al a ])i'<(a)ice in Oit'icctrics. <)3 



d.c'^ dif ^ dz'~^' 

 ■which juhnits of iiitognitiou in the Ibnn 



r bein<; the distance of the point (.f, j/, z) from 0. Hence it fol- 

 lows that tlic attraction varies inversely as the square of tho 

 distance. 



But in tlie ociieral case, K beino- variable, equation (C) does 

 not admit of integration, and the attraction at F cannot be 

 tbund, unless from the ditferential equation. In order to effect 

 this object, we will first obtain another form of equation (C), 

 a])[)licable to the whole of space outside any electrified system. 



11. Consider the series of equipotential surfaces due to such 

 a system, and let lines be drawn cuttino- them all orthogonally, 

 so as to form a " tube of force." 



Comparing tlu* equation (C) with the equation of continuity 

 in hydrodynamics, we see that an inconq)ressible fluid might 

 flow through all parts of the medium with component velo- 

 cities 



dx dy dz 



The direction of motion of such a fluid would evidently be at 



every point perpendicular to the surface V= constant through 



the point ; that is, it would be always along the axis of our 



supposed tube. 



Also if dv represent an element of length of such a tube, 



dY 

 the actual velocity of the fluid alono- it would be K -^ . 



^ dv 



\^^ then, a be a section of the tube perpendicular to the axis, we 

 have as the condition of incomi)ressibility, that (<K , isconstant 



throughout the tube. Our equij)otential surfaces nuist then 



. dY 

 possess this geometrical i)roperty, that «K— - shall be con- 

 stant throuo-hout every tube of force that can be drawn throuoh 

 them. 



, It can here be shown that the equation (C) is sujjported by 

 analogy ; for if, instead of a dielectric, the medium were a 



conductor having ^^ for resistance per unit length and unit 



area, then the equation cJv— r- = constant exi)resses Ohnrs 

 law. '^^ 



