30 ME. G. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 



Differentiating (48) it will be found that 



2-r 2 2-n-x dx 0'67x2 



-- --- ~ ~ ~ 



^ = --- TT\ 7T 



Since y is small, h^ and A 2 may be taken as a and b in places where they are not being 

 differentiated. Hence, since a/b = 1'8*, the right-hand side of (51) is equal to 



- 2 - 



a M ) 2-7T -= 



\Aj/ ci 



Differentiating (50) 



d //tj\ _ a 4oj sin X 



" ""~ 



(53) 



Combining (52) and (53) with (47) 



t*nfl = *? = 21cT_ a 4o,sin_A\ 



dy 27rx b c 



In (54), T = 12'4h., and from (43), 



, 2-rrX 



cot ^-= 244, 

 cJ 



hence 



cosec a ^=l+(2-44) 2 = 7, 

 also 



w, the angular velocity of the earth in radians per hour is , and sin A = 079. 

 Hence 



tanfl = 4 x |^x 079 = 0'88 



7 x 2-n- 24 



and 



9 = 41. 



The agreement between this and the measured angle, 36j, is quite as good as 

 could be expected. 



* See equation (45). 



