I 6 ON POTENTIAL. 



If we suppose that a liquid, in the permanent state, traverses the 

 element dK at right angles, with the velocity F, the product FdA 

 represents the volume of liquid which flows through the element dA 

 n unit time, or, more briefly, the flow of liquid corresponding 

 to this element. This flow is also expressed by the product F n dS, 

 obtained by multiplying any section of the tube by the component 

 of the velocity along the perpendicular to this section. 



By analogy, we shall apply the term quantity of force, or flow 

 of force corresponding to an element of surface, to the product F n dS 

 of the surface of the element, into the component perpendicular to the 

 force at this point. The flow of force for unit surface is equal 

 numerically to the perpendicular component of the force. 



The properties which we are about to examine will completely 

 justify this analogy. 



Fig- 4- 



The idea of lines of force is due to Faraday, and this eminent 

 physicist showed all the advantages which may be derived from it in 

 the study of electrical phenomena. What we have designated a 

 quantity or flow of force, Faraday called number of lines of force. 

 It seemed useful to adopt another designation, in the first place for 

 simplicity of expression, and secondly because the word flow seems 

 to correspond better with the character of continuity which we want 

 to determine. 



29. GREEN'S THEOREM. Let us consider in the dielectric an 

 entirely closed convex surface S (Fig. 4), and let + m be an electrical 

 mass situate at the point O outside this surface An infinitely slender 

 cone of aperture du, having its apex at O, cuts the elements d$ 

 and ^S' in this surface. Let /and/' be the values of the electrical 

 force at dS and dS',dA and dA' the corresponding perpendicular 



