of Oceanic Tides, 261 



having reconsidered the argument from which it was inferred 

 that the forms of the arbitrary functions contained in the ex- 

 pression for <f> might be determined by satisfying the given con- 

 ditions of the problem before obtaining by integration the general 

 value of that function, I became convinced that the intervention 

 of the general value is indispensable, and that the forms of the 

 functions must be ascertained by means of the equation 



The mode of using the equation for this purpose will be exem- 

 plified by the new solution of the problem I propose to give in 

 this communication. 



Although for the latter reason the theory of tides contained 

 in the January Number must be pronounced to be erroneous, 

 the general considerations by which it was prefaced may still be 

 regarded as applicable to this and other hydrodvnamical pro- 

 blems; and I may say also that this attempt was indirectly the 

 means of suggesting the solution I am about to offer, which w T ill, 

 I hope, be found to be free from objection. 



It will be supposed, as before, that the solid part of the earth 

 is spherical, that it is wholly covered by water, the depth of 

 which is uniform and small compared with the earth's radius, 

 and that the attracting body revolves about the earth in the 

 plane of the equator at its mean distance and with its mean an- 

 gular velocity. In order to abstract from the earth's rotation, 

 an equal angular velocity will be supposed to be impressed on 

 the earth and the body in the opposite direction, so that the 

 earth will have no motion. Centrifugal force will not be taken 

 into account, because the waters under the action of this force 

 alone would move as if they were solid, and consequently its 

 effect, according to the preliminary considerations above referred 

 to, cannot be included in an investigation which assumes that 

 udx + vdy-\-wdz is an exact differential. Also the only periodic 

 effect of centrifugal force is that which arises from the periodic 

 motion of the water in latitude, and, under the circumstances 

 supposed, is so inconsiderable in amount that, to avoid complexity, 

 it will be disregarded. For the same reason the small effect of 

 the spheroidal form of the earth is left out of account. It is evi- 

 dent, since the motion consists of small oscillations proper to a 

 fluid, that we may put (dcf>) for udx + vdy + wdz. 



This being understood, let the earth's centre be the origin of 

 rectangular coordinates, and, A being the north latitude, and 6 

 the longitude west from Greenwich, of any particle distant by r 

 from the origin, let 



a?=rcosXcos0, y=rcosXsin#, 2'=rsin\. 



