OF THE TIDES IN THE PORT OF LIVERPOOL. 
15 
If we subtract these mean heights from 15 -8, the remainders are very nearly as sin 2 &. 
The formula 6 sin 2 1 gives the following accordance : 
Decl . 
0 °. 
3 °. 
6 °. 
9 °. 
12 °. 
15 °. 
18 °. 
21 °. 
24 °. 
27 °. 
Obs 
•06 
•02 
•03 
•08 
•26 
•39 
•57 
•88 
1*06 
1-41 
Formula . . 
•00 
•02 
•08 
•14 
•26 
•40 
•60 
•77 
•99 
1-24 
Hence 15‘8 — 6 sin 2 h nearly is the non-periodical part of the Table. 
The periodical part, as appears by the remainder of Table XVI. (b.), follows nearly 
the law of the mean height already explained. The sum of the maximum inequalities 
is not definitely different for the different declinations, which agrees with the theory, 
according to which it is constant and equal to 2 h. 
Also by comparing the columns for decl. 0° and 2 7°, it appears that the interval 
between the times when the inequality is 0, is less for the greater decl., which also 
agrees with the theory, for in that case the fraction is greater, and the defect of 
symmetry in the curve increases with this fraction. 
There is no clear evidence of a variation of u in this Table. 
Trinity College , Cambridge, 
November 12, 1835. 
