Modified Theory of Gravitation. 83 



and (20) becomes 



. X = 4- HF2B, s 2 sin (st + e s ) . L 



- -f H 2 SB S sin (st + 6 S ).^B S s 2 sin (st + e.) . I*. (24) 



There is thus a gravitative field at (57, y, z) defined by the 

 average values 



(X,Y,Z) = -^-SB s 2 .^(I I ,I y) I.-) 



... (25) 



Within the limits of our assumptions, there is seen to be 

 universal mutual attraction of electrically neutral matter, 

 the Newtonian constant being 



G=^ p tB 2 8 s 2 (26) 



07T 



19. It has been pointed out above, as an assumption 

 essential to the theory proposed, that every effective wave- 

 length of the primary petherial disturbance must be very great 

 compared with the distance between any mutually attractive 

 bodies for which the Newtonian law of inverse squares has 

 been closely verified. It may be worth while to indicate 

 very briefly what would result if this condition were not 

 realized. By way of illustration, let the primary disturbance 

 take the form of plane progressive waves of harmonic type 

 and of definite wave-length \. Two bodies whose line of 

 centres was perpendicular to the direction of propagation of 

 the waves, and which were at a distance r apart, would 

 attract one another with a force proportional to 



r~ 2 cos 27rr/\, 



which, as r is increased, changes sign periodically at intervals 

 of \\. (If, in place of a single wave-length X, there were a 

 continuous distribution of wave-energy over a wide range of 

 wave-lengths, there would simply be a falling off of attraction 

 between the two bodies at a rate more rapid than that of the 

 inverse square of the distance-) 



With the primary disturbance in the form of progressive 

 waves travelling in one direction (as above) the case of two 

 bodies in a line not perpendicular to that direction would be 

 more involved ; but if the primary waves were travelling in- 

 differently in all directions, there would merely be a gradual 



G2 



