CHAPTER VIII. 



The Polar Diagrams of the General Alternating- 

 Current Transformer. 



IN this last chapter it is my aim to present, in as simple and lucid 

 a manner as possible, the general theory of the alternating-cur- 

 rent transformer, taking also the resistance of the primary into 

 account. The results of this consideration are partly known, but as 

 the road by which they can be reached, is a very easy one, it may de- 

 serve some consideration. I shall make use in my treatment of the 

 problem of the theorem of reciprocal vectors, known in kinematics 

 and geometry as the theorem of inverse points, and I will here make 

 good a sin of omission, of which I became aware only when by 

 chance glancing over the pages of Dr. Bedell's book, "The Princi- 

 ples of the Transformer," in November, 1900. As early as 1893 

 Messrs. Bedell and Crehore gave the theoretical proof of the fact 

 that the locus of the primary voltage in a transformer at constant 

 current is a semi-circle,* and in his paper on "Transformer Dia- 

 grams Experimentally Determined," read at the Electrical Congress 

 in Chicago, 1893, Dr. Bedell gave also the experimental proof for 

 the constant-current transformer that the potential at its terminals 

 can be represented by chords in a semi-circle. To develop the dia- 

 gram for the constant potential transformer was, however, reserved 

 to European physicists. 



DIAGRAM OF FLUXES AND MAGNETOMOTIVE FORCES. 



132. The principle of the conservation of energy requires thaf the 

 magnetomotive forces ,Yi and Xi of the primary and secondary of the 

 transformer tend to magnetize the core in opposite directions. X 



'See a series of ten article* on the "Theory of the Transformer," Electrical 

 World, May, 1893, and later. 



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