It needs only the most elementary conceptions of space, direction and motion to see that, as the earth makes its vast swing from one extremity of its orbit to the other, the stars, being fixed, must have an apparent swing in the opposite direction. The seeming absence of such a swing was in all ages before our own one of the great stumbling blocks of astronomy. It was the base on which Ptolemy erected his proof that the earth was immovable in the center of the celestial sphere. It was felt by Copernicus to be a great difficulty in the reception of his system. It led Tycho Brahe to suggest a grotesque combination of the Ptolemaic and Copernican systems, in which the earth was the center of motion, round which the sun revolved, carrying the planets with it.
With every improvement in their instruments, astronomers sought to detect the annual swing of the stars. Each time that increased accuracy in observations failed to show it, the difficulty in the way of the Copernican system was heightened. How deep the feeling on the subject is shown by the enthusiastic title, Copernicus Triumphans, given by Horrebow to the paper in which, from observations by Roemer, he claimed to have detected the swing. But, alas, critical examination showed that the supposed inequality was produced by the varying effect of the warmth of the day and the cold of the night upon the rate of the clock used by the observer, and not by the motion of the earth.
Hooke, a contemporary of Newton, published an attempt to determine the parallax of the stars, under the title of “An Attempt to Prove the Motion of the Earth,” but his work was as great a failure as that of his predecessors. Had it not been that the proofs of the Copernican system had accumulated until they became irresistible, these repeated attempts might have led men to think that perhaps, after all, Ptolemy and the ancients were somehow in the right.
The difficulty was magnified by the philosophic views of the period. It was supposed that Nature must economize in the use of space as a farmer would in the use of valuable land. The ancient astronomers correctly placed the sphere of the stars outside that of the planets, but did not suppose it far outside. That Nature would squander her resources by leaving a vacant space hundreds of thousands of times the extent of the solar system was supposed contrary to all probability. The actual infinity of space; the consideration that one had only to enlarge his conceptions a little to see spaces a thousand times the size of the solar system look as insignificant as the region of a few yards round a grain of sand, does not seem to have occurred to anyone.
Considerations drawn from photometry were also lost sight of, because that art was still undeveloped. Kepler saw that the sun might well be of the nature of a star; in fact, that the stars were probably suns. Had he and his contemporaries known that the light of the sun was more than ten thousand million times that of a bright star, they would have seen that it must be placed at one hundred thousand times its present distance to shine as a bright star. If, then, the stars are as bright as the sun, they must be one hundred thousand times as far away, and their annual parallax would then have been too small for detection with the instruments of the time. Such considerations as this would have removed the real difficulty.
The efforts to discover stellar parallax were, of course, still continued. Bradley, about 1740, made observations on γ Draconis, which passed the meridian near his zenith, with an instrument of an accuracy before unequalled. He thus detected an annual swing of 20″ on each side of the mean. But this swing did not have the right phase to be due to the motion of the earth; the star appeared at one or the other extremity of its swing when it should have been at the middle point, and vice versa. What he saw was really the effect of aberration, depending on the ratio of the velocity of the earth in its orbit to the velocity of light. It proved the motion of the earth, but in a different way from what was expected. All that Bradley could prove was that the distances of the stars must be hundreds of thousands of times that of the sun.
An introductory remark on the use of the word parallax may preface a statement of the results of researches now to be considered.
In a general way, the change of apparent direction of an object arising from a change in the position of an observer is termed parallax. More especially, the parallax of a star is the difference of its direction as seen from the sun and from that point of the earth’s orbit from which the apparent direction will be changed by the greatest amount. It is equal to the angle subtended by the radius of the earth’s orbit, as seen from the star. The simplest conception of an arc of one second is reached by thinking of it as the angle subtended by a short line at a distance of two hundred and six thousand times its length. To say that a star has a parallax of 1″ would therefore be the same thing as saying that it was at a distance of a little more than two hundred thousand times that of the earth from the sun. A parallax of one-half a second implies a distance twice as great; one of one-third, three times as great. A parallax of 0″20 implies a distance of more than a million times that of our unit of measure.
The first conclusive result as to the extreme minuteness of the parallax of the brighter stars was reached by Struve, at Dorpat, about 1830. In the high latitude of Dorpat the right ascension of a star can be determined with great precision, not only at the moment of its transit over the meridian, but also at transit over the meridian below the pole, which occurs twelve hours later. He, therefore, selected a large group of stars which could be observed twice daily in this way at certain times of the year, and made continuous observations on them through the year. It was not possible, by this method, to certainly detect the parallax of any one star. What was aimed at was to determine the limit of the average parallax of all the stars thus observed. The conclusion reached was that this limit could not exceed one-tenth of a second and that the average distance of the group could not, therefore, be much less than two million times the distance of the sun; if, perchance, some stars were nearer than this, others were more distant.
By a singular coincidence, success in detecting stellar parallax was reached by three independent investigators almost at the same time, observing three different stars.