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THE TRANSIT OF VENUS. 




Photo-heliograph of the British Expeditions. 



NATURE SERIES. 



THE 

TRANSIT OF VENUS. 



BY 



GEORGE FORBES, B.A., 

PROFESSOR OF NATURAL PHILOSOPHY IN THE ANDERSON1A.V UNIVERSITY, 

GLASGOW. 



WITH NUMEROUS ILLUSTRATIONS. 



Xonuosi anir Hcb ifork : 
M ACM I L LAN AND CO. 

1874 

\_The Right of Translation and Reproduction is resavcd.] 



cffO 



-~? 




Sf 



LONDON : 

R CLAY, SONS, AND T.4VLOR, PRINTERS, 

BREAD STREET HILL. 



B 



PREFACE. 

The following pages, revised from a series of articles 
published in Nature, are based upon a paper 
originally read before the Philosophical Society of 
Glasgow, in 1873. I believe that I have performed 
the duty of the historian with impartiality. I have 
done my best to make the technicalities compre- 
hensible. The account of the preparations of 
different nations is as complete as it was in my 
power to make it. 

My best thanks are due to Mr. W. H. M. Christie, 
of the Royal Observatory, Greenwich, for having 
kindly undertaken to revise the proofs during my 
absence from England. 

GEORGE FORBES. 

S.S. "ILLIMAM." 

/«3, 1874- 



CONTENTS. 





PAGE 


CHAPTER I 


I 


CHAPTER II 


• 15 


CHAPTER III 


. 29 


CHAPTER IV 


46 


CHAPTER V 


. 6O 


CHAPTER VI. . . . 


• 75 


CHAPTER VII 


. . . 89 



LIST OF ILLUSTRATIONS. 



FIG. PAGE 

I . 2 

2 ... 4 

3 6 

4 7 

5 • ... 7 

6 11 

7 • «3 

8 16 

9 . . , 18 

10 25 

11 3° 

12 36 

13 • ■ • 38 

14 39 

15 • 49 

16 51 

17. — Lord Lindsay's Photographic arrangements as set up at 

DunEcht 57 

18. — The transit-instrument of the British Expedition . . 69 

19. — Portable Altazimuth Instrument . . . . • 7 1 
20. — Equatorial of the British Expedition . . . .81 

21. — Photo-heliograph of the British Expeditions • - • 97 



THE 

TRANSIT OF VENUS. 

CHAPTER I. 

In days of old it was supposed that the earth held 
the central position of the solar system, and that 
moon, sun, and planets moved round it, each in its 
own orbit. The moon was supposed to be nearest to 
us, then came Venus, then Mercury, after that the sun, 
then Mars, Jupiter, and Saturn. We now know that 
of all these the moon is the only one which revolves 
round the earth, and that all the planets travel round 
the sun in paths at different distances from it in the fol- 
lowing order, the first being that nearest the sun : — 
Mercury, Venus, the Earth, Mars, Jupiter, Saturn. 
These are all the planets which were known to the 
ancients. Since Mercury and Venus were formerly 
supposed to be lower than the sun, and all the others 
higher, the name of inferior planets was given to the 
S B 



THE TRANSIT OF VENUS. 



fCHAP. 



former, and superior planets to the others. These 
terms are still retained by astronomers, though the 
ideas that gave rise to these terms are long since ex- 
ploded. Fig. I shows the appearances presented by 



FIG. I 





~J 



THE EAR T H 



C G o o D 



v a 



V V V- 

4 5 



Venus, one of the inferior planets, in the course of 
its journey round the sun. V is the planet. E is the 
earth, which is shown in the figure always in one 
position, although of course it also describes an orbit 



I.J THE TRANSIT OF VENUS. 3 

round the sun. We are naturally led by a study of 
the diagram to three points of interest concerning the 
motions of an inferior planet. 

The first is that the planet can never seem to be far 
distant from the sun. Venus moves round the sun in 
the direction shown by the arrow. The earth rotates 
in the same direction. We are supposed to be looking 
down upon the solar system from some point in the 
northern heavens. It will be noticed that when the 
planet leaves the point Vj, she will seem to recede 
from the sun more and more, until she reaches the 
position V 3 . She can never appear further from the 
sun than this, and is then said to be at her greatest 
eastern elongation. She then approaches the direction 
in which the sun is seen, until she is lost in the bright- 
ness of his rays. During all the time she is seen best 
in the early morning before sunrise, setting before the 
sun. When Venus has passed this position her distance 
from the sun appears to an observer upon the earth 
to increase until she reaches V 6 , her greatest western 
elongation, when she again begins to approach the sun. 

The next point to be noticed is that she is some- 
times a great deal closer to the earth than at others ; 
and when she is nearest to the earth she appears to 
be largest. At her closest approach to the earth she 
is only about 26,000,000 miles away; but when far- 
thest oft her distance is 158,000,000 miles. Her appa- 
rent size is therefore much greater in the first case 
than in the second. These differences are shown at 
the lower part of Fig. i r 

The third point to be mentioned is that she exhibits 
phases just as the moon does. In any position that 

B 2 



a THE TRANSIT OF VENUS. [chap. 

hemisphere alone is illuminated which is directed to 
the sun ; so that in the position V 3 , when we can only 
see one-half of that hemisphere, she will have the 
appearance of a half-moon. So in the position V 9 she 
has a crescent form, and at V 5 a gibbous one. The 
apparent size and shape of the planet in its different 
positions are shown in the lower part of Fig. I. 

The question now arises, what will happen when 
Venus is between us and the sun ? In the first place, 
since her illuminated hemisphere is turned away from 
us, she will be invisible indeed ; we shall have no 
chance of seeing her, unless she be seen as a black 
spot upon the bright surface of the sun. We should 
naturally expect that this would happen every time 
that the planet is at its least distance from us. A 
simple consideration shows that this need not be the 
case. The orbits of Venus and the earth do not lie 
in the same plane. In other words, we cannot re- 
present accurately the paths of Venus and the earth 
by a drawing upon a sheet of paper. The orbit of 
Venus would have to be tilted up above the plane cf 




the earth's orbit. Both of these planes pass through 
the sun, but they are inclined to each other at a 
certain small angle. This will be seen by a glance at 
Fig. 2, where V represents the orbit of Venus, E that 



i.J THE TRANSIT OF VENUS. 



of the earth. The line A B, which passes through the 
sun is called the line of nodes ; and it is quite clear 
that in order to see Venus as a black spot upon the 
sun, both the Earth and Venus must lie approximately 
on this line of nodes. Now it generally happens that 
when Venus is at her least distance from the Earth, 
these two planets occupy some such places as V and 
E, so that she seems to be above the sun ; and, as 
the illuminated side is turned away from us, she is in- 
visible. Only twice in a century does she reach the 
node, so nearly at the same time as the earth, as to 
be seen as a black spot upon the sun. Such a pheno- 
menon is called a Transit of Venus. If it happen that 
Venus seems to pass across the centre of the sun she 
takes about eight hours to complete the passage. The 
earth occupies the position A always in June, and thj 
position B in December. If there be a transit of 
Venus when the earth is at B, Venus is said to be at 
the descending node, because then she is descending 
from the northern portion of her orbit to the -southern. 
When Venus is at C she is at her ascending node. 

It has been said that there are, roughly speaking, 
two transits of Venus in a .century. The following 
table shows all the transits of which we know any- 
thing : — 

1 63 1. Predicted by Kepler, but not observed. 

1639. Predicted and observed by Horrox. 

1761. Predicted by Halley ; observed by many 

1769. Observed generally. 
1874. 
1S82. 
It will be noticed that the transits occur in pairs 



THE TRANSIT OE VENUS. 



[chap. 



eight years apart ; the reason of this can easily be 
rendered clear. The earth takes 365 '256 days to go 
round the sun ; Venus takes only 2247 days. 
Suppose then that at any particular date Venus and 
the earth are at the node simultaneously, viz. at V 
and E, Fig. 3 ; a transit of Venus over the sun's disc 

F/O. 3. 




will be seen. When Venus has completed a revolution 
the earth will have moved away to E 1 , and Venus will 
not overtake the earth until they reach the positions 
V 2 and E 2 . This is 583 - o,20 days from the time when 
they were at V and E ; but V 2 and E 2 do not lie upon 
the line of nodes ; hence there can be no transit. 
After another 584 days Venus will again be in con- 
junction with the sun, but still not on the line of 
nodes. But the fifth conjunction occurs after 2919-6 
days (5X583'920); and the earth completes eight 
revolutions in 2922^05 days. Thus it appears that, at 
this conjunction of Venus with the sun, the earth and 
Venus are very near to their old positions V and E. 
Hence they are almost on the line of nodes. In this 
case we can without difficulty examine the possibility 



I.] THE TRANSIT OF VENUS. 



of a transit. If we suppose the motion of the earth 
to be stopped, the apparent motions of the sun and 
Venus may be represented as in Fig 4, where a portion 
of the orbit of Venus where it cuts the ecliptic near the 



s 



APPARENT ORBIT/OF THE SUH 




nodes is shown. When the sun and Venus are on the 
line of nodes simultaneously S represents the sun and 
V Venus. At the fifth conjunction the sun will not 
quite have reached S, but will be 2\ days behind at 
S' ; Venus will then be at v'. Now in this case there 
can be no transit visible, for here Venus is quite out 
of range of the sun. But if in the original transit the 
sun was a little past the node as at S (Fig. 5), then eight 
years after he will be at s', and there will be another 



F / G.S 




S 

fiPPA REN T ORBIT 
OP THE SUN 



o/?&/ror~Z£ 



VJOS 



transit. It follows from this that there will be a pair 
of transits eight years apart, only when in the first 
one Venus does not pass close to the sun's centre- 
This equality of eight revolutions of the earth, with 
thirteen of Venus, is very interesting, because this 
fact was shown by the present Astronomer Royal to 
account for an inequality in the earth's motion due to 
the attracting influence of Venus. The result of a 



8 THE TRANSIT OF VENUS. [chap. 

— _ — ¥ 

short calculation informs us that for positions of 
Venus and the earth near the line of nodes, Venus is 
at one conjunction 22' \6" distant from her position at 
the conjunction which occurred eight years previously, 1 
this distance being measured at right angles to the 
ecliptic. Now the sun's diameter is 32'. This shows 
why, generally, there are two transits eight years 
apart. 

The first prediction of a transit of Venus was made 
by Kepler,- and was calculated from his Rudolphine 
tables. In 1631, the year predicted, astronomers of 
Europe were eagerly on the watch for so rare a 
spectacle. But the calculation was in error, so that it 
took place when the sun was below the horizon in 
Europe, and was consequently invisible. 

After this no astronomers seem to have interested 
themselves about the possibility of such an occurrence, 
with one exception— -Jeremiah Horrox, a curate of 
the village of Hoole, near Liverpool, who was much 
devoted to astronomical pursuits. 3 He possessed 
some tables for calculating the places of the planets ; 
but his observations did not agree at all with them. 
He had, however, before discovering the faults of 

1 For at tire fifth conjunction the earth is 2-45 days distant from her place 
at the original conjunction. This is equivalent to 2° 24' 59", when viewed 
from the sun, from which subtract 2' 44" ( = the retrogression of the node of 
Venus in eight years), and we have 2° 22' 15"= tlie angular distance of the 
earth from its corrected original position, as seen from the sun. The ratio 
of this to the angular distance of Venus from her original position as seen 

/ ., ,, dist. of Venus from earth 277 ,, ,.. , . _o __».-« 

from the earth = - =JJ- Multiplying 2° 22 15 

dist. of Venus Iromsun 723- 
by 723, and dividing by 277, we have 6° 11' 17". Multiplying this by 
•06 = tan 3 23' 3.", which is the inclination of the orbit of Venus, we 
have 22' i6" = the latitude of Venus at the fifth conjunction. 

2 " Admonitiuncula ad Curic'sos Reram Cceleslium," Lcipsic, 1626. 

3 Sec Nature, vol. viii. p. 113, 



I.] THE TRANSIT OF VENUS. 9 

Lansberg's tables, calculated from them the future 
positions of the planets. This work, with corrections 
deduced from his own observations, led him to predict 
a transit of Venus, visible in England, for the year 
1639. He acquainted his friend Crabtree, of Man- 
chester, with the results of his calculation, and then 
prepared himself for the observation. He considered 
the best method to be the employment of a telescope 
to throw an image of the sun on a white sheet of 
paper in a darkened room. A circle was drawn, of 
about 6 inches diameter, upon the paper, to make the 
sun's image exactly fill the circle. A plumb-line 
would give him the direction of the vertical, and by 
marking successive positions of the planet on the sun's 
disc, he would be able to calculate many of the 
elements of Venus. Such an observation is of course 
peculiarly well suited for determining the diameter of 
the planet, the inclination of its orbit, the position of 
the node, and the true time of passing this node. 
His calculation showed that the transit ought to 
commence on the afternoon of November 24 (old 
style) ; but to guard against disappointment, and 
because of discrepancies in various tables, he kept a 
watch from the 23rd. On returning from some 
clerical duties on the 24th (Sunday) lie was gratified 
by beholding a black spot on the sheet of paper, 
which indicated the presence of Venus on the sun's 
disc. He made three observations before sunset and 
has left us a drawing to illustrate the observations. 1 

It is curious to find an astronomer supporting the 
opinions of the astrologers ; but in his treatise we 

1 Venus in Sole Visa. 



io THE TRANSIT OF VENUS. [chap. 

find that the chance of a clouded atmosphere caused 
him much anxiety, for Jupiter and Mercury were in 
conjunction with the sun almost at the same time as 
Venus. This seemed to him to forebode great severity 
of weather. He adds, " Mercury, whose conjunction 
with the sun is invariably attended with storm and 
tempest, was especially to be feared. In this appre- 
hension I coincide with the opinion of the astrologers, 
because it is confirmed by experience ; but in other 
respects I cannot help despising their more than 
puerile vanities." But we must not laugh at Horrox 
for his opinion. In our own day there is a consider- 
able number of diligent astronomers who believe that 
the cyclones in the Indian Ocean, certain other winds, 
the growth of vines, and various other phenomena, 
are in part regulated by the positions of Venus and 
Jupiter with respect to the sun. 1 

Horrox's observations have been of great value 
in perfecting the tables of Venus. He was further led 
by a kind of analogy, much in vogue at the time, to 
deduce from his observations a value of the sun's dis- 
tance from the earth. It will readily be understood 
that if we could find out what size, in angular measure 
the earth would seem to have if viewed from the sun, 
we should have a means of determining how much 
greater the distance from the earth to the sun is than 
the diameter of the earth J For, suppose S (Fig. 6) to 
be the position of an observer placed upon the sun, 

1 See the researches of Messrs. De la Rue, Stewart, and Loewy on 
the connection of sun-spot frequency wiih planetary positions. " Phil. 
Trans." ; also the writings of Mr. Meldrum, Mr. E. J. Stone, Prof. 
Ballour Stewart, M. Poey, and others, on ihe cunnection between ler- 
restrial phenomena and sun-spot frequency. 



I.] THE TRANSIT OF VENUS. n 



S L, S M the directions in which he must look to see 
the opposite sides of the earth, so that the inclination 
of these lines is known. All we have to do now is to 
draw a circle of any size and move it about between 



r/c.G 




the lines SL, S M, until it just fills the interval, as at 
EE'. If now we measure with a ruler how much 
greater S E is than E e' we shall know the distance 
from the earth to the sun, the earth's diameter being 
taken as the unit of measurement ; and if we multiply 
this by the diameter of the earth measured in miles 
we shall know the distance from the earth to the sun, 
in miles. All that we require to know is the size of 
the angle E S e'. Horrox estimated the probable 
value of this angle in the following manner. From 
the observations of Tycho Brahe it appeared that dur- 
ing the transit of Venus the apparent diameter of the 
planet would be 12' 18"; while Lansberg found 12' 
21"; and Kepler 6' 51". Horrox found from his 
measurements that it was only i' 16". The error of 
ordinary observations arises from the apparent en- 
largement of the planet's disc through irradiation. 
Gassendi had in the same manner, during the transit 
of Mercury in 1631, reduced the apparent diameter of 
Mercury to scarcely 20". From these data it can be 
found that the apparent diameters of Venus and 
Mercury as seen from the sun would be 21" and 34" 
respectively. Proceeding to the other planets he 



12 THE TRANSIT OF VENUS. [chap. 

arrived at the general conclusion that each of them 
would, if viewed from the sun, have an apparent 
diameter of about 28". Applying this to the case of 
the earth, he showed that the distance of the earth 
from the sun must be 7,500 diameters of the earth (it 
may be well here to state that the latest measurements 
show the apparent diameter of the earth as viewed 
from the sun to be about 18", and the distance=i 1,400 
diameters). This analogy by Horrox gave a much 
closer approach to the truth than previous conjectures. 

Before taking leave of Horrox, we must say a few 
words on his work. Although he died at the early 
age of 23, during his career he showed a remarkable 
aptitude for the acquisition of knowledge, and for the 
striking out of new ideas. He lived at a time when 
the scientific spirit of the age was leading up to the 
theory of gravitation, and many passages in his writ- 
ings show that he had even then grasped the grand 
idea of the theory, and that he was well fitted to 
become its constructor and its expounder. His 
researches on the lunar and planetary theories also 
indicate his great genius. 

We have already mentioned some of the uses to 
which careful observations of a transit of Venus may 
be applied ; viz. the correction of the elements of the 
planet's orbit. But the observation also leads us to a 
knowledge of the distance of the sun from the earth, 
and in a manner much more direct and logical than 
that employed by Horrox. There is an opinion very 
prevalent that a transit of Venus affords the best 
means of determining this distance. So far as our 
present knowledge goes we are hardly justified in such 



I-] 



THE TRANSIT OF VENUS. 



a statement until after the observations that shall be 
made in the present year. 

Before entering upon the method by which we 
measure the sun's distance, let us devote a few lines 
to explaining what is meant by the word parallax, 
which is continually employed in such discussions. 
Let a man stand in a street exactly north of a lamp- 
post. The lamp-post will seem to be south of him. 
Now let him cross over to the other side of the street. 
The lamp-post will now be in some other direction, 
such as south-west. This movement of the direction 
of the lamp-post is the effect of parallax. Now let 
us suppose, by a stretch of imagination, that a man 
observes the moon from the centre of the earth. He 
will see it in the direction C M (Fig. 7). If now he 
goes to A he will see it in the direction A M. The 



r/G. 7. 



THE MOOfJ 



THEEARTh 




angle AMC through which the moon appears to have 
been moved is the parallax of the moon as observed 
from A. It will be noticed that the parallax is an 
error introduced into the observed position of the 
moon, and which must be allowed for if we wish to 
get the position as seen from C. Moreover, the paral- 
lax at B is different from what it is at A. But at no 



14 THE TRANSIT OF VENUS. [C HAP - 

point on the surface of the earth can the parallax be 
greater than at A. And if we know the parallax of 
the moon at A, we can deduce that at B from a 
knowledge of the relative positions of A, B, and C. 
Hence it is useful to have a distinct name for the 
parallax at A. Now it will be noticed that a line 
drawn from C to A is the vertical line at A ; hence 
the moon M will appear to be on the horizon to an 
observer at A ; and hence the moon has its greatest 
parallax when on the horizon. For this reason the 
parallax at A is called the moon's horizontal parallax. 
Further, since the equatorial diameter of the earth is 
greater than the polar, the parallax will be greater, 
when the moon is on the horizon, to an observer at 
the equator than to an observer at one of the poles. 
Hence the greatest parallax we can have occurs when 
the moon is on the horizon and the observer is at the 
equator ; this value of the parallax is the equatorial 
liorizontal parallax. In the same way the sun has an 
equatorial horizontal parallax, and if we knew its 
value we could find out the sun's distance from the 
earth as explained above (Fig. 6). 



ii] THE TRANSIT OF VENUS. 



CHAPTER II. 

There is perhaps no problem which has been so 
constant a source of interest to the learned in all 
ages as the solving of the mystery of the solar 
system. The labours of Copernicus, Tycho Brahe, 
Kepler, and Newton have given us a general know- 
ledge of the nature of the planetary motions ; and 
the investigations of later mathematicians have en- 
abled us to predict, with wonderful accuracy, the 
future positions of the planets. But the dimensions 
of the solar system are not known with the same 
precision. 

It is true that we know the relative distances of all 
the planets from the sun with tolerable exactness. 
This problem has been attacked by two totally differ- 
ent methods. The first consists in measuring directly 
the changes that are produced in the motions of the 
planets when the earth has moved through a certain 
portion of its orbit. In the case of the planets 
Mercury and Venus, which move in smaller orbits 
than that of the earth, the direct observation can 
easily be made. For let us suppose w' and EE 



i6 



THE TRANSIT OF VEAL'S. 



[chap. 



(Fig. 8) to be the orbits of Venus and the Earth, and 
S to be the sun. Let us watch the position of Venus 
night after night until she is as far away from the 
sun as possible. If we measure her apparent dis- 
tance from the sun by astronomical means, we shall 

f/g. a 




know that the Sun, Venus, and the Earth occupy 
positions such as S, V, and E ; the directions ES and 
E V being known from our observations. By measur- 
ing off the distances S V and S E on the diagram, we 
actually find the relation between the earth's distance 
from the sun and that of Venus. The same can be 
done with Mercury ; but for the superior planets the 
direct mode of observation is more difficult. 

But there is an indirect method which is much 
more easy to apply. Kepler's three laws have been 
shown to be necessary consequences of Newton's 
theory of gravitation. Now Kepler's third law tells 
us how to find the relative distances of two planets 
from the sun when we know the relation between 
their periods of revolution. The exact law is this : 
— Multiply the number of years taken by a planet 



,IL] THE TRANSIT OF VENUS. 17 



to go round the sun, by the same number. This 
gives us a first number. Then find a second number 
which, multiplied by itself twice, gives us the first 
number; this second number is the distance of the 
planet from the sun (the earth's distance being called 
I). To take an example: Jupiter takes about 11 
years to go round the sun ; 1 1 multiplied by 1 1 
gives us a first number, 121. Now if 5 be multiplied 
by 5 we get 25, and if this be again multiplied by 5 
we get 125, which is almost the same as the first 
number, 121. Hence we are right in saying that 
Jupiter is about five times as far from the sun as the 
earth is. If we had used the exact number of years 
we should have got the exact distance. Now it is 
very easy to find the period of revolution of a planet. 
For we can easily measure the interval between two 
dates when Jupiter and the Earth, for example, are 
in the same line with the sun ; in other words, we 
can measure the "synodical revolution" of Jupiter; 
and from this it is easy to calculate the time of 
Jupiter's revolution round the sun. 

By applying these methods to all the planets 
we can lay down their orbits upon a plan ; all we 
wish noiv is to find the scale upon which our plan is 
drawn. If we knew the distance of the earth from 
the sun, or if we knew the distance between any two 
of the planetary orbits, we should know the scale 
upon which our plan is laid down. Various methods 
have been adopted for this, but the one which makes 
use of a transit of Venus has generally been con- 
sidered to be the most accurate. 

One method which has successfully been applied to 

C 



i8 



THE TRANSIT OF VENUS. 



[chap. 



measuring the moon's distance is that used by sur- 
veyors. The surveyor chooses two spots, B, C, whose 
distance he measures. Suppose it to be one mile. 
He represents this distance, say, by a line one inch long 
on a sheet of paper. He then takes a telescope, moun- 
ted so as to enable him to measure any angle through 
which it is turned. He places the telescope at B, 
pointing towards C. He then turns it till it points at 
the distant object, and finds what the angle of B is. 
He then draws the line BA upon the paper, and he 
knows that the distant object lies somewhere on the 
line B A. He then does the same with c, and thus 
he knows that the remote object lies on c A. But A 
is the only point lying both on B A and C A ; hence 
c corresponds to the distant object. If on measuring 
C A he finds it to be 30 inches, then since C B, which 
is 1 inch, means I mile ; C A, which is 30 inches, 
means 30 miles, and this is what he wanted to find out. 

If, instead of taking a base-line (as it is called) of 
one mile, the diameter of the earth, or 8,000 miles, 




be taken; then, if the moon be the distant object, 
we can determine its distance in almost the same 
way. It is in this manner that the moon's distance 
has been measured. It is easy to see that if the 
angle at A (Fig. 9) were very small, a slight error in 



II.] THE TRANSIT OF VENUS. 19 

measuring either of the angles B or C would make a 
great difference in the distance deduced for the remote 
object. Hence, if the moon's parallax were not 
large, this method would be unsuitable. The paral- 
lax of the sun is very small, and hence we cannot 
find the sun's distance with any exactness by this 
method. 

But if any one of the planets ever came so close to 
the earth as to make its parallax tolerably large, then 
we could determine the scale upon which the solar 
system is built up. Now Venus and Mars are two 
planets which at certain times come closer to the 
Earth than any other planet does. But, unfortunately, 
when Venus is nearest the earth she is generally 
invisible, because the whole of her illuminated side is 
turned away from us. Mars, however, is a planet 
that gives us a very favourable opportunity for de- 
termining its distance. The advantage is increased 
by this peculiarity, that every fifteen years Mars is at 
its shortest distance from the sun, at the same time 
that the earth is at its greatest distance, the two 
planets being also in the same line with the sun, so 
that they are closer than we might have thought 
possible. In fact, on these occasions Mars is nearer 
to the earth by ^g-th part than she is if the conjunc- 
tion take place when both the earth and Mars are at 
about their mean distances from the sun. Suppose 
then that under such circumstances two observers, one 
at Greenwich and the other at the Cape of Good 
Hope (where there is a fine observatory), observe the 
position of Mars as compared with that of a star at 
the same time. The position of Mars will be dis- 

C 2 



23 THE TRANSIT OF VENUS. [chap. 



placed by parallax ; and by comparing the apparent 
angular distance of the planet from the fixed star at 
these two places we can find the sum of the parallaxes 
in these cases. Hence we can find the distance of 
Mars, as already explained. 

This was the method which first gave a value of the 
solar parallax with anything like accuracy. At the 
suggestion of Cassini, the French sent out an expedi- 
tion to the Cape, under the astronomer Picard. The 
value obtained for the sun's parallax was 9/5. Prof. 
Henderson in 1836, and Mr. Stone in 1862, utilised 
this method. Another opportunity will occur in 1877. 

Before proceeding to the method of the Transits of 
Venus, it will be well briefly to allude to some other 
methods by means of which the solar parallax, or the 
sun's distance, has been estimated. 

It has been found that light takes a sensible time 
to propagate itself through space. Hence, when one 
of Jupiter's satellites passes into the shadow of the 
planet, this fact is not communicated to our vision for 
something like 38 minutes, the time taken by light to 
pass from Jupiter to the Earth. Now, when we are 
on the same side of the sun as Jupiter, this distance 
is shorter by the whole diameter of the earth's orbit 
than when we are at the opposite side of the sun. 
Hence, in the former case, the eclipses will seem to 
take place sooner than the predicted time, and in the 
latter case later. The difference in either case is 
about 8 minutes, and as we know that light travels 
over 298,500 kilometres per second, 1 this tells us 

1 As determined by Foucault, Comptes Rendus de PAcad. dcs Sciences, 
vol. lv. p. 502 ; also by Cornu, Comptes Rendus, Feb. 10, 1873. 



II.] THE TRANSIT OF VENUS. 21 

that our distance from the sun is about 91,000,000 
miles. 

But our knowledge of the velocity of light has 
been utilised in another manner to solve the same 
problem. You see that if we know the earth's velo- 
city in miles, we can find its distance from the sun. 
For if it goes i| million miles in one day, it must go 
over 365 times that in a year, and that measures in 
miles the circumference of our earth's orbit, and hence 
we can get our distance from the sun. How then are 
we to find the velocity of the earth in miles ? This 
depends on a curious property of light. In a steady 
down-pour of rain you hold your umbrella upright 
if you are standing still, but incline it forward if you 
are walking fast. This is to make the umbrella catch 
the rain-drops. The amount of inclination you give 
it depends upon the rate at which you are walking 
compared with the velocity with which the drops fall. 
The same thing happens with light. We have to 
incline our telescopes forward a little in the direction 
in which the earth is moving to catch the rays of 
light ; and at opposite seasons of the year the earth 
is moving in contrary directions, and the telescope 
has to be pointed in sensibly different directions. 
The inclination that a telescope receives is known, 
and the velocity of light being known, we can find 
the velocity of the earth, and hence, as I have shown, 
the distance of the earth from the sun. 

There is another method of peculiar interest de- 
pending upon the motions of the moon. The law of 
gravitation says that the attraction of any body for 
any other one depends upon the distance between them. 



22 THE TRANSIT OF VENUS. [chap. 

The moon is attracted to the earth by a force, de- 
pending upon the distance of the moon, which is 
known in miles. But the moon is caused to deviate 
from its natural course on account of the sun's attrac- 
tion. This depends upon the distance of the sun 
from the earth, and if this be not known exactly in 
miles we shall see that it is impossible to apply cal- 
culation to foretell the motions of the moon ; for, if 
upon any scale we attempt to lay down upon paper 
the relative positions of the sun, earth, and moon, we 
shall place the moon at its proper distance, and the 
sun, though in its proper direction, will not be placed 
at the proper distance, and Ave shall not know the 
direction in which it attracts the moon, nor the 
magnitude of this attraction, and we shall make our 
calculation wrongly, and the moon's observed place 
will differ considerably from its calculated place. 

Such a difference was actually detected by the 
illustrious Hansen, whose tables of the moon are the 
best we possess. Hansen saw that this must be due 
to a wrong assumption as to the distance of the sun, 
and communicated his doubts to the Astronomer 
Royal 1 in the year 1854. This led to a re-discussion 
of our knowledge of the subject which has confirmed 
Hansen's views, and which leads us to see the im- 
portance of knowing accurately the sun's distance, 
if we wish ever to have our tables of the moon so 
accurate that we may determine the longitude by 
their aid. This method for investigating the solar 
parallax was first used by Laplace. 2 

1 Monthly Notices, R. A. S., vol. xv., Nov. 1854. 

2 Systems du Monde, t. ii. p. 91. 



II.] THE TRANSIT OF VENUS. 23 

More recently, M. le Verrier has suggested a new 
method that promises in time to be the best. 1 In 
the lunar theory, an equation appears connecting the 
relative masses of the earth and sun with the solar 
parallax, so that if we know the one we can find the 
other; and from a peculiarity in the equations, a 
small error in determining the relative masses will 
affect only very slightly the deduced parallax. Le 
Verrier finds the ratio of the masses of the earth and 
sun by determining the effect of the earth's attrac- 
tion upon Venus and Mars. This being applied to the 
lunar theory, a value of the solar parallax is obtained. 

The method, however, which has found most favour 
up to the present time, is the employing of transits 
of Venus to measure the sun's distance. When a 
transit of Venus occurs, the first evidence of the 
phenomenon is given by a slight notch being made 
in the contour of the sun's edge at a certain spot. 
This notch increases until the full form of the planet 
is seen. The first appearance of a notch is called 
the time of first external contact. But when the 
planet appears to be wholly on the sun, her black 
figure is still connected with the sun's limb by a sort 
of black ligament, of which we shall say more here- 
after. When the whole of the planet is just inside 
the sun's edge, the time of first internal contact has 
arrived. The breaking of the ligament is a very 
definite occurrence, and was, until lately, taken to 
indicate the true moment of internal contact. The 
second internal and external contacts take place as 
the planet leaves the sun. 

1 CompUs Rendus, July 22, 1S72. 



24 THE TRANSIT OF VENUS. [chap. 

In 1663, the celebrated James Gregory, in his famous 
work the "Optica Promota,"/;^/. 87, Scholium, alludes 
to the possibility of determining the sun's parallax 
by means of the transit of an inferior planet. He 
has been showing methods of finding the parallax of 
a planet by comparison of observations made at dif- 
ferent parts of the earth upon the position of the planet 
compared with that of a star. He then takes, in 
place of a fixed star, another planet, the two being 
in one line, as seen from the earth. The application 
of this to the case of Mercury or Venus and the sun, 
was obvious. 

But H alley was the first to see clearly what a power- 
ful means of determining the sun's parallax an obser- 
vation of contact really is. So far as I can discover, 
he first mentions the method in a letter to Sir Jonas 
Moore, written at St. Helena in 1677, 1 just after 
having seen a transit of Mercury. The exactness with 
which he believed the time of contact to be deter- 
minable, led him frequently afterwards to urge his 
countrymen to make every effort to utilise the method 
on the occasion of the transits of 1761 and 1769, 
when he should be dead. 2 And thus, in addition to 
his celebrated prediction of a comet, he left a second 
legacy to his successors, who, as Englishmen, might 
be entitled to be proud of his foresight though he 
could not live to reap the glory of it. 

It is a matter of some difficulty to show, in an 
elementary manner, the way in which the value of the . 
sun's parallax can be found from observation of 

1 Hooke's " Lectures and Collections," 1678. 

2 " Catalogus Stellaram Australium ;" also " Phil. Trans." 1694 and 

I7IS- 



II.] 



THE TRANSIT OF VENUS. 



25 



contact. We will try, however, to put it in a light 
which anyone, with a little attention, will under- 
stand. 

1. It must be thoroughly understood, from what 
has already been said, that if we know the amount of 
the sun's parallax ; in other words, if we know the 
angle subtended by any known distance on the earth's 
surface, at the sun, we know the sun's distance. 

2. We know that the relative positions of the earth, 
Venus, and the sun, are given by supposing the earth 



r/o. /o 




to go round the sun in 365 days, and Venus in 224 
days. Or, if we please, we may take no account of 
the earth's revolution, but suppose it fixed, in which 
case the revolution of Venus relatively to the earth 
(ie. the synodical revolution) is 584 days. 



26 THE TRANSIT OF VENUS. [chap. 



3. If, then, Venus moves round the sun through 

360 relatively to the earth in 584 days, she moves 

1 ^° 

through —- of that in one day, and through s8 " 4X2 ~ 

of a degree in one hour ; which is at the rate of about 
ii second of arc in a minute of time. 

Now we are ready to understand H alley's reasoning. 
Let A (Fig. 10) be the position of an observer on 
the earth at the time of first internal contact. S is the 
sun, and V, is now the position of Venus. This 
observer sees the contact earlier than a hypothetical 
observer at the earth's centre would see it, by the 
time Venus takes to move over v 3 v 2 . If we knew by 
calculation the instant when an observer at E would 
see it, and the observer at A saw it 8 minutes sooner, 
then, since Venus moves over 1 }" in a minute, she has 
moved over 8x i^ or 9 f of arc in this time, and 
hence we learn that the angle A S E = 9!". 

Suppose that by the time of the last contact the 
point A on the earth's surface has been carried by her 
rotation to B : the time of the last contact will now 
be too late by 8 minutes ; since the whole duration of 
the transit as seen by this observer is 16 minutes too 
long, and the angle moved over by Venus in 16 min. 
is the sum of the sun's parallax as seen from A and 
from B. 

But we cannot calculate with absolute accuracy the 
duration a transit would have when seen from E, 
because we should require to know more accurately 
than we do the values of Venus' and the sun's 
diameters. 

Halley got rid of this by taking another station 



H.] THE TRANSIT OF VENUS. 27 

which should be in the position A at the beginning of 
the transit. In the case we have been considering the 
time of the first contact would here be too late by 8 
minutes ; and if this place had reached B' by the end 
of the transit, the time of contact would be too soon 
by 8 minutes. Hence in this case the whole duration 
would be shortened by 16 minutes ; but in the former 
case it was lengthened by 16 minutes. Hence 32 
minutes is the time taken by Venus to pass over an 
angle equal to the sum of the parallaxes in the four 
cases considered. This difference of duration, whether 
it be 32 minutes or anything else, is a quantity which 
can be observed. Now Venus moves over about ii" of 
arc in a minute, or 38 1" in these 32 minutes. Hence 
one-fourth of 38-I" or g%" would appear, from the above 
hypothetical observation, to be the value of Venus's 
parallax. 

It must be noticed that we have here supposed 
that the transit takes exactly 12 hours, whereas the 
longest transit cannot exceed 8 hours. We have also 
supposed that two stations had been selected which 
were exactly situated so as to bring out the full effect 
of parallax at the time of each observation. These 
suppositions have been introduced only to simplify the 
explanation of the method. Anyone who has followed 
the above explanation will see how the method may 
be applied to actual cases that may occur. 

Halley saw (what many people fail to see even now) 

that the graat accuracy of the method consists in 

this, that in one second of time Venus moves over 

about o""02 ; and if we can determine the time of 

ontact, with an error of no more than a second, we 



23 THE TRANSIT OF VENUS. [chap. 

are measuring the sun's parallax with an error of no 
more than *02 of a second of arc. 

Halley even pointed out the best stations for 
observation. We may consider the earth to be at rest 
if we suppose Venus to move with the velocity she 
has relative to the earth. He supposed that the planet 
would cross near the sun's centre, and that the transit 
would occupy about eight hours. An observer in 
India wculd see the comraencem:nt of the transit 
four hours before mid-day, and the end of the transit 
four hours after mid-day. But, in the meantime, the 
part of the earth where he is has been moving from 
west to east, and Venus has moved from east to west, 
hence the duration of transit will have been shortened. 
But at Hudson's Bay the transit begins just before 
sunset and ends just after sunrise, that part of the 
earth having moved in mean time from east to west so 
as to lengthen the transit ; and thus at one place the 
duration of transit is lengthened, and at the other 
shortened, and the difference of time depends upon 
the parallaxes of Venus and the sun 1 at the two 
stations, and after finding these parallaxes we can 
calculate the equatorial horizontal parallax. 

1 This lengthening and shortening of the time of transit will be ren- 
dered more evident by an analogy. A person standing still sees a car- 
riage pass between him and a distant house. The carriage will take a 
certain time to pass the house. But if he also be moving, and in the 
same direction with the carriage, the transit of the carriage will take 
longer ; but if he move in the opposite direction to the carriage, the 
transit will take a shorter time. If, then, two persons be seated at 
opposite sides of a merry-go-round, so that at the time the carriage 
seems to be passing the distant house, one observer is moving with the 
carriage and the other in the opposite direction ; then one observer will 
see the time lengthened, and the other shortened. Now, the world is 
such a merry-go-round, and the positions of these two people corresDOud 
to the positions of India and Hudson's Bay, as pointed out by Haliey. 



in.] THE TRANSIT OF VENUS. 29 



CHAPTER III. 

In the previous chapters various methods have been 
indicated by means of which we may discover the 
scale upon which the plan of the solar system is drawn. 
The last one concluded by illustrating the nature of 
the methods of employing a transit of Venus, as pro- 
posed by Halley. It will be noticed that this method 
can be utilised in the way there indicated only when 
Venus passes nearly along a diameter of the sun. 
Halley, in fact, founding his calculations upon 
erroneous data, was led to conclude that this would 
be the case in 1761. In this he erred, and another 
slight but important mistake having been made in his 
calculations, it followed that at Hudson's Bay, his 
northern station, the transit was invisible. 

The present chapter will be devoted to a description 
of the methods to be employed in the coming transit 
for determining the solar parallax. In subsequent 
chapters the preparations which have actually been 
made for observing the transit of 1874 will be de- 
scribed ; and the difficulties encountered in this kind 
of observation enumerated. 



3^ 



THE TRANSIT OF VENUS. 



[chap. 



Let the reader now examine Fig. 1 1 and pa}' 
particular attention to the description of it, and he 
will thus be enabled to better understand what follows. 
The Earth, Venus, and the Sun are here represented in 
their relative positions ; and lines are drawn to show 
the directions in which two observers at opposite sides 
of the earth will see Venus upon the solar disc. It 
follows from this that an observer on the southern 




Fie. ii. 



portion of the earth will see Venus trace a path D E 
F upon the sun's disc further north than the path A B 
C which a northern observer on the earth sees it trace. 
Now Venus will be three times as far from the sun as 
from the earth on that date. From this it follows that 
the distance between the two lines ABC and DEF 
will be three times as great as the distance N S. But 
the distance N S upon the earth can be easily found 
out. Suppose it to be 6,000 miles. In that case 
the distance between ABC and DEF is known to 
be 1 8,oco miles. But it needs no demonstration to 
convince us that if we have a distance of 18.000 
miles measured out for us upon the sun's surface 



in.] THE TRANSIT OF VENUS. 31 

we can determine the distance of the sun from the 
earth. . 

Now the apparent distance between the two lines 
ABC and DEF is the least observed distances 
between Venus' centre and the sun's during the tran- 
sit. If, then, we can measure accurately the least 
distance between the centres of Venus and the sun, at 
two stations suitably chosen, we can determine the suns 
distance. 

There are three methods by means of which this 
may be effected ; the photographic method, the helio- 
metric method, and the method of durations. We 
shall consider these in order. 

I. The Photograplcic Method. — It is easy to see that 
by continuing during the transit, at each station, to 
take photographs of the sun, in which Venus will be 
represented as a black spot, these photographs may be 
so combined as to indicate definitely the apparent path 
of Venus as seen at each of these two stations. This 
method is looked forward to with much interest, be- 
cause it is the first time that photography has been 
extensively employed in delicate astronomical mea- 
surements. It is not generally known how extremely 
accurate a means of observation photography is. We 
owe much to Mr. De la Rue, whose success in the 
application of photography to astronomy has been 
unequalled, for having given us a most clear account of 
what has been done in this way. 1 The method has 
been employed in America to measure the distances 
between double stars. The double star is photographed 

x Acldre^ to the Mathematical and Physical Section of the British 
Association, Brighton, 187c. 



32 THE TRANSIT OF VENUS. [chap. 

and the distance is afterwards measured as accurately 
as possible. Prof. Bond finds that the probable error 
of a similar measurement is o"o"J2 ox'\ of the probable 
error of a similar measure made with a filer micrometer 
as estimated by Struve. Photographic pictures of 
the sun were for many years daily taken at Kew, and 
it was found that an extremely accurate measure of 
the sun's diameter could thus be made. If the lens 
of a common telescope were used to produce an image 
of the sun upon the sensitive plate the picture would 
be too small for accurate measurement. Hence a 
special instrument called a photoheliograph must be 
devised to give an enlarged picture upon the sensitive 
plate. Two perfectly distinct kinds of instruments 
are to be used for this purpose, the one English, the 
other American, Mr. Dallmeyer has, under the 
superintendence of Mr. De la Rue, constructed photo- 
heliographs for the English and Russian expeditions. 
In these instruments the image of the sun produced in 
the focus of an ordinary telescope is enlarged by a 
special arrangement so as to give a picture of the sun 
about four inches in diameter. This instrument based 
upon the principle of the Kew photoheliograph, is 
very perfect in its results and convenient in actual 
practice. It is mounted equatorially so as to follow 
the motion of the sun. The sensitive plate, which is 
prepared in an adjoining room, can be readily inserted 
and exposed. The intensity of direct solar light is so 
great that special means are necessary to give a short 
enough exposure. Before a photograph is taken a 
sliding shutter in the interior of the instrument cuts 
off all light from the sensitive plate. This shutter is 



in.] THE TRANSIT OF VENUS. 33 



held in its place by a cotton thread. So soon as this 
thread is cut, a strong spring draws down the shutter, 
in which is a slit about ^th of an inch wide. The 
time taken by this slit to pass over any part of the 
sun's image is the whole interval required for an 
exposure. 

The other method of obtaining a large picture of 
the sun is by employing a lens of great focal length. 
This method was originally proposed by Mr. Ruther- 
furd, of New York, and will be employed by the 
Americans, and also by Lord Lindsay in his observa- 
tions at the Mauritius. The focal length of the lens 
is forty feet. But a telescope of such dimensions 
could not be conveniently mounted in the ordinary 
way. To overcome this, a siderostat similar to the 
one originally constructed by M. Foucault for the 
Observatory of Paris is employed. This instrument 
consists of a plane mirror so mounted as to send the 
sun's rays always in the same horizontal direction. 
In the path of these rays, and close to the siderostat 
the lens is placed, and at a distance of forty i'eet an 
image of the sun about four inches in diameter is 
produced. At this place a window is arranged in a 
photographer's hut, and by means of this arrangement 
the photographer need never leave his dark room. 
After preparing a plate he places it in position at the 
window ; when exposure has been made he may 
remove the plate and develop it. 

Considerable advantage is likely to accrue by the 
employment of dry plates, which all diminish the 
labour of the photographer. Researches upon this 
matter have been undertaken by Prof. Vogel, in 



D 



34 THE TRANSIT OF VENUS. [chap. 

Holstein, Col. Smysloff, at Wilna, and by Capt. 
Abney, at Chatham. The employment of a dry 
process prevents all danger from the shrinking of the 
collodion-film. Herr Paschen 1 and Mr. De la Rue 
have made experiments upon this point. The latter 
gentleman finds that all shrinkages take place in the 
thickness of the film, so that the measurements would 
not be affected by it. But the more convenient dty- 
plate process is undoubtedly safer. Judging from 
the data furnished by Mr. De la Rue, this photo- 
graphic method will give results of the utmost value. 

II. The Heliometric Method. — The exact measure- 
ment of the distances of the edges of Venus from 
opposite edges of the sun would enable us easily to 
determine what is required, viz., the distance between 
the centres of the sun and planet at a given time. 
But the ordinary astronomical means are useless in 
measurements of this magnitude. To obviate this, a 
special instrument, called a Heliometer, will be em- 
ployed by the Germans and Russians, and by Lord 
Lindsay. This instrument was originally used for 
measuring the diameter of the sun. The object-glass 
of a common telescope is divided so as to form two 
semicircles. A screw adjustment allows us to slip one- 
half of the lens past the other one along their line 
of junction ; a fine scale measures this displacement. 
When the two halves of this object-glass are relatively 
displaced, two images of the sun are seen overlapping. 
The distance between the two images is proportional 
to the relative displacement of the two halves of the 
object-glass. This instrument has been brought to a 
1 Astronomische Nachrkhten, 1872, lxxix. 161. 



HI.] THE TRANSIT OF VENUS. 35 

state of great perfection by Mr. Repshold, of Ham- 
burg-. It is a very troublesome instrument to mani- 
pulate, and the corrections due to the influence of 
temperature are extremely difficult to apply. Yet 
with great care there is little doubt that very accurate 
measurements can be made. The nature of the 
measurements required to obtain the distance between 
the centres of Venus and the sun will readily be 
understood. The method has been most ably dis- 
cussed by Lord Lindsay and Mr. Gill in the Monthly 
Notices of the R. A. S., November 1872. At the same 
time it is difficult to conceive that this direct method 
will give results of equal value with the methods here- 
after described. In fact, an opposition of Mars would 
be expected to give equally good results ; for the 
distance of Mars from a fixed star can be more 
accurately observed with a micrometer than the dis- 
tance between the centres of Venus and the sun ; and 
a larger number of observations could be made. 

III. The MctJwd of Duration. — The third method 
of determining the least distance between the centres 
of the sun and Venus is less direct than either of the 
preceding methods ; but it has stood the test of a 
previous trial, and we cannot say but that it will be 
more satisfactory than the other methods in the 
coming transit. The method of duration closely 
resembles the method originally proposed by Halley. 
The duration of the transit, as viewed from two dis- 
tinct stations, is accurately determined. But the 
difference in this duration is affected by choosing 
stations upon a different system. Nevertheless this 
method is frequently called Halley's method. His 

D 2 



*G 



THE TRANSIT OF VENUS. 



TCHAP. 




in.] THE TRANSIT OF VENUS. 37 

methcd consisted in choosing two stations, so that 
during the transit the one should be moving eastward 
and the other westward. It is further essential for 
success that Venus should pass nearly along a 
diameter of the sun. In the method employed last 
century, the two stations were chosen — the one far 
north, and the other far south. On referring to Fisf. 1 1 
it will be seen that in each case Venus appears to pass 
along a chord of the sun. But in the one case this 
chord is further from the sun's centre, and conse- 
quently shorter than the other. The duration of the 
transit, so far as this effect is concerned, is directly 
proportional to the length of the chord traced out by 
Venus. Thus from observation we obtain the lengths 
of these chords ; and by geometry we can deduce the 
least distance between the centres of the sun and 
Venus at each of the two stations, and hence we can 
determine the sun's parallax. Fig. 12 illustrates this 
point very clearly. The duration is determined bv 
two distinct observations made at each station, the 
internal contact at ingress and the internal contact at 
egress. The time of an internal contact is the time 
at which Venus appears to be just wholly within the 
sun's disc. These two times must be accurately 
determined ; they will be separated by an interval of 
nearly four hours. Fig. 12 represents the illuminated 
hemispheres of the globe at the time of ingress and 
at the time of egress respectively in 1S74. At either 
of these epochs the sun will be visible from every 
place marked on the corresponding map. The sun 
will be vertical at the place occupying the centre of 
the map ; at all stations near the edges of the map 



So 



THE TRANSIT OF VENUS. 



[chap. 



the sun will at that time be near the horizon. The 
point from which the phenomenon will be first 
observed is there indicated, and likewise the point at 
which it is last seen. Straight lines are drawn across 
each map, and the hours marked upon them indicate 
the time at which the phenomenon will be seen. 



\AAAN \ 




Figs. 13. 14. taken from a paper by the Astronomer 
Royal in the Monthly Notices, show the same facts 
for the transit of 1882. 

Take now the case of two particular stations. At 
some point on the east coast of China the ingress is 
accelerated by 6 minutes, but at the same point the 



III.] 



THE TRANSIT OE VENUS. 



39 



egress is retarded 7 minutes ; consequently the dila- 
tion of the transit is lengthened 13 minutes. Again, 
at Kerguelen's Island the ingress is retarded 10 
minutes, while the egress is accelerated 5 minutes. 
Here then the duration of the transit is shortened 15 
minutes. The difference in duration as observed 




'Sabrina, Land 
Fig. 14. 



5F ^ 



from these two stations will therefore be about 28 
minutes. These maps have no pretension to great 
accuracy. They are calculated upon a certain 
assumption as to the value of the solar parallax which 
is probably not far from the truth. 

In 1761 considerable preparations were made for 



40 THE TRANSIT OF VENUS. [chai\ 



observing the transit of Venus in this manner. The 
English were represented by Messrs. Mason and Dixon 
at the Cape of Good Hope, and the French by the 
celebrated Pingre at the island of Rodriguez. A host 
of observers watched the phenomenon from northern 
regions. Unfortunately at scarcely a single station 
was the transit seen completely. Hence the method 
of durations was inapplicable, and another, originally 
proposed by De l'lsle, 1 came into use. This takes 
advantage of the fact that the ingress will take place 
later when seen from some parts of the earth than 
from other parts, as explained above ; so with the 
egress of the planet from the sun's disc. Hence, if 
the absolute time of contact of Venus with the sun's 
edge at ingress or at egress be observed at two places 
suitably chosen, the difference in time will be a measure 
of Venus's parallax. 

The method of De l'lsle will perhaps be better 
understood by looking upon the orbit of Venus as a 
vast protractor for measuring small angles. Venus 
moves, relatively to the earth, round the sun, that is 
through 360 , in 584 days. From this it follows that 
she passes over i' /- 5 in one minute of time. Now con- 
ceive two straight lines to be drawn from the sun's 
edge, the one to the Sandwich Islands, where the 
ingress is most accelerated, and the other to Kergue- 
len's Island, where it is most retarded. Venus passes 
across these two lines like the radial arm of a pro- 
tractor. The observed difference in the time of ob- 
serving the phenomenon at these two stations will 
be about 21 minutes. Of this about 11 minutes is 

1 Ilisloire dc V Acad, des Sciences, p 112. 



in.] THE TRANSIT OF VENUS. 41 

due to the fact that the Sandwich Islands are north 
of Kerguelen's Island, as before explained ; the re- 
maining 10 minutes or so will be a measure of the 
angle between the two lines drawn from the sun's edge 
to the two stations. Since Venus passes over i""5 in 
1 minute, 10 minutes gives us 15" for the effect of 
parallax looked at in this light. 

It is a comparatively easy matter to set one's clock 
accurately to local time by astronomical observations. 
But it is a matter of considerable difficulty for an 
observer in Kerguelen's Island to set his clock 
accurately to the local time of the Sandwich Islands, 
or vice versa. Consequently there will be some diffi- 
culty in determining the absolute difference of time 
cf contact as observed at these two stations. The 
difficulty simply consists in determining the longitude 
accurately. This is a matter involving a long series 
of astronomical observations even now ; still more 
so in i;6i. Such observations were then wanting. 
Hence the application of this method was not success- 
ful, and results of that transit were unsatisfactory. 

Not daunted by the comparative failure of that 
attempt, the astronomers of last century made vigorous 
efforts to make the transit of 1769 successful. The 
transit of 1761 was utilised in so far as it pointed out 
the difficulties in this kind of observation and gave 
them an approximate value of the sun's parallax to 
help them in choosing the most advantageous stations 
from which to observe the next transit. 

Halley had no conception, when he proposed this 
kind of observation, of the difficulties attending it. 
The difficulty chiefly consists in determining accurately 



THE TRANSIT OF VENUS. (chap. 



the exact instant when the contact seems to take 
place. The values which have been deduced from 
the observations of last century, and especially of the 
year 1761, have varied considerably according to the 
mode of reducing the observations. Thus in 1761, 
Lalande found, from the observations of Pingre. 9" 4 
for the solar parallax, while Maskelyne found from the 
work of Mason and Dixon S"6 ; Short 2 made it 8'"6s ; 
Wargentin, 8"'I to 8"'3. Encke 3 showed that the 
differences were partly due to an error in the longi- 
tude of Rodriguez.- This question will be capable of 
further discussion after this year, as Rodriguez is one 
of the stations chosen by the English from which 
to observe the coming transit. 

Since the observers are likely to differ considerably 
in the manner in which they observe the contact, and 
since it is difficult for us to be sure that all observers 
have really actually noted the same phenomenon, 
photography is once more brought to our aid. Some 
time ago M. Janssen proposed a method for deter- 
mining by the aid of photography the exact instant 
of contact. The value of his method was immediate- 
ly recognised, and steps have been taken to utilise it. 
The method consists essentially in exposing different 
parts of a prepared photographic plate in succession 
to the sun's light, so as to photograph that portion of 
the sun's limb at which the planet is visible. By the 
aid of no very complicated mechanism a circular plate 
is so arranged that sixty different portions of its surface 
near the circumference are successively brought into 

1 Phil. Trans., vol. Hi. p. 647 " Ibid. p. 648. 

3 Zach. Corn's}., ii. 1810, p. 367. 



in.] THE TRANSIT OF VENUS. 43 

position, and exposed to the action of the sun's rays. 
The plate completes a revolution once in a minute, so 
that sixty photographs are taken at intervals of one 
second. A person who is observing with a telescope 
can easily give a signal to commence these photo- 
graphic operations at the proper time. Thus one of 
the photographs will be sure to give us an indica- 
tion of the time of true contact. Furthermore each 
one of the photographs taken at one station can be 
compared with a corresponding one taken at another 
station so as to give us a means of deducinsr the sun's 
parallax. The advantages of this method are enormous. 
The uncertainty which exists with respect to eye 
observations is in a great measure due to fluctuations 
arising from tremors in the instruments and variations 
in the density of the intervening air. In the photo- 
graphic method, means have been taken to avoid these 
tremors as far as possible ; and the instantaneous 
manner in which the photographs are taken will 
reduce these uncertainties to a minimum. 

Various suggestions have been made as to the possi- 
bility of observing the exact time of the external 
contact by using a spectroscope in a beautiful manner 
originally devised by Mr. Lockyer and M. Janssen fcr 
observing the solar protuberances. Father Secchi has, 
in a very able memoir, pointed out a way by means 
of which this can be done ; M. Zollner has likewise 
pointed out the advantages of this method. 

The observation of external contact is doubtless 
very useful as supplementary to the internal contact. 
The chief difficulty consists in the uncertainty of 
fixing the telescope in the proper position, so as to catch 



44 THE TRANSIT OF VENUS. [chap. 

the exact point of the sun's limb. This difficulty 
would certainly be to a large extent obviated by the 
employment of the ingenious adjustable ring-slit 
devised by Lockyer and Seabroke. This device has, 
we believe, been already used with satisfactory results. 
It is much to be regretted that more observations 
to test its utilitv have not been made ; as on this 
account it is not likely to be employed in the coming 
transit. 

We have now completed the geometrical examina- 
tion of the nature of the observations on the transit 
of Venus, by means of which the sun's parallax will be 
deduced. The complete examination of the question, 
including analytical methods, cannot be here dwelt 
upon. Anyone who is interested in this should con- 
sult the valuable work, " Les Passages de Venus sur 
le Disaue solaire," by M. Edmond c'u Bois, lately 
published, in which the theoretical part of the question 
is very fully investigated. 

RECAPITULATION. — Before leaving the technical 
view of the matter it will be well to recapitulate what 
has hitherto been stated. 

1. We know the relative dimensions of the solar 
system accurately ; but we do not know the scale. 

2. The determination of the distance of the earth 
from the sun or from any of the planets, at a fixed 
date, fixes the scale. 

3. This may be determined (1) by the aid of a 
transit of Venus ; (2) by an opposition of Mars ; (3) 
by a knowledge of the velocity of light combined with 
observations of eclipses of Jupiter's satellites; (4) by 



III.] THE TRANSIT OF VENUS. 45 

the velocity of light and the constant of aberration ; 
(5) by the calculated effects of the sun's disturbance 
upon the lunar motions. 

4. A transit of Venus may be utilised : — 

(a) By the determination of times of contact 
at different stations, combined with a 
knowledge of the longitudes of these 
stations. 

(I) By determining the least distance between 
the centres of the sun and Venus during 
the transit, observed from different 
stations. 

5. This last determination may be mr.de by any 
of these methods : — 

(1) The Photographic Method. 

(2) The Heliometric Method. 

(3) The Method of Durations. 



4$ THE TRANSIT OF VENUS. [CHAP. 



CHAPTER IV. 

It has already been pointed out bow unsatisfactory in 
some respects were the results of the observations made 
in 1761. Those of the year 1769 were more successful, 
but the discrepancies of different observers still threw 
a doubt on the result. After Encke had discussed with 
all possible care the observations made upon these two 
occasions, 1 doubts were still raised as to the correct- 
ness of the value thus found for the solar parallax. The 
reasons of these doubts were manifold. In the first 
place, in order to get any value whatever of the solar 
parallax, Encke had been forced to assume that 
enormous errors had been committed by some of the 
observers ; and again, all the other methods of which 
we have spoken were found to give a tolerably accord- 
ant value of the solar parallax, but values that differed 
considerably from Encke's determination. 

It was with no small satisfaction then, that astrono- 
mers learnt that M. Powalky in 1864 had deduced a 
sensibly greater value for the solar parallax, by using 
more accurate values for the longitudes of the places 
of observation. 

1 Berlin Abhandlun^en, 1S35, pp. 295 — 310. 



iv.l 



THE TRANSIT OF VENUS. 



47 



But Mr. E. J. Stone, now her Majesty's astronomer 
at the Cape of Good Hope, has lately re-discussed 
these observations. 1 He finds that, when the remarks 
of the observers are rightly interpreted, all the obser- 
vations agree without any extravagant errors of obser- 
vations; and moreover, the value of the solar parallax 
thus deduced agrees with the values found by other 
means. Mr. Stone deserves the thanks of the scien- 
tific world for having convinced them that this method, 
which at one time was falling into disrepute, may 
really be rendered very trustworthy. 

The result of Encke's determination was that the 
mean distance of the sun from the earth is about 95 
millions of miles. It now appears that the true dis- 
tance is somewhere about 91 ■£ millions of miles. The 
annexed table gives the values of the sun's parallax 
and distance as determined by different methods. 



Method. 



Transit of Venus 2 . . 
Opposition of Mars 
Lunar Theory 4 . 
Lunar Theory 5 . . . 
Planetary Theory s . . 
Jupiter's Satellites and ) 

velocity of light 7 . ) 
Consiant of Aberration i 

and velocity of light 8 \ 



Parallax. 


Dist. of sun in mi'es. 


Computer. 


8 -"9 1 


91,580/00 


Stone 


8 -"943 


91,240,000 


Stone 


S'"gi6 


91,520,000 


Hansen 


8 "S;o 


92,200,000 


Stone 


8 -"859 


92,IIO,CCO 


Leverrier 


8 "86 


92,IOO,COO 


Foucau't 


8-"S6 


92,IOO,OCO 


Cornu 



The uncertainty of observation which Mr. Stone 

aimed at clearing away is one of a very curious optical 

1 Monthly Notices of the R. A. S., xxviii. p. 155. " Ibid, xxvai. 255. 

3 Ibid, xxiii. 183. 4 Ibid. xxiv. 8. 

5 Ibid xxvii. 271. c Comptes Rendus, July 22, 1S72. 

7 Ibid. 1862, 1 502. 8 Ibid. 1873, P- 34 J « 



48 THE TRANSIT OF VENUS. [chap. 

character. It is found that Venus at the time when 
she has almost completely entered within the sun's 
disc does not retain her round aspect, but becomes 
pear-shaped, or at least connected with the sun's limb 
by a "black drop" or "ligament." This ligament 
sometimes appears simply as a fine black thread 
connecting the planet with the limb of the sun. One 
observer in 1769 saw a number of black cones shoot- 
ing out to the sun's edge in a fluctuating manner. 

Many of these phenomena were doubtless due to 
bad definition of the telescope employed, cr to the 
instability of its mounting. But the existence of a 
" black drop" even under the most favourable circum- 
stances cannot be doubted ; it was well observed in 
the case of a transit of Mercury that occurred in 
1868. 1 If the planet be entering upon the solar disc, 
the first phase occurs when the edges of the sun and 
planet seem to be in contact. The second phase 
occurs at the instant when the " black drop " breaks 
off and a flood of light sweeps in between the planet 
and the sun. This occurs very suddenly, and has been 
supposed to indicate the true time of actual contact. 

By referring to the Philosophical Transactions of 
1769-70, a large number of descriptions of the phe- 
nomenon may be read. Some of the appearances are 
shown in Fig. 15, they are copied from the originals 
by Bevis, Hirst, Bayley, and Mayer, respectively — 
Prof. Grant states that the last one bears a resemblance 
to the appearance of Mercury as seen during its transit 
in. 1868 from the Glasgow Observatory, the sun being- 
near the horizon. 

1 Monthly Koikes, xxix. p. 17, &c. 



IV.] 



THE TRANSIT OF VENUS. 



49 



In the case of that transit of Mercury, studied by 
six experienced observers at Greenwich Observatory, 
two curious facts appear. Firstly, the times of contact 
as determined by different observeis vary to the ex- 
tent of 13^ seconds. And secondly, the shape of the 
planet varied considerably with different observers. 




Fig. 15. — Tne "black drop," as observed in 1769. 

Mr. Stone having noticed a confusion in the lan- 
guage of the astronomers of the last century as to 
which of the two phases was observed, carefully 
re-studied their words ; and by supposing the two 
phases to be separated by a constant interval of time, 
he utilised both kinds of observation. This constant 

E 



50 THE TRANSIT OF VENUS. [chap. 

interval of time was deduced from all the observations, 
and found to be about \J seconds. In this manner 
he arrived at the more accurate value of the sun's 
parallax. 

It has been asserted that astronomers claim undue 
credit for the accuracy of their measurements, since 
Encke made an error of three or four millions of miles 
in the calculation of the sun's distance. This is not 
so. A chemist may be able to weigh many substances 
with an error of j-Jq- per cent, or less ; but if the sub- 
stance to be weighed be only T ^ of a milligramme, 
he might have a larger percentage error. When we 
consider how extremely small an angle the solar 
parallax is, it is astonishing to find so great a con- 
cordance between the results of different methods. 

As to the cause of the phenomenon of the " black 
drop," Lalande ascribed it to irradiation. Irradiation 
is that curious phenomenon in virtue of which a star, 
or any bright object, appears larger than it really is- 
If a thin platinum wire be intensely heated by the 
passage of an electric current, it seems, to a person 
distant about fifty feet, to be as thick as a pencil. In 
this way the sun's diameter seems to be increased. 
The sun's light also encroaches upon the disc of the 
planet and makes it seem to be smaller than it really 
is. But when Venus and the sun have their edges 
almost in contact, as shown by the dotted line in Fig. 
16, then there is no light at that point which can en- 
croach ; hence we see at this point the " black drop'' to 
which allusion has been made. 

Father Hell, one of the observers in 1769, ascribed 
the phenomenon of the " black drop " to the sensible 



IV.] 



THE TRANSIT OF VENUS. 



51 



size which an illuminated surface must have before it 
can be visible. There is probably some truth in each 
of these suppositions. 

As to the cause of irradiation, it is difficult to speak 
with certainty. It is probably due in part to the 
telescope and in part to the eye. Great confusion 
has been introduced by persons neglecting to separate 
two perfectly distinct phenomena. True irradiation 




*1G. iC. 

is only observed with a powerful light. With less 
illumination similar results may be seen, but they are 
of a different nature, and are produced between the 
formation of an image on the retina and its reception 
by the brain. In accordance with the customary 
nomenclature, this error of vision may be called the 
mental aberration of the eye. It is a perfectly definite 
phenomenon capable of accurate investigation, and 
M. Plateau has made measurements of the mental 
aberration of his own and his friends' eyes. 1 True 

1 Nouv. Mem. del'Acad. Royale de Ernxelles, t. xi. p. 1, ccc. 

E 2 



S-2 THE TRANSIT OF VENUS. [chap. 

irradiation may be caused either -.vholly or in part by 
the spherical aberration or the chromatic aberration 
of the eye, or by diffraction, or by a spreading of the 
excitement of the nerves of the retina, which gives 
rise to the sensation of vision over a sensible space. 
In a telescope it is probably chiefly due to diffraction. 
The success or failure of all observations of contact 
in the coming transit will to a great extent depend 
upon our knowledge of the nature of this appearance. 
For this reason numerous experiments have been 
made with the object of gaining information upon the 
question. The Russians, Germans, Americans, and 
English have all mounted artificial transits of Venus 
for the practice of observers. The arrangement 
adopted by the Astronomer-Royal consists essentially 
of a metal disc with two arcs of circles drawn upon 
it to represent the sun's edge with the metal between 
them cut away. Behind these there passes a glass 
plate with a circle of metal to represent Venus let 
into it flush with its surface. The glass plate is moved 
by clock-work so that the different phenomena are 
observed in succession exactly as they will be seen in 
the true transit. As the artificial planet passes in 
succession the two arcs representing the sun's edge, 
the phenomena of ingress and egress are successively 
observed. Before contact takes place, the sun has 
two cusps at the point of contact where Venus is 
touching the edge of the sun. The distance between 
the points of these cusps rapidly diminishes, the space 
between them being intensely black. They suddenly 
meet. But between the planet and the sun's edge a 
light shade is still seen which lasts several seconds 



iv.] THE TRANSIT OF VENUS. 53 

before the planet appears completely detached. If 
instead of watching the meeting of the cusps, the 
part between them be studied, a sudden diminution of 
intensity of the blackness is seen about a second 
before the meeting of the cusps. The diminution of 
brightness is very sudden, and this is the phenomenon 
to be chiefly attended to in the actual observation. It 
occurs almost exactly at the moment of true contact, 
though the " black drop " does not disappear until 
some seconds later. It is of the utmost importance 
that the nature of these different phenomena should 
be carefully studied by all the observers. And at the 
present time experiments are being made with a view 
of determining the personal equation of each of the 
observers on the British expeditions. 

But the actual observation will be rendered more 
difficult for various reasons. Firstly, the enormous 
extent of atmosphere which the rays of light must 
penetrate before reaching the telescope will destroy 
the definition to a large extent. Secondly, the exist- 
ence of an atmosphere around the planet Venus may 
materially affect the nature of the phenomenon. 

In any case there is little doubt that as many of the 
observers as possible of all countries should describe, 
as accurately as can be done, the exact appearances 
which are noticed at successive stages of the ingress 
and egress respectively. Comparisons being also 
made between different observers and between dif- 
ferent telescopes, it will be possible to reduce the 
observation of any phase which may chance to be 
caught in the actual observation to the true time of 
contact. From observations with the Model Transit 



54 THE TRANSIT OF VENUS. [chap. 

of Venus made at Greenwich, the following facts 
appear : — 

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 ap- 
pear to follow each other sometimes rapidly, at othef 
times gradually ; so that in some cases all the pheno- 
mena 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 
employed, the time of any phase at ingress is earlier 
than with an instrument of less perfect definition. 

In the case of the observations of last century, it is 
easy to see how observers quite unprepared by pre- 
vious observations as to the nature of the appearances 
they were about to witness v/ere sometimes incon- 
sistent with each other. In fact, without preliminary 
practice, and with bad definition, observers might vary 
even with a Model Transit of Venus by as much as 15 
seconds. But, knowing what they are to observe, they 
would differ under no circumstances by more than 
about 2 seconds. Hence it is probable that in the 
actual transit, if the definition be good, the observa- 
tion may be accurate to within one second ; but if the 



IV.] THE TRANSIT OF VENUS. 55 

circumstances be not very favourable, they may differ 
to an extent of fully three seconds, even after con- 
siderable practice with the model. These estimates 
serve to give us some idea of the accuracy with which 
we may hope to have the observations made; and it 
is probable, from the care which has been taken to 
multiply the number of observers at each station, that 
each pair of observations of contact will give us a 
determination of the parallax of the sun true to about 
\ per cent. 

In the observations of contact, however, a great 
deal depends upon the experience of the observer; 
and it is fortunate that the idea originally thrown out 
by M. Janssen, and the mechanical execution of which 
has since been so ably carried out, will indelibly record 
the progress of the phenomenon and serve as a check 
to the observers. 

By the aid of this method photographs of particular 
sun-spots have already been taken with great success 
at intervals of one second during one minute of time. 
Each of these sixty photographs is perfect in itself, 
and would admit of very perfect measurements. 
Hence there is every reason to believe that in this 
manner an independent and very valuable observation 
of the true time of contact will be made at each sta- 
tion where a photo-heliograph is situated. 

The observations by means of photography during 
the progress of the transit have few difficulties to con- 
tend with. Their value will be largely increased by 
the fact that the actual measurements will be made 
afterwards when the observer cannot be carried away 
by the excitement of the moment. But even in this 



56 THE TRANSIT OF VENUS. [chap. iv. 

class of observation there are difficulties which must 
be carefully considered. It is found that if a sensi- 
tised plate be over-exposed, the image of the sun is 
considerably enlarged. This is due to photographic 
irradiation. It appears from experiments by Lord 
Lindsay and Mr. A. C. Ranyard to be mainly caused 
by the reflection of light from the back of the glass 
plate. 1 It can be almost entirely avoided by wetting 
the back of the plate, and placing black paper against 
it. There will still be probably a slight enlargement 
of the sun's diameter. This will not affect the relative 
positions of the centres of the sun and Venus ; but it 
will render it extremely difficult to determine the unit 
of measurement. 

There are two ways of applying the photographic 
method. The first is the same as the heliometric 
method. For this purpose it is necessary to have one 
station in the north and another in the south. By the 
other method we do not determine the distance 
between the sun and planet together with the exact 
time, but the actual position of the planet at each ob- 
servation. In other words, we determine the distance 
of Venus's centre from the sun's centre, and also the 
angular distance measured from the north point of the 
sun. To do this we must have in the focus of the 
photo-heliograph a fine thread to indicate the direction 
of the meridian in the photograph ; or in the American 
method we must have a thread suspended vertically 
which shall indicate the vertical direction in the solar 
photograph. The arrangements of the American 
method, as set up by Lord Lindsay at Dun Edit, are 
i Monthly Notices of the R. A. S., 1S72, p. 313. 



53 THE TRANSIT OF VENUS. [chap. 

shown in Fig. 17. The siderostat, lens, and hut, are 
all shown in position. 

The value of the different methods has been well 
discussed by De la Rue, 1 Tennant, 2 and Proctor." 
The method which takes into account the actual posi- 
tion of the planet on the sun is the more accurate, but 
it requires that the fiducial lines, or lines of reference, 
shall be exactly represented in the photographs. Mr. 
De la Rue says that this can be done to within one 
minute of space. 

Besides photographic irradiation, however, there is 
a very important difficulty which enters into both the 
photographic and heliometric methods. This is due 
to the refraction of our atmosphere. Everyone knows 
the distorted forms which the sun assumes at the 
time of sunset. In our own climate these appearances 
are seldom seen on account of clouds and the haziness 
of the atmosphere. But even from a high mountain, 
or from any position which allows the form of the sun 
to be accurately seen up to the time of sunset, its 
shape may be noticed to be either square, elliptical, 
or pear-shaped, according to the circumstances of the 
atmosphere. Now at the most favourable points of 
observation the sun will be comparatively near to the 
horizon. Consequently its form will vary with the 
temperature of the air and with atmospheric disturb- 
ances. With our feeble knowledge of the laws of re- 
fraction it will be a matter of some difficulty to deter- 
mine with accuracy the distance at different times 
between the centres of the sun and Venus. 

1 Monthly Notices of the R.A.S., xxix. pp. 48 and 282. 

2 Ibid. 280. 3 jbid. xxx. 62. 



iv.] THE TRANSIT OF VENUS. 59 

The same remarks apply to the heliometric method. 
But with stations chosen where the sun is not too low, 
we may expect accurate results. The value of a 
heliometer over other instruments designed for measur- 
ing small angles consists in this, that by it we can 
measure angles as large as the sun's diameter. It is 
expected by observers with this method that an ob- 
servation will be made each time with an accuracy 
comparable with that of an observation of the time 
of contact. In this case the heliometric method will 
give valuable results. For the same reasons observa- 
tions made by means of a double-image micrometer 
of the distance between the limbs of the sun and 
Venus near the time of contact will be as accurate as 
an observation of the contact itself. 

The last difficulty which we shall mention in con- 
nection with this kind of observation is due to atmos- 
pheric conditions as affecting the apparent time of 
contact. With regard to the British expedition, great 
care has been taken to choose stations where the 
weather can be depended upon. But in cases where 
the method of duration is applied, the observations 
will be useless if there be not a very clear atmosphere 
both at ingress and at egress. De l'lsle's method, on 
the other hand, requires a perfect observation only at 
the time of one of these phases. Hence the nations 
which have adopted this method are less likely to be 
disappointed than others. 



6o 7 HE TRANSIT OF VENUS. [chap. 



CHAPTER V. 

It is probable that the observations of contact will be 
very materially supported by additional observations 
made with the double-image micrometer. This in- 
strument was devised many years ago by Sir George 
Airy. 1 It is the most convenient eye-piece micro- 
meter which can be used for measuring the distance 
between a pair of stars, or, as in the present case, 
between the limbs of the sun and Venus. The pe- 
culiarity of Airy's double-image micrometer consists 
in this, that one of the lenses forming an erecting 
eye-piece is divided in two, like the object-glass of a 
heliometer. The one half can be slid past the other, 
and the amount of displacement accurately measured 
by a divided circle on the screw which gives this 
motion. When the halves of this lens are relatively 
displaced, two images of the object are seen, as in 
the heliometer. If the distance between a pair of 
stars be the subject of measurement, the line of 
separation of the half-lenses is made to coincide 
with the line joining the two stars. The screw is 
1 Greenwich Observations, 1840. 



v.] THE TRANSIT OF VENUS. 61 

now turned in one direction, until the image of one 
star given by one half of the lens coincides with the 
image of the other star given by the other half of 
the lens. The amount of displacement is then read 
off. The halves of the lens are again brought to 
coincidence. The screw is now turned in the opposite 
direction, and a similar observation made. Knowing 
the value of the divisions on the divided circle, these 
two observations give us a means not only of de- 
termining the distance between the two stars, but also 
of fixing accurately the reading of the instrument 
when the half-lenses are in coincidence. 

It is easy to see that after the internal contact at 
ingress, and before the internal contact at egress, 
measurements may thus be made of the distance of 
Venus from the sun's limb, from which the true time 
of contact may be deduced, just as in the Janssen 
photographic method. 

But, besides, this double-image micrometer gives a 
means of estimating the true time of contact in a 
manner which may possibly be one of very great 
accuracy indeed. Consider the case of ingress two 
minutes before the time of true contact. From this 
time up to the actual contact the distance between 
the cusps, where the limbs of Venus and the sun 
meet, will diminish with very great rapidity. By 
turning the micrometer so that the line of junction of 
the half-lenses is in a line with the points of these 
two cusps, the distance between them may be very 
accurately measured. The observation may be re- 
peated a number of times. The great rapidity with 
which these cusps approach, with a very slight motion 



Cz THE TRANSIT OF VENUS'. [chap. 



of the planet, makes it probable that each of these 
observations will give the means of determining very 
closely the true time of contact. 

There are great difficulties connected with observa- 
tions of the sun at such low altitudes as are required 
for the application of De l'lsle's and other methods. 
These will materially affect the definition of the cusps, 
and it is not certain that the micrometer method will 
give results so valuable as might have been anti- 
cipated. 

But even in the eye-observation of contact the low 
altitude of the sun will be a serious drawback. This 
difficulty has been fully recognized by the Astronomer- 
Royal, and, with the assistance of Mr. Simms, he has 
devised an ingenious eye-piece, which is likely largely 
to reduce the inconvenience. 1 The chief difficulty is, 
that at such low altitudes not only are the rays of 
light enormously refracted by the earth's atmosphere, 
but the colours are actually dispersed, as with a prism. 
Hence the definition cannot be perfect. The principle 
of the new eye-piece consists in employing a lens 
next the eye, larger than is required for the pencil of 
rays falling on it, so that different parts of it can be 
used for different altitudes of the star. The surface 
of this lens next to the eye is plane ; and the lens 
can be moved, by means of a screw and slight spring, 
in a socket which is a portion of a sphere the same 
radius as the lens. By turning the screw, various in- 
clinations can be given to the plane surface next the 
eye. But the curvature of the other surface remains 
the same, though a different portion of it is used. 

x Monthly Notices of the R.A.S., vol. xxx. p. 58. 



v.J THE TRANSIT OF VENUS. 63 

The practical result, then, of such an inclination of 
the lens in its socket is simply the introduction of a 
prism whose angle can be so varied as to correct 
totally the atmospheric dispersion. 

But in the case of photography the low altitude of 
the sun introduces a much more serious difficulty. 
The light has in this case to pass through a great 
length of the earth's atmosphere, in its lowest and 
densest regions. Much of the light is absorbed by 
the atmosphere, as is shown by the fact that the 
rising or setting sun may be gazed at with impunity. 
But further, it appears that of all the colours com- 
posing the sun's light, those which affect most power- 
fully a photographic plate are the most greedily 
absorbed. Hence it has been found at St. Petersburg 
that at mid-winter, when the altitude of the sun is 
about 6° or 7 , a photographic plate must be exposed 
to the sun 360 times as long as at the equinoxes. 
This is a difficulty which cannot be surmounted except 
by exposing the plate a longer time than is desirable. 

It has been already stated that considerable dis- 
crepancies in determining the times of contact might 
arise from observers noting different phenomena. The 
employment of the Model Transit of Venus insures 
concordance among the observers of each nation ; but 
all European observers will be much indebted to M. 
Struve, who has actually compared his own observa- 
tions with those of the Russian, German, English, and 
French observers, so that comparisons will be possible 
between the results obtained by these different nations. 

Everything being now prepared for observing as 
successfully as possible the actual phenomenon of 



64 THE TRANSIT OF VENUS. [chap. 

contact, it remains to describe the means by which 
the time can be determined accurately. All clocks 
and watches are set and regulated by observations of 
the stars, or by comparison with other clocks so re- 
gulated. An astronomical clock counts the hour up 
to 24I1. The clock is set to oh. at the instant when a 
certain point in the heavens passes the meridian. If 
then we have a means of determining the time when 
this happens, we can set our clock accurately to local 
time. But a star does not pass the meridian of 
Greenwich at the same time as it passes the meridian 
of a place having any other longitude. By the aid of 
a transit instrument the local time can be determined ; 
but to determine actual Greenwich time at another 
place we must, as before stated, know accurately the 
longitude of that station. These two tilings, the Green- 
wich time and the longitude, are so connected, that if we 
know the one, the other can be immediately deduced 
from the local time by simple addition or subtraction. 

The longitude may be determined in a variety of 
different ways. If the two places whose difference of 
longitude is to be determined be not very distant, a 
simple method may be employed. A rocket is sent 
up from some point between the two stations. An 
observer at each station notes the local time at which 
the rocket is seen to burst. The difference between 
these times give the difference of longitude. A flash 
from a lamp, or reflected sunlight, may be similarly 
employed. 

The Greenwich time (and consequently the longi- 
tude) can also be found by transporting chronometers 
from one station where it is known to another where 



V.] THE TRANSIT OF VENUS. 65 

it is not known. First-rate chronometers must be 
used, and a large number to check one another's 
errors. The main error of a chronometer is due to 
the influence of temperature on the momentum of 
the balance wheel and the strength of its spring. 
The Russians have of late years introduced with 
great success a method of secondary correction for 
this error. Along with the compensated chronometer 
at least one is sent without any compensation. The 
difference between this chronometer and others is a 
measure of the sum total of the temperatures to 
which they have been exposed ; and by the aid of 
a table carefully drawn up from a number of observa- 
tions, the amount of secondary correction necessary 
can be fairly estimated. It is said that the employ- 
ment of this device is of the very greatest service. 
Ten well-tried chronometers, accompanied by a single 
uncompensated one, if carried' between stations ten 
days apart (e.g. St. Petersburg and Cazan), will, in one 
journey, give the longitude of an intermediate station 
(such as Moscow) correctly within y 1 ^- of a second of 
time. By the aid of this contrivance chronometers 
may be employed, even for very long journeys, to 
determine the longitude. This method is quite new, 
and has not been tested by any nation except the 
Russians. The results obtained by them are, how- 
ever, perfectly satisfactory. Theoretically the idea is 
almost perfect ; the outstanding temperature error 
being the main fault of chronometers, and the em- 
ployment of an additional chronometer uncompen- 
sated giving us a means of determining the amount 
of this error, the time deduced by this means ought 

F 



65 THE TRANSIT OF VENUS. [chap. 

to give very satisfactory results. There is but one 
objection to the method, which is only a partial one. 
After a series of alternately very hot days and very 
cold nights, the difference between the compensated 
and uncompensated chronometers might be the same 
as after the same period, with a tolerably uniform 
temperature ; but the correction necessary in these 
two cases might be very different indeed. It is easy, 
however, to keep chronometers at a temperature which 
does not vary rapidly, and the experiments made by 
the Russians warrant us in saying that by the aid of 
this method longitudes may be determined, with very 
great accuracy indeed, in voyages of such length that 
the ordinary chronometric method would be unavailing, 
and that in every case where longitudes are required 
by the use of chronometers this method should be 
employed. 

A third way of determining the absolute time is 
by the use of telegraphic signals. An operator at 
Greenwich may arrange to telegraph a signal to 
another at Alexandria at a certain definite time of 
day. If the transmission of the current from Green- 
wich to Alexandria were instantaneous, the person at 
Alexandria would at that instant receive the exact 
time. But a current through a submarine cable is 
retarded. Suppose it to be retarded two seconds ; 
the time received at Alexandria will be too late by two 
seconds. If now an operator at Alexandria tele- 
graphs to Greenwich he will despatch the signal two 
seconds before it reaches Greenwich. The longitudes 
determined by the two currents in opposite directions 
will therefore differ by four seconds. The mean of 



v.] THE TRANSIT OF VENUS. 67 

these values gives the true longitude, and half the 
difference between the two determinations is the time 
of transit of the currents. It is found, however, both 
from theorv and experiment, that if there be a leak 
in the cable nearer to Greenwich than to Alexandria 
the current will pass more slowly in going to Alex- 
andria than in the reverse direction ; though this 
difference can never be very great. 

Considerable differences have been found by the 
Americans to exist between comparative observations 
of longitude by the telegraphic method and by the 
lunar method, which will presently be described. The 
Americans rushed to the conclusion that the error 
existed in the lunar method. This is not necessarily 
so. The American system of telegraphing over long 
distances consists in using a relay. A relay is an 
arrangement to overcome the difficulty of sending a 
current through a long line. It is placed at an 
intermediate station. It consists essentially of an 
electro-magnet which attracts a piece of iron when a 
current which has originally been sent through the 
primary station passes through its coils. This attrac- 
tion of a piece of iron makes contact with a new 
electric circuit with a separate battery, and so the 
current is passed on to the final station, or to a 
second relay. The piece of iron must move through 
a sensible distance before the second circuit is com- 
pleted. It has hitherto been supposed that the time 
lost in employing a number of relays could be elimi- 
nated by sending the current in alternate directions 
as above described. This is certainly not the case. 
The time elapsing before contact is made by a relay 

F 2 



6S THE TRANSIT OF VENUS. [chap. 

depends upon the strength of the current. The 
strength of the current depends upon the length of 
the wire through which it is passing, and also upon 
the strength of the battery. Consider now the case 
of a relay at the junction of a long and short wire. 
The current passing through the long wire is weaker 
than the other. Hence if the current first pass through 
the short wire, the loss of time introduced by the relay 
is less than when the current is first sent through the 
long wire. For this reason the time taken by the 
current to pass in one direction is less than in the 
other direction. It appears then that the employ- 
ment of a number of relays is injurious in longitude 
determinations, and if extraordinary precautions be not 
taken the resulting longitude will be erroneous. The 
same takes place with a submarine cable, with a leak 
near one end of it. 

It must be noticed that in all the methods here de- 
scribed for determining the longitude, the local time 
must be accurately known. This is done by aid of a 
transit instrument as before described. One of the 
transit instruments of the British Expedition, in its 
wooden hut, is shown in Fig. 18. 

Another class of methods for determining the longi- 
tude depends upon the motions of the moon. It has 
already been stated that what we want is to know at 
some instant the absolute Greenwich time. If then 
we could get something analogous to a huge clock in 
the heavens which an observer at any part of the 
world could see, we should be able to determine our 
longitude. The moon may be taken to represent the 
hand of such a clock, and the stars the hours and 



v. 



THE TRANSIT OF VENUS. 



69 




70 THE TRANSIT OF VENUS. [chap. 

minutes. The moon is chosen in preference to the 
planets because she moves more rapidly among the 
stars. She moves around the earth, that is, through 
360 in 27^ days, or through i° in two hours, or 
through one second of arc in two seconds of time. 
If then the tables in the Nautical Almanac predicting 
the place of the moon are absolutely correct, an 
observer, by watching the instant at which she seems 
to come to the position of any star, and knowing 
from the tables the Greenwich time at which she 
reaches that position, receives an intimation of the 
absolute time from this gigantic celestial clock. Or, 
if there be no star, it will suffice to observe the time 
when the moon reaches any definite position among 
the stars. As a matter of fact the tables of the moon 
are by no means perfect ; but this difficulty is over- 
come by the regular series of observations of the 
moon's place made at Greenwich on every possible 
occasion. Thus while the tables are sufficiently 
accurate to give the navigator a fair knowledge of his 
longitude, an observer in any country can, when con- 
venient, compare his observations with those made at 
Greenwich, and so determine the longitude with great 
accuracy. 

It is a fact of interest in connection with the present 
subject, that the transits of Venus will aid materially 
in perfecting the Lunar Tables. The motions of the 
moon are rendered irregular by the disturbing attrac- 
tion of the sun. But we cannot determine with great 
accuracy either the amount or the direction of the 
sun's attraction upon the moon until we know accu- 
rately the sun's distance. Hence if we wish to be able 



v.J 



THE TRANSIT OF VENUS. 




Fjg. 19. — Porlable Altazimutli Instrument 



/- 



THE TRANSIT OF VENUS. [chap. 



to compute tables of the moon sufficiently correct for 
the exact determination of longitude, we must employ 
every means in cur power to perfect our knowledge of 
the sun's distance. 

Of the methods available for determining the 
moon's position, three will be employed in the coming 
transit. The first is by observing, with a powerful 
telescope, the exact time at which the moon extin- 
guishes the light of a star in front of which it is 
passing. This is technically called an occultatiou of 
a star by the moon ; and when the occupation is made 
by the non-illuminated portion of the moon the 
observation has great precision, and, the position of 
the star being known, is very valuable for determining 
longitude. 

The second method is by observing, with the transit 
instrument, the exact time at which the moon passes 
the meridian, and by observing about the same time 
the transits of stars nearly in the same parallel whose 
positions are well known. 

The third method is by employing an instrument 
called an altitude-and-azimuth instrument, or shortly, 
an altazimuth. One form of this instrument is shown 
in Fig. 19. It consists essentially of a telescope 
mounted upon two divided circles so arranged that 
the one shall give the altitude of an object towards 
which the telescope is pointing, while the other gives 
its azimuth or its angular distance from the meridian 
measured in a horizontal direction. An instrument 
of this class has long been employed at Greenwich 
with great success for determining the position of the 
moon when out of the meridian. It thus acts as a 



v.J THE TRANSIT OF VENUS. 73 



supplement to the transit-circle, of the utmost value 
in so cloudy a climate as our own. One disadvantage 
of this instrument is that the numerical reductions are 
extremely troublesome ; but no trouble is too great in 
an observation of so much importance. 

It is not absolutely necessary that both altitude and 
azimuth should be observed. In equatorial regions 
the motion of the moon is chiefly in altitude, while in 
places of high latitude in summer, when the moon is 
low, the motion is chiefly in azimuth. Hence among 
the English stations the vertical circles alone are 
provided for the stations within 30 of the equator, 
while at Kerguelen's Island and New Zealand the 
azimuth circles are accurately divided. All these 
instruments have been well tested, and are found to 
be remarkably perfect. Not only the altazimuths but 
also most of the other instruments to be employed by 
the British have been constructed by Troughton and 
Simms ; they have all been well tried, and the results 
have been so satisfactory that these makers deserve 
great credit for the help they have thus given to the 
success of the expeditions. 

In all observations of the moon for determining the 
longitude there are of course numerous corrections 
which must be applied. Among these none is more 
important than the correction for the parallax of the 
moon. 

Recapitulation. — In the case of every nation 
depending upon De l'lsle's method, and in the 
case of every expedition when only one contact is 
observed, the longitude must be determined with very 



74 THE TRANSIT OF VENCS. [chap. 

great accuracy. This can be done by any of the 
following methods : — 

i. By rockets, or flashing signals. 

2. By a trigonometrical survey. 

3. By aid of chronometers, in which it would be 
unwise to neglect the method lately introduced of 
adding to the chronometers one which is uncompen- 
sated. 

4. The telegraphic method, in which it is not 
desirable to use relays, since very long lines with a 
Thomson's reflecting galvanometer will give good 
results, while the employment of relays is objection- 
able. 

5. By observations of the moon's position, which may 
be made by any of the three following methods : — 

(a) By occupations of the moon. 

(/3) By transit observations of the moon and 

culminating stars. 
(7) By aid of an altazimuth. 



vi.l THE TRANSIT OF VENUS. 



I D 



CHAPTER VI. 

HAVING now discussed all the methods to be em- 
ployed, and the chief difficulties to be encountered, 
it is time to examine what has actually been done. 
What method or methods ought to be chosen ? What 
stations are most suitable, taking into account the 
chances of good or bad weather and good or bad 
anchorage ? What preparations have been made by 
the various governments and by private individuals ? 
And are the arrangements satisfactory ? 

As to the choice of method,, the observation of con- 
tacts was the only kind originally contemplated. The 
employment of photography and heliometers is a 
comparatively new idea,, and will be spoken of later. 
The observation of contacts is applicable to three 
methods, for each one of which different stations must 
be chosen ; these are Halley's method, the method of 
durations, and De ITsle's method. We will consider 
these in order. 

I. Halley's method fails totally in the transit of 
1874, but may perhaps be applied in 1882, though not 
under good conditions. On referring to Fig. 13 in 



;6 THE TRANSIT OF VENUS. [chap. 

Chapter III., it will be noticed that Sabrina Land is a 
station where in 1882 the transit will commence just 
before sunset, and end just before sunrise. Hence 
during the transit this station and another located in 
America will be moving in opposite directions, thus 
fulfilling the conditions required by Halley in his 
communications to the Royal Society. B)' referring 
to Fig. 12 it will be seen that no such stations exist 
in 1874. 

2. The method of durations may be successfully 
applied, so far as mere geometrical position is con- 
cerned, in either of the two transits. This method is 
really combined of two parts, and includes Halley's 
as a particular case. The lessening of the duration 
of the transit depends partly upon the diminished 
motion" of one of the stations, or upon the fact that it 
moves in the opposite direction to the other ; and 
partly on the fact that in .one case the planet seems to 
trace a path on the sun further from his centre (and 
therefore shorter) than in the other. The difference 
in this last case is greatest when the path of Venus is 
far from the sun's centre. But in transits like the 
coming ones, where this is the case, the motion of 
Venus towards the sun's centre at the time of contact 
is very much slower than when she describes a large 
chord upon the sun. This has been well pointed out 
by Mr. Stone, 1 and from his paper we learn that the 
method of durations depending upon two such obser- 
vations at each of the two stations will not be so 
.satisfactory as we might otherwise have expected. 
But other very serious objections present themselves 
1 Monthly Notices of the R.A.S., vol. xxix. p. 250. 



vi.] THE TRANSIT OF VENUS. n 



to a method like this requiring four observations of 
contact, when we carefully consider the circumstances. 
In applying this method, one station must be chosen 
in high southern latitudes. Now diligent inquiries 
have been made upon this subject, and it appears very 
improbable that the weather at any suitable station 
will be such as to give much hope of observing both 
the ingress and egress in a satisfactory manner. 
Hence if we depended upon this method there would 
be a great probability of the expedition proving a 
failure. The method of De l'lsle requires the obser- 
vation of only one contact at each of the two stations. 
For these reasons hardly any expedition will use this 
method except as secondary to De l'lsle's, the photo- 
graphic, or the heliometric method. 

3. De l'lsle's method. The accuracy with which 
this method can be applied depends upon the certainty 
of longitude operations. From what was said in the 
last chapter, it will be seen that this is no easy matter; 
but it is absolutely necessary that the longitude should 
be accurately found if this method is to be employed. 
Sir George Airy says that longitudes can be deter- 
mined with an error of not more than one second by 
lunar observations ; and observers will receive orders 
to remain at their stations until they have a sufficient 
number of observations to accomplish this. The 
lunar observations will be supported, where practi- 
cable, by telegraphic determinations of longitude, and 
also by the transport of chronometers. The Russians, 
whose stations lie mainly along the whole length of 
Siberia, will employ a telegraphic line over that region, 
with branch lines to the subsidiary stations. The 



73 THE TRANSIT OF VENUS. [chap. 

English will probably fix the longitude of Alex- 
andria by submarine cable. They will employ chro- 
nometers to group together all neighbouring stations. 
The station at Rodriguez will be thus connected 
with Lord Lindsay's station at Mauritius, and with 
the Dutch station at Reunion. Lieut. Corbet, R.N., 
will connect by chronometers the various islands oc- 
cupied by the Germans, Americans, and French in 
the neighbourhood of the two English stations on 
Kerguelen's Island. The three English stations 
on the Sandwich Islands will likewise be connected' 
by chronometers ; and it would be very desirable 
to connect these islands with San Francisco on 
the one hand, and Yokohama on the other. The 
longitudes of both these places will have been com- 
pared with Greenwich by telegraph. It would be a 
matter of the utmost interest to complete the chain 
round the world by the transport of chronometers 
across the Pacific. M. Struve says that with the aid 
of an uncompensated chronometer this might be done 
with great accuracy. The Germans have also made 
valuable suggestions for comparing the longitudes of 
the observing stations of all nations ; and the French 
will also probably help in this matter. Thus it is 
likely that the longitudes of all the stations of diffe- 
rent countries suitable for the application of De l'lsle's 
method will be very accurately known. 

It will be noticed that the accuracy of De l'lsle's 
method depends upon two longitudes and two ob- 
servations of contact; while that of durations depends 
upon four observations of contact. Neglecting all 
considerations of climate the two methods are, so far 



vi.] THE TRANSIT OF VENUS. 



as the somewhat vague data at our command can tell 
us, very nearly equal. But the uncertain climate of 
southern seas renders the chance of many contact ob- 
servations doubtful and throws the balance in favour 
of De l'lsle's method. Add to this that before loner 
all the stations except the Kerguelen group will soon 
have their longitudes determined absolutely by tele- 
graph, and recollecting that the coming observations 
are to serve astronomers until the next transit of 
Venus in 2004, by which time even the Kerguelen 
group may perhaps be chronometncally determined : 
recollecting all this, there is little doubt that astro- 
nomers have been wise in settling upon De l'lsle's 
method for the main observations of contacts. 

It will be well, before going further, to mention the 
stations which have been chosen by different nations 
for the observation of the coming transit. 

I. The British, having selected for the reasons 
above mentioned the method of De l'lsle, originally 
fixed upon the following stations : — 

Alexandria, Sandwich Islands, Rodriguez, Ker- 
guelen's Island, and New Zealand. No alteration has 
been made in the choice of these stations. Supple- 
mentary ones have, however, been added. Thus at 
Kerguelen's Island there will be two expeditions : one 
at Christmas Harbour in the north, and the other in 
the south of the island. In the Sandwich Islands 
there will be three stations : one at Honolulu, a 
second on the island of Hawaii, and a third on the 
island of Kauai, sometimes called by English writers 
Atooi. The station at Alexandria will be supple- 
mented by a second one at Cairo, and a private one 



So THE TRANSIT OF VENUS. [chap 

by Col. Campbell of Blythswood, under the Astro- 
nomer Royal's direction at Thebes. The New 
Zealand station will be placed at Christchurch. Since 
the idea of photography has been introduced, an 
additional station has been added by the Indian 
Government under the superintendence of Col. 
Tennant, R.E. This is very completely equipped, 
and will probably be situated near Roorkee. 

Besides these the observatories at Madras, Cape of 
Good Hope, Melbourne, and Sydney will be utilised as 
far as possible. The New South Wales Government 
have voted 1,000/. for other observations in Australia. 
The English Government have voted 15,000/. for all 
the expeditions, but a much larger sum than this 
will be actually required. It will be understood that 
the principal method of observation is De l'lsle's, 
aided everywhere when possible by all the other 
methods except the heliometric. 

From the account that has been given of the diffi- 
culty of determining the longitudes of the different 
stations it will be seen that no little power of 
organisation is required for the execution of the fore- 
going programme. All preparations must be made 
for the observation of the moon and moon culminators. 
Altazimuths must be made, and also actually invented 
for the express purpose. More than seventy chro- 
nometers must be provided, and negotiations must be 
completed with telegraph companies. The photo- 
graphic operations have required the invention of a 
new photo-heliograph, and the Janssen method of a 
new application to it. The observations of contact 
have required the purchase of a large number of 



VI.] 



THE TRANSIT OF VENUS. 



equatorials ; for each station, besides having a 6-inch 
telescope, has also one or more smaller instruments. 
One of the larger ones, made by Simms, is shown in 




^mmm^smm 



", ■ ;•, \v-yw M' ,\ \ 
Fig. 20.— 6-Inch Equatorial of the British Expedition. 



Fig. 20. The transit instruments have also been made 
expressly for this expedition. Besides this all the 

G 



THE TRANSIT OF VENUS. [chap. 



accessories of these instruments had to be provided. 
Huts for receiving them had to be made. Forms for 
entering and reducing the observations had to be 
prepared and printed. For some of the stations 
sleeping arrangements, cooking apparatus, washing 
utensils, and provisions had to be provided. Work- 
men, masons, and assistant photographers, besides 
twenty-two observers, had to be collected and trained 
to the work. When this is considered it will be seen 
that no ordinary man could fulfil all the duties. 
Fortunately we have in our Astronomer Royal a man 
who combines to an exceptional degree theoretical, 
mechanical, and organising powers ; and we may 
safely say that the present expedition has been com- 
pleted under a generalship quite unparalleled in the 
annals of Science. Sir George Airy has accomplished 
all that was required in a manner that has called forth 
the applause of those who have been connected with 
the preparations for this, perhaps the most important 
astronomical event of the century. We must con- 
gratulate ourselves upon the fact that he has been 
most liberally supported on all points by the British 
Admiralty. If we cannot enter into the same details 
with regard to other nations, it is only because we 
have not had the opportunity of learning all their 
actions. But we cannot conclude this account of the 
British Government expedition without alluding to the 
valuable services which have been rendered to it by 
Capt. G. L. Tupman, R.M.A., who has spent the last 
three years in training himself and nearly all the other 
observers in the use of the instruments, seeing the 
instructions of the Astronomer Royal carried out, 



vi.] THE TRANSIT OF VENUS. 83 



ordering the stores, and in the most disinterested 
manner looking after the expedition ; so that (as the 
Astronomer Royal has lately pointed out) if the 
observations be successful their success will in a great 
measure be due to his exertions. 

II. Besides the expeditions under the direction of 
the British Government, another has been prepared 
which is perhaps the most completely equipped one 
which has ever been undertaken by a private individual 
in the interests of astronomy. Lord Lindsay has 
made preparations to take up his position at Mauritius, 
provided with means for utilising all the different 
modes of observation. He will combine his own 
results mainly with those of the Russians ; and it is 
probable that no station could have been found more 
suitable for a single observer to occupy when so many 
different methods are employed. All the instruments 
are of the most perfect description and made by the 
best makers. The photographic method which he will 
employ has been already described. The siderostat 
has been made expressly for this purpose, and its sur- 
face has been tested and found to be truly plane. 
Lord Lindsay and his assistant, Mr. Gill, lay consider- 
able stress on the employment of the heliometer, and 
have discussed its capabilities with great lucidity. 
They propose to make observations of the external 
contact by the aid of the spectroscopic method. The 
expedition will be provided with about 50 chrono- 
meters, including one uncompensated. These will be 
transmitted four times between Aden and Mauritius. 
It is probable that they will also connect the longitudes 
of the different stations on that group of islands by 

G 2 



84 THE TRANSIT OF VENUS. [chap 

chronometers. The German expedition at Mauritius 
will probably be connected with Lord Lindsay's by a 
trigonometrical survey. Of these islands two can be 
connected by direct signals with a heliotrope reflecting 
the sun's light. From experiments made in Russia, it 
appears that a signal may thus be seen in a mountain- 
ous country with a clear atmosphere at a distance of 
200 miles. There is little doubt then that the longi- 
tude of each station on this group of islands will be 
accurately known. 

III. The Germans are sending out five or six 
expeditions. At Cheefoo the accelerated ingress and 
retarded egress will be observed ; at Kerguelen Island 
the retarded ingress and the accelerated egress. The 
Auckland Islands will be favourable for accelerated 
egress ; Mauritius for retarded ingress, and Ispahan 
for retarded egress. 

They will probably employ all the four methods at 
most stations, viz. eye-observations of contact, helio- 
meters, photo-heliographs for the distance of centres, 
and also for position-angles. There will be no photo- 
graphy at Mauritius. Here will be employed four 
heliometers by Fraunhofer, 3 in. aperture, 35 ft. focus; 
four equatorially-mounted telescopes by Fraunhofer, 
44 in. aperture, 6 ft. focus ; two photo- heliographs by 
Steinheil, 5| in. aperture, and two with quadruple 
object-glasses of 4 in. aperture. Besides these, in- 
struments are required for determining the local time 
and the longitude ; for the Germans lay great stress 
on De lTsle's method. For this purpose transit instru- 
ments with diagonal telescopes on the Russian method 
of 2\ in. aperture will be supplied, and altazimuths 



vi.] THE TRANSIT OF VENUS. 85 



with divided circles 12 in. to 14 in. in diameter. The 
necessity of determining the longitudes accurately has 
led the German astronomers to consider carefully the 
best means by which this can be done. Dr. Auwers, 
to whom the direction of the arrangements has been 
intrusted, has discussed the matter in a very able 
manner. It appears from his inquiries that each group 
of stations will have their longitudes very accurately 
determined. Thus the stations in east Asia can be 
connected telegraphically. So also can those about 
Alexandria ; also those about the Caspian Sea and 
New Zealand. The group of islands near Kerguelen's, 
the Sandwich Islands group, and the Mauritius group 
will be determined by chronometers. The only diffi- 
culty is to connect these different groups. Many of 
them will be compared with Greenwich indirectly 
by telegraph. It is probable that Honolulu will be 
compared by chronometers with San Francisco and 
Yokohama, thus completing, as already mentioned, 
the telegraph and chronometer connection round the 
world. In any case there is little doubt that before 
the transit of Venus in 2004 the longitude of Hono- 
lulu will be determined by telegraph. Since Lord 
Lindsay intends to compare the longitude of Mauritius 
with that of Aden by four chronometer expeditions, 
aided by an uncompensated chronometer, there is 
little doubt that the longitude of that group of islands 
will be accurately known. The group of islands about 
Kerguelen's will depend very much upon the British 
observations of the moon ; but it will be well if 
chronometers can be employed to connect it with the 
Cape. The Germans rely very much upon the helio- 



85 THE TRANSIT OF VENUS. [chap. 

metric method. It will be a matter of great interest 
to learn how these observations agree with other 
methods as a guide to the arrangements for 1882. 
The expense of this expedition is about 1 30,000 thalers, 
besides the expenses connected with chronometric 
determinations. 

The organisation of the German expedition has 
been entrusted almost wholly to Dr. Auwers, as 
secretary of the commission. His contributions to 
the subject are of great value, and the zeal with which 
he has superintended the expeditions, even in the 
minutest details, cannot be overvalued. 

IV. The Russians are mainly employed in utilising 
the Siberian stations. The actual places which have 
been chosen from which to observe the transit are 
given in the following list, in order from east to west. 
The numeral 1 appended to a station means that 
there are good observers, practised with the model, 
good equatorials, and a heliometer or photo-helio- 
graph. The numeral 2 signifies the same without 
heliometers or photo-heliographs. When the numeral 
3 is appended, the observer has not practised with the 
model, and employs a small telescope. The stations 
are : 

Yeddo 2 Blagowvschtchenska 2 

Port St. Alga 3 Nertschinsk I 

Nakhodka 2 Xhita 1 

Wladivostock I Kiachta I 

Port Possiet 1 Tomsk 3 

Lake Hanka 1 Tachkent I 

Chabarovka 2 Port Peroffski 1 

Peking 2 Fort Uralsk 1 



VI.] THE TRANSIT OF VENUS. 5/ 



Orenburg 3 Tiflis 3 

Aschura-deh I Taganrok 3 

Teheran 2 Kertch 2 

Nachitzevan 2 Ialta 2 

Erivan 1 Thebes 2 

Besides these stations the following will be utilised, 
but the sun will be very low : Kazan, where the sun's 
altitude will be 8° or io° ; Nicolaif, where it will be 
6°; and Charkof and Odessa 5 ; at Moscow it will 
be exactly on the horizon. 

As to instruments, the Russians are employing 6- 
inch and 4-inch equatorials. Their heliometers are 
larger than those of the Germans, having 4 in. aper- 
tures. Their photo-heliographs are constructed on the 
English model by Mr. Dallmeyer. The telegraphic 
connections between the stations have been already 
discussed. The expense incurred will be defrayed by 
the Government. Besides this, the State contributes 
45,000 roubles. This will be spent mainly on the 
transport and maintenance of observers and instru- 
ments. The different observatories in Russia have 
shared the expense of providing the different instru- 
ments. The whole expedition has been conducted 
under the superintendence of M. Otto Struve. Some 
of the expeditions have already started provided with 
every means for resisting the cold of a Siberian winter. 
Great attention has been paid to the chances of good 
weather. The accelerated ingress and retarded egress 
will thus be admirably observed ; and the comparison 
which M. Struve has made with observers of other 
countries in practising with the model will make it 



88 . THE TRANSIT OF VENUS. [chap. 

possible to reduce the results to the same standard. 
Moreover, many of the Russian stations are admirably 
situated for the employment of the method of dura- 
tions ; and if the two internal contacts be observed 
at any of the stations in the neighbourhood of 
Kerguelen's Island, excellent results may be ob- 
tained. 



VII.] THE TRANSIT OE VENUS. 89 



CHAPTER VII. 

In our last chapter the preparations of Britain, 
Germany, and Russia were enumerated ; those of the 
French, Americans, Dutch, and Italians must now be 
spoken of. 

V. The French will occupy the following stations : 
— Yokohama, Peking, New Amsterdam or St. Paul's, 
and Campbell Island ; all equipped as first-class 
stations, besides Tientsin, Sagou, Numea, and pro- 
bably Nukahiva in the Marquesas, as secondary 
stations. Yokohama and St. Paul's will make an 
excellent combination for the method of durations ; 
at Campbell Island also the durations will be con- 
siderably lessened. But the longitude of these places 
will be determined, so that if only one contact be 
observed, De 1' Isle's method will be applied. MM. 
Wolf and Andre have made a series of experiments 
on the formation of the "black drop;" numerous 
trials have also been made with a view of em- 
ploying the photographic method as successfully as 



go THE TRANSIT OF VENUS. [CHAP, 



possible, and it is possible that spectroscopic obser- 
vations of external contact will be made. The pre- 
parations are by no means so far advanced as 
might have been wished. This is partly due to the 
disturbed state in which the country has been since 
the late war. 

We are glad to be able to state that the French 
will employ the daguerreotype process of photo- 
graphy. This method has many advantages, and it 
is much to be regretted that no experiments have 
been made by other nations to test its applicability. 
Photographs taken by this process are well known to 
be much more delicate and give clearer details than 
any others, while photographic irradiation is reduced 
to a minimum. It is even possible to correct for 
curvature of field by employing prepared plates whose 
surfaces are portions of spheres, a thing which would 
be impossible by any other process. There can be 
no shrinking of the film. The only objection is, that 
we cannot print copies from the plates conveniently. 
But it is not likely that we should trust to measure- 
ments of a printed copy even from a glass negative. 
The French are relying mainly upon the photographic 
method, and have chosen their stations for determining 
thus directly the least distance between the centre of 
the sun and Venus. With the apparatus proposed by 
MM. Wolf and Martin, the size of the sun's image 
will be 60 millimetres ; they hope to determine the 
instants of internal contacts with a probable error of 
one second of time. The commission into whose 
hands the business has been intrusted has drawn up 
a detailed report containing contributions not only 



VH.l THE TRANSIT OF VENUS. 91 

from the astronomers of France, but also from the 
most celebrated physicists and experimentalists : 
300,000 fr. has been voted for the enterprise. M. 
Tisserand of the Toulouse Observatory will aid in 
the actual observations ; and M. Janssen will proceed 
to Yokohama. 

M. Dumas takes the lead in the preparations. In a 
letter dated May 12, he says that the expeditions are 
on the point of starting, and that the Marquesas 
probably, and Numea certainly, will be occupied for 
De 1' Isle's method. 

VI. The Americans have a grant of 150,000 dols. 
They have paid great attention to the application of 
photography with the assistance of Mr, Rutherford, 
whose success in photographing the moon is so well 
known. They employ a lens of 40 ft. focus, as al- 
ready described. They will measure both angles of 
position and distances from the centre, and the pro- 
bable error of any measurement will be less than 
T^o" P er cen t- They have encountered some trouble 
in the manufacture of their siderostats. Besides 
photography eye-observations of contact will also be 
made. A very able report has been drawn up from 
the computations of Mr. Hill, who deserves great 
credit for the manner in which he has completed it. 
This report has reference to the choice of stations ; 
and is accompanied by very valuable charts. Other 
reports have been made upon the application of 
photography. 

The expeditions are to be composed of five per- 
sons each. The stations of observation and the heads 
of parties are as follows : — Wladivostock, Siberia, 



THE TRANSIT OF VENUS. [chap. 



Prof. A. Hall, U.S.N. ; Nagasaki, Japan, Mr. G. David- 
son, U S. Coast Survey ; Peking, China, Prof. James 
C. Watson ; Crozet's Island, South Indian Ocean, 
Capt. Raymond, U.S.A. ; Kerguelen's Island, South 
Indian Ocean, Lieut-Commander George P. Ryan, 
U.S.N. ; Hobart Town, Tasmania, Prof. W. N. Hark- 
ness, U.S.N. ; New Zealand, Prof. C. H. Peters ; 
and Chatham Island, South Pacific, Mr. Edwin 
Smith, U.S. Coast Survey. 

The whole organisation has been intrusted to a 
commission, the secretary of which is Prof. Newcomb, 
who has done so much valuable work for astronomy, 
and who has taken great pains to insure success for 
the expedition. 

VII. The Italians have arranged to send out three 
expeditions furnished with spectroscopes for the ob- 
servation of external contact. Little is known about 
these expeditions. 

VIII. The Dutch are sending one expedition to 
the island of Bourbon or Reunion. It will be 
furnished with a photo-heliograph, which Dr. Kaiser 
will manipulate ; Dr. Oudemans will also make 
observations with a heliometer. 

Having now completed our description of the 
details, and having also given an account, so far as 
possible, of the preparations of the various nations 
for the observations, we shall cast a general view over 
the whole subject, and recapitulate some of the 
principal points. 

The coming transit of Venus will be observed from 
about 75 stations, at many of which there will be 
a large number of instruments. The expense of the 



vii.] THE TRANSIT OF VENUS. 93 



whole of the expeditions will amount to between 
150,000/. and 200,000/. It may seem to some that 
the results to be arrived at are not worth so great an 
outlay, but the general voice of the non-scientific as 
Avell as of the scientific world has contradicted this. 
Wherever knowledge can be gained it is worth being 
gained ; and when individuals are unable to bear the 
cost, it is fitting that the expenses should be incurred 
by those governments that are really the gainers 
from many scientific researches for which the in- 
vestigator himself frequently receives no reward. 
But apart from this, these expeditions will lead to 
most valuable results. The sun's distance being 
known, the Lunar Theory may be vastly improved, 
and it will be possible to determine longitudes with 
much greater accuracy than at present. Still more 
will the tables of Venus be capable of readjustment. 
Even now we can calculate her place with great 
accuracy, and this is fortunate, since it enables us to 
predict the exact time at which Venus will first come 
in contact with the sun, viz. 1874, Dec. 8d. 14.I1. 4m. 
The error to which this is liable, owing to the tables, 
is not likely to exceed five minutes. Mr. W. H. M. 
Christie, Chief Assistant of the Royal Observatory, 
has determined the probable error in the calculated 
time of contact arising from this cause. 1 He has 
employed observations of Venus taken at this node 
at the following dates: — 1872, June 28; 1873, Jan. 
18; 1873, Sept. 14; and 1874, April 25; he has 
thence deduced the error in the tabular position of 
Venus, and from this the error in the time of contact 

1 Monthly Notices of the R. A. S., xxxiv. 300. 



94 THE TRANSIT OF VENUS. [chap. 

in the coming transit. It appears from each of these 
four comparisons that the tables of Venus give us the 
time of contact too early ; according as we adopt 
the first, second, third, or fourth of the above 
observations, the error will be 7'4m., S'3 n) -> 4 '2m., 
or 8im. 

Besides the astronomical advantages to be gained 
from the coming transit, there are several collateral 
issues of no small importance. In the first place, the 
longitudes of a host of stations all over the globe 
will be accurately determined, and it is a remark 
by no means unworthy of notice that the simple 
observation of the local time of contact will give the 
inhabitants of east Africa and of all Asia an accu- 
rate means of determining their absolute longitudes. 
If, moreover, as has been proposed, San Fran- 
cisco and Japan are to be compared directly as to 
longitude, the whole circuit of the globe will be 
completed by telegraphic and accurate chronometric 
determinations. 

Again, with the host of vessels by which scientific 
men will proceed to their stations, meteorological, and 
sometimes even magnetical, instruments will be pro- 
vided. These vessels will be traversing the different 
oceans of the globe about the same time, and thus 
the meteorology of the world will be much better 
understood. Many observers will be enabled to take 
note of interesting phenomena, such as hurricanes, 
volcanoes, and earthquakes. In addition, naturalists 
will be appointed to accompany some of the expedi- 
tions; birds and marine animals will be probably very 
generally collected ; the Royal Society has given 



vil] THE TRANSIT OF VENUS. 



95 



funds to aid in this matter. The Rev. A. E. Eaton, 
who has made valuable collections at Spitzbergen, will 
examine the marine life of Kerguelen's Island. 
Rodriguez is particularly interesting from a naturalist's 
point of view ; it is one of the few islands in mid- 
ocean which have not been raised by volcanic agency. 
The remains of some extinct birds have been found 
there. The Royal Society has appointed a geologist, 
a botanist, and a naturalist to go to this island. There 
is little doubt that Science in general will gain greatly 
by these expeditions. 

As to the main observation we can have no doubt, 
from the large number of expeditions, and from the 
multiplicity of methods to be employed, that we shall 
obtain excellent results, although the actual reduction 
of the observations will be exceedingly laborious. 
Each nation, while it generally adopts some special 
method for its choice of stations, will also utilise 
other methods. We have seen that the English, 
while they rely chiefly on De ITsle's method, will 
employ all the others except the heliometric, while the 
Germans depend mainly upon the heliometric method. 
The French and Americans have chosen their stations 
with reference to photography. The Russians are 
to compare observations of all kinds with different 
nations. These countries have all co-operated in the 
most harmonious manner, partly by correspondence, 
and partly by the personal visits of astronomers to 
different nations. 

Although the observations are to be made at the 
end of the present year, the actual reduction of the 
observations will take so long that we cannot hope 



96 THE TRANSIT OF VENUS. [chap 

for the complete and final results as to our distance 
from the sun before the year 1876. At each of the 
British stations the observers will remain at least 
three months to determine their longitudes. 

Here we may leave the subject. The preparations 
are for the most part completed ; many of the obser- 
vers of different nations are on their way to their 
various posts. It says a great deal for the civilisation 
of the world that on December 8 of the present year 
those quarters of the globe will be thickly studded 
with emissaries from so many nations to observe an 
important astronomical phenomenon. 

It will be well to conclude this account with 
a statement of the arrangements which have been 
made as to observers on the British expeditions. 
It is extracted from instructions published under 
authority : — 

Appointments of Observers to the several Districts 
of Observation, and Subordination of Observers. 

1. Capt. G. L. Tupmari, R.M.A., is head of the 
entire enterprise, and is responsible through the 
Astronomer Royal to the Government for every 
part. Every observer is responsible to Capt. 
Tupman. 

2. When the different expeditions are separated, 
the observers in each district of observation are re- 
sponsible to the local chief of the district, and the 
chief to the Astronomer Royal. The districts of 
observation and the observers will be the following, 
the name first following that of the local chief being 



THE TRANSIT OF VENUS. 



97 




Tic. 2i.— rhoto-heliograph of the British Expeditions. 



H 



93 THE TRANSIT OF VENUS. [chap. 

that of the deputy, who will, if necessary, take his 
place : — 

3. District A. Egypt : Chief, Capt. C. O. Browne, 
R.A., astronomer ; Observers, Capt. W. de W. Ab- 
ney, R.E., astronomer and photographer; S. Hunter, 
astronomer. 

4. District B. Sandwich Islands : General Chief, 
Capt. G. L. Tupman, R.M.A. : Deputy, if necessary, 
Prof. G. Forbes. 

Sub-divisions of the Sandwich Islands : — Honolulu: 
Chief, Capt. G. L. Tupman, astronomer ; Observers, 
J. W. Nichol, astronomer and photographer; Lieut. 
F. E. Ramsden, R.N., astronomer and photographer. 
Flawaii : Chief, Prof. G. Forbes, astronomer ; Obser- 
ver, H. G. Barnacle, astronomer. Kauai : Chief, R. 
Johnson, astronomer; Observer, Lieut. E. J. W. 
Noble, R.M.A., astronomer. 

5. District C. Rodriguez : Chief, Lieut. C. B. Neate, 
R.N., astronomer ; Observers, C. E. Burton, astro- 
nomer and photographer ; Lieut. R. Hoggan, R.N., 
astronomer and photographer. 

6. District D. Christchurch (New Zealand) : Chief, 
Major H. Palmer, R.E. ; Observers, Lieut. L. Darwin, 
R.E., astronomer and photographer ; Lieut. H. Craw- 
ford, R.N., astronomer. 

7. District E. Kerguelen Island : General Chief, 
Rev. S. J. Perry ; Deputy, if necessary, Lieut. C. 
Corbet, R.N. 

Sub-divisions of the Kerguelen Island : — Christmas 
Harbour : Chief, Rev. S. J. Perry, astronomer and 
photographer ; Observers, Rev. W. Sidgreaves, astro- 
nomer ; Lieut. S. Goodridge, R.N., astronomer ; J. B. 



VII.] THE TRANSIT OF VENUS. 99 

Smith, astronomer and photographer. Port Palliser : 
Chief, Lieut. C. Corbet, R.N. ; Observer, Lieut. G. E. 
Coke, R.N. 

8. In addition to these gentlemen, three non-com- 
missioned officers or privates of the corps of Royal 
Engineers will be attached to each of the five districts, 
and will be under the direction of the chief of each 
district. 



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