Mr. maxwell, ON FARADAY'S LINES OP FORCE. 29 



It is true, that if we introduce other considerations and observe additional facts, the two 

 subjects will assume very different aspects, but the mathematical resemblance of some of 

 their laws will remain, and may still be made useful in exciting appropriate mathematical 

 ideas. 



It is by the use of analogies of this kind that I have attempted to bring before the 

 mind, in' a convenient and manageable form, those mathematical ideas which are necessary 

 to the study of the phenomena of electricity. The methods are generally those suggested 

 by the processes of reasoning which are found in the researches of Faraday *, and which, 

 though they have been interpreted mathematically by Prof. Thomson and others, are very 

 generally supposed to be of an indefinite and unmathematical character, when compared with 

 those employed by the professed mathematicians. By the method which I adopt, I hope 

 to render it evident that I am not attempting to establish any physical theory of a science 

 in which I have hardly made a single experiment, and that the limit of my design is to 

 shew how, by a strict application of the ideas and 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 mathematical 

 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 positive 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 commence 

 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. 



• See especiaUy Series XXXVIII. of the Experimental Researches, and Phil. Mag. 1852. 



