of the Compound Dynamo. 481 
write 
q= | {AB+u(A+B) t; 
which shows that, among the various solutions which satisfy 
the condition A?Q=B’P, that will give the best self-regulation 
for which A and B are largest. 
The condition that A shall be large implies (since A=1/R,,) 
that the resistance of the machine must be small, the necessity 
for which could of course be readily foreseen. The condition 
that B should be large leads to less obvious conclusions. 
Thus, in the case of the Long-Shunt Machine, 
B;=(s,+ Sa) / S1P9 5 
and to make this as large as possible, we should have s,/s 
large and p, small. The first of these conditions is always, 
the second is never, fulfilled in practice. The reason of this 
is obvious, viz. that the efficiency would be reduced by dimi- 
nishing the resistance of the shunt. The maximum efliciency 
is given by the formula 
n=(Vp2—V Rn) /(V pot / Rm); 
which diminishes with p,. It is interesting therefore to note 
that a high shunt-resistance is not in itself conducive to good 
self-regulation ; and that, within the bounds of Dr. Frélich’s 
condition, there are still opportunities for choice by which 
improvements in the efficiency and regulation may be effected. 
Probably in practice the last adjustments will be best made by 
some system of experiment like that described by Dr. Frélich. 
The theory given above will, however, enable much to be done 
by a few preliminary calculations. 
Since | read the paper, Prof. Silvanus Thompson has called 
my attention to the question as to whether my formulz indi- 
cate the advantage of back winding in the case when a constant 
external current is desired. Dr. Froélich has constructed a 
machine on this principle, to which he was led by theory. 
To discuss this question fully would require an investigation 
of the problem when B is negative; but it may be remarked 
that in a case such as that discussed above, when a large value 
of B is desirable, it may be increased in the case of the Long- 
Shunt Machine (B,) by taking s, negative and <3). 
