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



Substituting in (21) from (18), (19) and (20), 



W n ,, = average value of j gp\ D ( H, -- - s sin 6 J 



(_ J A \J 



cos ^ (t + T,) V cos ^ (/ +T,,) sin 6 d* j. 

 Since the only terms which contain t are 



and cos 



we can integrate them with respect to t, to find the average value of the main 

 integral. Thus the average value of 



2-7T/. , ,p 

 COS -7=- (t + 1 ] 



is evidently 



icoS-rJ(T, ' 



Hence taking out all the quantities which are nearly constant across the section 



W,,,, = $gpV sin e cos ^ (T, -T () ) f D f H, - 2t r Sm X s sin 0) da. (22) 



JA g I 



To evaluate this it is only necessary to measure the depths at all points across. the 

 section. Actually this is not really necessary, for the depth is nearly uniform across 

 the section AB, the average depth being 37 fathoms. 



Under these circumstances, since the origin of s is taken at mid-channel, the value 



of D- s Bin 6 da is zero. If the channel had not happened to be nearly 



JA g 



uniform in depth, it would have been possible to evaluate this integral from the 

 charted depths across the section. Hence 



. . ..... (23) 



where L is the length of AB, 50 nautical miles. The numerical values of the other 

 constituents which occur in (23) are 



# = 981. 



p = density of sea water = 1'03. 

 V = 3'2 knots = 163 cm. per second. 

 6 = angle between current and direction of AB. 



