Of first-magnitude stars there are altogether about twenty; of second-magnitude stars about sixty-five; of third-magnitude stars about two hundred; and so the numbers increase till of the sixth-magnitude stars we find more than three thousand. These are all that can be commonly seen with the naked eye, amounting to five or six thousand. With telescopes the numbers rise rapidly to tens of thousands, hundreds of thousands, and even millions. For a long while it was found quite impossible to measure the distances of the stars. To this day the distances of not over two dozen, among all those tens of thousands, have been discovered. The difficulty of finding out the distance of the sun was as nothing compared with the difficulty of finding out the distances of the stars. No base-line sufficient for the purpose could for years be obtained. I must explain slightly what is meant by a “base-line.” Suppose you were on the brink of a wide river, which you had no means of crossing, though you wished to discover its breadth. Suppose there were on the opposite brink a small tree, standing alone. As you stood, you would see the tree seeming to lie against a certain part of the country beyond. Then, if you moved along your bank some fifty paces, the tree would seem to lie against quite a different part of the country beyond. Now if you had a long piece of string to lay down along the fifty paces you walked, and if two more pieces of string were tied, one from each _end_ of the fifty paces, both meeting at the tree, then the three pieces of string would make one large triangle, and the “fifty paces” would be the “base” of your triangle. If you could not cross the river, you could not of course tie strings to the tree. But having found your _base-line_, and measured its exact length, and having also found the shape of the two angles at its two ends, by noting the seeming change of the tree’s position, it would then be quite easy to find out the distance of the tree. The exact manner in which this calculation is made can hardly be understood without some slight knowledge of a science called trigonometry. The tree’s distance being found, the breadth of the river would be known. This mode of measuring distance was found comparatively easy in the case of the moon. But in the case of the sun there was more difficulty, on account of the sun’s greater distance. No base-line of ordinary length would make the sun seem to change his position in the sky in the slightest degree. Nor till the very longest base-line on the earth was tried could the difficulty be overcome. That base-line is no less than eight thousand miles long. One man standing in England looking at the sun, and another man standing in Australia looking at the sun, have such a base-line lying between them, straight through the center of the earth.