40 president's address — SECTION A. 



picture to ourselves the decrease of ^ with induction as an 

 increase of E with displacement, a phenomenon common 

 enough. 



Again, in comparing the strain theory with that of elec- 

 trostatics, we may represent a conductor as a part of the 

 medium in which E = ; or in which the medium is not 

 " tethered " at all, but able to move freely. In a paper I had 

 the honor to present to this Section last year, I worked out 

 the analogy with the theory of electrostatics. The develop- 

 ment is particularly simple — much simpler than it is on the 

 ordinary theory. 



It must always be remembered that this is only an analogy, 

 not a theory. It was first suggested by Maxwell; but I do 

 not think it has since received the attention it deserves. 

 There is no analogy which gives such a clear picture of the 

 relations between electric quantities considered by themselves, 

 and magnetic quantities considered by themselves, a picture 

 of which we stand very much in want at the present day. 

 So far as it goes the analogy is complete — it is almost a 

 theory ; it only breaks down when we come to the relation 

 between variation of magnetic induction and electro-motive 

 force caused thereby. It is, too, a decidedly good point in 

 this analogy, that it throws into prominence just those quan- 

 tities which are in constant use in modern work in magnetism. 



The permeability fx is represented by -=- ; in iron, for ex- 



ample, the elasticity is very small, it yields very easily to 

 magnetising force. B the magnetic induction is 4 tt x dis- 

 placement. Lastly, the magneto-motive force Q, whose line 

 variation is called H^ is the pressure. On the other hand, 

 the analogy does not so readily give a physical representation 

 of the less used quantities I and K, quantities which are 

 indeed superfluous if we use ju, B, and Q,. To see what is 

 the analogue of I we must proceed in this way : 



Consider a small volume within a mass of iron. Let B be 

 the induction there, H the line variation of il or the mag- 

 netic force, fx the permeability of the iron, and f/ that of the 

 air or other surrounding medium. Then I is defined by the 

 following relation : — 



^H = B = /H -h47rl 



/. I = !L^' H 

 47r 



