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XXXVII. A Method of Determining the Angle of Lag, By 

 Arthur L. Clark, S.B., Prof of Mathematics and Physics, 

 Bridgton Academy ; North Bridgton, Maine, U.S.A.* 



THE power or rate of expenditure of energy at any given 

 instant of time, on an electrical circuit, may always be 

 found from the equation 



W = EI; 



where W is the power in watts, E the E.M.F. in volts, and 

 I the current in amperes. But if the average power is 

 desired this formula is not general. It suffices only where E 

 and I are constant or nearly so. 



It is a problem at the present time to measure the power 

 expended on circuits through which flow alternating currents 

 whose E and I vary harmonically with the time. In this 

 case the formula becomes 



W =~y cos <f>; 



where <£ is the difference in phase or is the angular magni- 

 tude of the delay of the rise of I behind E. E and I are the 

 maximum values of the E.M.F. and current respectively. 



It is obvious that cos <f> is a very much desired value, and 

 different methods for determining it have been conceived. 

 There have been several phase-indicators brought before the 

 scientific world during the past year or two, but of these 

 there are very few, if any, which furnish a convenient means 

 of accurately measuring a difference of phase. 



The instrument herein described is the outcome of ex- 

 tended investigation carried on by the author during the past 

 year at the Worcester Polytechnic Institute. Many of the 

 different forms of apparatus which depend upon the inter- 

 ference of sound waves, vibrating wires, &c, were constructed 

 and experimented upon, with unsatisfactory results. 



It was found that indicators which are influenced to a 

 marked degree by small variations of the vibration-period are 

 of little value. As this variation interferes seriously with 

 results, and as no dynamo furnishes a current absolutely 

 periodic, such an indicator is worthless commercially. 



The well-known Lissajous's figures have been used at 

 different times as a means of determining the angle of lag, 

 and are the basis of the herein described apparatus. The 

 current from the dynamo passes through a single loop of wire 



* Communicated by the Author. 



