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Bdt Simpfon in his niifcellaneous tra£ls hasjufHy obferved, 

 that though this reafoning be indifputably true in Newton's 

 fenfe, yet there is a difference between the quantity of motion, 

 fo confidered, and the momentum, whereby a body, revolving 

 round an axis, endeavours to per'evere in its prefent ftate of 

 motion, in oppofition to any new force imprefled, which latter 

 kind of momentum it is that ought to be regarded in comput- 

 ing the alteration of the body's motion in confequencc of 

 fuch force. In this cafe, every particle is to be confidered as 

 aiding by a lever terminating in the axis of motion ; fo that 

 to have the whole momentum, the moving force of fuch par- 

 ticle muft be multiplied into the length of the lever by 

 which it is fuppofed to adl ; whence the momentum of each 

 particle will be proportional to the fquare of the diftance from 

 the axis of motion, as it is known to be in finding the center 

 of percuffion, which depends on the very fame principles. 



The corredlion arifing from this change in the procefs 

 amounts only to about ij", as will eafily appear in the fol- 

 lowing manner : 



The fluxion of the moment of a fphere, from what has 

 been faid already, is ipx^ yx; from the nature of the circle, 

 x' = I — j', as before ; therefore x x = — jj, x' x = y^j' — 



yy , and 2 p x' y x =: 2/ x j"* / — y^J, whofe fluent is rj /> 

 when^ = I. 



In 



