PreceJJlon of the Equinoxes. 5-25 
in the plane of the equator at the furface of the earth 
with a velocity equal to that of the earth round its axis. 
We are then to fuppofe, that the mean motion of the 
nodes of a latellite, revolving with fuch a velocity, is the 
fame with the motion of the nodes of a ring of rigid 
matter furrounding the earth at its equator, and revolv- 
ing with the fame velocity. This laft hypothefis is ad- 
mitted by Simpson, who thinks that his own fecond 
lemma contains a full demonftration of the point. For 
my own part, I believe with frisius, that we are to look 
here for the material error in newton’s folution of the 
problem. It is evident, that the true motion of the nodes 
of the fatellite, and the ring of matter, are not the fame; 
and it is by no means obvious, that their mean motions 
are fo. The mean motion of the nodes of a ring of hard 
matter cohering together is very eafily computed by the 
method in art. 4th to the 9th, and turns out nearly dou- 
ble the mean motion of a Moon revolving at the furface 
of the earth with the fame velocity. 
It is a very interefting enquiry to find out the real 
caufe of the miftake in the Principia, lib. III. prop. 39.; 
and therefore at a future opportunity I may, perhaps, con- 
iider this particular part of the fubjedl more attentively. I 
have long been fatisfied with the account already given, and 
Vol. LXIX. Z z z fhould 
