Emanation in Spherical Condensers. 311 



outer surface* permanently put to earth and its inner surface 

 (always very small) in contact with the needle of a charged 

 electrometer, the intervening space being air ionized by a 

 piece of phosphorus about as large as a split pea, suspended 

 at the center. 



A series of Konig's resonators seemed very suitable for the 

 purpose, as they were at hand in a large range of diameters, 

 and tig. 1 shows the adjustment. A is the brass resonator, 

 put to earth by the plug and wire E, B the curl of wire mak- 

 ing the inner face of the condenser, and holding the spherule 

 of phosphorus, P. C is an insulating glass tube about 30 cm 

 long, through which the electrical charge is conveyed along a 

 thin copper wire D, to be dissipated in the condenser. B is 

 thus in contact with the electrometer, and the capacity of the 

 latter, about 90 cm , is always large as compared with the conden- 

 sers (less than l cm ). 



3. Leaving the results as a whole to be discussed elsewhere, 

 I will merely instance the following example chosen at ran- 

 dom from a large number. In order to estimate the variability 

 of the ionizing source (due to temperature, environment and 

 other conditions which I have not yet made out) condenser Kb 

 was treated as a standard and observations made with it before 

 and after those for each of the other condensers. The obser- 

 vations for a single condenser consisted of 6 potential readings 

 (scale parts suffice) taken at intervals of one minute. From 

 these I computed the constants in the last column, to be pre- 

 sently explained. 



4. If, as in my preceding experiments, the motion of the ion 

 is supposedly independent of the potential difference, V, and of 

 the concentration {n particles per cub. cm.), or if the effect of 

 the potential gradient, V/B, is but a negligible contribution to 

 the number of ions which are absorbed by the (outer) surface 

 of the condenser distant from the emanating phosphorus, then 

 the accumulation in an elementary spherical shell of radius r 

 will be A.irk.d{rn)/dr.dr, per second. Here k is what I have 

 called the absorption velocity; Jen denotes the number of ions 

 absorbed per square cm. per second. The decay within the 

 element is per second, k'n^^irfdr^ if k' be the number vanish- 

 ing per second per cub. cm., when n — 1. Hence d(r~n)/dr = 

 (&y&)?iV; or if n 1 be the number of ions at a distance 1 

 from the center, r((k , /k)n J (l — r)-^r) = n 1 /n. If decay be 

 ignored, &'=0, and n 1 — nr'\ which as is otherwise clear, is 

 independent of k also. 



Now the electric conduction is dependent on the number of 

 ions which reach the external shell (r — B), or — dQ/dt = — 

 Cd V/dt =■■ ±ttB 2 U. V/B.ne, where Q denotes the charge, the 



* In the present instance left open around the stem. The closed condenser'is 

 liable to introduce hurtful conduction where the stem enters. 



