550 Sir Oliver Lodge on the 



interspaces so as to be extremely porous, — for a hetero- 

 geneous mass is more not less effective than a homogeneous 

 one, — the average force at any point in the interior o£ the 

 system at a distance r from its centre of gravity, introducing 

 the Newtonian constant to make the specification complete, is 



And the potential there is 



V = 27TyQ(R 2 -^ 2 )G. 



The speed of anything amenable to gravitation would be a 

 maximum near the centre of such a system and a minimum 

 near or outside the periphery ; consequently light unable to 

 escape would accumulate near the boundary, and if liberated 

 by an expansion or other catastrophe happening to the 

 system, such as might occur through a gradual growth of 

 instability, would burst forth in a blaze. Such a blaze, 

 rapidly rising in intensity, would die down gradually during 

 the time that the deeper seated portions of the luminous 

 shell took to rise to the surface. 



The speed which a heavy body could acquire by falling 

 from periphery to centre is ^/(g'R), 

 by falling from infinity to surface y/(2#R), 

 and by falling from infinity to centre V /(3#R), 

 ■g being the maximum gravitational intensity §7r/>RGr, where 

 GJ- is the Newtonian constant whose value in c.g.s. units is 

 666 x 10~ 10 and whose dimensions are the square of a velocity 

 divided by a linear density, or M -1 L +3 T~ 2 . 



This means that a body able to prevent light emanating 

 from centre from escaping altogether would have 



To prevent light from centre from reaching the surface 

 would need 



Po 



o 2 



4ttG 



while fo control light from surface into an orbit, the inter- 

 mediate value 



3c 2 



would suffice. 



The estimates are all of the same order : so, taking- tin 



