368 



REPORT 1872. 



possible of the mutual influence of the two largest tides, the lunar and solar 

 semidiurnal tides, in the two averagings performed to determine these two 

 tides. But the incommensurability of the periods renders it impossible to al- 

 together escape, in the direct synthesis for any one tide, the influence of the 

 others. Accordingly, the coefiicients Aj, B^, &c., shown above, are to be 

 regarded as first approximations in the mathematical solution of the problem. 

 The next step followed was to find corrections upon each summation for the 

 influence of the tides determined by the other summations, these corrections, 

 for a second approximation, being calculated on the supposition that the first 

 approximate values of A,, Bj, A^, t&c, already found, are correct. Auxiliary 

 Tables for performing this process have been formed for use along with the 

 other Tables (one being given as a specimen, p. 367) ; but the ultimate correc- 

 tions found from them, after very considerable labour, affected the terms which 

 represent genuine tide -components in so small a degree that their use has since 

 been discontinued. The S, K, L, M, N", and tides for Eamsgate, 1864, were, 

 however, so corrected, and the corrections thus formed are hei-e given. 



22. The corrections are to be subtracted from the values of A^, B^, A^, &c,, 

 to first approximation, and are as follow : — 



Table of Corrections of the 6 x 16 Coefficients A^, B^, (fee. 



