THE OPERATION OF THE DYNAMO AS A MOTOR. 99 



tromotive force 4>ZX is equal to the product I a x QZ'n\ and, 

 according to Lenz's law, this is equal to the mechanical power 

 developed by the torque T with which the field magnet acts upon 

 the rotating armature. Now, the mechanical power in watts 

 developed by a torque of T pound-inches acting upon a body 

 making n revolutions per second is : 



p 2^x2.54x453-6x980 nT watts 



io 7 

 or 



P= 0.7 \nT watts. (24) 



Therefore by Lenz's law we have 



7 o x QZ'n 0.7 inT 

 whence 



T= 1.41 QZ'I a pound-inches (25) 



in which Z r = pZ/p f io s , f a is the armature current in amperes, 

 4> is the magnetic flux entering the armature from one field 

 magnet pole, p is the number of magnet poles, p f is the number 

 of paths in parallel through the armature between brushes, and Z 

 is the total number of conductors on the armature. 



The net effective torque at the pulley of a motor is less than 

 T in equation (25) by the amount of the torque required to 

 overcome friction and other so-called " stray power" losses. 



If the net or useful torque is used for T in equation (24) the 

 power P will be the power actually delivered by the motor 

 pulley. 



54. Siemens* law of efficiency. The dependence of the effi- 

 ciency of a motor upon the conditions of driving is complicated 

 by the loss of power in field excitation, by friction, and by eddy 

 currents and hysteresis. This matter is fully discussed in Chapter 

 V. A very simple expression for the efficiency of a motor, due 

 to Siemens, is especially useful for purposes of general discus- 

 sion. The formula is only approximate, however, inasmuch as 

 it is based on the assumption that the only loss of power in the 



