' : -.;
' -*■ rf'>
■ ■ '
THE TRANSIT OF VENUS.
Photo-heliograph of the British Expeditions.
TRANSIT OF VENUS.
GEORGE FORBES, B.A.,
PROFESSOR OF NATURAL PHILOSOPHY IN THE ANDERSON1A.V UNIVERSITY,
WITH NUMEROUS ILLUSTRATIONS.
Xonuosi anir Hcb ifork :
M ACM I L LAN AND CO.
\_The Right of Translation and Reproduction is resavcd.]
R CLAY, SONS, AND T.4VLOR, PRINTERS,
BREAD STREET HILL.
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.
CHAPTER VI. . . .
. . . 89
LIST OF ILLUSTRATIONS.
I . 2
2 ... 4
5 • ... 7
7 • «3
9 . . , 18
13 • ■ • 38
15 • 49
17. — Lord Lindsay's Photographic arrangements as set up at
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
TRANSIT OF VENUS.
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
THE TRANSIT OF VENUS.
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
THE EAR T H
C G o o D
V V V-
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
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.
It will be noticed that the transits occur in pairs
THE TRANSIT OE VENUS.
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
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
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
fiPPA REN T ORBIT
OP THE SUN
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
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
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
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
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.
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
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
THE TRANSIT OF VEAL'S.
(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
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
THE TRANSIT OF VENUS.
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
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-
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
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,
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
THE TRANSIT OF VENUS.
contact. We will try, however, to put it in a light
which anyone, with a little attention, will under-
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
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
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
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
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
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
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.
THE TRANSIT OF VENUS.
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
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
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
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
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
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
THE TRANSIT OF VENUS.
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
THE TRANSIT OF VENUS.
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.
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
THE TRANSIT OE VENUS.
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
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
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
(I) By determining the least distance between
the centres of the sun and Venus during
the transit, observed from different
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.
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
1 Berlin Abhandlun^en, 1S35, pp. 295 — 310.
THE TRANSIT OF VENUS.
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.
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 \
Dist. of sun in mi'es.
8 -"9 1
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.
THE TRANSIT OF VENUS.
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
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
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
THE TRANSIT OF VENUS.
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
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.
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
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
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.
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
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-
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
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
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
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
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
THE TRANSIT OF VENUS.
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
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
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
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
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-
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-
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
(7) By aid of an altazimuth.
vi.l THE TRANSIT OF VENUS.
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
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
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
", ■ ;•, \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
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
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
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
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
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-
VII.] THE TRANSIT OE VENUS. 89
In our last chapter the preparations of Britain,
Germany, and Russia were enumerated ; those of the
French, Americans, Dutch, and Italians must now be
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
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
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
VII. The Italians have arranged to send out three
expeditions furnished with spectroscopes for the ob-
servation of external contact. Little is known about
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
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.,
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
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.
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
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.
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.
Tic. 2i.— rhoto-heliograph of the British Expeditions.
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,
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.
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.
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
LONDON : R. CLAY, SONS, AND TAYLOR, l'.UNTERS.
UXDER THE JOINT EDITORSHIP OF
PROFESSORS HUXLEY, ROSCOE, AND
"They are wonderfully clear and lucid in their instruction,
simple in style, and admirable in plan." — Educational Times.
The following are now Ready : —
CHEMISTRY. By H. E. Roscoe, F.R.S., Professor
of Chemistry in Owens College, Manchester. Third
Edition. iSmo. cloth.. Illustrated, is.
PHYSICS. By Balfour Stewart, F.R.S., Professor
of Natural Philosophy in Owens College, Manche^er.
Second Edition. iSmo. cloth. Illustrated, is.
PHYSICAL GEOGRAPHY. By A. Geikie, F.RS.,
Murchison Professor of Geology and Mineralogy at Edin-
burgh. Second Edition. i8mo. cloth. Illustrated, is.
GEOLOGY. By Professor Geikie, F.R.S. With
numerous Illustrations. iSmo. cloth, is.
PHYSIOLOGY. By Michael Foster, M.D., F.R.S.
Illustrated. i8mo. cloth, is.
In Preparation : —
INTRODUCTORY. By Professor Huxley, F.R.S.
BOTANY. By J. D. Hooker, C.B., F.R.S., Presi-
dent of the Royal Society.
ASTRONOMY. By J. Norman Lockyer, F.R.S.
MACMILLAN AND CO., LONDON.
ANATOMY. — ELEMENTARY LESSONS IN
ANATOMY. By St. George Mivart, F.R.S. With numerous
Illustrations. i8mo. 6s. 6d.
ASTRONOMY.— POPULAR ASTRONOMY. With
Illustrations. By Sir G. B. Airy, Astronomer-Royal. New Edition.
i8mo. 4-r. 6d.
ASTRONOMY— ELEMENTARY LESSONS IN
ASTRONOMY. With Illustrations. By J. Nokman-Lockver, F.R.S.
With Coloured Diagram of the Spectra of the Sun, Stars, and Nebula;.
New Edition. i8mo. 5s. 6d. — Questions on the Same, is. 6d.
BOTANY. — LESSONS IN ELEMENTARY
BOTANY. With Illustrations. By Professor Oliver, F.R.S., F.L.S.
New Edition. i8mo. 4?. td.
CHEMISTRY.— LESSONS IN ELEMENTARY
CHEMISTRY. By Professor Roscoe, F.R.S. With numerous Illus-
trations and Chromo-lithographs of the Solar Spectra. New Ediiion.
i8mo. 4-r. 6d.
CHEMISTRY.— OWENS COLLEGE TUNIOR
COURSE OF PRACTICAL CHEMISTRY. By F. Jones. With
Pieface by Professor Roscoe. New Edition. i8mo. 2s. 6d.
LOGIC— ELEMENTARY LESSONS IN LOGIC,
Deductive and Inductive. By Professor Jevons, F.R.S. With Copious
Questions and Examples, and a Vocabulary of Logical Terms. New
Edition. i8mo. 3s. td.
PHYSIOLOGY.— LESSONS IN ELEMENTARY
PHYSIOLOGY. With numerous Illustrations. By Professor Huxley,
F.R.S. New Edition. i8mo. 4s. 6d. — Questions on the Same, is. 6d.
POLITICAL ECONOMY FOR BEGINNERS. By
Mii.licent Garrett Fawcett. With Questions. New Edition.
1 8 mo. 2 s. 6d.
PHYSICS. — LESSONS IN ELEMENTARY
PHYSICS. By Balfour Stewart, F.R.S., Professor of Natural
Philosophy in Owens College, Manchester. With Coloured Diagram
and numerous Illustrations. New Edition. iSmo. 4s. 6d.
STEAM.— AN ELEMENTARY TREATISE ON
STEAM. By J. Perry, B.E., Whitworth Scholar, late Lecturer in
Physics at Clifton College. With Illustrations, Numerical Examples,
and Exercises. i8mo. 4^. 6d.
Others to follcnv.
MACMILLAN AND CO., LONDON.