Electromagnet and the Equations of the Dynamo. 293 



where E is the "maximal" value of E at that speed with 

 saturated magnets. And, again, writing e for the differ- 

 ence of potentials at the terminals of the machine, since e, 

 multiplied by the external resistance R=i under all circum- 

 stances, we have 



e=«W (4) 



It appears, then, that in the case of the series-wound 

 dynamo, each of the single electrical quantities is equal to the 

 difference between the " maximal " value which that quantity 

 could have at that speed if the field-magnet were separately 

 saturated and the " diacritical " value of the same quantity. 

 This important result was announced by Frolich* in 1885. 



It may be remarked that, since we may write 



R=Y W+W' 



we may deduce from (1) the result 

 E=nB-W, 



and from this derive equation (3) . 



It may be noted, in passing, that B is the electromotive 

 forces that would be generated in the armature at speed = 1 

 if the field-magnets were separately excited to absolute satu- 

 ration. It is the maximal value of E at unit speed. 



4. Egressions for the "Dead Turns." 



It is known that in every dynamo the current (with a given 

 resistance) is not proportional to the speed, but is proportional 

 to the speed less a certain number of revolutions per second. 

 This latter number is known familiarly as the " dead turns." 

 It is also known that (with given resistance) there is a certain 

 speed below which the dynamo does not excite itself. This 

 least speed of excitement (with given resistance) is the same 

 as the " dead turns." It is called by some the " critical " 

 speed ; though that name is preferably reserved for the speed 

 that is critical for self-regulation, and which is (unlike the 

 least speed of excitation) independent of the resistance. 



We can find an expression for the dead turns as follows : — 



Taking the expression for the current, 



._ nB ., 



equate it to zero ; the current of the machine (series-wound) 

 being nil when n is reduced sufficiently to n' (= the dead 



* Elektrotechnische Zeitschrift, vi. p. 133, March 1885. 



