36 MK. AIKT ON TBB LAWS OF THE TIDES 



S 

 exposed to the open sea, Laplace found ^ = 0*33. I imagine that, as r^ards the 



son's position in dectination, the present series of tides may be supposed to give a 



value for ^ differing very little from the mean, but rather too small than too great. 



If so, here is an undoubted dtscordanoe. Yet it is remariiable that the series of 

 numbers in this table presents a still greater discordance under circumstances where 

 we should hardly expect it. The littoral station of Castle Townsend is fully open to 

 the Atlantic ; and those of Dnnmore East, Kingstown, and Clogher Head, are more 

 and more subject to the effects (whatever they may be) of the inclosure of the Irish 



Channd. Yet all these stations, including Castle Townsend, give for ^ a value of 



about 0-28. 



In speculating on the causes of these discordances, it is important to observe, that 

 the rdatkm of the succesave changes of a progressive tide may be considered in two 

 different ways. One of these ways is applicable properly to rivers and similar chan- 

 nd; it consists in assuming that each semidiurnal tide is neariy independent of 

 every other semidiurnal tide, and that the quantities of the second and higher orders 

 of the range are sensible*. The other is applicable to open seas, where the vertical 

 oscillation is insignific;ant in comparison with the depth, and where the alteration of 

 the horizontal sur&ce, by the shoaling of the shore, is perfectly unimportant ; here 

 the principle of the superposition of small movements applies, and the solar and 

 lunar tides may be considered as perfectly independent. Thus considered, the dis- 

 cordance to which I have alluded may be stated thus: the lunar tide at Castle 

 Townsend is less than that at Kilbaha, in the proportion of 8' 13 to 9*82, but the solar 

 tide at Castle Townsend is less than that at Kilbaha, in the proportion of 2'4 to 4-Q. 

 There can be no doubt that in the lunar tide, the difference between 8*13 and 9*82 

 depends (among other circumstances) upon the periodic time of the tide^ inasmiH;h 

 as a tide infinitely slow would produce the same efiect at both stations ; and there- 

 fore we must not be surprised that the solar tide, whose recurrence is more rapid 

 than that of the lunar tide, should undergo a larger proportional alteration, like that 

 between 2*4 and 4*0. 



In another section I shall show that between Dnnmore East and Kingstown, the 



tide is suddenly and completely reversed, high water at one of these stations corre- 



sponcfing exacrtly (in time) to low water at the other ; while from Donmore East to 



Donaghadee, there is scarcely any perceptible difference of phase. It is worthy of 



S 

 remark, that during these changes and coincidences, the value of ^ is unaltered. 



The remarkable change in the values of ^ at Port Rush, Ballycastle, and Glenarm, 

 depends also, without doubt, upon the difference of the modifications produced in the 



* EaKTdopoB&i Metn^K^tana, TUet mmd Wmxs, Sectioii lY.. SubMctiam 3. 



