334 



REPORTS ON THE STATE OF SCIENCE. — 1920. 



denote respectively the times and heights of coDsecutive high and low tides, we 

 deduce from (30) and (31) 



y C« cos <T„t, - R„ cos e„ 



5=1 



+ H 1 - — ) '^OS I (<rr + (r„)<s -€,■ I I 

 N 



^ y C. sin <T„t, - K„ sin e^ 



8=1 



N 

 r 8=1 



(33) 



K'-^:)=" 



(o-/- : O's - «)■ 



}j 



If in the terms 



N 



we may approximate by substituting 



t, = ti + (i'-l)-, 



(T 



we get 





Nsin 



cos 



(<^,-<^„)(^, + V^-)-^,) 



(34) 



(35) 



(36) 



This vanishes when N is an exact multiple of 2ir/(<Tr-(r„), or when the tides taken 

 cover an exact number of synodic periods of the constituents of speeds (r„ and o-,-, 

 while if N has the value of (rj(a;. — (r„), or the tides taken cover exactly half a 

 synodic period of the constituents of speeds <r„ and ffr, and (o-,. - (r„)/<r be small, (36) 

 is equal to 



. . (37) 



cos |((T, - (r„) (t,+ -g TJ - f,.|, 



approximately. 



These are the equations and relations on which the method is based. 



When analysing for Mj, B„ cos ((tJ: — e„) is taken as this constituent, and N is 

 chosen so that the tides considered cover an exact number of semi -lunations. It is 

 then assumed that the summations on the right of (33) may be neglected, so that 



1 ' ^ 



E„ cos So = j^ 2 (i <^°s <^o^. 



.... (38) 



When analysing for Nj and L^, Ro cos ((r„< — e„) is again taken as Mj, but N is 

 chosen so that the tides considered exactly cover a semi -lunar-anomalistic period, 

 T^o series of 13 svich sees of tides ^re taken, the tides in each series being 



