INFINITY OF THE UNIVERSE 103 



second, though 1830 Groombridge is credited with 

 the extraordinary speed of 59 miles per second, 

 and the spectroscopic binary Lacaille 3105 with a 

 relative velocity of 380 miles a second. All these 

 speeds fall far short of the speed of light, which 

 we now believe to be the unattainable limit of 

 speed of all material things. 



An important conclusion may be drawn at once 

 from the observation that no stellar velocities 

 exceed ^th of the velocity of light. It is that 

 the mass comprised within a world-sphere increases 

 as its radius, and not as its volume, or in other 

 words, that the density within a world-sphere 

 varies inversely as the surface of the sphere. By 

 "world-sphere" I mean a sphere enclosing a 

 "visible universe" of any order. 



To make this clearer, we will assume that space 

 is strewn with other stellar systems comparable 

 to our own, and that some 100 million of these 

 systems make up a galaxy of their own. Instead 

 of a sphere of 3 x 10 21 cm., we might have a sphere 

 3 x 10 81 cm. in radius. We can hardly assume this 

 sphere to have the same average density as our 

 own stellar system, since all appearances are against 

 it. If it had, however, we should have a mass 

 10 30 times as large as before, and the energy of a 

 body falling to its surface from infinity would bo 

 10* times what it is at the limit of our stellar 

 system. Its theoretical speed would bo 10 10 times 



