164 



Dr. J. Hopkinson. 



[Mar. 10, 



March 10, 1887. 



Professor STOKES, D.C.L., President, in the Chair. 



The Presents received were laid on the table, and thanks ordered 

 for them. 



The following Papers were read : — 



I. " Note on Induction Coils or 1 Transformers.' " By John 

 Hopkinson, M.A., D.Sc, F.RS. Received February 17, 

 1887. 



The transformers considered are those having a continuous iron 

 magnetic circuit of uniform section.* 



Let A be area of section of the core, 



m and n the number of convolutions of the primary and secondary 



coils respectively, 

 R, r, and p their resistances, p being the resistance of the secondary 



external to the transformer, 

 x and y currents in the two coils, 

 a induction per square centimetre, 

 a the magnetic force, 

 I the length of the magnetic circuit, 



E = B sin 27r(£/T), the difference of potentials between the ex- 

 tremities of the primary, 

 T being the periodic time. 



We have 



(1.) 4ur(inx + ny) = lx; 



(2.) E = Rx-mAa; 



(3.) = (r+. P )y—nAa; 

 from (2) and (3), 



* For a discussion of transformers in which there is a considerable gap in the 

 magnetic circuit, see Ferraris, ' Torino, Accad. Sci. Mem.,' vol. 37, 1885 ; Hopkinson, 

 "On the Theory of Alternate Currents," 'Telegr. Engin. Journ.,' vol. 13, 1884, 

 p. 496. 



