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



In order to obtain physical ideas without adopting a physical theory we must make our- 

 selves familiar with the existence of physical analogies. By a physical analogy I mean that 

 partial similarity between the laws of one science and those of another which makes each of 

 them illustrate the other. Thus all the mathematical sciences are founded on relations between 

 physical laws and laws of numbers, so that the aim of exact science is to reduce the problems 

 of nature to the determination of quantities by operations with numbers. Passing from the 

 most universal of all analogies to a very partial one, we find the same resemblance in 

 mathematical form between two different phenomena giving rise to a physical theory of light. 



The changes of direction which light undergoes in passing from one medium to another, 

 are identical with the deviations of the path of a particle in moving through a narrow space 

 in which intense forces act. This analogy, which extends only to the direction, and not to the 

 velocity of motion, was long believed to be the true explanation of the refraction of light; and 

 we still find it useful in the solution of certain problems, in which we employ it without danger, 

 as an artificial method. The other analogy, between light and the vibrations of an elastic 

 medium, extends much farther, but, though its importance and fruitfulness cannot be over- 

 estimated, we must recollect that it is founded only on a resemblance inform between the laws 

 of light and those of vibrations. By stripping it of its physical dress and reducing it to 

 a theory of " transverse alternations," we might obtain a system of truth strictly founded on 

 observation, but probably deficient both in the vividness of its conceptions and the fertility of 

 its method. I have said thus much on the disputed questions of Optics, as a preparation 

 for the discussion of the almost universally admitted theory of attraction at a distance. 



We have all acquired the mathematical conception of these attractions. We can reason 

 about them and determine their appropriate forms or foimulte. These formula} have a 

 distinct mathematical .signifitance, and their results are found to be in accordance with natural 

 phenomena. There is no formula in applied mathematics more consistent with nature than 

 the formula of attractions, and no theory better established in the minds of men than that of 

 the action of bodies on one another at a distance. The laws of the conduction of heat in 

 uniform media appear at first sight among the most different in their physical relations from 

 those relating to attractions. The quantities which enter into them are temperature, flow of 

 heat, conductivity. The word /orce is foreign to the subject. Yet we find that the mathe- 

 matical laws of the uniform motion of heat in homogeneous media are identical in form with 

 those of attractions varying inversely as the square of the distance. We have only to substitute 

 source of heat for centre of attraction, flow of heat for accelerating effect of attraction at any 

 point, and temperature for potential, and the solution of a problem in attractions is transformed 

 into that of a problem in heat. 



This analogy between the formulae of heat and attraction was, I believe, first pointed out 

 by Professor William Thomson in the Cambridge Math. Journal, Vol. III. 



Now the conduction of heat is supposed to proceed by an action between contiguous 

 parts of a medium, while the force of attraction is a relation between distant bodies, and 

 yet, if we knew nothing more than is expressed in the mathematical formulae, there would 

 be nothing to distinguish between the one set of phenomena and the other. 



