SECONDARY ÜNDÜLUTIONS OF OCEANIC TIDES. 63 



where A^-i-dA,, = — p f-~ sin- _i^ dx , 



C, + Ja - i llÙ^LÇL co.^ ^ dx . 

 ^ 2 Ir J b I 



Hence, we get'-' 



-2 C. + oC, y{oC,, ,-p^jA„ „y 

 ^' A, + dA "^ A,A,,{pJ-p:r) 



■ A + oA,' 

 or denoting the period of the k th harmonic l)y T^ , 



/I . n JCTTX 7 

 Sin" dx 

 ^ S I 



^P'^^ ^^^ rlcos-^^cZo.' 

 J b I 



Pntting S=Sf, + AS and b = b,, + ^b, and neglecting the sqnares and 

 the prodncts of AS and âb, we get 



fsin^ i!^ dx { r^' sin^ I^dx f ^ cos'- i^!^ fZ^] 



^ ^ I COS" dx I sm- cte / cos- dx 



J I y J I J I 



where //,= — • If the integration Ix^ effected between the hmits 



and /, we get 



21 



n = 



kv^ghj"^^ 2 A, 2 27,, 2 j V v„ ^ ?>„/ / J ' ' 



where ^u = Z?^ , v^ = IS^^ , 



JA = fAbdx, Av=fjSdx. 



The above expression can also be transformed into a simpler 

 form : 



*) Eayleigh, Theory of Soiind, 2ik1. Edition, Vol. I. p. 115. 



