296 Dr. S. P. Thompson on the Formula of the 



armature part and a field-magnet part. This does not quite 

 correspond to the case. The " diacritical " term appertains to 

 field-magnet primarily ; but since the number of ampere - 

 turns of current that will produce a half-saturated magnetic 

 field depends also on the quantity and quality of the iron in the 

 machine, it is impossible to regard it as independent of the iron 

 masses of the armature. The " maximal " term is proportional 

 both to A, the total effective area of the armature-coils, and to 

 Y, the maximum value of the magnetic field. The " diacritical" 

 term for currents is lowered by increase in the number of 

 magnetizing coils, and for potentials is raised by increase in 

 the resistance of the magnetizing coils. The " maximal " 

 term is not altered by altering the magnetizing coils, but 

 increases with an increase in the number of coils of the arma- 

 ture, and, for currents, decreases with increasing resistance. 

 If the iron parts of a dynamo be given of a certain form, size, 

 and quality, then it may in general be said that yfr r depends 

 only on the windings (and, for currents, on the resistance) of 

 the field-magnet, and ^ depends only on the windings of the 

 armature (and, for currents, on its resistance) and not upon 

 the windings of the field-magnet, or on their resistance except 

 (and this only for currents) so far as their resistance contri- 

 butes to the resistance of the whole circuit through which the 

 current generated in the armature flows. 



7. Conditions of Self-regulation for Compound-wound 

 Dynamos. 



In this case we write the formula of the electromagnet in 

 terms of the ampere-turns ; Si a for the excitation due to the 

 coils in the armature part of the circuit, Zi s for that due to 

 the shunt, and </>' as the diacritical number of ampere-turns. 

 Then, writing 

 E=4?iAH; 

 e ='Ei — (r a + r m )i a ; 



H^Y ^. ' a =Y = — , by equation (11) ante; 



Ll s +oi a -r<p <p 



B = 4AY; 



we have 



ecf>' = i s Z{nB-e) + i a {S(nB)-e)-{r a + r m )$\ . . (12) 



The condition sought is to be such as to make e constant. 

 Now $ is a constant, so is i s if e is, and n may be made con- 

 stant at any value we please. Hence, as i a is a variable, the 

 condition of constancy can only be attained by giving the 



