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
