CH. VII ACCELERATION 



inertia of the mass to be moved, the velocity ratio, and the 

 resistance of the motor. 



If E is the tension of the line, R the total resistance 

 in the circuit, for the present considered constant, and M 

 the induction factor, we can write down the following 

 equation, which we know must hold good at any instant : 



(64). 



Substitute in this equation the value of c obtained from 

 Equation 63 and we have 



dn 1iM k/n 



(\ 77 



This equation is of the form - ' + P;/=Q I} the solution of 



CviXj 



which is 



(See Perry's ' Calculus for Engineers,' p. 326.) 

 The solution of Equation 65 is then 



(66). 



M 



) 



Now the expression -- f is the final speed of the 



motor when it has ceased to accelerate. If this is n f , we 

 then get 



-VfJ& " (67). 



To find the value of the constant K, we know that when 

 /,=o, n is the initial speed, if we call this ,,, and put n=n. 



