The Evolution of the Sciences 



when generalised it enables us to carry our 

 soundings of the heavens to the limits of the 

 visible world. If we consider the sky to be 

 filled with stars, all of one size and equally 

 distributed in space, it evidently becomes 

 possible to determine the proportion of stars 

 of each magnitude, since the most brilliant 

 stars must necessarily be the nearest. Calcula- 

 tions made on this assumption lead to the result 

 that the stars of any given magnitude are four 

 times as numerous as those of the class im- 

 mediately superior in point of brightness. Now 

 this is actually what is observed if the stars 

 of the first few magnitudes, which are too few 

 to be treated statistically, are left out of account. 

 There are 321 stars of the fourth magnitude, 

 1238 of the fifth, 4890 of the sixth; and, as will 

 be seen, these numbers vary in a geometrical 

 progression whose ratio is four. This confirms 

 our hypothesis regarding the homogeneity of 

 the heavens. 



Two methods are therefore available for 

 ascertaining the distances of the stars; one, 

 more exact, based on the measurement of their 



parallaxes, has so far only been applied to a 



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