454 Relations between Earth and Moon. [August, 
This acceleration of 0*24 hour again corresponds to the 
15 minutes the tide uses less time in rising than in falling. 
The delay of 32 minutes beyond the mean 3 hours during 
the syzigies, and the acceleration of about 30 minutes 
during the quadratures (the difference of two minutes being 
the 1-59*56 of the sum), or the variation of 1*03 hours, is 
to the remainder, 2*20 hours of the 3*24 hours, as solar is 
to lunar acftion generally, the former now increasing and 
delaying, now diminishing and accelerating, high water. 
Every particle of the ocean being a moon disturbed by 
moon and sun in its motion with the rotation of the earth, 
and in the motion round the earth of that ring of which it 
is a portion, the sun produces, as he does with the moon in 
her orbit , a retardation on the moving undulation, the tide, 
in the first and third quadrant (in the odtants), and an 
acceleration in the second and fourth. The highest and 
lowest tides do not coincide with the syzigies and quadra- 
tures, but fall 1*5 days later, — that is, divide the time or 
tidal effect, for each quadrant in the lunation, in proportion 
1 : (^2*83)% as the waves dividing oceans and land are 
divided in harmony with Kepler’s laws. 
A lunation is 1-12*37 of a year 
1 __ 1 __ 1 
I2‘08 12*37 ~~ 5*5* 
and 515 x 12*37 revolutions of the earth round her axis 
are equal to the sidereal period of the lunar nodes on her 
orbit. 
The difference of the 1-12*08 of the days of the year and 
of the days of the lunation is 1-40 of the latter ; 1-40 being 
equal to the extent of a polar zone to the sphere, minus 
the excentricity of the common orbit of earth and moon 
to— 
1 _ 1 
24*16 59*56* 
The difference between 1-12*37 of the year and 1-13*37, 
the tropical month, is 1-181 ; and half the 1-12*08 of the 
year, or 15*1 days, 181 times, is equal to the tropical revo- 
lution of the apsides of the lunar orbit. 
The surfaces of ocean and land are 2*83.: 1, their densi- 
ties being inverse. The lunar terrestrian orbit has an ex- 
centricity of 0*01679, and the lunar orbit one of 0*005504, 
or 3*05 to 1. We have— 
