Precejfion of the Equinoxes. 5 1 1 
ratio of st to sp; sl will reprefent the attraction on any 
particle p, and by the refolution of motion t m or pl will 
reprefent the perturbing force of the Sun on the fame 
particle. By the conftru&ion sl : sk :: sk 2 : sp 2 , and by 
divifion kl : sk :: sk 2 -sp 2 : sp 2 :: sk + sp x pic : sp 2 and pl 
or t m is nearly equal to 3?k, and as 3PK is to sk or st, 
fo is the fpace defcribed by p in any fmall time in the di- 
rection pk, to the fpace defcribed in the fame time by 
the center of the earth in confequence of the Sun’s at- 
traction. This laid fpace is equal to — where z repre- 
fents the arc defcribed by the earth’s center during any 
fmall motion in its orbit, and tbe former is equal to 
This is the fpace which would be defcribed by p 
in the direction pk if the particle was at liberty to move 
freely. Let us at prefent fuppofe that no other particle 
is difturbed by the Sun’s attraction except this one, and 
then proceed to enquire into the effeCts of this difturb- 
ance when p by its cohefion communicates a motion to 
the different parts of the earth, which is farther con- 
ftrained to turn round an axis t, the common interfec- 
tion of the plane cd and the terreftrial equator. From 
the laws by which motion is communicated, and the pro- 
perty of the lever, it eafily appears, as in the fecond arti- 
cle, that the fpace through which any particle of the 
X x x 2 earth’s 
