49l8 LECTURE XLI. 



much nearer to each other than the nearest to us ; and there may still be a 

 very great variety in their actual dimensions. There can be only twelve 

 points on the surface of a sphere as far from each other as Irom the 

 centre; in a sphere of twice tlie radius, there may be about 50 points at 

 the same distance; in a sphere of three times the radius, more than 100: and 

 it has been observed that these numbers do not greatly differ from the actual 

 numbers of tlie stars of the first, second, and third magnitudes; although it 

 is true that they are not by any means placed at equal angular distances 

 from each other. But, from a comparison of the light of ditierent stars, we 

 may infer, that if their real magnitudes are nearly equal tlieir distances 

 must increase much faster than in this arithmetical progression; that is, 

 that the stars of the second magnitude are more than twice as remote as those 

 of the first, and those of the third more than three times as remote. Mr. 

 Michell found the light of Sirius between 400 and 1000 times as great as that 

 of a star of the sixth magnitude; consequently, supposing these stars actually 

 equal, their distances must differ in the ratio of 1 to 20 or 30; since light 

 always diminishes in proportion to the square of the distance of the luminous 

 object. The light of stars of different magnitudes, situated near each other, 

 may be compared by viewing them through two apertures of different sizes, 

 cut in cards, one held before each eye, the apertures being reduced to such 

 magnitudes, that the stars may appear equally bright; and the com- 

 parison may be extended to the light of the sun, by finding a star 

 and a planet of equal brightness, and calculating what proportion of the 

 sun's light must be reflected by the planet, upon the most probable sup- 

 position respecting the disposition of its surface to reflect more or less of the 

 light which falls on it. 



The stars are in general dispersed without any regular order, but we may 

 observe in many parts of the heavens that a number of them are so much nearer 

 together than to the rest, as to form a cluster or nebula. The ancients had notic- 

 ed some of the most conspicuous nebulae, but Huygens first directed the atten- 

 tion of modern astronomers to the large one situated in the constellation Orion. 

 Herschel has now given us catalogues of 2500 nebulae: many of them can be 

 resolved by very high magnifying powers into separate stars; but others appear 

 to consist of a luminous matter, spread uniformly in the neighbourhood of the 

 •everal itars to which ihey seem to belong. (Plate XXI. I'ig. 45o . . 46"3.) 



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