1800.] Ilarmomc Analysis of Tidal Observations. 293 



Since e = 26'9294, * + l-4497 = 14'9144 ; and from (23) 



..... (28). 



If the same notation be adopted as that explained in 4 (the only 

 difference being that we now deal with quarter-lunar instead of 

 quarter-anomalistic periods), we have 



= E'sin 



= R' c 



... (29). 



Secondly, suppose the semi-lunar period indicated by 1 consists of 

 II + III, that 2 consists of IV + V, and so on. Then, obviously, 

 the result is got by writing t + \Tr\a for t ; that is to say, write i ^TT 

 for i and k ^(<r 2/7)777*7, or k ^Tr+rjirjff for k. But yir/ff is equal to 

 ie, and we write k %IT-\-\K for k. Therefore, following the notation 

 used in 4 for N and L, 



"1 



X30). 



SHisin \V m = R' sin (f'+i) R sin (, i) 



These four S's require correction for the disturbance due to the 

 semi-diurnal terms M 2 and S 2 , and I shall return to this point later. 

 In the meantime write 



~l COJ CO8 1T7- I Yl rji 7 COS i IT . 



/ = S h sin i^ + corr - Z } = S ^ sin $V M + corr. (31), 



W~l OJ CO8 



X 



and we have 



^(W4-Z)=-I? 8in(t -i)-.^8in^cos(^ + fe-(-^(2m + l)6),1 



> (32), 

 i(X-Y) = 7? cos(f -i)-^sin^sin(^ + A; + i( 2w + ^HJ 



i(W-Z)= E'sin(^ + t) 



+ l,"| 



> (33). 

 + l)6).J 



If we put 



..... (34), 

 M= 



