464 Prof. A. W. Riicker on the Self-Regulation 
We have at once 
Vane c! EE Ca 
1 a 
pa ~RY+R, po BYt+R, 
x npr=cR, and yep=cB's, 
ence 
RY, + R’ RY RY 
aM oh ragga 8 +a te 
K —2k = ——_—_, + a oa 
Lto| oes +37 ae ae 
a 
2 
/ 
2 
But 
imc irsPln 1s aM Ra a Si Se 
R, ar R%, th Pa RY an R% ay Pa R 
Hence, if we write 
RU+R% RY, RY Pa ys 
{6 Pa ie a Bats p2 f Ri + Ra eae 
we get 
K—nk= oa /(1+ =) 
or 
R nM 
(B—nk)(B+ =8)= at. 
If the machine has no external excitement / may be neg- 
lected, unless the conditions under which it begins to work 
are under investigation. Hence the equation becomes 
E= JnM—R/S} [Os 3 er 
If there is external excitement and the magnets have not 
reached the condition where the evidences of approaching 
saturation become important, terms in o may be neglected, 
and we have 
R/S—nM’ ° e e ° e e (2) 
If & and o be both neglected these equations lead to conclu- 
sions of no practical value; for if nM=R/S, both (1) and 
(2) make E indeterminate ; and if nM#R/8, we get H=o 
from (1) and H=O from (2). 
These results prove that no true approximation to the 
behaviour of the machine can be obtained by neglecting both 
the constants & and o. 
The above equations are exactly similar in form to those 
ordinarily given as applying to series and shunt machines ; 
