THE STABS AND NEBULAE 265 



latter, in their philosophy, are as capricious and arbi- 

 trary as the "inherent" motions themselves. The new 

 principles which I submit are these : 



(1) It follows mathematically from Newton's law 

 of inverse squares and the law of the energy of motion, 

 that if two bodies of different mass be conceived as oc- 

 cupying space alone, they will approach each other with 

 velocities inversely proportional to the square roots of 

 their respective masses. Dull stars, therefore, e. g., are 

 consequently both small and quick moving. 



2. Save in the cases of binary stars, where the cir- 

 culatory relation is patent, current astronomy regards 

 all star movements as rectilinear and dynamically in- 

 dependent. On the contrary, I regard all the stars as 

 organically interrelated in the greater cosmos, much as 

 the individual soldiers are constituent parts of a great 

 army. Thus, the earth and moon form by themselves 

 the simplest of all systems a binary; the sun and his 

 planets another, more complicated; the sun and one or 

 more of his near neighbors a still higher system, whose 

 extent and membership we have not yet been privileged 

 to discover and so on. You can see here that the minor 

 members necessarily move more rapidly than the major, 

 for the substantial reason that they have all the various 

 motions in cumulation. It is therefore only to be ex- 

 pected that the smaller stars, in whatever relation they 

 may find themselves, should, caeteris paribus, travel with 

 greater celerity than the more cumbrous; as, in fact, 

 they do. Star velocity, then, is a function of the mass, 

 not directly, but inversely as the square roots. 



BRIGHTNESS. Finally, as to the intrinsic brightness 

 of stars. If it were possible to determine which is in- 

 trinsically the brightest of all stars, it would be equal to 

 finding at the same time the very hottest and the very 

 biggest as well biggest not only in girth but in mass. 

 Furthermore, it would be the least dense, and (less cer- 

 tainly) the most sluggish in movement. The reason for 

 adding this last parenthesis is that pivot-stars (by which 

 I mean such as, by reason of their relatively great size, 



