118 C. Bancs — Ionization of Water Nuclei. 



essentially on E. Hence if the ionization is neutral (equality 

 of positive and negative ionization or charge), the current will 

 vanish with the potential gradient or with the charge in the 

 condenser. 



It is next in place to show that the exponential factor soon 

 becomes constant and equal to one. This is done in the fol- 

 lowing table by direct computation, using the constants already 

 summarized. 



ft+tfff/fa-rjs: 



001 cm. 



/sec. 



1 — c- a = -013 



010 





•121 



•100 





•736 



•000 





1-000 



Hence when the total nuclear velocity approaches the usual 

 values of ionic velocity in air (1*5 cm./sec.), the current is con- 

 stant and 



dE/dt=\6'1 n eVjG. 



Thus the character of the curve given in the chart is actually 

 predicted without an assumption as to radio-activity. 



It is further pointed out by the equation that uncharged 

 water nuclei cannot conduct appreciably, seeing that they owe 

 their effective velocity to the field, which becomes inactive in 

 the absence of charge. 



Finally the velocity of the water nucleus under an assumed 

 probable size may be computed. The resistance to motion at 

 velocity v, of an infinitely small sphere of radius R in air of 

 viscosity /jl is Gtt/jlRv dynes (Kirchhoff's Mechanik, lecture 26, 

 § 4). The pull of the field on the charge e is equal to this, 

 whence 



v = Eej (QTTfxE{r 2 -rj). 



If the nuclei diffuse appreciably, R is smaller than 10 -i cm. 

 which would follow for subsidence, and R may then be esti- 

 mated at 10- 6 cm. ; while p = 2x10 ~> 2 -r, = *73 cm , E= 20/ 

 300 and e = 200x7XlO -10 electrostatic units, if each nucleus 

 carries 200 electrons. Hence 



v = 3*4 cm./sec. 



which is about "12 cm./sec. in the field of one volt /cm. This 

 value is actually very large as compared with the values which 

 I found (§ 15) for the velocities of water nuclei in the absence 

 of a field, but it is naturally dependent on the uncertainty of 

 R. I shall waive the subject here, as I propose to return to it 

 more specifically elsewhere. 



15. Comparison of Phosphorus and Water Nuclei. — Between 

 phosphorus and water nuclei there is in the first place the 



