6()4: Mr. McCJluiio- on the Relation between Rate of 



Relation between Temperature and Coefficient of 

 Recombination. 



The other question which we set out to investigate was the 

 effect which a change of temperature o£ the gas produced 

 upon the value o£ the coeihcient of recombination a. 

 Although it has been shown that the same law of recombina- 

 tion holds true at the various temperatures, we cannot say 

 from this that the value of the coefficient a remains the same 

 at the different temperatures. There still remains to be 

 settled the question of the relation between the temperature 

 of the gas and the value of a. 



From the well-known equation q = an^ it follows, as has 

 been shown by the author in the paper already referred to, 

 that the absolute value of a. is given by the equation 



where K is a constant quantity depending entirely upon the 

 dimensions and position of the particular apparatus used, 

 and Q is the total number of ions produced per second in a 

 given volume of the gas, while N is the total number existing 

 in the same volume at the instant the rays are shut oflP. Now 

 if it is only a question of comparing the value of a at one 

 temperature of the air with the value at another temperature, 



it is only necessary to compare the values of the ratio -j^ 



at the two temperatures, if the dimensions and position of the 

 apparatus are kept unchanged, for K will be the same in both 

 cases. ^ In making this comparison, then, the only two 

 quantities to be measured are Q and N. 



N was measured as has been already described in testing 

 the law of recombination. If the electrode E be kept at a 

 steady saturation voltage, and the rate of leak per second 

 between the electrodes be measured in the usual w^ay, then the 

 deflexion of the electrometer-needle, which is proportional to 

 the charge received by the electrode E', is proportional to the 

 number of ions which are produced in the gas per second. 

 Therefore Q is proportional to the deflexion of the electro- 

 meter-needle per second. If d^ is the deflexion of the 

 electrometer-needle per second corresponding to Q, and if d2 



is the deflexion corresponding to N, then J^ is proportional to 



i^ . Therefore, to compare the values of a, at the different 



temperatures it is only necessary to compare the values of the 



