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

 Consequently 



^(^~^^ rrv-v'-avVcos (z' -Ti') -l-sm''-o{vcos2z- v' cos2z'), 

 dt ^ ' 2 ' 



neglecting the terms containing the very small quantities ve 

 and - sin^ o vV. 

 Again, by (17.)» 



^!^3zl3l = isin^ oleosa,'. ^ - cos 2^'^) -2^^cos(2-7r) 

 dt 2 \ dt dt; dt 



dz' 1 



+ 2^' -J- cos (2' — tt') = - sin^ o( v cos 22 — v' cos 2^') 



+ 2vVcos (^' — w'), 



neglecting the same small quantities as before. And 



d{^^-^'^) ^ d{^-l^ 

 dt dt 



very nearly ; therefore 



ndt ~ ndt ndt n n 



very nearly. Hence we have 



v' 

 8=1--. 

 n 



It would be better to divide the numerator and denominator 



F. 

 of the value of tan 2(<p'— /S'g) by Fg, and reduce -~ 8 to its 



simplest form. 



If we wish to make 8«; a complete variation relative to r and 

 ■Bj, the equation of condition is, leaving out the terms contain- 

 ing (s) as before, these being insensible, 



4- ^r^ sin^ 5 ^ + 2«r2 sin fl cos d '|^1 = - 2«r sin^ d -^. 

 rfr L dt^ dtj dtsdt 



Make 



^- =A sin/((p— ^), sinfl^ =Bcosi(f — §), 



A and B being functions of r and fl without A By substitution 

 and dividing the result by n sin 9 sin 2(<p — ^), we have 



-^ { - apr^B + 2r2 cos fl A } = 2?>B, 



