as shown at 1, 2, and 3, fig. 6; in other cases she 



5§ TRANSITS OF VENUS. 

appeared shaped like a pear, while in others she was 
altogether distorted by the combined effect of atmo- 
spheric disturbances and the optical distortion (what- 
ever its real nature may be) which causes the black 
drop and pear-shape figures. 

This was the first occasion on which the peculiar 
appearances in question were noted ; but as the diffi- 
culty thus introduced affected the discussion of the 
observations made during both the transits of the last 
century, this will be a convenient place for describing 
what was seen in 1769 as well as in 1761. Professor 
Grant has collected together in his fine ' History of 
Physical Astronomy ' several of the most interesting 
observations of this kind, and from his Avork I quote 
the following cases: — 

Mr. Hirst, who observed the transit of 1761 at 
Madras, stated that ' at the total immersion the planet, 
instead of appearing truly circular, resembled more 
the form of a bergarnot pear, or, as Governor Pigott 
then expressed it, looked like a nine-pin ; yet the pre- 
ceding limb of Venus was extremelv well defined.' 
Witt respect to the end of the transit, he remarked 
' that the planet was as black as ink, and the body 
truly circular, just before the beginning of egress, yet 
it was no sooner in contact with the sun's preceding 
limb, than it assumed the same figure as before at the 
sun's subsequent (following) limb; the subsequent limb 
of Venus keeping well-defined and truly circular.' 

A similar appearance Avas observed by Salunde at 
Paris, by Bergman at Upsal, and also by several other 
Individuals. 



THE TRANSIT OF 1761. 59 

Dr. Maskelyne, who observed the transit of 1769 
at Greenwich, gives the following description of a 
phenomenon of a similar nature witnessed by him at 
the egress of the planet : — 

' The regularity of Venus's circular figure was 
disturbed towards the place where the internal contact 
should happen by the addition of a protuberance dark 
like Venus and projecting outwards, which occupied 
a space upon the sun's circumference which bore a con- 
siderable proportion to the diameter of Venus. Fifty- 
two seconds before the thread of light was formed, 
Venus's regular circumference (supposed to be con- 
tinued as it would have been without the protuberance) 
seemed to be in contact with the sun's circumference, 
supposed also completed. Accordingly, from this time 
Venus's regular circumference (supposed defined in the 
manner just described) appeared wholly within the 
sun's circumference, and it seemed, therefore, wonderful 
that the thread of light should be so long before it 
appeared, the protuberance appearing in its stead. 
At length when a considerable part of the sun's cir- 
cumference (equal to one-third or one-fourth of the 
diameter of Venus) remained still obscured by the 
protuberance, a fine stream of light flowed gently 
round it from each side, and completed the same in 
the space of three seconds of time. But the protube- 
rance, though diminished, was not taken away till about 
twenty seconds more ; when, after being gradually 
reduced, it disappeared, and Venus's circular figure 
was restored. 



60 TRANSITS OF VENUS. 

Dr. Bevis states in the account of his observations 
that ' the planet seemed quite entered upon her disc, 
her upper limb being tangential to that of the sun ; 
but instead of a thread of light, which he expected 
immediately to appear between them, he perceived 
Venus to be still conjoined to the sun's limb by a 
slender tail, nothing near so dark as her disc, and 
shaped like the neck of a Florence flask. The said 
tail vanished at once ; and for a few seconds after, the 
limb of Venus, to which it had been joined, appeared 
more prominent than her lower part, somewhat like 
the lesser end of an egg, but soon resumed its rotun- 
dity.' 

The Rev. Mr. Hirst thus describes the appearance 
presented during the transit : ' The same phenomena 
of a protuberance which I observed at Madras in 1761, 
at both internal contacts, I observed again at this last 
transit. At both times the protuberance of the upper 
edge of Venus diminished nearly to a point before the 
thread of light between the concave edge of the sun 
and the concave edge of the planet was perfected, 
when the protuberance broke off from the upper edge 
of the sun, but Venus did not assume its circular form 
till it had descended into the solar disc some distance.' 

Mr. Dunn, who observed the transit at Greenwich, 
remarks that ' he saw the planet held as it were to the 
sun's limb by a ligament formed of many black cones 
whose bases stood on the limb of Venus, their vertices 
pointing to the limb of the sun.' 

' Mr. Pigott states that Venus, before she separated 



TEE TRANSIT OF 1761. 6 1 

from the sun, was considerably stretched out towards 
his limb, which gave the planet nearly the form of a 
pear ; and even after the separation of the limbs Venus 
was twelve or nine seconds before she resumed her 
rotundity.' 

The following cases, with their accompanying illus- 
trations, serve at once to indicate the nature and 
suggest the explanation of the peculiar appearances 
presented by Venus when nearly at internal contact. 

Fio-. 7 represents the appearance presented by 
Venus as observed by Mayer at St. Petersburg, in 
1769. A reference to Plate V will show that at St. 




Fig. 7. — Appearance presented by Venus at Internal Contact, as 
observed by Mayer. 

Petersburg the sun was almost upon the horizon at 
the moment of ingress, and close to the horizon at the 
moment of egress. There can be no doubt that the 
distorted appearance of Venus is due to atmospheric 
disturbances, such as are always recognisable when 
the sun is observed low down. I may remark that 
fig. 7 corresponds precisely to what I observed when 
examining the artificial transit of Venus as arranged 
at Washington, on a morning when the atmosphere 
was unusually disturbed. The American astronomers 



62 TJRAXSITS OF VENUS. 

consider that the corresponding arrangements at Green- 
wich are not so good as their own, because the distance 
between the observer and the artificial ' Sun and Venus' 
is not great enough to permit the study of these at- 
mospheric effects. We see clearly enough from Mayer's 
observation that such effects, though they would not 
be nearly so great with the sun even moderately raised 
(say 10°) above the horizon, must always be taken 
into account. The edge of the sun even at a con- 
siderable height is always rippled by the effects of 
atmospheric undulations. So also necessarily must 
the outline of Venus be rippled, and it is the contact 
of two rippling outlines, not of two sharply defined 
discs, that the astronomer is called upon to observe. 

The next picture (fig. 8) is from a drawing by Bay ley 
at Nord Cap. In this case the sun was raised about 



Fig. 8. — Contact of Venus, as observed by Bayley at Nord Cap. 

10° from the horizon, but the blurred outline given to 
the sun indicates the existence of imperfect atmospheric 
conditions, and we may partly attribute to this cause 
the wideness of the connecting ligament when contact 
was actually established. 

Fig. 9 is from a drawing by Hirst, who observed 
the ingress at Greenwich ; while fig. 10 shows how 



THE TRANSIT OF 1761. 



63 



Venus appeared to Bevis, who observed at Kew under 
nearly the same conditions. 




Fig. 9. — The 'Black Drop,' as observed by Hirst. 

There has been much discussion as to the cause 
f the ' black drop,' and in some instances considerable 
energy has been evinced in the attempt to show that 








] .—The ' Black Drop,' as observed by Bevis. 

this or that cause is the true one. It appears probable 
that the phenomenon is occasioned by the combina- 
tion of several causes, and is widely variable in its 
extent. The general cause — by which I mean the 
resultant of the various causes in operation— is mani- 
festly an apparent extension of the sun's disc, and an 
apparent contraction of the disc of Venus. Suppose, 
for instance, that the arc 8 sV (fig. 11) represents 
I tart of the true outline of the sun, then this outline 
jippears shifted outside its true place, or to the position 
indicated by the boundary between light and shade in 
the figure ; and the apparent outline of Venus is shifted 



64 TRANSITS OF VENUS. 

from s'v v', its true position, to that shown by the out- 
line of the black disc. Supposing this shifting of the 
outline to be uniform, and to continue unchanged in 





Fig. 11. Fig. 12. 

Illustrating the Formation of the ' Black Drop.' 

extent, as Venus gradually passes on to the sun's face, 
it is clear that at the moment of true contact, when 
the real outlines touch, as shown in fig. 12, the ap- 
parent outlines will belong to two circles which are 
far from touching. But at the actual point of contact, 
where the widening of one outline and the contraction 
of the other cannot be supposed to act, there will still 
remain a fine black ligament. Under less perfect 
conditions this moment of true contact would not be 
attained, and instead of a fine ligament being seen 
just before Venus separated from the sun's edge, a 
wider ligament would be observed. 

Thus far I have only indicated the general cause. 
And it may be said that this general cause is demon- 
strated by the observed effects. But we must now 
consider how this general cause is itself brought about ; 
and herein lies the difficulty of the matter, whether 
regarded as a problem or considered with reference to 
the practical mastery of this occasion of error. 



THE TRANSIT OF 1761. 65 

First, we have the rippling I have spoken of. 
Taking any point on the outline of the sun's disc or of 
Venus's, that point is swayed backwards and forwards 
across its true position by the eifect of atmospheric 
undulation, the range of oscillation being greater 
or less according as the atmosphere is more or less 
perturbed, and as the sun is observed nearer to or 
farther from the horizon. A moment's consideration 
will show that the effect of such oscillations, operating 
all round both discs, must be to cause the sun's disc 
to cover (on the whole) a larger space than it should, 
while the disc of Venus covers a less space than it 
should. For there is a certain fringe of space all 
round both discs which is partially illuminated by 
these oscillatory movements, and this partial illumi- 
nation extends the sun's disc outwards and contracts 
that of Venus. Probably this cause has but a small 
share in producing the general effect, except when the 
sun is low down. 

Secondly, there is the optical effect caused by the 
fact that the image of a bright point is not itself a 
point. And here we have three causes in operation, 
which Ave may consider together. First, in the most 
perfect telescope the image of a point is what is called 
the ' circle of least confusion ' between the two linear 
or almost linear) foci. Secondly, diffraction affects 
the dimensions of the focal image of a point of lio-ht. 
And thirdly, if the telescope is defective, spherical 
aberration may operate so as seriously to affect the 
definition. All these causes combine to alter the 

F 



66 TRANSITS OF VENUS. 

image of each point of the outlines of the sun and 
Venus into a small disc of light instead of a point. 
The result necessarily is that the outlines extend be- 
yond the true boundary of light and dark ; that is, the 
disc of the sun is enlarged and that of Venus is con- 
tracted. 

Thirdly, there is a cause which might, perhaps, 
have been combined with the last— the qualities of the 
eye regarded as an optical instrument ; for the image 
of a point on the retina is not a point but a minute 
circle, even when the object is viewed directly. 

Fourthly, there is the effect called irradiation, by 
which the apparent size of a bright object is enlarged. 
This effect will be greater or less according as the 
contrast between the bright object and the dark back- 
ground on which it is projected is greater or less. 
Moreover, it appears that irradiation not only differs 
in amount with different observers, but varies even 
with the same observer at different times. Nay, its 
amount varies from moment to moment with the vary- 
ing mental effort made by the observer to ascertain, 
more or less exactly, the true outline of the observed 
object. 

We cannot wonder if the observations of the 
transit of 1761, affected as they were by peculiarities 
of appearance resulting from these various causes, for 
the operation of which observers were not on that 
occasion prepared, led to no trustworthy results. 



TEE TRANSIT OE 1769 67 



CHAPTER III. 

THE TRANSIT OF 1769. 

The general impression among astronomers, after the 
observations of 1761 had been discussed, was that too 
much reliance had been placed on Delisle's method. 
' Experience,' wrote J. D. Cassini, later, in his ' His- 
toire du Passage de 1769,' 'is our chief instructor; 
the fruit of its lessons indemnifies us for the value of 
the years they cost us. The principal end had been 
missed, in 1761, for want of observations in places 
where the durations differed sufficiently. It was 
essential not to experience a second time the same 
disadvantage.' 

Among the first statements published respecting 
the transit of 1769 was that by the ingenious Ferguson, 
who wrote as follows in 1762 : ' On the 3rd of June, 
in the year 1769, Venus will again pass over the sun's 
disc, in such a manner as to afford a much easier and 
better method of investigating the sun's parallax than 
her transit in the year 1761 has done. But no part 
of Britain will be proper for observing that transit, 1 

1 This was an error, due to Ferguson's reliance on Halley's tallies ; 
not. I need hardly s.iy, the tables by which HaHey had arrived at Lis 

F 2 



63 TJRAXSITS OF VENUS. 

so as to deduce anything with respect to the sun's 
parallax from it, because it will begin but a little 
before sunset, and will be quite over before two o'clock 
next morning. The apparent time of conjunction of 
the sun and Venus, according to Dr. Halley's tables, 
will be at thirteen minutes past ten o'clock at London, 
at which time the geocentric latitude of Venus will 
be full ten minutes of a degree north from the sun's 
centre ; and therefore, as seen from the northern 
parts of the earth, Venus will be considerably de- 
pressed by a parallax of latitude on the sun's disc ; 
on which account the visible duration of the transit 
will be lengthened ; and in the southern parts of the 
earth she will be elevated by a parallax of latitude on 
the sun, which will shorten the visible duration of the 
transit with respect to its duration as supposed to be 
seen from the earth's centre ; to both which affections 
of duration the parallaxes of longitude will also con- 
spire- So that every advantage which Dr. Halley 
expected from the late transit will be found in this, 
without the least difficulty or embarrassment. It is, 
therefore, to be hoped that neither cost nor labour 
will be spared in duly observing this transit, especially 
as there will not be such another opportunity again in 
less than 105 years afterwards.' 

Ferguson also showed accurately the places where 
advantage could be best taken of Halle) 's method : 
* The most proper places for observing the transit in 

incorrect ideas respecting the circumstances of the earlier tiv.nsit, but 
those which Hulley had formed subsequently. 



THE TRANSIT OF 1769. 69 

the year 1769 are in the northern parts of Lapland, 
and the Solomon Isles in the Great South Sea, at the 
former of which the visible duration between the two 
internal contacts will be at least twenty-two minutes 
create r than at the latter, even though the sun's 
parallax should not be quite 9". If it be 9" (which 
is the quantity I had assumed in a delineation of this 
transit which L gave in to the Royal Society before 1 
had heard what Mr. Short had made it from the 
observations of the late transit), the difference of the 
visible durations, as seen in Lapland and in the 
Solomon Isles, will be as expressed in that delineation; 
and if the sun's parallax be less than 9" (as I now 
have very good reason to believe it is) the difference 
of durations will be less accordingly.' 

Later, Hornsby in England, and De Lalande and 
Pingre in France, discussed very carefully the cir- 
cumstances of the transit of 1769. De Lalande, in 
1764, illustrated the conditions of the transit of 1769 
bv a projection of the earth planned like that which 
Delisle had made for the transit of 1761. The 
tables of Cassini formed the basis of the calculations 
made bv these astronomers; and as Cassini had had 
the advantage of later observations of Venus, his 
tables were necessarily more accurate than those 
which Halley had completed earlier in the century. 

The circumstances of the transit of 1769 in dif- 
ferent parts of the earth can be inferred from what is 
shown in Plate V. Here the arcs a i b and A.' i' b' 
separate the dark and light hemispheres of the earth 



?0 TRANSITS OF VENUS. 

at the beginning of the transit, while the arcs CED 
and c' e' d' separate the dark and light hemispheres 
at the end of the transit. Thus the beginning was 
visible at all places on the hemisphere formed by 
combining the sections A I e d and a' i' b' d' ; and the 
end of the transit was visible at all places on the 
hemisphere formed by combining the sections ceda 
and c' e' d' a'. The whole of the transit was visible 
over the spaces Dei a and d' m a' ; but within the 
space i m e, though the beginning and end of the 
transit were seen, the progress of the transit was not 
wholly visible. No part of the transit was visible over 
the spaces b m C and b' i e c' ; but within the space 
?" m' e' ', though neither the beginning nor the end were 
visible, the progress of the transit was partially visible. 
At all points of the arcs aib and a' i' b' the ingress 
occurred with the sun on the horizon ; but whereas 
the sun was rising for the arcs A i and a' i ' , he was 
setting for the arcs B i and B r i\ At all points of the 
arcs ced and c' e' d' the egress occurred with the 
sun on the horizon ; but whereas the sun was rising 
for the arcs C e and c' e' , he was setting for the arcs 
ID e and D r e , At the points m and m' the sun was on 
the horizon both at ingress and at egress ; but whereas 
the whole transit, except ingress and egress, took place 
during the night at m, it took place during the day at 
in. All that has here been said has related to the 
passage of Venus's centre. 

The point I was that where ingress occurred 



THE TRANSIT OF 17G9. 



71 



earliest, 1 the point 1' being that where ingress occurred 
latest. It was around these points that observers of 
ingress by Delisle's method were to be placed, on that 
side of the arcs a b and on a' b' where the sun would 
be above the horizon at the time of ingress. We see 
that Great Britain was admirably placed for observing 
accelerated ingress, Greenwich being almost as well 
placed as any station could possibly be, though having 
the sun rather low (and unfortunately it appeared 
from Halley's tables as though the sun would be still 
lower). At Greenwich sunset was approaching when 
transit began. 1' was in a little known part of the 
Southern Seas. 

The point e', where egress occurred earliest, was, 
like i', placed in a part of the Southern Seas about 
which little was at that time known, e, where egress 
occurred latest, was so placed that the whole of 



1 Encke, in 1822, found the following elements for the transit of 
1769. I quote these, like the elements for 1761, from M. Dubois' 

' Les Passages de Venus sur le disque Solaire ' : — 



Ingress of Venus's centre 
Middle of the transit 
Egress of the centre 
Duration of the transit 
Least distance of centres 



Pole of accelerated ingress 
„ „ retarded „ 

,, ,, accelerated egress . 
,, ,, retarded ,, . 

,, ,, shortened durations 
„ ,, lengthened „ 



h. 


HI. s. 




7 


26 54o 


I Greenwich 


10 


27 20-8 


\ apparent 


13 


27 513 


> solar time. 


6' 


568 







10 81 




Latitude 


Longitude 





i 


/ 


49 


33N 


7 23 E 


49 


33 S 


172 37 W 


22 


30 S 


122 46W 


22 


30 N 


57 HE 


38 


37 S 


143 2W 


38 


37 N 


39 58 E 



72 THAXSITS OF VEXUS. 

India and the region between the north-west of India 
and the Sea of Aral was suitable for observing this 
p'lase. 

But chief interest was attached, as I have said, to 
the application of Halley's method. The Halleyan 
poles were at H and h', these being respectively the 
points where, in a geometrical sense (that is, without 
taking into account the actual visibility of ingress 
or egress), the transit would be respectively most 
lengthened and most shortened, h, we see, lay in a 
region whence no part of the transit could be seen, 
and the point m was the nearest to h where both the 
beo-innino- and end would be visible, but with the sun 
upon the horizon. The space im e was that which 
presented the most promising conditions, except that 
the sun would be low within this space, both at ingress 
and at egress (passing below the horizon for a greater 
or less portion of the progress of the transit). Ward- 
huus, in Lapland, close to this region, was selected for 
the most northerly Hallevan stations : and as the 
polar regions could not be occupied, the stations next 
in order of value were necessarily those lving on the 
opposite side of the arctic circle, from Kamschatka, 
through Alaska, &c, round to Hudson's Bay. These, 
however, were too far away from h to be of great 
value as Halleyan stations, while their great distance 
from I and e prevented them from having any special 
value as Delislean stations. The southern Halleyan 
pole n' was in the same unknown quarter of the 
Southern Seas in which i' and e' are seen to lie. In 



THE TRANSIT OF 1769. 7$ 

fact, the whole region around h' was of extreme im- 
portance for the observation of the transit of 1769, 
since any station placed there would not only be 
excellent for Halley's method, but also for Delisle's, 
both as respects retarded ingress and accelerated 
egress. 

In passing, let it be noted how the superiority of 
the second transit of a pair (in general) shows itself 
by the positions of H and h' in Plates IV. and V. 
respectively. In Plate IV. we see that h and m lie 
on opposite sides of the north pole, h' and m' on 
opposite sides of the south pole ; whereas in Plate V. 
we see that h and m are on the same side of the north 
pole, h' and rn on the same side of the south pole. 
Now, necessarily one Halleyan pole lies in the region 
whence no part of the transit can be seen, and we see 
that in such a case as that illustrated by Plate V. the- 
point m indicates how near that pai-ticular Halleyan 
pole H can be approached without losing either the 
beginning or end of the transit ; Avhereas in the case 
illustrated by Plate IV., m' , the point of nearest 
available approach, lies very much farther away from 
the corresponding Halleyan pole h'. Still, it is to be 
noticed that, even in the case of a transit like that of 
1769 (Plate V.), the really effective use of Halley's 
method requires that a station should be reached near 
the space corresponding to e m L If this cannot be 
arranged, the stations next in order of value are those 
lying on the farther side of the arctic or antarctic 
circle (as the case may be), and such stations will 



74 TRANSITS OF VENUS, 

commonly not be much better than one near m' for 
the transit of 1761 (Plate IV.), and may be even far 
inferior to stations available in the case of such a 
first transit as that of 1874 (Plate VI.). This is, in 
fact, the reason why Halley's method fails totally in 
1882 (see Plate VII.), though this is the second 
transit of a pair. 

The actual operations for viewing the transit of 
1769 were carried out on a widely extended scale. 
Preparations were made for sending observers to the 
South Sea, California, Mexico, Lapland and Kams- 
chatka. The King of Denmark invited Father Hell, 
the eminent German astronomer, to observe the transit 
at Wardhuus, in Lapland, and thither Hell betook 
himself with Borgrewing, the Danish astronomer. 
They arrived in the autumn of 1768, and passed the 
winter in that desolate region. Chappe d'Auteroche 
was selected by the French Academy to observe the 
transit from the Solomon Isles, in the South Sea; but, 
says M. Dubois, ' the South Sea at that epoch was 
under the rule of Spain, and it was only possible to 
visit those seas in a Spanish vessel, and with the 
permission of the Court of Spain. The Spanish 
Government refused such permission, but gave Chappe 
leave to embark in the Spanish fleet then about to 
sail for Western America.' Chappe eventually ob- 
served at St. Joseph, in California. 

' England,' says M. Dubois, ' did not wait for 
permission from Spain to send an astronomer to ob- 
serve the transit from the South Sea.' The following 



THE TRANSIT OF 1769. 75 

account, taken from * Cook's Voyages,' describes the 
preparations made for the journey : — 

' It having been long before calculated that the 
planet Venus would pass over the sun's disc in 1769. 
a phenomenon of great importance to astronomy, and 
which had engaged the attention of men of science, it 
was judged that the most proper place for observing 
this phenomenon would be either at the Marquesas 
or at one of those islands to which Tasman had given 
the several appellations of Amsterdam, Rotterdam, and 
Middleburg, but which are now better known under 
the general name of the Friendly Islands. This 
being a matter of so much importance in the science 
of astronomy, the Royal Society, with that laudable 
zeal they have ever shown for its advancement, pre- 
sented a memorial to his Majesty at the beginning of 
the previous year, requesting among other things that 
a vessel might be fitted out, at the expense of the 
Government, to convey proper persons to observe this 
transit at one of the places already mentioned. The 
petition being readily complied with, and orders 
having been given by the Admiralty to provide a 
vessel for that purpose, on April 3, Mr. Stephens, 
the Secretary to the Board, informed the Society that 
everything was progressing according to their wishes. 

1 Mr. Dalrymple was originally fixed upon to 
superintend this expedition : a man eminent in science, 
a member of the Royal Society, and who had already 
greatly distinguished himself respecting the geography 
of the Southern Ocean. As this gentleman had been 



7& TRANSITS OF VENUS. 

regularly bred to the sea, he insisted (very properly 
too) on having a brevet commission, as captain of the 
vessel, before he would undertake the employment. 
Sir Edward Hawke (afterwards Lord Hawke, a naval 
officer, and not a civilian), who then presided at the 
Admiralty, violently opposed this measure ; and being 
pressed on the subject, declared that nothing would 
induce him to give his sanction to such a commission. 

6 Both parties were inflexible, and it was therefore 
thought expedient to look out for some other person 
to conduct the expedition. Accordingly, Mr. Stephens, 
having recommended Lieutenant Cook, and this re- 
commendation having been strengthened by the testi- 
mony of Sir Hugh Palliser, who was well acquainted 
with Cook's merit and abilities for the discharge of 
this office, he was appointed to this distinguished post 
by the Lords Commissioners, and promoted to the rank 
of Lieutenant of the Royal Navy on May 25, 1768. 
He was now, be it remembered, close upon forty years 
of age. . 

1 This appointment having taken place, Sir Hugh 
Palliser was commissioned to provide a vessel adapted 
for such a voyage. After examining a great number 
then lying in the Thames, in conjunction with Cook, 
of whose judgment he entertained the highest opinion, 
they at last fixed upon the 'Endeavour,' a barque of 370 
tons, which had been built for the coal-trade. 

' In the interim, Captain Wallis having returned 
from his voyage round the world, and having signified 
to the Royal Society that Port Royal Harbour, in 



THE TRANSIT OF 1769. 77 

King George's Island, now called Otaheite, would be 
the most convenient place for observing the transit, 
his opinion was adopted, and the observers were ordered 
to repair thither. 

* Mr. Charles Green, the coadjutor of Dr. Bradley, 
the Astronomer Royal, was nominated to assist Captain 
Cook in conducting the astronomical part of the un- 
dertaking ; and he w T as accompanied also by Joseph 
Banks, Esq. (afterwards Sir Joseph, the President of 
the Royal Society). This friend of science possessed 
at an early period of life an opulent fortune, and 
being zealous to apply it to the best ends, embarked 
on this tedious and hazardous enterprise, animated 
by the wish of improving himself and enlarging the 
bounds of knowledge. He took two draughtsmen with 
him, and had likewise a secretary and four servants in 
his retinue. 

' Dr. Solander, an ingenious and learned Swede, 
who had been appointed one of the librarians in the 
British Museum, and who was particularly skilled as 
a disciple of Linnaeus, and distinguished in his know- 
ledge of natural history, likewise joined the expedition. 
Possessed with the enthusiasm with which Linnaeus 
inspired his disciples, he braved danger in the prose- 
cution of his favourite studies ; and being a man of 
erudition and capability, he added no small eclat to the 
vovao;e in which he had embarked. 

' Though the principal intention of this expedition 
was to observe the transit of Venus, it was thought 
proper to comprehend other objects as well. Captain 



78 THAXSITS OF FJSNUS. 

Cook was therefore directed, after he had accomplished 
his main business, to proceed in making further dis- 
coveries in the South Seas, which now began to be 
explored with uncommon resolution.' 

The expedition sailed from Deptford on July 30, 
1768, and on August 13 anchored in Plymouth Sound, 
from which after a few days' stay they proceeded to 
sea. It was not until April 10 that they saw Otaheite. 
' On the 10th,' says the narrative, ' upon their looking 
out for the island to which they were destined they 
saw land ahead. The next morning it appeared very 
high and mountainous, and it was known to be Kins' 
George the Third's Island, so named by Captain Wallis, 
but by the natives called Otaheite.' 

In May they ' began to make preparations for 
observing the transit of Venus ; and from the hints 
which Captain Cook had received from the Royal 
Society, he sent out two parties to make observations 
from different spots, that in case they failed at Otaheite 
they might succeed elsewhere. They employed them- 
selves in preparing their instruments, and giving in- 
structions in the use of them. On Thursday, June 1 
(the next Saturday being the day of the transit), they 
sent the long-boat to Eimayo, having on board Mr. 
Gore, Mr. Monkhouse, and Mr. Sporing, a friend of 
Mr. Banks, each furnished with necessary instruments 
by Mr. Green. Mr. Banks and several of the Indians 
went out with this party. Others were despatched to 
find out a convenient spot at such a distance from 
their principal station as might suit their purpose. 



THE TRANSIT OF 1760. 79 

Those who went to Eimayo in the long-boat, after 
rowing the best part of the night, by the help of some 
Indians on board a canoe which they hailed, found a 
proper situation for their observatory upon a rock, 
where they fixed their tents, and prepared the apparatus 
for the following day's observation. On Saturday, 
June 3, as soon as it was light, Mr. Banks left them 
to go to the island for fresh provisions. As he was 
trading with the natives who belonged to Tarras the 
king of the island arrived, with his sister, whose name 
was Nuna, in order to pay him a visit. . . . Mr. 
Banks returned to the observatory with his visitors, 
and showed them the transit of the planet Venus over 
the sun's disc, informing them that he and his com- 
panions had come from their own country solely to 
view it in that situation. Both the parties which were 
sent out made their observations with great success. 
They nevertheless differed in the accounts of the times 
of transits more than mio-ht have been imagined.' In 
Captain Cook's journal, the following account is 
given : ' The day proved as favourable to our purpose 
as we could wish ; not a cloud was to be seen the 
whole day, and the air was perfectly clear ; so that Ave 
had every advantage in observing the whole of the 
passage of the planet Venus over the sun's disc. We 
very distinctly saw an atmosphere, or dusky shade, 
round the body of the planet, Avhich very much dis- 
turbed the times of the contact, particularly the two 
internal ones. It was nearly calm the whole day, and 
the thermometer, exposed to the sun about the middle 



8o TRANSITS OF VENUS. 

of the day, rose to a degree of heat we have not before 
met with.' 

Chappe was specially fortunate at St. Joseph. His 
observation has given rise to a good deal of controversy, 
with reo-ard to its bearing on the question of the solar 
parallax. Powalky and others consider that Chappe's 
observation of the internal contact at egress was an 
observation of real contact, not apparent contact; Stone 
maintains the contrary. My attention was specially 
directed to this point by Newcomb, of Washington, 
U.S., and I must confess that Chappe's narrative 
seems to me unquestionably to bear the interpretation 
given to it by Powalky, with whom Newcomb agrees. 
Let the reader judge, remembering that real contact 
means the formation of the black drop or of the pear- 
shaped figure described at page 57 ; so that at total 
ingress real contact is later than apparent, while the re- 
verse is the case at egress. Chappe writes as follows : — 
' At the total ingress I observed very distinctly the 
second phenomenon, which had been noticed by the 
greater part of the observers in 1761. The edge of 
the disc of Venus lengthened itself, as if it had been 
attracted by the sun. I did not observe, for the instant 
of total ingress, the instant when the edge of Venus 
commenced to extend itself; but, not being able to 
doubt that this black point was not part of the opaque 
body of Venus, I observed the moment when it ended 
(' oil il etait a sa fin ') in such sort that the .otal 
ingress could not have occurred earlier, though perhaps 
later by two or three seconds. The black point was 



THE TRANSIT OF 1700. 8 1 

a little less dark than the rest of Venus ; I think it 
is the same phenomenon which I had observed at 
Tobolsk in 1761. . . . At the second internal con- 
tact' (that is, internal contact at egress), 'the sun was 
undulating as was Venus also, which rendered the 
observation very difficult. At this contact Venus elon- 
gated herself more considerably than in the morning, 
in approaching suddenly the edge of the sun.' It 
seems clear that Chappe here witnessed that sudden 
leap to the sun's edge at egress which is the counter- 
part of the sudden leap from the sun's edge at ingress ; 
and that if the contact differed at all from the con- 
tact at ingress, it was in the fact that a longer leap 
Avas made, in other words, that he caught an earlier 
phase at ingress, which would correspond of course to 
a later phase at egress. As Chappe says himself that 
real contact at ingress might have been two or three 
seconds later, but certainly not earlier, we see that the 
contact he observed at egress corresponded even more 
closely with what he regarded as real contact, — that is, 
the moment of the leap by which the black drop is 
formed and broken. Yet Mr. Stone considers that 
at egress Chappe missed the real contact and observed 
the later phase of apparent contact. 1 

Le Gentil experienced in 1769 the culmination of 

1 Here and at pp. 90-92, 1 retract the views I expressed in my ' Sun, 
and in reply to Prof. Newcomb's general criticism on my account of 
Stone's work. So soon as we met, and he described his objections in 
detail, I recognised their force. The Astronomical Society had, in fact, 
pronounced so decisively in favour of Stone's treatment of the transit of 
17G9, that I was not prepared to find errors so serious in ii. 

G 



82 TRANSITS OF VENUS. 

his misfortune. With a persistent courage worthy of 
better success he determined, after his failure in 1761, 
to return to Pondicherry as soon as an opportunity 
presented itself, and to await there during eight years 
the transit of 1769. Dubois remarks that Le Gentil 
usefully employed those years in studying the astro- 
nomy of the Brahmins, on which subject he published 
an interesting work upon his return to France. But 
the object he had specially in view Avas unfortunately 
not attained. ' On June 3, 1 769,' says Dubois, ' at the 
moment when this indefatigable observer was preparing 
to observe the transit, a vexatious cloud covered the 
sun, and caused the unhappy Le Gentil to lose the fruit 
of his patience and of his efforts.' Pondicherry would 
have been a useful station for observing the retarded 
egress, as we see from Plate V. 

Pingre, who had observed the transit of 1761 at 
Rodriguez, was sent to observe the transit from a 
French station in the island of St. Domingo. 

Although the observations made in 1769 were on 
the whole much more satisfactory than those which had 
been made in 1761, yet there was much to throw doubt 
on anv determination of the sun's distance based even 
on the later transit. We have seen already that the 
peculiar distortion of Venus, illustrated in pp. 61-63, 
was presented in a marked degree in 1769 ; but even 
more unpromising was the observed difference in time 
between the moments of real and apparent contact. It 
is onlv necessary, as M. Dubois points out, to consider 
the difference recognised by those observers who noted 



THE TRANSIT OF 1769. 83 

the two phases to see how largely the accuracy of the 
deduced solar distance must be affected by this 
cause. 

Wales, at Hudson's Bay, using a telescope two 
feet long, magnifying 120 times, found a difference 
of 24 seconds between the real and apparent contacts 
at egress. Green, at Otaheite, found a difference of 
40 seconds at ingress and 48 seconds at egress. Cook, 
at the same station, found the difference 60 seconds 
at inoress and 32 seconds at egress. Yet these two 
observers used two similar telescopes, magnifying 140 
times. Maskelyne, at Greenwich, using a telescope 
magnifying 140 times, found the difference 52 seconds; 
while Horsley, at the same station, with an achromatic 
telescope, 10 feet in length, magnifying 50 times, found 
the difference to be 63 seconds. Maskelyne remarks 
that the difference was greater than he had expected, 
considering that the telescopes were all nearly of the 
same quality, except a reflector of six feet used by 
Hitchins. The superiority of this instrument ap- 
peared to Maskelyne to account for the difference of 
26 seconds, by -which interval Hitchins observed the 
internal contact earlier than Maskelyne. Hornsby, at 
Oxford, used an achromatic telescope of 7^ feet, magni- 
fying ninety times, and found the difference to be 57^ 
seconds; while Schuckberg, also observing at Oxford, 
found a difference of 69 seconds between the real and 
apparent contacts. An unknown observer at Caen, 
using a very small telescope, found the enormous dif- 
ference of fully 150 seconds! Wilke, at Stockholm 

o 2 



84 TRANSITS OF VENUS. 

also using a very small telescope, estimated the dif- 
ference at 43 seconds. Lastly, Euler, observing at 
Orsk, with a telescope 12 feet in length, noted for the 
instants of contact two epochs differing by 50 seconds. 

When we consider these wide and widely varying 
differences among observers who observed both kinds 
of contacts, we cannot wonder if considerable differences 
of absolute time were noted between observations of 
the same contact by different observers either at the 
same stations or at stations near enough for instituting 
a comparison. Thus, Le Monnier and De Chabert, at 
St. Hubert, noted instances of contact differing 36 
seconds from each other ; while between Duval le Roy 
and De Verdun, at Brest, there was a difference of 30 
seconds. 

It is well remarked by Dubois that observations of 
external contact at ingress can have no value. He adds 
that observations of external contact at egress are 
somewhat more reliable ; but it must be very dif- 
ficult to distinguish the moment when the solar limb 
resumes an exactly circular shape. Accordingly the 
fourteen exterior contacts noted by different ob- 
servers could have no real value. Yet it is worthy 
of remark that the difference between moments of ex- 
ternal contact observed at St. Petersburg by Mayer 
and Stahl amounted only to 27 seconds ; while at 
Gurief the difference between two such observations 
amounted to 28 seconds. So that, as Newcomb has 
remarked of the observations made during the transit 
of Mercury in November 1868, it would seem as 



THE TRANSIT OF 1769. 85 

though the errors in the estimated instant of an ex- 
ternal contact might be expected to be of the same 
order as those affecting- the estimated instant of an 
internal contact. 

Dubois tells us that upwards of two hundred 
memoirs were sent to the Academy of Sciences on the 
value of the solar parallax deducible from the obser- 
vations made in 1769. How many were sent to the 
Royal Society I do not know ; but probably as many 
as four hundred were sent to the different learned 
bodies of Europe. 

A comparison of the results obtained by the most 
competent computers showed that the observations of 
1769 were much more valuable on the whole than 
those of 1761 ; for, whereas the results obtained in 1761 
ranged in value between 8""5 and 10 //# 6, we find the 
following five results selected as those most carefully 
calculated on the basis of the observations of 1769 : — 

De Lalande fixed the parallax at 8 '50 
Fr. Hell „ „ 8-70 

Hornsby „ „ 8 -7 8 

Euler „ „ 8-82 

Pingre „ „ 8 -88 

The solar distances corresponding to the parallaxes 
8"-50 and 8 r/ -88 are respectively 96,162,840 miles 
and 92,049,650 miles. 

It is somewhat singular that, notwithstanding the 
clearest evidence of a cause of uncertainty sufficing to 
account for such differences as the above table presents, 



86 TRANSITS OF VENUS. 

Lalande and Pingre, who had obtained the most widely 
different results, were both quite confident of the 
accuracy of the values they had deduced. Lalande 
says in his memoir, that regarding the whole series of 
observations of 1769, the solar parallax is incontestably 
8"'5 ; while Pingre says in reply, ' of two things one : 
either no result at all can be deduced from the transit 
of 1769, or it must be admitted that the value of the 
solar parallax is very close indeed to 8"*8 (est a tres- 
peu pros de 8"-8).' 

In his first memoir, in which the above tabulated 
value, 8"*82, was given, Euler had not taken into 
account the observations made at Otaheite by Green 
and at St. Joseph, in California, by Chappe. Going 
over his work afresh, and introducing these observa- 
tions, he deduced the parallax 8"'G8. Dionis du Sejour, 
employing only observations of duration, and combining 
the transits of 1761 and 1769, deduced the value 8"*84. 
But in his ' Traite Analytique des Mouvements 
Apparents des Corps Celestes ' he adopts as the final 
result of his calculations the solar parallax 8""8128. 

It is worthy of notice that when chief reliance was 
placed on observations made at Halleyan stations o 
the first class, the value of the parallax approached 
more nearly to that now recognised as probably the 
more correct. Thus, combining observations made at 
Otaheite with Father Hell's observations at Wardhuus, 
De Lalande obtained the value 8"*72, and yet larger 
values when Hell's observations were combined with 
other observations. Yet, as we have seen, De Lalande 



THE TRANSIT OF 1769. 87 

adopted 8"%5 as the best mean value of the solar 
parallax. 

Doubts, indeed, were thrown upon Father Hell's 
observations, on account of corrections which had 
been made in his MS. notes of the phenomena, (and 
partly, also, because of the known fact that he alone of 
all the observers of the transit recognised no distinc- 
tion between real and apparent contacts). The idea 
that Hell's records were forged was thrown out by 
the Astronomer Royal. But such a suspicion need 
hardly be seriously considered. Not only is nothing 
known about Fr. Hell which for a moment justifies 
the supposition that he could be guilty of the ac: 
charged to him, but we know now that his observations 
accord better with the latest estimates of the parallax 
than those of other observers. 

Encke in 1824 published an analysis of the observa- 
tions of the transit of 1769, from which he deduced for 
the solar parallax the value 8"'6030. By combining 
the observations of both transits he deduced that value 
8 //, 5776 (corresponding to a solar distance of 95,274,000 
miles) which for more than a quarter of a century 
thereafter maintained its ground in treatises on astro- 
nomy. 

But about the vear 1850 it began to be recognised 
that the 6un's distance had been over-estimated. 
Various methods of determining the solar parallax, 
inferior singlv to the observation of transits of 
Venus, but collectively superior— and superior, more- 
over, because of the greater accuracy with which 



88 TRANSITS OF VENVS. 

(owing to the improvement in instruments of precision) 
they could be applied — concurred in showing that the 
sun's distance was less than had been supposed by at 
least three millions of miles. The consideration of 
these methods in detail would occupy more space than 
is here convenient. The reader will find them fully 
described in the second chapter of my treatise on the 
sun. In this place let the following summary 
suffice : — 

In 1854 Hansen announced that by a method 
based on observations of the moon's motions he had 
deduced the parallax 8"-9159, corresponding to a dis- 
tance of 91,659,000 miles. Leverrier, from the care- 
ful study of the sun's apparent motions, as affected by 
the earth's monthly revolution around the common 
centre of gravity of herself and the moon, deduced a 
solar parallax of 8"*95, corresponding to a distance of 
91,330,000 miles. Prof. Newcomb, of Washington, 
U.S., obtained by the same method the parallax 8 //- 84, 
distance 92,500,000 miles. From observations of 
Mars when at his nearest to the earth Prof. Newcomb 
deduced the parallax 8" -85, corresponding to a distance 
of 92,300,000 miles. Stone, formerly of Greenwich, 
obtained by this method the distance 91,400,000 miles; 
while Winnecke deduced the distance 91,200,000 miles. 
Foucault, measuring the velocity of light by means of 
a rapidly revolving mirror (a plan devised by Wheat- 
Stone), and comparing the value so obtained with that 
inferred from the observation of the eclipses of Jupiter's 
satellites and the aberration of light, deduced the 



THE TRANSIT OF 1769. 89 

solar parallax 8"'86, corresponding to a distance of 
92,100,000 miles. From the study of those planetary 
perturbations which depend on the relative masses of 
the earth and the other planets Leverrier deduced the 
value 8"-859 for the parallax, or 92, 11 0,000 miles for 
the sun's distance. Tt will be seen that the values 
thus obtained indicate a solar parallax of 8" '89, corre- 
sponding to a distance of about 91,950,000 miles. The 
limits of probable error are considerable, however, 
and we scarcely know more at present than that the 
solar parallax almost certainly lies between the values 
8"*82 and 8 //- 96, corresponding to the distances 
92,6~6,000 miles and 91,228,000 miles. 

As soon as it became clearly recognised that 
Encke's estimate of the sun's distance from observa- 
tions of the transit of 1769 was considerably in error, 
doubt necessarily fell upon the method itself which 
had till then been regarded as the most satisfactory for 
determining the sun's distance. Efforts, however, were 
made to restore the credit of the method by a re-ex- 
amination of the observations made in 1769. These 
efforts have been regarded by many, especially in 
this country, as successful ; but it must be con- 
fessed the investigation has shown us rather how the 
error crept in than how it can be avoided in future 
applications of the method. This will appear when 
Ave consider the nature of the researches by which 
astronomers have sought to restore the waning credit 
of the observations of 1769. 

Powalky in 1864 discussed forty-four observations, 



90 TRANSITS OF VENUS. 

made at nineteen stations, the latitude of which seemed 
to him satisfactorily determined. He dismissed seven- 
teen of these observations, and treated six of the re- 
maining twenty-seven as of inferior worth, giving to 
them only half the weight assigned to the other twenty- 
one. The observations thus retained were made at 
only thirteen stations. Amongst the observations 
were nine external contacts, four at ingress and five 
at egress. Powalky gives no sufficient reason for some 
of the selections made by him (between conflicting 
observations made at stations in the same regions), nor 
for regarding as real contacts some observations which 
were not described with sufficient exactness to justify 
that interpretation. On the whole, it seems impossible 
to regard his conclusion as satisfactorily established. 
All he can be said to have proved is that amongst the 
observations made in 1769 it is possible to select several 
which, when combined, give a value of the solar paral- 
lax according fairly with the estimate recently adopted 
in preference to Encke's. 

The investigation published by Mr. Stone, of 
Greenwich, in 1868, has been regarded as more trust- 
worthy ; but it does not appear that those who have 
expressed approval of it had critically examined his 
memoir on the subject. When Sir John Herschel de- 
scribed Stone's work as removing the reproach from 
astronomy which had fallen upon the science in conse- 
quence of the large error detected in the estimate of the 
sun's distance, he appears to have taken Stone's results 
for granted, and not only so, but to have mistaken 



THE TFANSIT OF 1769. 9 1 

their real significance. I followed him in my treatise 
on the sun, being partly influenced by the fact that 
the Astronomical Society had adopted Stone's con- 
clusions. But my attention having been directed by 
Professor Newcomb, of America, to the slightness of 
the examination given to Stone's memoir by those 
who had accepted its results, I have been led to ex- 
amine it for myself, and I am obliged to admit that it 
has much less weight than some in this country have 
supposed. 

What Stone has done has been simply this. He 
has endeavoured (as others had done) to ascertain 
from the account given by each observer, whether real 
or apparent contact was observed. And he introduced 
in the equations of condition a constant correction 
(seventeen seconds) for the difference in time between 
the two contacts. Now, this constant is inferred from 
the equations themselves whence the parallax deduced 
by Stone, 8"'91, is obtained; and his analysis really 
amounts to the distribution of the disposable errors 
affecting the observations of contact, in such sort 
that a part goes to change the parallax from Eucke's 
value to 8"91, and the remainder to form the constant 
correction between real and apparent contacts. This 
would render the result unreliable, even if we had 
reason to believe that the correct time-difference be- 
tween real and apparent contacts in any given transit 
really had a nearly constant value, and that value not 
far from seventeen seconds. Knowing as we do from 
the accounts of the observers themselves that the differ- 



92 TRANSITS OF VENUS. 

ence varied greatly with the varying circumstances 
under which the observations were made, and always 
largely exceeded seventeen seconds, it seems quite im- 
possible to adopt Mr. Stone's method as trustworthy. 
We cannot, therefore, wonder that Continental and 
American astronomers have, by common consent, de- 
clined to accept Mr. Stone's results as having much 
weight, or indeed as proving anything except what 
had already been ascertained — the fact, namely, that 
the observations made in 1769 afford but unsatisfac- 
tory evidence respecting the sun's distance. 

But the imperfect nature of the observations made 
in 1761 and 1769 can be sufficiently explained with- 
out attributing inferiority to the method of determin- 
ing the sun's distance in pursuance of which the 
observations were made. It cannot be doubted that 
the measurement of the sun's distance resulting from 
those observations was more trustworthy than any 
which could have been obtained at that time by other 
methods. We have learned to apply other methods 
so much more accurately than they could have been 
applied in the last century, that they give better results 
than a superior method could then give. But it still 
remains probable that the method depending on the 
observation of Venus in transit is superior to other 
modes of determining the sun's distance ; and that when 
this method is applied with the improved instruments 
of our time its superiority will be rendered manifest. 







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OF TRANSITS AND THEIR CONDITIONS. 93 



CHAPTER IV. 

OF TRANSITS AND THEIR CONDITIONS. 

Before we proceed to the consideration of the transits 
of 1874 and 1882, it will be desirable to enter on a 
more complete examination than heretofore of the 
general principles on which the determination of the 
sun's distance by observation of Venus in transit de- 
pends. To this subject the present chapter is there- 
fore given. It deals with the various methods which 
are available for determining the sun's distance, the 
order in which transits recur, and lastly, the considera- 
tions on which the choice of stations will depend, in 
any given transit. These various points I wish to 
treat in an entirely popular manner, and therefore I 
shall leave out of account all those minor details 
which hav° to be considered in the complete discus- 
sion of the subject, referring the reader who may 
wish for a more thorough investigation of the matter 
to my ' Essays on Astronomy ' and * The Universe 
and the Coming Transits.' 

First, then, let us consider the passage of Venus 
between the earth and the sun on the occasion of a 
transit, and see how the sun's distance may be inferred 



94 TRAySITS OF VENUJ3. 

from the various appearances presented when the transit 
is viewed from different parts of the earth. 

Let ee' (fig. 13) be the earth, and V Venus passing 
between the earth and the sun (at s) on the course 




Fig. 13. — Illustrating the general principles on which the determination 
of the Sun's distance by transit observation depends. 

shown by the arrow, so that at the moment indicated 
by the figure a transit is in progress. At this moment 
let us suppose that from a northern station e' Venus 
is seen projected upon the sun's face at v' ', while from 
a southern station E she is projected at v (v and v' 
marking the place of her centre). It is to be noted 
that true perspective being quite out of the question, 
I here for convenience suppose the circle 8 to represent 
the disc of the sun seen from E, so that in considering 
what follows the reader need not trouble himself about 
the curved nature of the sun's surface. 

Now, the proportions of the solar system being well 
known ever since the Copernican theory was established 
— or rather, since Kepler's laws were discovered — we 
know that the distance of V from the sun bears to the 
distance of E from the sun the proportion of about 72 
to 100 ; whence, immediately, we see that E v bears to 
vy the proportion of about 28 to 72, or 7 to 18. And 
manifestly the opening-out of the lines v E and v e' 
at the earth is less than their opening-out at the sun 



OF TEAXSITS AND THEIR CONDITIONS. 95 

in this same proportion of 7 to 18 ; so that, for instance, 
if the two stations E and e' are 7,000 miles apart 
(meaning the distance in a straight line, and for sim- 
plicity assuming that ve and te' are equal lines sym- 
metrically placed with respect to the earth's globe), then 
v v is a distance of 18,000 miles. But such a deter- 
mination as this, if justly and satisfactorily made, would 
in point of fact amount to a determination of the sun's 
size, and therefore of the sun's distance. Observe — 
the astronomer at E is supposed to have accurately 
determined the apparent position of Venus's centre at 
v, while the astronomer at e' has accurately determined 
the apparent position of her centre at v' ; thus they 
know what proportion v v' bears to the diameter of 
the disc S, that is, to the sun's diameter. Say, for 
instance, they find it to be the 47th part of this dia- 
meter. But they know also that vv' is 18,000 miles 
in length. So that the sun's diameter is 47 times 
18,000 miles, or 846,000 miles. 

So soon, however, as we know the real size of the 
sun we know his distance. We know how large he 
looks, and a globe of given size can only present a 
certain apparent size at a certain distance. For ex- 
ample, a globe one inch in diameter looks just as large 
as the sun at a distance of about 107 ^ inches, or a 
little less than 9 feet ; ' a globe two inches in diameter 

1 A halfpenny, which has a diameter of one inch, will be found to 
exactly conceal the sun when placed at a distance of 107s inches, the 
sun being at about his mean distance— that is, the observation being 
ma'le in March, April, September, or October. 



96 TRANSITS OF VENUS. 

must be set twice as far away to look just as large as 
the sun ; a globe three inches in diameter thrice as far 
away ; and so on. In brief, the sun (like any one of 
these globes when placed as described) lies at a dis- 
tance 107^ times as great as his own diameter. So 
that multiplying 846,000 by 107^ we get for the sun's 
distance (as resulting from the observations imagined 
above) 90,160,000 miles. 

The considerations just discussed form the basis 
of all the various methods for determining the sun's 
distance by transit observations. These methods are 
only so many contrivances for bringing out the true 
result as satisfactorily as possible, by eliminating the 
various possible sources of error. 

We may call the method just sketched the direct 
method, because it depends on the simple observation 
of the place of Venus on the sun's face. I shall have 
occasion presently to discuss the method somewhat 
more in detail. Let it suffice, here, to notice that 
the method presents manifest difficulties. The two 
observers, at e and e', are of course not in direct com- 
munication ; yet it is essential that their observations 
should either be made exactly at the same time or that 
at least the exact difference of time should be known. 
Again, it is not an easy matter to ^measure the place 
of Venus on the sun's face with the accuracy that the 
method requires. For these reasons Halley was led, 
in anticipation of the transit of 1761, to devise another 
method. 

Let us suppose, for simplicity, that the two stations 



OF TRANSITS AND THEIR CONDITIONS. 9/ 

at e and e' are not shifted by the earth's rotation while 
the transit lasts. In this case the observer at e would 
see Venus traverse such a path as / v m, while the 
observer at e' would see her traverse the parallel path 
/' v' m' . The time occupied by Venus in each case 
would of course be proportional to the apparent length 
of the lines / m and I' m' ; so that if the time were 
accurately noted by the two observers, the apparent 
lengths of these lines would be known ; whence, of 
course, the simplest possible geometrical considerations 
would give the position of the two chords and the ap- 
parent distance v v separating them from each other. 
This known, the sun's size and distance follow as in the 
direct method. Seeing that the moment when Venus 
has just made her complete entry on the sun's face at 
ingress, and is just about to begin to leave his face at 
egress (in other words, the moments when her disc 
just toviches the sun's edge on the inside), were sup- 
posed by Halley to be determinable with great ac- 
curacy, such a method as has just been described 
seemed to him admirably adapted for determining the 
sun's distance. 

But clearly the difference of time in the imaginary 
case we have been dealing with, where the earth's rota- 
tion was neglected, will depend on the position of the 
chord of transit. Supposing Venus to traverse the centre 
of the sun's face, the two chords being equal in length, 
there would be no difference of time, while the differ- 
ence would be great if the two chords were near the 
edge of the disc. In the latter case the method would 

H 



9S TRANSITS OF VENUS. 

be most advantageously applicable, while in the former 
it would not be applicable at all. Now, Ave have seen 
that the transit of 1761, as calculated by Halley (see 
pp, 34 and 35), was nearly central. Nevertheless, 
owing to the rotation of the earth, a difference of dura- 
tion would occur in the case of such a transit. In a 
general way this has been already shown in the note 
on pp, 34 and 35. But it is also easy to show that a 
displacement comparable with the v v of fig. 13 can 
be inferred from time observations applied as Halley 
suggested for the supposed conditions of the transit of 
1761. 

Let us suppose that in fig. 14 Ave are looking down 
upon the earth E and Venus v from the north, Venus 



El § -\ ' 5 



Fiff. 14. — Illustrating the effect of the Earth's rotation on tne motion ot 

Venus in transit. 

travelling (with respect to the earth) 1 in the direction 
shown by the arrow. Let us suppose I E to represent 
a chord of transit across the face of the sun S. Now, 
the earth is rotating in the direction w e e along 
the arc w e\ and as a transit may last several hours, 

1 It is genprally convenient to suppose the earth at rest, and Venus 
travelling; only with the (xcess of her motion over the earth's motion 
around the sun. 



OF TRANSITS AXD THEIR COXDITIOXS. 99 

a place which was at ir when transit began (that 
is, when Venus appeared to he at i) would be carried 
by rotation to some point e by the time the transit 
ended (that is, when Venus appeared to be at e). 
In order to see the effect of such a rotation-shift or: 
the apparent motion of Venus, let us take two lines, 
one from w, the other from e, through the centre of 
Venus (supposed at rest at v, near the middle of the 
transit) to the chord IE; we see that the line from 
the earlier position w passes to v, while the line from 
the later position e passes to v' . Thus the effect of the 
rotation of the earth during the time of transit, if con- 
sidered alone, corresponds to a shifting forwards of 
Venus by the amount v v' '. In other words, transit is 
shortened by the effect of rotation in direction in e. 
Suppose now another observer placed at the pole 
( whichever pole happened to be in sunlight at the 
time), so as not to be at all affected by rotation ; or 
that, being placed near either pole, he were much less 
affected by rotation ; or that, being placed on the side 
of the pole farthest from e w, the duration were 
lengthened through the effects of duration, instead of 
beinir shortened. Then there would arise on this ac- 
count a difference of duration, which would lead to 
the determination of the sun's distance precisely as in 
the case before supposed. For in reality the result 
would be the determination of the apparent amount of 
the displacement /; v' along the chord of transit, corre- 
sponding to the known displacement w e upon the earth ; 
and the mere fact that both displacements are in an 

II 2 



IOO TRANSITS OF VENUS. 

east-and-west direction does not render the observa- 
tions less effective than those which in the former case 
gave the apparent displacement v v corresponding to 
the observers' displacement E e', both displacements 
being; on a north-and-south line. 

In all ordinary cases, Halley's method depends 
partly on the distance of the observers measured in a 
north-and-south direction, and partly on the effect of 
rotation ; and in the selection of stations both con- 
siderations have of course to be taken into account, 
the aim being to make the difference of duration as 
great, and therefore as exactly measurable, as possible. 
The considerations on which the selection of sta- 
tions depends will be dealt with in a simple manner 
farther on. 

We ma} r conveniently call Halley's method the 
' method of durations ' — a name descriptive of the 
M ualities of the method. But it certainly seems a 
mistake to limit the title ' Halley's method ' to the 
case more particularly considered by him. 1 We may, 
therefore, use both names indifferently. 

Halley's method requires the whole transit to be 
seen, or at least the beginning and end. Apart from 
other difficulties which this requirement introduces, 
the probability of favourable weather both at ingress 
or egress is manifestly less than the probability of 



1 An effort has of late been made to dismiss from use the title 
' Halley's method.' which Sir J. Herschel and others had long used. I 
cannot see why Halley's name should thus be summarily dismissed from 
the position it lias so long occupied. 



OF TRANSITS AND THEIR CONDITIONS. 1 01 

favourable weather for a single observation only. It 
occurred to Delisle, when preparations were being 
made for the transit of 1761, that assuming Halle v 
was right in supposing the moment of contact at 
ingress could be determined with great exactness, a 
single observation of the sort might be employed in- 
stead of two terminal observations. 

It is clear that the observer who sees Venus 
traverse such a chord as I'm' (fig. 13) will see the 
transit begin earlier than one who sees her traverse 
such a chord as lm,iov I is a point more advanced than 
the point /'. Suppose now that each observer notes 
the exact moment of local time when the transit begins 
(internal contact), and that, knowing his exact longi- 
tude, each can change his local time into Greenwich 
time ; then these two Greenwich epochs will differ 
by an interval corresponding to the amount by which 
/ is in advance of /'. But this gives a geometrical 
relation whence the distance between the chords I m 
and /' m' can manifestly be determined, just as well 
as though the length of each chord were ascertained. 
Hence v v' becomes known, and thus, as in the 
direct method, the sun's size and distance can be 
determined. 

Similar remarks apply [mutatis mutandis) to the 
observation of egress. The method, whether applied 
at ingress or at egress, is called Delisle's method. 1 

The employment of photography to record the 

1 It is singular that Delisle's name, like Halley's, is not used in Sir 
G. Airj's programme for the trans-its of 1874 and 1882. 



102 



THAXSITS OF VENUS. 



place of Venus on the sun's face at any particular 
instant need not detain us here, as it manifestly intro- 
duces no new astronomical relations. 

And now let us consider how transits of Venus 
recur, in other words, how those opportunities are 
from time to time offered which admit of beinij utilised 
in the various ways above described. 

Let us examine, first, how successive conjunctions 
of Venus are brought about. 

Let the paths of Venus and the earth around the 
sun s (fig. 15) be represented by the circles vv' and 
k i:' ; and let us suppose that Venus and the earth are, 




Fig. 15. — Illustrating the conjunctions of the Earth and Venus. 

in the first instance, in conjunction, as at v, E, so that 
s v E is a straight, line; AVe need take no account, at 



OF TRANSITS AND THEIR CONDITIONS. 103 

this stage, of the slight eccentricity of the two orbits, 
and of the fact that they are not exactly in the same 
plane. Thus, we may be supposed to be looking 
directly down upon the moving planets, which, instead 
of travelling, as they actually do, with a slightly 
varying velocity, are supposed to travel with their 
mean or average motion. 

Now, the simplest way of determining when and 
where the two planets will be again in conjunction is 
perhaps the following : — 

Imagine that a straight pointer from the sun to 
Venus, extending to the earth's orbit, like the line 
S v E, is carried round s as a central pivot by the 
motion of the planet Venus. Then whenever this 
pointer comes up to the earth, the three bodies — sun, 
earth,, and Venus — are in conjunction. Now, Venus 
travels with a mean motion of 96' 7"*8 per day around 
the sun (completing a revolution in 224*701 days), 
while the earth travels with a mean motion of 59' 8"-3 
(completing a revolution in 365*257 days ')* so that 
in each mean solar day Venus gains, on die average, 
36' 59"'5 upon the earth. This is the rate at which 
our imaginary pointer, starting from a position such as 
S v E, sweeps onwards from the advancing earth, so as 
to again reach the earth by overtaking it, just as the 
minute-hand of a clock, after being in conjunction 
with the hour-hand, passes on towards its next con- 
junction, with the excess of its motion over the hour- 

1 Sidereal revolution ie here considered, not the tropical revolution 

which forms the year of seasons. 



J04 TRANSITS OF VENUS. 

band. We have only, then, to ask how long it will 
take the pointer, with its mean daily gain of 36' 59"*5, 
to gain one complete circuit, to have the interval in time 
between successive conjunctions of the earth and Venus 
— in other words, there Avill be just as many days in 
this interval as the number of times that 36' 59"*5 is 
contained in 360°, or, reducing both to seconds, as 
2219-5 is contained in 1,296,000. The division is 
easily effected, and gives us 583*9 days. 

Our Venus-carried pointer thus takes 583*9 days 
in overtaking the earth. This is more than a year by 
about 218*6 days, in which period, with her mean 
motion of 59' 8"*3 per day, the earth travels round 
nearly 215^ degrees. Now, 216 degrees would berths 
of a complete circuit. We see, then, that the next 
conjunction-line, S v' e', must be set almost exactly J-ths 
of the way round from s v e, or in the position s v, e, ; 
the next will have the position sv 2 e 2 ; the third will 
have the position sv 3 e 3 ; the fourth, the position 
S V 4 E 4 ; and the fifth will be close up to sve, in the 
position s v s E 5 , about 2^ degrees behind sve. 

Since the interval between each conjunction is 
about a year and three-fifths, the whole time occupied 
before the position s v g e 5 is reached by the conjunc- 
tion-line will be five times If years, or 8 years, less 
the short interval corresponding to the earth's motion 
over the arc E 5 E. We see, then, how it comes 
to pass that an interval of eight years brings round 
nearly the same circumstances as at the beginning of 
the interval, and why, therefore, when a transit has 



OF TRANSITS AND THEIR CONDITIONS. 105 

occurred, another may occur eight years later. A 
second interval of eight years, as we shall presently 
see, changes the conditions too largely (though they 
are still approximated to). 

It may be mentioned in passing that since Venus 
gains one complete circuit on the earth between two 
successive conjunctions, and the earth goes nearly 
eight times round for the five conjunctions just con- 
sidered, it follows that Venus goes nearly thirteen times 
round. In other words, thirteen revolutions of Venus 
are nearly equivalent to eight revolutions of the earth. 

And now let us consider the effect of the inclina- 
tion of the orbit of Venus to that of the earth, still, 
for the sake of simplicity, leaving out of account the 
slight eccentricity of the orbits. 

If ee', vv' (fig. 16), represent the two orbits, 
and J£ be the place of the earth at the autumnal 
equinox, then the line E e' represents the intersection 
of the two orbit-planes ; and if, as before, we regard 
the plane of the paper as containing the orbit e e', then 
the part v v v' of the path of Venus is to be as re- 
garded slightly above, the part v' v' v as slightly below, 
the plane of the paper. Accordingly, the end of the 
pointer which Ave have supposed Venus to carry round 
the sun, passes above the semicircle e?e' and below 
the semicircle e'/e, And supposing this pointer to 
be of the length S E, so that its end appreciably travels 
round e e E V (except for the displacement above and 
below the plane of this orbit), it is easy to calculate 
how much above or below the level EeE'e' the end of 



io6 



TRANSITS OF VENUS. 



the pointer runs. When in the direction se or se', 
of course the Venus-carried pointer has its extremity 
on the earth's path; when in direction s v e or s v' e , 




Fig. 16.— Showing the parts (pp' and qq') of the Earth's urbit where 

transits can occur. 

at right angles to E e', the end of the pointer is at its 
farthest from the plane EceV, The inclination of 
the orbit of Venus being about 3° 23^', and the dis- 
tance s e (the earth's distance from the sun) being 
about 9 \, 430,000 miles, it is easily calculated that the 
extremity of the pointer passes above e and below e 
at a distance of about 5,409,000 miles. At any other 
point, as p or p', the end is above or below by an 
amount less than 5,409,000 miles in the same decree 
that pm or p' m is less than es or e' s (pmp' beir.a- 
drawn square to E e'\ 



OF TRANSITS AND THEIR CONDITIONS. 107 

Now, it is clear that, for a transit to occur, a line 
from the sun's centre through Venus to the earth's 
orbit, at the time of a conjunction, must not pass more 
than a certain distance above or below the earth's 
orbit — that is, a conjunction must occur near the 
positions v e or v' e'. And it is easy to determine 
roughly how near the earth must be to e or e' at the 
time of conjunction, for a transit to occur. For let 
s v e, fig. 17, be our imaginary pointer at the time of 




Fig. 17- — Illustrating the occurrence of transits. 

a conjunction, and s v e, s y' e lines touching the sun. 
Then it is manifest that if the earth be anywhere on 
the line e' E e at the time of conjunction, a line from 
the earth to Venus must meet the globe s s /, or, in 
other words, there is a transit. But if the earth be 
above e or below e at the moment of conjunction, 
there can be no transit. Now, s s, the sun's radius, is 
about 426,000 miles, and therefore e e and e' e are 
each less than 426,000 miles in the proportion in 
which v E is less than V s, or, roughly, as 277 to 723 : 
so that Ec and E e' are each equal to about 163,000 
miles — a small distance compared with the actual 
range of the end of our Venus-carried pointer above 
and below the earth's orbit. And it is easily calcu- 



108 TEAXSITS OF VENUS. 

lated ] that the range on either side of E or e' (fig. 
16), within which a transit is possible, is represented 
by the arcs pEp' and qEq', each equal to about 3^ 
degrees. 

Now, having found that the circuit of the earth's 
orbit has these two transit-regions, so to call them, it 
is not difficult to ascertain the general conditions under 
which the conjunction-line will fall from time to time 
upon one or other region. 

Let it first be noted that the points E and e' are 
at present those traversed by the earth on or about 
December 7 and June 6. The line ese' does not, 
however, bear a fixed position with respect to the 
point M, but the points E and e' slowly shift, forwards, 
that is, in the direction indicated by the arrow. The 
node of Venus's orbit shifts backwards with respect to 
the stellar sphere by about 20" *5 per annum ; but as 
the point m shifts backwards annually by about 50" -1 
(the precession of the equinoxes), it follows that the 
nodes v and v', and therefore the points e and e', 
advance with respect to je by about 29"*6 (the excess 
of 50"*1 over 20""5) annually. Still, in dealing with 
the general question of the recurrence of transits, we 
must not regard the node of Venus as advancing bv 
29""6 annually, but as receding by 20 //, 5 ; for in what 



1 We require to have 

up 163,000 

eT = 5,409,000 

that is, the sine of the arc v.p = 163 -=-5409. Whence vp is an arc of 
about 1° 44', and each of the arcs pp' and qq' about 3° 28'. 



OF TRANSITS AND THEIR CONDITIONS. 109 

has hitherto been said about successive conjunctions 
of Venus and the earth, we have used the sidereal 
periods of both planets, and we cannot substitute the 
tropical year without making corresponding corrections. 

We may regard the system of five conjunction- 
lines shown in fig. 15 as a spoked wheel, which slowly 
but continuously shifts backwards in such sort that 
any one spoke, s E, shifts to the position S 5 E 5 in eight 
sidereal years less the time occupied by the earth 
in moving over e 5 e, or about 2*449 days. This 
shift of position amounts to rather less than 2° 25' ; 
but as the transit regions are themselves shifting back- 
wards at the rate of 20"'5 annually, or about 2£' in 
eight years, we have the shift of the conjunction-lines, 
with reference to the transit regions, equal to about 
2° 22' in eight years. 

Now let us suppose that the conjunction-line has 
at starting the position which it actually had on the 
occasion of the transit of the year 1631. Thus, let 
pp' (fig. 18) represent what may be called the December 
transit region, and q q' the June transit region, and let 
s v e, the first conjunction-line, fall so that E is the 
place of the earth on December 6. 1 The five next 
conjunction-lines have, as already shown, the positions 

v i e p v 2 E 2> y 3 E 3» v 4 E 4> an d v 5 E 5 ? and we see that e 5 
being 2° 22' from e, while pp' is an arc of nearly 3|°, 
e 5 falls within p p , and there is again a transit, on or 

1 Iu the seventeenth century, but corresponding to her position on 
December 9 in the nineteenth century. 



I 10 



TRASS-ITS OF VEKUS. 



about December 4. 1 This corresponds to the transit of 
1639. The next five conjunctions take place indue 




Fig. 18.- Illustrating the regression of the conjunction-lines over a 

transit region {pp'). 

order on the lines marked 6, 7, 8, 9, &c. We see, then, 
that there will be no December transits, that is, no 
conjunction within the arc p ;/, until the gradual 
advance of the conjunction-line E 2 v 2 has carried it by 
eight yearly steps to the transit region pp'. This 
manifestly requires as many eight-yearly intervals as 
2° 22' is contained in the arc Ej E 2 , or roughly the 
fifth part of the complete circuit ; or, in other words, we 
must multiply 30f by 8 to obtain roughly the number 

1 In the seventeenth century, or about December 6 in the nineteenth. 



OF TRANSITS AND THEIR CONDITIONS. Ill 

of years. This gives 243 as the nearest whole number 
of years ; and this, it will be noted, is the interval 
from the December transit of 1631 to the next 
December transit of 1874, or from the June transit of 
1761 to the next June transit of 2004. But we see 
that while the conjunction-line E 2 v 2 is travelling by 
eight yearly steps to the transit region p ]/, the con- 
junction-line e, v, will have travelled by similar steps 
to the position E 4 v 4 , passing over the transit region 
q q ' , and giving therefore two June transits in the 
middle of the period of 243 years. 

And here, for the first time we have to note the 
effects of the slight eccentricity of the orbits of the 
earth and Venus. If the two paths were concen- 
tric circles their centre being the sun, the conjunction- 
lines would be distributed with perfect uniformity, 
so that the arcs E E 2 , e 2 e 4 , e 4 e,, e, e 3 , and e 3 e. 
would be exactly equal; but owing to the eccen- 
tricity of the orbits, and the consequent variation 
in the motions of both Venus and the earth, this 
uniformity does not hold. The five arcs just named, 
or others similarly formed from any other conjunction 
as a starting-point, are slightly different in length . 
being largest always when the earth's orbit npproaches 
nearest, to that of Venus, so that the angular motions 
of the two bodies around the sun differ least, and 
smallest where the orbits are farthest apart so that the 
angular motions of the two bodies differ most.' 

1 Anything like an exact discussion of the varying relative motions 



I 1 2 TRANSITS OF VENUS. 

At the present time, for instance, the conjunction- 
lines have such positions as are indicated in fig. 19, 

of Venus and the earth -would be altogether out of place in a work of 
this nature. Let it suffice here to note the following values : — 

The Earth Venus 

O I It O I II 

Maximum daily motion . . 1 1 10 1 37 30 
Mean „ ,, . . 59 9 1 36 8 

Minimum „ „ . . ,57 11 1 34 52 

Now, the perihelion of Venus is in longitude about I24j°, the perihelion 
of the earth in longitude about 99^°, or nearly 25° behind. As the eccen • 
tricity of the earth's orbit is greatest, being nearly twice that of Vcnus's 
orbit (if measured in miles, still greater), we should not be far wrong 
in biking the earth's perihelion for the point of nearest approach to the 
orbit of Venus ; but inasmuch as opposite this point Venus is approaching 
perihelion, we somewhat diminish the longitude to obtain the actual 
point of nearest approach, which will be in about 70° of longitude, or at 
the place occupied by the earth on or about December 2. Here the 
daily motion of the earth is about 1° 0' 56", that of Venus about 
1° 36' 49", the excess of the motion of Venus in longitude being there- 
fore 35' 44". [When the earth is in longitude 90° her mean daily motion 
is about 1° 1' 7'5'', that of Venus in the same longitude being about 
1° 37' 0'5", an excess of 35' 53"; so that the daily motions are not so 
nearly equal as in longitude 70°. In fact, it chances that' the motions 
of Venus and the earth in conjunction are nearest to equality almost, at 
the time corresponding to a December transit.] Now, at the opposite 
part of the two orbits, or in longitude about 250°. we have the earth's 
daily motion about 57' 29'', that of Venus 1° 35' 19", an excess of about 
37' 50", or more by about 2' 6" than that in longitude 70°. It follows 
necessarily that successive conjunction lines (after successive tight- 
yearly periods) fall nearer together in the June part of the orbits than 
in the December part. For the exact eight years which carry the earth 
from position e (fig. 15), to position e again soon after conjunction at e 5 
with Venus at V 5 , correspond to thirteen complete revolutions of Venus 
plus 0'955days, wherever e may be. Now let a be the place reached by 
Venus when the earth is at e, then v v is the space traversed by Venus in 
0955 days. But v v also measures the gain of Venus on the earth, while 
the earth has been passing from e 5 to e. Now, in longitude 70°, Venus, 
being nearer her perihelion, moves faster than in longitude 253° ; hence 
on this account the arc v v will be greater for a December conjunction 
than for a June one. Since, then, the gain v v of Venus is greater at a 



OF TRANSITS AND THEIR CONDITIONS. 113 

where the eccentricities of the two orbits are properly 
shown, and the conjunction-lines are placed in longitude 

December conjunction than at a June one, while yet it accrues at a less 
rate as we have seen above, it follows that it requires a longer time to 
accrue : in other words, the arc corresponding to k 5 e requires a longer 
time, and if the earth moved uniformly would be a longer arc at a 
December conjunction than at a June one. But the earth is moving 
faster in December than in June ; a fortiori therefore the arc corre- 
sponding to ee 5 will be greater for a December than for a June conjunc- 
tion. Thus is explained the greater distance between the transit lines 
of a December pair than between the corresponding lines of a June pair. 
See Plate I. To further illustrate this, and also to make this reasoning 
more directly applicable to the subject-matter of this chapter, I will 
now proceed to calculate the actual displacement of the conjunction-line 
in eight years, for the two transit regions respectively. 

Suppose a conjunction to occur on or about { j « f • Then 

in eight sidereal years from this conjunction the earth has gone eight 
times round, while Venus has gone round thirteen times plus her motion 

in 0955 d. This motion takes place at the daily Fate of < 100.-/10//}-. 

r 554 1 // 1 
and therefore places Venus in advance of the earth by < ,-j.-f!// / '> 

i.i j -i • c v f2H7"1 • t • 1 ("2-582 ~l 

and the daily gam of Venus, or < 2 9«q" ( ls contained < .,.,,.- > 

{5544' "\ 
,.„„>. Therefore conjunction must have occurred 

f 2-582 (H ,. „ ., • 1 -i t - • ("3950" 1 

1 9-j.rr / f ear l ler ! or smce the earths daily motion is < „,,,„ [> 

f 2° 37' 26" 1 
conjunction must have occurred < " -<,/ yi \ m longitudo behind the 

conjunction-line of the earlier transit. Diminishing each arc by 2|' for 

the change of the nodal line in eight years, we obtain a motion (witli 

f 2° 35' "i 
respect to the node) of about < J ,., >, — near enough for our presen^ 

purpose. 

In the above, no account is taken of perturbations of the motions of 
Venus and the earth by the other planets. 

It will be convenient to add here a more exact ealcu'ation of the 
transit arcs p p' and qq', fig. 16. We may follow the same plan as at 
page 107. 

I 



114 TRANSITS OF VENUS. 

3°, 77°, 155°, 225°, and 292°, which correspond, nearly 
enough for our purpose, to the inferior conjunctions of 

We have, — the distance of Venus from sun at < -, 1 ° > node 

^descending J 

is < ««"„„', \ nn > miles (-where the earth's mean distance is taken as 
^oo,394.000j 

91,430,000 miles), and the earth's distance in the same longitudes respec- 
tively is < n.> 017 ooo f m ^ es ! so that the distance of the earth from 
Venus at conjunctiou is respectively < ~„ ' „„ " \ miles; and diminish- 
ing the sun's radius (which here for greater exactitude we take at 426,450, 
its true value if sun's mean distance be 91,430,000 miles) in the ratio 

J"24,171,000: 65.865,000 1 Ui .. • f ,, ,».. ,. 

1 26,423:000: 66,394,000 j ' We obtain for the dlstance correspondmg 

to ec and Ee' fig. 17 the value < .„„'»„» > miles; and it thence follows 

^e = e/= 156,500 cosec (3° 23J') = 2,645,300 miles 
that 2 e' = e'5'=169.720 cosec (3° 23*-') = 2,868,700 miles 

while the arc-measure of me, or €—, is equal to 1° 41', so that pp' is an 

e s 

arc of 3° 22'; 

o k' 
and the arc-measure of q e', or Y -, is equal to 1° 46', so that q q' is an 

e' s 

arc of 3° 32'. 

These values are for the centres of Venus and the earth. It would 
be easy, but is scarcely worth while, to calculate them for exterior or 
interior contact, and for the whole earth,— that is, to determine the arc 
fp' or q q' for the extreme cases where if any part of Venus be seen on 
the sun's, disc from any part of the earth, a transit shall be considered to 
have taken place, or where no transit shall be considered to have taken 
place unless the whole of Venus be seen within the sun's disc even from 
the station which throws her farthest from the sun's centre at the moment 
of nearest approach. Into such niceties, however, we need not here 
enter, as they are merely questions of curiosity, and neither present any 
difficulty nor involve any important principle. 

It will be seen that since at two successive conjunctions near 
December 7, the conjunction-lines are separated by 2° 37' 26" (or about 
2° 35' measuring from the node), while the transit arc is about 3° 22' in 
range, whereas at two successive conjunctions near Juno 5, the conjunc- 
tion-lines are separated by oi_ly 2° 18' 1'' (or about 2° 15' measuring 



OF TRANSITS AND THEIR CONDITIONS. I 1 5 

Venus on the dates, September 26, 1871, December 9, 
1874, February 24, 1870, May 5, 1873, and July 14, 
1876. Now it is clear that the conjunction-line v 5 e, is 




Fig. 19. — Showing the actual position of conj unction-lines of the earth 

and Venus. 

farther from the nodal line v' e' than is the. conjunction- 
line v 3 e 3 . In fact the longitude of v', the node, is 
about 255^° ; and v 3 is only 30^° or so from the node, 
while V 5 is about 36^° from the node. Hence the con- 
junction-line V 5 E 5 will take longer, in marching up by 
eight yearly steps to v', than the half of the period of 243 
years, which is the time in which it comes up to the 

from the node), and the transit are lias a range of 3° 32', there is a much 
greater chance of a pair of transits when the conjunction -line is sweeping 
over the June transit-region, than when it is sweeping over the December 

transit-region. 

i 2 



Il6 TRANSITS OF VENUS. 

position v 3 e 3 . We need not enter here into the calcula- 
tions by which the exact time occupied in each part of 
the progression is determined. Let it suffice that the 
considerations just adduced serve to explain how it is 
that from June 1761 the epoch of the first transit 
of tli/e last pair, to December 1874 the epoch of the 
first transit of this century's pair, is a period of only 
113^ years, whereas from December 1874 to June 
2004 the epoch of the first transit of the next pair, 
is a period of 129^ years. The former is the time 
occupied by the conjunction-line in moving from the 
node v' to the position v 3 , when of course the other 
conjunction-lines have the position shown in fig. 19, 
and December transits occur ; while the latter is the 
longer time occupied by the conjunction-line V 5 E 5 
in moving up to v' e'. The sum of the two periods 
1 13^ and 129^ is the period 243, just mentioned as 
that which separates two first transits either of a June 
pair or of a December pair. It is clear that if we 
fetart from the first of a June pair, we have the following 
intervals between successive transits: 8 years, 105^ 
years (8 from 113^ years), 8 years, \2\\ years (8 from 
129^ years), and so on continually in the order 8, 105^, 
8, 121^, so long as there is no break on account of a 
single transit occurring instead of a pair. This can 
manifestly happen, both at the December region and at 
the June region, though more readily at the former 
than at the latter. The conjunction-line steps back (so 
to speak) over the December region by steps of about 
2° 35' (see note, p. 113), and this region is about 3° 22' 



OF TRANSITS AND THEIR CONDITIONS. 11/ 

in width ; so that if the first step falls on the beginning 
of the interval or within 45' of it, the next will fall 
within the transit region, and there will be two transits • 
but if the first falls anywhere between 45' and 2° 35' of 
the beo-innins of the transit region the next will fall 
outside. The number of occurrences of a pair of transits 
in the December region will therefore bear to the 
number of occurrences of but one transit, the propor- 
tion which 45' bears to 1° 50', or which 9 bears to 22. 
That is, on the average of a great number, there will 
ofrener be one transit only in the December region 
than a pair. Applying the same reasoning to the 
June period, we have (see note, p. 113) 2° 15' for the 
regression and 3° 32' for the width of the transit-region, 
giving; 7n' favourable for the occurrence of a pair of 
transits, and 58' for the occurrence of but one. Hence, 
on the average of a great number of cases of June 
transits there will be a pair oftener than a single 
transit, in about the proportion of 77 to 58., or nearly 
as 4 to 3. 

It chances, however, that the interval between one 
December set and the next, or between one June set 
and the next, so nearly reproduces the same exnct 
circumstances, that when a pair of transits has occurred 
in one instance it is almost certain that on the next 
occasion there will be a pair also. Accordingly, for 
many successive passages of the December transit- 
region, and for a yet greater number of successive 
passages of the June transit-region, there will be a pair 
of transits at each passage. Then will follow long 



n8 



TRANSITS OF VENUS. 



intervals during which each passage will bring but a 
single transit. The series 8, 105^, 8, 121^,8, &c. will 
then be modified into the series 113^, 12JH, 113^, &c. 
But various other modifications occur in the course of 
long periods of time. Thus the triplet of intervals 
105i, 8, 12H, in the complete series may be changed 
either into the pair 113^, 121^, or into the pair I05i, 
129^; while the triplet 12H, 8, 105^, may be changed 
either into the pair 12H, 105^, or into 12H, 1131, 
according to circumstances. 

So much for the order in which transits recur, 
either at the ascending node in December or at the 
descending node in June. Let us now consider how 
stations are selected for applying the various methods 
which are available. 

Let s, fig. 20, represent the sun, and v Venus, 
the arrows showing the direction in which Venus 




Fig. 20. — Illustrating Venus' s shadow-cone. 

and the earth are travelling around s. Let svjd 
represent the Venus-cai-ried pointer of which we have 
already made frequent use, its extremity ]> being in 
the figure rather above the earth's orbit, and travelling 
inwards with the excess of Venus's motion, so as to 
overtake the earth. Now let a cone, having the centre 



I'LATE X. 




Fig. 22, Ingress 1631 and 1874. Fig. 23, Egress 1031 and 1874. 



* l 9 2 ^- 



riy ar, 



/dm- ~'e. 






w 



\ Fij.2* 



Fig. 25, Ingress 1639 and 1882. Fig. 26, Egress 1639 and 1882. 

Illustrating Passage of Vexus's Shadow-conk over Earth in 
1631, 1639, 1874, AND 1882. 



OF TRANSITS AND THEIR CONDITIONS. 119 

of Venus, v, for its vertex, and s v for its axis, be 
supposed to envelope the sun after the manner shown 
by the section s v s' in the figure, and let the prolonga- 
tion of this cone beyond v, be vv v, v v being a 
circular section through /;. Then we may regard this 
circular section (which corresponds to e e' in fig. 17) 
as travelling onwards like a gigantic wheel more than 
300,000 miles in diameter, to overtake E ; and if v is 
near enough to a node, then will this great circle pass 
athwart e in such sort that E will traverse a chord of 
the circle v v'. Let us try to picture such a passage. 
Suppose v to be near an ascending node so that the 
circle v v' as it overtakes E has a slight upward motion : 
also if we are looking from s towards e (and v v' were 
a real circular outline) we should see v v moving from 
right to left to overtake e. It will be convenient to 
regard E as at rest so that we consider only the excess 
of the motion of v v over that of the advancing 
earth. 

In fig. 21, Plate X., v 1 v' represent the circle v v' 
of fig, 20 on an enlarged scale at the moment when 
the earth e e' is first touched at the point i. At this 
moment an observer at i will of course see the centre 
of Venus just crossing the edge of the sun. (This is 
manifest from fig. 20, where we see that a line drawn 
to v from any point, as i, fig. 21, on the surface of the 
cone v v v' will touch the globe ss'.) To an observer 
at i then, but to no one else on the earth e e' ', transit 
will have begun (reference being always made to the 
centre of Venus). 



120 . TRANSITS OF VENUS. 

The centre of v v' advancing from P, to p 2 , the 
circular section reaches the position v i' v' touching the 
earth at i'. Its edge has all this time been passing 
over the face of the earth ee, moving nearly parallel 
to itself ; and transit has now begun for every part of 
the illuminated hemisphere of the earth. So that i' is 
the place on the earth where transit begins latest. We 
have then i the place of earliest beginning (or, as it is 
technically called, the pole of accelerated ingress), and /' 
the place of latest beginning (or the pole of retarded 
ingress). The points i and i' are not exactly opposite 
each other even on the circle e e' , x still less are they 
exactly opposite points on the globe e e' ' , which has 
been rotating all the time that the centre of v v' has 
occupied in advancing from P 1 to P 2 , a process lasting 
several minutes (more than 25 m. for instance in the 
transit of 1874, and 17 m. in the transit of 1882), 

Still, as a first approximation, we may consider the 
points i and i' to be at opposite extremities of a 
diameter of the earth, taking (in order to reduce errors 
as much as possible), the face of the earth turned sun- 
wards when the advancing edge of v v' crosses the 
centre of the earth's disc, and taking that diameter i i' 
of the earth which is at right angles to the advancing 
edge in this intermediate position. With this assump- 
tion, the passage of the edge of the circle v v' over the 

1 For a tangent to v I v' at i is not parallel to a tangent to v i' v' at i', 
whereas tangents at the extremity of any diameter of a circle are neces- 
sarily parallel. (In fig. 22, the tangents at i andi', are taken parallel to 
a tangent to the circle v v' at the point where, and at the time when, its 
edge crosses the centre of the disc t i' of fig. 21.) 



OF TRANSITS AND THEIR CONDITIONS. 12 r 

earth's face is illustrated by fig. 22 (Plate X.) which 
represents on an enlarged scale the disc i i' of fig. 2 1 , 
the edge of the circular shadow being represented in 
ten successive stages of its (supposed ) uniform advance. 
The earth is shown in the proper position for a 
December transit. Nothing can be easier than to 
determine the position of i and i', the poles of ac- 
celerated and retarded ingress. For all the circum- 
stances of the motion of Venus are known, whence the 
motion of the projection of her centre along p, p 2 P 3 v t 
is determined. With reference to the earth e e' we 
know also what face of the earth is turned sunwards 
at the moment when the section v v' crosses the centre 
of the earth's disc. The size of the section v v' is also 
known (see note at p. 1 14 Avhere it is calculated both for 
December and June transits), except of course in so far 
as it depends on the more exact determination of the 
sun's distance. And indeed, we see from this in a 
new way, how the circumstances of the transit as 
viewed at different stations depend on the distance of 
the sun, and therefore conversely how our estimate 
of the sun's distance depends on the circumstances of 
the transit as viewed at different stations. For while 
the disc ee'of the earth has a known diameter of 
about 7,900 miles, and the section v v has the posi- 
tion and path of its centre along r, p 4 determinable 
independently of the sun's distance, the size of the 
section (as we see from the note, p. 114) depends on 
the sun's distance and size. Now if we enlarge or 
diminish v v\ while leaving ee unchanged in position, 



122 TRANSITS OF VENUS. 

and the motion of the centre of v v along p.p. also 
unchanged, we manifestly modify the nature of the 
passage of the edge of v v' over the disc e e . 

The section v v' passing on, arrives at length at the 
position v e \' touching the disc of the earth at e. At 
this moment the centre of Venus is seen, by the observer 
at e, on the edge of the sun ; in other words, egress 
(of the centre of Venus) is taking place, and e is the 
station where egress is first seen. The section v v' 
passes on until it has the position v e' v', when it is 
about to leave the earth finally, its last contact with 
the earth being at e' — where egress takes place latest. 
In the interval the edge of v v' has been passing over 
the disc e e' , moving nearly parallel to itself: we 
have then e the pole of accelerated egress and e the 
pole of retarded egress. As in the case of ingress, e 
is not exactly opposite to e even on the circle e e ', 
while rotation has affected the globe e e , so that e is 
still farther from being opposite to e' on the earth. 

We may, however, in this as in the former case, 
regard (for a first approximation) e and e' as points on 
opposite extremities of a diameter of the earth, taking 
the moment intermediate between earliest and latest 
egress. With this assumption, the passage of the edge 
of the cii'de v v' across the earth's face is illustrated 
by fig. 25 (Plate X.), which represents the disc e e' of 
fig. 21 on an enlarged scale, the edge of the circular 
shadow being shown in ten successive stages of its 
supposed uniform retreat. The earth is shown in the 
proper position for a December transit. 



OF TRANSITS AND THEIR CONDITIONS. 12$ 

It need hardly be said that the face of the earth 
turned sunwards when the section v v' has advanced 
to the position v V / is greatly changed from the face 
which had been turned sunwards when ingress was in 
progress. But the time of egress is easily calculable, 
like that of ingress, from the known motions of Venus 
and the earth ; the face of the earth turned sunwards is 
also known ; and all the circumstances of the passage 
of the edire of v v' over the earth's face at egress are 
easily determined. In fact, all that was said respecting 
ingress is true, mutatis mutandis, in the case of egress. 

The conditions represented in fig. 21 are actually 
those of the transit of 1874. The shadow-cone of 
Venus passes slantingly upwards with reference to 
the earth, and the centre of the circular section v v* 
passes north of the earth. The earth passes, therefore, 
through the shadow section as along the dotted line, 
in the manner shown farther on in fig. 35. But the 
conditions of the transit of 1631 so nearly resembled 
those of the coming transit that fig. 21 conveniently 
illusti'ates both transits. 

In order to more thoroughly master the above 
reasoning, the reader would do well to run over it 
again, using figs. 24, 25, and 26, instead of figs. 21, 
22, and 23 respectively. Fig. 24, with its companion 
projections, illustrates the transit of 1882 (and approx- 
imately also the transit of 1639). See also fig. 35. 

Then the reader can apply the explanation given 
above, with very slight changes, to the case of June 
transits, illustrated by fig. 27. Figs. 28 and 29 are 



124 



TRANSITS OF VENUS. 



the companion June projections of the earth for the 
earlier of a pair of June transits (as the transits of 
1761 and 2004), while figs. 30 and 31 are the com- 



/if ,1 ^ 



2^m? 



£>7 * 



«S~*~ / 




/ ?^ 



*£-#PC 






Fiy.27. 



<oi?-' n 



Fig. 27- — Illustrating the passage of Venue's shadow-cone over the earth 
during the transits of 1761, 1769. 2004, and 2012. 

Fig. 28.— Ingress, 1761 and 2004. Fig. 29.— Egress, 1761 and 2004. 

Fig. 30.— I"g.e>s. 1769 and 2012. Fig. 31.— Egress, 1769 and 2012. 

panion projections for the later of a pair of June 
transits (as the transits of 1769 and 2012). Moreover 
it chances, so neai-ly similar in position are the northern 
and southern transit chords for the four transits just 



PLATE XL 




TRANSITS OF 1874 AND 1882. 



Illustrating internal contacts and mid-transit, and showing relative 
dimensions of the discs of venus and the sun. 



OF TRANSITS AND THEIR CONDITIONS. 1 25 

named, that one and the same figure illustrates all four 
with sufficient approximation for illustrative purposes. 

Now it is easy to see how Delislean stations are to 
be selected in any given case. Take the transit of 
1874. We find first the hours at which the circle v 0' 
(fig. 21) crosses the centre of the disc of the earth 
i e i' e' at the beginning and end of the transit, or, 
which is precisely the same thing, the moment when 
the centre of Venus, as seen from the earth's centre, 
reaches the positions b and U , Plate XI. This is in 
point of fact the ' calculation of the transit,' and de- 
pends on principles corresponding to those involved in 
the calculation of an eclipse. Having these two 
epochs of the beginning and end of transit, and also 
the positions of the transit chord b V Plate XL, and 
a b of fig. 21 Plate X., we make a sun-view of the 
earth at the beginning of the transit as Plate XII., 
and another of the earth at the end of the transit as 
Plate XIII. (Plates XII. and XIII. really represent 
the aspect of the earth for the times of internal con- 
tact — illustrated in Plate XI. — at the beginning and 
end of transit, but they sufficiently illustrate the present 
description). 

Then the positions of the points i and t fig. 21, 
Plate X. are known at once, from the geometrical 
relations pictured in fig. 21, 1 and thus we have the 
poles of accelerated and retarded ingress placed as i 
and i' in fig. 22, Plate X., or as a and B in Plate 

1 Of course the vertical line xs in figs. 21, 21, and 27, represents 

north an 1 houtli line of tlio earth's disc 1 e I' c'. 



126 TRANSITS OF VUXUS. 

XII. , these positions being the same, it will be observed, 
as the positions of i and i' on the small disc i e i t 
of fig. 21. The observers of the accelerated ingress 
must be near i on the illuminated hemisphere it', fig. 
22, while the observers of retarded ingress must be 
near i'. The amount of acceleration or retardation 
will depend on the distance from c c ', a station at anv 
point in any one of the parallels in fig. 22 having 
equal acceleration or retardation (according as the 
parallel is nearer i or i'). The parallel lines of the 
figure are of course circles on the globe of the earth ; 
and i and i' are the poles of these circles. 1 

Again, the positions of the points e and e' , fig. 21, 
Plate X., are known ; and thus we have the poles of 
accelerated and retarded egress placed as e and e in 
fig. 23, Plate X., or as C and D in Plate XI I L, these 
positions being the same as those of e and e in the 
small disc ieie of nV. 21. The observers of the 
accelerated egress must be placed near e on the illu- 
minated hemisphere e e' fig. 23, while the observers 
of retarded egress must be placed near e. The amount 
of acceleration or retardation will depend on the dis- 
tance from c c , a station at any point on any one of 
the parallels of fig. 23 having equal acceleration or 
retardation (according as the parallel is nearer e or e ). 

1 The acceleration or retardation at a station for observing ingress 
manifestly varies as the distance of the station from the plane of the 
great circle having i and i' as poles ; and similarly for retarded ingress, 
and for aeceleratod and retarded egress. Or in other words, the accele- 
ration or retardation varies as the cosine of the arc-distances from i or /" 
i or e. 



PLATE XII. 




Sun-view of the Earth at the Beginning of the Transit of 1874. 



1. Station at Hawaii. 

2. „ „ Kergut-len Island. 

3. ,, „ Rodriguez. 

4. „ ,, New Zealand. 

6. „ „ Nertschinsk. 

7. „ (proposed only) at Possession Island. 

8. „ ., Mauritius. 

9. ,, in North China. 



PLATE X1U. 




Sun-view of the Earth at the End ov the Transit of 1374. 



2. Station at Kereuelen Land. 


3. , 


, „ Rodriguez. 


4. , 


, in New Zealand. 


5. , 


, at Alexandria. 


8. , 


, „ Nertschinslc. 


7. 


, (proposed only) at Possession Island. 


8. , 


, „ Mauritius. 


9. , 


in North China. 



lu. The North Indian Region (now occupied). 



. 



PLATE XIV. 




Sux-view of the Earth at the Beginxixg op the Trasht of 1882. 



1 . Sir G. Airy's proposed station at Repulse Bay. 

2. „ „ on Possession Island. 



PLATE XV. 




Sun-view of the Eaktu at the End op the Transit of 1882. 



1. Sir G. Airy's proposed station at Repulse Bay. 

2 - » »> on Possession Island. 



OF TRANSITS AND THEIR CONDITIONS. 1 27 

These parallel lines of the figure are circles on the 
|lobe of the earth, and e and e' are the poles of these 
•ircles. 

Similar remarks apply to the case of the transit of 
J882, illustrated by figs. 24, 25, and 26, Plate X., and 
By Plates XIV. and XV. The reader is recom- 
mended to go over the last three paragraphs afresh, 
■sing these last-named figures and plates. 

It is easily seen that Delisle's method is applicable 
in every possible case. The poles of accelerated and 
Itarded ingress and egress lie always (as i, i' , e, and e) 
it the edge of the illuminated hemisphere, and stations 
fcn always be found near to these points, and in sun- 
light. Xor do the conditions of success depend at all 
Ibon the position of the chord of transit. We see 
ndeed that in the case of a short chord as in fio-. 21 
ie difference of time between ingress at i and i', or 
press at e and e, is greater than in the case of a longer 
&ord as in fig. 24 ; for p, p 2 and p 3 p 4 are greater in 
ig. 21 than in fig. 24. But it is easily seen that this 
^vantage in the case of the shorter chord is counter- 
ialanced by the slowness with which Venus crosses 
be sun's edge. 1 Of course the more slowly Venus seems 
) cross the sun's edge the more difficult it is to deter- 
dne the true moment of contact whether at ingress or 
gress, complicated as contact is by the phenomena of 
lack-drop formation. 

y Plate XI. shows us that from b to the centre of Verius's disc at ?is 
later than from s to the centre of her disc at 1'. I„ fact this slowness 
crossing corresponds exactly to the lengthening of the distances .• , 



128 TRANSITS OF VEXUS. 

Delisle's method is then always applicable, ai 
always under similar conditions. It is otherwise wi 
Halley's method. Let us briefly consider this meth 
in the approximate manner already used for Delisl 

method. 

To apply Halley's method both the beginning a 

end of transit must be seen. Now i ?*, fig. 22, & 

enlarged into a sun-view of the earth as in Plate X. 

(for the case of the transit of 1874), shows the face 

the earth in sunlight when transit begins, while e 

fig. 23, similarly enlarged, shows the face of the eai 

in sunlight when transit ends. We must select statio 

common to both these projections or sun-views of t 

earth in the case of any transit we are dealing wi 

For example, in the case of the transit of 1874, we s 

that such a station as 1, near A in Plate XII. (one 

the Sandwich Islands), though excellent for observi 

the beginning of the transit by Delisle's method, coi 

not be employed for Halley's, because this station h 

akeady passed to the dark side (in other words, the s 

has set there) before the end of the transit when i 

face of the earth pictured in Plate XIII. was turr 

sunwards. Again, the station marked 5 in Plate XI 

(Alexandria) was an excellent station for seeing the e 

of the transit by Delisle's method, but it could not 

employed for Halley's, because it was on the dark s 

of the earth (in other words, the sun had not risen), 

the beginning of the transit, when the face of the ea 

pictured in Plate XII. was turned sunwards. But 

any station in Australia, for example, the whole tran 



OF TRANSITS AND THEIR CONDITIONS. 12 9 

could be seen, and therefore Halley's method could be 
employed there so far as visibility of transit was con- 
cerned. It remained, however, to select among stations 
where both the beginning and end could be seen, those 
particular stations where the transit was considerably 
lengthened and shortened in duration compared with 
the mean transit (transit of Venus's centre supposed 
to be seen from the earth's centre). I„ the case of 
Delisle s method, whether applied to ingress or to egress 
we had two poles {i and i> for ingress, , and ,' for 
egress), and could estimate the value of any station 
at once by referring its position to these poles. 

We have now to inquire whether there are an y 
corresponding Halleyan poles-a pole of lengthened 
duration, and another pole of shortened duration. I 
believe Encke was the first to point out that there are 
such poles, and. to give an analytical proof of the fact ■ 
but the following simple geometrical demonstration is' 
so tar as I know, original. 1 

The parallel lines across the disc of the earth in 
fag. 22, represent circles on the earth having i, i< as 

1 Prof. Adams mentioned the fact that <-W» l 

indicated their position, at a meeting o the Is! , T "' "* 

-hich I was present-March 1873 if f ^n , ^f ™ 1 Societ J at 

to him a da / or twoafter tl t z£szsz sffiu : ub d mit ; ed 

reply he remarked that the demonstration J 1 ' W h,S 



K 



130 TRANSITS OF VENUS. 

poles, and corresponding to times of ingress successively 
later and later, by equal intervals, as the parallel is 
farther and farther from i. Now if we suppose the 
o-lobe of the earth rotated about an axis it, these 
parallel circles will still appear as parallel and equi- 
distant straight lines. In fact, so long as the points 
i and f are on the edge of the visible disc the parallel 
circles will appear as equidistant parallel lines. Similar 
remarks apply to the parallels in fig. 23 ; so long as e 
and e are on the edge of the visible disc these parallel 
circles will appear as parallel and equidistant lines. Let 
us suppose, then, that the globe of the earth is so placed 
with respect to the observer that all four points i, i , 
e, and e' are on the circumference of the visible disc. 
This is clearly possible, for i i' are extremities of one 
diameter, e e those of another diameter of the sphere, 
and any two diameters must lie in one plane, which 
plane intersects the sphere in a great circle ; so that we 
have only to place the sphere so that this great circle 
shall form its apparent outline, to have i, i' , e, and e' 
(the extremities of two diameters of this great circle) 
on the outline of the visible disc. 

Now let fig. 32 represent on an enlarged scale the 
face of the globe thus brought into view, i a and I,, 
corresponding to the points i and i' , while E a and E 
correspond to the points e and e'. Also the number 
of parallels has been doubled to make the illustration 
more complete, the maximum accaleration and retard- 
ation at ingress and egress being divided into ten 
equal parts corresponding to the ten equal spaces on 



OF TRANSITS AND THEIR CONDITIONS. 131 

either side of the lines e e' and c c' . For convenience 
of explanation this maximum is regarded as 10 minutes, 
which is a little short of its value in the transit of 1874 
and a little in excess of its value in the transit of 1882. 
Now consider any point n where a parallel of one 
system crosses a parallel of tire other system. Since 
a lies on the fourth parallel from cc' towards j a , the 




Fig. 32. -Illustrating the position of the Halleyan polos botweon the 

Delislean poles. 

ingress is accelerated by 4 minutes, and since a lies on 
the third parallel from c<f towards e„ the egress is 
retarded by 3 minutes. On the whole, therefore, the 
duration of the transit at a is 7 minutes greater than 
the mean. At the point I, where the next parallel 
from i a and the next toward* E r intersect, ing-ss is 

K 2 



132 TBANS1TS OF VENUS. 

accelerated 3 minutes, and egress is retarded 4 minutes ; 
so that the duration here, as at a, is 7 minutes greater 
than the mean. At the point m the ingress is accele- 
rated 5 minutes, and egress retarded 2 minutes ; so that 
at m also duration is lengthened 7 minutes. The same 
is the case at n. These points m, a, b, and n, lie mani- 
festly on a straight line which produced either way 
to k and k' passes through other points of intersection 
of our two systems of parallels, at which points, by the 
method of reasoning already applied to a, b, m, and n, 
the duration is lengthened by the same number of 
minutes. At e, the lengthening is similarly shown to 
be 8 minutes, and the same at all points on the line 
/ e V. At d, the lengthening amounts to 6 minutes, and 
the same at all points on the line j ef. Along coc' 
the duration has its mean value. And at any point 
on jj', k k', or IT, on the other side of coc, the 
transit is shortened by six, seven, or eight minutes, 
respectively. So with other cases for all points over 
the disc c o c'. 

Now very little knowledge of geometry is required 
to show that these lines jf, hk r , IV, jj', k k', and 
1 T, and the other lines of fig. 32 similarly obtained, 
form a series of parallel equidistant lines ; these lines 
being parallel to CO c', the bisector of the angles 
E r o i r and i a OE a . These parallel lines are parallel 
circles on the sphere, having for poles the two points H! 
and ii s the middle points of the arcs I E r and i r E n . 
The farther one of the dotted parallels is from coc' 
towards Hi the greater is the lengthening of the transit, 



OF TRANSITS AND THEIR CONDITIONS. 133 

and the farther such a parallel is from coc towards 
H s the greater is the shortening of the transit. The 
absolute maximum duration is at H„ and the absolute 
minimum is at H s . These points, then, are the Hallevan 
poles, and any one of the parallel circles having these 
points as poles indicates the position of stations at 
which the lengthening or shortening is in proportion 
to the distance of the plane of the circle from the plane 
of the great circle C o c', towards h l or h s respectively. 
But while the Halleyan poles and circles corre- 
spond thus geometrically with the Delislean poles and 
circles, there is one important difference. A Delislean 
pole for any phase is a point where the sun can actually 
be seen at that phase. But this is not necessarily the 
case with a Halleyan pole. The northern Halleyan 
pole for example, in the transit of 1874, is, by Avhat 
has just been shown, the point midway between the 
a of Plate XII. and the d of Plate XIII. D beinsj 
still on the darkened side of the earth at the time 
pictured in Plate XII., and A having passed to the 
darkened side at the time pictured in Plate XIII., it 
is manifest that the middle point of an arc from d to 
a must also lie on the darkened side at both these 
epochs; and therefore the northern Halleyan pole, 
though geometrically the point where transit lasts 
longest, is in reality a point where neither the begin- 
ning nor the end of transit can be seen. On the other 
hand, the southern Halleyan pole in 1874, is in sun- 
light throughout the whole transit, as we see by notinu 
that the points B and c of Plates XII. and XIII. are 



134 TRANSITS OF VENUS. 

themselves in sunlight throughout the transit, and that 
therefore the point midway between them must be 
so. The relations here described are those illustrated 
in fig. 32, where the dark lune i q c J r represents a 
part of the eaith where the beginning of the transit 
is not seen, the dark lune E r c E a representing a 
part where the end is not seen, and ii[ lying on 
a part where these lunes overlap, on which therefore 
neither the becnnnino; nor end of the transit can be 
seen. 

The reader will find no difficulty in making a 
con*esponding construction to illustrate the transit of 
1882. In fact, so far as the parallels are concerned, 
fig. 32 will represent the case of the transit of 1882 
very nearly, for we see from Plates VI. and VII. that 
the distance between the two northern Delislean poles, 
and therefore between the two southern, is nearly the 
same in both transits — in other words, the arcs corre- 
sponding to i a E r , E a i r in fig. 32 are nearly right for the 
transit of 1882. But the darkened lunes must have 
the position they assume when fig. 32 is inverted ; for 
we see from Plates XIV. and XV. that while the 
northern Halleyan pole is in sunlight in 1882, the 
southern is on the darkened hemisphere. 

But besides that one Halleyan pole or the other is 
so placed that no part of the transit can be seen from 
it, the circumstances of different transits vary as re- 
spects the advantages offered by Halley's method. 

For example, take h s the accessible Halleyan pole 
in such a transit as that of 1874. We see that at this 



OF TRANSITS AND THEIR CONDITIONS. 1 35 

point the ingress is retarded and egress accelerated by 
the maximum acceleration or retardation, less only 
about If tenths, so that the shortening is less than the 
sum of the maximum acceleration and retardation by 
only 3^ tenths of either. But if E a and i r were farther 
apart the shortening of the transit would not be so 
great. This is seen from fig. 33, which illustrates the 




Fig. 33. — Illustrating a case unfavourable for Halley's method. 

conditions of the transits of 1761 and 2004. Here E a 
and i r are farther apart than i a and E r in fig. 32 ; the 
southern Halleyan pole H, is in this case the inaccessible 
one. We note first, that owing to the greater distance 
between i a and E r the point of nearest approach to the 
pole Hi is still a long way from that pole. Moreover, 
we see that at H g in fig. 33, the retardation of ingress 



136 TRANSITS OF VENUS. 

and the acceleration of egress are less than the maximum 
by 4^ tenths, so that the total shortening is less than 
the sum of the maximum acceleration and retardation 
by fully 9 tenths of either. If the interval in time 
corresponding to the space between successive parallels 
were 1 minute, as we before for convenience assumed 
it, then in the case illustrated by fig. 32, the total 
shortening at the sunlit Halleyan pole h s would 
amount to nearly 17 minutes, whereas in the case 
illustrated by fig. 33 the shortening at the sunlit 
Halleyan pole H a amounts to little more than 11 
minutes. 

Thus, apart from geographical considerations, which 
may in some cases be of paramount importance, the 
applicability of Halley's method depends principally 
on the arc-distance between the two Delislean poles in 
the northern hemisphere, which of course is equal to 
the distance between the Delislean poles in the southern 
hemisphere. 

This seen, it is easy to perceive that the first 
transit of a pair separated by eight years will be less 
suitable than the second. 

First take a pair of December transits like those 
of 1874 and 1882 — transits when Venus is at her 
ascending node. In this case the first transit always 
carries Venus north of the sun's centre, as along 
i> b' in Plate XI., while the second carries her south 
of the sun's centre as along s / ; for this being her 
ascending node, and the second transit finding her, as 
already explained, less advanced in her orbit, she is 



OF TRANSITS AND THEIR CONDITIONS. 1 37 

beyond her ascending node at the first transit and 
behind that point at the second transit — that is, in nortli 
latitude in the former case, and in south latitude in 
the latter. Accordingly, the centre of Venus's shadow- 
cone passes north of the earth as in fig. 21 in the case 
of the earlier transit of a pair at the ascending node, 
and south of the earth as in fig. 24 in the case of the 
later transit of such a pair. Thus the first contact is 
in the north-eastern quadrant as at i in fig. 22, and 
the last in the north-western as at e' fig. 23 ; and the 
point i on the earth having been carried round by the 
earth's rotation to the darkened side and (remembering 
the position of the earth's axis) on a course giving it 
a greater distance from e than it would have if the 
rotation were round an axis N s, we have the two 
Delis] ean poles farther apart than they would be but 
for the inclination of the earth's axis. Or we mio-ht 
have deduced the same result by considering the two 
poles i' , fig. 22, and e, fig. 23 ; for we see that the 
motion of i along its upward-bowed latitude-parallel 
is such as to give it a greater distance from e than it 
would have if the axis of rotation were n s. But in 
the case of the transit of 1882, we see that f, fig. 25, 
the place of second contact, is brought by rotation 
nearer to e, the place of third contact, 1 than it would be 
if the rotation were around an axis N s ; or Ave may 
infer the like by considering the relative motion of the 
northern Delislean poles i and e . 

1 The reader should note that the effects here considered depend 
entirely on the tilt of the earth's axis. 



138 TRANSITS OF VENUS. 

The position of the axis of rotation is then un- 
favourable to the earlier transit of a pair occurring in 
December. 

It will be easy for the student to apply similar 
reasoning to the case of transits occurring in June, as 
illustrated by figs. 27, 28, 29, 30, and 31 ; and it will 
be found in these cases also the rotation brings the 
Delislean poles (the northern pair or the southern pair) 
closer together, ccetcris paribus, in the case of the later 
transit of a pair than in the case of an earlier transit. ' 

But another circumstance clearly affects the dis- 
tance of the two northern, as of the two southern, 
Delislean poles. If the transit chord be short as in the 
case illustrated by fig. 21, the points i and e' (reference 
is now made to the small disc of fig. 21) will clearly 
be nearer together than where the transit chord is 
longer, as in the case illustrated by fig. 24 ; for the 
shorter the transit chord the greater is the angle 
enclosed between the intersecting arcs I i and e' e. 
Hence shortness of duration by tending to bring the 
two northern and the two southern Delislean poles 
close together renders a transit more favourable for 
the application of the method of duration. 

To see, lastly, how geographical considerations 
enter into the discussion of this problem, compare 
Plates VI. and VII., illustrating the transits of 1874 
and 1882. It will be seen that the northern or 

1 The same is proved in another way in ' The Universe and the 
Coming Transits," — see also pp. 158, 159 of the present -work; and in 
yet another way at pp. 38 and 39 of my treatise on the ' Sun." 



OF TRANSITS AND THEIR CONDITIONS. 1 39 

darkened Halleyan pole is nearly as far from the 
neighbouring sunlit region (for the whole transit) in the 
case of the former transit, as the southern darkened 
Halleyan pole is in the case of the latter transit. But 
the region where such approach would have had to be 
made in 1874 was altogether accessible, though doubt- 
less bleak and cheerless during the northern winter pre- 
vailing there when transit occurs ; whereas the sunlit 
region nearest to the southern Halleyan pole in 1882 
is the inaccessible antarctic continent. Keeping away 
from that continent and within the space defined by 
the lines a' b', c' d ', which show where the sun is ten 
degrees high at ingress or egress, there is absolutely no 
spot to be occupied which is near enough to h" to be 
worth the trouble of journeying thither. In both cases 
the region around the sunlit Halleyan pole affords many 
good stations, though the transit of 1874 was not in this 
respect comparable with that of 1882 ; but the absolute 
absence of any southern station whatever in 1882 
where the duration of transit is usefully lengthened, 
causes the method of durations to be wholly inap- 
plicable on that occasion. 

Thus far we have for simplicity considered the 
centre of Venus, or we may be said to have regarded 
Venus as a point. It is easy, however, to see what 
modifications are introduced when we take into account 
the fact that Venus is a globe. Thus, instead of a 
double cone, such as s s' v v v' in figr. 20, having the 
centre of Venus at its vertex, we must consider two 
double cones such as are shown in fig. 34, each 



140 TRANSITS OF VENUS. 

enveloping both Venus and the sun, but one having 
its vertex outside the path of Venus (giving the shaded 
cone of the figure) and the other having its vertex 
within the path of Venus. It is manifest that any 
observer on the surface of the last-named cone, as for 
example, at v , will see Venus touching the sun on the 
outside, i.e. in external contact; for the line of sight 
?/ v / touches both Venus and the sun, but on opposite 
sides, and is therefore directed to a point of contact on 
opposite sides of which the discs of Venus and the sun 
lie. On the other hand, an observer on the surface of 
the shaded cone, as on the prolongation of s v, will see 




Fig. 34. —Illustrating internal and external contacts. 

Venus just within the sun's disc, or in internal contact; 
for the line of sight touches both the sun and Venus 
on the same side, so that it is directed to a point of 
contact on the same side of which lie both the discs of 
Venus and of the sun. 

We see then that taking: the two concentric circular 
sections v v' fig. 34, we have only to substitute external 
contact and internal contact for what was said of the 
passage of the centre of Venus in the former case. 

In order, however, to still further familiarise the 
student with these fundamental relations, I shall give 



OF TRANSITS AND THEIR CONDITIONS. 141 

an independent description of the relations presented 
in fig. 34, modifying into a more convenient form the 
explanation of the actual circumstances of the passage 
of the section of Venus's shadow-cone (for so the v v' 
of both figs. 20 and 34 may be regarded) over the less 
swiftly advancing earth. 

If an observer were carried through the double 
cone shown in fig. 34 beyond Venus, he would see the 
following successive phenomena. When he came to 
the outer surface Venus would be in exterior contact ; 
as he passed on to the inner surface Venus would 
enter more and more on the sun's disc, until when he 
reached the surface she would be in interior contact. 
Then as he travelled on through the inner cone Venus 
Avould seem to cross the sun's disc, and she would just 
touch it on the inside when our observer reached the 
surface of this inner region on his passage outwards. 
Next, as he passed onwards to the surface of the outer 
region, Venus would be seen crossing the edge of the 
sun's disc. And lastly, as he passed that surface he 
would again see Venus in exterior contact, the transit 
thereupon coming to an end. 

During a transit of Venus the earth does actually 
pass in such a way through these regions ; or rather 
these regions overtake and pass over the earth. 

Since the cones overtake the earth in the direction 
shown by the arrows, we may consider that the earth 
passes through the cones in the contrary direction. 

Suppose v v' (fig. 35) to represent the same section 
of the outer cone as v v in fig. 34 ; v v' the section of 



142 



TZAXSlTS OF VEX VS. 



the inner cone; and E (fig. 35) the earth, as shown at 
E in fig. 34. Then v v' is really moving towards the 
left ; but we are to suppose that E is moving towards 
the right through v v\ Furthermore, if Venus is 
near an ascending node, as she will be during the ap- 
proaching transits, we must suppose the earth to pass 
descendingly along such a course as E E' through the 
region v v' . The actual course, both as respects posi- 




Fig. 35. — Illustrating internal and external contacts. 

tiou and direction, is determined from the calculated 
elements of the transit. With this calculation we 
need not here concern ourselves. 1 The figure shows 



1 As to the size of v v' and V v' compared with that of the earth, it is 
easily seen from fig. 34 that o v is greater and o v is less than the radius 
calculated in the note, p. 114, for the centre of Venus, by the radius of 
Venus increased in the proportion that the earth's distance from the sun 
exceeds the distance of Venus from the sun. 



OF TRANSITS AND THEIR CONDITIONS. 1 43 

the course actually traversed by the earth in 1874 and 
1882. 

Now, taking the earth through v 1/ for the 1874 
transit, let us consider the various critical points, so to 
speak, of her course. When she first touched the 
outer circle v v' external contact had begun at that 
point of the earth which first reached this circle. She 
passed on, falling more and more within vv , until she 
Avas just wholly within. All this time external contact 
was taking place wherever the outline v v' intersected 
the earth's disc ; at parts within that line Venus was 
seen partly within the sun's disc, and at parts outside 
of it external contact had not yet taken place. When 
the earth had passed wholly within the circle v v ', 
external contact had taken place at all parts of the 
visible hemisphere. But as at this time no part of the 
earth had reached the circle v v', 1 internal contact had 
nowhere commenced. In other words, Venus was not 
yet fully upon the sun's disc as seen from any part of 
the earth. 

Now, this part of the earth's motion is not illus- 
trated in fig. 35, because external contacts and the 
passage of Venus across the sun's outline are not 
phases to, which the observers of transits pay great 
attention. We now come to the important phases. 

1 Tho distance between the circles v v' and v v' is obviously greater 
than tho earth's diameter, if we consider how the two circles v v' and 
v v' are obtained. For the diameter of Venus is very nearly equal to 
tlie earth's ; so that the diverging lines from s or s' (fig. 34) are already 
separated at v by a distance nearly equal to the earth's diameter, and 
therefore at v or t/ are wider apart. 



144 TRANSITS OF VENUS. 

When the earth just reached the inner circle v v', 
interior contact had just begun at the point on the 
earth which first touched this circle. Here, then, 
earliest of all, internal contact began, and there oc- 
curred at this point the phenomenon called by astro- 
nomers first, internal contact most accelerated. The 
earth was then in the position numbered 1 in fig. 35. 

She passed on, the outline v v' encroaching more 
and more over her face until she was wholly within this 
outline or in position 2. All this time internal contact 
was taking place wherever the outline v v' intersected 
the earth's disc. At parts of the earth within that 
line internal contact had passed, or Venus was already 
fully upon the sun's disc. At parts of the earth out- 
side that line Venus still broke the outline of the 
sun's disc. When the earth was at 2, internal contact 
had taken place for all places on the earth's illuminated 
hemisphere. This contact took place latest of all at 
that point on the earth's surface which at this moment 
touched v v\ It was here, then, that there occurred 
the phase which astronomers call first internal contact 
most retarded. 

Then the earth passed onwards through the posi- 
tions shown severally along her track in fig. 35. 

As the earth passed out of the spaces v v', v v', 
similar phases occurred in reverse order. We need 
note only the positions numbered severally 14 and 15. 
The first shows where the earth first reached v v', and 
the point on her surface which first touched V v' is the 
place where occurred the phase called second internal 



OF TRANSITS AND THEIR CONDITIONS. 1 45 

contact most accelerated; while 15 shows where the 
earth just passed clear of v v', and the point on her 
surface which was the last to touch v v' was the place 
where the phase occurred called second internal contact 
most retarded. The circumstances of the progress of 
the earth from one position to the other precisely 
corresponded to those already considered in dealing 
with the earth's motion from 1 to 2, only they took 
place in reverse order. 

Plate XVI. illustrates the progress of the earth 
within Venus's shadow-cone during the transit of 
1874, through the positions marked 1,2,... 14, 15, 
in fig. 35. The path of the earth in this figure is, for 
convenience of engraving, broken up into three parts, 
shown in fig. 36, and the earth is represented at each 




Fig. 36.— Explaining Plate XVJ. 

part of her progress, precisely poised and rotated, as 
she would have appeared if she could have been viewed 
from the sun during the course of the transit of 1874. 
Leaving the cross-lines out of consideration for the 
present, let the student study this plate, interpreting 
it by reference to figs. 34 and 35, and he will be able 
to form more exact conceptions of the real relations 

L 



146 TRANSITS OF VENUS. 

presented during the transit than he could from a long 
and recondite explanation. He sees in the first picture 
of the earth those regions whence the beginning" of 
the transit was visible. He sees in the last those 
regions where the end was visible. Those parts of 
the earth which appear in both these views are those 
from which the whole transit was visible. And, finally, 
those parts which do not appear in either of these 
views (nor, therefore, in any of the fifteen) are those 
whence no part of the transit could be seen. 

Plates XVII. and XVIII. represent the earth as 
supposed to be seen from the sun at the beginning 
and end of the transit. 

Of these views the first represents the earth as she 
would appear from the sun when her centre was just 
crossing the circle v v' of fig. 35 at ingress, and the 
second represents her as she would appear when her 
centre was just crossing the same circle at egress. So 
that the first corresponds to an epoch between those 
represented in the Jirst two. earth-pictures of the fold- 
ing plate, while the second corresponds to an epoch 
between those represented in the last two pictures of 
that plate. The seemingly parallel cross-lines in 
Plate XVII. represent the encroaching outline of the 
circle vV (fig. 35) at intervals of a single minute of 
time between the epochs represented by the first two 
figures in the folding plate. The corresponding cross- 
lines in Plate XVIII. represent the same outline 
gradually passing off the earth's face between the 
epochs corresponding to the last two figures in the 



-=M 





^_J 



148 TRANSITS OF VENUS. 

But now, lastly, it remains to show how the actual 
progress of a transit as seen from the earth corre- 
sponds with the progress of the earth through Venus's 
shadow-cone as illustrated in figs. 34 and 35. For 
although the plan of dealing with the problem by 
considering the passage of the earth through these 
cones is, on the whole, the most convenient which can 
be adopted, and especially on this account, that it shows 
us directly what face of the earth is turned sunwards 
at the beginning or end or at any other stage of the 
transit, yet there is something artificial in this way of 
considering the subject. The student who wishes 
to know what can actually be seen from the earth 
seeks for something more than a description of what 
miuht be seen from the sun under certain imagined 
conditions. 

A very simple consideration will enable us at once 
to transpose the relations illustrated in fig. 35 in such 
a way as to correspond to the actual transits across 
the solar disc. 




Fig. 37. — Illustrating the connection between the passage of Vcntis over 
the sun's face, and tlio passage of the earth through Venus's shadow-cone. 

Suppose S (fig. 37) the sun's centre, s s s a dia- 
metral plane of the sun square to the line s v o, which 



OF TRANSITS AND THEIR CONDITIONS. 149 

forms the axis of the shadow-cones we have heen 
dealing with (for simplicity taking the cone as in tig. 
20). Thus s s' is a circle directly opposite to v v' ', the 
planes of these circles being parallel. (The left-hand 
halves of the ovals / s and v v' are supposed to be the 
nearer.) Now imagine a straight line passing through 
v to the centre of the earth e on one side, and to the 
circular disc s s on the other. Since the earth's centre 
carrying this line travels along E e' athwart v v' on the 
path ie, such as is shown in fig. 34, passing slantinglv 
downwards below the centre of v v , it is clear that the 
other end of the line will travel along ff', across s s', on 
the path «&,moving slantingly upwards above the centre 
of s s'. If we looked at v v' from v, the motion of the 
earth would be from left to right along ie; and mani- 
festly, if we looked at s s from v, the motion along a b 
would also be from left to right, In other words, 
whereas ab, as a projection of ie, is inverted, it is not 
reversed right and left, provided we are supposed to 
view v v and s s' , in turn, from the point v. The 
chord a b, then, so viewed, is a perfect projection of 
i e, inverted without being reverted right and left. 

And clearly this principle of projection may be 
extended to all that is pictured in fig. 35, not only as 
respects motion along the transit chords of 1874 and 
1882, but also as respects the sun-views of the earth 
supposed to be presented by the numbered discs, and 
actually presented on a much enlarged scale in Plate 
XVI. The circle ss, of fig. 37, which represents the 
solar disc, is a perfect projection of v v' in this sense. 



ISO TRANSITS OF VUXUS. 

that Avherever an observer be supposed to be placed 
on the circle v v' , he would see the centre of Venus 
projected at a point of .<? s' corresponding to his own 
position, only inverted as respects north and south. 
And if we imagine a small figure of the earth properly 
placed on the chord ie, with correct pose of axis and 
rightly rotated, to correspond to the time at which the 
earth actually reaches that part of ie, then for every 
point on the sunlit-half of that small globe there will 
correspond a point on s s'. If, further, we imagine a 
straight line extending from v to this globe of the 
earth on one side and to s s' on the other, and that the 
former extremity is carried along all the outlines of 
continents and islands on the sunlit-half of the adobe, 
the other extremity will describe on the disc *• / an 
inverted, but not reversed, picture of those continents 
and seas. Any point in this inverted picture will indi- 
cate the point on the sun's disc occupied by the centre 
of Venus, as supposed to be seen at the corresponding 
moment by an observer placed at the corresponding 
point of the earth's globe. So that when once we 
have constructed such a picture as Plate XVI., giving 
a series of sun-views of the earth during her passage 
through the sections vv\ v v' (fig. 35), of the shadow- 
cones shown in fig. 34, we have at once the means of 
determining the apparent path of Venus's centre 
across the sun's disc for any station whatever upon 
the earth. In fact, Plate XVI., held up to the light, 
inverted, and looked at from behind, pictures the por- 
tion of the sun's disc traversed by Venus ; the pictures 



OF TRANSITS AND THEIR CONDITIONS. 1 5 I 

of the earth inverted without reversion are such pro- 
jections as I have been speaking of; and we have 
only to dot down the place of any island or town in 
these successive projections, and to connect the succes- 
sive dots by a line, to have the path of Venus's centre 
across the sun's disc as viewed from that island or town 
during her passage. 

Plate XIX. has been constructed in the way here 
indicated, only that I have thought it better to show 
projections separated throughout by a quarter of an 
hour, instead of having internal contacts (most accele- 
rated and most retarded) illustrated specially as in 
Plate XVI. Plate XX. is intended to explain more 
clearly the meaning of Plate XIX. It shows the 
northern half of the sun's disc. Outside and inside 
this disc are circles, one having a radius exceeding the 
sun's bv Venus's semidiameter, and the other having 
a radius less than the sun's by the same amount ; so 
that when Venus's centre crossed the outer circle her 
outline just touched the sun's on the outside, or she was 
in external contact, while when her centre crossed the 
inner circle her outline just touched the sun's on the 
inside, or she was in internal contact. Parts of these 
circles are shown in Plate XIX. Across the disc five 
parallel lines are drawn. The central one is the path 
of Venus's centre supposed to be viewed from the 
centre of the earth. The line next to the centre, 
above, shows the path of Venus's centre supposed 
to be always so viewed from a southerly station as 
to be thrown as far as possible from the central 



152 TRANSITS OF VENUS. 

path on the northern side; 1 and the line next to the 
centre, below, shows the path of "Venus's centre as sup- 
posed to be always so viewed from a southerly station 
as to be as far as possible from the path of the central 
path on the southern side. The lines next outside the 
two last-mentioned mark the boundaries of the track of 
Venus's disc as supposed to be seen from the centre of 
the earth. And lastly, the outside dotted lines mark 
the northern and southern boundaries of the tracks pur- 
sued by Venus's disc if so viewed that her centre would 
follow the tracks shown north and south respectively of 
the central path. No part of Venus could be seen, from 
any part of the earth, outside these dotted lines. 

In Plate XIX., the tracks followed by Venus's 
centre as seen from twelve important stations, are 
marked in. The student can readily add, either on 
the plate itself or on a tracing from it, the transit path 
for any other station. It will be found a useful exer- 
cise to trace from Plate XIX. the central path and 
the outline of the sun's disc, and the path of any 
stations whether of the twelve dealt with in the plate 
or such others as the student may desire, and then 
having cut the picture thus formed into three parts by 
horizontal lines (where the black spaces fall in the 
plate) to connect them into one long strip correspond- 
ing to the transit band of Plate XX. 

1 There was no fixed point in the earth where this relation would hold. 
The observer would have had to be placed at the point of the earth whieh 
just touches the southern transit-parallel in Plate XVI., and this was a 
point continually travelling backwards along a southern latitude parallel. 
A similar remark applies to the corresponding northerly positions. 



B 




OF TRANSITS AND THEIR CONDITIONS. 1 53 

It remains only to be added that the process applied 
n the construction of Plates XVI. and XIX. to illus- 
trate the transit of 1874, can easily be applied to any 
other transit. Take for instance the transit of 1882. 
Here a portion of the work has been already done, 
since Plates XIV. and XV. illustrate the beginning 
and end, with the position of the circles V v' of fig. 35. 
A picture of the space enclosed between the transit 
chords for 1882 fig. 35, and the circle vv' ought to 
be made on such a scale that the distance between the 
transit chords would equal the diameter of the discs in 
Plates XIV. and XV. Or, if that scale be too large, 
then figs. 38 and 39 may be used instead. A series 
of sun-views can readily be drawn on tracings of the 
meridians and parallels either of Plates XIV. and 
XV., or of figs. 38 and 39, corresponding to successive 
equal epochs (say fifteen minutes apart) all through 
the transit. These must be arranged in a row as in 
Plate XVI., in their proper order, and so posed that 
the central cross-lines (marked mean time in Plates 
XIV. and XV., and m in figs. 38 and 39) may cross 
the track of central transit at the equal angles at which 
the circle v v' crosses that track in fie-. 35. Then 
will a picture corresponding to Plate XVI. have been 
constructed, except that internal contacts will not have 
been specially illustrated by projections corresponding 
to these contacts (as most accelerated and most re- 
tarded). The picture so drawn, if inverted and looked 
at from behind (or if inverted and viewed in a mirror), 
will correspond to Plate XIX., and enable the student 



154 



TRANSITS OF VENUS. 



to trace the path of Venus's centre as seen from any 
station whatever on that occasion. 

Other transits may be illustrated with equal 

TRANSIT OF 1882. (INGRESS.) 



Retarded 
Ingress 




Acre/eratrd 
Iiiyress. 



Fig. 38. — Illuminated side of the earth at ingress, Dec. 6, 2h. 15m. 56s. 
(Greenwich mean time.) 

readiness. Nor need the details of the process be any 
further illustrated by examples, since any student who 
takes sufficient interest in these matters to attempt the 
projection of a transit in the manner here applied to 
the approaching transits, will have sufficiently examined 
the earlier portions of this chapter to be able to recog- 
nise clearly the relations involved in constructions of 
the kind. 



OF TRANSITS AND THEIR CONDITIONS. 1 55 



The construction of such illustrative projections as 
Plates II., III., &o. . . . IX., needs no explanation; 
for these are simply stereographic polar projections 

TRANSIT OF 1882. (EGRESS.) 



l2 -^\'\ 6 C{' 




e" gm 4m 



a m 



Fig. 39. — Illuminated side of the earth at egress, Dec. 6, 8h. Om. 32s. 
(Greenwich mean time.) 

of the earth, upon which various lines and points, 
obtained by the methods already described, are laid 
down for convenience of study and reference. 



156 TXANMTS OF VENUS. 



CHAPTER V. 

THE TRANSITS OF 1874 AND 1882. 

The discovery that the sun's distance, as determined 
by Encke from the transits of 1761 and 1769, was con- 
siderably in excess of the truth, naturally directed 
special attention to the transits of the present century. 
It was in 1857, only three years after Hansen had 
announced to the Astronomer Royal the correction in 
the sun's distance resulting from the lunar theory, 
that Sir Gr. Airy first called the attention of astrono- 
mers to the subject of the approaching transits, and to 
the inquiry how the opportunities presented by these 
transits might best be employed. In a lecture 
delivered before a meeting of the Astronomical Society 
in May 1857, he examined the various methods avail- 
able for determining the sun's distance, and ascribing 
to the observation of Venus in transit the highest 
value, he considered in a general way the ch*cum- 
stances of the transits of 1874 and 1882. , He pointed 
out that, cceteris paribus, the second transit of a pair is 
superior to the first for Halley's method ; but unfor- 
tunately failed to observe that special circumstances 
may modify or even reverse this relation. Although 



THE TRANSITS OF 1874 AND 1882. 1 57 

I have given one demonstration (in the preceding 
chapter) of the general law and of the fact that the 
coming transits present an exception to it, it will be 
well to show here the nature of Airv's reasoning : — 

Let fig. 40 represent the face of the earth as sup- 
posed to be seen from the sun during a December 
transit, such as either of the approaching transits. 
Now, the earth during the transit is moving from rio-ht 
to left, or in the direction shown by the long arrow 
(the slant of the axis is for simplicity neglected;. 
Her rotation shifts points on her surface in the way 
shown by the small arrow on the equator, the shift 
due to this cause being greatest on the equator. This 
motion manifestly takes place in a sense adverse to 
that of the earth's motion of revolution, everywhere 
except at stations on the shaded lune of the disc. 
Now, Venus transits with the excess of her motion of 
revolution over the earth's; and anything which tends 
to reduce the effects of the earth's motion of revo- 
lution, increases the excess of Venus's motion— -or in 
other words, hastens Venus in her transit. So that at 
every point of the unshaded portion of the disc in 
fig. 40 Venus is hastened, more or less, by the effects 
due to the earth's rotation. On the contrary, at every 
point on the shaded portion of the disc Venus is 
retarded in her transit. 

These circumstances affect diversely the two transits 
of such a pair as we are now awaiting. If fig. 41 
represents the sun's disc, the north point being upper- 
most, then the lines a b, c d, represent chords of 



153 



TRANSITS OF VENUS 



transit in 1874 (a b being the chord for a northern, c d 
being the chord for a southern station) ; and a! b\ 
c d! will represent chords of transit in 1882 (V b' beino- 
the chord for a northern, c' d! the chord for a southern 
station). 

It is manifest that in 1874 the conditions affectino- 
the duration of the transit as seen at a northern station 




Fig. 40. — Illustrating the effect of the earth's rotation on the progress 

of a transit. 

were adverse. The chord a b was longer, owing to the 
northerly latitude of the observer; but Venus was 
hastened on her course, and therefore the lengthening 
was not so great as it otherwise would have been. We 
had then one favourable and one unfavourable condi- 
tion, the latter to some decree cancelling the former. 
(In some transits of the kind the effect of rotation 
wholly cancels, or even more than cancels, the effect due 
to latitude.) The southern station, if taken where, 



THE TRANSITS OF 1874 AND 1882. 159 

throughout the transit, the observer was on the portion 
of the disc represented Avithout shading in fig. 40, 
would give conspiring effects. The chord of transit c d 
would be shortened, and Venus would be hastened on 
her course. Hence we had for such a station two 
favourable conditions. In all we had three favourable 
conditions and one unfavourable condition — so that if 




Fif. 41. — Illustrating the effect of the position of transit chords. 

the conditions had been all equal in value we had a 
balance of only two favourable conditions. 

On the other hand, in such a transit as that of 1882 
we can theoretically secure four favourable conditions. 
We have at the northern station the shortened transit 
chord a' b' , and a hastening of Venus — or two conspir- 
ing conditions. At a southern station we have the 
lengthened transit chord c' d ', and by taking a station 
which throughout the transit lies on the shaded part 



160 TRANSITS OF VENUS. 

of the disc (that is, an Antarctic station passing below 
the pole during the transit hours), we have Venus 
retarded on her transit path, or again we have two 
conspiring conditions. In all, then, we have four 
favourable conditions, or twice as many as we obtained 
for the balance of favourable conditions in 1874. 

This is theoretically sound. Moreover, it is quite 
commonly the case that the effects due to rotation are 
equivalent to those due to latitude, and that therefore 
the adverse conditions at a station placed as the 
northern station in 1874 may be regarded as cancelling 
each other. In the transit of 1769, for example, the 
conspiring effects of rotation and latitude were nearly 
equal. The Astronomer Royal, in his ' Popular 
Astronomy' (published in 1848, be it noticed), justly 
assigns to rotation 10 minutes out of the observed 
maximum difference of duration, 22 minutes. It does 
not seem rash to infer that he had this result in his 
thoughts when, after mentioning that the best northern 
stations would probably not be occupied in 1874, -he 
proceeded to remark (in 1857) that the ' observable 
difference ' in the earlier transit would ' probabh/ not 
be half of that in 1882.' 

Although the observable difference in 1874 was 
really half as great again as in 18^2, yet it mattered 
very little, at that early epoch, if any mistake of this 
sort crept into what claimed to be little more than a 
popular account of the general subject of transits. No 
one probably considered that the Astronomer Royal 
attached any weight to the details of his paper of 1857. 



THE TRANSITS OF 1874 AND 1882. l6l 

In fact, so roughly was the paper prepared that the 
time of mid-transit in 1874 was an hour wrong — an 
error not resulting from incorrectness of the tables, for 
the time of transit of 1882 was very nearly correct. 
In fact, the paper of 1857, accurate enough for its 
purpose, had not, and did not seem intended to have, 
any scientific weight. 

But unfortunately, the Astronomer Royal, when 
next he dealt with the subject, seems to have regarded 
the transit of 1874 as demonstrated by his former rough 
paper to be unfit for the application of Halleys 
method. For, in 1864, he published a sufficiently 
accurate investigation of the transit of 1882, illustrated 
by projections (corresponding to those forming Plates 
VI. and VII.) well executed by Mr. J. Carpenter of 
Greenwich, and in this paper the transit of 1874 was 
not considered at all. In 1865, he again commented 
on the circumstances of the transit of 1882 without 
mentioning the earlier transit. When at length, in 
1868, he published what purported to be a detailed 
description of the circumstances of the two transits. 
and of the duties not of English astronomers only, but 
of astronomers generally with respect to the transits, 
he remarked that Halley's method had been shown to 
fail totally in 1874. 

It will serve, I think, to remove misconoeptions if 
I quote here the remarks addressed to the scientific 
world by Sir George Airy in 1868 respecting the 
important transits of 1874 and 1882. 

'On two occasions,' he writes, ('Monthly Notices,' 

M 



1 62 TRANSITS OF VEX US. 

1857, May 8, and 1864, June 10) 'I have called the 
attention of the Society to the transits of Venus across 
the sun's dis^, which will occur in the years 1874 and 
1882 ; and have pointed out that, for determination of 
the difference between the sun's parallax and the 
parallax of Venus, the method by observation of the 
interval in time between ingress and egress at each 
of two stations at least, on nearly opposite parts of 
the earth (on which method, exclusively, reliance was 
placed in the treatment of the observations of the 
transit of Venus in 1769), 1 fails totally for the transit 
of 1874, and is embarrassed in 1882 with the difficulty 
of finding a proper station on the almost unknown 
Southern Continent. 

' The publication of M. Le Verrier's new Tables 
of Venus, and of Mr. Hind's inferences from them as to 
the points of the sun's limb at which ingress and egress 
will take place in each transit (which inferences I have 
in part verified), has induced me again to examine the 
whole subject. And, without giving up the hope of 
using the observation of interval between ingress and 
egress at each of two stations in 1882, I have come to 
the conclusion (from all the information which has 
reached me) that it will be unsafe to trust exclusively 
to the chance of securing observations on the Southern 

1 As it has been said (as a correction of my own criticism of the 
above paper) that SirG. Airy did not describe the 'method of durations ' 
as failing totally, but only Halley's method, meaning the method of 
durations as applied to a nearly central transit, I invite special attention 
to his careful wording. The parenthesis removes all doubt as to his 
real meaning (for the transit of 1769 was far from central); though in- 
deed without the parenthesis the meaning is unmistakable. 



THE TRANSITS OF 1874 AND 1882. 1 63 

Continent ; and that, while observations are by all 
means to be attempted in that manner, it is also very 
desirable to combine with them observations of the 
same phenomenon (at one time the ingress, at another 
time the egress), made at nearly opposite stations 
whose longitudes are accurately known, and recorded 
in accurate local time. This principle being once 
admitted, the transit of 1874 is, or may be, as good 
for observations of that class as the transit of 1882 ; 
and the selection of localities for the observations must 
be made with equal care for the two transits.' 

He then explains how the maps which illustrate 
his paper were constructed, and proceeds to discuss 
the individual maps Avith reference to the selection ot 
stations for observing the several phenomena. Plate 
VI. will serve as well as these maps to illustrate what 
follows : — 

I. — ' Stations for observing the Ingress as accelerated 
by Parallax ' — that is, Stations near I {Plate VI.), on 
the Illuminated side of A B, but not too near to A B. 1 

' Owhyhee and the neighbouring islands are excel - 

1 If 10° be assumed as the lowest elevation at which useful obser- 
vations can be made, then the stations must not lie within 10° of the 
circle a b. The arcs a b, cd, a' b', d d', Plates VI. and VII., indicate 
this limit for the transits of 187-1 and 1882. Thus a station for 
observing ingress accelerated by parallax (in 1874) should not be 
anywhere within the zone a b ba ; so that the best point lor observing 
accelerated ingress would be that point on a b which lies nearest to 1. 
Similar remarks apply to observations of retarded ingress near x', of 
accelerated egress near e', and of retarded egress near k, the dotted 
curves a'b', c'd', and c t/ marking t ho limits outside which stations sh<>ii. J 
be placed. 



1 64 TRANSITS OF VENUS. 

lent. The factor of parallax J is about 0*92, and the 
sun is at nearly two hours' elevation. There i- English 
society at Woahoo. These islands are just within the 
tropics. For use of this station the absolute longitude 
must be accurately determined. 

* At the Marquesas Islands the factor of parallax 
is 0*7, and the sun is nearly as high as at Woahoo. 
Our neighbours across the Channel have, from the 
time of Louis XIV., taken an honourable lead in 
scientific enterprise of every class. I trust that we 
may rely on them for accurate determination of longi- 
tude at Marquesas, and for accurate observation of the 
ingress in 1874. 

' The desert Aleutian Islands can scarcely be recom- 
mended, although the factor 0*8 for the westernmost of 
them, where the sun is highest, is favourable. But 
it is very probable that the Russians will soon have 
established telegraphic communication Avith the mouth 
of the Amoor, by which its absolute longitude will be 
accurately determined ; and though the factor is only 
0*57, the sun is 15° high, and the station will be valu- 
able. 

' On the Avhole, if the British Government will 
undertake the accurate determination of longitude of 
Woahoo, and the careful observation of ingress there 
in 1874, we may consider that good provision is made 
for the accelerated ingress.' 



c 



1 This expression indicates the acceleration or retardation at the 
station, regarding the maximum acceleration as unity. 



THE TRANSITS OF 1874 AND 18S2. 165 

II. — ' Stations for observing the Tngress as retarded by 
Parallax' — that is, Stations near \' {Plate VI.), on 
the Illuminated side of a' b', but not too near to a'v'. 
See note, p. 163. 

' The best station, as referred to the test of numbers, 
is Kerguelen's Island, where the factor is 0*91, and the 
sun is 25° high. This island is emphatically known 
as " The Island of Desolation." I know not whether 
its character is so repulsive, or its utility as a zero of 
longitude so small, as to make our nautical authorities 
unwilling to determine its longitude, and to station 
observers there in 1874. If these difficulties are not 
thought too great, it will be an excellent position. At 
Crozet's Islands the factor 0*98 is very favourable, but 
the sun is rather low (10° altitude). 

' The next stations in order of merit are Rodriguez, 
Mauritius, and Bourbon. Mauritius possesses this 
claim, that it will be a fairly good station, though not 
so good as Bourbon, in 1882; in 1874 as well as in 
1882, it has this disadvantage, that the sun will be 
low. If only one longitude can be determined in this 
chain of islands, it ought to be that of Mauritius ; if 
two can be determined, they ought to be those of 
Rodriguez (for 1874) and Bourbon (for 1882). 

* At Madras and Bombay the factors, 0*47 and 0*44, 
are small ; but the value of either station does not 
depend entirely on its simple factor, but upon the sum 
of its factor with the factors at the stations under 



1 66 TRANSITS OF VENUS. 

head I. These two observatories, with well-known 
longitudes, will prove very useful stations. 

' With the assistance which we may hope to 
receive from the British Government, we may con- 
sider the observation of the retarded ingress as w r ell 
secured.' 

III. — ' Stations for observing the Egress as accelerated 
by Parallax ' — that is, Stations near e' {Plate VI.), on 
the Illuminated side of c' I)' ', but not too near to c' d'. 
See note, p. 163. 

' Excluding from consideration the Southern Conti- 
nent as not to be entertained in our thought with- 
out the most absolute necessity, the stations in order 
of merit are the Auckland Islands, Canterbury, 
Wellington, and Auckland, in New Zealand (factors 
ranging from 0-83 to 0*77), Norfolk Island (0-66), Mel- 
bourne and Sydney (0-6). I omit Chatham Island, 
where the sun is rather low. The existence of the 
observatories at Melbourne and Sydney makes the 
observation of the accelerated egress almost secure, 
although, in confirmation, I should much desire to 
have one station at least on the New Zealand group.' 

IV. — ' Stations for observing the Egress as retarded by 
Parallax" 1 — that is, Stations near E (Plate VI.), on 
the Illuminated side of C D, but not too near to C P. 
See note, p. 163. 

' The stations which are favourable for this ob- 
servation are almost entirely on Russian and Turkish 



THE TRANSITS OF 1874 AND 1882. 1 67 

territories. At none of them is the factor less than 
0*84; and we have, therefore, only to consider the 
elevation of the sun, leaving to the national Govern- 
ments to estimate the facilities or difficulties depend- 
ing on the locality, the climate, or the season. Any 
station either to the east or to the west of the Lower 
Caspian will have the sun well elevated. Omsk, Orsk 
(whose longitude has been determined with peculiar 
care;, Astrakhan, Erzeroum, Aleppo, Smyrna, and 
Alexandria, have the sun sufficiently high. At 
Tobolsk, Perm, Kazan, Kharkov, Odessa, Constanti- 
nople, and Athens, the sun will be rather low, and at 
Moscow it will be on the horizon. We may, with the 
utmost confidence, leave the selection of the stations, 
the determination of longitude, and the observation 
of the phenomenon, to our Russian friends. 1 One 
station, however, ought specially to be considered as 
being, for this purpose, in British hands, namely, 
Alexandria. It appears not improbable that we may 
soon have very direct telegraphic communication 
with Alexandria; but, failing this, I trust that no 
efforts will be- wanting to determine accurately its 
longitude — a longitude which was in the survey of 
Admiral Smyth, and which always must be, the 
zero of longitude in the Levant. This being as- 
certained, Alexandria would probably be the best 

1 It cannot but be manifest from the whole tone of this passage that 
the conditions of the transit for the scientific world, and not for British 
astronomers only, were intended to be presented in the Astronomer 
Royal's paper. 



1 68 TRANSITS OF VENUS. 

of all the stations for observation of the retarded 

egress.' x 

Transit of Venus, 1882, December 6. 

First, by the Method of Absolute Longi- 
tudes. 

V T . — ' Stations for observing the Ingress as accelerated 
by Parallax'' — that is, Stations near l' [Plate V1L), 
on the Illuminated side of a' b', but not too near to 
a' b'. See note, p. 163. 

' Omitting for the present all allusion to the 
Southern Continent, it will be seen that the best 
station is Kerguelen's Island, its factor being 0'98, 
and the sun's elevation (12°) probably sufficient. 
This circumstance, in addition to its value as ex- 
plained in the discussion of Plate II., renders it well 
worthy of attention. At Crozet's Islands the factor is 
- 9, and the sun's elevation 23° ; abstractedly it is 
preferable to Kerguelen's Island, but not in quite so 
<»reat a degree as that in which Kerguelen's Island is 
superior in list II. The next in value are Bourbon 
and Mauritius, with factor about - 78, the sun 
being higher at Bourbon. On comparing these quali- 
licationswith those remarked under head II., the reasons 

1 The absolute omission of the Indian stations here, though they 
had been mentioned among those useful for observing retarded ingress, 
is remarkable, but is readily understood when the Astronomer Royal's 
maps are examined. North India is nearer to e (Plate YI.) than Alex- 
andria, and has a higher sun. 



THE TRANSITS OF 1874 AND 1882. 1 69 

will be evident for my recommendation that either 
the longitude of Mauritius or the longitudes of Bourbon 
and Rodriguez should be determined. 

' At the Cape of Good Hope the factor is about 
0*62, and the observation there will be valuable. 

• The satisfactory observation of the accelerated 
ingress requires, however, some longitude-determi- 
nations.' 

VI. — ' Stations for observing the Ingress as retarded by 
Parallax' 1 — that is, Stations near I {Plate VII.), on 
the Illuminated side of A B, but not too near A B. 
See note, p. 163. 

' Every city near the seaboard of the United States 
of America, and every important city of Canada, 
commands this phenomenon most favourably. The 
lowest factor is 0*95, and the smallest elevation of the 
sun is 12°. The utmost reliance may be placed on 
the zeal of our American brethren for observing the 
ingress. As great facility exists for determining the 
absolute longitude of any place within the range of 
American telegraphs (Harvard having been accurately 
referred to Greenwich), it is unnecessary to look 
further. Otherwise it might be remarked that Ber- 
muda, Jamaica, and the West Indian Islands, and both 
sides of Central America, are excellent stations, but 
requiring determinations of longitude.' 



170 TRANSITS OF VENUS. 

VII. — ' Stations for observing the Egress as accelerated 
by Parallax'' — that is, Stations near E {Plate }"II.), 
on the Illuminated side of c D, but not too near C D. 
See note, p. 163. 

' All the American stations mentioned in the last 
paragraph, from Halifax to New Orleans, and Ber- 
muda and the West Indian Islands, are well situated 
for this observation, the factors being near 0*85, and 
the sun's altitude varying from 4° at Halifax to 32° at 
New Orleans and Jamaica. The coast of South 
America also is favourable, from its union with the 
isthmus to the harbour of Rio de Janeiro. It is 
believed that efforts have been made for exact deter- 
mination, in a nautical sense, of the longitude of Rio ; 
it may now be desirable to give to that longitude the 
utmost accuracy.' 

VIII. — ' Stations for observing the Egress as retarded 
by Parallax'' — that is, Stations near e' (Plate VII.), 
on the Illuminated side of c' T>' , but not too near c' d'. 
See note, p. 163. 

' Omitting for the present the Southern Continent, 
this observation will be amply secured by the obser- 
vatories of Sydney and Melbourne, where the factor 
is 0-96, and the sun's elevation 12° to 14°. If, how- 
ever, the longitudes of the New Zealand stations can 
be ascertained, they, with factor 0*8 and sun's eleva- 
tion 32°, will form a valuable addition.' 



THE TRANSITS OF 1874 AND 1882. 171 

Second, by the Method of Interval be- 
tween Ingress and Egress. 

' On comparing Plates VI. and VII., it will be seen 
that the North American localities supply, in a manner 
which leaves nothing to be desired, the demand for 
stations, at which the ingress is retarded and the 
egress accelerated, or the whole interval is diminished, 
by parallax. 

' With these, it is necessary to combine one or 
more stations, at which the ingress is accelerated and 
the egress retarded, or the whole interval is increased, 
by parallax. On examining' Plates VI. and VII., ' it 
will be seen that the only possible method of respond- 
ing to this demand is by the selection of stations on 
the Antarctic Continent, in which the observation will 
be made when the sun is neai'lv below the Pole. 

' In so far as the coast of the Antarctic Continent 
follows nearly a parallel of latitude, the best position 
for a station is at 7 h east longitude. The factors 
would be, for ingress and egress, about - 95 and O68. 
The sun would be, at each station, about three hours 
from the sub-polar meridian. But its elevation above 
the horizon would scarcely exceed 4°, and any altera- 
tion of the longitude, with the view of increasing the 
elevation at one phenomenon, would diminish it at the 
other. 

' Advantage may, however, be taken of the deep 
southern inlet discovered by Sir James Ross, to the 
western side of which is given the name of South 



172 TRANSITS OF VENUS. 

Victoria. If a station cau be established in latitude 
exceeding 72° S., it will be preferable, for observation 
of ingress, to the station in 7 h longitude, and if the 
expedition could be pushed on to an observing place 
in the neighbourhood of Mounts Erebus and Terror, 
that position would be greatly preferable. For ob- 
servation of egress, it is manifestly far superior; the 
sun's altitude being about 27°. The factors for the 
two observations are respectively about 0*78 and 0*58. 
' The decision on the choice to be made between 
these two stations, and the judgment on the facility, 
or even the possibility, of using either of them, must 
rest with persons who have had some familiarity with 
polar, and, if possible, with south polar voyages.' 

' In partial correction of some small inaccuracies in 
these remarks, it may be observed that — 

' The ingress, as viewed from the earth's centre, is 
always a few minutes earlier, and the egress always a 
few minutes later, than is supposed in the maps.' 

' As affected by parallax, the phenomenon is always 
retarded with ascending sun and accelerated with 
descending sun.' 

' As referred to apparent solar time, the phenomena 
are slightly retarded.' 

' The only phenomena which are critically affected 
by these corrections are those' of Plates IV. and V., 
' and in both the circumstances of solar elevation are 
rendered more favourable.' 

This account of Sir G. Airy's treatment of the 



THE TRANSITS OF 1874 AND 1882. 1 73 

two transits would be incomplete without some de- 
scription of his views as to the occupation of Antarctic 
stations, or without an account of the opinions ad- 
vanced in support of his views by authorities whom he 
had invited to attend the meeting;; of the Astronomical 
Society before which the above programme was 
advanced. 

Passing over the Astronomer Royal's remarks in 
the ' Monthly Notices ' for May 1857, and June 1864, 
I quote from a paper in the ' Monthly Notices ' for 
May 1865, pp. 201-203, called a 'Letter from the 
Astronomer Royal to the President of the Royal 
Geographical Society,' and running thus : — 

' I have learned, through the public papers, the 
tenor of late discussions at the Royal Geographical 
Society in reference to a proposal for an expedition 
towards the North Pole. I gather from these that 
the object proposed, as bearing on science, is not so 
much specific as general ; that there is no single point 
of very great importance to be obtained, but a number 
of co-ordinate objects whose aggregate would be valu- 
able. And I conclude that the field is still open for 
another proposal, which would give opportunity for 
the determination of various results, corresponding in 
kind and in importance to those of the proposed 
Northern Expedition, though in a different locality, 
and would also give information on a point of great 
importance to astronomy, which must be sought within 
a few years, and which it is desirable to obtain as early 
as possible. 



174 TRANSITS OF VENUS. 

'In the ) 7 ear 1S82, on December 6, a transit of 
Venus over the sun's disc will occur ; the most favour- 
able of all phenomena for solution of the noble problem 
of determining the sun's distance from the earth, 
provided that proper stations for the observation can 
be found. (It will be remembered that it was for 
the same purpose that the most celebrated of all the 
British scientific expeditions, namely, that of Captain 
Cook to Otaheite in 1769, was undertaken. The 
British part of the enterprise was perfectly successful ; 
but there have always been doubts of the accuracy 
of the corresponding observations in Lapland, which 
render a repetition of the observation very desirable.) 
In the " Monthly Notices of the Royal Astronomical 
Society " for June 10, 1864, I have very carefully 
discussed the circumstances of the coining transit, in 
reference to the selection of observation-stations. For 
the northern stations there will be no difficulty ; they 
will be on the Atlantic seaboard of North America, or 
at Bermuda ; all very favourable and very accessible. 
For the southern stations the selection is not so easy ; 
the observation must be made on the Antarctic Con- 
tinent ; if proper localities can be found there, and if 
the circumstances of weather, &c, are favourable, the 
determination will be excellent; if those favourable 
circumstances do not hold, no use whatever can be 
made of the transit.' . . . * The astronomical object of 
a southern expedition is, I trust, sufficiently explained 
in the sentences which I have quoted. In the event 
of such an expedition being undertaken, the precise 



THE TRANSITS OF 1874 AND 1882. 1 75 

determinations which T have indicated as bearing on 
the astronomical question must (from the nature of 
the case) take precedence of all others. But there 
would be no difficulty in combining with them any other 
inquiries, of geography, geology, hydrography, magnet- 
ism, meteorology, natural history, or any other subject 
for which the localities are suitable. 

' And I have now to request that you will have 
the kindness to communicate these remarks to the 
Royal Geographical Society, and to take the sense of 
the Society on the question, whether it is not desirable, 
if other scientific bodies should co-operate, that a 
representation be made by the Royal Geographical 
Society to Her Majesty's Government on the advan- 
tage of making such a reconnaissance of the Southern 
Continent as I have proposed ; primarily in the interest 
of astronomy (referring to my official responsibility 
for the importance of the examination at this special 
time) ; but conjointly with that, in the interests, per- 
haps ultimately more important, of geography and 
other sciences usually promoted by the Royal Geo- 
graphical Society.' 

In December 1868, notwithstanding the relatively 
unfavourable circumstances for applying this (Halley's) 
method to the transit of 1882, and the very favourable 
conditions under which Delisle's method can then be 
applied, the Astronomer Royal urged that only three 
stations should be occupied for Delisle's method in 
that year, the instruments of the five 1874 expedi- 
tions, ' thus set free from two stations,' being required 



176 TRANSITS OF VENUS. 

at an observing- station on the Southern Continent. 
' The choice of station being made,' he said, ' I would 
not recommend any reconnaissance, but I would pro- 
pose that an expedition should go direct to the 
selected point in good time for the observation of the 
phenomenon. The season is early for South Polar 
expeditions, and any difficulties produced by ice 
would probably diminish every day. A station being 
gained, all that is necessary in the way of subsidiary 
observation is a few days' observation to give clock- 
rate ; then the clock times of the two phenomena 
will furnish all that is required. The first action to 
be undertaken by the Government,' he proceeds (and 
I invite special attention to the point), ' is to procure 
the stock of instruments, and this ought to be done 
without delay. An observing plant like that ' (de- 
scribed in the earlier part of the same paper) ' is not 
to be obtained in haste, and the proposed expedition 
might be entirely crippled by a small negligence 
on this point. The equipment of ships and the 
selection of officers would probably require much less 
time.' 

It appeared to the naval authorities Avho followed 
the Astronomer Royal in addressing the meeting, that 
the more certain course for achieving the desired 
result would consist in the preparation of an expedition 
to winter in Possession Island. I quote the following 
passages as bearing specially on the feasibility of such 
an expedition : — 

Admiral (then Captain) Richards, Ilydrographer to 



THE THAKS'ITS OF 1874 AND 1882. 1/7 

the Admiralty, said : ' My own opinion, looking to the 
uncertainty of finding a wintering station for a ship, is 
that landing a party on Possession Island,' or one of 
the islands farther south, ' would be the most feasible 
course, and there would be little doubt of the facility of 
reaching one or other of these islands with a suitable 
steam-vessel, making Tasmania or New Zealand the 
base of operations. Doubtless a year passed in this 
region would be most profitably employed in adding to 
our knowledge of magnetism, and various other branches 
of physical science.' 

Admiral Ommanney said, inter alia : ' I fully con- 
cur in all that has fallen from the Hydrographer to the 
Xavy, and hope ere long to hear that operations an 
making for sending out to explore the Antarctic 
Seas.' 

Commander J. A. Davis, avIio had accompanied 
Sir James Ross in that most gallant expedition during 
which Victoria Land was discovered, and who had 
himself landed at Possession Island, said that ' he 
believed there would be no difficulty whatever in again 
effecting a landing in the same place.' ' With regard 
to the period of the season at which the transit took 
place, it was to be remembered that the 6th of 
December was so early that no ships had ever reached 
the Antarctic Circle by that date; and as it would 
be necessary to arrange the instruments, &c. prepara- 
tory to the observation, he might say that the ships 
• night to be on the spot at least a month before. This 
would be the Gth of .November, a date altogether nut 

> 



178 TRANSITS OF VENUS. 

of the question ; and as the ships could not winter in 
the South, the party would necessarily have to land 
the year before ; but with good tents he had no doubt 
they could pass the winter very comfortably ' (this, of 
course, and what follows, will not be taken strictly 
an pied de la lettre) : ' they would have a pleasant 
prospect before them and plenty of penguins to live on. 
In comparison with Kerguel en Island and the Crozets,' 
he proceded, ' the chances of observing the transit — 
meteorologically speaking — would be greatly in favour 
of South Victoria.' 

Captain Toynbee also expressed an opinion strongly 
adverse to the meteorological chances at Prince 
Edward's Islands, tKe Crozets, and Kerguelen Land, 
since their neighbourhood is, he said, ' so far as my 
experience goes, subject to a great deal of thick 
weather.' 

There were several points in the Astronomer 
Royal's communication to the Astronomical Society 
on this occasion which were calculated to attract the 
attention of those who had followed his former pro- 
ceedings in connection with the transits of 1874 and 
1882. Thus far he alone of all the leading astro- 
nomers had publicly dealt with the subject, and there 
was much in the tone of his preceding papers to sug- 
gest that in a sense he guaranteed a sufficient examina- 
tion 01 the conditions of the transit to enable astronomers 
genexaiiy, not those of England alone, to await his 
announcement of what the different scientific nations 
might be e>pected to do, and to follow his instructions 



THE TRANSITS OF 1674 AND 1882. 1 79 

whensoever such announcement should be made. In 
the paper of December 1868 he still adopted this tone, 
while nevertheless it was apparent that he was not 
treating the subject in an exact manner. For instance, 
the statement in the very beginning of his paper that 
the method of duration had been shown to ' fail totally,' 
even if correct in itself-— which subsequent examination 
showed not to be the case — was not in accordance with 
former papers, in which he had only expressed his 
opinion that in all likelihood it would not be advan- 
tageously applicable. Then secondly, the maps accom- 
panying the paper were of the roughest possible de- 
scription, insomuch that the shapes of the continents 
and oceans Avere barely recognisable : nor did these maps 
extend beyond the parts immediately adjacent to the 
points corresponding with i,i', E, and e' in Plates VI. 
and VII. ; so that if by any possibility (which seemed 
at that time, however, incredible) Halley's method 
were available in 1874, the maps could not have 
shown the fact, though this was precisely the sort of 
service for which alone maps could have any real 
value. Thirdly, the necessity for exact accuracy 
seemed so little to be suspected by Sir G. Airy, that 
the elements of the transit, given correctly by Hind, 
were not even congruously employed, the times of 
ingress and egress being these corresponding to b, V of 
Plate XL, while the positions were those corresponding 
to external contact, points which in reality are farther 
away from b and 1/ than are c and c respectively. 

Whether these circumstances operated with Puiseux, 

a 2 



I SO TRANSITS OF VENUS. 

Hansen, Petevs, and others who about this time began 
to inquire into the conditions of the two transits (and 
sooner or later published correct, results), I do not know ; 
but, for my own part, I was led to deal with the subject 
by the manifest signs of incompleteness in Sir Gr. Airy's 
paper. It appeared to me that there w T as room for a 
rediscussion of the whole problem, even though, as I 
fully expected, the general views advanced in that 
paper should prove to be altogether correct. 

Having now ascertained that the subject had not as 
yet been thorouo;hlv dealt with, I submitted to the 
Astronomical Society in May 1869 a paper accom- 
panied by six projections (from two of which Plates 
XVII. and XVIII. have been reduced by photo- 
lithography) illustrating the transit of 1874. This 
paper was published in the June number of the 
' Monthly Notices.' In this paper, where it was neces- 
sary to call due attention to the changed values of the 
various stations, I presented these in a tabular form, — 
Airy's values under head A, those of Puiseux under 
head B, and my own, which closely accorded in the 
main with those of Puiseux, under head C. From this 
paper I quote the following summary of the conclusions 
therein demonstrated : — ■ 

1. ' The application of Delisles method of absolute 
time differences. The relative as well as the absolute 
values of many stations are affected. Some which 
had hitherto appeared unsuitable are found to be un- 
objectionable. Others which seemed good appear unfit. 
In other cases the relative values of two stations are 



THE TRANSITS OF 1874 AXD 1882. iSl 

so affected that the results of a comparison between 
them are directly reversed. Lastly, many stations 
not hitherto thought of in connection with the transit 
are found to be well suited for the application of Delisle's 
method. 

2. ' The comparison between DelisWs and Halley's 
methods. Halley's method ' (estimated by Sir G. 
Airy's own test) ' is found not merely to be applicable 
with advantage, which is all that can be said of it when 
central passages are considered, but to be superior to 
Delisle's — slightly, when reference is made only to 
such stations as had been hitherto dealt with, notice- 
ably when Antarctic stations are made use of.' 

3. ' The comparison between the transits of 1874 
and 1882 with reference to Halley's method. This 
comparison shows that Halley's method may be applied 
much more advantageously to the transit of 1874 than 
to that of 1882.' * 

The tables (which are given in abstract at the end 
of this volume) were followed by these remarks: — 

' It will be seen, on a comparison of tables A, B, 
and C, that the effects of the change of phase are in 
some cases important. The coefficients of parallax are 
affected in several instances by more than O'l and in 
two cases by 0-22. In the cases of Crozet Island 
(Table II.) and Chatham Island (Table III.) solar 

1 Chapter IV. presents in pp. 128 et seq. an abstracl of the reason- 
ing liy which the applicability of Halley's method in 1871 was demon- 
strated, and also indicates the places where the method can be most 
suitably applied. But the tables at the end of the boot should be con- 
sulted, especially Table V. 



1 82 TRANSITS OF VENUS. 

elevations are so improved, that these stations, which 
would have to be rejected if central passage were con- 
sidered, are shown to be well suited for the observation 
of internal contacts. The diminution of all the co- 
efficients in Table III., through the change of phase, 
has an important influence on the value of Delisle's 
method, so far as egress observations are concerned. 
It is important to notice, also, that under the heads C 
in Tables III. and IV. many stations not hitherto 
recognised as available are included among the best 
places for observing egress. The Indian stations in 
Table IV. seem too valuable to be neglected. 1 Pesha- 
Avur is better even than Alexandria ; Delhi is not 
inferior to the latter station (when solar elevation is 
considered as well as coefficient of parallax). Bombay, 
Calcutta, and Madras are also excellent. It may be 
noticed also that Bombay and Madras, which, when 
considered with reference to central passage, had 
seemed suitable places for the observation of retarded 
ingress, are found to have so poor a coefficient of 
parallax when reference is made to internal contacts, 
that it would seem useless to observe ingress there (so 
far at least as the application of Delisle's method is 
concerned). 

' Of course, it will be impracticable for this country 
to send observers to more than a certain number of 

1 Several times during tho past year the mistake has been made of 
stating that I originally advocated North Indian stations for applying 
the photographic method. The above passage, written before this method 
had been thought of, contains my first reference to those stations. 



THE TRANSITS OF 1874 AND 1882. 183 

stations. But it is not unlikely that besides Russia, 
France, and England (the only countries specially 
concerned in the transit of 1874), other nations may 
care to take part in the solution of the noble problem 
of determining the sun's distance ; and thus it seems 
advisable that all the stations where there will be any 
chance of obtaining useful observations, should be 
tabulated as nearly as possible according to their rela- 
tive values.' 

A discussion followed in which an attempt was 
made to show that Delisle's method was equal in value 
to Halley's. Even if this could have been proved, it 
would have been little to the purpose, since the ques- 
tion was not whether Halley's method was more or 
less favourably applicable than Delisle's, but whether 
it was applicable at all. This discussion was carried 
on in public. A private correspondence arose out of 
a letter which I addressed to Sir G. Airy, assuring 
him that my sole wish was to assist in securing what 
every astronomer agreed was desirable — the best pos- 
sible utilisation of the opportunities available in 1874 
and 1882. Sir G. Airy wrote me a letter, forwarding 
a copy to Admiral Manners, then President of the 
Astronomical Society, in which he complained that his 
paper of December 1868 had been treated as though 
it claimed to be an exact discussion of the condition*, 
due allowance not beino; made for his own statement 
that it was but a preliminary and comparatively rough 
investigation of the problem. This led me to believe 



1S4 TRANSITS OF VENUS. 

(mistakenly, as afterwards appeared) that I had taken 
up the subject too hastily; for Sir G. Airy seemed 
not merely to promise a thorough analysis of the whole 
subject, but to imply that this was what had been 
intended all along, the suggestions made in December 
18H8 being merely provisional, and the actual arrange- 
ments to be proposed to Government depending on the 
promised thorough investigation. 

Nothing could have been more satisfactory than 
the course thus indicated; and, accordinerly, from that 
time (the summer of 1869) until the summer of 1872, 
I addressed no communication whatever on the subject 
of the controversy, 1 either to Sir G. Airy personally 
or to the Astronomical Societv. Nothing:, however, 
was done in this interval except to carry out the 
arrangements proposed in 1868. Accordingly, in 
1872 I wrote to Sir G. Airy, recalling his attention 
to the promised investigation of the subject. I then 
learned for the first time that the old arrangements 
were still adhered to. On this, I made such protest 
as a student of astronomy, independent of official 
trammels, might properly (in my judgment then and 
now) address to the official astronomer to whom the 
charge of the matter had been left in accordance with 
ancient custom. 

After this protest I allowed yet half a year more 



1 A paper of mine appeared in the ' Monthly Notices ' for January 
1870, in which the application of photography to the observation of the 
transit was dealt with ; but this paper bore no reference to the ques- 
tions which had been raised by me in 1869. 



THE TRANSITS OF 1874 AXD 1832. 1S5 

to elapse, and then, nothing having been done, it 
seemed time to take more earnest measures. 1 

I accordingly resumed the discussion in the ' Spec- 
tator ' for February 8. By a singular coincidence a 
powerful paper appeared in the ' Times ' of February 
13 supporting the views which I had advanced. This 
paper was commonly, and I believe correctly, attri- 
buted to Sir Edmund Beckett. (In his ' Astronomy 
without Mathematics' he mentions the rumour without 
contradicting it.) And many believed that the co- 
incidence was not accidental — that is, that the nearly 
simultaneous appearance of the two papers had been 
planned beforehand. But this Avas not the case. 
Neither had Sir E. Beckett any prior knowledge of 
my intention, nor had 1 of his. 

In his reply, the Astronomer Royal opposed the use 
of Halley's method on the ground (i.) that the Russians 
would probably not occupy Nertschinsk, the station in 
Siberia (marked 6 in Plates XII. and XIII.) which I 
had specially recommended, (ii.) that Puiseux had pro- 
bably abandoned his ideas respecting the use of Halley's 
method (which ideas, said Airy, ' have not again 
been promulgated on the Continent '), and (iii.) that 
no other nations would care to provide for northern 
H alley an stations. A few days later, Mr. Goschen, 
then Secretary of the Admiralty, said that even at 



1 In the interval events had taken place within the Astronomical 
Society to which I see Sir Edmund Beckett has thought it desirable to re- 
fer in the latest edition of his ' Astronomy without Mathematics.' Those 
events had no real importance, however, except for the animus shown. 



1 86 TRANSITS OF VENUS. 

those stations already provided for, where, as I had 
shown, durations could be readily noted, they would 
indeed be noted, but little reliance would be placed on 
them ! l 

But fortunately within a few days news came that 
Russia proposed to occupy not only Nertschinsk, but ten 
other Halleyan stations in Siberia ; that America pro- 
posed to occupy three other northern Halleyan stations ; 
Germany two others ; and before long it was announced 
that France would occupy two other northern Halleyan 
stations. 

It was still possible that these energetic proceed- 
ings by other nations might be rendered useless by 
shortcomings on our part ; for as yet no adequate 
provision had been made for southern Halleyan 
stations, and it was manifest that other nations were 
looking to England to take a large share in this part of 
the work. Eighteen northern Halleyan stations were 
provided for, and as yet there was only one first-class 
southern Halleyan station, Kerguelen's Land, — and 
that originally named without the least idea that it 
w r as a Halleyan station at all. 

The time had come for very plain speaking. Be 
it noted that if Delisle's method succeeded at each of 
the selected stations, then the transit would yield very 
good results ; but even then not so good as though 



1 Sir George Airy soon after wrote to me that there had been some 
misunderstanding* here. It can be easily understood that Mr. Goschen 
■who, of course, had no technical familiarity with the subject, might hare 
misapprehended some statement addressed to him by Sir G. Airy. 



THE TRANSITS OF 1874 AND 1882. 1 87 

Halley's method were extensively applied in addition. 
For every method successfully applied, and indeed 
every observation, reduces the probable error in the 
final result. But there was at this stasre a risk that 
the operations would fail altogether. If, as was 
possible, Delisle's method were frustrated by bad 
weather at the Sandwich Islands or at Kenruelen 
Island and neighbouring stations, then ingress obser- 
vations would fail. If egress observations were frus- 
trated by bad weather at New Zealand and neighbour- 
ing stations, or at the opposite region, then egress obser- 
vations would fail. In either case very imperfect results 
would be attained; but if both events were to happen, 
then no result at all would be achieved. Now there 
were eighteen northern Halleyan stations admirably 
suited to supply a third chance of success by Halley's 
method if they were but properly balanced in the 
southern hemisphere, but otherwise valueless. For 
although, besides being Halleyan, they were also ex- 
cellent as subsidiary Delislean stations (each having a 
double chance, because either the beirinninor or the 
end would serve for that method), yet the multipli- 
cation of northern Delislean stations could not remove 
the chances of failure on account of the fewness of 
southern stations. In either respect, whether to 
balance the northern Halleyan stations as such, or to 
give new Delislean chances, nothing was at that time 
promised. Apart from all question of the choice of 
methods, there was no suitable provision for southern 
observation. Kerguelen's Land was the only first- 



1 88 TRANSITS OF VENUS. 

class Halleyan southern station yet provided for, and 
none of the other southern stations could be regarded 
as high even in the second class. These others — 
Canterbury Island, Auckland Island, Mauritius, and 
Kodriguez, stood fairly well in the second class, and 
that was all that could be said. The only good station, 
Kerguelen's Land, was one at which all the meteoro- 
logists had said that bad weather was far more pro- 
bable than fair weather. I had already pointed out, 
as geometrically suitable, Kemp Island, Crozet Island, 
Macdonald Island, the group of islands of which 
Campbell Island is the chief, St. Paul's Island, and 
several others of less value, yet well worth occupying 
if geographically suitable. But Admiral Richards, 
without mentioning these islands by name, had in the 
'Times' described me as recommending the occupation 
of places which were 'little better than geographical 
myths.' 

It began to appear as though, after all, nothing 
would be effected until too late, so that perhaps some 
time about the year 1877 or 1878 astronomers would 
be lamenting that the favourable opportunities presented 
by the transit of 1874 had not been properly utilised. 

But at this critical stage a new force appeared 
on the field, and compelled the Admiralty to retreat 
from the position they had so bravely defended. The 
Board of Visitors at Greenwich met on June 7, 1873, 
and it was there proposed, by Professor Adams, and 
earned unanimously, that Professor Cayley, who in 
his capacity as President of the Astronomical Society 



THE TRANSITS OF 1874 AND 1882. 1 89 

was Chairman of the Board, should apply to. Govern- 
ment ' for the means of organising parties of observers 
in the Southern Seas, with the view of finding addi- 
tional localities in the sub- Antarctic regions for observ- 
ing durations ' — that is, for applying Halley's method. 
Other nations had not been deterred by the 
dangers and difficulties which unquestionably have to 
be encountered in voyages to sub- Antarctic stations. 
America, inquiring among sealing captains, found that 
the Crozet Islands could be occupied, and deter- 
mined to send an observing party to that first-class 
Halleyan station, as well as to occupy second-rate 
Halleyan stations in Tasmania, New Zealand, and 
Chatham Island. The French Government decided 
to occupy Campbell Island and St. Paul's Island 
(those inaccessible 'geographical myths'), besides a 
second-rate southern station at Caledonia Island. 
Thus already the first-class Halleyan stations had 
been quadrupled in number, and the second-class 
largely strengthened. Germany and America both 
proposed to occupy Macdonald Island, if possible, but 
found that this island (sometimes called Heard Island) 
really is almost, if not quite, inaccessible, though an 
attempt was made to land a party there. England 
decided to send a second observing party to Kerguelen 
Island (to be stationed fifty miles from the ether). 
Regarding the four Kerguelen stations as equivalent 
to at least two separate chances of success, adding 
the first-class Halleyan stations, Crozet, Campbell, 
and St. Paul, and the second-class stations, Bourbon, 



190 TRANSITS OF VEXUS. 

Rodriguez, Mauritius, Hobart Town, Melbourne, 
Sydney, &c., as well as the first-class Delislean 
stations in the South, and remembering that ah the 
southern stations were good Delislean stations, while 
several of the added Halleyan stations were doubly 
good Delislean stations because serving both for in- 
gress and for egress, it must be admitted that the risk 
of failure to which I pointed in May 1873 was as com- 
pletely removed as circumstances allowed. 

The North Indian station, Roorkee, which had been 
first intended only for photographic work, was pro- 
vided for as a Delislean and Halleyan station. 

In the meantime, a new and most important aux- 
iliary method of observing the transit — the photographic 
method — had been suggested by Dr. De La Rue. 

In December 1868 he read a paper before the 
Astronomical Society containing the following re- 
marks, inter alia : — 

6 The conditions Avhich transits of Venus offer for 
the determination of the relative position of the sun's 
and planet's centres are more advantageous than those 
presented by solar eclipses, inasmuch that it is far 
more easy to measure directly the distances between 
the centre of the disc of the sun and that of the imasre 
of the planet upon it, than it is to measure the dis- 
tances between the peripheries of the sun and moon, 1 
or the angular opening of the cusps 2 of the partially 
eclipsed sun. And in transits of Venus any error of 
observation would not affect the final result nearlv so 
much as in solar eclipses ; for example, in the transits 

1 Phil. Tra/is., p. 383, Table I. 2 lb. p. 55, Table III. 



THE TRANSITS OF 1874 AND 1882. 191 

of 1874 and 1882, an error of 1" in the measurement 
would, for the maximum displacement, give an error 
of only 0"*185 in the deduced solar parallax. 

' Moreover, it may be observed that in photo- 
graphic records it is by no means important to catch 
exactly the phases of contact, as two photographs 
obtained at a sufficient interval afford the means of 
calculating to a great degree of refinement, and of 
tracing, the path of the planet, which, for the condi- 
tions of the problem, may be considered to be a straight 
line between the two positions recorded. 

' Nor is it in any way essential, as it is with eye- 
observations, that favourable conditions should exist 
for retarding the period of contact at one station and 
accelerating it at another, because the chords repre- 
senting the planet's path can be derived from photo- 
graphic records with as much accuracy under what 
would be considered unfavourable conditions as under 
favourable conditions for eye-observations, for the 
length of the chords need not be directly considered 
in determining the nearest approach of the sun's and 
planet's centres. 

' During the duration of the transit, it would be 
possible, in a clear state of the atmosphere, to obtain 
a series of photographs at intervals of two or three 
minutes, and any or all of these would be available for 
comparison with the records obtained at all the stations 
selected. 

' The epoch of each photographic record is deter- 
minable with the utmost accuracy: 1st, because the 
time of exposure is not more than the g^th or the -. 1 th 



192 TRANSITS OF VENUS. 

of a second ; and 2nd, because the instantaneous slide, 
as it flashes before the secondary lens, affords an 
audible signal ' by striking against a stop a small 
fraction of a second after it has shut off the image of 
the sun. This interval might be determined by ex- 
periment and taken into account. 

' In the Kew Photoheliograph the solar disc would, 
at the epoch of the transit of 1874, have a semi- 
diameter of 1965'8-thousandths of an inch (a diameter 
of nearly four inches), Venus a semi- diameter of 63*33 
of these units, and the parallax of Venus referred to 
the sun would be represented by 47'85 of these units ; 
the maximum possible displacement being 95*7 units, 
or nearly p^h of an inch. In 1882 the sun's semi- 
diameter would be 1964*9 units; that of Venus 63*31 
units ; the parallax of Venus referred to the sun 
47*82 units; the maximum possible displacement 95*6 
units. 

' When the photographs have been secured, the 
measurements by means of the micrometer, which 
would have to be performed, consist in determinations 
of the sun's semi-diameter, in units of the arbitrary 
scale of thousandths of an inch, the angle of position 
of different positions of the centre of Venus, and the 
corresponding distances of her centre from the centre 
of the sun. ' The measurements by means of the 
micrometer described in the " Phil. Trans." 1862, pp. 
373-374, can be obtained to the 2oVo tn °f an " lcn 
(0""25), and the position angles to one or two seconds 

1 Phil. Trans., p. 364. 



THE TRANSITS OF 1874 AND 1882. 193 

of arc. For each photograph measurements made at 
different times are remarkably accordant; the greatesl 
difference between the semi-diameter of the sun of" the 
several eclipse pictures of 1860 was T oVo tns °f an i ,K ' M < 
or about 4 //# 5 ; but, on taking the mean of measure- 
ments of forty-five photographs by two different 
methods, the difference was only T ^_ths, or about 
0"*75. I am inclined to believe that the distance 
could be ascertained to within \" by means of a i'uw 
pictures, and possibly to 0"-25, if a sufficient number 
of photographs were obtained. 

' Fears have been expressed that the collodion, in 
drying, becomes distorted ; experiments, however, in 
1860-61 have demonstrated that the shrinkage is onlv 
in the direction of the thickness. But as, in the case 
of the solar parallax, no refinement of correction ou«ht 
to be neglected, it would be quite easy to ascertain 
once more whether any distortion does take place, by 
taking photographs on glass plates on which lines 
about a quarter of an inch distant had been previously 
etched; the collodion, which should be rendered 
purposely contaminated with particles in suspension, 
should be poured on the ruled sides to avoid parallax. 
After all the operations of photography, the film would 
have to be examined from the back, and the position 
of certain impurities with reference to the ruled lines 
noted whilst the collodion was wet, and after it had 
dried.' 

Three months later, Col. Tennant wrote a paper 
commenting on the practical details of Dr. De La 





194 TSANSITS OF VENUS. 

Rue's plan, in the course of which he pointed out 
that 'there is an advantage in this mode of observing; 
the transit of Venus to which Dr. De La Rue has not 
alluded. 1 If accurate micrometrical observations can 
be made by means of photographic pictures, then the 
range of suitable stations can be greatly enlarged ; for 
any two stations, 140° or 150° apart, can have the ob- 
servations combined by choosing a suitable time, and, 
of course, by means of equations of condition, the ob- 
servations of stations in all sorts of places could be 
used with their proper weight.' 

To this Dr. De La Rue replied as follows: — 
' With respect to the localities to be selected, the 
employment of the photographic method of observing 
transits of Venus has, as I have already stated, the 
advantage of rendering us independent of conditions 
favourable or indeed essential for eye-observations ; 
for a few photographs obtained at each station would 
afford the means of ascertaining the path of the planet 
and its position at any given moment ; and hence the 
proposal to determine the position of the planet's centre 
in relation to the sun's centre really includes the 
particular case contemplated by Major Tennant in the 
foot-note appended to his paper ; but it is possible 

1 ' Dr. De La Rue has pointed out,' says Col. Tennant, ' the facility 
with which the nearest approach can be got from the photographs at 
any one station, but if photographs be taken at two stations at a time 
when Venus is in the plane which includes them both as well as the 
earth's centre, these will show the whole effect of parallax; and it is 
the positions at these instants, and not the nearest approaches to the 
sun's centre, which should be compared.' 



THE TRANSITS OF 1874 AND 1882. 1 95 

that the sun might be obscured at the critical time, at 
one of the two stations selected.' 

In December 1869 I read before the Astronomical 
Society a paper, from which the following passages 
are extracts : — 

« It is impossible to read Dr. De La Rue's account 
of the results of careful measurement applied to pho- 
tographs of the solar eclipses in 1860 and 1868 with- 
out recognising that we have in photography, as 
applied to the approaching transit of Venus, one of 
the most powerful available means of determining the 
sun's distance. Within the last few years, solar pho- 
tography has made a progress which is very promising 
in regard to the future achievements of the science 
as an aid to exact astronomy. So that doubtless, in 
1874, astronomers will apply photographic methods 
to the transits of that year with even greater success 
than we should now be prepared to anticipate. It has 
therefore seemed to me that the photographic obser- 
vation of the coming transit merits at least as full a 
preliminary inquiry as either Halley's or Delisle's 
method of direct observation. 

' The result of an inquiry directed to this end has 
led me to the conclusion that photographers of the 
approaching transit should adopt for their guidance 
considerations somewhat different from those which 
have hitherto been chiefly attended to. 

' It is undoubtedly true, as Dr. De La Hue has 
pointed out, that the photographer of the transit can 
readily take a large number of pictures, and by com- 



196 TRANSITS OF VENUS. 

bluing these, can ascertain with great accuracy the 
path of Venus across the solar disc. And by com- 
paring the paths thus deduced for different stations a 
satisfactory estimate can be formed of the solar parallax. 
I do not wish to suggest any departure from this course 
of procedure. 

' On the other hand, it is undoubtedly true, as 
Major Tennant has remarked, that the greatest effect 
of parallax will be obtained, .for any two stations, 
when both stations — the earth's centre and the centre 
of Venus — are in one and the same plane. So far as 
those two stations are concerned, his remark is just, 
that it is the position of Venus at the instant when the 
stations are so situated, and not the nearest approach 
of Venus to the sun's centre, which should be com- 
pared. And further, Dr. De La Rue's comment on 
this, to the effect that his method in reality includes 
Major Tennant's, is also correct. In fact, there can 
be no doubt that the position of Venus at the particular 
instant referred to by Major Tennant can be far more 
exactly ascertained by a reference to the complete 
path of Venus for each station than from any attempt 
to secure nearly simultaneous photographic records at 
stations far removed from each other. 

' But it appears to me that the method I am about 
to suggest, according to which the whole question will 
be reduced to the determination of a parallactic dis- 
placement of Venus on a line through the centre of 
the sun's disc, is the one by which the fullest assist- 
ance will "be obtained from photography; while a source 



THE TRANSITS OF 1874 AND 1882. 1 97 

of error, which has not hitherto bean specially con- 
sidered, Avill be practically eliminated. 

' It mnst be remembered that in the comparison of 
photographic records, whether for the determination 
of the path of Venus across the sun's disc at a par- 
ticular station, or for the comparison either of Venus's 
apparent position or of her path as seen from two 
different stations, the accuracy of the results will 
depend in part on the certainty with which two or 
more pictures may be brought into comparison by 
means of a fiducial line or set of lines. It seems 
certain that no method can be devised by which all 
chance of error from this source can be eliminated. 
The great point would, therefore, seem to be to render 
its effect as small as possible. 

' Now, let us consider for a moment Major Tennant's 
proposition, as giving a convenient illustration of the 

A 




D 
Fig. 42. — Illustrating the photographic and direct methods. 

effects of any error either in the position of the fiducial 
lines, or in bringing those belonging to two pictures 
into exact correspondence. Let fig. 42 represent the 
result of a comparison between two photographs of the 



198 TRANSITS OF VENUS. 

sun. A B and c u are fiducial cross-lines common to 
both pictures ; a is the centre of Venus for one pic- 
ture, b is her centre for the other ; and on the exact 
measurement of a b depends the determination of the 
sun's parallax, so far at least as these two pictures 
are concerned. Now it is very obvious that if the 
lines A B, C D, for one picture, have not been brought 
into perfect correspondence with those belonging to 
the other, the distance a b will be correspondingly 
affected. In fact, it would appear that if the usual 
methods for making the correspondence as exact as 
possible are followed, almost as large an error would 
be introduced through this cause alone as by errors in 
the measurement of a b, since the two processes — the 
measurement of a b and the adjustment of the sets of 
cross-lines — depend on the very same circumstance, 
the nicety, namely, with which the eye and the judg- 




Fig. 43. — Illustrating the photographic and direct methods. 

ment can estimate minute quantities of about the same 
relative dimensions. 

' But now, if a and b, in place of having the position 
shown in fig. 42, were situated as in fig. 43, it is clear 



THE TRANSITS OF 1874 AND 1882. 199 

that the distance a b will not be appreciably affected 
by any smaJl error in the adjustment of the fiducial 
lines. 

< The object, therefore, which it seems most desir- 
able to secure is that Venus, as seen from two dif- 
ferent stations at a particular instant, should have a 
relative parallactic displacement towards the sun's 
centre, or as nearly towards the sun's centre as possible. 
This amounts to adding to Major Tennant's conditions 
this further one, that the sun's centre should be in the 
same plane with the two stations — or rather to making 
this condition a substitute for that one which requires 
that the earth's centre should be in the same plane 
with the two stations. For, as a rule, we must not 
expect to be able so to arrange matters that two con- 
venient stations on the earth, as well as the centres 
of the earth, Venus, and the sun, should be in the 
same plane. 

' The object which Plate XVI. was originally i:> 
tended to subserve was to determine what station 
were most suitable for applying photography to the 
transit of 1874, on the principles above enunciated ; 
though, as we have seen, the drawing illustrates also 
the character of the transit.' 

In Chapter IV., in pp. 148-152,1 have shown how 
all the chief elements of the transit could be deduced 
by considering the motion of Venus relatively to a pair 
of cones, each enveloping the sun and the earth, but 
one having its vertex outside the earth, the other 
havino; its vertex between the earth and the sun. In 



200 TRANSITS OF VENUS. 

the paper from which I have been quoting, after ex- 
plaining the construction of Plate XVI., I proceeded 
as follows : — 

' We have only to invert fig. 35, and look at it 
from behind, to see what sort of path Venus Mould 
seem to traverse upon the sun's disc, either with 
reference to the earth's centre, or to anv Doint of the 
earth's surface supposed to be properly depicted upon 
the small discs 1-15 in fiV 35. 

• It follows, therefore, that if we want to determine 
two stations at which at any instant Venus would 
appear to have a relative parallactic displacement 
towards the sun's centre, all that is required is that 
Ave select two stations which are on the same radial 
line from the common centre of the circular sections 
in fig. 36. 

' The positions of those radial lines which cross the 
earth's track c d are exhibited in Plate XVI.' 

The paper went on to show that (from Plate 
XV T I.) North India, Siberia, Cape Town, Kerguelen's 
Land, Crozet Island, and other places would be avail- 
able for the application of the photographic method. 

The American astronomers relied chiefly on the 
photographic method, applied at stations vhere the 
whole transit can be seen. 

The plan they adopted for photographing the sun 
differed essentially from that which European astro- 
nomers propose to employ. ' For the purpose of 
obtaining an enlarged image on the photographic plate,' 
writes Professor Hilgard, of Washington (describing 



THE TRANSITS OF 1874 AND 1882. 201 

the ordinary method), ' the image of the sun, after 
being formed in the focus of the telescope, is enlarged 
by a lens or camera to the desired size, the photohelio- 
graphs, as they are called, being thus enlarged to a 
diameter of about four inches. This plan has been 
adopted for the photographic apparatus to be used by 
the British, German, and Russian parties commissioned 
to observe the transit of Venus. A different plan has, 
however, been adopted for the American parties, with 
the view of avoiding some difficulties to which the 
former method may be thought subject. These are 
conceived to reside in the fact that not only all imper- 
fections in the focal image are thus enlarged, but that 
the optical imperfections of the camera are superadded. 
To avoid this objection it was deemed best to make 
the telescope so long that the image formed in its 
principal focus would need no further enlargement. 
Here another difficulty presented itself. The telescope 
must be forty feet in length in order to give an image 
four inches in diameter.. Such a telescope, pointed at 
the sun, would scarcely be manageable. Hence the 
plan was devised, which Professor Winlock was the 
first to put into practical operation. It consists in 
fixing the long telescope in a horizontal position, and 
reflecting the sun's rays into the object-glass by means 
of a plane glass mirror, moved by clockwork, so as to 
throw the image of the sun continually into the tele- 
scope. This need not be done with great precision, 
since, as has already been said, the time of exposure is 
exceedingly small, and the mirror can at any time be 



202 TRANSITS OF VENUS. 

adjusted. It is obvious that, in this arrangement, as 
much depends upon the perfect figure of the mirror, 
as in the other upon that of the enlarging lens ; but 
it is, doubtless, an advantage that different methods 
should be employed, so long as a sufficient number of 
stations are occupied to give an independent result for 
the sun's distance from observations by each method 
alone, since such only can be considered as strictly 
comparable. This condition is amply fulfilled by the 
abundant provision made by the American Govern- 
ment for the observation of the important event in 
prospect.' 

I may remark, however, that Professor Newcomb, 
with whom I had the pleasure of a conversation rela- 
tive to the subject, attaches very great importance to 
the advantages of the American method. He remarked 
that by employing this method the astronomer is 
enabled to measure the distance of Venus from the 
sun's centre with an exact knowledge of the value of 
the deduced distance, because, the focal length of the 
telescope being known, the value of any distance indi- 
cated in the focal image is at once determined. All 
that is necessary, then, is to determine the centre of 
the solar image, which can be safely done by measure- 
ments made from the limb. Manifestly no photographic 
effects affecting the position of the limb in the photo- 
graph could appreciably affect the determination of the 
centre even though such effects were not absolutely 
uniform all round. But in the ordinary method of 



THE TRANSITS OF 1874 AND 1882. 203 

photographing the determination of the arc-distance of 
Venus from the centre is not reliable (in a problem of 
such extreme delicacy), because the estimated dimen- 
sions of the solar image could not be accurately 
determined, while the observed dimensions, being 
determined from the photographic limb of the sun, 
would be affected more or less by photographic irradi- 
ation. No apparent sharpness of the limb can render 
certain the fact that the limb in the photographic 
image corresponds to the true solar limb. I must 
confess that Professor Newcomb's reasoning seems 
to me irresistible. It will be observed that it does 
not depend on practical or technical knowledge of 
photography, since the photographic irradiation demon- 
strably exists, and is demonstrably variable in amount. 
In a conversation with Dr. H. Draper, of New York, 
whose experience in those matters is well known to be 
unsurpassed, I found Professor Newcomb's doubts 
fully confirmed. It is true that Dr. Rutherfurd, 
whose great practical experience in solar photography 
is unquestioned, agreeed with his eminent British rival 
in such work, Dr. De La Rue. But then it is to be re- 
membered that both Rutherfurd and De La Rue viewed 
the matter as photographers, while Newcomb and 
Draper view it chiefly from an astronomical standpoint, 
and in this case the astronomical, not the photographic 
relations, were chiefly in question. Not handsome 
solar pictures, but pictures which could be confidently 
measured were wanted; and certainly the plan adopted 



204 THAXSITS OF VENUS. 

by the American astronomers is that which best met 
this requirement. 1 

Experiments were made on the phenomena of con- 
tact by means of an artificial transit. Although the 
results obtained at Greenwich were not altogether so 
satisfactory as they might be, owing to the short distance 
from the observer at which the artificial discs have 
been placed, yet they only differ in degree, as presented 
in the following passage, from the more marked pecu- 
liarities observed at Washington (where I studied the 
phenomena myself): — 

1. It requires considerable experience for an ob- 
server to appreciate all the definite changes of appear- 
ance which occur. 

2. When two observers describe a particular phase 
which they see, and determine to observe this phase 
together, the times recorded by each are generally 
accordant within a fraction of a second. 

3. The successive phases of an ingress or egress 
appear to follow each other sometimes rapidly, at 
other times gradually; so that in some cases all the 
phenomena are observed within three seconds, on other 
occasions the same series of phases is completed in ten 
seconds. 

4. The time at which any particular phase is ob- 
served varies very slightly with the aperture of the 
telescope. When a telescope of good definition is 

1 Lord Lindsay, it is to lie noted, employed the same method as 
the American astronomers, after carefully testing with Mr. Ranyard, in 
a series of photographic experiments, the reliability of the two methods. 



THE TRANSITS OF 1874 AND 1882. 205 

employed, the time of any phase at ingress is earlier 
than with an instrument of less perfect definition. 

Observations such as these necessarily served to 
diminish the error of contact observations, especially 
as the observers not only measured the distances be- 
tween the cusps as contact proceeded, but caused the 
phenomena of contact to be indicated photographically 
by an ingenious arrangement contrived by Janssen. 

In considering the results obtained last December, 
it will be well to deal with the several methods sepa- 
rately, rather than to take the stations in order ; in 
fact, no otherwise can clear or satisfactory ideas be 
obtained of the success of the whole plan of operations. 

AVe may consider the methods in use as divided 
into three broad classes : the Delislean, the Halleyan, 
and the mid- transit method. This classification in- 
cludes the photographic and heliometric operations, as 
well as the spectroscopic method for observing external 
contact ; for both photography and heliometry may be 
regarded as means for determining the position of 
Venus at given instants, either near the beginning or 
end of transit, or near the middle of her chord of 
transit; and observations of external contacts, either 
at the beginning; or end of transit, come under the 
head of Delislean operations, while the observation of 
the interval of time between the two external contacts 
is a Halleyan operation. But also the Halleyan and 
mid-transit methods can be considered together, be- 
cause all good Halleyan stations are good stations for 
observing mid-transit. Let us take the classes in the 



206 TRANSITS OF VEXUS. 

order indicated, viz., first, the Delislean ; secondly, 
the Halleyan. Speaking generally, it may be said 
that the English scheme was the only one which made 
direct provision for Delisle's method. The Americans 
declined, totidem verbis, to occupy any station where the 
whole transit could not be seen ; the French refused 
to occupy the Mauritius or Suez (calling forth from 
English official astronomers an expression of strong 
dissatisfaction) ; and the Germans, though they occu- 
pied a station in Persia where the ingress could not be 
seen, yet specially provided for photographic work there 
during the middle of the transit. The Russians alone, 
having provided eleven Halleyan stations in Siberia, 
consented also to have observers at Delislean stations 
nearer to Russia in Europe, extending around e' to 
the Black Sea, Caspian Sea, and Sea of Aral. 

The only Delislean stations, properly so termed, 
near I, Plate VI., were those occupied by the three 
English parties, under Captain Tupman, in the Sand- 
wich Isles, at Honolulu, Atooi, or Kauaii, and 
Owhyhee (or Hawaii). At the first two observations 
were successfully made, but at Hawaii, the least im- 
portant, fortunately, of the three, the observers, 
Forbes and Barnacle, had bad weather. 

Captain Tupman, at Honolulu, says that e the sky 
was cloudless — a circumstance not altogether in our 
favour, as the heat of the sun was terrific' At 
Waimea, Atooi, the weather was equally fine ; ' not 
the faintest cloud or mist appeared.' On the whole, 



THE TRANSITS OF 1874 AND 1882. 207 

the observations made at the Sandwich Island stations 
were successful. Captain Tupman ' Avas not satisfied 1 
with the determination of the moment when Venus 
had just completely entered upon the sun's face. A 
circumstance which appears to have taken many by 
surprise, though in reality it had been observed in 
previous transits, rendered the observation more 
difficult than it otherwise would have been. Venus 
has an atmosphere probably as dense as our earth's, 
and consequently there is a twilight-circle on Venus, 
and not only so, but the sun would be raised by the 
atmospheric refraction just as the setting sun with 
us is raised above the horizon after he has in reality 
(that is, in a geometrical sense) passed below it. 
The sun is raised at this time by more than his 
whole diameter. Now suppose Venus drawing near 
to the sun, and that we look at the point of her 
outline farthest from his. In so doing (and taking 
no account of the part of her atmosphere on her other 
side), we are looking at the sun in the same direction 
as an inhabitant of Venus stationed at that point we 
are looking; at. But this being would see the sun 
close to his horizon, and raised as much as our sun is 
raised near the time of sunset (always supposing the 
atmosphere of Venus just like ours). The terrestrial 
observer is, as it were, behind the supposed inhabitant 

1 The passage "which follows is quoted from an article written by 
me for the ' Cornhill Magazine,' and appeared in the number for May, 
1875. 



2o8 TRANSITS OF VENUS. 

of Venus, so that both see the same effect produced, 1 
only the terrestrial being so far behind, the displace- 
ment of the sun is proportionately diminished. Never- 
theless, he also would see the sun round that edge of 
Venus, even on our supposition that the near half of 
the atmosphere of Venus produced no effect. But in 
reality that half produces just the same effect as the 
other half, doubling the displacement, so that the 
observer on earth cannot fail to receive sunlight round 
that part of Venus, even, which is remotest from the 
sun. All along the edge of the half of Venus farthest 
from the sun his light is bent round and sent earth- 
wards, though it need hardlv be said that the result is 
to give only the finest possible thread of sunlight 
around that side of Venus, and no doubt, to ordinary 
observation, this thread would be imperceptible. 2 
Now, the nearer Venus draws to the sun the brighter 
would this thread of light be, and when more than 
half of her disc had passed on to the sun's, the circle 
of light bounding the other half could hardly fail to 
be perceptible to a good observer armed with a power- 
ful telescope. But then conceive the difficulty thus 
occasioned. What the observers had been specially 
instructed to look for (without, it would appear, the 
least hint of the peculiarity in question, though very 

1 Much as though an insect were to look through a decanter of 
water at a page of print from a distance of a yard or so, while another 
looked in the same direction, but from a distance of two yards. 

2 Nevertheless, Prof. Newton, of Yale College, has seen the fine 
circle of light completely formed round Venus, during one of those 
passages of the sun which occur at intervals of about 684 days, but 
ordinarily carry her past him without transit. 



THE THAA'SITS OF 1882 AXD 1874. 209 

carefully instructed about the quasi-mythical black 
drop) was the appearance of the sunlight between 
Venus and the sun, as her motion separated her 
from the sun's edge : but, on account of the action 
of Venus's atmosphere, a line of light (real sunlight, 
too) appeared round the part of Venus which would 
last cross the sun's edge, and became distinct before 
that part Avas even near true contact. Here, then, 
was the criterion of contact suddenly rendered useless, 
and the observer left to judge of contact in another 
way, if in the excitement of the moment he were not 
deceived by this thread of light so as to suppose it 
indicated that Venus had fully entered on the sun's 
face.' We find that Captain Tupman, though discon- 
certed, was not deceived, while Mr. Nichol, who 
observed with a smaller telescope, was deceived, but. 
apparently, not disconcerted. Mr. Nichol withdrew 
from observation thirty seconds before Captain Tup- 
man, ' conceiving,' writes the latter, ' that contact was 
passed,' and recording nothing later. ' I am not at all 
surprised,' proceeds Captain Tupman, 'for there was 
nothing sudden to note, and the complete submergence ' 
(here he regards Venus as sinking into the sun's disc) 
' was so gradual, any one might have recorded ten 
seconds before I did, -and have been quite as accurate. 
My first impression was, such an observation could 
not possess any value. It was something similar in 
principle to having to decide where the Zodiacal Light 
terminates; bearing in mind, of course, that we ex- 
pected to get the contact within a second or so of time. 

P 



2IO TRANSITS OF VENUS. 

Unfortunately a photographic arrangement, by 
which it had been hoped that the true instant of con- 
tact would be indicated, was not successfully applied. 
This arrangement was what has been called the 
' Janssen turning-wheel.' A circular photographic 
plate was so arranged "that a series of sixty pictures 
could be obtained all round the edge, a second being 
given to each, so that the whole process would last 
one minute. If this minute were so taken as to 
include the moment of contact, then that moment 
would be known, because the successive pictures were 
all carefully timed. Now it would appear that Cap- 
tain Tupman gave the signal at exactly the right time, 
and the atmospheric conditions were excellent; the 
turning-wheel was set going, and everything seemed 
to have worked well; but unfortunately, when the 
pictures were developed, it was found that the tele- 
scope had been wrongly directed, so that in every 
one of the sixty pictures 'the planet is cut in half.' 
This is the interpretation of the unpleasant telegram 
received from Honolulu, a few days after the transit, 
announcing that 'Janssen failed.' 

At Port Possiet and "Wladiwostock, near the 
western shores of the Sea of Japan, the ingress was 
well seen by Russian aud American observers ; but 
the acceleration there only amounted to about 6£ 
minutes, whereas, at the Sandwich Isles, it amounted 
to 11 minutes. At Yokohama and Nagasaki the 
Americans and the French (under Janssen) made 
srood observations. 



THE TRANSITS OF 1874 AND 1882. 21 r 

Accelerated ingress was fairly provided for ; 
though at the best English stations for that phase 
Janssen's method failed, and the ingress was not very 
satisfactorily seen. 

In the opposite region around I, Plate VI., there 
were three English observing parties, two in Ker- 
guelen Island, and one on Rodriguez ; while Lord 
Lindsay's station at the Mauritius, though noc 
specially intended for Delislean operations, was even 
better placed than the Rodriguez station. I shall 
speak more at length of Lord Lindsay's operations 
further on. Here it is only necessary to say that 
his party missed ingress, though otherwise successful. 
At Rodriguez ingress was successfully observed, but as 
yet full details have not been published. It is known 
that the various parties stationed on Kerguelen 
Island were successful ; but the nature of their suc- 
cess is not known, all the news yet received from 
that dismal island having been derived from the inter- 
change of signals between the parties stationed there 
and a passing ship. 

It would appear that a fair success has attended 
the employment of Delisle's method, as applied to 
ingress. At least, whatever defects may appear here- 
after in the results bv this method will be due to the 
inherent defects of the method itself, requiring as it 
does the observation of contact when the sun is not 
far from the horizon. Janssen's contrivance, by which 
it was hoped that this difficulty would be removed, 
failed entirely for ingress. 

r 2 



212 TRANSITS OF VENUS. 

Turning next to egress, we have first to consider 
the operations around the point e', Plate VI., where 
accelerated egress was to be observed. The stations 
provided by England for observing this phase were in 
New Zealand, though the Government Observatory 
at Melbourne, and the Observatory at Sydney, were 
fairly placed. It must be remembered, however, that 
everything depends on securing observations at both 
ends of either Delislean base-line by similar methods 
and by observers similarly trained. The only stations 
thus provided for were those in New Zealand ; and 
unfortunately bad weather prevented the observation 
of egress at any of these stations. The American 
party, stationed at Queenstown, in Otago, w r ere able 
to observe and photograph all the transit except 
egress, but the English parties were not even favoured 
with this partial success — or rather, I should say, with 
a degree of success which, in their case, would have 
been but partial ; for to the Americans the observa- 
tion of egress was a matter of small importance. It is 
impossible not to sympathise with Major Palmer, on 
account of this unfortunate end to a campaign for 
which he had made very complete arrangements. As 
a member of his party, writing from Wellington, 
remarks, ' it certainly seemed not too much to expect 
that, towards evening of a summer day in December, 
one of the finest months in the year (in New Zealand), 
an hour's clear sunshine might be vouchsafed to at 
least a considerable part of a colony somewhat larger 
than Great Britain, and famed for the beauty of its 



THE TRANSITS OF 1874 AND 1882. 213 

climate. Unhappily, these hopes and expectations 
were crushed by a day of pitiless weather. All 
through the 8th, and till mid-dav on the 9th, from 
every quarter of both islands, telegrams conveying 
the same dismal tidings of mist and rain, cloud, gloom, 
and falling barometers, poured in on Major Palmer, 
the English chief, warning him that unless some 
sudden and unlooked-for change should verv soon 
take place, the careful plans to which he and his 
colleagues had for so long given their time and 
energies would prove to have been made in vain. 
No change came, and failure was the result.' ' To 
crown their trouble, the day after the transit was 
provokingly, almost mockingly, fine. Some excellent 
sun-photographs, which were taken at Burnham on 
that day, showed how carefully the dry plates had 
been prepared, and how successful this, the least 
certain branch of the work, would have been. That 
the choice of stations was judicious, and that all 
Avas done that could be done with the means at 
command, is the opinion expressed everywhere.' This 
opinion will certainly be shared in England also ; nor 
will astronomers be slow to accord to Major Palmer 
their fullest sympathy for his misfortune. 

The Germans at the Auckland Islands, a station 
superior in value to any in New Zealand, achieved 
great success. Ingress, irdeed, was obscured, ' but 
ten minutes later the sun shone out, and, the sky 
remaining clear to the end of the transit, some 150 
jshotographs, as well as the observation of egress. 



214 TRANSITS OF VENUS. 

were obtained.' The French at Caledonia Island 
saw everything except the egress. The French at 
Campbell Island had bad weather, as had also the 
Americans at Chatham Island. On the whole, egress 
was not well provided for. 

Turning next to the region around e, Plate VI., 
where retarded egress was to be observed, we have 
to consider results of a mixed character. At all the 
best stations, viz., those occupied by the Russians, 
bad weather prevailed. The Russian Delislean ob- 
serving parties were spread over Western Siberia, and 
included such important stations as Erivan, Tiflis, 
Taschkent, Astrakhan, Omsk, Blagowestchensk, &c. 
At some of these stations the retardation Avould have 
been fully twelve minutes, whereas, at the English 
stations in Egypt and North India, the retardation 
amounted only to ten minutes. At Ispahan, where a 
German party Avas stationed, there would have been 
a retardation of 10^ minutes ; and as the results would 
have been directly comparable with those obtained at 
the Auckland Isles, a very valuable Delislean success 
would have been obtained had good weather prevailed 
at Ispahan. Unfortunately, though some good mid- 
transit photographs were secured, the contact at egress 
was missed through clouds. A Russian party, but 
not provided with fh'st-class instruments, were success- 
ful at Teheran. But the chief success, so far as 
retarded egress was concerned, was obtained in Egypt 
and in North India : a circumstance which makes the 
ill-success of Palmer in New Zealand the more un- 



THE TRANSITS OF 1874 AND 1882. 21 5 

fortunate, as it was with his observations that the 
Egyptian results were to have been compared. In 
Egypt thick haze prevailed on the important morning, 
until within a few minutes of the moment of contact. 
Then, however, the sun passed clear of the low-lying 
haze, and the contact was well observed. It was at 
first announced that Captain Abney had succeeded in 
getting a photograph of the contact by the Janssen 
instrument, but this news turned out to be incorrect. 
He just missed the actual contact, though it would 
appear that the moment of contact can be approxi- 
mately determined from the photographs. 1 The 
German observers stationed in Egypt also made very 
satisfactory observations. At Rooi'kee, in North 
India, egress was well observed (as also the whole 
transit). 

On the whole, the Delislean observations for egress 
have been fairly provided for. The special English 
plans have been defeated by bad weather in New 
Zealand ; but the observations at Melbourne and 
Sydney will combine tolerably well with those made 
in Egypt and at Roorkee. The German observations 
in the Auckland Isles will combine admirably with 
the German observations in Egypt. 

Before passing to the operations by other methods, 
it may be well to consider the general Delislean results, 
and the lessons they teach us as to future operations. 

1 It seems tolerably clear that, in future applications of the Janssen 
arrangement, provision must be made for a lunger interval than one 
minute. 



2 1 6 TRANSITS OF VENUS. 

It is, in the first place, certain, that if only Delislean 
operations had been provided for, as in the original 
programme, the measure of success achieved would 
have been very far from satisfactory. Early ingress 
was not, on the whole, well observed, and Janssen's 
method failed, so that the complete ingress opera- 
tions are to some degree imperfect. The English 
special operations for observing egress have completely 
broken down through the failure in New Zealand. 
The success of the Germans is a strong point, but one 
success counts for little in a process where everything 
depends on reducing the final error through the number 
of successful observations. It is to be noted that the 
German success results entirely from the fact that the 
Auckland Isles were occupied. These are among the 
island groups to which I directed attention in 1869. 
At another of these, Chatham Island, the Americans 
had bad weather. At two others, St. Paul's Island 
and Campbell Island, the French had divided success, 
beinu - fortunate at the former and unfortunate at the 
latter. All of these were specially named by me as 
suitable for applying the Delislean method, and also 
for observing the whole transit. Their occupation by 
America, France, and Germany, and the success of 
the Germans and French, sufficiently justify my sug- 
gestions, and more than meet the comments made on 
these suggestions by official persons. On the other 
hand, the partial failure of the English Government 
operations in no sense supports my position, except in 
so far as to justify the anxiety I expressed. Bad 



THE TRANSITS OF 1874 AXD 1832. 217 

weather might equally have thwarted those arrange- 
ments proposed by me, which other nations carried 
out. 

Turning now to Halleyan and mid-transit opera- 
tions, we have a series of excellent results to consider, 
(lji the first place, let us examine the northern suc- 
cesses. At Nertschinsk, where the duration fell short 
of the mean by fully 15^ minutes, the Russians ob- 
served the whole transit with excellent telescopes, and 
obtained a number of measures and photographs. The 
success is particularly gratifying, as Nertschinsk was 
the best of all stations for applying Halley's method. ) 
So far back as 1869 I called special attention to this 
point. But we have seen that even so late as February, 
1873, the Astronomer Royal declined to believe that 
observations avouIc! be made there. ' Nertschinsk,' he 
said, 'is a station in high latitude, nearly 1,000 miles 
from the nearest sea. I presume that its climate is 
truly continental. At St. Petersburg, in the winter, 
the sun sometimes is not seen for several weeks 
together. I suppose that the same may happen at 
Nertschinsk. I doubt greatly the probability that any 
observations can be made there.' This he assigned 
as the sole reason why England should not occupy 
Southern Halleyan stations. Though four years had 
passed since I pointed to Nertschinsk as a suitable 
northern station, the fact remained still unknown to 
the person principally responsible for the English 
arrangements that eighty per cent, of winter days are 
clear at Nertschinsk. Of course Russia occupied this 



2l8 TRANSITS OF VENUS. 

excellent station. She also occupied ten others in the 
region extending thence to the Sea of Japan, obtaining 
more or less complete success at six of them. The 
Americans were successful at Wladiwostock and Pos- 
siet, the Germans at Chefoo, the French in Japan and 
at Pekin. The duration was not, indeed, secured at 
all the Northern Halleyan stations, though it was at 
most of them ; but where either ingress or egress was 
missed, the position of the chord of transit was effec- 
tually secured by mid-transit photographs and helio- 
metric measurements. At Roorkee, in the long-neg- 
lected Indian region, the whole transit was observed 
and photographed under Col. Tennant's skilful super- 
vision. The Germans photographed mid-transit at 
Ispahan, the Russians at Teheran. The whole transit 
was also observed by amateur astronomers at Kurra- 
chee, Indore, and Calcutta, a fact rather showing what 
ought to have been done by official astronomers in 
England to strengthen the north Indian position, than 
(in all probability) adding much to the value of nor- 
thern Halleyan operations^ 

In the Southern Hemisphere corresponding suc- 
cesses have been already reported, though as yet we have 
not received full accounts from some of the best south- 
ern stations, nor have we sufficient news of the nature of 
the success known to have been achieved at Kerguelen 
Island. But the Germans were successful in securing 
mid-transit photographs in the Auckland Isles, and the 
Americans at Otago and in Tasmania. At Sydney, 
Melbourne, and Adelaide, the chord of transit had been 



THE TRANSITS OF 1874 AND 1882. 219 

well secured. At Melbourne, in particular, the obser- 
vations may be regarded as presumably most valuable, 
on account of the Government Observatory there. 
From the French stations in St. Paul's Island we have 
news, as already stated, of complete success ; while at 
Campbell Island, unfortunately bad weather prevailed. 
At Rodriguez the whole transit was seen, and mid- 
transit well photographed. The French also secured 
more than two hundred daguerreotypes at Caledonia 
Island, and these will prove exceedingly useful. 

But the most complete mid-transit success was that 
achieved by Lord Lindsay's party at the Mauritius, 
where photographic arrangements much more satis- 
factory than those made at the Government stations 
were combined with heliometric observations of mid- 
transit and spectroscopic observations of exterior con- 
tact, neither of which methods had been provided for 
at all by our official astronomers. 1 

1 It seems to me that Lord Lindsay's recent work in the cause of 
science is worthy of more than ordinary recognition. It is no new 
thing, indeed, for men of wealth and leisure to devote large sums to 
the advancement of science, though even in this respect what Lord 
Lindsay has done is noteworthy, seeing that the expedition fitted out 
by him will involve, first and last, a cost more than the entire amount 
devoted to the British Government expeditions. The remarkable 
feature in the present case is the personal activity displayed in the 
cause of science by one who might well have been content with the 
contribution of some seventeen thousand pounds to a single scientific 
expedition. Moreover, it is to be remembered that this was not by any 
means the first of Lord Lindsay's services to science. On the occasion 
of the eclipse of December 1870, Lord Lindsay fitted out an expedition 
at his own expense, all the preparations being much more complete 
than those made for either of our Government expeditions. On that 
occasion he accompanied his party, and took an important share in the 
work of observation. The next great astronomical event in which he 



220 TRANSITS OF VENUS. 

On the morning of the transit, at Mauritius, the 
sun rose concealed by clouds. Minute after minute 
passed without any sign of a break in the cloud-bank 
behind which the sun lay hidden. The important 
period of ingress, from first external contact to first 
internal contact, passed without a single opportunity 
of observing the motions of Venus as she entered on 
the sun's face. Had Lord Lindsay's party been rely- 
ing upon the views entertained by astronomers five 
years ago, according to which only the Delislean 

assisted was the Total Eclipse of December 1871. On that occasion lie 
fitted out an expedition at great expense, the results obtained by which 
were the most important ever obtained in eclipse observation, seeing 
that Lord Lindsay's party stationed at Baikul secured a series of photo- 
graphs of the corona which finally established the solar nature of that 
wonderful object. Lord Lindsay did not himself join the expedition to 
India, but he took a large part in the work of analysing the results 
.then obtained. A laboratory was fitted up by him in London, where, 
in company with Mr. Davis (to whose skill the success of the operations 
was in large part due) and other skilful assistants, he investigated care- 
fully all the details of the photographs obtained in India. Even at 
that time preparations were being made and experiments carried on for 
the expedition to observe the transit at the Mauritius. Lieut. Gill was 
placed as superintendent over Lord Lindsay's observatory at Dunecht, 
where all the instruments and methods to be emplovedduring the transit 
were carefully tested. At the laboratory in London experiments were 
made by Lord Liudsay and Mr. Eanyard on the peculiarities of solar 
photographs, in order that the best method of photographing the pro- 
gress of the transit might be adopted. Lord Lindsay not only took a 
share in such work, and in superintending the preparations at Dunecht, 
but visited continental astronomers, physicists, and instrument-makers, 
inquiring into the qualities of various methods, processes, and instru- 
ments, in order that every available means for securing the best results 
might be employed. Lastly, he was not content to send out the expe- 
dition thus carefully provided for, but himself went to the Mauritius 
and shared in the work of observation. 



THE TRANSITS GF 1874 AND 1882. 22 1 

method could be applied, their whole scheme of opera- 
tions would have already failed, since the egress at 
Mauritius was not worth observing for that method. 
But the failure thus far signified only that one method 
out of three which the party had hoped to apply had 
failed them. We may say, indeed, that Halley's 
method had also failed, seeing that the duration of the 
transit could not now be determined ; but the essential 
object in Halley's method is to determine the position 
of the chord of transit, and it still remained possible 
that this end might be secured. Fortunately the 
clouds which had so long concealed the sun cleared 
partly away about one hour after transit began, and, 
though the sun Avas visible only for a few minutes, 
photographs and measures were obtained. It was not 
till eiojit o'clock in the morning that it became fairly 
fine, and from that time the course of observation 
steadily proceeded until the end of the transit. 

Lord Lindsay's place was in the photographic 
room. 'I took,' he says, '271 plates, out of which 
number perhaps 100 will be of value : cloud and the 
high temperature of the camera were much against 
me, the temperature varying from 96° to 100°. With 
the heliometer Mr. Gill obtained five complete deter- 
minations of greatest and least distance of the centres 
of the sun and Venus, besides nine measures of cusps, 
and two determinations of the diameter of Venus near 
the end of the transit. Dr. Copeland obtained fifteen 
measures of least distance of Venus from the sun's 



222 TRANSITS OF VENUS. 

limb, and ten measures of cusps. The last internal 
contact was observed successfully, as also the last ex- 
ternal contact. 

I come next to a point which I would willingly pass 
over, but that the history of the transit would be in- 
complete without some account of it. It had been 
shown by me, in 1869, that Cape Town would be an 
excellent station for observing the middle of the transit. 
A letter published in the ' Times,' for February 15, 
from Mr. Dunkin, informed astronomers that the egress 
of Venus was satisfactorily observed at Cape Town 
by Mr. Stone, Astronomer Royal at the Cape. The 
satisfactory observation of egress at Cape Town unfor- 
tunately counts for very little more than the satisfac- 
tory observation of a sun-spot on the morning of the 
transit. The valuable stations for egress were those 
already considered, where egress was either notably 
accelerated near e', Plate VI., or notably retarded 
near e. Cape Town is remote from either region, and 
observations of egress there had scarcely any value 
whatever. But Cape Town as a southern mid-transit 
station was better titan any station occupied either 
by our oion country or by others. Mid-transit photo- 
graphs secured there, especially with all the advan- 
tages of a well-provided national observatory, would 
have been invaluable : so, also, would have been helio- 
mctric measures of Venus at the time of mid-transit, 
and afterwards until the end of the transit. It is now 
known that absolutely no provision whatever had been 
made for these most important purposes, Mr. Stone not 



THE TRANSITS OF 1874 AND 1882. 22?, 

possessing even the roughest appliances for observing 
mid-transit. 1 If the opportunity of utilising the Cape 
Town Observatory for mid-transit observations had 
simply been overlooked, little need have been said. 
That would have been no novelty, unfortunately. But 
special attention had been directed to the value of the 
station. In reply to a letter by Admiral Sir H. Cooper 
Key, inquiring whether Sir G. Airy had made arrange- 
ments for photographing mid-transit, the answer came 
that the method had been amply provided for ; yet at 
the very best station for the purpose no provision had 
been made, though the station was exceptionally suit- 
able, because of the Government Observatory there, 
and the presence of skilled astronomers. This would 
have been unfortunate as a mere case of neediu-ence, 
but in its real aspect the matter is much more serious. 
It will not readily be forgotten. 

In summing up the results of Halleyan and mid- 
transit operations, we must distinguish between contact 
observations, photographic results, and heliometric 
measurements. We must also draw a distinction be- 
tween the various modes of photographing the transit 
employed at different stations. 

1 It is impossible not to connect this with what happened in the 
case of the important total solar eclipse of April 1874, when totality 
lasted more than four minutes. On that occasion, though the track of 
total shadow passed close by our Cape Colony, Mr. Stone received no 
assistance whatever towards the proper observation of the eclipse. He 
had not even an equatorial telescope ; but was obliged to observe with an 
altazimuth telescope ' borrowed fiom Mr. H. Solomon,' to which Mr. 
Stone attached a spectroscope with 'wrappers of wash-leather,' for want 
of more suitable appliances. 



224 TJRAXS1TS OF VENUS. 

It seems probable that in future transits less re- 
liance will be placed on contact observations than on 
photographic work. It is true that the results obtained 
during the recent transit show that the phenomenon 
of the ' black drop,' which in 1761 and 1769 occasioned 
so much trouble, depends on instrumental imperfec- 
tions and atmospheric disturbances, 1 and can be prac- 
tically eliminated by employing good telescopes and 
choosing stations where the sun will not be too low at 
the time of either internal contact. Nevertheless, a 
' personal equation ' comes in, depending on the fact 
that the eye itself is part of the optical arrangement 
for observing contact, and thus the observed moment 
of contact depends — to the extent of three or four 
seconds at least — on the observer's idiosyncrasies. 
This equation may be estimated by practice on 
models ; but it must always remain doubtful how far, 
in the excitement of transit observation, the personal 
equation remains the same as in the calm of ' model 
transit ' operations. 

Heliometric measurements, again, seem inferior to 
the instantaneous work of photography. On any reason- 
able assumption as to the skill of the observer, it is 
impossible to believe that he can measure the position 

1 Mr. Stone's ideas on this subject, on which so much stress was laid 
in 1868, have been entirely overthrown by the recent transit observa- 
tions. Of all whose results have reached us, Mr. Stone himself was the 
only observer of skill who with a good telescope, saw any approach to 
the ' black drop ' required by his theory. Certainly he saw and pictured 
what accorded most perfectly with his own ideas ; but that only shows 
how likely preconceived opinions are to make the observer fancy he sees 
what he thinks he ought to see. 



THE TRANSITS OF 1874 AND 1882. 225 

of Venus with an accuracy comparable to that with 
which the photographic picture can be measured, if 
only that picture is clearly defined, and not affected by 
imperfections such as w T ould render the process of 
measurement uncertain. For instance, specks an* 1 
stains on the photograph do no harm. A contraction 
of the film in photographs on glass would be mischie- 
vous, as also would be the effects of so-called photo- 
graphic irradiation, if measurement depended on the 
size of the photographic image of the sun as affording 
a scale of measurement, while of course any optical 
defects would be fatal. But if such sources of error 
as these last can be in any way avoided, then photo- 
graphy must take its rank as facile princcps among 
the available methods for dealing with transits of 
Venus. 

We must then, in considering the photographic 
results, attach chief — if not sole — value to the successes 
obtained by the Americans and Lord Lindsay using the 
long focal method, and by the French using Daguerre's 
process. Fortunately a sufficient number of results 
have been obtained by both methods, and in both 
hemispheres, to ensure the determination of the solar 
parallax to a much greater degree of accuracy than 
heretofore. 

It is not too much to hope that the sun's distance 
may now be ascertained within limits of error nut 
exceeding 100,000 miles on either side of the true 
distance. 

On the whole, Science has every reason to be 

Q 



226 TRANSITS OF VENUS. 

congratulated on the results achieved during the 
observation of the late transit. There were errors 
at the outset, and there were some points to be re- 
gretted in the final arrangements, but the more im- 
portant mistakes were corrected in good time. In 
portioning to the different natior.s the honours due to 
them, we must assign to some countries special credit 
for some matters, while in other matters other countries 
took the lead. America devoted a larger sum to the 
expenses than any two nations together, and adopted 
excellent arrangements. Russia provided for the 
greatest number of stations ; in fact, far more than 
England, America, and France together. Germany 
alone combined photographic and heliometric opera- 
tions in both hemispheres. France distinguished 
herself by occupying the greatest number of difficult 
island stations in the southern seas. Lastly, to England 
must be assigned whatever credit is due to the first 
discussion of the subject, and the promulgation of a 
programme for the whole scientific world : had this 
programme been but correct, and had other nations 
only accepted the parts assigned to them, England 
would have been as easily first as she was in 1769, and 
as she may be — who knows ? — in 1882. 

As regards the transit of 1882, it may be hoped 
that what has happened in the case of the transit of 
the present year will serve in some sense as a warning 
to astronomers not to place implicit reliance on the 
opinions of any astronomer, however deservedly emi- 
nent, and also to prevent any unduly hasty expression 



THE TRANSITS OF 1874 AND 1882. 227 

of opinion by persons whose official position would cause 
the admission of error to be unpleasant. .Adding to this- 
consideration the fact that a large amount of practical 
experience in the value of the various methods of 
observation has probably been acquired during the 
transit of 1874, we may well hope that in 1882 even 
more valuable observations will be made. It needs but 
a short study of the sun- views forming Plates XIV. 
and XV. (or, preferably in some respects, figs. 37 and 
38), and of the stereographic projection of Plate VII., 
to see that American astronomers will have to take by 
far the most important share in the work of observation 
in the northern hemisphere. Let it be permitted to 
us, however, to hope that England, by well-considered 
expeditions to southern stations, will remove any 
doubts that other nations may have entertained as to 
her zeal for science. 

I may note here that while Halley's method fails 
totally for the transit of 1882, a method which, in 
some degree, would take its place may be applied 
with considerable advantage if stations in Patagonia, 
Tierra del Fuego, the Falkland Isles, or, better still, 
the sub- Antarctic islands directly south of Cape Horn, 
could be reached. I refer to a method which may be 
called the mid-transit method, and which consists in 
the determination (preferably by photography) of the 
distance of Venus from the sun, near the middle of 
the transit, at two stations where the difference of her 
distance from the sun's centre will be the jrreatest 
possible. It will be manifest to the student, if he 

Q 2 



228 



TRANSITS OF VENUS. 



considers what I have said in pp. 209, 210, that 
the advantages claimed for stations on a radial line 
through the centre of Venus's shadow-cone (o in fig. 36) 
culminate when the earth is near the centre of her 




Fig. 44. — Illustrating the Mid- ransit Method (Transit of 1882). 

chord, of passage through the shadow-section v v\ 
Wherever convenient stations exist for advantageously 
photographing the whole chord of transit, it would of 
course be absurd to select a station only advantageous 



THE TRANSITS OF 1874 AND 1882. 229 

for the middle of the chord ; but in the transit of 1882 
the whole chord cannot be very advantageously photo- 
graphed at southern stations ; and there will be a 
decided advantage in securing mid-transit photographs 
(as well, of course, as photographs of the beginning 
and end, and series of photographs for the whole transit 
where practicable). 

Fief. 44 illustrates the conditions under which this 
method would be applied in 1882. The face of the 
earth here shown is that turned sunwards at the time 
of mid-transit. The parallel lines show where the 
displacement from and toivards the sun's centre (in 
northern and southern regions respectively) equals 1 . 
2, 3, . . . 8,9, tenths of the maximum displacement 
at M and N respectively. The circles indicate the 
solar elevation. The shaded lunes include all regions 
where the displacement is not less than half the 
maximum, and the sun not less than 150° above the 
horizon. Unfortunately, the southern lime is a region 
singularly wanting in convenient stations. Possession 
Island and Victoria Land occupy the very best posi- 
tion possible. 

It is not probable, judging from what Sir G. C. 
Lewis has shown respecting centenarians, that any of 
my readers will witness the transits of 2004 or 201 v 2. 
Nevertheless, it may be interesting to know the cir- 
cumstances of those transits and the regions of the 
earth where they will be wholly or partially visible. 
Mr. Hind, Superintendent of the ' Nautical Almanac,' 
has calculated the elements of the two transits of the 



230 TRANSITS OF VENUS. 

beginning of the twenty-first century. His results are 
thus presented in the ' Notices ' of the Royal Astro- 
nomical Society for February 1872, p. 184 : — > 

Transit e/2004. 

Greenwich Mean Time of Conjunction in Right 
Ascension = June 7 d 20 h 51 m 28 s '8. 

For the centre of the Enrth. 

A h m s ° 

First external contact June 7 17 3 43 at 115-0 

First internal contact „ 17 22 35 „ 118-0 

Second internal contact „ 23 5 40 „ 2140 

Second external contact „ 23 24 32 „ 2185 

The angles are reckoned from N. towards E. for 
the direct image. 

At Greemvich the entire transit will be visible. 

Transit of 2012. 

Greenwich Mean Time of Conjunction in Right 
Ascension = June 5"* 13 h 4 m 44*'3. 

For the centre of the Earth. 

d h m s ° 

F>sf external contact Ji.ne 5 10 22 11 at 40-3 

First internal contact „ 10 39 56,, 37-8 

Second internal contact „ 16 42 6 203-1 

Second external contact ,, 17 2905 



' M. Leverrier's Tables of the sun and Venus represent so closely 
the motions of the earth and Venus in their orbits, that there can he 
little reason to doubt that the Tables will be as sensibly perfect in 2J04 
as they are at the present tune. 



THE TRANSITS OF 1874 AND 1882. 23 1 

At Greenwich the egress only will be visible, the 
sun rising at 15 h 46 ra . 

These results are illustrated by the projections 
forming Plates VIII. and IX., and by the transit 
chords shown in Plate I. (the Frontispiece). The 
reader who has followed the explanations of Plates 
IV. and V. will have no difficulty in understand- 
ing the plates illustrating the transits of 2004 and 
2012. 

We cannot doubt that Avhen the transits of 2004 
and 2012 are approaching, astronomers will look back 
with interest on the operations conducted during the 
present ' transit-season ; ' and although in those times 
in all probability the determination of the sun's dis- 
tance by other methods — by studying the moon's 
motions, by measuring the flight of light, by estimating 
the planets' weight from their mutual perturbations, 
and so on, will far surpass in accuracy those now 
obtained by such methods, yet we may reasonably 
believe that great weight will even then be attached to 
the determinations obtained during the transits of the 
present century. The astronomers of the first years of 
the twenty-first century, looking back over the long 
transitless period which will then have passed, will 
understand the anxiety of astronomers in our own 
time to utilise to the full whatever opportunities the 
coming transits may afford ; and I venture to hope 
that should there then be found, among old volumes 
on their book-stalls, the essays and charts by which I 



232 TRANSITS OF VEX VS. 

have endeavoured: to aid in securing that end (perhaps 
even this little book in which I record the history of 
the matter), they will not be disposed to judge over- 
harshly what some in our own day may have regarded 
as an excess of zeal. 



THE TRANSIT OF 1874. 



233 



TRANSIT OF 1874. 



Table I.— Places where Ingress 
was accelerated. 



Table II. — Places where Ingress 
was retarded. 



Station 


Sun's 
elevation 


Accele- 
ration in 
minutes 


Station 


c 


s > 


Retarda- 
tion in 
minutes 


Woahoo 


deg. 
19-8 


m. 
11-2 


Crozet Island 


deg. 
150 


m. 
12-6 


Hawaii . 


19-7 


11-1 


Enderby Land 


20-0 


11-8 


Aitou Id., Aleutian 


10-8 


10-3 


Kerguelen Land . 


27-5 


11-6 


Marquesas Island . 


177 


7-9 


Macdonald Island . 


31-0 


11-2 


Mouth of Amoor R. 


14-0 


7-6 


Kemp Island 


30-0 


11-1 


Jeddo . 


32-1 


6-8 


Bourbon Island . 


12-4 


11-1 


Otaheite ; 


29-7 


6-4 


Mauritius 


14-1 


3 0-7 


Nertchinsk • 


10-1 


5-8 


Amsterdam Island 


34-1 


:o-3 


Tsitsikar 


17-0 


5-8 


Rodriguez 


19-0 


9-9 


Kirin-Oula . 


19-5 


5-7 


Sabrina Land 


450 


8-2 


Nagasaki 


32-7 


53 


Adelie Land . 


450 


68 


Tientsin 


22-2 


50 


South Victoria Ld. 


385 


60 


Pekin . 


20-8 


4-3 


Perth (Australia) . 


650 


53 


Shanghai 


28-5 


3-9 


Royal Co. Island . 


62-0 


45 


Nankin . 


27-1 


3-6 


Madras 


210 


40 


Canton . 


35-5 


1-6 


Bombay 


125 


38 


Hongkong . 


36-2 


1-6 


Macquarie Land . 


520 


35 








Hobart Town 


670 


28 








Adelaide 


75-0 


2 5 








Melbourne . 


750 


22 



234 



TRANSITS OF VENUS. 



TRANSIT OF 1874. 



Table III. — Places where Egress 
was accelerated. 



Table IV. — Places where Egress 
was retarded. 



j ■ 

Station 


a 

_o 

s > 


Accele- 
ration in 
minutes 


Station 


Suu's 
elevation 


Retar- 
dation in 
minutes 


i 

South Victoria Ld. 


(leg. 


m. 




deg. 


m. 


(Possession Ilnd.) 


250 


11-4 


Orsk . 


125 


118 


Adelie Land . 


340 


106 


Omsk 


11-5 


117 


Campbell Island . 


260 


10-3 


Astracan . 


120 


116 


Emerald 


300 


10-3 


Aleppo 


14-6 


lOo 


Macquarie Island . 


320 


9-8 


Peshawur . . 


31-5 


103 , 


Chatham Island . 


16-0 


9-8 


Alexandria 


14-0 


100 


Canterbury (N.Z.) 


22o 


9-3 


Suez . 


16-1 


9-8 


Wellington . 


200 


9-2 


Nertchinsk 


101 


9-8 


Sabrina Land 


430 


92 


Delhi 


38-0 


9-4 


Enderby Land 


39-0 


8-5 


Tsitsikar . 


120 


8-7 


Eoyal Co. Island . 


420 


8-5 


Bombay 


45-0 


8-5 


Auckland 


192 


8-5 


Pekin 


210 


86 


Kemp Island 


51 


76 


Kirin-Oula 


14-0 


8-4 


Hobart Town 


400 


76 


Tientsin . 


17-1 


8-4 


Melbourne . 


43-0 


66 


Calcutta . 


453 


82 


Sydney . 


37-2 


66 


Aden 


30-0 


7-8 


Adelaide 


47-8 


58 


Nankin 


27-0 


7-6 . 


Kerguelen Land . 


57-1 


5-0 


Madras 


52-0 


7-4 


Crozet Island 


47-5 


4-2 


Shanghai . 


26-0 


7-2 


Perth (Australia) . 


66-2 


\ 3-6 


Canton 


37'0 


6-6 






) 


Hongkong. 


37-0 


6-5 



THE TRANSIT OF 1874. 



235 



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236 



TRANSITS 01 VENUS. 



Table VI. 



For determining the effect of changes in the value of the Sun's equatorial 
horizontal parallax {at his mean distance) on the esti?nated mean 
distance. 



Parallax 


Mean Distance 


Difference for 0"*01 




(in miles) 


(in miles) 


8-0' 


102,173,020 


126.142 


81 


100,911,600 


123.061 


8-2 


99,680.990 


120.097 


83 


98,480,020 


117-240 


8'4 


97,307,620 


114,478 


8-5 


96,162,840 


111.820 


86 


95,044,640 


109,244 


87 


93,952,200 


106,766 


8-8 


92,884,540 


104,362 


89 


91.840,920 


102045 


9-0 


90,820.470 


99,805 


9-1 


89,822,420 


97,632 


92 


88,846,100 


95.532 


93 


87,890,780 


93.504 


94 


86,955.740 


91,530 


9-5 


86,040.440 


89,624 


96 


85,144.200 


87-780 


9-7 


84,266,400 


85,986 


9-8 


83.406,540 


84.248 


9-9 


82,564,060 


82,564 


100 


81,738,420 











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