. Astronomy for high schools and colleges . enoughto contain 37 stars ;the second will have125 times the volume,and will therefore con-tain 125 stars, and sowith the successivespheres. The figureshows a section ofportions of thesespheres up to thatwith radius 11. Abovethe centre are giventhe various orders ofstars which are situ-ated between the sev-eral spheres, whilein the correspondingspaces below the cen-tre are given the num-ber of stars which the region is large enough to contain ; for in-stance, the sphere of radius 7 has room for 343 stars, but of thisspace 125 parts belong to the sphe
. Astronomy for high schools and colleges . enoughto contain 37 stars ;the second will have125 times the volume,and will therefore con-tain 125 stars, and sowith the successivespheres. The figureshows a section ofportions of thesespheres up to thatwith radius 11. Abovethe centre are giventhe various orders ofstars which are situ-ated between the sev-eral spheres, whilein the correspondingspaces below the cen-tre are given the num-ber of stars which the region is large enough to contain ; for in-stance, the sphere of radius 7 has room for 343 stars, but of thisspace 125 parts belong to the spheres inside of it : there is, there-fore, room for 218 stars between the spheres of radii 5 and 7. Herschel designates the several distances of these layers ofstars as orders ; the stars between spheres 1 and 3 are of the firstorder of distance, those between 3 and 5 of the second order, andso on. Comparing the room for stars between the several sphereswith the number of stars of the several magnitudes, he found theresult to be as follows :. Fig. 137.—orders op distance of stars. STRUCTtlME OF THE HEAVENS. 487 Order of Distance. Number of Starsthere is Room for. Magnitude. Number of Starsof that Magnitude. 2 26 98 218 386 602 866 1,178 1,538 123 456 7 17 57 3 206 4 454 5 1,1616,1036,146 6 7 8 The result of this comparison is, that, if the order of magnitudescould indicate the distance of the stars, it would denote at first agradual and afterward a very abrupt condensation of them. If, on the ordinary scale of magnitudes, we assume the brightnessof any star to be inversely proportional to the square of its dis-tance, it leads to a scale of distance different from that adopted byHerschel, so that a sixth-magnitude star on the common scalewould be about of the eighth order of distance according to thisscheme—that is, we must remove a star of the first magnitude toeight times its actual distance to make it sliine like a star of thesixth magnitude. On the scheme here laid dow
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