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660 PERIODIC PRECIPITATES [445
In considering an explanation, the first question which presents itself is why should the precipitate be intermittent at all ? I suppose the answer is to be found in the difficulty of precipitation without a nucleus. At a place where the second material (silver nitrate) has only just penetrated, there may be indeed a chemical interchange, but the resultant (silver arsenate) still remains in a kind of solution. Only when further concentration has ensued, can a precipitate in the usual sense be formed, and a visible line of silver arsenate constituted. But this line will not thicken itself far outwards, since the silver arsenate forming a little beyond, as the diffusion progresses, will prefer to diffuse back and deposit itself upon the nucleus already in existence. In. this way the space just outside the nucleus becomes denuded of the weaker ingredient (sodium arsenate). This process goes on for a time, but ultimately when the stronger solution has penetrated to a place where a sufficiency of the weaker still remains, a condition of things arises where a new precipitation becomes possible.. But between these lines of precipitation there is a clear space. The process then recurs and, as it appears, with much regularity. This view harmonizes with the observed diminution of the linear period as the concentration increases.
We may perhaps carry the matter a little further, considering for simplicity the case where the original boundary is a straight line, the strong solution occupying the whole of the region on one side where x (say) is negative. For each line of precipitation x is constant, and the linear period may be called dx. According to the view taken, the data of the problem, involve three concentrations—the two concentrations of the original solutions and that of arsenate of silver at which precipitation occurs without a nucleus. The three concentrations may be reckoned chemically. There are also three corresponding coefficients of diffusion. Let us inquire how the period dx may be expected to depend on these quantities and on the distance x from the boundary at which it occurs. Now doc, being a purely linear quantity, can involve the concentrations only as ratios; otherwise the element of mass would enter into the result uncompensated. In like manner the diffusibilities can be involved only as ratios, or the element of time would enter. And since these ratios are all pure numbers, dx must be proportional to x. In words, the linear period at any place is proportional, cceteris paribus, to the distance from the original boundary. In this argument the thickness of the film— another linear quantity—is omitted, as is probably for the most part legitimate. In imagination we may suppose the film to be infinitely thin or, if it be of finite thickness, that the diffusion takes place strictly in one dimension.
The specimens that I have prepared, though inferior to M. Leduc's, show the leading features sufficiently well. I have used the arsenate of silver procedure, and the broadening of the intervals in passing outwards is very evident when the plate is viewed through a Coddington lens.here /u, is the cosine of the angle between the secondary (or scattered) ray and the backward direction of the incident ray. W. F. S.]spheres are easily demonstrated.