58 Art. 9.-T. Ter.'ula: 



The same substitution makes (0), for progressive waves toward N, 



JX= co^7it — ax-{- — + (p), 



an ^ '2 / 



.(90 



fxn 



JZ= — '— cos())t — ax), 

 [Jtn 



and for retrograde waAes toward S, 



JX=— üm(nt-{-ax + <f), 



^^" _ } (9") 



JZ=—-^ äm()}t + ax-h^] 

 im \ 2 / 



Hence for the case of stationary waves (7'), tlie ratio of tlie 

 amplitudes of Z and A^ is given by 



ÂZ 



JX,„ A 



cotg ax (11) 



which can assume any value whatever between — cc and +x, 

 as we proceed normal to tlie wave ridges. Moreover, âZ is 

 retarded after âX by <p given by (10). 



Again, in the case of progressive and retrograde waves, 

 the ratio of the amplitudes is 



^^=^=— ^= (12) 



JA„, A V/?- + r 



which is always less than, and tends to, unity as the frequency 

 decreases, since 



^^=^9- + r=V'a^+l6;ry^W (13) 



Besides, âZ lags behind JA" by f + ^ or f— if according as the 



Avaves are progressive or retrograde. 



Now, the angle determining the pliase is given by 



to- c = J— — l'^"-' " ^^ ^■^' i ^-'khv — é 



which becomes zero for small value of kn and tends to unity for 

 large values. Hence, in the case of stationary waves, the 

 retardation of the vertical component will increase from to 

 -^ when kn increases from to c/: . In the case of progressive 



