SOME CONTEMPORARY ADVANCES IN PHYSICS 111 



(probably electrons) which dash against the anode with the entire 

 kinetic energy acquired during unobstructed passage through the 

 anode-fall. 5 



The heat generated at the cathode must arise in the converse way, 

 from the kinetic energy of positive ions pulled violently against the 

 cathode surface. K. T. Compton of Princeton, has made elaborate 

 calculations for the arc in air with a carbon cathode and the arc in 

 hydrogen with a tungsten cathode, and comparing the results with the 

 experimental evidence, concludes that a few per cent of the current 

 at the cathode is carried by positive ions, the remainder by electrons 

 moving away from the cathode. Compton then attacked the same 

 problem in an entirely different manner; he assumed that the region 

 near the cathode, in which the cathode-fall occurs, is a region in which 

 positive ions are moving gradually towards the cathode, accelerated 

 by the field, and retarded by their collisions with neutral molecules 

 and by their mutual space-charge repulsion. The problem is form- 

 ally similar to that of determining the current-voltage relation in a 

 thermionic vacuum-tube, and the solution is a relation between 

 cathode-fall, current, and width of the region in which the cathode- 

 fall occurs. The first quantity is known; the third is assumed to be 

 the mean distance which an electron travels from the cathode before 

 striking a molecule; the second quantity, the current of positive ions 

 into the cathode, comes out to be a few per cent of the observed 

 total current. These two methods thus support one another in 

 indicating that in the arc-discharge some 90-98% of the current 

 near the cathode is carried by electrons, and the small remainder 

 by positive ions. In the glow-discharge, according to experiments 

 by Gunther-Schulze, the rate at which heat is generated at the cathode 

 is 25% to 75% of what it would be if all the current were carried 

 by positive ions, falling against the cathode with the entire energy 

 derived in passing through the cathode-fall. Expecting that a much 

 larger fraction of the energy of the positive ions would be dissipated 

 in collisions with neutral gas molecules, he concludes that the region 

 of the cathode-fall must be a region in which the gas is abnormally 

 rarefied because abnormally hot; the hotness in turn being due to the 

 collisions between ions and molecules. 



In the central region of the arc, the potential-gradient is uniform 

 and consequently the positive and negative charges per unit volume 



' It is obviously necessary to be very cautious in making deductions of this kind, 

 for the entire energy iV (i representing the current and V the anode-fall or cathode- 

 fall, as the case may be) is dissipated as heat in the region of the anode-fall or cathode- 

 fall; and if this region is very narrow it is hard to distinguish between heat gener- 

 ated within it and heat generated at the anode or cathode surface. 



