hy the Motion of Positive Tons in a Gas. 609 



obtained bv comparino- tbe values of a and /S at the different 

 pressures, and tbe investioation leads to a very simple nietbod 

 of representino- tbe values of tbese quantities corresjiondino- 

 to tbe different fore(v>^ and ])ressures. It bas already been 

 sbown tbar j« is oivtMi in terms ol: X and ji by a formula of 



tbe form ' =/{ ]. Tbe tbeorv also requires tbat S sbould be 



connected witb tbe variables by a similar formula. Tbese 

 results may be obtained from tbe following simple considera- 

 tions. If tbe pressure' is increased from p to xp all tbe free 



])atbs are reduced to - of tbeir orioinal value. If tbe force 



remained unaltered tbe velocities on collision would be* 

 reduced, but if tbe force X is increased to .x x X tbe velocities 

 will be restored to tbeir original values and tbe number of 

 ions arising from a given number of collisions will be tbe 

 same as before. Since tbe total number of collisions per 

 centimetre is increased by increasing tbe pressure, we see 

 tbat wben X and^> are altered in tbe same proportion tben a 

 and ^ must be altered in similar proportions. 



The results of tbe experiments show tbat /S, as well as a, is 

 connected with the quantities X and p by a relation of tbe form 



R /X\ 



— =(^f — J. This may be seen from the accompanying 



diagrams (fig. 3) in which tbe points whose coordinates are 



R X 



— and— are marked, n being in millimetres of mercurv and 

 p p ^ " 



X in volts per centimetre. The pressure of the gas in tbe 



B 

 experiments from which the value of - was derived i^ oiven 



p 



by the number beside each point. Some of the values of 

 o 



— were obtained from experiments at two or three different 

 P 



pressures. It is evident tbat a single curve passes throuob 

 the points derived from all the experiments. 



The properties of the negative ions as shown by the curves 

 x=f(y) for different gases have already been investigated in 



the previous researches. The values of — correspondino- to 



.X . p ^ ^ « 



the smaller values ot — as previously obtained agree verj- 



accurately with the values derived from the present experi- 

 ]nent<. The method of tinding a and ^ simultaneouslv, as 



