The apparatus for Impact experiments, which was exhibited to the Society on 20th February 1888, has been greatly improved by the substitution of a very true slab of plate-glass, thinly covered with printing-ink, for the sheet of cartridge paper. The record is made by a needle-point which projects from the falling body, and which is kept in constant contact with the plate by means of a light spring. The time of rotation of the plate is given by a tuning-fork, with a small bristle attached, which is kept in vibration by a periodic current, and records alongside of the other tracings.

The properties of generating lines and surfaces often afford an easy and beautiful mode of demonstrating geometrical theorems which, if done by the ordinary method, would be long and tedious. As the subject, so far as the writer is aware, is new, a short paper upon it may not be unacceptable.

The portable dust-counting apparatus described in a previous communication to this Society was designed with a view of making observations on the air at situations where it would be inconvenient to work with the larger laboratory apparatus; and also to enable these observations to be made under conditions more favourable for avoiding local impurities than is possible when working in a house. As the construction of this portable apparatus was completed just as I was about to start for the Continent, the opportunity seemed a favourable one for continuing the investigation into the number of dust particles in the atmosphere, and extending our knowledge on the subject in other countries. The portable apparatus is reduced to such dimensions that it adds but little to one's personal luggage, and can be easily carried to’ the place where the observations are to be made.

The special point that I wish to bring before the Society relates to a case of the common larch being made use of by Hylesinus piniperda for purposes of oviposition. As occasion demands, this insect has been found to utilise as a breeding-place every species of Pinus, but, so far in Europe or North America, no case has been noted of any trees belonging to the genus Larix having been similarly attacked. In Asia an observer, namely, Middendorff, has recorded one case which came under his notice in the district of the Boganida, in Siberia, in 71° north latitude (Sibirische Reisen, Band iv. Theil i. p. 603).

Dr P. W. Latham, in the Harveian oration at the Koyal College of Physicians, on October 17, 1888, supported my own researches (which have already been published in the Proc. Roy. Soc. Edin., vol. xiv. pp. 97–106, and vol. xv. pp. 33–63), on the subject of “disease germs.” He says:—” “We might hope to find that the action and growth of the bacilli [of phthisis] might be inhibited by certain substances, and then, by injecting these substances into the blood, disease might be prevented, or if disease existed it might be arrested or cured.”

The method of solution developed in this paper, while perfectly general in its character as regards three-term equations, may also be considered as a solution of the complete equation of the 5th degree; because, by known methods resulting from the theory of equations, every equation of the 5th degree is reducible to three terms.

The caustics here considered are those resulting from the reflexion of systems of parallel rays. The subject is purely geometrical. The caustic is considered as a derived curve, and is denned as the envelope of a system of lines drawn from the primary curve, whose inclination to a given line is double the inclination of the normal at the incident point.

It is comparatively easy to find an expression for a caustic in mixed cöordinates. But, where the cöordinates of the primary curve have to be eliminated, the problem becomes more difficult, and unless this condition be fulfilled the expression cannot be considered a true analytical solution of the locus. In the present paper, differential and algebraic expressions are first found containing the cöordinates of the focal point corresponding to a point in the primary or reflecting curve, and the cöordinates of the latter are then eliminated between the differential and algebraic equations.

The synthesis of the diethyl ether of this new acid was effected by the electrolysis of a strong aqueous solution of potassium ethyl sebate, COOC2H6(CH2)8COOK. This salt was prepared by adding the calculated quantity of alcoholic potash to an alcoholic solution of diethyl sebate. After some time the potassium ethyl salt began to separate out: the whole was then boiled, allowed to cool, and filtered. What remained on the filter was dissolved in water; the aqueous solution was extracted twice with ether, and then evaporated to a concentration suitable for electrolysis (cf. this vol. p. 54).

Suberic Acid.—In continuation of our syntheses of dibasic acids by* means of electrolysis, we have prepared suberic acid from glutaric acid, and from the former again a new acid, which we term w-dicarbododecanic acid.

The recent improvement in the process of manufacture of pure aluminium, and the consequent lowering in its price, has placed it within the reach of those who desire to make any experiments requiring large quantities of this substance. It seemed desirable that an investigation of the thermal conductivity of aluminium and its alloys should be made, but before obtaining the necessary bars a smaller bar was obtained from experiments on which a preliminary notion was got of the thermal conductivity; this being necessary in order to determine the most convenient dimensions for the long bars used in Forbes's method of conducting these experiments.

At the suggestion of Professor P. G. Tait, I undertook the further investigation of an experiment, an account of which he communicated to this Society on Monday, the 15th of April 1878.

In this experiment a platinum plate of moderate thickness is inserted between the electrodes of an electrolytic cell, so as to completely fill the cross-section. This platinum plate thus becomes the common electrode of two cells, and on perforating it it is found that a comparatively small hole at once changes its functions to that of an obstacle in one cell.

“There were but few land fowls. We saw none but eagles of the larger sort of birds, but five or six sorts of small birds. The biggest sort of these were not bigger than larks, some no bigger than wrens, all singing with great variety of fine shrill notes; and we saw some of their nests with young ones in them. The water-fowls were ducks (which had young ones now, this being the beginning of the spring in these parts), curlews, galdens, crab-catchers, cormorants, gulls, pelicans, and some water-fowl such as I have not seen anywhere besides.”

It is necessary for a clear understanding of the chemical changes which occur on treating morphine in various ways, and for comparing its physiological action with that of the bodies so formed, that we should summarise at some length the exact position of our present knowledge regarding its chemistry and pharmacology.

Morphine has the composition represented by the formula C17H19NO3. It is generally supposed to crystallise with one molecule of water, but there is reason to believe that the composition of the hydrated base is really 8 C17H19NO3, 9 H2O, the water being present in the proportion of 1⅛ molecule. Morphine is a monacid base, forming neutral and readily soluble salts with all the stronger acids. Like all alkaloids, it is built up on the ammonia (NH3) type, and is a tertiary amine, all the hydrogen atoms having been replaced by more or less complex radicals.

In the phosphines and their derivatives, which we have investigated from, time to time, considerable uncertainty has always attended the determinations of phosphorus by the ordinary methods recommended for the purpose. In fact, we never felt any confidence in the result, for no matter how carefully the determinations were made, duplicate analyses led to different numbers.

The uncertainty depends partly upon the difficulty of oxidising the phosphorus in such compounds to phosphoric acid. For, as a rule, in any dry combustion process which may be employed, volatile oxidation products, containing phosphorus, are formed of great stability, which frequently pass over the red-hot oxidising mixture almost unchanged. Moreover, the glass of the tube is attacked by the oxidising mixture, and this undoubtedly leads to inaccuracies, probably of considerable magnitude.

No district of Great Britain is so rich in genera and species of Carboniferous Dipnoi and Ganoidei as that of Fife and the Lothians, and in the frequency of entire specimens of these fishes it is only approached by North Staffordshire.

Another feature of the greatest geological interest is the abundance of fish remains in estuarine strata below the horizon of the Millstone grit, whereby a means of comparing the Ganoid fish faunæ of the Upper and Lower divisions of the Carboniferous formation is afforded.

In the course of an extended series of investigations into the relations of magnetism and stress, part of which is already published in the Transactions (vol. xxxv.), I was led to consider the effect of a current passing along a wire upon its longitudinal magnetic intensity. Wiedermann, Buff, and Villari have discussed this problem in some of its aspects. It does not seem possible, however, to deduce from their results completely satisfactory conclusions as to the effect of the current upon the apparent longitudinal permeability. The question, as it presented itself to my mind, was not so much as to the effect of a varying current along the wire upon the apparent longitudinal moment, but rather as to the behaviour of the wire in various longitudinal fields according as it was carrying a current or not.

As the Chairman for this evening, I have been asked by the Council to lay before you a brief summary of the events of the session, which will conclude the public business of the session.

In this retrospective view the most interesting point is the number and variety of the papers which have been read. Of these there were in all 74 papers, of which 19 were in the department of Natural Philosophy, 16 in Mathematics, 11 in Chemistry, 1 in Geology, 9 in Zoology, 1 in Botany, 6 in Physiology, 2 in Anatomy, 5 in Meteorology, 2 in Physical Geography, and 2 in Philology.