.sou/-: co.\rr.Mi'(yii.iRy .ini.iwis i\ riivsus n \2-> 



in which lo reprt'si-iils iht- i<ini/iiiK-P"l*^'')'>->' "f 'lif Hi's^: ^ rt-prfsi-nls 

 the (lUMii fri'e path of thi- rli-ciron; (', its a-ciprocal, is the luimliiT 

 (if collisions suffered !>%■ the electron in each centitneire of the [latli: 

 and. since (" is proportional to the pressure of the j;as, it is replaced 

 l)y Pp in the final foriniilalion.'' 



It is already clear that the new .issiiniplion leads lo a llieor\ which 

 re<iiiires a different latii;iiaKe and a different set of ideas from those of 

 the foregoing section. \ot the ioni/ing-potenlial, Init the niiinlier 

 of ionizations performed li\ an electron in a centimetre of its |).iih. 

 is the quantity to he measured ii\ experimental de\ices; not i1h> 

 voltage between the electrodes, hut the field strength in the gas, is 

 the factor which controls the phenomena.'" In dealing with gases 

 which are expected to conform to the theory, the appropriate (iro- 

 cedure is to measure the nund)er of molecules which an electron ionizes 

 in a centimetre of its path, for all [)ractical values of the field strength 

 .V ami the density of the gas (or its pressure p) as independent vari- 

 ahles. I will designate this numher, following the usual practice, 

 hy a; if the theory is true it cannot he greater than a', it may he less. 

 These ciuantities a and a' are statistical quantities, not like tlic ioniz- 

 ing-potential qualities of the indi\idual atom or molecule, aiul ihi> 

 is a misfortiuie and disachantage of the theory and of the experiments 

 which it interprets; we are not, so to speak, in the presence of the 

 ultimate atoms as hefore, we are one step rem')\'e(l from ihcin, and this 

 step a difficult one to take. 



The measurement of a is effected !)>■ \arying the distance d hetween 

 anode and cathode, and determining the current as function of d. If 

 -Vo electrons flow out of the cathode in a second, the ionization com- 

 mences at the distance rfo= V'X from the cathode, and from that 



' Since the nunilier of free paths, out of a total number No, which exceed L in 

 length is equal to A'o exp ( — L \): and since the potential-difference between the be- 

 ginning and the end of the path of length L, if parallel to the field, is XL. It may 

 fx? objected that the electrons fiounre in all directions from their impacts, while the 

 language of this paragraph implies that they are always moving exactly in the 

 direction of the field. The rebuttal is, that if they do lose almost all of their energy 

 in an impact, or all but an amount not much greater than the mean speed of thermal 

 agitation, they will soon be swerved around completely into the direction of the 

 field no matter in what direction they start out. 



'"The ionizing-potential determines the distance from the cathode at which ioniza- 

 tion commences; this is ecjual to (/o=''o/A', and within this distance from the 

 cathode there is no ionization and the theorj- does not apply; beyond this distance 

 the ionization is controlled entirely by the field strength and by the number of in- 

 flowing electrons and the voltage between cathode and anode affects it only insofar 

 as it affects these. 



