124 nni.L SVSTBAf TECHNICAL JOURNAL 



Now if an electron on its way throuj^h the electric field from cathode 

 to antKle strikes atoms so often that it rarely has a chance to acquire 

 more than say half a volt of energy from the field between one impact 

 and the next, and if in each impact it loses most of the energy it has 

 just acquired — if this condition prevails, we need not wonder that the 

 voltage between the electrodes must be raised far be\ontl the ionizing- 

 potential of the gas before there is the least sign of iniensificalion of 

 current. 



In interpreting the experiments upon such gases and at such pres- 

 sures as these last, it has been customary to make a more drastic assump- 

 tion, the opposite extreme from the one which justified itself in dealing 

 with rarefied helium; it is assumed that the electron surrenders at 

 every impact all the energy which it has derived from the field since 

 its last preceding impact. One ma\' be inclined to make mental reser- 

 vations in accepting so extreme an assumption, and it could almost 

 certainly be advantageously modified; but as a tentative assumption 

 it is successful enough to be legitimate. If it is true the electron 

 can never build up a capital of energy step by step along its path; 

 the only chances it will have to ionize will come at the ends of un- 

 usually k)ng free flights. 



Let us imagine a specific case pour fixer les idees : supposing the 

 anode and the cathode to be parallel plates d apart, and representing 

 the potential-difference between them by V and the field strength 

 between them by .V (A'= V/d), we will set d = Q cm., F = 300 volts, 

 ,Y = oO volts/cm.; we will imagine that the interspace is filled with 

 a gas having an ionizing-potential equal to 15 volts, and so dense 

 that the average free path of an electron between collisions is one 

 millimetre. I say that the average free path is 1 mm. long; if all the 

 sixty free paths which the electron traverses in going from cathode 

 to anoile were equal, it would never acquire more than 5 volts of 

 energy, and could never ionize an atom; but owing to the statistical 

 distribution of free paths about the mean value, there will be a certain 

 number out of the si.xty which will be longer than three millimetres, 

 and long enough, therefore, for the electron to acquire the 1.5 volts of 

 energy which are necessiiry to ionize. In this case there will be (iO e'-', 

 about eight, of these long free paths. In each centimetre tluri' will 

 be 10, t- of them. I will use the letter a' to designate this latter num- 

 ber, which is the number of atoms struck by the electron in each centi- 

 metre of its path, at moments at which it has energy enough to ionize 

 an atom; a' is therefore the number of chances to ionize vvliiili tiie 

 elccirnn \\.\- per centimetre. The formula for a' is: 



