Philosophical Transactions of the Royal Society (1701-)

...principally interesting in showing how far Sir W. Thomson’s Sir William Thomson, later known as Lord Kelvin, a pioneer in thermodynamics and physics results are changed by the assumption that elasticity fails under continued pressure.

In this paper, I follow these hypotheses. It will be shown that the results are just as opposed to the idea of a highly mobile or fluid interior of the Earth as Sir W. Thomson’s results were.

The only evidence on Earth of a bodily tide tides that occur within the solid or semi-solid mass of a planet rather than just its surface oceans would be that the ocean tides would be lower than theory predicts. Therefore, the subject of this paper is closely connected to the theory of ocean tides.

In the first part, the equilibrium tide-theory a model that assumes the ocean adjusts instantly to the gravitational pull of the moon and sun is used to estimate how much ocean tides are reduced and how their timing is shifted by bodily tides. However, it is widely recognized that this theory is quite flawed when explaining tides that occur over short periods.

In the second part of this paper, I have therefore considered the dynamical theory a more complex model involving the actual movement and momentum of water of tides within a canal at the equator surrounding a core distorted by tides. The results are almost the same as those given by the equilibrium theory.

The first two sections of the paper adapt Sir W. Thomson’s work* to the current hypotheses. Since it was impossible to include his entire argument here, I fear this investigation will only be understandable to those who are already familiar with his work or are willing to accept my quotes from it as proven.

Because some readers may want to know the findings of this inquiry without studying the mathematics, I have provided a summary of the whole work in Part III. As much as possible, I have moved my comments and conclusions to that section. However, I have tried to provide enough explanation in the main text to show the direction of the argument.

I consider the case of pure viscosity a measure of a fluid's resistance to flow; its "thickness" first, because the analysis is somewhat simpler and the results can later be easily applied to the case of elastico-viscosity the property of a material that behaves with both elastic (solid) and fluid properties.

1. The similarity between the flow of a viscous body and the strain of an elastic one.

The general equations for the flow of a viscous fluid, when the effects of inertia original: "inertia"; the tendency of an object to resist changes in its state of motion are ignored, are

* His paper can be found in Philosophical Transactions of the Royal Society, 1863, page 573, and sections 733–737 and 834–846 of Thomson and Tait’s Natural Philosophy, 1867 edition.