1890 ] Harmonic Analysis of Tidal Observations. 279 



When a question of this kind is attacked, the solution cannot be 

 deemed complete unless the investigation is left in such a state that 

 an ordinary trained compnter is able to use it as a code of instruc- 

 tions by which to reduce a series of observations, without any know- 

 ledge of tidal theory. 



An actual numerical example is thus essential, both to test the 

 method and to serve as instructions to a computer. The Appendix 

 contains so much of the reduction of three months of observation at 

 Bombay as will serve as such a code. If the series be longer than 

 three months, or in such cases as the proper treatment of gaps in the 

 series, it is necessary to refer back to the body of the paper for 

 instructions. 



I now pass to the theoretical reasons for the rules for reduction. 



2. Notation. 



The notation of the Report to the British Association for 1883, 

 and in use in the Indian tidal work and elsewhere, is here followed. 



The earth's angular velocity is denoted by 7 ; the hourly mean 

 motions of the moon, sun, and lunar perigee by <r, ?/, w (717, <re\rji>T), 

 7/Xos) ; the mean longitudes of moon, sun, and lunar perigee by 

 , h, p, and the mean solar hour angle by t. The B.A. and longitude 

 in the lunar orbit of the intersection of the equator with the lunar 

 orbit are v, f ; and N is the longitude of the moon's node. 



The several harmonic tides are denoted by arbitrarily chosen initial 

 letters. Those with which we shall principally have to deal are 



Semi-diurnal. 



Name. Initial. Speed. Equilibrium argument 



Principal lunar M 3 2(7 a) 2i + 2(h >) 2(s-f) 



solar S 2 2(7-17) 2t 



Luni-solar ____ K 2 2<y 2t + 2(fc-i/') 



Larger elliptic N 27-3<r + *r 2t+2(fc *) 2( f) (<-p) 



Smaller L 2-/-<r ar 2t+2(AiO2(* ) + ( j>) + 



Diurnal. 

 Luni-solar.... Kj 7 i+(h 1>') ^TT 



Lunar ...... 7-2<r 



Solar ........ P 7-2 7 



The symbol H denotes the mean semi-range of any one of the 

 tides, and K its retardation of phase behind what it would be accord- 

 ing to the equilibrium theory ; f denotes a certain factor of augmen- 

 tation of the lunar and luni-solar tides depending on the value of N. 



The particular tide to which H, :, f refer will in general be 

 indicated by a subscript small letter, the same as the letter constitute 



