s 
THE REV. W. WHEWELL ON THE EMPIRICAL LAWS 
The Semimenstrual Inequality . 
13. In order to obtain the semimenstrual inequality of the times of high water, I 
take Mr. Lubbock’s Table VII., and from each column of intervals (of tide and 
moon’s transit) I subtract the mean of that column; and I thus obtain Table VII. (a), 
which exhibits the semimenstrual inequalities for each minute of parallax. I then 
take the means of the horizontal lines in this, interpolating in H. P. 60' and omitting 
H. P. 61'. The resulting intervals are those of the mean tide. 
Table VII. (a.) 
Mean of each column subtracted from the column “Interval” of times. 
H. P 
54'. 
55'. 
56'. 
57'. 
58'. 
59'. 
60'. 
61'. 
Mean. 
Mean \ 
h m 
h m 
h m 
h m 
h m 
h m 
h m 
h m 
h m 
Interval J 
11 12-7 
11 11-5 
11 8-3 
11 6-5 
11 3-7 
11 0-3 
10 58-5 
10 54-3 
11 6 
D ’sTransit. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
Remainder. 
0 30 
+ 13-7 
+ 11-6 
+ 8-0 
+ 11-6 
+ 12-2 
+ 12-9 
+ 13*3 
+ 11*8 
+ 12-2 
1 30 
- 5-2 
- 6-8 
— 6*5 
- 3-9 
— 5-3 
— 2-8 
- 2-5 
— 2-8 
- 4-6 
2 30 
— 23-2 
— 22-0 
— 22-0 
-20*8 
— 18-6 
-17-5 
-16-6 
-17+ 
-20*0 
3 30 
— 41-4 
-36-7 
-34-7 
— 33-0 
— 32-1 
-29-3 
-30-4 
-33-9 
4 30 
-49-0 
-47-8 
— 44-0 
— 41-8 
— 40-4 
— 38-4 
-38-7 
— 42-8 
5 30 
-47-7 
— 45-7 
— 43-6 
-43*2 
-39-4 
— 38-5 
-37-3 
— 43-2 
6 30 
—27-2 
— 26-4 
—24-5 
-25-7 
— 25-6 
— 24-8 
— 21-5 
-25-0 
7 30 
+ 14-3 
+ 13-4 
+ 11*9 
+ 9-2 
+ 6-5 
+ 1-6 
+ 11 
+ 9-6 
8 30 
+ 44-8 
+ 41-8 
+ 40-1 
+ 37-4 
+ 34-1 
+ 31-1 
+ 20-2 
+ 36-6 
9 30 
+ 50-9 
+ 49-3 
+ 47*9 
+ 45-0 
+ 44-1 
+ 41-6 
+ 39+ 
+ 39 
+ 45-6 
10 30 
+ 42-5 
+ 41-8 
+ 41-3 
+ 40-1 
+ 38-6 
+ 38-0 
+ 36+ 
+ 35-8 
+ 39-8 
11 30 
+ 28-5 
+ 28-1 
+ 26-6 
+ 25-7 
+ 23-6 
+ 25-7 
+ 24*4 
+ 25-4 
+ 26-1 
Max. Diff. 
99*9 
95-1 
91-9 
88-2 
84-5 
80-1 
78*5 
88-8 
On comparing the mean numbers in the last column with the theoretical formula 
tan 2 (6' — l!) = — 
c sin 2 (<p — «) 
1 + c cos 2 (<p — «)’ 
it appears that they may be very accurately represented by making X’ = ll h 6™, 
a = l h 15 m , c = sin l h 29 m . The agreement of this formula with observation is as 
follows : 
Moon’s 
Transit. 
Formula. 
Obs. 
Diff. 
h 
m 
m 
S 
m 
S 
m 
s 
0 
30 
+ 12 
16 
+ 12 
12 
— 
0 
4 
1 
30 
— 4 
7 
— 4 
36 
— 
0 
29 
2 
30 
— 20 
6 
-20 
0 
+ 
0 
6 
3 
30 
— 34 
0 
— 33 
54 
+ 
0 
6 
4 
30 
-43 
6 
42 
48 
+ 
0 
18 
5 
30 
— 42 
40 
-43 
12 
— 
0 
32 
6 
30 
— 25 
8 
-25 
0 
+ 
0 
8 
7 
30 
+ 9 
2 
+ 9 
6 
+ 
0 
4 
8 
30 
+ 36 
28 
+ 36 
36 
+ 
0 
8 
9 
30 
+ 44 
30 
45 
36 
+ 
1 
6 
10 
30 
+ 39 
40 
39 
48 
+ 
0 
8 
11 
30 
+ 27 
36 
26 
6 
— 
1 
30 
This accordance is complete, the difference amounting in only two cases to l m . 
