Emanation in Spherical Condensers. 313 



capacity of the condenser, and where U is the mutual velocity 

 of the ions and e the (average) charge of each. Since n=n 1 /r* r 

 — d(\og V)/dt = {AtireTJ/C){nJR). Here the first term is 

 obtainable from the observations directly, krreTJ/C — K'\% a 

 constant, n 1 expresses the waning intensity of the ionizing 

 phosphoric source, and R is the external radius of the conden- 

 ser selected. The equation therefore admits of being tested. 

 The integral value is V = y^-^U^/cm, which in a 

 general way suggests the observations. In the above table 

 nj£\% computed for each case. 



5. I have also represented the quantity n L K graphically in 

 the chart, fig. 2, to show the outstanding dependence on the 

 radius R of the condenser, obtaining a curve which here as else- 

 where is sinuous in outline but ascends from low values of the 

 radii of the condensers. The situation is referable to the fluc- 

 tuation of the intensity of the phosphorus ionizer, and to una- 

 voidable conduction. To show this I have numbered the 

 points in the order of measurement : thus point 8, which is too 

 high, corresponds to a rise in the standard from point 7 to point 

 9 ; point 4 being too low, to a fall from point 3 to 5 ; etc., remem- 

 bering that the standard affords a means of suggesting the 

 reason of the discrepancy, not of eliminating it. Waiving 

 further discussion, I will state my conclusion, that the quantity 

 nJL increases from the values for small condensers rapidly to 

 constant values for larger condensers, attaining the latter when 

 the radius exceeds 4 cm. Since K—^nretf/C contains no 

 variables, it follows that n„ the number of ions at 1 cm. from 

 the center is relatively greater for larger than for smaller con- 

 densers, though the limit is soon reached as stated. But as the 

 initial potential difference, T , is the same throughout (40 volts), 

 the fields for the smaller condensers are greater. Hence without 

 stopping to reconstruct the above theory, the general inference 

 of §1 may be asserted. The experiments of the next para- 

 graph, however, in which larger condensers are used and strong 

 fields applied directly, showed me that in my smallest conden- 

 sers the current may be 20 or 30 per cent too small. This is 

 due to the easy access of air and the loss of ions around the 

 stem (fig. 1), which with small condensers is necessarily a much 

 more serious discrepancy than with large condensers. It fol- 

 lows that the initial parts of the curve,' fig. 2, are considerably 

 too low. Indeed it seems to me a more probable inference, 

 that with an ideal adjustment and a constant ionizer this curve 

 would become appreciably horizontal and njl constant through- 

 out, compatibly with Ohm's law. 



6. In addition to the above experiments with series of con- 

 densers, I completed a number of correlative tests by varying 

 the potential difference of the same condenser from 20 to 300 



