Page:On Faraday's Lines of Force.pdf/52

206 closed curve, and ﬁnd by integration what we may call the entire electro-tonic 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 curve is equal to the sum of the intensities round each of the small areas, all estimated 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 eggect 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 pisses 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 conduction.

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 system 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 the induction of currents within conductors.