Condensation, and on the contrast of Colors. 91 



density of distribution. Moreover, that in a spherical receiver, 

 nucleated at the time t = 0, N nuclei are found per cub. cm. 

 at a distance r from the center. The distribution is in any 

 case concentric, but otherwise disposable at pleasure. Since 

 the absorption of nuclei is supposed to take place at the inner 

 surface of the receiver only, there is a continued flux outward. 

 The solution of the problem requires some understanding as to 

 the manner in which this flux takes place. 



(1) If there is a mere motion outward for all particles, the 

 partial differential equation is found to be d{r' i N)/dt 4- 

 kd(r*JV)/dr=0, of which the integral determined by Lagrange's 

 method is JV= JV r 6 /(r ~ W)_Inr2 , where/" is an arbitrary function. 

 This is found for an initial distribution independent of r. 

 The result is clearly not in keeping with the actual case of 

 experiment, as is to be inferred if the nucleus moves in all 

 directions. 



(2) The next case would be that of diffusion. The partial 

 differential equation is d(rJV)/dt = Tc d\rJY)/dr 2 , where rJV is 

 zero at the surface and the center and the initial condition is 

 rJV = rN Q . This equation is integrable in the well known 

 way, but the result again fails to meet the actual condition of 

 the experiment as set forth in the next paragraph. 



(3) Remembering that the investigations above were pur- 

 posely conducted in wide receivers, with the object among 

 others of keeping the contents in a homogeneous state of 

 nticleation through the agency of convection currents, it may 

 be safely assumed that iv is not a function of r but of time 

 only. If this were not so the coronas w T ould show color distor- 

 tion (as they do in marked degree in benzine vapor) as well as 

 the time changes observed. In case of water vapor, the ever 

 present convection will not allow either the distribution (1) or 

 (2) to persist. Hence whatever removal of nuclei takes place 

 at the inner w r all of the large receivers is a deduction or drain 

 of nuclei from the whole volume of vapor, uniformly. This 

 experimental condition simplifies the computation and offers 

 an easy interpretation of the results obtained. In case of 

 absorption with the adequate convection, therefore (if R be 

 the radius of the receiver), - {±irR z /Z) dJST/dt = Ah lirR'N', 

 where k is the absorption velocity of the nucleus and A a 

 coefficient, stating what part of k is effective in view of the 

 given degree of convection maintained. For mild convection the 

 loss of nuclei at the surface will take place largely by diffusion 

 through relatively fixed layers and A will be a small fraction ; 

 whereas in case of very turbulent agitation, as when the nuclei- 

 bearing air is driven through fine bore or capillary tubes, A 

 will be nearly one. The air is soon washed clean of nuclei. 

 Hence (2) N = JV \0~ 3A kt QW R , an equation identical in form 

 with that actually found in the experiments. 



