1892.] facilitating the Reduction of Tidal Observations. 361 

 ^ (T) j =H ^OS K ^ 



&6 (T) 1 r COS 1 



|jj (T) > := HK g j n KM, - = lQ'0504 cos (&o + 30 x + 94 ) 



(17). 



When the series of successive values of the g^'s and g's are har- 

 monically analysed (by processes which we shall consider shortly) the 

 several coefficients resulting from such analysis will be defined by 



glo (T) ' = A Q + A! COS 30r + S v sin 30r, 



Mean gt 4 (r) = A^ Mean $ 4 < T > = B, 



Mean g, 6 W = A 8 , Mean 6 < T > = J? 6 (18). 



Then the subsequent procedure as given in (13) and (14) holds 

 the only difference being that we do not obtain the semi-annual 

 solar elliptic tides. 

 We shall now consider the harmonic analysis of an imperfect series 

 )f values. 



It must be premised that each monthly value of ^ T) , J 2 ^ T) is to be 

 livided by its corresponding PW before the analysis is made. 



Suppose that OM denotes a function which is subject to semi-annual 

 inequality, and that 



0< T > = Ao + A 2 cos 60T+B 2 sin 60V 

 Then it is clear that 



&c. &c. 



I now define D , A, A thus : 



