Account of some Bxpcrhnent<! on Frtcllon. 123 



resistance is greater when the velocity is greater : but it 

 will shortly be seen whether this increase of resistance may 

 not be attributed to the air. 



I will now proceed to estimate the intensity of these re- 

 sistances from the facts reUited ; 



The grindstone being 5i?i inches diameter and 20i inches 

 thick, its solid contents were consequently 25^ cubic feet; 

 the specific gravity of a piece of stone of the same kind was 

 accurately taken, and found to be 2.208 : a cubic foot of it 

 would therefore weigh 13Slb., and the whole grindstone 

 3J0llb. The iron spindle and wooden pulley were by calcu- 

 lation 200lb., makmg the whole weight that was supported 

 by the pivots of the spindle in round numbers 3700lb. 



The resistance which a particle of matter at the distance 

 X from its centre of motion opposes to a change of angular 

 motion is as x'-, the resistance being measured by a power 

 applied at a constant distance from the centre. In order to 

 find the sum of resistances of all the matter in the stone, it 

 is to be considered that the number of particles at the di- 

 stance X is tmxx {t. being = the thickness of the stone, and 

 VI = 6,283 &c = the circumference of a circle whose ra- 

 dius is 1) ; and as the resistance of every one of these par- 

 ticles is, as before said, .r- the fluxion of the sum of all the 

 resistances = tmx^x whose fluent, or sum of resistances 



= = when X = r, (the radius or the stone) . 



If all the particles of the stone had been at the distance r 

 from the centre, the sum of resistances would have been as 



the solid content x r2 = ; it is therefore evideiit that 



2 



the sum of resistances of all the particles of the stone is 

 half wh&t it would be if every particle were at the circum- 

 ference, and had the same anc!;ular velocity : for - — - 



to . ^ . 



By the experiments it appeared that w-hen the resistance 

 of the air might be esteemed inconsiderable (the velocity of 

 the stone being comparatively small), the retardation of the 

 velocity was about 26 turns per minute attributable to the 

 friction on the pivots. It may therefore be asked, What 

 power acting uniformly would give to hnlfxhc quantity of 

 matter in the stone (= 1750lb.) a velocity equal to 26 

 limes its circumference? Twenty-six times the circumfe- 

 rence of the stone is about 35] i itet. Gravity would give 



a velocity 



