Study of Transformers. 169 



transformers. Every year I give to students in an " Applied 

 Mathematics " class the old-fashioned formulae concerning 

 two or more circuits ; my students have generally worked a 

 few numerical examples on transformers, and we have then 

 gone on to other subjects. 



I venture now to think that I have lost almost nothing by 

 remaining for so long ignorant of the vague but reckless 

 statements made by writers of papers on this subject, and 

 that students will gain something by coming back to the old- 

 fashioned method of treating it. 



I say, on the assumption of constancy of magnetic permea- 

 bility, of no hysteresis, and no heating of either iron or copper 

 by eddy currents, what are the laws of a transformer ? 



Let this be found out first. 



On comparing the theoretic and experimental results, we 

 shall be in a position — we have never yet placed ourselves in 

 this position — to theorize on the effect of the new phenomena, 

 and even this it will not be wise to do until we observe 

 whether magnetic leakage will not account for some of the 

 discrepancy. 



If one gives numerical values to resistances, sizes of iron, 

 numbers of windings, &c. it is quite easy — a matter of a few 

 hours at most — to calculate everything about all the currents 

 for a transformer with two, three, or more coils. 



This year, instead of asking my students to work a few 

 numerical exercises, I asked them to work out quite a number 

 of exercises on a transformer with two coils, and I venture to 

 think that the numbers given by them in the following Tables 

 are of even more interest — just now — than experimental 

 results. The tables give results that no experimenter could 

 give. I have had some experience myself, and really I cannot 

 say that I see my way, with any ordinary dynamometer, to 

 distinguish between a lag of 175° and 180° ; whereas in these 

 tables the lag sometimes varies for no load and full load be- 

 tween 179°-940 and 179°-942. The graphical method of 

 working cannot distinguish differences so small as these. 



As for the trouble of working, — my students have much 

 other home-work to do, and they do it, and yet one of them 

 has brought me two complete tables worked out at home 

 between Friday and Monday. 



Let Y be the primary voltage, C the primary current, R 

 primary resistance, L the primary self-induction, C the 

 secondary current, R' the secondary resistance, L' the 

 secondary self-induction, and M the mutual induction. Let 

 p be a non-inductive part of the resistance of the secondary, 

 the part external to the transformer. Let V be the voltage 



