ETHEE AND GRAVITATIONAL MATTER. 221 



where /// denotes the attraction on unit of lua.ss at unit distance. 

 Hence writing- for una CA, 7/^//'CA CA~, we see that the attraction on 

 an infinite cokinin under the influence of a force decreasing according 

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

 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 097 Xl(/ cms., and gravity at his surface is 27 

 times'" terrestrial gravity, or say 27,000 dynes per gram of mass. 

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

 section, if of density 5x10^'", and extending from his surface to 

 infinity, would be 9 '4X10"'' 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 majority of the bodies in the uni- 

 verse would each experience infinitelv great gravitational force. This 

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



Sec. 12. Let V be an}^ 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 

 densit}' of the whole matter in the volume V. We have 



M=pY (1). 



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

 tional force at all points of S. We have 



QS = l:;rM = 4;rpV (2), 



by a general theorem discovered by Green sevent3^-three j^ears 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 comj)onent 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 l)e reckoned negative. In equation (2) the 

 normal component force luay 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. 18. Let now the surface l)e sph(M'ical of radius /•. We have 



S=4;rr^;V = ^r';V-|yS .".... (3). 



*This is founded on the following valuen for the sun's mass and radius and the 

 earth's radius: Sun's mass=o24000 earth's mass; sun's radius— 697000 kilometers; 

 earth's radius=6371 kilometers. 



