168 Lord Kelvin on Ether and 



terrestrial gravity, or say 27,000 dynes per gramme of mass. 

 Hence the sun's attraction on a column of ether of a square 

 centimetre section, if of density 5 x 10 — 18 , and extending from 

 his surface to infinity, would be 9'4 x 10~ 3 of a dyne, if ether 

 were ponderable. 



§ 11. Considerations similar to those of November 1899 

 inserted in §9 above lead to decisive proof that the mean 

 density of ponderable matter through any very large 

 spherical volume of space is smaller, the greater the radius ; 

 and is infinitely small for an infinitely great radius. If it 

 were not so a majority of the bodies in the universe would 

 each experience infinitely great gravitational force. This is 

 a short statement of the essence of the following demon- 

 stration. 



§ 12. Let V be any volume of space bounded by a closed 

 surface, S, outside of which and within which there are 

 ponderable bodies; M the sum of the masses of all these 

 bodies within S ; and p the mean density of the whole 

 matter in the volume V. We have 



M= P Y (1). 



Let Q denote the mean value of the normal component of 

 the gravitational force at all points of S. We have 



QS = 4wM=47r / oV (2), 



by a general theorem discovered by Green seventy-three 

 years ago regarding force at a surface of any shape, due to 

 matter (gravitational, or ideal electric, or ideal magnetic) 

 acting according to the Newtonian law of the inverse 

 square of the distance. It is interesting to remark, that the 

 surface-integral of the normal component force due to matter 

 outside any closed surface is zero for the whole surface. If 

 normal component force acting inwards is reckoned positive, 

 force outwards must of course be reckoned negative. 

 In equation (2) the normal component force may be 

 outwards at some points of the surface S, if in some places 

 the tangent plane is cut by the surface. But if the surface 

 is wholly convex, the normal component force must be every- 

 where inwards. 



§ 13. Let now the surface be spherical of radius v. We 

 have 



4-7T 1 



S = W; V=^>; V=^rS. . . . (3). 

 Hence, for a spherical surface, (2) gives 



Q= -3-^=^7 (4). 



