SECT, vin.] OF THE REGULATION, &c. 257 



engine, the fly is used. Its heavy mass of matter must be so shaped, as to balance 

 itself in any position on an axis connected with the machinery, and turning round 

 with a part of it. 



The proportions of the fly wheel must be derived from the laws of rotary motion. 

 They are not often stated very clearly, and rather in too comparative a form for 

 the purpose of application : Dr. Jackson's equation 1 is derived most in unison with 

 my own methods, and adding the time, the radius corresponding to the angular 

 velocity of the exterior ring of the wheel, and comparing with the force of gravity 

 to obtain the coefficient, it is 



32 P a r t 



= n v. 



bx* 



In this equation 



P = the mean quantity the moving force varies in its intensity in excess 

 above the resistance, 



t = the time in which that variation takes place ; 



v = the velocity, 



n v = the greatest variation of velocity, 



a = the leverage the force P acts with, 



r = the radius corresponding to the velocity v, and 



w = the weight of the fly acting at the distance x from the axis. 



It is obvious that the mass of the fly must be sufficient to receive the excess of 

 force during the time it acts, and afford it again to the machine in an equal lapse 

 of time, and so that the velocity shall not vary more than the wth part. The only 

 point, therefore, which depends on practical experience, is what variation of velocity 

 may be allowed. On this point however there is no difficulty, as the practice of 

 different makers is so different, as to show that it may be taken with considerable 

 latitude. 



The weight of the rim may always be considered to be collected at the extremity 

 of the radius ; and then x = r, and the equation becomes, 



32 P at 



= n v. 



w r 



The effect of the arms of the wheel may be neglected, as it is a problem which 

 neither requires nor admits of a very refined solution, in consequence of the un- 

 certainty regarding the precise variation of the intensity of the moving force ; 

 hence it ought not to be rendered complicated. 



537. From this equation it appears, that when the weight or the diameter of 



1 The9retical Mechanics, art. 400 403. 

 2K 



