My position in relation to the problem was very different. I wanted to make a capillary electrometer from the description given in Lippmann’s Theses. In order to get better results, I determined by actual experiment what were the conditions of sensitiveness and rapidity, and in doing this found out so much about the instrument that the “ einfachste denkbare Annahme,” referred to by Hermann, would not have commended itself to me.
My paper on the “ Time-Relations of the Capillary Electrometer ” was a condensed account of a small portion of the work done by me. For various reasons I did not then enter into my views as to the theory of the instrument, and will confine myself here to a statement of them, which must be regarded as preliminary.
Professor Hermann speaks of my theory having been empirically obtained. I demur to that expression as open to misconstruction. My working formula may rightly be called empirical, since it neglects certain terms of the complete expression, which I have found to neutralise each other in a suitably selected instrument, but my theory of the time-relations of the capillary electrometer was founded upon first principles and verified by experiments.
My starting point was the fundamental fact that in the capillary electrometer a mechanical effect is produced by an electrical cause. But there are several links between the cause and the effect, and a strong probability that each of them involves a time-function. They are shown in the following scheme :
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S | I 1 IT. h i . IV.
1 A difference of potential (tlie establishment of which is delayed by the (varying) internal ohmic resistance of the ! electrometer) produces A change in the constant of capillarity at two interfaces between mercury and an electrolyte. Presumably giving rise to polarisation at the aforesaid interfaces. j And does work in moving a column of mercury against the force of gravity (with more or less rapidity according to the (varying) amount of fluid friction in the tube).
Poiseuille showed in 1846 that the flow of a liquid through a capillary tube varies directly as the pressure. Of this I was not aware till later, but it leads to precisely the same differential equation as that adopted by Hermann.
Writing Q for the quantity of electricity, C for the constant of capillarity, P for polarisation, and W for the work done, the symbolical expression of the problem is—
/ ( Q/, C,, P*) = 0 (W,).
