MR. LUBBOCK ON THE TIDES IN THE PORT OF LONDON. 
387 
+4»,n^i cos (2 9, — 2A.,) 
This expression coincides with that given by Laplace, (M6c. Cel. vol. v. 
p. 169, at foot,) when the terms multiplied by sin 4 -j- are neglected, n t 
(in the notation of the Mec. Cel.) being equal to the hour angle & at the equi- 
noxes and solstices, that is, when 1 = 0, 90°, 180° or 270° ; but Laplace neg- 
lects the term cos 2 l. 
Laplace supposes that 
A = (1 + nx) B -^i= ( 1 + n t x) B 
n being the mean motion of the luminary in its orbit, and x an indeterminate 
quantity, to be determined by the observations. Making these substitutions, 
differentiating the expression for the height to find the time of high water, and 
supposing d 6 = d & t and a = 
gBl ;;.+ W ^sin(29,-2a — 2A, + 2A)+ JaR 
sin 2 w cos 2 l 
m t n/ 3 (1 + v) 
tan (2 9, — 2 A,) = 
2 m. n. 3 ... x sin 2 co) 
' ' (1 + n,x) (1 
+ C 1 sin (2 9, — 2 A, — 21) 
sin (29,-29-2A, + 2A) 
1 + + C qs(29,-29-2A, + 2a) + mW 
m ( n ( 3 (1 + n,x) 
2 m, n , 3 
sin 2 uj cos 2 l 
(1 + K,x)(l- S i. n !g> 
cos(29,— 29— 2A, + 2/) 
+ C' cos (2 9, — 2 A, — 21) 
C' being a constant different from C, 6 and being the values of those varia- 
bles at the instant of high water. 
If we consider the mean of all the months of the year, column A, Table III. 
tan (2 9, — 2 A ( ) = 
mJF (1 + »*) sin (2 9. — 2 9 — 2 A. + 2 A) 
m, n, 3 ( 1 + n,x) V ' ' ' 
l + (1 + . n J l cos (2 9, — 2 9 — 2 A, + 2 A) 
m, n, 3 (1 + n,x) ' ' ' 
The constants which enter into this expression may be determined by means 
of column A. The mean of this column is l k 25 m ; I therefore take 
A, = l h 25 m , A — A, = 2 h , A = 3 h 25 m 
tangent of twice the difference of the interval when the moon 
mil 3 (I + nx) 
m, n, 3 (l + n t x) 
passes the meridian at 2 h and at 5 h . I take 
1q m II 3 (1 +nx) _ 9 . 5784858 
° m, II, 3 (1 + n t x) 
