S2 Dr. C. V. Burton on a 



and subtracting from this the equation proper to the primary 

 motion, there remains 



d 2 < fr _ _ I'd** . /^\ 



'dt.'dx p "dx ' 



which with (11) gives 



"dx ~ 47r "dt 2 



JF'IG)^'^' 



where 



~ 47T Bi 2 '*' ^ ^ 



J *=j§i^ d *' d y' dz '- • ■ ■ (17) 



Hence the secondary motion gives rise to a force upon a 

 mass m of atomic matter at (#, y, z), the ^-component of 

 which is, by (2), 



_, nF g = _ m ^|iPl i=m X( S ay) ; . (18) 



with corresponding expressions for the y- and ^-components. 

 In (18) F may be written F + SF, where F is the mean 

 value of F, and BF. to a sufficient approximation, represents 

 a variable term, arising from and proportional to the variable 

 pressure-term p, which corresponds to the primary dis- 

 turbance. Thus 



F = F + SF = F-Hp, .... (19) 



by (1); so that (18) becomes 



47T 1 



The mean value of X is therefore given by 



*=-[£ H2 pS'4 • • • ( 21 ) 



18. As the primary wave-motion is now supposed to 

 involve only very great wave-lengths, so that the (primary) 

 pressure-variation throughout the region of space considered 

 is sensibly a function of the time only, and not of a?, y, z, we 

 may write 



p= SB, sin (*« + e,); (22) 



each B being of the nature of a pressure (in general infinite- 

 simal), while the e's are phase-terms. Hence 



H = -SB 55 2 sin(^ + 6J; . . . . (23) 



(_HFp + H^)l, . . (20) 



