338 The Rev. Brice Bronwin on the Theoty of the Tides. 



precipitate. Accordingly, none of the oxides are changed 

 either in colour or in chemical character by their union with 

 cotton. The hydrated oxide of copper, for example, precipi- 

 tated upon calico, becomes carbonate, or arsenite, when ex- 

 posed to carbonic or arsenious acid. The protoxide of iron 

 changes speedily in the air into the red sesquioxide, and that 

 again may be converted into prussian blue, or into a black or 

 purple lake — every new compound, if it only be insoluble, 

 adhering firmly to the wool. 



XLIII. 0?i the Theory of the Tides. 



By the Rev. Brice Bronwin. 



[Concluded from p. 270.] 



IF we now take account of a second planet, marking the 

 quantities relative to it with an accent, we have 



3/=F2Cos 2((p-/32) + F'acos 2(<p'-^'2) + Fi cos (f-/3,) 



+ F'iCos(^'-/3\). 



But Fi cos (<p — /3i) + F'j cos (<p'— /S'^) is very small in our seas, 

 and perhaps generally so ; therefore, neglecting it, 



y-Y^Qos 2{f-3^) + F'gcos ^{(p'-^'^). 



We cannot affirm that (S'g is exactly equal to /Sg, though we 

 may suppose their diiference to be very small. Make 



or 



then 



i/ = F2Cos2(f'-/3'2-A) + F'2Cos2(<p'-/3'2). 



^ =- (2;,'n-2^)F,sin2(9'-^',-A)-2p'nF,sin2(^'-/3g 



+ ^^cos2(^'-/3',-A)+ ^cos2(^'-/3y. 



If we suppose the first planet to be the sun and the second 



dF . dF' 



the moon, —r^ is very small compared with -j^, and may be 



neglected. Moreover the variable part of FL contains only 



dF' 

 very small quantities, and in -— ^ they will be multiplied by 



dF' 

 the small quantity v'; we shall therefore neglect — ^. Then 



dt 



dij „ . 

 -77 = gives 

 dt *' 



