STAR 315 were all of them shaped like gigantic cylinders, of length vastly exceeding their breadth. This supposition being altogether untenable, it is certain that these clustering aggregations con- tain stars of many orders of real magnitude, distributed according to various laws of rich- ness. In fact the range of magnitude and of richness of distribution must be as great as in the case of the solar system, from the giant bulk of Jupiter and Saturn to the minute and (relatively) closely aggregated asteroids. Ancl here in passing we may note that this legitimate inference from the observations of Sir W. Her- schel is abundantly confirmed by Sir John Her- schel's examination of the Magellanic clouds, in which all varieties of stellar magnitude and aggregation, from sparsely strewn stars of the eighth and ninth magnitudes to a nebulosity irresolvable by his 18-inch mirror (besides all orders of nebulae), coexist within limits of distance not differing in proportion more than as 10 to 9. According to the assumptions on which Sir W. Herschel's second method of star gauging was based, the limits of distance to include such varieties of stellar distribution should differ in proportion more than as 300 to 1. Passing over the work of Sir J. Herschel, who, so far as stellar distribution is concerned, contented himself by extending his father's first method of star gauging to the southern heavens, we come to the work of W. Struve, whose researches are distinguished by a further extension of the theory of non-uniformity in stellar distribution. He, first of all astronomers ince Herschel's papers were written, perceived their real purport, and the incorrectness of the lescription given by Arago, at least partially. Te does not seem to have sufficiently weighed significance of Herschel's remarks re- specting the rounded figures of many cluster- ing aggregations, and he quite misunderstood Herschel's observation that " when he could not jsolve rich stellar regions, it was because they were unfathomable." (He appears to have read the word "when," in this sentence, as equivalent to the German wenn, since it is ren- lered by si in Struve's HJtudes d'astronomie stellaire.) But he clearly perceived that Her- schel had given up as early as 1802, if not earlier, the theory of a general uniformity of stellar distribution. Having found, indeed, that the stars down to the eighth magnitude are more richly spread over the milky way than elsewhere (whereas if stars were uniformly distributed within the system, these brighter orders, lying all far within even the nearer limits of the galaxy, should appear uniformly distributed over the heavens), he at first sup- posed that he had obtained a result opposed to the views of Sir "W". Herschel ; but having re- examined the whole series of Herschel's papers, he found that the result was quite accordant with Herschel's later views, and opposed only views which Herschel had abandoned early his career as an observer. But now Struve, laving thus obtained evidence of a want of uniformity in the distribution of the stars, and having found that Sir W. Herschel had recog- nized an even wider range of irregularity, nevertheless proceeded (as Herschel had done, but in other directions) to assume laws of uni- formity which, to say the least, should have been demonstrated before they were adopted as the basis of stellar theories. He assumed that stars gather more richly toward the medial plane of the galaxy, but that at equal distances from that plane the distribution is equally rich (on the average for that distance), and that stars in different regions have equal average dimensions. He counted all the stars down to the ninth magnitude in each hour of right as- cension between 15 N". and 15 S. of the equator (or rather he took the numbers from Weisse's catalogue), and supposed them gathered on the equator, toward each "hour" of the equator its proper number, spread uniformly. Then he supposed the equatorial ring of stars thus formed spread over an equatorial disk, in horary sectors, and uniformly over each segment of such sectors limited by radii corresponding to star magnitudes. Thus, suppose E E' to be a horary arc of the equator, and therefore 15 in length, A ED, BE'C parts of hour circles, AB, DC parts of parallels having 15 N. and S. declination, S the sun ; and let S J, S c rep- resent the greater limit, and S , S d the lesser limit of stars of the seventh magnitude. Then Struve, having counted the stars of all magni- tudes down to the ninth in the space A B D, conceived them first distributed uniformly along the equatorial arc EE', and next spread them over the sectorial area SEE', distributing all of the seventh magnitude uniformly over the plane surface abed. Thus he obtained Ms equatorial section of the galaxy ; and he per- suaded himself that this artificial method of distributing the stars was based entirely upon observation, without any arbitrary hypothesis whatever. Prof. Forbes said justly, speaking of Struve's method : " I am persuaded that the popular writers and reviewers who have given additional publicity to the most striking and positive of M. Struve's conclusions, have (very naturally) done so on the strength of the au- thor's well deserved reputation as an observer, and without attempting to analyze his reason- ing, which it must be owned is sometimes ob- scure. My objections," he proceeds, "to M. Struve's argument were put in writing several years ago (1850), but not published except in my lectures. It was only in 1 855 that I saw for the first time a memoir by Prof. Encke in the
