84 Dr. 0. Y. Burton on a 



extinction of gravitational attraction as the bodies concerned 

 were removed to distances apart not wholly inconsiderable 

 in comparison with the smallest effective wave-length of the 

 primary disturbance. 



It will be remarked that, when the distance between two 

 bodies is small compared with the mean effective wave-length 

 of the primary disturbance, the attraction between them 

 exhibits only a second order deviation from the Newtonian 

 law of gravitation. 



Motional Forces. 



20. The next question to be considered concerns the forces 

 arising from the motion of neutral matter with respect to 

 the aether. The expressions for these forces, as will appear, 

 contain a factor F 2 , F being (as defined in § 7) the extrusion 

 of aether per unit mass of matter : so that if the mean value 

 F were zero, these forces — which correspond to nothing so 

 far observed — would disappear. 



Let (#, y, z) be the co-ordinates of a particle of mass m at 

 time t, and let (V, y\ z') be the simultaneous co-ordinates of 

 another particle of mass m r , all referred to axes fixed with 

 respect to the general mass of aether. As in § 10, the type 

 of aetherial motion which here concerns ns, and which arises 

 from the motion of m and m', with respect to the aether, is 

 sensibly irrotational. 



Let us consider the forces exerted on m owing to the 

 motion of m\ and let <j> be the velocity-potential at (#, y, z) 

 due to the motion of m' only, while r <2 ~^(x — w') <2 + (y — y*) 2 

 4-(z — z') 2 . Then, the effect of the motion of m' being re- 

 presentable by a source-sink doublet at (a?', y', z') we readily 

 find 



Fm' d'n\ ,„ 



where d'/dt operating on any quantity represents the time- 

 flux of that quantity due to variations of x\ y', z' only. 

 Hence also, 



._ Fm' d /2 /l\ 



■*- 4tt dt 2 \r) 



Fm '_[/!_ 



~ 4tt LV 3 



-S^)fe)+ ■■:• + - 



Ky-y')(z-z f ) dx' dy> 



r h dt * dt 



x-x } d\x f _ y-y ' dfy _ Z-J dVl 

 r> dt 2 r* dt 2 r» dt* J" ' * ^ 



