Relations between Electrical Measurements. 443 



point. The dimensions of the unit of magnetic potential are 



T 



11. Lines of Magnetic Force. — There is another way of explo- 

 ring the magnetic field, and indicating the direction and mag- 

 nitude of the force at any point. The conception and applica- 

 tion of this method in all its completeness are due to Faraday*. 

 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 direction 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 f 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 lines which start 

 from unit or area is equal to the number representing the inten- 

 sity 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 Sw- 

 faces. — The lines of force are always perpendicular to the equi- 

 potential 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 

 equidistant ; and the equipotential surfaces are planes perpen- 

 dicular 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 47rm. The equipotential 

 surfaces are a series of spheres, whose centres are at the pole, 

 and whose radii are m, \m, \m } ^m, &c. In other magnetic 

 arrangements these lines and surfaces are more complicated; 



* Experimental Researches, vol. iii. art. 3122 et passim. 

 t Vide Maxwell on Faraday's Lines of Force, Cambridge Phil. Trans. 

 1857. 



2G2 



