1WK).] Ifarmomc Analysis of Tidal Observations. 281 



Let 



2 = i COB (F, V,) + cos (7,+ F,) = cos V p cos V q ,~] 



A = cos (F,- F f ) - cos (7,+ F,) = sin F, sin F v , | 



1- .... (5). 



= i sin (F,- F f ) -i sin (F, + F,) = -cos F, sin V q . J 

 Also let 



F= S + fcA f = 



.......... (6). 



Then our equations are 



fccos V = 



(7). 

 h sin F = 



A similar pair of equations will result from each H. and L.W. 

 When a series of tides is considered, we may take the mean of the 

 equations and substitute a mean F, G, f, g. 



The general principle here adopted is to take the means over such 

 periods that the mean F, G, f, g become very small. In fact, we 

 shall, in several cases, be able to reduce them so far that these terms 



are negligible, and get simply -- -~S.h V p = -D ; but in other cases, 



where what is typified as the p tide is a small one, whilst one or more 

 of the tides typified as q is large, it will be necessary to find F, G, f, g. 

 The finding of these coefficients is clearly reducible to the finding of 



the mean values of ^(Fp+F,,). 

 sin v p 



Another useful principle may be illustrated thus : if the q tide does 

 not differ much in speed from the p tide, we may put F ? = V p + vt, 

 where v is a small speed. Then we write 



= cos 



+ sin V p { n p sin p R q sin (<,) }. 



If we neglect vip, the condition for maximum and minimum in 

 conjunction with this gives 



VOL. XLVIII. 



hcos Vp = R p coa 



h sin Fj = Ef siu % f E, q sin (vt t ). 



