Power by Dynamo-electrical Machines. 525 



work of which is at our disposal in various ways. Hence, if 

 we are to make investigations as to the maximum of the work 

 transferred, we must first of all accurately define the conditions 

 to which this maximum refers. 



§ 4. Determination of the Work T 2 when the Velocity v 1 is 

 supposed to be given. 



In reference to the circumstance last mentioned, that the 

 source of power, which we have to use for driving the first 

 machine, is in various ways at our disposal, we will first make 

 the assumption that the source of power is of such a kind as 

 to do work of any magnitude, so that the work T x which can be 

 expended in the first machine is unlimited. This would be the 

 case, for instance, if a great water-power were at our disposal, 

 which would far exceed the demand even with the greatest 

 possible consumption of work. The question is, How can 

 the greatest work T 2 be obtained from the second machine 

 under these circumstances ? 



If T 2 is to be large, then from (15) v 2 and i must be large, 

 and a great value of i presupposes again (12) a great value of 

 the difference v x — v 2 . The two conditions that v 2 and v 1 — v 2 

 must be great can only be fulfilled when v x is great ; and the 

 first condition for a great value of T 2 is therefore that v l9 the 

 velocity of rotation of the first machine, must be as great as 

 possible. In this respect we are confined within certain 

 limits^ arising from the mechanical difficulties which oppose 

 the production of very great velocities ; and we will ac- 

 cordingly consider the greatest attainable velocity as a given 

 magnitude, and assume that Vi is this velocity. 



Of the two velocities of rotation, v 2 only remains undefined; 

 and we may accordingly regard the work T 2 as a function of 

 this magnitude. To determine this function we will use the 

 equation already deduced, that is, 



• in which we may replace i by its value given in (12). The 

 magnitudes u and u' y which occur in this latter, are functions 

 of v 1 and v 2 in accordance with (6) and (10); and hence also the 

 entire expression for T 2 obtained in this way is a function of 

 Vi and v 2 . As, further, we must consider v\ as given and only 

 v 2 variable, we may also say that in this way T 2 is represented 

 as a function of the single variable v 2 . 



In order now to find that value of v 2 for which T 2 is a 

 maximum, we must apply the well-known method of differen- 

 tiating T 2 in respect of v 2 , putting the differential coefficient 



Phil. Mag. S. 5. No. 109. Suppl. Vol. 17. 2 N 



