SECONDARY UNDULATIONS OF OCEANIC TIDES. 59 



„,,, ..2 IGPa'bJp . , 27Tt 



r/ib-pç^ -^ ^j^. sm- 



TVi T ' 



where Iq is the vakie of ^ at x=o, and P is of the dimension 

 of a number. Neglecting the potential energy outside the bay, 

 which is very small, we have 



4:aH''bp . „ ^Ttt cclhgp .^IttI 16 Pa'lrl'p . „^rrt 

 rp2j^ sm- -^ + —^ cos- -^ + ^^ sm-— = const. ; 



the relation is to be satisfied for all values of t. 



T 

 4 



Putting ^=0 and also t=^-f, we get 



a-hlc/p , 

 ii- = const., 



4 



-, àa-Php , 16 Pa-Pb'p , crblc/p 

 and — TT, — — + ~ = const. = ^^^ 



Hence t^^^(i + 4:F±^ 



gh 

 l/gW 



or ^=Ä(' + ^^t)' (2) 



Lord Rayleigh found the reaction of air upon a vibrating 

 rectangular piston, whose length y is very great compared with 

 its breadth h, to be equal to the addition of a mass 



V f?j , Jib \ 



9_ 



where r is Mascheroni's constant and = 0.5772, and ^^ = ^, -^ bein^- 

 the wave length. If the reaction be uniform over the piston, 

 we have for y=^h, 



111? 



W ( 3 , nb \ 



-(,-2-/--log-2-J- 



Now, in a problem of long waves, we usually neglect ver- 

 tical acceleration and consider the horizontal acceleration nearly 



