Electrical Resistance of Gases. 209 



Now D'-D, D"-D, D'o-D, and D'^-D are nothing else 

 but the differences between the electroscopic tensions in the 

 respective planes, the first two being positive, and the last two 

 negative. 



We obtain, then, the conclusion that the difference between 

 the electroscopic tensions of two planes is proportional to the 

 intensity of the current, multiplied by the principal resistance 

 between those planes. 



These deductions of Ohm's law, of the development of heat, 

 and of the distribution "of electroscopic tension at the surface 

 of the conductor, are applicable only to the case in which there 

 are solid and liquid bodies in the circuit, since only for those 

 bodies is it proved that the total resistance is proportional to 

 the intensity of the current. 



§3. 

 The fact that electromotive force, or electric tension, need 

 not exceed a certain limit in order that the current may be 

 able to pass through a solid or liquid conductor, depends, then, 

 according to the unitarian theory, on this — that the effective 

 resistance opposed by a conductor of that sort is proportional 

 to the intensity of the current. If the electromotive force is 

 little, the intensity of the current will also be little, and con- 

 sequently the resistance will become so feeble that the elec- 

 tromotive force will be able to overcome it. Experiment 

 teaches us that it is quite otherwise with gases. To compel 

 the current to pass through a column of gas a determined 

 electric tension upon the electrodes between which that column 

 is situated is necessary ; if the tension is below the above- 

 mentioned limit, the current will not pass. It is true that the 

 insulating property exhibited by the gas must not be attri- 

 buted to its effective resistance alone; in fact experiments 

 have led to the admission of the rise, at the electrodes, of elec- 

 tromotive forces obstructing the propagation of the electricity 

 by the gas. If the gas is nevertheless sufficiently dense, ex- 

 periment has shown that the tension necessary for bringing 

 about a discharge is proportional to the distance between the 

 electrodes. The electromotive forces which have their seat 

 upon the electrodes having no connexion with the distance 

 which separates the latter, it follows that, when the gas has 

 sufficient density, it is chiefly its resistance that constitutes 

 the true cause of the discharge not taking place if the electric 

 tension remains below a certain limit*. We arrive, therefore, 



* The resistance of the gas diminishes when it is highly rarefied, while 

 the electromotive forces which originate upon the electrodes are seen to 

 increase ; but it is not necessary to take that circumstance into conside- 

 ration here. 



