of Oceanic Tides. 263 



of tidal phenomena, it seemed to give too small an amount 

 of tide. I was therefore induced to try whether, on substi- 

 tuting in the equation (a) an expression for <£ of the same form 

 as that resulting from the previous investigation, viz. 



F(r)cos 2 Xsin2(<9-/^), 



the value of the function F(r) was determinable by the condition 

 of satisfying that equation ; and I found, in fact, that this con- 

 dition is fulfilled if F(r) be deduced from the equation 



tP.V{r) s rf.P(r) 6F(r) = Q 

 dr 2 rdr r 2 



The integral of this equation is 

 F(r)=CV*+J 



in which C and C may be taken to be arbitrary constants. Con- 

 sequently we have at once the following results : — 



= (o 2 + ~\ cos 2 X sin 2{6-pt) } 

 ^ = -2^0^ +^cos*\cos2(d- fit), 

 M =^ = (2Cr- 3 ^)cos 2 Xsin2(^- / ,/), 



^~T ^= 2 (o + ?) cos X cos 2(0-^), 

 osX d& \ ir/ v . ' 



r cos X 



w 



= ^ = -(^+^)sin2Xsin2(^-^) 



The arbitrary quantities C and C must be capable of satisfying 



the given conditions of the problem ; otherwise the solution fails. 



It will therefore be proper, in the next place, to try the solution 



by this criterion. 



One condition to be satisfied is, that at the inferior boundary 



of the ocean the velocity u is zero at all points and at all times. 



Let b be the radius of this surface. Then evidently this will be 



the case if 



op , 3C n a 26 5 

 2(tf— ^=0, or ^- = -3- 



To fulfil another condition, recourse must be had to the expres- 

 sion already obtained for the pressure p. 



In the subsequent reasoning, terms involving a higher power 



