Power by Dynamo-electrical Machines. 527 



This equation shows that the value of v 2 which corresponds 

 to the maximum of T 2 is not equal to t^/2, as the above law 

 states, but approaches this value with increase of v lt 



§ 5. Determination of the ivork T 2 when the work T x is given. 



The second assumption which we can make in regard to the 

 source of power which drives the first machine, may be that 

 it can only perform a work T x of definite magnitude. The 

 question then arises, Does the work T 2 to be gained from the 

 second machine depend on the working of the machines ? 



It is here to be observed that, if Tj is given, only one 

 of the velocities of rotation t\ and v 2 is to be considered as 

 independent. As three equations, (III.), (V.), and (3), are 

 given between the five magnitudes v ly v 2 , T 1? T 2 , and i, from 

 two of these magnitudes the other three can be determined. 

 We will consider vi as that magnitude which, along with T 1} 

 serves to define the other three values. 



In order to define i as a function of T x and v } we use the 

 equation (III.), that is, 



which we may bring into the following form : — 



(e + i)i 2 = T L _ (1W + \_\vr _ 



(a + i)(b + i) pv x \a + ij\ b + i)p' ^ ' 



The solution of this equation in respect of i is rendered 

 more difficult by the second member on the right hand, which 

 contains i in the denominator in a higher power than the 

 member on the left hand. It is to be observed, however, that 

 the member on the right hand is affected by the factors a and 

 X, which are so small that we may disregard magnitudes in 

 reference to them w T hich are of higher than the first order. 

 This fact may be utilized in treating the equation. We first 

 of all determine that value of i which results from the equation 

 when w r e disregard the member containing the factors a and X. 

 If we denote this value for distinction by i f } the equation for 

 its determination is 



(^+ty _ % (27] 



(a+i'Xb + t)*^ V ; 



The value of i ! resulting from this can only differ from i by a 

 magnitude of the order of the factors a and X ; and if we 

 return to (26), and in the member affected by these factors 

 replace i by the value i f , the expression on the right hand only 

 changes by a magnitude which in reference to a and X is of 

 the second order, and therefore may be neglected. Hence 



2N2 



