During the last generation the idea of reducing the “setting “of cloths to mathematical accuracy has been gradually taking hold of the minds of thinking men in the various textile trades. That this end is perfectly attainable is perhaps an open question, but there can be no doubt that the investigation of such problems must lead to a more satisfactory knowledge of the factors which determine the construction of fabrics.

The recent publication of Prof. Chittenden's Physiological, Economy in Nutrition tends to establish a new standard of dietary requirements, if not for the labouring classes, at least for men, middle-aged and young, who are not undergoing continued and sustained muscular work.

In a recently written paper dealing with a continuant first considered by Cayley, it was pointed out that the function in question owed its complicated law of development to peculiarities of specialisation, there being a much more general continuant governed by a simpler law.

Professor Becker's paper “On the Spectrum of Nova Persei and the Structure of its Bands,” recently published in the Transactions of this Society, contains an interesting confirmation of some results already pointed out by Messrs Campbell and Wright of the Lick Observatory, which seem to be of considerable importance for the theory of temporary stars. By most careful micrometric measurements of the positions of the bright and dark bands in the photographic spectrum of Nova Persei, Professor Becker arrives at the conclusion that all the bands are similar in type, and that the distances of corresponding maxima and minima from the centres of the bands are proportional to the wave-lengths. The results derived from the Lick photographs point to exactly the same conclusion. It appears, therefore, from these two carefully and independently executed series of observations, that the chemical nature of the elements, whose light-vibrations gave rise to the selective radiations and absorptions noticed in Nova Persei, had no influence on the appearance of the bands. According to the Lick observers, there is no evidence that the structure and character of these bands were affected by other considerations than that of wave-length.

The hypothesis of Laplace on the genesis of the solar system from an extensive nebula presents difficulties of so serious a character that important modifications appear to be required in order to make it conformable with the laws of dynamics. The objection most frequently brought forward refers to the mode in which Laplace assumes the separation of the planets from the contracting nebula to have taken place.

§§ 32–64. Canal Ship-Waves.

§ 32. To avoid the somewhat cumbrous title “Two-dimensional,” I now use the designation “Canal † Waves” to denote waves in a canal with horizontal bottom and vertical sides, which, if not two-dimensional in their source, become more and more approximately two-dimensional at greater and greater distances from the source. In the present communication the source is such as to render the motion two-dimensional throughout; the two dimensions being respectively perpendicular to the bottom, and parallel to the length of the canal: the canal being straight.

It is well known that melted sulphur when heated becomes suddenly dark brown and viscous in the neighbourhood of 160- 170°. These and other facts rendered it probable that there was a transition point in liquid sulphur, and that two liquid states could be proved to exist, one of them being stable below the transition point, and the other above it. According to the phase rule, a single substance can exist in three phases (two liquid and one vapour phase) only as a non-variant system at a single temperature and pressure. Thus, if the two liquid forms were not completely miscible, the lower one might form the greater part of the material until, as the temperature rose, it became saturated with the upper one and a new phase separated out. This phenomenon would mark the transition point, and the smallest further rise in temperature would cause the complete disappearance of the first phase. The substance would then contain a small proportion of the lower form in solution in the upper, and this proportion would diminish with rising temperature. No case of an exactly parallel nature is known; but the transition from “liquid crystals” to an isotropic liquid in the case of certain organic compounds is to a certain extent analogous.

The hardening of plastic sulphur was investigated, and it was found that partial reversion to soluble sulphur prevents the securing in quasi-solid form of the whole of the amorphous sulphur present. It was discovered, however, that sulphur formed by precipitation in presence of concentrated acids does yield 100 per cent, of insoluble sulphur, and that only the impossibility of realising the requisite condition of very fine subdivision is therefore responsible for the smaller yields from melted sulphur which has reached the highest temperatures previous to being chilled.