formed a figure which represented the relative depths to which he had penetrated into space; and in case he could be certain that he had gone absolutely through the stratum in every instance, and had grasped every star, even where the extent was most profound, the figures thus constructed would represent the form of the line cut from the outside boundary of the Milky Way by the plane of the circle in which the explorations had been made.

Did he then actually penetrate the deepest portions, or any portion of the Milky Way? This was now his grand question, and to its decision he gave all his power and ingenuity. As a unit wherewith to measure the space-penetrating power of his telescopes, he assumed the power of the human eye, and knowing that stars of the sixth magnitude are within the reach of the unaided eye, he concluded, from the law regulating the decrease of light, that these minute stars were twelve times more distant than the nearest or brightest stars. Now, a telescope having an aperture such as to concentrate twice as much light as the eye, would penetrate into space twice as far, or would reach stars of the twenty-fourth order of distances, and so on for telescopes of all sizes. In this way, he concluded that his great forty-foot reflector, with a diameter of four feet, would penetrate 194 times as far as the naked eye, or that it would still see a star of the first magnitude, if it were carried backward into space, 2328 times its present distance !

Such, then, was the computed length of the sounding-line employed in gauging these mighty depths. Suppose, then, it was required to determine whether this line actually penetrated any given region of the Milky Way. Even with a single telescope, a series of experiments may be performed which go very far to determine this great question. As the space-penetrating power of a telescope depends on the diameter of its aperture, it is easy to give to the same instrument different powers, by covering up, by circular coverings, certain portions of its objectglass. Take circles of paste-board, or any other suitable material, and, in the first, cut an opening one inch in diameter, in the second an opening of two inches, and so on, up to the diameter of the object-glass. These diaphragms being successively applied to the object-glass, give to the telescope space-penetrating powers proportioned to the diameter of the openings.

In this way, Herschel prepared himself to explore one of the