69 Prof. Thomson on the Mathematical Theory of 



action due to the charged surfaces, produce the resultant force 

 at any point. It is no doubt possible that such forces at a 

 distance may be discovered to be produced entirely by the action 

 of contiguous particles of some intervening medium, and we 

 have an analogy for this in the case of heat, where certain effects 

 which follow the same laws are undoubtedly propagated from 

 particle to particle. It might also be found that magnetic forces 

 are propagated by means of a second medium, and the force of 

 gravitation by means of a third. We know nothing, however, 

 of the molecular action by which such effects could be produced, 

 and in the present state of physical science it is necessary to 

 admit the known facts in each theory as the foundation of the 

 ultimate laws of action at a distance. 



St. Peter's College, Nov. 22, 1845. -'^ 



NOTES. 

 Note I. 



Coulomb has expressed his theory in such a manner that it can only be 

 attacked in the way of proving his experimental results to be iaaccurate. 

 This is shown in the following remarkable passage in his sixth memoir, 

 which follows a short discussion of some of the physical ideas then com- 

 monly held with reference to electricity. " Je previens pour mettre la 

 th^orie qui va suivre a Vahri de toute dispute syst^matique, que dans la 

 supposition des deux fiuides electriques, je n*ai d'autre intention que de 

 prisenter avec le moins d'eMmens possible, les resultats du calcul et de 

 I'exp&ience, et non d'indiquer les v^tables causes de V4lectr%cit^. Je 

 renverrai, h la Jin de mon travail sur I* electricity, Vexamen des principaux 

 systhnes auxqiiels les ph^iomenes Electriques out donnE naissance." — H«*- 

 toire de VAcademie, 1788, p. 673. 



Note II. 



This theorem may be stated as follows. Let A be a closed surface of 

 any form, and let matter, attracting inversely as the square of the distance, 

 be so distributed over it that the resultant attraction on an interior point 

 is nothing : the resultant attraction on an exterior point, indefinitely near 

 any part of the surface, will be perpendicular to the surface and equal to 

 47r/), if pa) be the quantity of matter on an element to of the surface in the 

 neighbourhood of the point. Coulomb's demonstration of this theorem 

 may be found in a preceding paper in the Mathematical Journal, vol. iii. 

 p. 74. He gives it himself, in his sixth memoir on Electricity {Histoire 

 de VAcad^mie, 1788, p. 677)j in connexion with an investigation of the 

 theory of the proof plane in which, by an error that is readily rectified, he 

 arrives at the result that a small insulated conducting disc, put in contact 

 with an electrified conductor at any point, and then removed, carries with 

 it as much electricity as lies on an element of the conductor at that point 

 equal in area to the two faces of the disc ; the quantity actually removed 

 being only half of this. This result, however, does not at all afiVict the 

 experimental use which he makes of the proof plane, which is merely to 

 find the ratios of the intensities at difi'erent points of a charged conductor. 

 As the complete theory of this valuable instrument has not, so far as I am 

 aware, been given in any English work, I annex the following remarkably 



