206 ON FARADAY'S LINES OF FORCE. 



closed curve, and find by integration what we may call the entire electro-tin, n 

 intensity round the curve. 



PROP. I. If on any surface a closed curve be drawn, and if the surface 

 within it be divided into small areas, then the entire intensity round the closed 

 cm-re is equal to tlie sum of the intensities round each of the small areas, all 

 xtnnated in the same direction. 



For, in going round the small areas, every boundary line between two of 

 them is passed along twice in opposite directions, and the intensity gained in 

 the one case is lost in the other. Every effect of passing along the interior 

 divisions is therefore neutralized, and the whole effect is that due to the 

 exterior closed curve. 



LAW I. The entire electro-tonic intensity round the boundary of an element of 

 surface measures the quantity of magnetic induction which passes through that 

 surface, or, in other words, the number of lines of magnetic force which pass 

 through that surface. 



By PROP. I. it appears that what is true of elementary surfaces is true also 

 of surfaces of finite magnitude, and therefore any two surfaces which are 

 bounded by the same closed curve will have the same quantity of magnetic 

 induction through them. 



LAW II. The magnetic intensity at any point is connected with the quantity 

 of magnetic induction by a set of linear equations, called the equations of con- 

 duction*. 



LAW III. The entire magnetic intensity round the boundary of any surface 

 measures the quantity of electric current which passes through that surface. 



LAW IV. The quantity and intensity of electric currents are connected by a 

 ."intern of equations of conduction. 



By these four laws the magnetic and electric quantity and intensity may be 

 deduced from the values of the electro-tonic functions. I have not discussed 

 the values of the units, as that will be better done with reference to actual 

 experiments. We come next to the attraction of conductors of currents, and to 

 ithe induction of currents within conductors. 



See Art (28). 



