1000 Sir J. J. Thomson on a 



The ratio of the number attached to the glass to the 

 number of free molecules is thus 2/3* 7?^? ; thus, when p is 

 equal to unity, there would, even on a tube a centimetre in 

 diameter, be more molecules on the glass than in the body 

 of the tube. 



When we take the gas condensed on the surface into 

 account, the number of ions produced per second in a section 

 of the tube- whose thickness is Ax is, if cr is the surface 

 density of the surface layer, 



2tttA# . ?Vc 2 (E~E ) + irr 2 Ax . £/oc(E-E ), 



The first term is due to the condensed and the second to the 

 free gas : as the two are not in the same physical state, 

 the constant c for the condensed gas has been differentiated 

 from that for the free gas. The number of ions produced 

 per second is thus 



ttv'Ax , ico 1 1 + - - -1 (E -E ) . 

 L r p cj 



So that the number produced in unit volume per unit time is 



This is the quantity we have denoted by q, and we see that 

 we can take account of the influence of the size of the tube 



by writing in our previous equations cpll-\-~ — - j instead 

 of cp. ° 



We have seen (equations (13) and (20)) that the thickness 

 of the bright parts of the striation in the unrestricted 

 discharge is proportional to (cp)~* ; hence in the discharge 

 through a tube this thickness will be proportional to 



c^K-;x> 



For a very small tube the second term inside the bracket will 

 be more important than the first, and the thickness of the 

 dark space will be proportional to r^(2ac 2 )~i, and thus vary 

 as the square root of the radius of the tube. Since in 

 Goldstein's equation the value of m for hydrogen is very 

 nearly 1/2, the distance between the striation s in this gas 

 would vary as ?•*. If cr is proportional to p, the results got 

 by the preceding theory are for small tubes containing 



