_TRANSITS OF VENUS._
As a transit of Venus, visible in this country, occurs in December,
1882, my readers, although they may not care for an account of the
mathematical relations involved in the observation and calculation of a
transit, will probably be interested by a simple explanation of the
reasons why transits of Venus are so important in astronomy.
Of course it is known that a transit of Venus is the apparent passage of
the planet across the face of the sun, when, in passing between the
earth and sun, as she does about eight times in thirteen years, she
chances to come so close to the imaginary line joining the centres of
those bodies that, as seen from the earth, she appears to be upon the
face of the sun. We may compare her to a dove circling round a dovecot,
and coming once in each circuit between an observer and her house. If
in her circuit she flew now higher, now lower, or, in other words, if
the plane of her path were somewhat aslant, she would appear to pass
sometimes above the cot, and sometimes below it, but from time to time
she would seem to fly right across it. So Venus, in circuiting round the
sun, appears sometimes, when she comes between us and the sun, to pass
above his face, and sometimes to pass below it; but occasionally passes
right across it. In such a case she is said to transit the sun's disc,
and the phenomenon is called a transit of Venus. She has a companion in
these circuiting motions, the planet Mercury, though this planet travels
much nearer to the sun. It is as though, while a dove were flying around
a dovecot at a distance of several yards, a sparrow were circling round
the cot at a little more than half the distance, flying a good deal more
quickly. It will be understood that Mercury also crosses the face of the
sun from time to time--in fact, a great deal oftener than Venus; but,
for a reason presently to be explained, the transits of Mercury are of
no great importance in astronomy. One occurred in 1861, another in 1868;
another in May, 1878; yet very little attention was paid to those
events; and before the next transit of Venus, in 1882, there will be a
transit of Mercury, in November, 1881; yet no arrangements have been
made for observing Mercury in transit on these occasions; whereas
astronomers began to lay their plans for observing the transit of Venus
in 1882, as far back as 1857.
The illustration which I have already used will serve excellently to
show the general principles on which the value of a transit of Venus
depends; and as, for some inscrutable reasons, any statement in which
Venus, the sun, and the earth are introduced, seems by many to be
regarded as, of its very nature, too perplexing for anyone but the
astronomer even to attempt to understand, my talk in the next few
paragraphs shall be about a dove, a dovecot, and a window, whereby,
perhaps, some may be tempted to master the essential points of the
astronomical question who would be driven out of hearing if I spoke
about planets and orbits, ascending nodes and descending nodes, ingress
and egress, and contacts internal and external.
Suppose D, fig. 42, to be a dove flying between the window A B and the
dovecot C _c_, and let us suppose that a person looking at the dove just
over the bar A sees her apparently cross the cot at the level _a_, at
the foot of one row of openings, while another person looking at the
dove just over the bar B sees her cross the cot apparently at the level
_b_, at the foot of the row of openings next above the row _a_. Now
suppose that the observer does not know the distance or size of the cot,
but that he does know in some way that the dove flies _just_ midway
between the window and the cot; then it is perfectly clear that the
distance _a b_ between the two rows of openings is exactly the same as
the distance A B between the two window-bars; so that our observers need
only measure A B with a foot-rule to know the scale on which the dovecot
is made. If A B is one foot, for instance, then _a b_ is also one foot;
and if the dovecot has three equal divisions, as shown at the side, then
C _c_ is exactly one yard in height.
[Illustration: Fig. 42.]
Thus we have here a case where two observers, without leaving their
window, can tell the size of a distant object.
And it is quite clear that wherever the dove may pass between the window
and the house, the observers will be equally able to determine the size
of the cot, if only they know the relative distances of the dove and
dovecot.
[Illustration: Fig. 43.]
[Illustration: Fig. 44.]
[Illustration: Fig. 45.]
Thus, if D _a_ is twice as great as D A, as in fig. 43, then _a b_ is
twice as great as A B, the length which the observers know; and if D _a_
is only equal to half D A, as in fig. 44, then _a b_ is only equal to
half the known length A B. In every possible case the length of _a b_ is
known. Take one other case in which the proportion is not quite so
simple:--Suppose that D _a_ is greater than D A in the proportion of 18
to 7, as in fig. 45; then _b a_ is greater than A B in the same
proportion; so that, for instance, if A B is a length of 7 inches, _b a_
is a length of 18 inches.
We see from these simple cases how the actual size of a distant object
can be learned by two observers who do not leave their room, so long
only as they know the relative distances of that object and of another
which comes: between it and them. We need not specially concern
ourselves by inquiring _how_ they could determine this last point: it is
enough that it might become known to them in many ways. To mention only
one. Suppose the sun was shining so as to throw the shadow of the dove
on a uniformly paved court between the house and the dovecot, then it is
easy to conceive how the position of the shadow on the uniform paving
would enable the observers to determine (by counting rows) the relative
distances of dove and dovecot.
Now, Venus comes between the earth and sun precisely as the dove in fig.
45 comes between the window A B and the dovecot _b a_. The relative
distances are known exactly, and have been known for hundreds of years.
They were first learned by direct observation; Venus going round and
round the sun, within the path of the earth, is seen now on one side
(the eastern side) of the sun as an evening star, and now on the other
side (the western side) as a morning star, and when she seems farthest
away from the sun in direction E V (fig. 46) in one case, or E _v_ in
the other case, we know that the line E V or E _v_, as the case may be,
must just touch her path; and perceiving how far her place in the
heavens is from the sun's place at those times, we know, in fact, the
size of either angle S E V or S E _v_, and, therefore, the shape of
either triangle S E V or S E _v_. But this amounts to saying that we
know what proportion S E bears to S V--that is, what proportion the
distance of the earth bears to the distance of Venus.[17]
[Illustration: Fig. 46.]
This proportion has been found to be very nearly that of 100 to 72; so
that when Venus is on a line between the earth and sun, her distances
from these two bodies are as 28 to 72, or as 7 to 18.
[Illustration: Fig. 47.]
These distances are proportioned precisely then as D A to D _a_ in fig.
45; and the very same reasoning which was true in the case of dove and
dovecot is true when for the dove and dovecot we substitute Venus and
the sun respectively, while for the two observers looking out from a
window we substitute two observers stationed at two different parts of
the earth. It makes no difference in the essential principles of the
problem that in one case we have to deal with inches, and in the other
with thousands of miles; just as in speaking of fig. 45 we reasoned that
if A B, the distance between the eye-level of the two observers, is 7
inches, then _b a_ is 18 inches, so we say that if two stations, A and
B, fig. 47, on the earth E, are 7000 miles apart (measuring the distance
in a straight line), and an observer at A sees Venus' centre on the
sun's disc at _a_, while an observer at B sees her centre on the sun's
disc at _b_, then _b a_ (measured in a straight line, and regarded as
part of the upright diameter of the sun) is equal to 18,000 miles. So
that if two observers, so placed, could observe Venus at the same
instant, and note exactly where her centre seemed to fall, then since
they would thus have learned what proportion _b a_ is of the whole
diameter S S' of the sun, they would know how many miles there are in
that diameter. Suppose, for instance, they found, on comparing notes,
that _b a_ is about the 47th part of the whole diameter, they would know
that the diameter of the sun is about 47 times 18,000 miles, or about
846,000 miles.
Now, finding the real size of an object like the sun, whose apparent
size we can so easily measure, is the same thing as finding his
distance. Any one can tell how many times its own diameter the sun is
removed from us. Take a circular disc an inch in diameter,--a halfpenny,
for instance--and see how far away it must be placed to exactly hide the
sun. The distance will be found to be rather more than 107 inches, so
that the sun, like the halfpenny which hides his face, must be rather
more than 107 times his own diameter from us. But 107 times 846,000
miles amounts to 90,522,000 miles. This, therefore, if the imagined
observations were correctly made, would be the sun's distance.
I shall next show how Halley and Delisle contrived two simple plans to
avoid the manifest difficulty of carrying out in a direct manner the
simultaneous observations just described, from stations thousands of
miles apart.
We have seen that the determination of the sun's distance by observing
Venus on the sun's face would be a matter of perfect simplicity if we
could be quite sure that two observations were correctly made, and at
exactly the same moment, by astronomers stationed one far to the north,
the other far to the south.
[Illustration: Fig. 48.]
The former would see Venus as at A, fig. 48, the other would see her as
at B; and the distance between the two lines _a a´_ and _b b´_ along
which her centre is travelling, as watched by these two observers, is
known quite certainly to be 18,000 miles, if the observers' stations
are 7,000 miles apart in a north-and-south direction (measured in a
straight line). Thence the diameter S S´ of the sun is determined,
because it is observed that the known distance _a b_ is such and such a
part of it. And the real diameter in miles being known, the distance
must be 107 times as great, because the sun looks as large as any globe
would look which is removed to a distance exceeding its own diameter
(great or small) 107 times.
But unfortunately it is no easy matter to get the distance _a b_, fig.
48, determined in this simple manner. The distance 18,000 miles is
known; but the difficulty is to determine what proportion the distance
bears to the diameter of the sun S S´. All that we have heard about
Halley's method and Delisle's method relates only to the contrivances
devised by astronomers to get over this difficulty. It is manifest that
the difficulty is very great.
[Illustration: Fig. 49.]
For, first, the observers would be several thousand miles apart. How
then are they to ensure that their observations shall be made
simultaneously? Again, the distance _a b_ is really a very minute
quantity, and a very slight mistake in observation would cause a very
great mistake in the measurement of the sun's distance. Accordingly,
Halley devised a plan by which one observer in the north (or as at A,
fig. 47) would watch Venus as she traversed the sun's face along a
lower path, as _a a´_ fig. 49; while another in the south (or as at B,
fig. 47) would watch her as she traversed a higher path, as _b b´_ fig.
49. By timing her they could tell how long these paths were, and
therefore how placed on the sun's face, as in fig. 49; that is, how far
apart, which is the same thing as determining _b a_, fig. 48. This was
Halley's plan, and as it requires that the duration of the transit
should be timed, it is called the method of durations. Delisle proposed
another method--viz., that one observer should time the exact moment
when Venus, seen from one station, _began_ to traverse the path _a a´_,
while another should time the exact moment when she _began_ to traverse
the path _b b´_; this would show how much _b_ is in advance of _a_, and
thence the position of the two paths can be determined. _Or_ two
observers might note the _end_ of the transit, thus finding how much
_a´_ is in advance of _b´_ This is Delisle's method, and it has this
advantage over Halley's--that an observer is only required to see
_either_ the beginning or the end of the transit, not _both_.
I shall not here consider, except in a general way, the various
astronomical conditions which affect the application of these two
methods. Of course, all the time that a transit lasts, the earth is
turning on her axis; and as a transit may last as long as eight hours,
and generally lasts from four to six hours, it is clear that the face of
the earth turned towards the sun must change considerably between the
beginning and end of a transit. So that Halley's method, which requires
that the whole duration of a transit should be seen, is hampered with
the difficulty arising from the fact that a station exceedingly well
placed for observing the beginning of the transit might be very ill
placed for observing the end, and _vice versâ_.
Delisle's method is free from this objection, because an observer has
only to note the beginning _or_ the end, not both. But it is hampered by
another. Two observers who employ Halley's method have each of them only
to consider how long the passage of Venus over the sun's face _lasts_;
and they are so free from all occasion to know the exact time _at_ which
the transit begins and ends, that theoretically each observer might use
such an instrument as a stop-watch, setting it going (right or wrong as
to the time it showed) when the transit began, and stopping it when the
transit was over. But for Delisle's method this rough-and-ready method
would not serve. The two observers have to compare the two moments at
which they severally saw the transit begin,--and to do this, being many
thousand miles apart, they must know the exact time. Suppose they each
had a chronometer which had originally been set to Greenwich time, and
which, being excellently constructed and carefully watched, might be
trusted to show exact Greenwich time, even though several months had
elapsed since it was set. Then all the requirements of the method would
be quite as well satisfied as those of the other method would be if the
stop-watches just spoken of went at a perfectly true rate during the
hours that the transit lasted. But it is one thing to construct a
time-measure which will not lose or gain a few seconds in a few hours,
and quite another to construct one which will not lose or gain a few
seconds in a journey of many thousand miles, followed perhaps by two or
three months' stay at the selected station. An error of five seconds
would be perfectly fatal in applying Delisle's method, and no
chronometer could be trusted under the conditions described to show true
time within ten or twelve seconds. Hence astronomers had to provide for
other methods of getting true time (say Greenwich time) than the use of
chronometers; and on the accuracy of these astronomical methods of
getting true time depended the successful use of Delisle's method.
[Illustration: Fig. 50.]
[Illustration: Fig. 51.]
Then another difficulty had to be considered, which affected both
methods. It was agreed by both Halley and Delisle that the proper moment
to time the beginning or end of transit was the instant when Venus was
just within the sun's disc, as in fig. 50, either having just completed
her entry, or being just about to begin to pass off the sun's face. If
at this moment Venus presented a neatly defined round disc, exactly
touching the edge of the sun, also neatly defined, this plan would be
perfect. At the very instant when the contact ceased at the entry of
Venus, the sun's light would break through between the edges of the two
discs, and the observer would only have to note that instant; while,
when Venus was leaving the sun, he would only have to notice the instant
when the fine thread of light was suddenly divided by a dark point. But
unfortunately Venus does not behave in this way, at least not always.
With a very powerful and very excellent telescope, in perfectly calm,
clear weather, and with the sun high above the horizon, she probably
behaves much as Halley and Delisle expected. But under less favourable
conditions, she presents at the moment of entry or exit some such
appearance as is shown in figures 51, 52, and 53, while with a very low
sun she assumes all sorts of shapes, continually changing, being for one
moment, perhaps, as in one or other of figs. 51, 52, and 53, and in the
next distorted into some such pleasing shape as is pictured in fig. 54.
[Illustration: Fig. 52.]
[Illustration: Fig. 53.]
Accordingly, many astronomers are disposed to regard both Halley's
method and Delisle's as obsolete, and to place reliance on the simple
method of direct observation first described. They would, however, of
course bring to their aid all the ingenious devices of modern
astronomical observation in order to overcome the difficulties inherent
in that method. One of the contrivances naturally suggested to meet
such difficulties is to photograph the sun with Venus upon his face. The
American astronomers, in particular, consider that the photographic
results obtained during the transit of 1874 will outweigh those obtained
by all the other methods. The German and Russian astronomers, as well as
those of Lord Lindsay's expedition, while placing great reliance on
photography, employed also a method of measuring the position of Venus
on the sun's disc, by means of a kind of telescope specially constructed
for such work, the peculiarities of which need not be here considered.
[Illustration: Fig. 54.]
The observations made in 1769 were so imperfect that astronomers deduced
a distance fully 3,000,000 miles too great. Of late, other methods of
observation had set them much nearer the true distance, which has been
judged to lie certainly between 91,800,000 miles and 92,600,000 miles--a
tolerably wide range.
But it may perhaps occur to some that the distance of the sun may be
changing. The earth might be drawing steadily in towards the sun, and so
all our measurements might be deceptive. Nay, the painful thought might
present itself that when the observations of 1769 were made, the sun
really was farther away than at present by more than 3,000,000 of miles.
If this were so, the earth would, in the course of a century, have
reduced her distance by fully one-thirtieth part, so that, supposing the
approach to continue, she would in 3,000 years fall into the sun, while,
long before that period had elapsed, the increased heat to which she
would be exposed would render life impossible.
Fortunately, we know quite certainly that no such approach is taking
place. It is known that the distance of the earth from the sun cannot
change without a corresponding change in her period of revolution--that
is, in the length of the year. The law connecting these two (indicated
in the note, page 279) is such that, on the reduction of the distance by
any moderate portion the period would be reduced by a portion half as
great again. For instance: if the distance of the earth from the sun
were reduced by a thirtieth part (or about 3,000,000 miles) the length
of the year would be reduced by a thirtieth and half a thirtieth--that,
is, by a twentieth part, or by more than eighteen days. We know that no
such change has taken place during the last century, or since the
beginning of history. Nay, from the Chaldean estimate of the length of
the year, which only exceeded ours by about two minutes, it is easily
shown that the distance of the earth from the sun has not diminished 200
miles within the last 2,500 years. So that, assuming even that the earth
is approaching the sun at this rate, or eight miles in a century, it
would be 1,250,000 years before the distance would be diminished by
100,000 miles, which is the probable limit of error in the determination
of the sun's distance.
If, finally, it be asked, What, after all, is the use of determining the
sun's distance? the answer we shall give must depend on the answer given
to the question, What, after all, is the use of knowing any facts in
astronomy other than those useful in navigation, surveying, and so on?
And I think that this question would introduce another and a wider
one--viz., What is the use of that quality in man's nature which makes
him seek after knowledge for its own sake? I certainly do not propose to
consider this question, nor do I think that the reader will find any
difficulty in understanding _why_ I do not. But accepting the facts: (1)
that we _are_ so constituted as to seek after knowledge; and (2) that
knowledge about the celestial orbs is interesting to us, quite apart
from the use of such knowledge in navigation and surveying, it is easy
to show that the determination of the sun's distance is a matter full of
interest. For on our estimate of the sun's distance depend our ideas as
to the scale, not only of the solar system, but of the whole of the
visible universe. The size of the sun, his mass, and therefore his
might, the scale of those wonderful operations which we know to be
taking place upon, and within, and around the sun; all these relations,
as well as our estimate of the size and mass of every planet, and
therefore our estimate of the earth's relative importance in the solar
system, depend absolutely and directly on the estimate we form of the
sun's distance. Such being the case (this being in point of fact the
cardinal problem of dimensional astronomy) it cannot but be thought
that, great as were the trouble and expense of the expeditions sent out
to observe the transit of 1874, they were devoted to an altogether
worthy cause.