Revolving about Fixed Axes. 277 



■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 conchide 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 arc 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 x 2 is to unit, or as 

 six to one, nearly ; and with eight revolutions in a second the 

 ratio is as 3.141 x 8 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 revolutions in a minute, the excited or centrifu- 

 gal force in the rim would be 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. 



* Cavallo's Nat. Philos. p. 66. t Fisher's Nat. Philos. 



Vol. XXXIX, No. 2.— July-September, 1840. 36 



