1892.] facilitating the Reduction of Tidal Observations. 359 



annual and semi-annual inequality were denoted by B , E 1? F 1? E 2 , F 2 , 

 and the constituents of J 2 were denoted by e , e^ f x , e 2 , f 2 . Hence the 

 ten corrections to the E's and F's are (with an easily intelligible 

 alternative notation) 



E , i, 2 = ( Pa , i, 2 + Q7o, i, 2) A z + (Q* , i, 2 



1, 2 



0) 1.2= ( R*0, 1, 2 S<y , 1. 2) 



On substituting the numerical values of a, j8, 7, 

 I find 



P, Q, R, S, 



Most of these corrections are negligible, but the four which affect 

 bhe solar elliptic tides T, R must be included, because those tides are 

 so small that a small error affects them sensibly. Hence we may 

 take, with sufficient accuracy, 



0-011 J5 2 , aJfd + F!) = 0-002^2, 

 0-009 J? 2 , H(E! f x ) = +0*0006 J. 2 + 0-002J? 2 



...... (16*), 



where A 2t B z are the components of the M 2 derived from the re- 

 duction of that tide by the process of 6. 



Provision for these corrections is made in the computation forms. 



4. Evaluation of A , Sa, S r , S 2 , 84, S 6 , K 2 , KI, P, when a complete 

 year of observation is not available. 



It is now proposed to consider the case where the period of ob- 

 servation is as much as six complete months and less than a complete 

 year. 



2 B 2 



