2 ' * L 2 sin fl J 



The Rev, Brice Bronwin on the Theory of the Tides. 193 



tities are insensible, o- and t may be very considerable, since 

 the terms depending on Wg* '^a' "i> ^i "'^y 1^^ negative portions 

 of the displacements. 



We now proceed to find the terms depending upon the 

 argument 2((p — ^g^j ^"^ ^^^^ ^^ '^^y I'^sult from m^, Vj. 



From the first paper of this series we have 



(,____Ai__«i p_. Bi _ giCos9 

 w w * n sin fl w sin 9 * 



Substituting in (3.) the values of Wj and Vj, there result 



1 



^. 

 cos 2(^-^1) +a2i8iiT(l- I sin2 6^ sin 2(«p-gi) J 



If we turn to the second paper of this series, we find 



Dj = w«i sin fl cos 9. 



But Di is the coefficient of sin (f — ^1) in the value of^ 



Now n= — ; but if we consider for a moment the height o' 



the tide at any place whatever, we must conclude that «, is 

 very much less than this quantity, and therefore that the above 

 terms, including a^^ in their coefficients, may be neglected. 



In finding the terms which result from combining Uc^, v^ 

 with Uq, Vq, we must observe that the terms of o- and t do not 

 contain ct, and that we must not employ the differentials of 

 these quantities relative to the time ; thus we shall easily find 

 these terms to be 



e(sin2fl- cos^&)4!?i^B<rcos^f-S^)-h^^{{fiin^Q-cos^Q) 



4-n2A<r— Sn^sind cos 6B(r}siu2(«p— §2)— ^^(A + sinflcos9B) 



4„2 ^ cos 2(^ - Q - 85(sin2 QB + sin Q cos fl A)4«2 &in2(<p - §^) . 



From the first paper of this series we have by comparison, 



(4-) 



tea 



■~ 2» 2- 2n\ ' 



2sin- 



coy*- cos- 

 2 2 



) 



2» sin fl , .6 2»* 

 4n cos* - 



By the substitution of these values the coefficients would be 

 Phil. Mag, S. 3. Vol. 36. No. 242. March 1850. O 



