Methods of Theoretical Physics, 41 



assailed the old system of centres of force and forces at a 

 distance ; it might be said to have been from the exactly 

 opposite side, because they were particularly fond of the 

 variegated garment of mechanical representation ; it might 

 also be said to be from an adjacent side, as they also dis- 

 pensed with the recognition of a mechanism lying at the 

 basis of the phenomena, and in the mechanism which they 

 themselves invented they did not see those of Nature, but 

 mere images and analogies*. Several men of science, follow- 

 ing the lead of Faraday, had established a totally different 

 conception of Nature. While the older system had held the 

 centres of force to be the real, and the forces themselves to be 

 mathematical conceptions, Faraday saw distinctly the con- 

 tinuous working of the forces from point to point in the inter- 

 mediate space. The Potential, which had hitherto been only a 

 formula for lightening the work of calculation, was for him the 

 really existing bond in space, the cause of the action of force 

 itself. Faraday's ideas were far less lucid than the earlier 

 hypotheses, defined as they were with mathematical precision, 

 and many a mathematician of the old school had but a low 

 opinion of Faraday's theories, without, however, by the 

 clearness of his own conceptions making such great dis- 

 coveries. 



But soon, and especially in England, it was attempted to 

 get as plain and tangible a representation of the ideas and 



* The relation of the directions of the old system of centres of force, 

 and of forces at a distance to the purely mathematical one represented 

 by Kirchhoff, to Maxwell's own point of view is expressed by him in 

 the following words : — " The results of this simplification may take the 

 form of a purely mathematical formula (Kirchlurff), or of a physical 

 hypothesis (Poisson). In the first case we entirely lose sight of the 

 phenomena to be explained and though we may trace out the conse- 

 quences of given laws, we can never obtain more extended views of the 

 connexions of the subject. If, on the other hand, we adopt a physical 

 hypothesis, we see the phenomena only through a medium, and are 

 liable to that blindness to facts and rashness in assumption which a 

 partial explanation encourages. We must therefore discover some method 

 of investigation which allows the mind at every step to lay hold of a 

 clear physical conception without being committed to any theory in 

 physical science from which that conception is borrowed, so that it is 

 neither drawn aside by analytical subtleties, nor carried beyond the truth 

 by a favourite hypothesis." 



Compare the theory of elasticity worked out by Kirchhoff in his 

 Lectures, of almost etherial delicacy, clear as crystal but colourless, with 

 that given by Thomson in the third volume of his Mathematical and 

 Physical Papers, a sturdy realistic one, not of an ideal elastic body but of 

 steel, india-rubber or glue ; or with Maxwell's language, often almost 

 childlike in its naivety, who, right in the middle of his formulae, casually 

 gives a really good method of removing grease spots. 



