THE STARS AND NEBULAE 301 



VELOCITY. Owing to two misconceptions hitherto 

 prevailing, namely; (1) that dull stars are old, and hence 

 presumptively massive, and (2) that proper motions are 

 "inherent", Newtonians have been unable to formulate 

 any rule whatsoever regarding stellar velocities. These 

 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. Thus dull stars being according 

 to my hypothesis small, they are therefore 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 



