We might naturally think from Fig. 46 that Venus must pass at every
revolution directly between the earth and the sun; and therefore it
might appear that what is called the transit of Venus across the sun
ought to occur every time between the appearance of the planet as the
evening star and the next following appearance as the morning star.
No doubt on each of these occasions Venus seems to approach the sun
closely; but the orbits of Venus and the Earth do not lie quite in the
same plane, and hence the planet usually passes just over or just under
the sun, so that it is a very rare event indeed for her to come right
in front of the sun. But this does sometimes happen. It happened, for
instance, in the year 1874, and again in the year 1882; but, alas!
I cannot hold out to you the prospect of ever seeing another such
spectacle. There will be no further occurrence of the transit of Venus
until the year 2004, though there will be another eight years later, in
2012.
It seems rather odd that one transit of Venus should be followed by
another after an interval of eight years, and that then a period of
much more than a century should have to elapse before there will be
a repetition of a similar pair. This is in consequence of a curious
relation between the motion of Venus and the motion of the Earth, which
I must endeavor to explain with the help of a little illustration.
Let us suppose a clock with ordinary numbers round the dial, but so
arranged that the slowly moving short hand requires 365.26 days to
complete one revolution round the dial, while the more rapidly moving
long hand revolves in 224.70 days. The short hand will then go round
once in a year, and the long hand once during the revolution of Venus.
Let us suppose that both hands start together from XII, then in 224.70
days the long hand is round to XII again, but the short hand will have
only advanced to about VII, and by the time it reaches XII the long
hand will have completed a large part of a second circuit. It happens
that the two numbers 224.70 and 365.26 are very nearly in the ratio
of 8 to 13. In fact, if the numbers had only been 224.8 and 365.3
respectively, they would be exactly in the proportion of 8 to 13. It,
therefore, follows that eight revolutions of the short hand must occupy
very nearly the same time as thirteen revolutions of the long hand.
After eight years the short hand will of course be found again at XII;
and at the same moment the long hand will also be back at XII, after
completing thirteen revolutions.
We can now understand why the transits, when they do occur, generally
arrive in pairs at an interval of eight years. Suppose that at a
certain time Venus happens to interpose itself directly between the
earth and the sun, then, when eight years have elapsed, the earth is,
of course, restored for the eighth time since the first transit to the
same place, and Venus has returned to almost the same spot for the
thirteenth time. The two bodies are practically in the same condition
as they were at first, and, therefore, Venus again intervenes, and the
planet is beheld as a black spot on the sun’s surface. We must not
push this argument too far; the relation between the two periods of
revolution, though nearly, is not exactly 8 to 13. The consequence is
that when another eight years have elapsed, the planet passes a little
above the sun or a little below the sun, and thus a third occurrence of
the transit is avoided for more than a century. The next transit will
take place at the opposite side of the path.
We were fortunate enough to be able to see the transit of Venus in 1882
from Great Britain. Perhaps I should say a part of the transit, for the
sun had set long before the planet had finished its journey across the
disk. Venus looked like a small round black spot, stealing in on the
bright surface of the sun and gradually advancing along the short chord
that formed its track.
[Illustration: FIG. 51.--Venus in Transit across the Sun.]
An immense deal of trouble was taken in 1882, as well as in 1874, to
observe this rare occurrence. Expeditions were sent to various places
over the earth where the circumstances were favorable. Indeed, I do not
suppose that there was ever any other celestial event about which so
much interest was created. The reason why the event attracted so much
attention was not solely on account of its beauty or its singularity;
it was because the transit of Venus affords us a valuable means of
learning the distance of the sun. When observations of the transit of
Venus made at opposite sides of the earth are brought together, we are
enabled to calculate from them the distance of Venus, and knowing that,
we can find the distance of the sun and the distances and the sizes of
the planets. This is very valuable information; but you would have to
read some rather hard books on astronomy if you wanted to understand
clearly how it is that the transit of Venus tells us all these
wonderful things. I may, however, say that the principle of the method
is really the same as that mentioned on pp. 19–25. When you remember
that not we ourselves, nor our children, and hardly our grandchildren,
will ever be able to see another transit of Venus, you will, perhaps,
not be surprised that we tried to make the most of such transits as
have occurred in our time.