THE THEORY OF THE DYXAMO 231 



the electro-motive force does not vary with the size, but we shall pres- 

 ently see how this is modified so as to get greater electro-motive force 

 for the larger machine. 



The work done is C 2 R in any part of the machine, or in the whole 

 machine, just as you please. This varies directly as I. Therefore the 

 one machine which is twice as large as the other requires twice as much 

 power to run it, and twice as much electrical energy comes out of it. 

 But it is to be remembered that the weight of the machine varies as I s , 

 and we only get work proportional to I out of it. 



So far as results go, we have constructed two machines which differ 

 only in size. The efficiency of these two machines is a constant quan- 

 tity. That will be rather startling to some, who think a large machine 

 is more efficient than a small one. As far as we have gone in any two 

 machines, one of which is simply larger than the other, the efficiency is 

 the same. 



But if we calculate the angular velocity of the armature to keep the 

 proper current we shall find that it varies inversely as the square of the 

 linear dimensions. In other words, in one machine twice as large 

 as another the velocity of the armature must be only one-fourth as 

 great in order to produce the proper current in the wires. This takes 

 account, I think, of every irregularity in the machine. The two 

 machines are exactly the same in every respect. I have not added the 

 loss for the self-induction of the coil. I have an idea that this also 

 should be taken into account, but Mr. Fitzgerald will consider that 

 point. 



ISfow the question comes up, can we increase the velocity of the arma- 

 ture above that point? Is it practically necessary that we should run 

 one machine at one-fourth of the angular velocity if it is twice as large ? 

 It is a practical question; but I should certainly think the velocity was 

 not in that proportion. I should think it would be more nearly in- 

 versely as the size and not inversely as the square of the size. If so, 

 then by so arranging the wire of the armature as to increase the pro- 

 portion of external resistance we can have the same current per unit 

 of section when running the armature faster and the same electro- 

 motive force. If we do that, this whole theory applies; but we shall 

 have increased the external resistance of the machine in comparison 

 with the resistance of the armature, and when we do that we increase 

 the efficiency of the machine. 



I think it is from this cause that we find large machines more efficient 

 than smaller ones; but it is also evident that there is a limit to this, 



