APPENDIX I. 



armature will then be exactly equal to the tangential force which 

 in reality is transmitted by the armature to the belt at its proper 

 working speed, and we may thus calculate the torque exerted by the 

 motor as if the latter were worked as a generator backward at a 

 much slower speed, the whole of the power supplied being used up 

 in heating the armature bars. The object of approaching the prob- 

 lem from this point of view is, of course, to simplify as much as 

 possible the whole investigation. If we once know what torque is 

 required to work the machine slowly backward as a generator, it will 

 be an easy matter to find what power it gives out when working 

 forward as a motor at its proper speed. 



Let in Fig. 105 the horizontal a, c, b, d, a represent the interpolar 

 space straightened out, and the ordinates of the sinusoidal line. B, 

 the induction in this space, through which the armature bars pass 

 with a speed of ~ revolutions per second. We make at present no 

 assumption as to how this induction is produced, except that it is 

 the resultant of all the currents circulating in the machine. We as- 

 sume, however, for the present that no magnetic flux takes place 

 within the narrow space between armature and field wires, or, in 

 other words, that there is no magnetic leakage, and that all the lines 

 of force of the stationary field are radial. The rotation being counter 

 clockwise, each bar travels in the direction from a to c to b, and so on. 

 The lines of the field are directed radially outwards in the space 

 d a c, and radially inward in the space c b d. The e. m. f. will, there- 

 fore, be directed downwards in all the bars on the left, and upwards 

 in all the bars on the right of the vertical diameter in Fig. 49. Let 

 E represent the curve of e. m. f. in Fig. 50, then, since there is no 

 magnetic leakage the current curve will coincide in phase with the 

 e. m. f. curve, and we may represent it by the line I. It is important 

 to note that this curve really represents two things. In the fir-t 

 place it represents the instantaneous value of the current in any one 

 bar during its advance from left to right ; and in the second place, it 

 represents the permanent effect of the current in all the bars, provided, 



01 



