526 



PROFESSOR KELLAND ON THE THEORY OF WAVES. 

 25. Also, u = bsm-^ice-x) 



s = h + a sin->r- (c/ — a:; : 



d« ,27r 27r, . 

 " dx A A. 



(it X A 



27r. _„/! S'TT^ . fl_„z,^27r 



f cos( 



Consequently, ^^^^ ^^^,_^_^ ^ .i^^cose = -^ a. 



27r , g cos e siu^ g + sin e cos g (/t + a sin 6) 

 ~ "^ /j + a sin 6 



Multiplying out, this gives 



(a^-6c + 6^sin0)(A + asin0) = 6^«sin^0 + 6^sin0(A + asine), 



or {ag-bc){h + aBm6) = ly'a&m^6. 



Whence we get */,._„. 



hag — noc — o, 

 ag=^bc. 



But 





rfa; rfa du 



and dt dt dx 



da _ du 



hence ST" dx ' 



du _lda__^ ^. 

 'dz~ad7~ s ' dt' 



whence, by substitution, 



(A + asin0)6cos0 = 2acos(9(c-6sin5) + .. 

 hb=2ac 



or if we put for b its value found above, 



c 



/<^ = 2c^ 



That is the square of the velocity of transmission in a triangnlar channel. Is halt 

 ril^a^ oHhe velocity in a rec.ang,Uar channel of the same max.mnm depth. 



