HARMONIC AlsTALYSIS AND PREDICTIOISr OF TIDES. 107 



Summing 



n=365 n=365 



S Vn COS 24(n-l)a = JL'S cos^^ 24(n-l)a 



n=l n=l 



n=365 



+ A" S sin24(w-l)acos24(n-l)a 



n=l 

 n=365 



■\-B' S cos 24(7i-l)& cos 24(n-l)a 



n=l 

 n=365 



+ B" S sin 24(n-l)& cos 24 (n-l)a 



n=l 



n=365 



+ C' S COS 24(n-l)c cos 24(n-l)a 



n=l 

 n=365 



+ C" S sin 24(ri-l)c cos 24(ri-l)a 



n=l 

 n=365 



+ Z>' S cos24(7i-l)(Zcos 24(n-l)a 



n=l 

 n=365 



+ D" S sin 24(n -l)d cos 24(n -l)a 



n=l 

 n=365 



+ E' S cos 24(n-l)e cos 24(n-l)a 



n=l 

 n=365 



+ E" S sin 24(n-l)f^ cos 24(n-l)a (429) 



n=l 



which is the normal equation for the unknown quantity A' . 



In a similar manner we have for the normal equation for the quan- 

 tity A" 



S 2/n sin 24(n — l)a 



= A' S cos 24(n-l)asin 24(n-l)a + ^" 2 sin^ 24(n-l)a 



+ 5'Scos24(n-l)&sin24(n-l)a + 5"Ssin24(n-l)6sin24(n-])a 



+ C"2cos 24(ri-l)csin24(w-l)a+C"Ssin 24(n- l)c sin 24(n- l)a 



+ D'^ cos 24(71 - 1)(Z sin 24(n - l)a + Z)" S sin 24(n -l)d sin 24 {n-l)a 



+ E'^ cos 24(n- l)e sin 24(7i- l)a + ^" S sin 24(n - l)e sin 24 (n - l)a 



(430^ 



the limits of n being the same as before. 



Normal equations of forms similar to (429) and (430) are easily 

 obtained for the other unknown quantities. 



72934— 24t 8 



