a Leyden Phial and of a Telegraph Wire. 533 



quantity of heat conducted across, in the analogous thermal cir- 

 cumstances, would be k times as great as in the case correspond- 

 ing to the air dielectric, with the same difference of tempera- 

 tures ; and in the actual electrical arrangement, the quantity of 

 electricity on each of the conducting surfaces would be k times 

 as great as with air for dielectric and the same difference of 

 potentials. The expression for the capacity of an actual Leyden 

 phial is therefore 



47tt' 

 k being the inductive capacity of the solid non-conductor of 

 which it is formed, t its thickness, and S the area of it which is 

 coated on each side. 



To investigate the capacity of a copper wire in the circum- 

 stances experimented on by Faraday, let us first consider the 

 analogous circumstances regarding the conduction of heat ; that 

 is, let us consider the conduction of heat that would take place 

 across the gutta-percha, if the copper wire in its interior were 

 kept continually at a temperature a little above that of the water 

 which surrounds it. Here the quantity of heat flowing outwards 

 from any length of the copper wire, the quantities flowing across 

 different surfaces surrounding it in the gutta-percha, and thequau- 

 tity flowing into the water from the same length of gutta-percha 

 tube, in the same time, must be equal. But the areas of the 

 same length of different cylindrical surfaces are proportional to 

 their radii, and therefore the flow of heat across equal areas of 

 different cylindrical surfaces in the gutta-percha, coaxial with 

 the wire, must be inversely as their radii. Hence, in the corre- 

 sponding electrical problem, with air as the dielectric instead of 

 gutta-percha, if R denote the resultant electrical force at any 

 point P in the air between an insulated, electrified, infinitely 

 long cylindrical conductor, and an uninsulated, coaxial, hollow 

 cylindrical conductor surrounding it, and if x be the distance of 

 P from the axis, we have 



X 



where A denotes a constant. But if v be the potential at P; by 

 the definition of " potential " we have 



ax 



Hence 



dv__ _A 



dx x ' 



and, by integration, 



v= —A log.r + C. 



