162 



It may be noted that 7 (gamma) is an angle which is m,easured in 

 radians, if a is expressed in radians per second, or in degrees, if a is 

 expressed in degrees per second: 



Substituting the expressions for M and P, from equations (219) and 

 (220) in equations (221) and (222), and solving for N and Q 



N=(Ai cos ai—Ao COS ao COS 7) /sin 7 (224) 



Q= — iAi sin ai — Ao sin ao cos 7) /sin 7 (225) 



323. Component tides. — ^Substituting the expressions for the con- 

 stants found in the last paragraph, equation (211) becomes: 



y=[Ao cos ao cos (ax/c) 

 + (^1 cos ai—Ao cos ao COS 7) sin (ax/c) /sin 7] cos at 



— [Ao sin ao cos (ax/c) 



+ [(^1 sin (Xi~Ao sin ao cos 7) sin (ax/c) /sin 7)] sin at 

 = {Aq cos ao [sin 7 cos (ax/c)— cos 7 sin (ax/c)] 

 -\-Ai cos cci sin (aa^/c) }cos at /sin 7 



— {^0 sin Q;o[sin 7 cos (ax/c)— cos 7 sin (ax/c)] 



-\-Ai sin «! sin (ax/c)] sin ai/sin 7 

 = [^0 cos ao sin (y — ax/c)~\-Ai cos ai sin (ax/c)] cos a^/sin 7 



— [^0 sin ao sin (y — ax/c)-\-Ai sin ai sin (ax/c)] sin at /sin 7 

 = [(^0 cos ao cos at—Ao sin ao sin at) sin (y — ax/c) 



-{-(Ai cos «! cos at—Ai sin ai sin a^ sin (ax/c)]/sin 7 

 =^0 cos (a^+ao) sin (y — ax/c) /sin 7 



+^1 cos (a^+ai) sin (ax/c) /sin y (226) 



Since, from, equation (223): 



ax/c=(x/L)y (227) 



equation (226) also may be written: 



y=Ao cos (a^+ao) sin (1— ar./i/)7/sin 7 

 +^1 cos (a^ + «i) sin (x/L) y/sin 7 (228) 



324. Component currents. — The equation of the corresponding com- 

 ponent of the current, obtained by substituting in equation (215) the 

 sam,e expressions for M, N, P, and Q, similarly reduces to: 



v=(g/c)Ao sin (ai + ao) cos (y— ax/c) /siny 



— (g/c)Ai sin (at+a^) cos (ax/c) /sin 7 (229) 



And this equation may be further transformed into: 



v=(g/c)Ao sin (a/ + ao) cos (1 — x/Z)7/sin 7 



-(g/c)Ai sin (at+a^) cos (x/L)7/sin 7 (230) 



