the Rotatory Motion of Bodies, 327 



circle as often as y fliall become equal to ^ X w, or ^j x «; 



the parts of the track between the points of contad being per- 

 fedly fimilar. If Dw' be = Crf^ (D«^ being- then = B^z% and 



-confequently ^ X^«= -j- y.n — a), the faid track will make 



an infinite number of revolutions about a certain point, con- 

 tinually approaching nearer and nearer thereto, without arriv- 

 ing thereat in any finite time, though the length of the fpiral 

 fo defcribed cannot exceed a certain finite quantity. 



M. EuLER has computed, that if the motive forces to turn 

 the revolving body about AB, AC, AD, be relpe<5lively de- 

 noted by H, I, K ; 



xflux. of ^/3 -— 5 . B/7^, 



C23T 



X flux, of el-—-. . Ce-(3y; 



-X flux, of ^>' + :;-5 . De^f^Q, 



y being fuppofed to decreafe as T increafes : and he has put the 

 value of each of thofe forces (H, I, K) = o. In doing fo, it 

 feems to me, that he has erroneoufly affumed equations as 

 generally true, which are only fo in a particular cafe. For 



—5 • B^V^is the motive force to turn the body about AB, ariling 



from the centrifugal force of its particles revolving ?!>out the 

 momentary axis AP, fuppofing the pole to keep its place; 



and — • — A X flux, of eQ h the value of the motive force 



requlfite to caufe the ivhole variation of the velocity (y j about 



AB. But the firfl mentioned force dlojie does not, in general, 

 Vol. LXXV. Xx caufe 



