Weight and Fate of Light. 551 



intermediate value, we find that a system able to control 

 and retain its light must have a density and size com- 

 parable to 



9 7 x 10 20 

 p W= ,, -;* 1A , = 1-6 x 10 27 c.g.s. 



It is hardly feasible for any single mass to satisfy this con- 

 dition ; either the density or the size is too enormous: — 



A globe as big as the earth must have a density 

 4 x 10 9 grammes per c.c. ; as big as the sun a sufficient 

 density is 4 X 10 5 grammes per c.c. If of the density of water 

 its radius must be 4 x 10 13 centimetres, or 600 times the 

 linear dimension of the sun, so that the mass would be 

 excessive — about 10 41 grammes. 



For a body of density 10 12 , — which must be the maximum 

 possible density, as its particles would be then all jammed 

 together, — the radius need only be 400 kilometres. This is 

 the size of the most consolidated body. For anything 

 smaller than that the effect would be impossible. 



If a mass like that of the sun (2'2 x 10 33 grammes) could 

 be concentrated into a globe about 3 kilometres in radius, 

 such a globe would have the properties above referred to ; 

 but concentration to that extent is beyond the range of 

 rational attention. The earth would have to be still more 

 squeezed, into a globe 1 centimetre in diameter. 



But a stellar system— say a super spiral nebula — of aggre- 

 gate mass equal to 10 16 suns, say 10 49 grammes, might have a 

 group radius of 300 parsecs, or 10 21 centims., with a corre- 

 sponding average density of 10 ~ 15 c.g.s., without much 

 light being able to escape from it. This really does not 

 seem an utterly impossible concentration of matter. Though 

 it is true that the average empty space enclosing each 

 " sun " would have a radius of only about 22 times the 

 distance of Neptune ; and the suns would subtend nearly 

 one and a half seconds of arc as seen from each other. 



Note on Units. 



The constant G/c 2 is the reciprocal of a linear density, and is 

 666xl0 -l0 H-9xl0 20 = 74xl0- 30 centim. per gramme. The quantity 

 Gm/c 2 is accordingly of the dimensions of a length, and is commonly 

 spoken of by relativists as a mass of so many kilometres. In this 

 sense the sun's mass is said to be 1*5 kilometres, while the earth's 

 mass is only half a centimetre. 



Inattention to dimensions, and consequent incomplete specification, 

 often seems to save arithmetic, but it can hardly be conducive to 

 philosophic thinking save in exceptionally skilled hands. It is legitimate 

 to employ £xlO -10 second as a unit of time, if worth while, so as to 



2 2 



