so Mr. maxwell, ON FARADAY'S LINES OF FORCE. 



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 ve- 

 locity of the fluid is inversely as the section of the tube, We may make the velocity vary 

 according to any given law, by regulating the section of the tube, and in this way we might 

 represent the intensity of the force as well as its direction by the motion of the fluid in these 

 tubes. This method of representing the intensity of a force by the velocity of an imaginary 

 fluid in a tube is applicable to any conceivable system of forces, but it is capable of great 

 simplification in the case in which the forces are such as can be explained by the hypothesis 

 of attractions varying inversely as the square of the distance, such as those observed in elec- 

 trical and magnetic phenomena. In the case of a perfectly arbitrary system of forces, there 

 will generally be interstices between the tubes; but in the case of electric and magnetic forces 

 it is possible to arrange the tubes so as to leave no interstices. The tubes will then be mere 

 surfaces, directing the motion of a fluid filling up the whole space. It has been usual to 

 commence the investigation of the laws of these forces by at once assuming that the phenomena 

 are due to attractive or repulsive forces acting between certain points. We may however 

 obtain a different view of the subject, and one more suited to our more difficult inquiries, 

 by adopting for the definition of the forces of which we treat, that they may be represented in 

 magnitude and direction by the uniform motion of an incompressible fluid. 



I propose, then, first to describe a method by which the motion of such a fluid 

 can be clearly conceived ; secondly to trace the consequences of assuming certain conditions 

 of motion, and to point out the application of the method to some of the less complicated 

 phenomena of electricity, magnetism, and galvanism ; and lastly to shew how by an extension 

 of these methods, and the introduction of another idea due to Faraday, the laws of the 

 attractions and inductive actions of magnets and currents may be clearly conceived, without 

 making any assumptions as to the physical nature of electricity, or adding anything to 

 that which has been already proved by experiment. 



By referring everything to the purely geometrical idea of the motion of an imaginary 

 fluid, I hope to attain generality and precision, and to avoid the dangers arising from a 

 premature theory professing to explain the cause of the phenomena. If the results of 

 mere speculation which I have collected are found to be of any use to experimental 

 philosophers, in arranging and interpreting their results, they will have served their purpose, 

 and a mature theory, in which physical facts will be physically explained, will be formed 

 by those who by interrogating Nature herself can obtain the only true solution of the 

 questions which the mathematical theory suggests. 



1. Theory of the Motion of an incompressible Fluid. 



(1) The substance here treated of must not be assumed to possess any of the properties 

 of ordinary fluids except those of freedom of motion and resistance to compression. It is not 



