In a closed vessel containing only a liquid and its vapour, all at one temperature, the liquid rests, with its free surface raised or depressed in capillary tubes and in the neighbourhood of the solid boundary, in permanent equilibrium according to the same law of relation between curvature and pressure as in vessels open to the air. The permanence of this equilibrium implies physical equilibrium between the liquid and the vapour in contact with it at all parts of its surface. But the pressure of the vapour at different levels differs according to hydrostatic law. Hence the pressure of saturated vapour in contact with a liquid differs according to the curvature of the bounding surface, being less when the liquid is concave, and greater when it is convex.

1. The mathematical work of the present paper has been performed to illustrate the hypothesis, that space is continuously occupied by an incompressible frictionless liquid acted on by no force, and that material phenomena of every kind depend solely on motions created in this liquid. But I take, in the first place, as subject of investigation, a finite mass of incompressible frictionless fluid completely enclosed in a rigid fixed boundary.

I have already communicated to the Royal Society a description of experiments by which I found that iron, when subjected to magnetic force, acquires an increase of resistance to the conduction of electricity along, and a diminution of resistance to the conduction of electricity across, the lines of magnetization. By experiments more recently made, I have ascertained that the electric conductivity of nickel is similarly influenced by magnetism, but to a greater degree, and with a curious difference from iron in the relative magnitudes of the transverse and longitudinal effects.

The mathematical physicist and engineer William Thomson, 1st Baron Kelvin (1824–1904) is best known for devising the Kelvin scale of absolute temperature and for his work on the first and second laws of thermodynamics. The lectures in this collection demonstrate an attempt by Baron Kelvin to formulate a physical model for the existence of ether. This concept of a medium for light propagation became prominent in the late nineteenth century, arising from the combination of Maxwell's equations stating that light is an electromagnetic wave with the demands of Newtonian physics that light must move in a unique reference frame. First published in 1904, Kelvin's lectures describe the difficulties inherent in this model. These problems with the concept of ether are credited for inspiring Einstein to devise the theory of special relativity and the photoelectric effect, both of which are central to modern physics.

After noticing Helmholtz's admirable discovery of the law of vortex motion in a perfect liquid, that is, in a fluid perfectly destitute of viscosity (or fluid friction), the author said that this discovery inevitably suggests the idea that Helmholtz's rings are the only true atoms. For the only pretext seeming to justify the monstrous assumption of infinitely strong and infinitely rigid pieces of matter, the existence of which is asserted as a probable hypothesis by some of the greatest modern chemists in their rashly-worded introductory statements, is that urged by Lucretius and adopted by Newton; that it seems necessary to account for the unalterable distinguishing qualities of different kinds of matter. But Helmholtz has proved an absolutely unalterable quality in the motion of any portion of a perfect liquid, in which the peculiar motion which he calls “wirbel-bewegung” has been once created. Thus, any portion of a perfect liquid which has “wirbel-bewegung” has one recommendation of Lucretius' atoms—infinitely perennial specific quality. To generate or to destroy “wirbel-bewegung” in a perfect fluid can only be an act of creative power. Lucretius' atom does not explain any of the properties of matter without attributing them to the atom itself.