ETHER AND GRAVITATIONAL MATTER. 221 



where m denotes the attraction on unit of mass at unit distance. 

 Hence writing for mw CA, mwQA CA ". we see that the attraction on 

 an infinite column under the influence of a force decreasing - according 

 to inverse square of distance is equal to the attraction on a column 

 equal in length to the distance of its near end from the center and 

 attracted by a uniform force equal to that of gravity on the near end. 

 The sun's radius is 697 XlO 8 cms., and gravity at his surface is 27 

 times" terrestrial gravity, or say l ; 7.o<><> dynes per gram of mass. 

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

 section, if of density 5 XlO -18 , and extending from his surface to 

 infinity, would be 9*-fXlO" 3 of a dyne, if ether were ponderable. 



Sec. 11. Considerations similar to those of November, 1899, inserted 

 in section 9 above lead to decisive proof that the mean density of pon- 

 derable 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 majorit}^ of the bodies in the uni- 

 verse would each experience infinitely great gravitational force. This 

 is a short statement of the essence of the following demonstration: 



Sec. 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=pV . (1). 



Let Q denote the mean value of the normal component of the gravita- 

 tional force at all points of S. We have 



QS=-l7rM = 47rpV (2), 



by a general theorem discovered by Green seventy-three years ago 

 regarding force at a surface of any shape, due to matter (gravita- 

 tional 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 inward is reckoned positive, force 

 outward must of course be reckoned negative. In equation (2) the 

 normal component force may be outward at some points of the sur- 

 face 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 

 everywhere inward. 



Sec. 13. Let now the surface be spherical of radius r. We have 



S=4*rr»; V^r 5 ; V=|rS (3). 



"This is founded on the following values for the sun's mass and radius and the 

 earth's radius: isun's ii]ass=.">24000 earth's mass; sun's radius=697000 kilometers; 

 earth's radius=6371 kilometers. 



