354 Prof. G. II. Darwin. On an Apparatus for [Dec. 15, 



Now let V with appropriate suffix denote the initial "equilibrium 

 argument" at 0* O h of month 0, so that 



..-* -i , TT 7 I TT" c\ 7. c\ " 



then the general expression (9) for the tide in the month T becomes 

 A + H sa COS (ijt + V, a + 30r- K M ) + S ssa COS 

 cos iS^- 



(90^ 

 ", cos [(30 



-30<V-:J (10). 



Each of these terms falls into the type cos [(IS ^ P) fit an d ft 

 is in every case either + 17, 2iy, or 0. 



Now, when harmonic analysis of the mean of 30 days is carried 

 out, coefficients $ are introduced. 



Write therefore 



4f ^ x 30 sin \^, . _ 24 X 30 sin 17 



sin 360 rf sin 720 17 



With the known value of 97, 



log <|i = 0-00483, log J 2 = 0-01945. 



In applying the method investigated above, it will be observed 

 that a term of any frequency 15qp only contributes to the 

 harmonic constituent of order q. 



Then applying our general rule (8) term by term, and observing 

 that 359ih = 1476, and 719?/ = 29'53, the result may be written as 

 follows : 



TT 



~ cos (K, a -V, fl _30 T-1476) 



TT 



H--p cos (K wa -V wa -60T-29-53) j 



<3|2 



