OF THE TIDES IN THE PORT OF LIVERPOOL. 
9 
14. The semimenstrual inequality of the heights for each minute of horizontal 
parallax, and the mean semimenstrual inequality of the heights, are in like manner 
obtained by subtracting 1 from each column of heights in Mr. Lubbock’s Table VII. 
the mean of that column, and taking the means of the horizontal lines as is done in 
Table VII. (a.) 
Table VII. (b.) 
Mean of each column subtracted from column “ Height of Tide.” 
H. P 
54'. 
55'. 
56'. 
57'. 
58'. 
59'. 
60'. 
61'. 
Mean. 
Meanheight 
14-20 
14-41 
14-84 
15-22 
15-63 
16-02 
16-43 
16-66 
2) ’sTransit. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
30 
+ 2-38 
+ 2-47 
+ 2-45 
+ 2-31 
4 - 2-33 
4 - 2-35 
4 - 2-19 
4 - 2-51 
4 - 2-35 
1 30 
+ 2-26 
+ 2-23 
+ 2-25 
+ 2-41 
+ 2-49 
4 - 2-43 
4 - 2-66 
+ 2-73 
4 - 2-39 
2 30 
+ 1-62 
+ 1-61 
+ 1-83 
+ 1-82 
+ 1-91 
4 - 2-02 
4 - 2-32 
4 - 2-21 
+ 1-88 
3 30 
+ 0-49 
+ 0-70 
+ 0-74 
+ 0-95 
4 - 0-95 
4 - 1-17 
4 - 1-27 
4 - -90 
4 30 
— 0-61 
— 0-55 
— 0-64 
- 0-33 
— 0-27 
— 0-15 
— 0-10 
- -38 
5 30 
- 1-92 
— 1-92 
- 1-93 
— 1-83 
— 1-62 
— 1-53 
- 1-57 
- 1-76 
6 30 
— 3-13 
— 3 - C 5 
— 3-14 
- 2-69 
- 2-79 
— 2-73 
- 2-85 
- 2-91 
7 30 
— 2-81 
- 2-96 
— 2-74 
— 2-89 
- 2-97 
— 3-06 
— 3-14 
- 2-94 
8 30 
— 1-52 
— 1-62 
- 1-69 
— 1-86 
- 1-86 
- 2-09 
— 2-33 
— 1-85 
9 30 
— 0-06 
— 0-08 
— 0-18 
- 0-43 
- 0-54 
— 0-60 
— 0-75 
- 0-60 
- -38 
10 30 
+ 1-18 
+ 1-16 
+ 1-13 
4 - 0-82 
+ 0-80 
4 - 0-60 
4 - 1-61 
- 0-65 
4 - 1-04 
11 30 
+ 2-10 
+ 1-89 
+ 1-95 
+ 1-78 
4 - 1-63 
4 - 1-64 
4 - 1-65 
+ 1-78 
+ 1-81 
Max.diff. 
5-51 
5-52 
5-59 
5-30 
5-46 
5-49 
5-80 
5-33 
Mean . . 
Half . . . 
5-44 
2-74 
The theoretical height of the high water above the mean surface of the ocean is 
V {h! 2 -f- h 2 + 2 h h! cos 2 (<p — a)} ; and therefore if k be the mean of all the high- 
water heights, we shall have for the semimenstrual inequality of height the expression 
V {h' 2 + li 2 + 2 h h' cos 2 (<p — «)} — k. 
This will agree very nearly with the result of observation if we make 
h = 274, h! = 6-872, k = 7 m 19, a = l h . 
The accordance is as follows : 
Moon’s 
Transit . 
Formula . 
Obs . 
h m 
f . 
0 30 
2-35 
2-35 
1 30 
2-35 
2-39 
2 30 
1-83 
1-88 
3 30 
0-84 
0-90 
4 30 
— 0-48 
- 0-38 
5 30 
- 1-89 
- 1-76 
6 30 
- 2-90 
- 2-91 
7 30 
- 2-90 
- 2-94 
8 30 
- 1-89 
— 1-85 
9 30 
- 0-48 
— 0-38 
10 30 
0-84 
1-04 
11 30 
1-83 
1-81 
The greatest deviation is about an inch, the mean a small fraction of an inch. 
MDCCCXXXVI. C 
