in tlte Discharge at Low Pressures. 191 



cathode beam is here acting as a detector rather than as a 

 measuring instrument. The result that the extension of the 

 field becomes practically independent of the pressure is rather 

 surprising, for one would think this length would be a 

 function of the mean free path in the gas and therefore of 

 the pressure. It is to be expected that the length should 

 depend on the diameter of the tube, for with wider tubes the 

 pressure can be reduced further, with a consequent greater 

 extension of the field, before the charging of the walls 

 changes the character of the discharge, after which the 

 length of the field remains practically independent of the 

 pressure. 



Perhaps it is possible to correlate these results with those 

 at higher pressures. Referring to Aston's work* on air it 

 can be seen that at a certain pressure and tor a certain 

 current density the length of the dark space was 1*805 cm. 

 Decreasing the pressure in the ratio 9/12 caused the dark 

 space to expand to 2*180 cm., while increasing the current 

 density at the lower pressure to four times its previous value 

 caused a contraction from 2*180 cm. to 1*900 cm. De- 

 creasing the pressure caused an extension of the field oE 

 force ; increasing the current density caused a contraction, 

 and the two effects may be made to balance. 



When the pressure is so low that the visible discharge is 

 concentrated into the central portions of the cathode, 

 Wehneltf has shown that practically the whole flow of current 

 from the cathode is concentrated in this beam, the current 

 from the outer spaces being but a very small fraction of the 

 total current. In the experiments described in this paper 

 the field of force began to become almost independent of 

 pressure always when the discharge began to be concentrated 

 into the centre. At this point, therefore, decrease of pres- 

 sure may increase the current density, as the cross-sectional 

 area of the discharge rapidly becomes smaller when the 

 beam of cathode rays is developed. The extension of the 

 field due to decrease in pressure may be counterbalanced by 

 the contraction due to this increase in current density, and the 

 result of the two effects be to make the length of the field 

 almost independent of the pressure. 



The conditions of the discharge, even at higher pressures, 

 are so complicated that no quantitative theory has ever been 

 proposed, and at low pressures the conditions become more 

 complicated still. It may be that the effect mentioned above 



* Aston, Proc. Rov. Soc. A. lxxix. 1C07. p. 04. 



T Wehnelt, Deutsch. Phys. Gesell. Vcrh. xv. ii. pp. 47-r>2, Ji.n. 1913. 



