C. Barus — Ionization of Water Nuclei. 117 



10 volts, gave n = '9x 10 6 

 2 -5 



(negative only) *2 



J. J. Thomson (1. c.) accounts for these phenomena by a 

 bold and original hypothesis that each nucleus is superficially 

 polarized with positive oxygen and that negative corpuscles 

 are, as a consequence, projected from it into the medium. A 

 constant current independent of the electromotive force results 

 when as many corpuscles are produced per second as are con- 

 sumed by the current. 



To me it seems, however, that the hypothesis of this paper 

 points to a simpler explanation. 



In the first place the equations used in the case of water 

 nuclei 



dE/dt= 7 (1 T - e --W7W(r,+r I >/F) . . (1) 



and in case of phosphorus nuclei, 



(dE/dt)IE= ^^J(l - c-^mr.+rJ/Y) U. . (2) 



contain an exponential factor, which is increasingly more 

 important when k is small. Furthermore in equation (1), Jc 

 cancels out in the coefficient of the parenthesis, and may there- 

 fore be any function of the potential gradient within the con- 

 denser. Equation (1) is thus true, no matter whether k is a 

 function of E/(r 2 —rj or not, and an equation involving both 

 (1) and (2) may be written, if (1 — e — «) stands for the exponen- 

 tial factor, 



7 „ /7 16*7 n eV 1 ... „ x ,. 



dE dt— -? 7 , , ^^ , , ^ (1— £-«).. (3) 



where IT is the combined velocity of the ions or charges in the 

 unit electric field, and k is the effective velocity of the nuclei. 

 In other words, k is now replaced by h + UE/ir^—r^). 



Hence if the value of h is large as compared with UE/fo—r^, 

 i. e., if the nuclei have a specific velocity large in comparison 

 with the ionic increment due to the field, that is if the nuclei 

 are very small, equation (2) may be assumed, as was done for 

 phosphorus nuclei. 



If the value of k is small as compared with UE/{r^—r^ 

 i. e., if the nuclei are relatively large, then equation (1) is 

 approached, as was found to be the case for water nuclei. The 

 full value of the exponential term is 



1 _ e --B7Ur 2 + r 1 )(k+UE/(r 2 -r 1 ))l/V i 



and from the small value of h under consideration, it depends 



