the Rotatory Motion of Bodies, ^ip 



If we refolve each of the three forces H, I, K, into two 

 ^hers ; the one to turn the body about the diameter NAN, and 

 tlie other to turn it about the momentary axis PAP, at right 

 angles to that diameter ; the forces to turn it in the laft men- 

 tioned diredlion, arifiiig from the faid forces H, I, K, will be 



— t= _ . — __ X ^ flux, of ^/S - — . Be-M, 



— = _ . — T—yiy flux, of ey + -—^ ' T)e~^y^, 



_ = r-x^flux. of e^ -, 'Ce'fiyl 



The fum of thefe forces, it is obvious, muflberro; the di- 

 re»£lion wherein they are fuppofed to a6l being at right angles 

 to that in which the body will be actually urged to turn by the 

 joint centrifugal force of its particles, and that being the only 

 force whereby the motion of the body is fuppofed to be affedted : 



which fum (B + C - D being s=o) is, when divided by — :-, 



d- +c' . 13^' e '\- d' -{• b' . y- e ^ c' + b~ . ^'e 



= 0. 



J- + c^ . e(3(3-i-d~-{-b~ . eyy-\-c'+b- . ed^ 

 But 13^-hyy + f^ being before found = 0, we have 



^' + r + i^'XiSiQ 4- 7/7 + ^^=0; and F~(l(3'\-c'yy'\-d'U being 

 alfo found = ; it evidently follows, that 



d'^c"-. /G/3 + ^N^. y'y\- c' •{■ b"- . ol wilIbe = o. 

 Therefore F+? . /GV + F+¥ . y'e + c' + b"- . Ve will be = o : 

 confequently e will be = o, and e invariable; which agrees with 

 what is faid above refpeding the momentum of rotation. 



The other forces arifmg by refolution from the forces H, I, , 

 K, to turn the body about the diameter NAN, will be 



XX2 



