f !890.] Harmonic Analysis of Tidal Observations. 333 



W = -15-99 X = +12-75 



Z = + 7-53 Y = + 0-16 



W + Z = - 8-46 X+Y = +12-91 



W-Z = -23-52 X-Y = +12-59 



= - 4-23 i(X+Y)= + 6-46 



i(W-Z)= -11-76 (X-Y)= + 6-30 



(q.) Computation of Astronomical and other Constants. 



Find s<>, the moon's mean longitude (see ' Nautical Almanac,' 

 Moon's Libration), and h the sun's mean longitude (sidereal time 

 reduced to angle) from the 'Nautical Almanac," and p the longitude 

 of moon's perigee, from Baird's Manual,* Appendix Table XII 

 (there called TT), at the epoch O h , January 1, 1887, Bombay mean 

 time, in E. Longitude 4 h '855. 



From Baird, Tables XIV, XV, XVIII, find N the longitude of 

 Moon's node, and I, v, at mid-period, February 14, 1887.f 



With the value of /find i m from XIX (1) for the tides M 2 , N, L ; 

 from XIX (3) find f for the tide ; from XIX (8) find f ' for the 

 tide K T ; from XIX (9) find f ' for the tide K 2 ; from XX find v for 

 the tide Kj ; and from XXI find 2v" for the tide K 2 . 



The results are 



s = 359-43, h = 280-63, p = 165-36. 



v = -9-60, = 9-00. 



l/f = 0-9709, l/f = 1-161, f = 0-915, f" = 0'802. 



v ' = -6-30, 2*" = -11- 75. 



Then compute initial equilibrium arguments, in the symbol for 

 which the subscript letters indicate the tides referred to, 



u = (ho-i>)-2(8 -fi +JT, tt, = 0, 

 = 203-60, = 3 c -37, 



for K!, u' = 1i 9 fa for K 2 , u" = 2^,-2v", 



= 196-93, = 213-01, 



= m (*o P) , Ul = U m + (S p) + T, 



= 9-53, = 217-67, 



= 169-37. 



* ' Manual for Tidal Observations,' by Major Baird. Taylor and Francis, Fleet 

 Street, 1886. 



t In making these reductions I have really used the value of N for July 1 , 1887, 

 because I am operating on tidal predictions made for the whole year 1887, winch 

 were doubtless made with mean N for that year. The difference is almost insen- 

 sible. 



