EXPERIMENTS WITH IONIZED A IK. 



51 



To iuteri)i'et tbe above I'esults 1 will sin)pose as a first trial, that c' = c' KY"^, 

 where c' = n Ue{A/e.v)\og^ as given above. The folio wiiia; table is a sumtiiary of 

 completed series of e.xperinients computed in this way, the value of d in the 3d 

 column being taken at once from the preceding table 6. It will be noticed, how- 

 ever, that the value of c' at x =1.7 cm. has fallen off considerably during the course 

 of the e.\periment. Its probable value at the successive times and x = 1.7 is given 

 under <■". For any values of x, the observed value, c', is then to l)e referred to the 

 value (■" (./■ — 1.7 cm.), corrected for the apparent decreased intensity of the phos- 

 phoric ionization above referi-ed to. These computed values (f ai'e given in table 

 7, as well as the values & (colunui 5) reduced in terms of them. 



T.ABLE 7.— TRANSMISSION OF THE PHOSPHORUS EMANAIION JN AIR. 



SUMMARY 



10" "• ; (? = .25 ; c' X / i 



»/>>»■ 



' The time correction is made linearly. At .«■ = 1.7 cm. the value c' fell fion 

 per minute. This result is referred to above in relation to tables i and 2. 



.20 to .14 in 67 minutes ; i. e., .ooog 



Table 7 deduces the mean value of a to be .25, whence it follows that at 

 1 / rt = 4 cm. the value e is but 1/10 of the original number. Similar i-atios 

 c'A'o = 10-"'', are given in the last column. For x= \ cm., .5 cm., .1 cm,, the relative 

 numbers are .56, .75, .94, showing how ra[)idly the satui'ation is I'educed even close 

 to the phosphorus grid. 



9. Another computation. — -The above table exhibits the character of the 

 phenomena, faii-ly well. From another point of view I also tested the equation 

 6''=c'o / (1 + ^''O- I \^'^\Q given the constants so obtained in the following table, 

 8. The equation 1 / c' — 1 / c\ — hx/v\, whei'e h / c\ — 8.8 is closely in accord 

 with the observations, but the result foi- small values of d is absurd, as c' is 

 negative. Inasmuch as the erroi-s in the last two tables are cumulative, better 

 results than this ai-e not to be expected, seeing that the reason for the apparent 

 decay specified has not been made out. Taking the observations at their face 

 value, preference would have to be given to the exponential first discussed. 



Neither of these expressions however can be expected to i-epi-esent the case 

 fully, for in both differential equations all allowance for those particles which 

 escape laterally from between the plates is left out. The term ignored may be 

 much more than a coiTection ; indeed I shall presently show that by introducing 

 it and disregarding the mutual destruction of the ions altogether, one obtains 

 a much better explanation of these data than by either of the preceding methods. 



