294 Prof. G. H. Darwin. [June 10, 



the equations (33) may be written 



-L =-R sin (fr-t), 



. (35). 

 = #, cos ().. 



The four equations (32), (33) involve six unknown quantities, 

 B, ', BO, , B p , p, and are insufficient for their determination. 



In reducing a short series of observations it is necessary to assume 

 what is usually nearly true, viz., that K P = K', and H^/H' = 0'3309, 

 as would be the case in the equilibrium, theory of tides. 



Then, writing q for O3309, we have approximately B p = Tf p = qW . 

 The argument of the K^ tide is t + (7i 1>') ^IT K, where v is a 

 certain function of the longitude of the moon's node (tabulated by 

 Baird) ; and the argument of the P tide is t ln,-\-\ir K P . 



At the noon which is taken as epoch t = 0, h - h , and the two 

 arguments are equal to f' and j^,. 



Hence 



Therefore & = g + 2h i>'r+ (*>-*'). 



Putting K P =: K as explained above, 



where I = Tc-i= [l -450-(ff 



= -255 + 2^ 0> a small angle .......... (36). 



Then, if = 2h - v + 1 + (2m + l)e, 



(37), 



Pm = 2/" COS 4 e J 



we have 



|(W Z) = f'H' sin (C' + i) -^H'sin (g + i- 



'...(38). 



Let TcosY' = f p m cosO, "] 



} .............. (39), 



T sin ^ = p m sin 6. J 



whence T and ^ may be computed ; and 



-Z)= H'T sin ('+;- y,), 



(40). 

 f). 



From these we compute H' and ' and '+i. 



