MR. G. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 19 



da- being an element of surface, and the integral extending over the whole surface of 

 the Irish Sea included between the two sections AB and RC. 



The potential of the moon's attraction on the sea is represented by the function 



0=11 fft'- cos**)* (28) 



111 



where 



~1 is the constant of gravitation. 



M is the mass of the moon. 



D,,, is the radius of the moon's orbit. 



R is the earth's radius. 



3- is the angle between the line joining the centre of the earth to the moon, and 



the radius of the earth which passes through the point on the earth's surface 



which is being considered. 



If X be the latitude of the place (i.e., 52 in the case of the Irish Sea), and if be 

 the angle through which the earth has turned relative to the radius vector to the 

 moon, since the moon was on the meridian, then by spherical trigonometry, 



cos & = cos X cos (29) 



Also, if 2H be the range of tide at the place which is being considered, 



where <f> is the phase' of the tide at the time when the moon crosses the meridian. 

 Combining (26), (28), (29), (30), it will be seen that 



(-2T 

 m = - ~ 



MR 2 f 2 "' 



PI -p cos 2 X cos 2 (<(> + < ) d (cos 2 0) 

 D m Jo 



MR 2 j ( 2 \\ /Ql\ 



3 sm n (cos X). . . . _ V-U 



(31) may be written 



nE\/M\/R 3 \-R 



m == -th-pH cos a X sin 2 ^ j ( g H'-pl/ K - 



where E is the mass of the earth. 



-J is the attraction of the earth at its surface, i.e., 



-tli 



^^ = g = 981 in C.G.S. units. 



* See LAMB'S 'Hydrodynamics,' p. 339 (1906 edition). 

 D 2 



