MR. LUBBOCK ON THE TIDES IN THE PORT OF LONDON. 
393 
croissement de Taction lunaire et en r£flechissant que ces quantites sont du 
meme ordre que les p6tites erreurs dont l’application du principe de la coexist- 
ence des ondulations trks petites aux phenomenes des marges est susceptible ; 
je n’ose garantir l’exactitude de cette valeur de la masse lunaire, etj’incline 
a penser que les phenomenes astronomiques sont plus propres a le fixer.” 
A very slight change in the interval employed produces a considerable 
alteration in the mass of the moon. 
After differentiation d 6 was supposed = d but since the time of the moon’s 
synodic revolution is 29.530 days, and that in this time the hour angle of the 
moon is less by one circumference than that of the sun, 
d 0 = 2 --‘ 5 — d 0. 
28.530 ' 
The observations of the times and height of high water in different months 
of the year may be nearly represented by neglecting in the expression for the 
height, the term of which the argument is 2 0 + 2 l — , but it is not easy to 
see why the coefficient of this inequality differs so much from that of the in- 
equality of which the argument is 2 Q — 2l — 2 X, the cause of this difference 
must be clearly established before the theory can be considered complete. 
If be the longitude of the moon reckoned from her perigee, and increased 
by a constant, considering the terms depending on the changes of the moon’s 
parallax, the height of the water may be represented by 
or 
mil 3 cos (2 0 — 2 X) 
+ m t ri, 3 jcos(2 0,-2 A,) + C ^cos (2 0,-2 X, - Z,) + cos (2 0, -2X,+ j 
m II 3 cos(2 0 — 2 X) +m / II, 3 { 1 + Ceos Z, } cos (2 0 / — 2 X,) 
tan (2 0, — 2X,) = 
m n 3 sin (2 0 ( — 2 0— 2 X, + 2 X) 
m,n, 3 ( 1 + C cos l t ) 
mn 3 cos (2 0, — 2 0 — 2 X ( + 2 X) 
«i ; n, 3 (l + Ccos/j 
According to this formula, the variation in the interval which elapses between 
the time of the moon’s transit, and the term of high water, is equal to zero 
when the moon passes the meridian at 2 o’clock or 8 o’clock; and this is the case 
whatever value be given to the constant C, or the constant which I have sup- 
3 e 2 
