EXPERIMKNTS WITH IONIZED AIR. 41 



diluted, the new ions produced are in excess of the old. From this one may argue 

 that their velocity must diminish. Admitting the delicate nature of this specula- 

 tion, it is certain, unless I have misunderstood the observations with wide tubes, 

 slow currents, and weak ionization, Jc here in all my experiments has never ex- 

 ceeded \ and often fallen below -^ of the very definite values for small bore tubes, 

 swift air currents, and nearly saturated ionization. 



9. Oase of decay without absorption. — It will be interesting to contrast with 

 this, the second special case in which ^=0, and h' is alone significant. Here, in brief, 

 the diminution of nuclei is due to decay while sojourning in the tube. If in the 

 narrow tubes the destruction of nuclei were merely the result of decay due to their 

 mutual reaction, then the time of their sojourn within the tubes, *'. e.,(x—x^/v, should 

 be of paramount importance, apart from the diameter of the tubes. The differen- 

 tial equation foi' this case becomes on integration, \/n — \/n^ = {k'/v) (x — x^), or 

 n/n., — 1/(1 +-t;'«o (x/v)), if n„ coi-responds to x^ = 0. Since v = 1000 F/7r60?'^ — 

 5.30 V/r^, and since 7i V=n„ V^, 



y-y, 5-3° y. 



h'= 



y«nn 



80 that k' cannot be found absolutely in this way. 



Moreover since for a given tube of i-adius, r, the i-atio ( V— V„) /x is very nearly 

 constant for the larger values of T^, /t' vai'ies nearly as I^and is not theiefore a con- 

 stant. The equation for k' may be otherwise written ^'=(( V— Va)/x) {v/n^ V^), so 

 that (k'rv' being the number of particles decaying per cubic centimeter per second) 

 k' varies with the velocity of the ionized air current through the absorption tube, 

 roughly speaking. 



I conclude that an explanation in terms of decay alone is inapplicable, and 

 even with modifications inferior to the explanation (^' = 0) given above. 



