392 
MR. LUBBOCK ON THE TIDES IN THE PORT OF LONDON. 
from which equation combined with the equation 
771 TI 3 ( 1 ~f" 71 x) 2 
wi y IV(l + n,x) ~~ ’ 
I nx may be determined. 
The theory of Laplace differs essentially from that of Bernoulli, in sup- 
posing the constants to be modified by local circumstances, which considera- 
tion introduces the factor \ + -- — . 
According to the observations at Brest, 1 + nx = 1.0 189 1,1 + ^# = 1.25291 
■. m —- ILdL^fL = 9.5385031 ? 
m t a, a (1 + n t x) 
mIF (!+»*)- 3455. 
m l n ; 3 ( 1 + n t x) 
Whence 
log. = 9.6283227 
which gives the mass of the moon equal to that of the earth divided by 74.946. 
If m n be the mass of the earth, by an extension of the third law of Kepler, 
(m + wt") i f . g near ]y e q ua i t 0 the ratio of the squares of the periodic times of 
( 771 ^+ m u) 
the moon about the earth, and of the earth about the sun, or of their mean 
motions. This ratio is known very accurately to be .0748013. Hence neglect- 
ing m u with regard to m, we have 
m IT 3 
(*»* + m u ) n / 3 
= (.0748013) 2 . 
If we neglect the factor \~^~ x which is nearly unity; 
log. m .-— = 9.57846 
6 m t n, 3 
log. mIP = 7.74782 log. m ' + - m " = 1.83064 
( m i + m u ) II, 3 ° m l 
m , 1 
m i + m u ~ 67.7* 
which gives the mass of the moon equal to that of the earth, divided by 66.7- 
Astronomers will, no doubt, concur in following the opinion of Laplace. 
“ En consid£rant la p£titesse des quantity qui m’ont servi k determiner l’ac- 
