EXPERIMENTS WITir IONIZED Mil 13 



size of the particles. Let n be the luiiuber per cultie ceiitiiueter. Then the late 

 of decay is —{</n/df)—k'n'^, wliere h' is a constant. Hence 1 / n,, — 1 / n ^—h' 

 (t^ — t ), for any two given ()l)servatious. Now if tin; number of particles 

 entering the color tube per second is N, and V the inflowing volume of gas per 

 second carrying them, N= Vn. At the two times of obsei-vation therefore, 

 l/.«2 = V/N^ and l/'«i = V/N,. Hence, V (l/N, - \/iV,) = JC (t^ - t,). 

 The colors seen in the color tube at the times <, and t.^ correspond by the ne.xt 

 chapter to different volumes, \\ and V.^, of similarly dusted air, per second. 

 Thus if JV^be the number of dust particles here and n the common concentration 

 of each of the two volumes specified, A\ = V^n and N.^ = V,^n, where N^ and N,, 

 must have the same value as above. Hence ( V/n) (1/ Fg — 1/ V^) — h' (t^ — t^). 

 Here F, the convection volume flowing out of the vessel per second, may be 

 estimated from the time taken to empty it, oi- otherwise determined. Thus, 

 .)i — ( V /V^ — V /V-^) / h' (t., — /,). Supposing that h' were knowni from other 

 sources, the value of w would follow, this being the number of particles per cubic 

 centimeter for neaidy saturated air; or vice versa. The following is a rough 

 measurement. 



The equation may be put in the form, Jc' n^ /n^^{V/V.^- V / V, ) /(t.^ -t^), 

 which states the numbei' decaying per cubic centira., per second relatively to the 

 total number present. 



The only datum of the preceding table available here is marked by a bracket. 



Hence, 



/"a = 6o sec. opaque-blue. 



/, = 30 sec. blue-gray. 



The volume of the bell jar was 2690 cubic centims. The time to empty it 

 is 10-15 seconds, by the table. Hence, F= 210 cub. cm. / set:- = 12.6 liters/ 

 min. In the next chapter the data are roughly for 



blue-opaque, 2. lit./min. = V^ 



blue-gray, . 7 lit./min. = Fj 



Thus h'nl/n^ = (18 - 6.3) / 80 = .4, that is ^\ of the ions per cubic centim. 

 mutually destroy each other per second, in the saturated region. If «„ = 4 X 10*, 

 Jc' = .000010. 



These results are naturally uncertain from the character of the measurements, 

 which in the above table are mere estimates. So also the times of emptying the 

 vessel are not sharp values. The experiment is chiefly interesting from a theoretical 

 point of view but does not lend itself for accurate measurement. Apart from this 

 it will be argued in Chapter III et seq. that k' may be ignored if each ion is endowed 

 with a velocity k of its own. In such a case the loss of ions results from their 

 absorption at the w^alls of the bell jar. In other words, ions wander out of the 

 interior of the jar in all dii'ections to eventually impinge on the walls where they 

 are destroyed. It is in this sense that I understand the action of cotton and othei' 

 filters, these being a means of increasing the absorbing surface enormously. 



17. Persistence of nuclei in long jJmJ^s. — Experiments with a similar bearing 



