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



as any which can be selected for the trial we propose for all 

 methods computing magnetic declination. I would therefore 

 respectfully suggest to the Magnetical Committee of Obser- 

 vation, that every method be required to fulfill the demands of 

 this test. 



Manchester, Feb. 1.5, 1850. 



XXVI. On the Theory of the Tides. 



By the Rev. Brice Bronwin. 



[Continued from vol. xxxv. p. 345.] 



A T the close of my last paper on the Theory of the Tides, 



'^*- I expressed an intention of examining the terms of the 



second order, considering that there might be some among 



them which might produce a sensible effect. This I have now 



done, but do not find any so large as I had anticipated ; still 



they may be sufficiently large to have a sensible effect on the 



largest of the variable terms in the coefficients, and ought 



therefore to be noticed. 



Neglecting quantities of the third order, and those of the 

 second where s enters, and also putting a=l, p = l, we have 

 Mec. CeL, book 1. chap. 8, No. 35, 



Also 



sin 6'= sin(d+w)= sind + Mcosfl— --tt^sinfl, r'=r+s. 

 These values being substituted in 



neglecting the same quantities as before, and leaving out the 



term -H — -* we find 

 dr 



du dv u cos 9 du dv du dv du cos Q 



d$ "*" ^ "^ sin 9 "*" dSd^"^ d^TQ '^^dQaiHT 



dv cos 9 1 o „ 

 + u-r--r—7 —-u^=0. 

 d'ot sin S 2 



Such is now the equation of continuity ; in the terms of the 

 first order change u and u into u + Au and v + Av. With 

 these values, leaving out the resulting terms of the first order, 

 the last equation gives 



dAu dAv All cos Q du dv du dv u cos 9 

 ~W rfw" sind 'M'd^~ d^~dl sinfl 



/du dv\ 1 2 ^ M^*) 



.,.., 



