MR. 0. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 5 



is not sufficiently great to give rise to much difference between the square root of the 

 mean square of the velocity and the mean velocity, or between this and the cube root 

 of the mean cube of the velocity. By taking V = 2^ knots =114 cm. per second 

 in (8) we slightly under-estimate the friction ; we shall not in any case over-estimate it. 

 Using in (8) the value K = 0'002,* and remembering that p, the density of sea- 

 water, is 1'03, it will be found that w. the mean rate of dissipation of energy, per 

 square centimetre per second, in the Irish Sea at spring tides is 



/ A \ 



-ir = 0'002(r03)(ll4) 3 ( J = 1300 ergs per square centimetre per second. (9) 



Using the least admissible value of Kt it will be found that 



w = 1040 ergs per square centimetre per second (10) 



Mr. STKEET'S estimate, when reduced to C.G.S. units, is 7 ergs per square 

 centimetre per second, which is only yr,?v th of our minimum estimate.! 



Rate at which Energy enters the Irish Sea owing to the Action of External Forces. 



The amount of dissipation found by the method just described is so different from 

 that obtained by Mr. STREET, and so much larger than any previous' estimate of 

 tidal friction that I have come across, that it seemed worth while to try and verify 

 it, if possible, by some different method. Instead of trying to measure the rate of 

 dissipation at every point of the Irish Sea, I have calculated the rate at which energy 

 enters the Irish Sea through the North and South Channels. To this must be added 

 the rate at which work is done by lunar attraction on the waters of the Irish Sea. 

 The sum of these will give the rate at which the energy of that sea is increasing. 

 plus the rate of dissipation of energy. When the average values of these expressions 

 are taken during a complete tidal period it is evident that, since the energy of the 

 Irish Sea does not increase or decrease continually, the average value of the rate of 

 increase in energy is zero. Hence the average rate of dissipation of energy by the 

 tidal currents can be found. 



Rate at which Energy flows into the Irish Sea. The calculation of the rate at 

 which energy flows into the Irish Sea is very simple, Consider the flow of energy 

 across the surface, S (fig. l), formed by the vertical lines between a closed curve, s, 

 on the surface of the sea and its projection on the bottom. 



* See equation (7). 

 t See equation (4). 



J Mr. STREET informs me that since publishing the paper already referred to, he has obtained other 

 results which confirm his previous results. He hopes to publish them when circumstances permit. 



