EXPEKIMENTS WITH IONIZED AIK 



53 



Then if C is the effectiv^e ciipacity of tlie condenser, U the relative velocity of the 

 ions to each other, e the charge of each, — 



- {d V/dt) = AU Vne/Cx = A UVn^e/Cx s "^^^ 

 when the above value of ■», is inserted. 



Now in the data of table 7 the leakage of the condenser was computed as 

 V= Q FlO~''', which when substituted in the last equation gives on reduction 

 <:' = (A Un^e/C\n 10) (\/x e "•'•'), remembering that c' i-efers to minutes. 



12. Constants Comjnited. — This equation may now be tested with the corrected 

 values (corrected foi' loss of potency of the ionizer in the lapse of time) of f' in 

 table 7 as related to x, figure G, the distance apart of the plates. These com))utations 

 are made in the following table by choosing the constant /t'= A TJn^e/Qi In 10) so 

 that the first observations (c' = .200 and x = 1.7) coucide. There is no smoothing. 



TABLE 9.— VALUE OF A' 



Cln lo 



; -[dVldt)IV=c'\n lo ; / 



The curve so computed is shown on the chart, figure 6, and the observations 

 are inserted with refei'ence to it. It will be seen that the coincidence is surpris. 

 ingly good, far superior to the cases of tables 7 and 8, lending to the new equation 

 deduced a degree of probability which becomes enhanced when viewed in connec- 

 tion with the similar result of my last chapter. 



13. Ntimher of ions in tlie saturated enianat loll. — It is even possible to make 

 an approach toward computing the constant n^. If, conformably with c', the value 

 of K be taken relative to minutes instead of seconds, the equation becomes 

 7ir=:26 A Un^e/O. Now if the velocity of the ions produced by phosphorus is like 

 that of the other gases, U is of the order (say) of 1 centirn. per sec. (Thomson, 

 Rutherfoid, Townsend, Chattock), and e of the order of 7/10'" electrostatic units or 

 2.4 X 10"'^ coulombs (Thomson). The ratio of areas in my condenser was .35, tiie 

 area A = 132 cm~, the capacity, C, estimated at GO ceiitims. oi- .7 x 10 '" farads. Fi- 

 nally the value of /iT found in the last table is A' = .634. Thus the initial satura- 

 tion, or the number of ions n, = .634 x .7 x 1 0-'y26 x 1 32 x 1 x 2.4 x 10"''' = 5.5 x 1 0^ 

 Hence if all the ions which reach and ai-e absorbed by the condenser plates actually 

 convey charge, less than 10'' and more than 10^ ions i>er cubic centim. occur in tlie 

 satui-ated emanation contiguous to the sui'face of the phosphorus grid. 



If the emanation of phosphorus is ionized aii', ^=1.5 cm/.'^ec (Thomson, 

 Rutherford, Chattock) and n^ — 3.6 x 10*, agreeing very well with J. J. Thomson's 

 4 X 10^ as the number of ions in air ionized to saturation by the X-rays. 



