Theory of the- Striated Discharge. 985 



Since ^mw? 2 = E, and q = ipf(E) where /(E) denotes a func- 

 tion of E which does not involve either i or p, all the terms 

 in this equation can be expressed in terms of E ; so that 

 when /(E) is known, (7) is the differential equation from 

 which E must be determined. 



In a uniform positive column E is constant ; hence we 

 have by equation (7) 



qwe 2 = /3i 2 



pm(~j$*=& (») 



Now /(E) vanishes when E is < Y e, where V is the 

 ionizing' potential of the gas ; and for such values of E as are 

 found in the positive column it is probable that the ioniza- 

 tion is proportional to the excess of E over E , where 

 E = V £. Putting /(E) = c(E — E ), equation (8) becomes 



E °>=|?> ^ 



which leads to a cubic equation to determine E. For small 

 values of ijp an approximate solution of this equation is 



ffi A / m 

 cpe 2 V 2E ' 



When E is independent of x, we have by equation (6) 



Since X is proportional to p, X for small values of i will 

 be proportional to the density of the gas in the discharge- 

 tube. 



The connexion between the force along the positive 

 column and the pressure of the gas and the current has been 

 the subject of many investigations. These indicate a linear 

 relation between the force and the density of the gas. The 

 connexion between the force and the current is more com- 

 plicated ; in some experiments the force diminished as the 

 current increased, in others it increased. The expression 

 we have obtained indicates that, provided the ionization is 

 confined to that due to the collision of electrons, the force 

 should increase with an increase of current. It should be 

 remembered that an increase of current will increase the 

 temperature of the gas, and so in many types iA discharge- 

 tubes diminish the density ; the diminution of the density 



Phil Mag. S. 6. Vol. 42. No. 252. Dec. 1921. 3 T 



©'<* 



E 1 =E + / , 



