CONTEMPORARY ADVANCES IN PHYSICS 579 



negative sign. We have to form a fourfold sum: charges borne by 

 positive ions going up and charges borne by negative ions going down, 

 with plus sign; charges borne by negative ions going up and charges 

 borne by positive ions going down, with minus sign. The terms of 

 this fourfold sum may vary from one to another of the surfaces 

 intersecting the tube (in general, they do) but the sum remains the 

 same; it is the current through the gas. It is also the current flowing 

 through the plane of the cathode-surface (it may then consist of two 

 terms only, electrons emerging from the cathode metal and positive 

 ions impinging on it; or it may involve the two additional terms, 

 because of electrons falling upon the cathode and positive ions re- 

 bounding from it). It is also the current flowing through the wires, 

 and the current measured by the galvanometer at G. 



Now for a high-frequency discharge, this must be modified. The 

 fourfold sum aforesaid is not the whole of the current. Or rather, we 

 might call it the whole of the current, but then we should be compelled 

 to say that the current across the various cross-sections of the circuit is 

 not the same, and is not measured by the galvanometer. We do 

 better to follow Maxwell, or rather the usage which developed out of 

 Maxwell's theory: call it the "net convection current" and introduce 

 the name "displacement current" for the quantity which must be 

 introduced, in order to get a sum which is the same for all the cross- 

 sections of the circuit and equal to the reading of the galvanometer. 

 Nor is this "sum" to be obtained by simple addition. We are obliged 

 to take into account another complication, from which direct-current 

 discharges are free: the necessity of distinguishing between a current- 

 component which is proportional to the voltage and a current-com- 

 ponent which is proportional to the rate of change of the voltage; or, 

 to take the simple case of a sinusoidal voltage, the current-components 

 which are respectively "in phase" and "in quadrature" therewith. 

 The displacement-current belongs entirely to the latter component, 

 while the convection-current may belong partly to the one and partly 

 to the other, as I will presently illustrate. 



It is, then, not required that the net convection-current should be 

 the same all through the gas; much less, that it should be the same 

 as the current reported by the galvanometer. At sufficiently high 

 frequencies, electrons and positive ions may oscillate in the interspace 

 between anode and cathode without reaching either, if they start 

 their independent careers far enough off from both. Can one attain 

 a condition in which there is a convection-current of oscillating ions 

 in the middle of the gas, but none whatever in the vicinity of the 

 electrodes, and no electrons escape from the metal of the cathode into 



