226 
MR. LUBBOCK ON THE TIDES. 
<?• 
Moon’s 
Transit. 
Correction for H. P. 54'. 
Interval. 
Height. | 
Observation. 
B. 
Theory. 
Residue. 
C. 
Observation. 
B. 
Theory. 
Residue. 
c. 
o o 
h in 
m 
m 
m 
1 
0 or 180 
0 30 
0 
0 
— 1*4 
- *66 
- *66 
+ *10 [ 
15 — 195 
1 30 
- 1-5 
— 2-1 
— 1*2 
- *57 
- -66 
— -08 
j 30 — 210 
2 30 
— 4*3 
— 4-2 
— 1*8 
- *60 
- *64 
— *02 
45 — 225 
3 30 
- 7-5 
- 6-5 
— 3*2 
— *70 
- *62 
- -10 
60 — 240 
4 30 
— 8-5 
- 8-7 
- 4*6 
- -75 
- -61 
- *08 
75 — 255 
5 30 
- 7*1 
— 8-4 
— 5*4 
— *80 
- -64 
— *12 
90 — 270 
6 30 
0 
0 
- 5*0 
- *66 
- -66 
- *06 
105 — 285 
7 30 
+ 7-1 
+ 8-4 
- 5*4 
- -80 
- *64 
+ 'll ! 
120 — 300 
8 30 
+ 8-5 
+ 8-7 
— 4*6 
- -75 
- -61 
+ *08 
135 — 315 
9 30 
+ 7*5 
+ 6-5 
— 3*2 
- -70 
— -62 
+ *10 
! 150 — 330 
10 30 
+ 4-3 
+ 4-2 
— 1*8 
— *60 
- -64 
+ *01 
j 165 — 345 
11 30 
+ 1-5 
+ 2*1 
— 1*2 
- -57 
- *66 
+ -08 
B + C = A. 
The residue of the interval may, I think, be represented by 
constant x 3 P 
J + A cos 2 <p 
which is not inconsistent with theory. The residue of the height is small. The re* 
suits of the preceding Table are displayed in diagrams at foot of Plate XX. 
Table XXXI. offers a comparison between the moon’s declination-correction in the 
interval and in the height, as deduced from Bernoulli’s theory and from the obser- 
vations. 
It appears that the semimenstrual, declination and parallax-corrections are in 
accordance with the laws assigned to them by Bernoulli’s theory, at least taken 
in the manner which I have attempted to define in this paper, and within the limits 
of the errors of the observations. This view of the question accords with that given 
by Laplace in the following passage of the Exposition du Systtdne du Monde, p. 289: 
“ Chacun de nos ports peut etre considere a cet egard, comme etant a l’extremit£ 
d’un canal, a I’embouchure duquel les marees partielles arrivent au moment meme 
du passage des astres au ineridien, et emploient un jour et demi a parvenir a son 
extremite.” 
This view of the question is also adopted by Mr. Whewell; but I do not think 
with Mr. Whewell that the “ retroposition of the tide in longitude and in time is 
affected by changes depending upon variations of the moon’s force*.” I think that 
what Mr. Whewell attributes to the change in X 1 , “ the retroposition of the tide in 
longitude,” is chiefly due to the variation in the intervals between the successive 
transits of the moon, which has hitherto been overlooked. 
From the expression 
tan 2 = 
A sin 2 <p 
I + A cos 2 <p 
* “ On the Empirical Laws of the Tides in the Port of Liverpool.” Philosophical Transactions, 1836, p. 22. 
