TABLE I.-Absorption of the Ionized Phosphorus Emanation in Tubes of Grey Rubber. Diameter 2r='64 centim., p=4 centim., 0=26°.

A brief summary of the chief results is appended for reference.

TABLE II.-Summary of Data for Absorption Velocity k.

These results are entered in the chart with greater fulness, where the abscissas are the lengths of the absorption-tubes, the ordinates the volumes per minute producing the fiducial blue. The curves drawn through the points are computed

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from the theory presently to be given. For the wider tubes and greater lengths the higher volumes sometimes show a break in the curve (cf. lead), meaning, I think, that the phosphorus ionizer is being overtaxed by the quantity of charged air demanded.

CHART showing the litres per minute of air saturated with phosphorus emanation, needed to produce a full blue field in the colour-tube for different lengths of absorption-tube.

In view of the difficulty of observing, subject to colour criteria, the widely different values of the velocity with which the ionized air traversed the absorption-tubes, the high velocities employed, and the marked difference of material

Add to this the variable ionizing intensity of phosphorus, the most baffling of discrepancies.

(conducting and insulating) which makes up the absorbingwalls, the proximity of the values of k is particularly noteworthy. No relation to diameter is apparent. In case of glass, of impure grey rubber, of pure brown rubber, and of lead, this velocity k, so far as observation warrants, is the

same.

4. In contrast with these results with tubes of relatively small bore, I shall now add data for wide tubes. They were 5 centims. in diameter (2-inch drain-pipe of tin plate), and they may be regarded as direct prolongations of the influxpipe C' of the colour-tube. The air passing through these tubes is moved by the suction of the steam-jet, and is independent of the ionizing current through the gasometer. The velocity of the air-current through the tubes (often 50 feet long) was about 100 centims. per second, and was determined by the time it takes the "dust," suddenly injected into one end of the tube, to show itself at the other end by colouring the steam-jet. The phosphorus emanation (V litres per minute) was introduced into the current at distances 150 and 1500 centims., respectively, from the jet, as the data show. The table gives but a single series among many. The velocity is here computed from

k=(rv/2(x−x')) log (V/V'), where the volumes V and V' correspond to the tube-lengths x and x.

TABLE III.-Absorption of Phosphorus Emanation in Tin drain-pipe. Diameter, 2r=5 cm., p=4 cm., 0=28°.

These results have also been constructed in the chart on the same scale as the other curves, the data selected being those showing the maximum effect of length. In fact, these results are liable to be very variable, as the colours for the

long tubes become dull, and are unsuitable for sharp comparisons. One may state that more dust is required for long than for short tubes, but that the difference is a relatively vanishing quantity and out of all proportion with the data for small tubes. The difference between the present and the preceding experiments with tubes is this, that whereas in the latter case (small bore) the saturated air is conveyed in the undiluted condition through the tubes, in the case of wide tubes (5 cm.) the saturated dust is necessarily diluted on being introduced into the tube, having its own independent current of air. The present series shows the remarkable preservative tendency of this operation of dilution, and points out a reason for the constancy of behaviour of the colourtube itself after the nuclei have once been captured.

5. In the endeavour to frame at least a working hypothesis for these phenomena two possible occurrences are prominent: the first is the decay of the particle so far as its activity in producing condensation is concerned. This may be due to growth and loss of charge, to the action of ordinary dust particles floating in the air, or any similar cause whatever. It constitutes a loss within the ionized medium itself. The second relates to losses at the boundary, to the motion of the ionized particle, whether stimulated by an electric field, or a diffusiongradient, or not, occurring in the latter case as a mere ionic velocity. Since electric field is absent, it would at the outset be natural to treat the motion as a case of diffusion, and due to a concentration gradient. It seems hardly probable, however, that in a swift turbulent current of air diffusion can be recognized. I have therefore thought it best to regard the nucleus as moving with a definite (absorption) velocity k independent of direction and (for a given class of experiments) independent of concentration. So circumstanced, the swarm of nuclei are transferred by the air-current. As the nucleus. impinges upon but does not rebound from a barrier, k may still be regarded as an external diffusion coefficient, corresponding to the constant in Newton's law of cooling.

Let da be the thickness of an infinitesimal right section of the absorption-tube of radius r, traversed at velocity v by an air-current charged with nuclei. Let n be the number per cubic centim., and k the number absorbed per square centim. per second if n= =1. Hence k is the absorption velocity discussed.

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If, as in cases considered elsewhere, the absorption-tube were a condenser with the field acting radially outward, k would be replaced by UeE/(R-R), where e is the charge of an electron, U the velocity of the ions relatively to each other, E/(R2- R1) the potential gradient, R, being the axial and R, the circumferential radius of the condenser. I mention this here for future reference.

Let be the number of particles decaying by mutual destruction, &c., per cubic centim. per second, if n=1, so that 'n is the number vanishing for the density of distribution n.

Fig. 2

Hence the number of particles accumulating per second in the element is r2(dn/dx)dx; the number absorbed per second by the walls of the tube, kn2πr.dæ; the number decaying per second within the element, k'n'r2dx. Thus

This equation is integrable in finite form, and putting no as the concentration at o, the equation becomes

n=2kn ̧[(€2k(x−rg) /re (2k + k'rn ̧) —k'rno).

The direct discussion of this equation is cumbersome. Its bearing on the present results is best shown by evaluating the two special cases in which k=0 and k'=0, respectively. The former case is incompatible with the observations, and may be dismissed.

Let then K=0, so that decay within the element from any causes whatever is absent. The only loss of nuclei is at the surface of the absorption-tube.

if n is the concentration at x=0, i. e. in the absence of the absorption-tube. But v=1000V/602, if V litres per minute produce the velocity v centims./sec.

The total number of nuclei injected into the colour-tube is thus nV. Let these produce the fiducial clear blue field. In the same manner let n'V' nuclei produce the same field when the dimensions of the absorption-tube are ' and ', and the air passing V' litres per minute. Then, since nV=n'V',

Ve-krx/265VV'e-kr'z' 2-65 V'.

If Vo be the volume per minute when the tube-length is '=0 and the field the identical blue,

k=2·65(V/rx) log (V/Vo),