370 Prof. J. J. Thomson on easily Absorbed 



where x is measured from the cathode to the anode. When 

 the discharge is steady dn/dl = 0, and the equation becomes 



i(™) = ™\f(Xe»-/3 } (1) 



Integrating this equation, we find 



]ognu = C+\ V -\f(Xe\)-l3\clr, 



where C is the constant of integration. From this equation 

 Ave can find nu when / and /3, and the distribution of 

 electric force nlong the tube, are known. 



In any region of the tuba where the conditions do not 

 change as we travel along the line of discharge, d(nu)/da; = 0; 

 hence from equation (1) in this region f(Xe\)—/3 = 0, i. e. X,\ 

 has a definite value determined by this equation; as neither (3 

 nor /involves the current through the gas or the pressure of 

 the gas in the tube, XA does not depend upon the current or 

 the pressure : thus X will vary inversely as X. As \ the 

 mean free path of the corpuscles is inversely proportional to 

 the pressure of the gas, it follows that in a uniform part of 

 the discharge X must be proportional to the pressure. We 

 get this uniformity along the line of discharge in the case of 

 the uniform positive column in the discharge at low pressures, 

 and also in the case of long sparks at higher pressures. The 

 following results are given by Skinner (Phil. Mag. Dec. 1900) 

 for the gradient along the positive column at various pressures 

 7> for the discharge through nitrogen. 



p. X. X/p. 



*6 mm. 27 volts/cm. 45 



TO mm. 40 volts/cm. 40 



1*5 mm. 56 volts/cm. 38 



While for sparks in air Liebig found : — 



760 mm. 31,000 volts/cm. 40'8 



Thus through a very wide range of pressures there is but 

 little change in the values of X/p. The value of X in the 

 uniform positive column is the minimum strength of the field 

 which can increase the number of ions in a gas at the same 

 pressure by setting in motion previously existing ions. If we 

 produce ions in a gas by Rontgen rays, the current through 

 the gas will not exceed its saturation value until the electric 

 field attains this strength. 



The condition f(Xe\)—/3 = expresses the condition that 

 each corpuscle produces one and only one other corpuscle 



