The Rev. Brice Bronwin on the Theory of the Tides. 345 



and 



E D 



/3, = €, — YY' p^ sin ^, sin v cos v + p,** nearly. 



Change Dj into D, +w' sin^ v, and make 

 Dq _ y + 9' sin^ w 



FT" d; 



in conformity with the similar assumption made in the last 

 paper, and on the same grounds ; then 



^x—^i — n'P^sin ^1 sin t;cos v+ fr + ^ s\\\^v 



^ E, . p . »' <?' . o 3eE, 



= 5i — fv^sm b, sin t; cos t;+ fr + pr- sm-* w+ j^- 



sin ^1 sin t; cos v cos (z— tt). 



Putting for §, its value from (17.)j P^ge 268 (paper referred 

 to), and reducing the result, vs^e find 



1 E 



/3,=^j+jp'+ -sin^osin22'— Y^ sin ^^sinsycostJ — 2^sin(z— tt) 



3^E 

 + q's\nH-\ — =Y^ sin^i sin ucosz;cos (^— tt). . . (20.) 



Here Dj is constant, as in the terms of the first order, and 



&r,Y\ have been changed into /»' and g-'. The last might 



perhaps be put under a somewhat more simple form, but we 

 have not much ground for attempting a general reduction of 

 the quantities Fj and /3j. 



If for any particular place we can make a near estimate of 

 the comparative values of Dj and Ej, we may perhaps be able 

 to put the expressions of these quantities under a better form. 



It is evident from (17.) that they may vary very greatly 

 from one place to another. If the diurnal equation be very 

 small or insensible on our shores, it is possible that it may be 

 very large in some other places. But this will chiefly depend 

 upon the form of the shores and of the bottom of the sea. 



It may happen in some places that the supposition on which 

 we have obtained approximate values of P'gs fi<2. ™^y "^^ ^^ 

 admissible. In that case we must have recourse to the equa- 

 tions (11.), and endeavour to deduce the values of these quan- 

 tities from them otherwise. The values of these quantities in 

 this theory have been deduced from a supposition which we 

 know to be true on our own shores. 



It may not be amiss to ascertain whether the disturbing 

 Phil. Mag, S. 3. Vol. 36. No. 244. May 1 850. 2 A 



