IV. On the dynamical theory of incompressible viscous fluids and the determination of the criterion

1. The equations of motion of viscous fluid (obtained by grafting on certain terms to the abstract equations of the Eulerian form so as to adapt these equations to the case of fluids subject to stresses depending in some hypothetical manner on the rates of distortion, which equations Navier seems to have first introduced in 1822, and which were much studied by Cauchy and Poisson) were finally shown by St. Venant and Sir Gabriel Stokes, in 1845, to involve no other assumption than that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a co-efficient depending on the physical state of the fluid. By obtaining a singular solution of these equations as applied to the case of pendulums in steady periodic motion, Sir G. Stokes was able to compare the theoretical results with the numerous experiments that had been recorded, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved. This was also the result of comparing the flow of water through uniform tubes with the flow calculated from a singular solution of the equations so long as the tubes were small and the velocities slow. On the other hand, these results, both theoretical and practical, were directly at variance with common experience as to the resistance encountered by larger bodies moving with higher velocities through water, or by water moving with greater velocities through larger tubes. This discrepancy Sir G. Stokes considered as probably resulting from eddies which rendered the actual motion other than that to which the singular solution referred and not as disproving the assumption.

XXII. Bakerian lecture.—On the laws connexion between the conditions of a chemical change and its amount.—III. Further researches on the reaction of hydrogen dioxide and hydrogen iodide

Nearly thirty years ago we laid before the Royal Society the results of our inquiries into two cases of gradual chemical change, viz.: (1) the reaction of hydrogen permanganate and hydrogen oxalate, and (2) the reaction of hydrogen dioxide and hydrogen iodide. We have continued at intervals our investigation into the latter reaction, and have obtained some further results, which we desire now to communicate to the Royal Society.

XIX. On the occlusion of oxygen and hydrogen by platinum black. - Part I

The word “ occlusion ” was first used by Graham, to signify the absorption of, or shutting up, of gases in solid substances. Many porous bodies, such as charcoal, possess this property, and it is also to be met with among the metals, pre-eminently among the metals belonging to the eighth group of the Periodic Table, and especially among the platinum metals. Platinum in the coherent state, and also in the state of sponge, has been very fully investigated by Graham, in his classical researches. A large number of observations on platinum black are also on record, but these, for the most part, have been made with impure material, and the results are often contradictory.

XV. On the ratio of the specific heats of some compound gases

The experiments to be described in the present paper are a continuation of those of which I gave an account in the ‘Phil. Trans.,’ vol. 185, p. 1. It is shown there, from experiments on methane, ethane, and propane, and their derivatives, that the monohalogen derivatives of any one paraffin have in the gaseous state the same ratio of the specific heats, and that this ratio is the same as that of the hydrocarbon itself in two of the three series. Methane proved to be an exception, having a higher ratio than its derivatives.

XIII. On the velocities of the ions

In a previous communication to the Royal Society (‘Phil. Trans.,’ 184 (1893), A, p. 337), I have described a method of experimentally determining the velocities of the ions during electrolysis, by observations on the phenomena at the junction of two salt solutions, one at least of which is coloured, when a current of electricity is passed from one to the other. For the success of the method it is necessary to choose two solutions which (1) are different in density, (2) different in colour, and (3) have nearly equal conductivities at equivalent concentrations, i. e , when the number of gram-molecules dissolved in 1 litre of solution is the same for both. These conditions seriously restrict the number of cases to which the method is applicable, but the results obtained for copper and for the bichromate group (Cr 2 O 7 ) agree well with the values theoretically deduced by Kohlrattsch from measurements of the conductivity. Alcoholic solutions of cobalt nitrate and chloride were also used, and the sum of the velocities of the opposite ions, in each case, observed in my experiments, was as nearly as could be expected, the same as their sum calculated from the conductivities by Kohlrausch’s method.

VI. Argon, a new constituent of the atmosphere

"Modern discoveries have not been made by large collections of facts, with subsequent discussion, separation, and resulting deduction of a truth thus rendered perceptible. A few facts have suggested an hypothesis, which means a supposition, proper to explain them. The necessary results of this supposition are worked out, and then, and not till then, other facts are examined to see if their ulterior results are found in Nature.”— De Morgan, “A Budget of Paradoxes,” ed. 1872, p. 55.

XII. The oscillations of a rotating ellipsoidal shell containing fluid

In a paper published in 'Acta Mathematica,’ vol. 16, M. Folie announces the fact that the latitude of places on the earth’s surface is undergoing periodic changes in a period considerably in excess of that which theory has hitherto been supposed to require. This result has been confirmed in a remarkable manner by Dr. S. C. Chandler, in America ( vide ‘ Astronomical Journal,’ vols. 11, 12), who, as the result of an exhaustive examination of almost all the available records of latitude observations for the last half-century, has assigned 427 days as the true period in which the changes are taking place. The old theory, based on the assumption that the earth was rigid throughout, led to a period of 305 days, and M. Folie proposes to account for the extension of this period by attributing a certain amount of freedom to the internal portions of the earth. The earth he supposes to be composed of “a solid shell moving more or less freely on a nucleus consisting of fluid at least at its surface.” The argument advanced by M. Folie in favour of this constitution of the earth, namely, the independence of the motions of the shell and the nucleus, appeared to me to be unsatisfactoiy, and I therefore proposed to myself to test the validity of it by examining a particular case which lent itself to mathematical analysis, namely, that in which the internal surface of the shell is ellipsoidal and the nucleus consists entirely of homogeneous fluid. The principal axes of the shell and of the cavity occupied by fluid are assumed to be coincident, and the oscillations are considered about a state of steady motion in which the axis of rotation coincides with one of these axes. It is clear that a steady motion will be possible in this case, and that such a motion will be secularly stable in the event of the axis of rotation being the axis of greatest moment for both the shell and the cavity.

IX. The latent heat of evaporation of water

It is possible that I have in succeeding pages, when describing apparatus and methods of observation, entered unnecessarily into matters of detail. In defence, I would urge that the accuracy of determinations of physical constants depends on the amount of attention devoted to apparently trivial matters, and that in the absence of full information, it is impossible to rightly estimate the value of the results. Corrections are often rendered necessary by subsequent re-determinations of the constants involved, and the application of such corrections is only possible when the writer has given his data in full. Much valuable experimental work has with lapse of time become useless, owing to the author’s natural reluctance to overcrowd his communication with details which may at the time very possibly appear both unnecessary and trivial. Although the experiments described in this paper were not commenced until the Summer of last year (1894), the preparation of the apparatus and the standardisation of the instruments has engaged my attention for a considerable time. Nearly the whole of the Spring and Summer of 1893 were expended in fruitless efforts to render the calorimeter and its connections absolutely air-tight, and I found it impossible to secure perfection in this respect until in the Autumn of that year I succeeded in obtaining an alloy, by means of which I was able to unite glass and metal tubes in a satisfactory manner. The calorimeter and connections had then to be practically reconstructed and some improvements added, which experience had shown to be desirable.

XXIII. Theorems on the attraction of ellipsoids for certain laws of force other than the inverse square

1. To find the potential at an internal point P of a thin ellipsoidal shell bounded by similar concentric ellipsoids, the law of force being the inverse k th power of the distance. Let ( x, y, z ) be the coordinates of P; ( l, m, n ) the direction cosines of a radius vector drawn from P to any point Q on the surface; and let PQ = r . Let ( a, b, c ) be the semi-axes of the ellipsoids, and ( α, β, γ ) their squared reciprocals. Then from the equation of the ellipsoid ( αl 2 + βm 2 + γn 2 ) r 2 + 2 ( αlx + βmy + γnz )r - (1 - αx 2 - βy 2 - γz 2 ) = 0.