[ 468 ] 



XXXVII. On Transformer Indicator Diagrams. By 

 Thomas R. Lyle, M.A., Sc.D., Professor of Natural 

 Philosojjliy in the University of Melbourne*. 

 [Plate XIII.] 



1. ri^HE term u transformer indicator diagram " has been 

 A applied by Professor Fleming to any series of 

 periodic curves which gives the forms, relative phase-positions, 

 and magnitudes of the waves of current and E.M.F. on both 

 the primary and secondary sides of a transformer when 

 working. Such diagrams have been obtained by many 

 investigators in different ways, but by none of the methods 

 hitherto used has it been possible to determine directly and 

 independently either the wave of magnetic flux F in the 

 core, or the wave of magnetizing-current turns usually 

 represented by the vector sum ?i 1 C 1 + t? 2 C 2 . 



Both these quantities are of fundamental importance in 

 the theory of the transformer. When they are known for 

 any given load, all the other quantities (currents and E.M.F. s) 

 can be determined for the same load when the primary and 

 secondary turns, resistances, and leakage coefficients are 

 known f . 



In addition, since, as will be shown later, the integral 



jOiA + ^C^F 



for one cycle is equal to the total iron loss per cycle, the 

 advantage of being able to determine both ^C^-j- n 2 (j 2 and F 

 directly and accurately is apparent. 



Theoretically, ?i 1 C 1 + w 2 C 2 can be obtained hy the vector 

 addition of 7i 1 C 1 and ?i 2 C 2 , but as the latter quantities are, 

 when the transformer carries a load, approximately equal in 

 magnitude and opposite in phase, their vector sum is a small 

 quantity compared with either of them. Hence small errors 

 in the magnitudes of n 1 C 1 and ?i 2 C 2 may cause a large per- 

 centage error in the magnitude of ^Ci + t? 2 C! 2 , while very 

 small errors in the magnitudes and phase-difference of n 1 G l 

 and n 2 C 2 may render the phase of n 1 C 1 -\-n 2 C 2 calculated from 

 them utterly unreliable. 



By means of the wave-tracer J designed by the author not 

 only can the E.M.F. and current waves be accurately deter- 

 mined, but also the wave of magnetic flux pulsating in the 

 core of the transformer, and in addition, as will be shown in 



* Communicated by the Physical Society : read February 22, 1907. 

 t See Lyle : " The Alternate Current Transformer," Proc. Roy. Soc. 

 Victoria, vol. xviii. pt. 1. 



X Lyle : " Wave-Tracer and Analyser," Phil. Mag. Nov. 1903. 



