TUBES AND FLOW OF INDUCTION. 99 



or flow of induction across a surface-element, to the product of this 

 element by the perpendicular component of induction ; the preceding 

 results may then be expressed in a very simple manner. 



We observe, in the first place, that in gaseous media, or at any 

 rate in a vacuum, //, = i ; the induction and the force have the same 

 numerical expression, and tubes of force are identical with tubes 

 of induction just as are the two kinds of flow. 



In the case of continuous media whose specific inductive 

 capacities are /x x and /* 2 , the ratio of the perpendicular components 



ft 1 F 1 cos t\ = /* 2 F 2 cos /g 

 gives 



FS cos t = *F^S cos 



an equation which signifies that the flow of induction across the 

 element dS retains the same value in the two media. We are thus 

 led to the following law : 



In a tube of induction the flow of induction retains a constant 

 value, whatever be the dielectric media which it traverses, so long as 

 it does not meet a really electrified body. This law merges into that of 

 the conservation of the flow of force when we are only considering 

 a single medium. 



If the tube encounters a mass of electricity m situate in the 

 dielectric medium, we may always look upon this mass as sepa- 

 rated from the dielectric by a layer of air ; in this layer the flow of 

 induction merges into the flow of force ; as the latter varies by ^irm, 

 this is also the case with the flow of induction, in virtue of the pre- 

 ceding theorem. 



116. CHARACTERISTIC EQUATIONS OF INDUCTION. If we apply 

 this theorem to a volume-element dxdydz in a dielectric whose 

 specific capacity is /*, at a point where the real density of electrifi- 

 cation is p, we obtain the following equation, analogous to that 

 of Poisson. 



av\ a / av\ a / av\ 



+ 4^/0 = 0. 



As, for the present, we are only considering isotropic media, the 

 factor fj. is constant, and this expression reduces to 



/*AV + 47T/D = 0. 

 H 2 



