Harmonic Analysis of Tidal Observations. 323 



Cosines (continued). Form columns ii + iii, iv + v, vi + vii, viii+ix, 

 x + xi, xii + xiii. Form difference columns (ii + iii) (iv + v), 

 (vi + vii) (iv + v), (vi + vii) (viii + ix), (x + xi) (viii + ix), 

 (x + xi) (xii + xii); add the 5 difference columns together; multiply 

 by cosine factors ; sum and multiply by <!> or 0'00295. 



The result is : 



Si"7i cos V w = -8-38. 



/Sines. From Table (f) of Sums, enter 18 "sine" numbers, in 

 accordance with (h) in xiii vertical columns. 



Perform all the same operations as those on " cosine " numbers, 

 save that we use sine factors, which are the same as cosine factors in 

 inverse order, vi/,., beginning with 0"044 and ending with O999. 



The two results are 



S% sin V m = + 5-94, S*^ sin V = + 10*06. 



Collecting results, proceed thus : 



S7i cos V m = +11-38. S^fccos V, = - 8-38. 



S**A sin V= +10-06. S/ismV OT = + 5'94. 



Sum = +21-44. Sum = 2*44. 



Diff. = + 1-32. Diff. = -14-32. 



P = i sum = +1072. E = \ sum = - 1'22. 



Q = \ diff. = + 0-66. S = i diff. = - 7-16. 



(i.) Evaluation M 2 (continued). 



From the Table (g) of Sums for M 2 enter in one vertical column 

 18 cosine numbers, in accordance with (h) ; multiply them by 

 cosine factors ; add up and divide by the total number of entries for 

 6 semi-lunations, viz., 342. 



The result is : 



A M = -3^27* cos V = -30-58. 



Then enter in vertical column 18 sine numbers, in accordance with 

 (h) ; multiply them by sine factors, add up, and divide by 342. 

 The result is : 



B M = jd^h sin V* = +38'47. 



(k.) Sorting according to Values of V,, and Evaluation of S 3 , K 2 . 



The H. and L.W. are treated in separate tables, similar in form 

 save that the signs of the L.W. heights are omitted. 



