president's address — SECTION A. 37 



themselves, and form closed curves, as, for example, in the 

 case of a bar magnet. There is also one other way in which 

 these closed curves may be made, i.e., by electric currents, 

 which, running round a certain area, are able, by a sort of 

 sideways action, to cause induction through the area. I think 

 that when we come to consider the " strain " analogy we shall 

 find that it will then be possible to picture these things very 

 easily. 



Meanwhile let me consider for a moment two more of our 

 analagous theories. 



One of these is that of the steady flow of electricity. In 



this the sources of heat in the heat problem become sources 



of electricity : the medium is a conductor of electricity, and 



we have everywhere the equation C (current) = — c (con- 



dV 

 ductivity) x -%-, where V represents electric potential. The 



data are : — 



(1) The value of c in all parts of the body ; 



(2) The value of V or of C at all parts of the boundaries. 



If, however, the value of V be the same over any 



boundary, it will be enough to know this value of 



y or the average value of C over the surface. 



The condition y^ y = holds good : also Cj = C, or 



Cj -r— + c, -j — = at any pomt of a surface separatmg a 



medium of conductivity c, from one of conductivity c^. 



This is of course, in principle, the same problem as before. 

 The main difference of detail is that c varies between such 

 wide limits. The conductivity of copper is enormously greater 

 than that of air. Let us take an example which will 

 illustrate the analogy and yet bring out the points of differ- 

 ence. Imagine a long bar of copper joining two sources of 

 electricity, one positive, one negative, the air being the 

 surrounding medium. The hues of flow of electricity will be 

 practically straight along the bar. If a bar of soft iron join 

 two sources of magnetic displacement, the lines of induction 

 will b(? very nearly along the bar ; but some will leave it, 

 and, making a curved detour through the air, return to the iron 

 again. Lastly, if the bar be made of ebonite and the sources 

 be sources of electric displacement, the presence of the bar 

 will not much affect the shape of the lines. 



The hydrokinetic analogue, which I shall take next, is due 

 to Sir William Thomson. Imagine a porous sohd, and an 

 incompressible frictionless fluid flowing through the solid in 



