4S THE STEl'CTUKE OF TITE NUCLEUS. 



eases. The exhaustions ft)i' tlie gh)be iiiid tlie corresponding supi)ly of nuclei are 

 tjreater in the ratio of 1 — y = .18 to I — // = .08, and there is probably greater 

 homogeneity in case of the globe. This implies that the initial uueleation is 

 usually undersaturated, if indeed saturation is the terra to be used when tiie source 

 of nuclei is not active within the medium, as it would in any case dei)eud on the 

 intensity of this source. To Ijegiu with saturation, therefore, one should devise 

 other means of nucleation than the phosphorus methods used above, which have 

 been shown to be inefficient within a damp medium. 



In <'-eneral, the nuclear ratio corresponding to two different colors in the drum 

 and the globe is about the same for the two cases, so far as it can be made out. 



The results of tables 19, 22 and 23 may be constructed in a chart, the order of 

 the coronas being horizontal and the nucleation vertical. Instead of this, log iV is 

 often a preferable ordinate, as the curves are then linear and need only be shifted 

 laterally for dilfereiit initial nucleations, since, 



log yV = z (1 + k) log 2/ + 2o- 



The fundamental difference between a.xial and coronal color as to origin, etc., 

 has already been insisted on above. 



27. 2ime losses interpreted. — Some conclusion must be derived as to the nature 

 of the time loss, which, in the above equation, has been very fully reproduced (apart 

 from the inevitable eiTors) hy N = N^tf^ where iVis the number of particles per 

 cub. cm., surviving in the receiver after the lapse of time, t: y = .825, i = .1 by 

 experiment. Thus, on reduction, if ^3 = .0083, Nz= N^IO'^K (1) 



As in my preceding papers, I will suppose that the absolution velocity of the 

 nucleus is h cm./sec, independent of the density of distribution. Moreover, that 

 in a spherical receiver, nucleated at the time i = 0, iV nuclei are found per cub. cm. 

 at a distance r from the center. The distribution is in any case concentric, but 

 otherwise disposable at [)leasure. Since the absorption of nuclei is supposed to 

 take place at the inner surface of the receiver only, there is a continued flux out- 

 ward. The solution of the pi'oblem 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 pai'tial differential 

 equation is found to be d{i-^N)/dt -j- k d(^r^N)/dr = 0, of which the integral de- 

 termineil by Lagrange's nietho(l is ^V = JV^e ■''"■""' """■', where/ is an arbitrary 

 fuiicti(jn. This is found for an initial distril)Ution independent of r. The result is 

 clearly not in keeping with the actual case of ex[ieiiment, as is to be inferred if the 

 nucleus moves in all directions. 



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

 tion is d(rN)/dt = k d'^{rN)/dr^, wiiere /'iVis zero at the surface and the center, 

 and the initial condition is /'iV = ryV^. This equation is integrable in the well- 

 known way, but the result again fails to meet the actual condition of the exi)eriment 

 as set fr)rtli in the next pai'agraph. 



(3) Remembering that the investigations above were pur[)osely conducted in 

 wide receivers, with the object among others of keeping the contents in a homo- 



