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Page:Popular Science Monthly Volume 61.djvu/172

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POPULAR SCIENCE MONTHLY.

view-points from which to examine the foundations of the theory. There are three advances in the details of the theory with which his name is generally mentioned, as follows: (1) He showed that the analogy between the coefficient of diffusion for gases and the conductivity for the propagation of heat can not be pushed to the conclusion that since the conductivity is a constant magnitude, the coefficient of diffusion is a constant also, for experiments with the same pair of gases. Tait showed that this expectation is not justified by the formula in terms of which the coefficient is deduced, showing in fact that it depends at any instant not only on the temperature and on the pressure of the mixture, but also on the ratio in which the two gases have mixed with each other by that time. (2) He showed that in applying Maxwell's law of the distribution of velocities (a law deduced for a gas without total progressive or rotational motion) to the case of a gas the body of which is in rotation, the interval of time within which the mechanical theorems (deduced for the static conditions) remain valid with sufficient exactness for a single layer (the whole body of gas being considered as divided into layers between which the interchange of energy is slow) may be long enough to allow the very rapidly resulting arrangment in the distribution of velocities according to Maxwell's law to occur. In each of these layers, then, Maxwell's law holds good for the distribution of velocities on the condition that the velocity in which a particle shares by the flow or rotation of its layer is to be subtracted from the value which it would have in the state of rest and equilibrium of the gas as a whole. (3) The calculation of the coefficient of viscosity on the assumption of Maxwell's law of distribution of velocities.

In reading Tait's papers on the kinetic theory of gases it is interesting to note the author's frank confession: "I have abstained from reading the details of any investigation (be its author who he may) which seemed to me to be unnecessarily complex. Such a course has, inevitably, certain disadvantages, but its manifest advantages far outweigh them!"

Tait's chief experimental research was that on the compressibility of water, undertaken in connection with an investigation of the errors of the deep-sea thermometers used on the famous voyage of the Challenger. It is an interesting record of a laborious investigation undertaken to decide a very important practical question.

Several earlier investigators had studied the compressibility of liquids, always chiefly of water. Only the chief among them need be mentioned here. Canton, a hundred and twenty-six years before, had not only exhibited the compressibility of water, but had shown that it decreases as the temperature is raised; and Perkins in 1826 showed very clearly that in water at 10° C. the compressibility diminishes as the pressure increases, quickly at first, afterwards more and more slowly;