It is my privilege to welcome you at the commencement of this new Session, which, from many indications, promises to be one of great activity among the Fellows of the Society.

In a former paper, printed in Trans. Boy. Soc. Edin., 1886, I showed that the recovery of the “special” state by a gas supposed to consist of equal hard spheres takes place, at ordinary pressures and temperatures, in a period of the order of 10−9 seconds, at highest.

During part of the recent summer (1886), in addition to the ordinary temperature observations here, a set of readings were taken in a Stevenson screen, at a height of 112 inches above ground—that is, at about two and a half times the standard elevation of 48 inches. The high level screen was mounted at the top of a stand used to carry the thermometers in winter, and consisting of two stout upright posts or battens, with cross bars between them at every 2 feet or so; the screen is placed with the lower edge of the back resting on one bar, and is tied to the one above it or to the side posts. The screen used on this stand is smaller than the standard Stevenson screen, but it is constructed in exactly the same manner, with double louvred sides and the bottom open. It measures inside 10 inches broad by 6 inches deep and 15 inches high.

It is well known that the solution of the mathematical problem of the motion of liquid arising from the motion through it of solids has been effected in comparatively few instances, and in these, such as the sphere and the ellipsoid, the surface is defined by a single equation. In the following investigation, however, we seem naturally to come across cases where the solid might be described as “a compound body,” consisting as it does of parts defined by different equations. It is possible that the method employed might lead to the solution of analogous problems in Sound, Heat, or Electricity.

The question raised is very closely connected with § 6 of my paper on the Kinetic Theory of Gases (Trans. R.S.E. xxxiii. 71). The result arrived at is that, when (in the thin layer) some particles prevent others from doing their full duty, the formula should be

as given in the text.

1. 1. Each crossing divides the cord into two loops.

2. 2. Any other crossing either lies on both these loops, say is linked to the former crossing, or on one loop only, say is not linked to the former crossing.

3. 3. It can be shown without difficulty that if crossing a is linked to crossing b, then crossing b is linked to crossing a; and therefore, also, if crossing a is not linked to crossing b, crossing b is not linked to crossing a.

4. 4. Hence pairs of crossings are of two sorts, viz., linked and unlinked.