THE STARS AND NEBULAE 263 



certaining the extent of this difference in any particular 

 case. Some of my readers may suppose this knowledge 

 obtainable from the spectra of the stars, but these give 

 no clue whatever as to either the quantities, absolute or 

 relative, nor, since the revelation of an element in the 

 spectrum depends on the temperature intensity, do these 

 spectra even settle the problem as to the mere number of 

 elements. Except, therefore, where we can assign some 

 definite ground for hypothesizing otherwise, we have no 

 option but tentatively to assume that all stars, if not 

 exactly, are yet approximately enough alike chemically 

 to validate comparisons between them on this basis. 



Having thus ruled out the factor of differential 

 chemical composition, not because of its immateriality 

 but because of its indeterminateness, we are relegated to 

 the two remaining factors of self-compression and tem- 

 perature. These two I associate, making the latter de- 

 pend on the first as a causal effect. Construing density 

 to decrease with temperature increase, we may begin by 

 imagining all stars cold to begin with, and all of them 

 virtually of the same density. This last would, of course, 

 not be exactly true, inasmuch as the larger stars, because 

 of their more powerful self -compression, would necessar- 

 ily pack their contents into smaller compass; but this, 

 you can see, is a negligible consideration inasmuch as 

 the condition requiring to be elucidated is not why the 

 big bodies are more compact but why they are vastly less 

 compact than the small. As said before, then, density 

 being taken as initially the same for all bodies, mass and 

 volume become synonymous, and we have for the ratio 

 of the integral attractions of cosmic bodies in general the 

 formula, 



M m 



in which M is the mass of the large body, m that of the 

 smaller, and 8 i/M~ and *i/m~ are their respective radii; 

 the latter terms being squared and placed under the line 

 in conformity with the law of inverse squares. Sub- 

 stituting, by way of illustration, the sun's mass for M 



