Electromagnet and the Equations of the Dynamo. 297 



dynamo such a speed n x that the coefficient of i a shall be zero, 

 or that 



SKB-e) = (?•„ + n„)0 (13) 



Bat cj), the maximal number of ampere-turns, is not itself a con- 

 stant, since it contains as one of the three terms in its sum the 

 quantity $i a . Hence we gather that absolute self-regulation 

 is physically impossible ; and it approaches to perfection as 

 Zi 8 + (j)' are great as compared with S/ a . In other words, 

 there must be so much iron in the machine that the diacritical 

 excitement is very great, and it must have a small armature- 

 resistance ; otherwise S (and S«' a ) cannot be small as compared 

 with Z (and Zi s ). This is known already to electric engineers. 

 Assuming that the dynamo is well designed in these respects, 

 <f> will be very nearly constant, and the equation of condition 

 may be accepted as adequately true. This leaves equation ( 12) 

 in the form 



ec/) / = i s Z(n 1 B— e), 



e<b' D 



^ f = nfi-e. 

 Putting in this value of ?*,B — e into equation (13), we have 



z<£ = — s~ <£ ( u ) 



Now (// may be written either as S^a / or as Z«/, and <f> may 

 be written either as S?" a or as Zi s . Choosing the second form 

 in the first case and the first form in the second case, we may 

 obtain 



fs 1s = ya ~r Vm) ^a i 



or, finally, _ 



e 8 ' = e a+m ; (15) 



or, the diacritical value of the potential at terminals for the 

 shunt-wound part of the circuit must be equal to the maximal 

 value of the potential at terminals for the armature and series- 

 wound part. The equation (14) also gives 



<t>' 



Phil. Mag. S. 5. Vol. 22. No. 136. Sept. 1886. X 



(16) 



