THE INDUCTION MOTOR. 361 



in which the factor (1 + s 2 k~) in the denominator shows 

 the modification in the value of torque produced by leakage. 



At light loads the slip will be very small, and the factor 

 1 + s 2 & 2 will be practically equal to 1. 



At very heavy loads 1 + s ' 2 k z will be almost equal 

 to s 2 & 2 , since 1 will be small compared with the value 

 of s z k z . Also the current c in the numerator of the 

 fraction is proportional to the slip. Hence at light 

 loads the torque is proportional to the slip, and at heavy 



loads the torque is proportional to- p . Thus the speed 



torque curve begins as a straight line, coinciding with 

 the theoretical curve corresponding to no leakage, and 

 ends by becoming a hyperbola as the slip of the motor 

 increases up to the point of still-stand. The actual 

 shape is that shown as the result of a later experiment : 

 its general form is shown in Fig. 180. 



It is important to notice that the value of k = = 



JLii 



can always be altered by inserting resistance in the 

 rotor circuit so as to change R. By doing this we should 

 vary both the current and slip of the motor corresponding 

 to a given torque, i.e., a given load overcome by the 

 shaft. 



Thus it is always possible with any given load to 

 alter the slip at which the motor will overcome this load 

 by altering the resistance in the rotor circuit. 



This is of advantage especially at starting, since 

 with suitable variation of the rotor resistance the motor 

 can be made to give any desired torque at low speeds. 

 This will become more evident from the experiments 

 which follow. 



It must be remembered that in the formulae just 

 given only " absolute " or C.G.S., units have been used, 

 and that consequently the torque is expressed in dyne- 

 centimetres, and the current and voltages in units, 



which are respectively 10 amperes and 8 volts. 



The following relations may be found convenient for 

 reference in converting the expression just obtained 

 into other units. 



