16 
MR. a. 1. TAYLOR OX TIDAL FRICTIOX IX THE IRISH SEA. 
Substituting in (2l) from (18), (19) and (20), 
= average value of ^gp j” D f Hj — \ g gin 6 ) 
cos ^{t + TO V cos y (^ + T,0 sin 0 dsj. 
Since the only terms which contain t are 
cos^(^ + T0 and cos^(^ + To), 
we can integrate them with respect to t to find the average value of the main 
integral. Thus tlie average value of 
cos Y (^ + Ti) y ('" + "I'o) 
is evidently 
Hence taking out all the quantities which are nearly constant across the section 
= ^gp\ sin B cos ^ (Ti-To) D ( H, 
2wv sin A 
9 
s sin Oj ds. 
( 22 ) 
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 
2wv sin X 
9 
s sin 0 ds 
is zero. 
If the channel had not happened to be nearly 
imiform in depth, it would have been possible to evaluate this integral from the 
charted depths across the section. Hence 
= ^gpY sin 0 cos ^ —'I'o) DHiL. 
(23) 
where L is the length of AB, 50 nautical miles. The numerical values of the other 
constituents which occur in (23) are 
g = 981. 
p = density of sea water = 1*03. 
V = 3'2 knots = 163 cm. per second. 
6 = angle between current and direction of AB. 
