Theory of the . Striated Discharge. 999 



increase to one within our power of attainment. Thus we 

 might get striations showing the iight ol the electronegative 

 gas in a mixture, though it might not be possible to obtain 

 them in the pure gas. 



Relation between the Lengths of the Striations ana! the 

 Diameter of the Tube. 



It is well known that the distance between the striations 

 depends upon the diameter of the tube, and that in narrow 

 tubes the striations are nearer together than they are in 

 broad ones, the pressure of the gas being the same in both 

 cases. 



Goldstein (Berliner Ber. 1881, p. 877) came to the con- 

 clusion that the relation between I, the distance between the 

 striations, r the radius of the tube, and p the density of 

 the gas could be expressed by the equation 



\ =C(pr) : ™, 



where m is a number less than unity ; and this relation for 

 a limited range of values of r has been confirmed by the 

 experiments of Wehner (Ann. der Phys. xxxii. p. 49, 1910) 

 and Neubert {Ann. der Phys. xlii. p. 1454, 1913). Inasmuch 

 as this formula makes I infinite when r is so, it involves the 

 disappearance of striations in very wide tubes ; this, how- 

 ever, is contrary to experience. The relation must therefore 

 be an empirical one, holding for only a limited range of 

 values of r. 



The diminution of the length of the striations with the 

 bore of the tube is, I think, due to the presence of a layer of 

 condensed gas on the inner surface of the tube : this layer 

 of gas will be ionized by the impact of electrons, and will 

 furnish a supply of positive ions and electrons. 



A simple calculation will show that the supply from this 

 source may, in narrow tubes, easily exceed that from the 

 free gas ; for if the layer of condensed gas was only one 

 molecule thick, there would be on each square centimetre of 

 surface of the tube about 10 16 molecules of gas ; so that, if 

 r is the radius of the tube, the number of molecules on a 

 length Am of the tube would be 2irrAx . 10 16 . Since the 

 number of molecules in 1 c.c. of gas at standard pressure 

 and temperature is 2'8 X 10 19 /if the pressure of the gas in 

 the tube is p mm. of Hg, the number of molecules of tree 

 gas in the length A# is equal to 



irr^Ax • f^r X 2-8 X 10 19 = irr»A* .p X 3'7x 10 16 , 



700 



