122 On the Tules. 
heavenly bodies from the earth, and the laws of their increase 
and decrease in proportion as they recede from thejr maxi- 
mum and from their minimum. In the Mécanique Céleste 1 
had not considered those laws relatively to the variations of the 
distances of the moon from the earth. Here 1 take them into 
consideration, and I find the same agreement between the obser- 
vation and fine theory. 
The retardation of the greatest and least tides which follow 
the times of syzygies and quadratures, was observed by the an- 
cients themselves, as we read in Pliny the naturalist. Daniel 
Bernouilli, in his paper on the Tides, that gained the prize 
proposed in 1740 by the Academy of Sciences, attributes 
this retardation to the inertia of the water; and perhaps also, 
adds he, to the time taken by the action of the moon to trans- 
mit itself to the earth. But 1 have proved in the fourth book 
of the Mécanique Céleste, that by allowing for the inertia of 
the water, the highest tides would BERET with the syzygies, 
if the sea covered “uniformly the whole surface of the earth. As 
to the time of the transmission of the action of the moon, I have 
discovered by a comparative view of the whole of the celestial 
phzxnomena, that the attraction of matter is transmitted with a 
velocity incomparably greater than even the velocity of light 
itself. “We must therefore seek some other cause for the retar- 
dation in question. I have proved in the book quoted above, 
that this eause is the rapidity of the motion of the celestial body 
in its orbit, combined with the local circumstances of the port. 
I have remarked, moreover, that the same cause may increase 
the ratio of the action of the moon on the sea to that of the 
sun; and I have given a method of determining this increase by 
means of the observations, the idea of which is this: Let us 
suppose the motion of the sun to be uniform :—if we consider 
only the great inequality of the tides whose period is about half 
a day, the solar tide is decomposed very nearly into two others, 
which are exactly those that would be produced by two eelestial 
bodies moving uniformly, but with different velocities, in the 
plane of the equator, at the mean distauce of the sun from the 
earth. The mass of the first body is that of the sun, multiplied 
by the cosine of the inclination of the ecliptic to the equator: 
its motion is that of the sun in its orbit. - The second body con- 
stantly corresponds with the spring equinox, and its mass is that 
of the sun multiplied by the half of the square of the sine of 
the obliquity of the ecliptic. At the equinox these bodies are 
either in conjunction or in opposition, and the tide is the sum 
of the tides produced by each of them :—at the solstice the bodies 
are in quadrature, aud the tide is the difference of these partial 
tides. The observations of the solar tide in these two points 
show, 
