52 J1R. A. B. BASSET ON THE MOTION OF 



by successive integration by parts. The above series is convergent for all values of t, 

 and is zero when t = oo. 



For a second approximation, (22) gives 



Let 



r='(t)=fe--fka 



and 



,. = V - M + {(1 - -') fka A/- [' e-* <fr(t v) du. . . (28) 



A. 7T JQ 



Let 



X() = | JV** {-)** ....... (29) 



and (27) becomes 



Whence to a third approximation 



and the last equation becomes 



-u)dn, .... (31) 



and 



-") + V- A( -fka *"^ ~ ") d+ 1 -*^(* -)<. (32) 



We must now express all the above integrals in terms of <f>(t). From (29) we 

 obtain 



o J o 



