1*00.] Harmonic Analyri* of Tidal Observation*. 28< 



Tlie meanings of h a , 8 , v, , f, have been explained in the last 

 section. 



6. The- Tide* S. 2 and K,. 



These are the principal solar and luni-solar semi-diurnal tides. 



If the tide S 2 is in the same phase as K 2 at any time, three months 

 later they are in opposite phases. Hence, for a short series of obser- 

 vations, the two tides cannot be separated, and both must be con- 

 sidered together. It is proposed to treat a long series of observations 

 as made up of a succession of short series ; hence I begin with a short 

 series. 



For the sake of brevity all the tides excepting S 2 and K 2 are 

 omitted from the analytical expressions. 



Since 



h = 



= cos F,{5,cos , + .K"co8 (2?* -*')} 

 + sin F,{E,sin - 



Hence, taking into account the equation which expresses that It is 

 a maximum or minimum, and neglecting the variation of 2h or 2// 

 compared with that of F,, we have 



h cos V, = R, cos, + R" cos 



ft sin V, = R, sin , R" sin (2rjtg"). 



The mean interval between each tide and the next is 6 h< 210. Then 

 if g be the increment of 2/t in that period (so that with 2ij equal to 

 J- 082 per hour, g is equal to 0'510), the equations corresponding to 

 the (r + l) th tide are approximately 



h cos F, = J2,cos &+R" cos (rg "),! 



> ....... (17). 



h sin F, = R t sin V R" sin (rg g") J 



Now, if P be the cube of the ratio of the sun's parallax to its mean 

 parallax, the expression for S ? , together with its parallactic inequality 

 (the tides T, R of harmonic notation), is PH, cos (2t *,). 



Since t is the mean solar hour angle, 2t is the same thing as F,. 



Hence E, = PH 



,, , = 



Also if P be the value of P at epoch, then for a period of two or 

 three months we may take P = P (l-f/rt), where P p is equal to 

 dPJdt. 



