140 On the Precession of the Equtnoxes. 
equator, containing } of its quantity of matter. (Vince’s 
Astron. Vol. 2. p. 114—15, and old Encyclop. Art. Preces- 
sion.) Witb these agree the calculations of Frisius, Brad- 
ley, D’Alembert and Euler. But it is said that these things 
are not * positively known.” If they are not, it is true that 
conclusions drawn from these data correspond with fact, 
which | consider a strong argument in their favor. 
2. It is said that “the case is not exactly parallel 
with that of the Lunar motions,” for the ring surrounds 
the equator, and the centre of the equator “‘and the 
centre of the ring is the centre of the attraction,” and 
consequently ‘‘all the effect the sun can have in con- 
sequence of the ring arises merely from the different dis- 
tances” of its perihelion and aphelion. Perhaps the case 
is not exactly parallel with that of the Lunar motions. But 
their analogy is such that one may fitly be used to illus- 
trate the other. If the writer means by ‘‘ centre of attrac- 
tion,” the centre of gravity in relation to the sun, then I say 
that the centre of attraction and the centre of the ring, 
(meaning the the centre of matter in the ring) cannot coin- 
cide. For the different distances of the perihelion and 
aphelion of the ring, which the writer considers too small 
to produce any effect, will manifestly prevent such a coin- 
cidence. In fig. 1 Plate Il. Let PRP be the earth, RR’ 
a ring of matter about the equator. C the centre of revolu- 
tion which I call also the centre of matter in the protube- 
raot ring, and Sthe sun. Then if C be the centre of grav- 
ity towards the sun. the momentum of the half of the ring 
RC=H‘C, the other half. But the momentum is equal to 
the quantity of matter multiplied into the velocity. —-In this 
case the quantities of matter are by supposition equal. 
The momenta of'the parts of the ring will vary then as their 
velocities i. e. as the attraction of the sun upon the parts 
R and R’. Now the attraction of the sun diminishes as 
the square of the distance increases. Its attraction: then 
upon R%: its attraction upon Ri: 1,345 $1 nearly. 
Wherefore C the centre of motion cannot be the centre of 
gravity of the ring towards the sun. It must be at some 
point between R and C3; say pn. Wherefore it is evident 
that the greater attraction for R the part of the equatorial 
ring nearest the sun will have the same effect upon the mo- 
tion of the earth as though the earth was a sphere with a 
