5if Prof. Thomson on the Mathematical Theory of 



a detailed account of the experiments by which these phenomena 

 are investigated, reference must be made to Mr. Faraday's own 

 memoirs, published in the Philosophical Transactions, and in 

 a separate form in his " Experimental Researches." 



8. The hypothesis adopted by Faraday, of the propagation of 

 inductive action, naturally led him to the idea that its effects 

 may be in some degree dependent upon the nature of the insu- 

 lating medium or dielectric, by which, according to this view, it 

 is transmitted. In the second part of his memoir he describes 

 a series of researches instituted to put this to the test of experi- 

 ment, and arrives at the following conclusions. 



If the dielectric be air, the inductive action is quite inde- 

 pendent of its density or temperature (which, as Mr. Faraday 

 remarks, agrees perfectly with previous results obtained by Mr. 

 Harris) ; and in general, if the dielectric be any gas or vapour 

 capable of insulating a charge, the inductive action is invariable. 

 Hence he concludes that " all gases have the same power of or 

 capacity for, sustaining induction through them (which might 

 have been expected when it was found that no variation of density 

 or pressure produced any effect.) '^ 



When the dielectric is solid, the induction is greater than 

 through air, and varies according to the nature of the substance. 

 Numbers which measure the ** specific inductive capacities" of 

 the dielectrics employed (sulphur, shell-lac, glass, &c.), are de- 

 duced from the experiments. 



To express these results in the language of the mathematical 

 theory, let us recur to the supposition of a body, A, charged 

 with a given quantity of electricity, and insulated in the interior 

 of a closed conducting shell, B. The potential of the system at 

 the interior surface of B, and at every point without this surface, 

 will be nothing ; at the surface and in the interior of A it will 

 have a constant value, which will depend on the form, magni- 

 tude, and relative position of the surfaces A and B, on the 

 quantity of electricity on A, and, according to Faraday's dis- 

 covery, on the dielectric power of the insulating medium which 

 fills the space between A and B. If this be gaseous, neither its 

 nature, nor its state as to temperature, pressure, or density, will 

 "affect the value of the potential in A ; but if it be a solid sub- 

 stance, such as sulphur or shell-lac, the value of the potential 

 will be less than when the space is occupied by air, and will vary 

 with the nature of the insulating solid. 



The result in the case of a gaseous dielectric is what would 

 follow from Coulomb's theory, if we consider gases to be quite 

 impermeable to electricity, and to be entirely unaffected by 

 electrical influence. The phsenomena observed with solid dielec- 

 trics, which agree with the circumstance observed by Nicholson, 



