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



on the resistances of the electric circuit; (2) that for machines 

 which have their exciting coil in series with the armature and 

 main circuit, there is a certain relation between speed and 

 resistance such that they do not excite themselves at all unless 

 the quotient of speed by resistance attains a certain minimum 

 value ; (3) that in machines which have their exciting coil 

 connected as a shunt to the main circuit there is again a cer- 

 tain relation between the speed and the electric resistances of 

 the various parts of the circuit, such that with a given speed 

 self-excitation does not take place unless the resistance of the 

 external circuit exceeds a certain limiting value. 



On June 26, 1886, I had the honour of bringing before the 

 Physical Society* some formulae relating to the performance 

 of dynamo-electric machines, in which this matter was touched 

 upon, and in which, on the assumption that the law of mag- 

 netization might be adequately represented by the Lamont- 

 Frolich formula, expressions were obtained for the relations 

 between speed, magnetization, resistance, and current. As an 

 important conclusion it was shown, always upon the above 

 assumption, that at a given speed of driving and with a given 

 resistance in the electric circuit, the current, of any given 

 series-wound machine, was always less by a certain fixed 

 quantity than that current which would have been produced 

 (at that speed and with the given resistance) had the mag- 

 netism been actually at full saturation. This difference 

 between the actual current and the current that there would 

 'have been at saturation was a definite number of amperes, 

 and was shown to be that number of amperes which would 

 have been sufficient to produce exactly half-saturation in the 

 given machine. This half-saturating number of amperes I 

 had previously denominated the u Diacritical " current. This 

 proposition having been established, it became obvious that 

 the machine would not excite itself if the speed and resistance 

 were such — the speed so low or the resistance so high — that 

 the current which would have been produced with field- 

 magnets independently saturated was less than the diacritical 

 current. Or, if the resistance of the circuit were prescribed, 

 there would obviously be a least-speed of self-excitation. 



The assumption in the above investigation of an approxi- 

 mate expression for the law of magnetization necessarily 

 made the argument less satisfactory than would be the case 

 were no such assumption made. In the argument which fol- 

 lows no assumptions are made of an empirical character as to 

 the law of magnetization, absence of secondary phenomena, 



* See Phil. Mag. September 1886. 



