the Rotatory Motio?j of Bodies, : 3 ij 



that a folution of it, inveftlgatcd by M. John Albert 

 EuLER (after a method fiinilar to his father's) obtained the 

 prize given by the Academy of Sciences in the year 1761. The 

 conclufions deduced by thofe very Jearned gentlemen diiFcriiig 

 greatly from mine made me fufpeci, for fome time, that I had 

 fomewhere erred in my inveftigation, and induced me ^o revile 

 my procefs again and again with the grcateft circumipeclion. 

 At length my fcrutiny has fo removed my doubts, that, being- 

 well aflured of the truth of my theory, I now beg leav^e to 

 present it to the Royal Society ; prefuming that it will be found 

 not unworthy of the notice of fuch readers, as are curious in 

 contemplating the various motions which bodies ma)^ naturally 

 have, in confequence of Inftantaneous or continued impulfe. 



In the Philofophical T^ranfacimis referred to above, I gave a 



fpecimen of this theory, as far as it relates to the motion of a 



Jpheroid and a cylinder. The improvements I have fmce made 



in it, enable me now to extend it to the motion of any body 



whatever^ how irregular foever its form may be. 



What I here infer therefrom will be found to differ very ma- 

 terially from the deductions in the folutions given by the gen- 

 tlemen above-mentioned. They reprefent the angular velocity, 

 and the momentum of rotation of the revolving body, as ahvays 

 variable^ when the axis about which it has a tendency to re- 

 volve is a momentary one, except in a particular caie. By my 

 inveftigation it appears, that the angular velocity and the mo- 

 mentum of rotation will always be invariable in any revolving 

 body, though the axis about which it endeavours to revolve be 

 continually varied ; and the tracks of the varying poles upon 

 the furface of tlxe body are thereby determined with great 

 facility. 



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