270 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Methods of Using the Machine. 



The following methods are all based on the assumption that we 

 have a sinusoidal E. M. F. of known period, acting in a circuit con- 

 taining only true resistances and inductances. The current at any 

 instant will be expressed by the equation 



i = = sin I Pi — tan~ l — - • 



VR 2 + P'L 2 \ R) 



The maximum value of the sine term being unity, we have 



1 _ 1 



E ~ V-R' 2 + R 2 L 2 ' 



I and E being the maximum current in, and maximum E. M. F. im- 

 pressed upon, the part of the circuit under discussion. Also the lag 



LP 



between current and E. M. F. is expressed by tan 6 = -^5- . From 



R 



these two equations we have 



E . E 



L = y~ sin 6, and R = — cos 6. 



Our aim is, therefore, to obtain the values of the impedance, angle 

 of lag, and frequency, and to calculate the coefficient of self-induction 

 and the resistance for any given periodicity by the above formulas. 



(a) If we make up a circuit of the movable armature, a known 

 resistance of negligible inductance, and the unknown coil, all in series, 

 we may, by means of the measuring arrangement already mentioned, 

 obtain E and /, the latter by the maximum P. D. around the known 

 resistance. The angle 6 would best be found by taking measurements 

 on both sides of the zeros of current and E. M. F., and interpolating 

 for the zero points. The difference of readings of the micrometer so 

 obtained divided by 20 gives the angle 6. L and R are to be calcu- 

 lated by the above formulae. 



(b) If we have a carefully made plot, like Figure 6, connecting the 

 maximum E. M. F. and field current of one dynamo, we may proceed 

 as follows. As the wave forms are alike, both following the sinu- 

 soidal law, we may apply Poggendorf's method of balancing E. M. F.'s 

 directly, using a suitable telephone instead of a galvanometer. To do 

 this make up a circuit of the stationary armature, known inductionless 

 resistance, and unknown coil. Keep the field current of this dynamo 

 constant. Attach the second armature through the telephone, first to 

 the terminals of the known resistance. Adjust the phase relation for 



