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.
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.
Fig. 43.
Fig. 44.
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]
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.
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.
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.
............