THE LIGHT OF THE STARS 295 



There is in nature a tendency to wide variation, coupled with a coor- 

 dinate tendency to uniformity in averages, when the number of classes 

 is limited. Thus the land mammals range in size from elephants, say 

 15 feet long, to mice and shrews of a few inches. If we divide the 

 earth into a good many faunal regions, the average sizes of the mam- 

 mals in the different provinces may vary considerably; but if we divide 

 the earth into only two halves, the averages will be almost identical. 



For the present research, I take Sir John Herschel's " General 

 Catalogue of Nebulae and Clusters of Stars," which, coming from a 

 single hand, and that the hand of a master, may be considered fairly 

 homogeneous; and excluding the clusters which are known to be asso- 

 ciated with the Milky Way, and are therefore comparatively near, I 

 divide the remaining objects into two classes: (1) large nebulae, or 

 those having a diameter greater than 2'; and (2) small nebulae, or 

 those which are less than 2' across; and I shall assume that the small 

 nebulae are on the average farther away than the large nebulae in the 

 ratio, x : 1, leaving the value of the ratio to be determined by consid- 

 erations to be drawn from the result, and which will appear in the 

 sequel. 



A point-source of light diminishes in brightness as the square of its 

 distance increases; but light from a large number of points so close 

 together that they can not be discriminated must be treated as a 

 luminous surface; and since the angular area of a surface also dimin- 

 ishes proportionally to the inverse square of the distance, the intrinsic 

 brightness, or the brightness of the unit of angular area, does not 

 change with the varying distances of the nebulae. We must therefore 

 inquire : Is the intrinsic brightness of a small, and therefore presumably 

 distant, white nebula equal to, or less than that of a large one ? If the 

 average brightness of the unit of angular area is less for the smaller 

 white nebulae the presumption is that the light of the smaller and more 

 distant objects has been absorbed in passing through space. To apply 

 this test, I further subdivide each class into three groups — (vf) very 

 faint, (/) faint and (b) bright, or, if desired, the last two may be 

 combined into a single group. 



Dividing the nebulae in Herschel's catalogue into groups of four 

 hundred each, and taking the ratios of the small to the large nebulae in 

 each of the thirteen groups, I find that without exception the faint and 

 small nebulae are more numerous than the bright and small in a rela- 

 tively very much larger ratio than occurs in the corresponding divisions 

 of the large nebulae. With only three exceptions the same relation is 

 obtained by comparing the very faint and the faint nebulae. Treating 

 the groups separately, and taking the mean of the ratios, I find 



Small divided by large: vf, 8.38; /, 6.83; b, 1.48. 



The sums for the entire catalogue are 



