When observers essayed to apply to the sun the same procedure which had proved so successful in regard to the moon, they encountered disastrous failures, partly because the base, even the largest practicable one, was found to be comparatively very small; partly because, when the sun shines, no star is visible near by from which to measure an angle; and also because the atmosphere is so disturbed by the rays of solar heat that, when seen through a large telescope, the sun's edge is quite tremulous. Hence a very large element of uncertainty is introduced when angles are taken with the zenith. No astronomer would look with confidence on the result obtained under such circumstances. Two hundred years ago, their instruments were much less perfect than those we now have; yet, even with our best instruments, to-day, too much uncertainty remains. That mode of ascertaining the sun's distance has been abandoned.
Ancient astronomers, long before the invention of telescopes, and before the discovery of the Copernican system, devised an ingenious method of getting some light on the distance of the sun. It is attributed to Aristarchus of Samos. They reflected that, when the moon appeared precisely half full, this arose from the fact that the sun and the earth were at right angles to her; the sun illumining the half turned to him, and the plane of division between the illumined and unillumined portions extended stretching directly to the earth. They conceived the three bodies to stand at the angles of a right-angled triangle, of which the distance of the moon from the earth was the base, and the distance of the sun was the hypothenuse. Hence they had only to measure the angle at the earth, which they could do, and then take into account their estimate of the moon's distance, to arrive at the result sought. The plan is ingenious, and taught them that the sun was at least twenty times further off than the moon. But their estimate [pg 153] of the moon's distance was altogether wide of the mark. They had no means of correctly estimating it. Moreover, even keen eyesight is a bad judge of whether the moon is precisely half full or not. The error of half a dozen hours would give a large mistake. Even with instruments such as we have, it cannot be precisely determined by direct observations; for the surface of the moon, as developed in a powerful telescope, is so uneven, jagged, and volcanic that the division between light and shade is a line too uneven and broken to be determined except by guessing at its mean course.
Another method has been also used in these later centuries. Kepler's law applies to all the planets. The planet next outside the earth is Mars, whose mean distance from the sun is about one-third greater than that of the earth. It periodically happens that Mars is in opposition—that is, is precisely on the other side of the earth from the sun. In that case, he makes his nearest approach to our planet. Cannot his distance from the earth be then observed and determined, so that he will give us the means of calculating by Kepler's formula the distance of the sun? It was tried, and with some success. The base-line was found large enough; the observations were made at night, when the atmosphere is comparatively quiescent, and when fixed stars may be seen in the vicinity of the planet, to aid in taking the requisite angles. Yet, as in the case of Venus, there are, as we have stated, subsidiary calculations to be made on account of the eccentricity of his orbit and his varying velocity. In the case of Mars, these variations were too full of anomalies to allow confidence in the calculations. When afterwards these anomalies were understood to proceed from interplanetary attraction, they were so complicated that their numerical value almost escaped calculation. The whole subject has been gone over in our own day under the light of more perfect observations, and with the aid of the highest calculus. We doubt, however, if even now the results are sufficiently established to warrant a calculation as to the sun's distance to which reasonable exception may not be taken.
Anyhow, this method cannot compare, either in facility of calculation or in accuracy of result, with the method of determining the solar distance by observations for the transit of Venus.
Of the theory and mode of such observations we will now say a few words.
In 1677, while Halley, the great English astronomer, was at St. Helena, for the purpose of observing and cataloguing stars south of the equator, he observed a transit of Mercury across the face of the sun, and, from his efforts to measure its positions and movements, was led to believe that a transit of Venus could be so accurately observed and measured as to yield a precise and definite determination of the sun's distance. From the knowledge he had of the movements of Venus, he knew that there had been a transit of Venus in 1631, as Kepler had predicted, although no eye in Europe had seen it; and another in 1639, which had been observed, but, of course, not for this purpose, which in 1639 was yet unthought of. The next transit would be in 1761. He could not hope to live to see it. But he did the next best thing. He studied out all the conditions of the question, published his plans, and made all the preliminary [pg 154] calculations required, so as to aid in securing, as far as possible, good observations and good results when the time came.
As the year 1761 was approaching, the scientific world was astir, pretty much as it is now. Halley's computations were again gone over, and such corrections and improvements were introduced as the advance of astronomy since his day warranted and required. Governments gave their aid and supplied means liberally. One hundred and twenty positions had been carefully chosen, and the best results were confidently expected. The grand problem was about to receive a final and definite solution. The error in the ultimate result would certainly not exceed one-fifth of one per cent.
The astronomers were doomed to a sad disappointment. Wars then waging prevented some of the most important positions from being occupied by the observers. It was bitter for a well-appointed party to sail for months and months over two oceans, only to see a hostile flag floating over the port they were about to enter. Sadly they sailed away, and could only see the transit from the rolling deck of their ship. Cloudy weather rendered other positions valueless. And even where everything seemed to promise success, an unforeseen phenomenon interfered to mar their work. The astronomer might have his best telescope duly mounted, and directed to the proper point of the heavens, and carefully adjusted; his eye might be glued to the instrument, as he watched on one side of his field of vision a portion of the circular edge of the sun's disk, and on the other the round, black spot gradually approaching. As they drew near, his hand was raised to give the signal; his assistant stood ready to mark the very second when the two edges, coming nearer and nearer, would at last just touch. They hoped to seize the time of that first contact so accurately as to escape even the one second of error or doubt which Halley thought unavoidable. Vain hope! Before the contact, while Venus was still distant about two-thirds of her own diameter from the edge of the sun, a dark streak or band seemed to interpose between them like a black cushion or wedge. As they pressed against it, the curved outlines of their edges seemed to be pressed back or flattened, as if by the resistance of the cushion, and to lose their normal shape. There was a pause in the onward movement, a quivering, a struggle, and then, by an irregular, convulsive jump, like that of two drops of water coalescing into one, Venus was seen to have already entered some way on the disk of the sun. The discomfited and astonished observer was forced to record that his uncertainty as to the precise time of the contact was not of one second only, but of at least twelve or fifteen seconds. Was it the defect of the instrument, or the fault of his own eye, over-strained by long use, by the brilliant light, or by his intense anxiety? Or was there some unknown atmospheric cause at work producing this band? Anyhow, he might hope that other observers would be more fortunate than he had been. Again he was in error. Everywhere the same unexpected and puzzling phenomenon appeared. There was trouble in the astronomical world. The fault was generally thrown on the instruments. But whatever the cause of the mishap, there was some room for consolation. They would soon have another opportunity, and [pg 155] might make another trial. In 1769, only eight years off, there would be another transit, and by that time some means would certainly be devised for escaping the evil.
In 1769, the stations were as numerous, the governmental aid fully as great, the instruments, they said, more perfect, and the observers, we may be sure, as earnest and as careful as before. Perhaps they were more skilful because of their previous experience. But again all in vain. The same evil reappeared. The resulting uncertainty was even greater. It was held to reach fully twenty seconds. When they undertook to calculate, from such observations, the distance of the sun, some made it not more than 87,890,780 miles, while, according to others, it reached 108,984,560 miles, the majority finding intermediate values. On the whole, it did not appear that there was much improvement on the estimate made by Cassini a century and a half before, that it was not less than 85,000,000 miles. Again and again were the records of the observations studied, scrutinized, and weighed, and the calculations based on them repeated and criticised. Finally, in 1824, Encke, after several years of special study of them, summed all up, and gave, as the best result attainable, 95,274,000 miles. The scientific world, hopeless of anything better, seemed for a time to acquiesce. Some even upheld the estimate of Encke as “so successfully determined as to leave no sensible doubt of its accuracy.”
But, despite this, its accuracy has since been impugned, and on very strong grounds. It was known that light travels from the sun to the earth in about 8 minutes 13 seconds. Experiments carefully and ingeniously made by Arago, Foucault, and Fizeau show that light travels with a velocity of nearly 186,000 miles a second. This would give the distance of about 91,400,000 miles.