158 ON FARADAY'S LINES OF FORCE. 



methods of Faraday, the connexion of the very different orders of phenomena 

 which he has discovered may be clearly placed before the mathematical mind. 

 I shall therefore avoid as much as I can the introduction of anything which 

 does not serve as a direct illustration of Faraday's methods, or of the mathe- 

 matical deductions which may be made from them. In treating the simpler 

 parts of the subject I shall use Faraday's mathematical methods as well as 

 his ideas. When the complexity of the subject requires it, I shall use analytical 

 notation, still confining myself to the development of ideas originated by the 

 same philosopher. 



I have in the first place to explain and illustrate the idea of " lines of 

 force." 



When a body is electrified in any manner, a small body charged with posi- 

 tive electricity, and placed in any given position, will experience a force urging 

 it in a certain direction. If the small body be now negatively electrified, it will 

 be urged by an equal force in a direction exactly opposite. 



The same relations hold between a magnetic body and the north or south 

 poles of a small magnet. If the north pole is urged in one direction, the south 

 pole is urged in the opposite direction. 



In this way we might find a line passing through any point of space, such 

 that it represents the direction of the force acting on a positively electrified 

 particle, or on an elementary north pole, and the reverse direction of the force 

 on a negatively electrified particle or an elementary south pole. Since at every 

 point of space such a direction may be found, if we commeilce at any point 

 and draw a line so that, as we go along it, its direction at any point shall 

 always coincide with that of the resultant force at that point, this curve will 

 indicate the direction of that force for every point through which it passes, and 

 might be called on that account a line of force. We might in the same way 

 draw other lines of force, till we had filled all space with curves indicating by 

 their direction that of the force at any assigned point. 



We should thus obtain a geometrical model of the physical phenomena, 

 which would tell us the direction of the force, but we should still require some 

 method of indicating the intensity of the force at any point. If we consider 

 these curves not as mere lines, but as fine tubes of variable section carrying 

 an incompressible fluid, then, since the velocity of the fluid is inversely as the 

 section of the tube, we may make the velocity vary according to any given law, 

 \>y regulating the section of the tube, and in this way we might represent the 



