296 TEE POPULAR SCIENCE MONTHLY 



Small: v/=1765, /=897, b = 241. 

 Large: t;/= 235, f— 172, & = 204. 



The division into separate groups with the result that the same gen- 

 eral law is given by every one of the groups is of course the more 

 severe test ; but taking the ratios for the sums as answering our present 

 purpose, we have for the ratio of 



Small nebute . 

 Large nebulas 

 or approximately v/:/:6 = 6:4:l; that is, the very faint nebulas are 

 in excess over the bright ones among the small nebulas in the ratio 6 : 1, 

 but are of nearly equal frequency among the large nebulas. In other 

 words, the large nebulas are intrinsically much brighter than the small 

 ones. 



I next performed the same operation with the 744 objects in a 

 " Catalogue of New Nebulas Discovered on the Negatives " taken with 

 the Crossley reflector at the Lick Observatory, dividing them into two 

 groups : ( 1 ) very small, or not over one half minute in diameter, and 

 (2) those which are above this size and which may be called "large." 

 These groups were divided into two classes: (a) very faint, including 

 those which are described as " very faint " and " very very faint," 

 and ( b ) pretty bright, or those given in the catalogue as " faint " to 

 " bright." The result of this examination is that three fourths of the 

 large nebulce are pretty bright, and one fourth very faint; while the 

 very small nebulas have just the opposite distribution of brightness, 

 three fourths of them being very faint, and only one fourth pretty 

 bright. 



In comparing the two catalogues, it must be recognized that the 

 photographic method is far more delicate. Most of the objects in the 

 photographic catalogue could not be detected by visual examination. 

 The photograph also includes faint margins and therefore increases 

 the apparent size of such nebulas as are visually perceptible. Conse- 

 quently, Herschel's small nebulas are about equivalent to the " large " 

 nebulas of the photographic catalogue, and we should expect that the 

 photograph would include a much wider range of brightness — all of 

 which is confirmed by a discussion of the observations. 



Let us suppose that the average distances of the several classes of 

 nebulas are given in andromedes, and denoted by the letter a, and that 

 the coefficient of transmission of light through space is t a ; also that 

 the mean distances are inversely proportional to certain assumed 

 apparent diameters which are fairly typical. Each class of nebulas 

 includes objects having a considerable range of actual diameter, that is, 

 the variation of distance is not as great as that of the apparent diam- 

 eter. Instead of taking a mean value of 4/ to represent the diameter 

 of that class which includes nebulas less than A/ in diameter, I take 



