290 Prof. G. H. Darwin. [.June 19, 



From these two equations, H" and K" may be computed, and since 

 II n' is very small, approximate values of H, cos K S , II, sin ^ 

 suffice. 



7. The Diurnal Tides K l5 0, P. 



Amongst the diurnal tides I shall only consider K a the luni-solar 

 diurnal, the principal lunar diurnal, and P the principal solar 

 diurnal tides. 



There is the same difficulty in separating P from K x as in the 

 case of K 2 and S 3 , and therefore in a short series of observations P 

 and Kj have to be treated 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 K l5 O, P are 

 omitted from the analytical expressions. 



If \V m denotes (7 o)t, we have 



= V m -<rt, 7^ = 17 +0-2^, and 



h = E'cos 



+ R p cos 



Hence, taking account of the equation which expresses that h is a 

 maximum or minimum, and neglecting the variation of ct compared 

 with that" of %V m ,* we have 



hcosV m = B'cos(rf n+^ cos (* + &) +B, cos ((<r2 7 )*&), 



hsinV m = B 1 sin (>') +R sin (<rf + &) -R p sin ((<r 2i/)f &). 



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



Then if e be the increment of s, and 2 the increment of s2h in 

 that period (so that with a equal to 0'5490 per hour and a 2i/ 

 equal to 0'4G69 per hour, e is equal to 3'4095 and z equal to 2"8994) ; 

 and if a, b, c denote the values of at ', at + , (* 2q) & at the 

 time of the first tide under consideration, the equations corresponding 

 to the (r + l) th tide are approximately 



= R' sin (a + re) + R sm (b + re) Epsin (c+rz}. } 



If we take the mean of n + \ successive tides, the first pair of terms 



* I have satisfied myself by analysis, which I do not reproduce, that on taking 

 means this error becomes very small. 



