PROFESSOR KELLAND ON THE THEORY OF WAVES. 507 



it is = I (p -p') dy- 1''^'^' p dy 



C dz P' + T' , 



dz 1 2</a; da. 

 -^^ dx 2^ dt dt 



/ dz 

 ^'''gg{z-y)dy involves a^ as a factor. 



Hence the accelerating force is 



da 



d^x _ dz dx dt 

 U" ~^~di^'dl' ~^ 



But it has been shewn (Art. 2), that 



But 



J dx , . 2'K , ^ . 



and -;- -= o sin ^-— (ct—x) 



dt X ^ ^ 



where b is supposed undetermined. By substituting these values, we get 



■dx 



2'wb a I dx\ 2'jr a dt 2'Kac 



—:r . COS 



a I dx\ 2'jr n dt 2'Kac n 



a I c \ = o a . -^— cos a . — ;- — . cos tf 



\ dt I A h K 



2irb n , , ■ ci\ 2* /, 2'Kacb . „ a 



at — ;r — . COS V (c — b sm t7) = -.r— ya cos a i^-; — . sin a cos o : 



A. \ ■ A« 



and, equating coefficients, we get 



bc—ga; i^=——; 



Iwhence *=^ 



ac ■J 



■ah ) 



the values which we obtained before. 



8. Next, having these approximate formulae as our guide, let us proceed to 

 the general solution of the problem. 

 Retaining the same notation. 



