The Theory of Automatic Begidaton 
285 
the generatx)r voltage is normal again. When this is the case, /*2 is once 
more in equilibrium. A similar action occurs for a pressure rise, contacts 
-r^ „ , . , . 1 rT^^ ,1 , • ^iuic of short-circuit of r-, 
K^ii-r, being now, however, separated. Thus the ratio , . . , . p 
i- ^ o ' ' ^ time ot insertion oi 
is altered according to the voltage conditions of the network. Compared with 
a sluggish regulator fig. 8 shows that the required exciting voltage is reached 
very much more rapidly. From to Yo the voltage rise with a sluggish 
regulator would follow curve 2, for a fast regulator it is along ah. 
Let the maximum exciting current (r^ short-circuited) be a^I. The 
equation of the corresponding exponential curve, C, is (equation 2). 
la = a^l[l - , - -^^), whence 
£ — 
h _ a^I — ia 
and according to equation 3, 
dda _ Y, _,*L ^ I -A 
dt^ ~~ L ^ "•^'^ t,, ' 
Inserting the value of £ - we obtain 
dia _ a^I — ia ^J^^^J 
dt^ a^t. 
For curve we have, if the final exciting current with inserted is 
expressed by a^l (see equation 5). 
i'a = oj. f 1(1 - u,) £ 
s k i'a — Ool 
(1 — Oo) £ - — 7 — 
^ ~^ a.ito 
Also according to equation 6 
di'a _ 1 — I J2_ 
— I X £ — , 
dto Oo to f'2*o 
J 
(15) 
Assuming a large number of vibrations of h^, the time elements will be 
very small, and for a stationary state the current pulsates round the mean 
value ia with the difference dia between maximum and minimum values. 
The variations dia and - dia are equal and ia = i'a- From equations 14 
and 15 follows : 
^ — ^ ^ h .... (16) 
dtr, Oo 0^]^! - ia 
For each value of ia we have thus a definite value of This ratio is 
influenced by the position of lever k^, and on it depends the mean value 
