NEBULA, CLUSTEES, ETC. 35 



Herschel, W. : Abstracts of Memoirs— Continued. 



AD. Vol. P. 



of stars in each class we must also allow that the stars 

 of each succeeding magnitude beginning with the first, 

 are, one with another, further from us than those of the 

 magnitude immediately preceding. The relative magni- 

 tudes give only relative distances, and can afford no in- 

 formation as to the real distances at which the stars are 

 placed. 



II. Of a standard by which the relative arrangeynent of the 

 stars may be examined. 



A standard of reference for the arrangement of the stars 

 may be had by comparing their distribution to a certain 

 properly modified equality of scattering. The equality 

 which I propose does not require that the stars should 

 be at equal distances from each other, nor is it necessary 

 that all those of the same nominal magnitude should be 

 equally distant from us. 

 1817 107 305 It consists in allotting a certain equal portion of space to 

 every star, in consequence of which we may calculate 

 how many stars any given extent of space may contain. 



This arrangement is explained by means of a figure. Plate 

 XV, Fig. 1. 

 306 III. Comparison of the order of magnitudes with the order 

 of distances. 



Comparison of the order of distances by the foregoing 

 scheme with the magnitudes assigned in Bode's catalogue 

 of 14,144 stars. 



308 The result of this comparison is, that if the order of mag- 



nitudes could indicate the distance of the stars, it would 

 denote at first a gradual, and afterwards a very abrupt, 

 condensation of them ; but that, considering the principle 

 on which the stars are classed, th«ir arrangement into 

 magnitudes can only apply to certain relative distances, 

 and show that, taking the stars of each class, one with 

 another, those of the succeeding magnitudes are farther 

 from us than the stars' of the preceding order. 

 IV. Of a criterion for ascertaining the profundity or local 

 situation of celestial objects in space. 



309 It will be admitted that those stars, the light of which we 



can experimentally prove to be \, \, T a s of the light 



of any certain star of the first magnitude must be 2, 3, 



4 times as far from us as the standard star, provided 



the condition of the stars should come up to the supposed 

 •mean state of diameter and lustre of the standard star. 

 V. Of the equalization of star light. 



