84 KXTKKIMEN'rS AVI Til IONIZED Am. 



incieixses u itli R whicli is not tulmissible. Neitlier of these cases is open to com- 

 putation and tliey are thus without immediate interest. Tliey may be treated in a 

 different manner, as already set fortii in Chapter IV., by inticxlucinrj the ion velocity 

 in the unit tield U, in place of the absoiption velocity k, and they then become 

 suggestive. If l/>.4 is replaced by m,, liie number of ions per cubic centimeter at 

 a distance of 1 centiin. from the center, the al)Ove concentration n at a distance r 

 niav be written, ii^/it = r[^(i''/k)i> ^ (1 — /■) + '"]• If decay is ignored, the number 

 n = >'t/'^' i^ i'^ otherwise clear, is independent of k also. 



Now if the electric conduction is determined by the luimltci- of ions whicli 

 reach the external shell {r = R), -dQ/dt= - C'dV/dt = \n R' U {V / R)m. 

 It is understood that this number is not appreciably modified by the occurrence of 

 the fiehl so that when decay is absent (A;' = 0), /i = )i^/R~, as above deduced. 

 Hence, - {dV/dt)/V= - d{\\\ V)/dt ^UeUnJCR. Here the first member is 

 eipiivalent to —d(\\is)/dt, and is obtainable from the observations directly, AneU/C 

 is a constant, ?/j ex[)resses the apparent waning intensity of the phosphoric source 

 of ionization, and R is the e.vternal radius of the condenser. The equation, tiiere- 

 fore, admits of being tested. The integral of the equation found for the potential 

 gradient becomes V ^ V^e -{i^eVn,;cR)t^ which is compatible with the data of tables 

 1-4. In these tables I have therefore inserted the (piantity, n ^ /\'= (4;r eZ7/6')«j, 

 com[)uted from — {d V/dt)/ V.R for each pair of values of .s- antl /, usually 3 minutes 

 or ISO seconds apart. The values ii^Kiwii given in terms of common logarithms 

 and seconds. Hence Rd{\n V)/dt=z 2.3 n^K. 



9. Comparison of data. — The values so found, i.e., n^K = ^(/(log V)/dt, are 

 siiown graphically in figure 12, as ordinates' in terms of R as abscissas. Besides 

 the data of tables 2, 3, 4, I have added those of table 1 taken from figure i\. The 

 cui've here is apparently sinuous due to the abnormally high values of K (>, 

 and the abnormally low values of K 4, alluded to, both of which remain un- 

 explained. In the ab.sence of these there would be a rise of /' , A', of a grad- 

 ual character with increasing radius. Since in ')i^K, K is constant, this means 

 that I'clatively more ions ii^ are available at the lai-ger radii of the con- 

 den.ser.s, corresponding to weaker fields, than for smaller radii and correspondingly 

 stronger fields. But as there is no reason for excludinij K4 and IvC), and no su<"Tes- 

 tiou for the occurrence of the sinuous curve obtained, n , K must be resrarded as 

 increasing rapidly from the values foi- condensers of small I'adii, /• = 2 centim., but 

 reaching a practically constant result after the radius 4 centim. has been sui- 

 passed. On the whole therefore, the ilata, so lar as investigation lias been [mssible, 

 agree with the remarks made in §1, tliat the evidence in case of dilution is rather 

 in favor of an increased number of ions and that an occurrence of decay is not 

 manifest. This means more generally that whereas in the saturated emanation the 

 i(Uis are [Jioduced at lue same rate at which they decay, so that n is constant, in 

 the diluted emanaticm at a distance from the center (m = n^/r), the production is 

 in excess of the decay and conduction relatively too great. 



Another method of tieatin<4 n, K \fi to refer it to streutrth of field. This, how- 



' Common logarithms and seconds are used, R being as usual in cm. 



