ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 



49 



If we put 



we have, from (19), 





tan (^ — ^) = - 



Ssinx 



M + Scosx^ (21) 



H2=M2+S2 + 2MScosx) 



</> 



moon's transit. 



High water occurs approximately — or ^^f after 



2(7— ff) 



The determination of <f> and H may be conveniently carried out by a 

 graphical construction. If we take O as a fixed centre, O S as an initial 

 line, and S a point in it such that O S=S, and set off the angle A O M equal 

 to X, and M equal to M ; then O M S is the angle n—((>, and S M is the 

 height H. 



The angle x increases by 360° from spring-tide to spring-tide, and 

 therefore one revolution in the figure corresponds to 15 days. 



\ 



As a very rough approximation, M lies on a circle, but the parallactic 

 and declinational corrections ^iRm and c^Rra cause a considerable depar- 

 ture from the circle. 



The angle f and the height H are also easily computed numerically. 



If cos x is positive, let d be an auxiliary angle determined by 



tan^ 6=:—. cos x, 

 M 



and we have 



tan (/x — ^)^sin2 0tanx, H^Scosec (/j. — ^) sin x. 

 If cos X is negative, let be an auxiliary angle determined by 



sm- 0= — , - cosx, 

 M 



and we have 



tan (/i— ^)^tau2 Otanx, H=Scosec (/i— ^) sinx. 

 These formulae are adapted for logarithmic computation. 



§ 5. Correction for Diurnal Tides. 



The tide-table has to be corrected for the effect of three diurnal tides, 

 designated O, Kj, P. 

 If we write 



Y„=t+li-2s-v + 2'^ + W, 



1886. 



Y'=t+h-i'' -i 



