472 Prof. S. P. Thompson on the Conditions of 



tion, it will be seen that, for a given dynamo, all its factors, 

 except the speed n, are invariable. Hence the main fact 

 brought out by this equation is that in a series dynamo, 

 driven at constant speed, the product of the magnetic resist- 

 ance into the electric resistance is a constant. We have here 

 the key to the behaviour of the self-exciting dynamo ; — the 

 explanation why it is that the machine, though exciting itself 

 up " at a compound-interest rate/'' stops short of absolute satu- 

 ration in the degree to which its magnetization is raised. As 

 the field-magnets get more and more highly magnetized, the 

 magnetic resistance increases. Suppose that such a dynamo, 

 running at a constant speed, works at a certain degree of 

 magnetization when there is a certain resistance in the elec- 

 tric circuit. Suppose that resistance to be now reduced : the 

 current increases ; as a result there is higher magnetization, 

 higher electromotive force, and therefore still greater current. 

 To what point will these things go on increasing ? Equation 

 (6) gives the answer: until the decrease in the electric re- 

 sistance is exactly balanced by the increase in the magnetic 

 resistance. 



Other phenomena of the action of the dynamo now become 

 more intelligible. As is well known, in ascending magneti- 

 zations of iron there is a certain stage at which the magnetic 

 permeability increases, instead of decreasing, with an increase 

 in the magnetization. In a dynamo at this stage of excitation, 

 any increase in the electric resistance, causing a decrease in 

 the current, will also cause an increase in the magnetic resist- 

 ance ; hence this stage of excitation is one of instability. The 

 dynamo is either excited above this stage, or else its excitation 

 falls below this stage — virtually to zero. 



The two factors of the product Xp . ^R are both complex 

 quantities, containing constant as well as variable terms. We 

 may write tp = * + %. 



Here the constant part a relates to the magnetic resistance of 

 the gap between the armature-core and the polar surface of 

 the field-magnets ; which gap, filled partly with copper, partly 

 with air, and partly with insulating materials, possesses, so 

 far as is known, a constant magnetic resistance. The variable 

 part f of the magnetic resistance relates to the iron portions 

 of the magnetic circuit : it is in general the sum of a number 

 of terms such as 1/fiA, where I is the length, A the sectional 

 area, and //, the permeability, for the time being, of the various 

 portions — cores, yoke, &c. 

 Similarly, we may write 



