ON STANDARDS OF ELECTRICAL RESISTANCE. 135 
values at different points of space, was brought into form by Laplace*. The 
name of potential, and the application to a great number of electric and 
magnetic investigations, were introduced by George Green, in his Essay on 
Electricity (Nottingham, 1828). 
An equipotential surface in a magnetic field is a surface so drawn, that the 
potential of ail its points shall be equal. By drawing a series of equipotential 
surfaces corresponding to potentials 1,2,3...... nm, We may map out 
any magnetic field, so as to indicate its properties. 
The magnetic foree at any point is perpendicular to the equipotential sur- 
face at that point, and its intensity is the reciprocal of the distance between 
one surface and the next at that point. The dimensions of the unit of mag- 
L? we 
v 
11. Lines of Magnetic Force-—There is another way of exploring the 
magnetic field, and indicating the direction and magnitude of the force at 
any point. The conception and application of this method in all its com- 
pleteness is due to Faradayt. The full importance of this method cannot be 
recognized till we come to electromagnetic phenomena (§§ 22, 23, & 24). 
A line, whose direction at any point always coincides with that of the force 
acting on the pole of a magnet at that point, is called a line of magnetic force. 
By drawing a sufficient number of such lines, we may indicate the direc- 
tion of the force in every part of the magnetic field; but by drawing them 
according to rule, we may indicate the intensity of the force at any point 
as well as its direction. It has been shown? that if, in any part of 
their course, the number of lines passing through unit of area is proportional 
to the intensity there, the same proportion between the number of lines in 
unit of area and the intensity will hold good in every part of the course of 
the lines. 
All that we have to do, therefore, is to space out the lines in any part of 
their course, so that the number of limes which start from unit of area is 
equal to the number representing the intensity of the field there, The 
intensity at any other part of the field will then be measured by the number 
of lines which pass through unit of area there ; each line indicates a constant 
and equal force. 
12. Relation between Lines of Force and Equipotential Surfaces.—The lines 
of force are always perpendicular to the equipotential surfaces; and the 
number of lines passing through unit of area of an equipotential surface is 
the reciprocal of the distance between that equipotential surface and the next 
in order—a statement made above in slightly different language. 
In a uniform field the lines of force are straight, parallel, and equi- 
distant ; and the equipotential surfaces are planes perpendicular to the lines 
of force, and equidistant from each other. 
If one magnetic pole of strength m be alone in the field, its lines of 
force are straight lines, radiating from the pole equally in all directions ; 
and their number is 47m. The equipotential surfaces are a series of spheres, 
whose centres are at the pole, and whose radii are m, 3m, 14m,4m, &. In 
other magnetic arrangements these lines and surfaces are more complicated, 
but in all cases the calculation is simple; and in many cases the lines and 
surfaces can be graphically constructed without any calculation. 
netic potential are 
* Mécanique Céleste, liv. iii. 
+ Experimental Researches, vol. iii. art. 3122 e¢ passim. 
{ Vide Maxwell on Faraday’s Lines of Force, Cambridge Phil. Trans. 1857. 
