PreceJJion of the Equinoxes, 3 65 
quantity of matter at E equal to * m, and at the fame time to 
have a quantity, of matter to move equal to 4 M, and then from 
this and art. 3. it appears, that the effedt will be the fame as 
the accelerative force of the fun to turn about the earth. 
Hence that accelerative force is, from art. 2. equal to 
x £ = ' aAl X / > S ravit y be ‘ng unity- Now, 
if TE : TP :: 1 : 1 — r, then M : M — m :: 1 : 1 — 2 r, there- 
fore, M : m :: 1 : ir, hence — = r, confequently the accele- 
- qEK x KT x p z x r 
rative force = - p — • 
5. Let z — the arc defcribed by a point of the equator about 
its axis in an indefinitely lmall given time, which may there- 
fore reprefent its velocity ; and let az reprefent the arc de- 
fcribed in the fame time by a body revolving about the earth at 
its furface ; then ‘—f — the fagitta of the arc defcribed by the 
body in the fame time, and confequently az z — the velocity 
generated by gravity whilft a point of the equator defcribes z, 
TT 1 1 3EK x KT x x r 
Hence, by art. 4. we have 1 : p — - — :: arz : 
?EK x the. velocity of the point E of the equator 
generated by the adlion of the fun, whilft the equator defcribes 
z about its axis ; confequently the ratio of thefe velocities is as 
3EK x KT x p 1 x a 1 z 
p : I. 
6. Let y be an arc defcribed by the fun in the ecliptic to a 
radius equal to unity, whilft a point of the equator defcribes i; 
about its axis ; then (as ap ~ the time of the earth’s rotation, and 
the arcs defcribed in equal times to equal radii are inverfely as the 
periodic times) p : ^ :: y : ; hence, if v and w be put 
ap 
for 
