3.24 Dr. Tyndall on the Progress of the Physical Sciences : 



be the amount of electricity which passes through any cross sec- 

 tion in a given space of time. 



If the conductor AA' be composed of material which offers a 

 greater resistance to the passage of the electricity than that above 

 supposed, as long as its length remains unaltered the distribu- 

 tion of the electricity will be the same. But inasmuch as the 

 moving force, that is, the difference of tension between two 

 neighbouring cross sections, is also the same as before, a less 

 quantity of electricity must pass from section to section in a 

 given time than in the case of the good conductor ; that is to 

 say, the current must be weaker. A greater length of the better 

 conductor would produce precisely the same effect. These results 

 find definite expression in the law, that the strength of the current 

 is inversely proportional to the resistance of the circuit. Preserving 

 the length and material of AA' unchanged, and regarding the 

 force AA' + BB' as variable, we deduce the law, that the strength 

 of the current is directly proportional to the electromotive force. 



One additional reference to the manner in which Ohm pictured 

 to himself the electroscopic state of the circuit will suffice. Let 

 the conductor AA', fig. 3, consist of the same material throughout, 

 but of two portions, possessing different cross sections. Let the 

 cross section of Ad, for example, be m times that of dh! ; then if 

 equal quantities pass through all sections in equal times, if 

 through a unit of length of wire of m times the cross section no 

 more fluid passes than through the thinner wire, the difference 

 of tension at both ends of this unit of length in the former must 



be only — th of what it is in the latter. Thus the electric " fall," 



as Ohm terms it, that is, the decrease in the length of the ordi- 

 nate for the unit of length of the abscissa, will be less in the case 

 of the thick wire than of the thin, as shown by the line Be in the 

 figure. The distribution of the electricity in such a circuit will be 

 no longer represented by a continuous gradient, but can never- 

 theless be easily ascertained by calculation when the electromotive 

 force of the circuit and the cross sections of its different portions 

 are known. If, instead of one wire being thinner than the other, 

 its specific resistance were greater, it would follow from the hypo- 

 thesis of Ohm, that the greater the resistance of the metal the 

 greater would be the electric fall. The result is summed up in 

 the law, that the " electric fall " is directly proportional to the 

 specific resistances of the metals and inversely as their cross sections. 

 Thus far we have travelled through a region of pure specula- 

 tion. To test whether the actual distribution of electricity 

 throughout a galvanic circuit bears any resemblance to that here 

 supposed, an electrometer of surpassing delicacy was necessary. 

 We shall give a brief description of the refined instrument made 

 use of for this purpose by M. Kohlrausch. 



