Electromagnet and the Equations of the Dynamo. 295 



But is the same thing as the " maximal " value of e 



which the machine would give, if the magnets were sepa- 

 rately saturated, when working at the speed n through resist- 

 ances as given ; it may therefore be written as e. 

 Whence, finally, 



e=-e-e' (8) 



From which we get at once also for the shunt-current, 



i s =i s —i 8 'l ( 9 ) 



and for the main -circuit current, 



t = i-i' (10) 



6. General Equation of the Self-exciting Dynamo* 

 Let yfr be any one of the currents or potentials of the 

 dynamo, ty its '"'maximal" value, that is to say the value it 

 has when the magnet is separately saturated, and yjr f its 

 "diacritical value." 



^=/(»,A,Y,[R]); 



and, by the very nature of the case, whatever the form of the 

 function /, 



f=/(«,A,H,[R]); 

 and 



H=Y * • 



whence 



- ^ 



and, finally, 



^ = ^-o|/; (11) 



which is the general equation of the self-exciting dynamo. 



It may here be pointed out that the two terms on the right- 

 hand side of this equation — the " maximal " and " diacritical " 

 values of the quantity on the left — possess certain properties. 

 In a given dynamo the " diacritical " term is a constant, whilst 

 the " maximal " term is a variable which increases with the 

 speed of driving. The maximal term when representing a 

 current varies also with changes of resistance, in an inverse 

 way, but differently in shunt dynamos from series dynamos : 

 when it represents an electromotive force it does not vary 

 with changes of resistance. A year ago Dr. Frolich sought 

 to divide the equation of the dynamo into two parts — an 



