[ 39i ] 
ecliptic!'- in about 18 years and two thirds. And this 
ofcillation is compleated in the time of the revolution 
of the pole of the lunar orbit about the pole of the 
ecliptic ; that is, in about 1 8 years and two thirds. 
It will appear in the memoir, that there is a relation 
purely geometrical between the quantity of the nu- 
tation, during the time of the femirevolution of the 
pole of the lunar orbit, and the quantity of the pre- 
cedion, caufed likewife by the moon in the fame 
time. This relation is quite independent of the force 
of the moon, of the quantity of the earth’s fl'atnefs, 
of the quantity of the terreftrial matter, and, in a 
word, of every thing of a phylical nature that can 
enter into the problem. 
We are content to examine the motions of the pole 
of the earth produced by the fun and the moon. 
The fame method, and the fame formula, will give 
likewife the motions of the terreftrial pole arifing 
from any other planet, as Saturn, Jupiter, &c. but 
thefe motions are too minute to merit attention. 
Whatever has been faid of the action of the fun 
on the redundant matter about the earth’s equator, is 
alfo applicable to his action on a limple ring placed 
at the equator, without adhering to the terreftrial 
globe ; and the motion of the pole of fuch ring may 
be determined by the fame method, and confequently 
the motion of its nodes on the plane of the ecliptic, 
and the alteration of the inclination of its axe to the 
fame plane. And fnce thefe motions are the fame, 
whether the ring be fuppofed entire, or a fmall por- 
tion of it only be confidered, or a mere point thereof, 
the motions of the nodes, and the alteration of the 
inclination of a moon, or a fatellite of a planet, may 
thereby 
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