[ I^ ] 



body falling freely by the force of gravity ; p — the periphery 

 of a circle whofc diameter is unitv ; alfo let A C =: i •, S. angle 

 D C A = J ; Cos. D C A = r; arch C L = s ; fine of C L =^. 

 Then L M = cy, and C M = jj. 



The difturbing force of the fun is equal toy ^ L M (Cor. 17. 

 Prop. 66. Lib. i. Princip.) and the force of a particle of matter 

 at L to move the annulus about the centre, in the diretaon 

 P Qj\ D, is CM X y X L M, adling by the povrer of the lever 

 C M ; that is, the force of this quantity or matter at I, is = f ^/j*; 

 therefore the fluxion of the force of the matter in a quadrant of 

 the annulus is csfy^ % — csf^^ y'^ y -. 



v^i — 



•, > 



but the fluent of 



is 



\z — 3 J X I — J' \ and therefore the whole fluent is 



^csf% — hcsfy X I — y '^i ; and when ^ = r, the force of the 

 matter' in a quadrant of the annulus is = —-ULy and the force 



p c sf 

 of the whole annulus is pcsf— to the fimple force - ading 



at the diftance ^/i" from the centre, that is, at the diftance of the 

 centre of gyration from the centre of the annulus. This is the 

 force of the fun, to diflurb the annulus, when at the grcateft 

 diftance from the nodes ; call this Ample force ^ cs. 



The 



