the Rotatory Motion of Bodies . ^2 j 
circle as often as y fhall become equal to x w, or- J -~| x n; 
the parts of the track between the points of contact being per- 
fectly fimilar. I f D/s 1 be = Ca 2 ( Dn z being then = B;z 2 , and 
confequently 
D 
c 
X m 
B 
Xn = aJ, 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 refpeCtively de- 
noted by H, I, K ; 
H will be 
I 
K 
M 
d 2 +d 
3 
a 3 T 
M 
d 2 +b 2 
3 
a*T 
M 
d+d _ 
3 
a 3 T 
X flux, of e/3 - 
X flux, of ey -f 
X flux, of e$ 
M 
3“ 5 
M 
3* 5 
M 
3« 5 
Bryl 
Defl 
Cef y; 
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 
leems to me, that he has erroneoufly aflumed equations as 
generally true, which are only fo in a particular cafe. For 
— 5 • Be^^is the motive force to turn the body about x-\B, arifing 
from the centrifugal force of its particles revolving about the 
momentary axis AP, fuppofing the pole to keep its place; 
, M d+r 
ma ~3~ * ~TF * “ ux * e @ is the value of the motive force 
requifite to caufe the whole variation of the velocity ^ about 
AB. But the firfl mentioned force alone does not, in general, 
Vol. LXXV« X x caufe 
