eat 
Revolving about Fired Ares. Q77 
with a few remarks designed to show the amount of force exci- 
ted by the rotation of heavy bodies about fixed axes, and the ex- 
tent to which we may reasonably conclude it might be employ- - 
ed, if it could be controlled, by giving the relative proportions of 
the power necessary to revolve a body and the central force exci- 
ted, considered abstractedly, apart from friction and atmospheric 
resistance. ‘The are which the revolving body describes in a 
given time is a mean proportional between the radius of the cir- 
cle and double the space which its centripetal force alone, acting 
uniformly, would cause it to fall through in the same time.’’* 
Consequently the diameter is to the circumference as the circum- 
ference is to the space which the centripetal force of the body 
would make it fall through in the time of one revolution. "That 
space, therefore, is to the circumference as 3.141 is to unit, [3.141 
being the circumference of a circle whose diameter is unit,] and: 
the central velocity or force for an entire revolution in a second 
Is equal to the circumference multiplied by 3.141. Hence the 
ratio of the central force to the force in the direction of the circle, 
or the moving power, is as the product of the number of revolu- 
tions in a second by 3.141 is to unit. That is, if there be two 
entire revolutions in a second, whatever be the weight of the 
body or its distance from the centre, the ratio of the centrifugal 
force to the moving power would be as 3.141 x2 is to unit, or as 
Six to one, nearly; and with eight revolutions in a second the 
ratio is as 3.141 x8 to unit, or as twenty-five to one. And since 
“the velocity of rotation is almost unlimited,”} if a fly-wheel, 
similar to the one described above, were revolved at the rate of 
twelve hundred lutions in a minute, the excited or centrifu- 
gal force in the rim would he equal to sixty-two and a half times 
the amount of power employed to give the requisite velocity, 
some deduction being made for friction and atmospheric resist- 
ance. 
a 
* Cavallo’s Nat. Philos. p. 66. t Fisher’s Nat. Philos, 
Vol. xxx1x, No. 2.—July-September, 1840 
