In the figure 1 following, the knot 9Aj has a triangular section Prr cutting away on each side of it a (3 + r)-gonal mesh, and 9Ar2 has such a section Rpp, through one crossing only. Make in these knots creases at rr that approach to meet at R in 2, and creases pp that meet at P in 2. In 3, 2 is prepared for a rotation through two right angles about the fixed axis PE, through the crossing P and the crease-kiss R, or, as a more learned man would say, through the decussation P and the plicatorial osculation R–taking 2 for 9Aj: exchange here P and R if 2 is 9Ar2.

The structure of all animal hairs is very complicated, and presents many difficulties, both to the scientific observer and to those who require to manipulate these fibres in the various processes of textile and other manufactures.

As appendages of the skin they are liable, like all the epidermal growths, to great variation in structure, which is seen in its extreme form in the feathers of birds, and in the horns, hoofs, nails, and claws of the higher mammals.

For many years past some little amount of isolated work has occasionally been accomplished in photographing certain of the brighter stars. But lately, stellar photography has gone forward with leaps and bounds; so that at a dozen different Observatories in Europe, America, South Africa, and Australia, so much is now being done in that line, that there is a speedy prospect of, in a manner, the whole sidereal heavens being photographed, and after a fashion that would not only have astonished Hipparchus, but been equally surprising to either Sir William Herschel, or Argelander or Struve up to within a very few years ago.

The purpose of this paper is to give rules for the construction of knots Mn of n crossings, having each one or more linear sections PR, such that by unkissing at P and at R, shall be obtained two unifilar knots of n – 1 crossings. See my paper “On the Twists of Listing and Tait,” page 363 of the Proc. R.S.E. The knot Mn is always made by a section ffc, i.e., by uniting the P's and R's of two 2-gons (PR) on Ke+2 and Ln-e, after cutting away the four edges PR.

In August of last year I was in South Uist on an angling expedition, and, while fishing one of the lochs on the island, my attention was drawn to some very remarkable balls that were lying in great numbers at the bottom. I examined a good many of these, and found that they were composed of innumerable algal filaments so intertwined and matted together as to form an outer covering of an almost felt-like consistency, which could, however, be torn open without difficulty. This outer coating varied (speaking very roughly) from about a twentieth to two-twentieths of an inch in thickness, or even more, and the interior of the balls consisted, so far as the naked eye could see, only of mud. The microscope, of course, tells a different story.

The first point referred to in this paper is the source of the vapour that condenses to form dew. A few observations of the temperature of the ground near the surface and of the air over it, first raised doubts in the mind of the author as to the correctness of the now generally-received opinion that dew is formed of vapour existing at the time in the air. These observations, made at night, showed the ground at a short distance below the surface to be always hotter than the air over it; and it was thought that so long as this excess is sufficient to keep the temperature of the surface of the ground above the dew-point of the air, it will, if moist, give off vapour; and it will be this rising vapour that will condense on the grass and form dew, and not the vapour that was previously present in the air.

The first question to be determined was whether vapour does, or does not, rise from the ground on dewy nights. One method tried of testing this point was by placing over the grass, in an inverted position, shallow trays made of thin metal and painted. These trays were put over the ground to be tested, after sunset, and examined at night, and also next morning. It was expected that, if vapour was rising from the ground during dewy nights, it would be trapped inside the trays. The result in all the experiments was that the inside was dewed every night, and the grass inside was wetter than that outside. On some nights there was no dew on the outside of the trays, and on all nights the inside deposit was heavier than the outside one.