1890.] Harmonic Analysis of Tidal Observations. 335 



whence, on reducing from inches to feet, 



H,, = 3-98 ft. 



Also * = * + u m = 128-49 + 203-60 = 332'09, 



where the value of u m is taken from (q). 



(s.) Final Evaluation of N and L. 

 Taking the values of P, Q, B, S from (i), 



f,H K sin (&,-./) = -P = -1072, f m Hj sin (ft+y) = +Q = + 0'f 6, 



f-H.cos (-./) = -S = + 7-16, f,H,cos (&+j) = -R = +1-22. 



? ./ lies in 4 th quad., ?i+J lies i n 1 st quad. ; 



whence n j = 56'27. 



Then H = -L cosec (f.-j) x (-P) ; 



i/ 



whence, on reducing from inches to feet, 



H n = 1-04 ft. 



Again, since from (q) j = +6'54, we have f = 49' 73 = 310'27, 

 and *: = n +u n = 310'27 + 9 u -53 = 319'80, where the value of is 

 taken from (q). 



Turning to the second pair of equations, 



ft +j = 28'4. 

 Then H; = 1 sec (ft+;) x (-R) ; 



Im 



whence, on reducing from inches to feet, 



Hi = O'll ft. 



Again, since j= +6'5, we have ft = 21'9, and rj= 

 = 21'9-f 217'7 = 239'6, where the value of ui is taken from (q). 



(t.) Final Evaluation of S 2 and K 2 



From (k) B, = +3'62, A, = +21-08 ; tan , = B * ; 



Ai 

 B, and A, are + , so that , lies in 1 st quadrant ; 



whence f = 971. 



