480 Transformer Indicator Diagrams. 



both the external resistance R and the external inductance L 

 can be calculated, or if R is known two determinations of L 

 •can be obtained from each order of harmonic. 



If, however, as in the present case &>L/R is considerable, 

 the first order is the only one suitable for this purpose ; for 

 if ^-j, fa, and y}r 5 be the difference of phase of the first, third, 

 and fifth harmonics respectively of E 2 and C 2 , then, since 



&)L ?>wh 5<wL 



tan i/rj = -g-, tan -f 3 .-= -^- , tan ^ 5 = -^- , 



and eoL/R is large, a small error in the observed values of yfr 3 

 or y]r 5 will cause a large error in the value of L deduced 

 :£rom them. 



For the first harmonics, as ^ i= =43°-3, R = 76*52, a>=342;4, 

 we find from 



tanti = - S - 



wthat L = *2106 henry ; and from 



v/R' + w-L 2 

 'that L = '2084 henry. 



These give a mean value for L of '2095 henry, which is as 

 likely to be correct as the value *212 already given and which 

 was obtained by the Wheatstone's bridge method. As co or 

 2tt/T was determined by the chronograph attached to the 

 wave-tracer, the above constitutes a new method of measuring 

 an inductance in terms of a resistance and a time. 



9. In Table I. § 7, it will be noticed that the iron loss for 

 the 3rd harmonic is negative ( — '28 watt). This means 

 that all the watts put down as iron loss for the 1st harmonic 

 are not dissipated as heat, but that some of them are trans- 

 formed by .the iron to 3rd harmonic power ; a portion of 

 these are dissipated as heat, while the remainder *28 watt 



. are given out as electrical power by the iron to the copper 

 circuits. This phenomenon has already been drawn attention 

 to in a former paper * by the author. 



10. In the diagrams, figs. 2, 3, and 4 (PL XIII.), it is worth 

 drawing attention to the approximate permanence of form of 

 the magnetizing current wave, and to the permanence of the 

 relative phase xelations of E 1 , ^iCi + ^g^j an( l F, for the 

 three essentially different conditions of working for which 

 the diagrams were obtained. 



* " Variation of Magnetic Hysteresis with Frequency," Phil. Mag. 

 Jan. 1905. 



