140 OUTLINES OF NATURAL PHILOSOPHY. 



The sum made by multiplying each particle of the 

 cylinder, into the square of its distance from the 

 axis, supposing the thickness of the cylinder, in the 

 direction of that axis, to be m, is found by fluxions, 

 or the quadrature of curves, to be \ K m r 4 , and 

 therefore (by 92.) the velocity acquired in the 

 first second by the circumference of the cylinder is 



* m r 9 = the solidity of the cylinder), = 



Q Tj' _, 



- - '-~ , g being the velocity acquired by a 



heavy body in the first second of its descent. 



As F + W to 2 F, so the force of gravity to the 

 force accelerating the cylinder at its surface. 



220. The quantity A a 2 + B 6 2 , &c. in 216, 

 which is the sum of all the products made by mul- 

 tiplying each particle into the square of its distance 

 from the axis of motion, is called the momentum 

 of the inertia of the revolving body. It is compu- 

 ted for any given body, either by the method of 

 fluxions, or the quadrature of curves. 



'Saite-r ->ff 



221. Let the circle ADB (fig. 15.) represent 

 a sphere moveable about an axis that passes 

 through the centre C, and is perpendicular to the 

 plane of the circle ADB ; and let it be put in mo- 



tion 



