The Rev. Brice Bronwin on the Theory of the Tides. 343 



The other particular integral of (7.), when 2=2, found by 

 means of the above, is 



bg cos d ,^ . o .. 



SO that the complete integral is 



A,= ^. + *S^»(2 + sin'«). 

 sm"^9 sm'^fl ^ ^ 



This is the form in which I first found it. But each of these 

 particular integrals is infinite at the pole. Make 



1 



2 

 then 



The second of these particular integrals is infinite at the 

 pole J we must therefore make Cc^ = 0. Then 





K 



_ /I— cos 6 COsfl\_ ^2 / 1 -\ 



\^cos^2 / 



/_l__X+2sin4\=a,sin4/-^+2\ 



(l+Scos^l), 



2sind 



sm- 



COS"'- 



2 



which is also a particular integral of (7.), and the value before 

 given to Ag. 



From (19.) and (20.) we may find equations containing A 

 only, or B only. By elimination and differentiation, and then 

 eliminating again, we shall easily find 



(i2_4cos29)r2'l^ + (9i2_4-16cos2a)r^ + (16?"2-16)A = 



(/2-4cos2fi)r2^ + (9i"2-4-16cos2fl)r^ + (l6i2-16)B = 0. 



The integrals of these are obtained by assuming A = Cr'", 

 B=Dr'", and each of them gives the same values of wz, and 

 these will be found the same as those before obtained. 



Suppose, for the sake of illustration, that there is only one 



