40 MR. AIRY ON THE LAWS OF THE TIDES 



the high water at Kingstown coincides precisely with the low water at Dunmore East, 



and vice versd. Moreover, between these two stations occurs the station Courtown ; 



and here, as will appear in Section XVII., the semidiurnal tide is nearly insensible. 



The difference in the times at Dunmore East and Kingstown does not therefore arise 



from a slow transmission of tide ; but arises from a sudden inversion of the wave, the 



point which separates elevation from depression being not far from Courtown. And 



the question now is, whether, on the supposition that the tide-wave enters the Irish 



Sea by this southern entrance, it is possible to explain the existence of this neutral 



point and the inversion of the tide beyond it. 



The explanation which I have to give rests upon a proposition long known to me 



as a matter of theory, but for which I never expected to lind a practical application. 



In the Encyclopaedia Metropolitana, Tides and Waves, Art. 307, I have shown that 



when the tidal wave enters a gulf (considered as a canal of uniform breadth and 



depth, stopped by a transverse barrier), the expression for the elevation of the water at 



^ 



the time ^ at a point whose distance from the sea is x^ is sin w/+B.cos ma—mx ; 



cos Wfl 



where n is the constant proper to the periodic time of the tide-wave, —=^^x depth, 



and a is the whole length of the canal. This expression shows that the vertical 

 oscillations are simultaneous throughout ; the coefficient in each place being 



^ 



cos ma— mx. Now if the canal is so long and so shallow that ma is greater 



cos ma 



T , . t . T 



than g; then, on taking x=a—^ the coefficient vanishes ; and on taking .r greater 



than a—— the coefficient changes its sign. This case then agrees, as regards the 



simultaneity and the inversion, with the case of observation before us, and all that is 

 necessary for its complete application is, that the virtual head of the channel be sup- 

 posed to be at a distance from Courtown equal to that which a progressive wave 



would pass over in 3^ 5"* (which would make ma=^). Without professing myself 



able to enter into details upon the depth of the water and the form of the supposed 

 channel, I express my belief that this solution does accurately apply here : and I re- 

 gard it as one of the most remarkable cases that has ever been noticed in the obser- 

 vations of tides. 



Assuming then that the tide of the Irish Sea is explained, we have only further to 

 explain the apparent passage of the tide through the North Channel. This is merely 

 a case of the proposition in Art. 310 of the Tides and Waves, relating to a canal join- 

 ing two tidal seas, from which it appears that there will always be in such a canal an 

 apparent passage of the tide-wave in the same direction at every part. To represent 

 the circumstances completely, it would be necessary to introduce the consideration of 

 friction. 



