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the Rotatory Motion of Bodies. 
that a folution of it, investigated by M. John Albert 
Euler (after a method ftmilar to his father’s) obtained the 
prize given by tire Academy of Sciences in tne year 1761. I ns 
conclulions deduced by thofe very learned gentlemen aiifenng 
greatly from mine made me fufped:, for (ome time, that I had 
fomewhere erred in my inveftigation, and induced me to revile 
my procefs again and again with the greateft circumipe&ian. 
At length my fcrutiny has fo removed my doubts, that, being 
well allured of the truth of my theory, I now beg leave to 
prefent it to the Royal Society ; preluming that it will be found 
not unworthy of the notice of luch readers, as arc cunous mi 
contemplating the various motions which bodies may naturally 
have, in confequence of inftantaneous or continued impulle. 
In the Philofophical ' Tranjadlions 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 fince 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 wdll 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 always 
variable , when the axis about which it has a tendency to re- 
volve is a momentary one, except in a particular cafe. 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 the body are thereby determined with great 
facility. 
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