Art. 1. — TJls Alternate Current Transformer. 



By THOMAS R. LYLE, M.A., 



Professor of Natural Philosophy in the University of Melboiirne. 



(With Plates I.-V.). 

 [Bead 9th June, 1904]. 



The following paper is divided into three Sections. 



In Section I. the mathematical theory of the closed-circuit 

 transformer for sinusoidal wave forms is developed, and reduced 

 to a form suitable for practical application. 



In Section II. is given an example of the application of the 

 practical formulae obtained in Section I. to the design of trans- 

 formers to operate different classes of load. 



Section III. contains analytical investigations relating to 

 magnetic leakage in transformers, to what are called the 

 transformer numerics, and to tlie determination of the most 

 efficient shapes of transformers of different types as well as a 

 general solution of the transformer problem in which no assump- 

 tions with regard to leakage are made. 



Section I. 



1. It is well known that when an alternate magneto-motive 

 force (M.M.F.) operates in a magnetic circuit (laminated), the 

 M.M.F. per unit length (H, say) and the average flux density (B, 

 say) can be expressed as follows : — 



H = Hi[Sinzf;/ + k,^in3{wi -js) + (fee] 



B = Bi[Sin(z£// -8) + l>Sin3{wi-fis) + ^c.] 

 where the period is 2TrJ7V ; and that the iron losses per cycle, 

 per unit volume, due to hysteresis and eddy currents are equal 

 in this case to 



^i^^[SinS + 34^3Sin3(/33 - y,) + &c.] 

 4 



If Bi = yLioHi then /Aq and 8 will depend on Bj, lu, and the wave 



form of H, as well as on the quality of the iron and the thickness 



of the laminae. 



