At the opening of another session the attention of the Fellows ought to be directed to certain points concerning the administration of the affairs of this Society. One gratifying feature is the completion of the card catalogue of the volumes in the Society's library. After the removal to our present quarters in 1909 it became apparent that the old catalogue in three large volumes was unsatisfactory. The original entries were not up to modern requirements, and, in view of a new catalogue being prepared, the new marks caused by the altered arrangement of rooms and shelves had been imperfectly registered. The library staff realised that nothing short of a card catalogue prepared from the volumes as they stand on the shelves would meet existing requirements. This was an arduous undertaking, involving considerable outlay. Dr Knott has estimated that the library at present contains forty-six thousand volumes, the greater part of which consists of scientific serials. To accomplish the task of cataloguing this large collection it was necessary to obtain outside expert assistance.

Adolf Ritter von Baeyer was born on October 31, 1835, in Berlin. His interest in chemistry began at the early age of nine, when his father gave him a copy of Stöckhardt's Schule der Chemie. Subsequently he studied under Bunsen at Heidelberg, and also under Kekulé, whom he followed to Ghent, and whom he always considered to be his real teacher. In I860 he returned to Berlin, and became Privatdozenten at that University. From this day onwards he published numerous papers. After three years spent in Strassburg as Professor of Chemistry he finally settled at Munich, where most of his chemical researches reached maturity. The influence Baeyer exerted in the development of chemical science, and especially of organic chemistry, was greater probably than that of any other single man, for almost every professor of chemistry now in Germany passed through his laboratories at Munich and received a stimulus there from the enthusiastic head.

1. The period of survival in distilled water is shortest with post-moult crabs, longer with pre-moult, and longest with inter-moult.

2. Further, a relatively constant percentage of salts is lost, irrespective of size; hence one of the determining factors in survival is the rate of loss of these salts. The other factor is the rate of osmosis of water, causing œdema.

3. With regard to the moult cycle, the concentration of the blood and the structure of the membranes are seemingly little altered, but the amount of calcium in the latter varies with moult-age, being least in post-moult and most in inter-moult membranes.

4. It is concluded, that the higher the percentage of calcium, the less permeable are the membranes and the longer is the duration of survival.

5. Œdema and loss of salts naturally disturb the tonicity equilibrium of the body fluid, and thus cause death.

1. The adsorption of a gas has been investigated thermodynamically with special reference to the heat effects accompanying adsorption.

2. Expressions are developed for three isothermal heats of adsorption of a gas and for the heat of immersion of a powder in a liquid.

3. The effect of the variation of the surface of an adsorbent when adsorbing is examined, and it is shown from Titoff's observations (assuming, of course, the adsorption to be reversible) that the divergence between calculated and observed values of the heat of adsorption can be explained on the assumption of a change of surface area. The fractional change of surface per c.cm. adsorbed can be calculated, and also the surface energy per grm. adsorbent in vacuo.

Throughout 1915 and 1916 a study was made of the dietaries of forty-seven labouring class families in Glasgow, and in February 1917, shortly after the publication of the Devonport Voluntary Ration, ten of the original families were investigated for a second time. The results of all these studies were published in the Proceedings of the Royal Society of Edinburgh, vol. xxxvii, p. 117, 1917.

In November 1917, after nine months of voluntary rationing, after the price of bread had been reduced from to per 2 lbs., and just before the introduction of the Rhondda Voluntary Ration, the diets of eight of the families were studied for a third time.

(a) The direction of the respiratory current is postero-anterior, whether the crab is above the sand or buried in it.

(b) Reversal of this direction also occurs and is more frequent when the animal is buried or when a strong ink suspension is used during an experiment.

(c) The sub-branchial cleft may be divided into four separate spaces which are in direct communication with gaps between certain gill origins, the whole constituting the sub-branchial inlets.

(d) The direction of these inlets varies from postero-anterior to almost latero-medial.

(e) They determine the direction of the inhaled currents within the branchial chambers.

(f) The relation between the position of the gills and these inlets allows for a convenient and maximal flow.

Given two sets of linear homogeneous equations in n1 and n2 variables respectively

Let us form another set by multiplying every equation of (1) by every equation of (2). Thus

or

where

This set (A) of n=n1·n2 equations is linear and homogeneous in the n=n1·n2 variables w.

In the course of an investigation regarding rotating fluids, I have had occasion to make considerable use of Legendre's function of the second kind, which, as is well known, may be expressed in the form

where Pn is Legendre's polynomial, and fn−1 a polynomial of degree n−1. Various expressions of fn−1 have been given, particularly in terms of Legendre's polynomials of lower degrees; but I found that none was satisfactory in regard to the practical computations which I had to perform.

On Monday, 3rd December 1917, in brilliant weather, a meteor was observed by many persons in S.E. Scotland. Its luminous course lasted apparently for some seconds. It is described as extremely bright, like limelight, or a length of wire at white heat; it left a trail, part of which became detached but continued to follow it, and it was accompanied by two thin streamers. It was seen from Hexham, Northumberland, 120 miles from where it fell, low down on the horizon. From Edinburgh several observers noticed it at an angle which may be put at 45° from the horizon and a bearing somewhat to the east of north. From Dunfermline it was reported at “no great altitude” and travelling in a line inclined about 15° to the horizon.

The studies of which the present paper is the first are intended to accumulate observations and discussions on all necessary points connected with exact time-keeping, such as the maintenance of motion, air-resistance, barometric error, escapement error, temperature compensation, and so forth. It may be taken that no clock so far made behaves uniformly so as to keep regular time. The clock is one of the fundamental measuring instruments of astronomy, but astronomical practice has kept in advance of the precision reached by its clocks by determining the clock error in the midst of each set of observations and so dispensing with the need for carrying forward for any length of time a doubtful clock rate. But there are many reasons why we should not be content with this, which amounts to an elimination of the clock. In the first place, it is not always feasible.

The explosion which occurred in East London at 6.51 p.m. on January 19, 1917, was one of the greatest ever experienced in this country. The sitex of the explosion is indicated approximately by the star in the accompanying maps. The total amount of explosives lost is known, if at all, only to those in authority.

In order to determine the forms of the sound-areas, I wrote letters to most of the principal newspapers published in London and within and near the districts concerned, and I am greatly indebted to the courtesy of many editors in allowing me space for which there were so many important claims, and also to the numerous correspondents who so kindly answered my inquiries. After the boundaries of the sound-areas had been drawn from an unusually large number of positive records, I wrote to the incumbents of many parishes in small towns and large villages, and to superintendents of police within the silent zone and just within and for some distance outside the boundaries of the sound-areas as I had drawn them. The total number of positive records is 571 from 391 places, and of negative records 75 from 71 places. In addition to these, there are 79 records from 71 places at which the sound was apparently not observed, but at which windows were shaken or pheasants disturbed; making a total of 725 records from 533 places.

In Meschinelli's Iconographia (5) mention is made, and a short description given, of eleven species of fossil Phycomycetous fungi. Since the publication of this book, additions to the list have been made by Oliver (7), Weiss (12), Magnus (4), and the present writer (3). Altogether, therefore, fifteen species have been described which could definitely be assigned to the Phycomycetes. With such small data at our disposal it is evident that the time is not yet ripe for the framing of general propositions regarding the history of the Phycomycetes in past ages, and more especially as the information that we possess concerning several of these fifteen species is very meagre.

(1) The essence of Cayley's mode* of arriving at the formation of an orthogonal substitution lies, as is known, in the observation that if two sets of variables

x, y, z, w, and ξ, η, ζ, ω

be taken linear functions of a third set

in such a way that the determinant of the coefficients is in the one case

and in the other the conjugate of this, then the first and second set of variables are orthogonally related.

During the spring of 1916, while making observations from an economic point of view on the Holly Tortrix Moth, Eudemis nœvana (Hb.), I found that, owing to the transparency of the egg and its flattened form, the development could be followed in the living egg in a general way with unusual clearness.

Investigations have been carried out on the embryology of about eighteen species of Lepidoptera, but as far as I am aware no account has been published of the embryology of the Tortricidæ.

Most of us who have thought at all of mirage have thought of it as a phenomenon belonging essentially to distant parts of the world, such as the great Sahara Desert. Few of us would not be surprised to find it almost a daily spectacle on a familiar road so near our city.

You may imagine my surprise when, in the early days of April of this year, while walking westward along the Queensferry Road, and when opposite the quarry at the north end of Corstorphine Hill near the point at which the Corstorphine Hill road joins the Queensferry Road, I saw on the surface of the road, at a distance of about one and a half the spacing of the telegraph poles (they are about 50 paces apart), what appeared to be pools of clear water reflecting the green grass and foliage very clearly, and further down the road other pools. As I watched, a white horse with a rider went along, and as it passed beyond the “pools” of the mirage water (the road being perfectly dry) it was reflected, with the effect that the horse appeared to be about twice its height, as if on stilts.

The period of oscillation of a free pendulum increases with the arc of oscillation. This effect is known technically as the Circular Error. Its theoretical amount for the simple pendulum is readily calculated, and the following tables give it. I have called it the Circular Equation in place of the Circular Error, employing the word equation in its astronomical meaning of a theoretical numerical adjustment of a result, and distinguishing it thus from discrepancies of unknown source and amount which may also present themselves. The relation between arc and rate in the maintained motion of the pendulum of a clock will be a subject for examination experimentally and otherwise in future numbers of these studies. It may contain several elements, but must include the Circular Equation among them.

1. The theorem which expresses the product of two determinants as a sum of like products is the main instrument for investigating the relations between the determinants of an oblong array. It is justifiably spoken of as “Sylvester's theorem of 1839 and 1851,” although simple cases of it date back to far earlier times; for example, the case

which was brought to light by Bezout in 1779.