PROFESSOR KELLAND ON THE THEORY OF WAVES. 



dx dx 



and similarly of the others. 



=Q (7) 



dx 



ttZ+ d h x -=<> W 



Thus it appears that b is constant, or at least varies only periodically, 

 Also a (z+hax)=f(z) by integrating 8. 



/C*) 

 = T" 



2 + /t a # 

 X- 



Let \ o be the value of A when a?=0 

 A=? 



M 



from which equation we learn that the length of the wave diminishes directly as 

 the depth diminishes. 



COR. The length of the wave varies as the depth, in the case in which motion 

 extends throughout the fluid. 



55. Again, from equation (6) we obtain 



,/,. (*-0 j? 



dx~ at 



x c t d . 

 . -- T- log a 

 / dx 



_ -_ 



t dx z+hax 



_x ct a 



t ' z+&az 



dc a _ ax 



dx z + h ax c ~t(z + h ax) 



_ xdx , 



- -ax 2 +<? 



ax z + h 1 . . 



= log - - -- h - . - - -- hF () 

 at z+h at z+h ax 



c =1 (z + h-ax) logil + + .TA^F F (.) 





=1 (, + *-) log (l-^) + f*+ (c.~ Z -~) 



+ A aa: 



