‘476 Prof. A. W. Riicker on the Self-Regulation 
sponding to w and m are equal, then 
pel igunonied Cees IE Q ® 
where ® is the maximum value of ¢. 
If, now, the following quantities are given, viz. :— 
(1) the value of ¢ which is to be attained (¢, or ®); 
(2) the extreme values of x (« and m); 
(3) the percentage variation in the value of @ which can 
be allowed (100g or 100p); 
(4) the usual value of w (€), together with the condition 
that the maximum efficiency shall be attained for that value ; 
(5) the value of the required maximum efficiency ; 
then we have four equations, viz. either (16) or (17) and the 
two equations which connect y and € with A and Y (see p. 471) 
to be satisfied by the five constants A, Y, B, P, and Q. Of 
these, A and Y are absolutely determined by the conditions ; 
but any one of the three P, Q, or B may be given any con- 
venient value if the maximum value of ® does not lie between 
wand m. If it does, we have the additional relation 
d=(/ P—VQ)’/(A—B); 
and if the values of both p’ and p” are assigned, there 
are in all five equations by which the five constants are 
determined. When these five quantities are known, we 
may equate them to their appropriate values in terms of the 
resistances &c. of the various parts of the machine; and we 
thus obtain five equations between eight quantities, viz.:—n, 
M, o, 81, Sa (OF 8), Ta P1y Pa (OF p,); in the selection of 
which, therefore, there is considerable range for choice. 
Although the problem of the Self-Regulation of the Com- 
pound Dynamo is solved as far as the algebra is concerned, 
it is possible that the values of P,Q, &c. found for arbitrarily 
selected values of ¢, w, m, Ke. may be negative, or such as it 
would be impossible to attain in practice. 
The question as to what value of g it is physically possible 
to attain in any given case can only be answered if we have 
regard to the limitations to the values of A, B, P, and Q which 
apply to that case. If this be done, it is possible to obtain 
limits to g, that is to the perfection of self-regulation. 
I shall add two examples of the use of equations (16) and 
(18) for this purpose. 
Case II]. A<B, P>Q. 
As the values of ¢@ diminish as w increases, the value 
