Most common oils and fats are mixtures of ethereal salts, termed glycerides or glyceric ethers, formed from glycerine and acids of the fatty, the oleic, and other allied series.

Of the methods employed for the decomposition of oils and fats, the following are the most usual:—

1. 1. Distillation of the oil or fat; those which yield volatile acids, such as the acetins, butyrins, &c., may be more or less distilled without decomposition; but those which yield fixed acids, e.g., palmitin, olein, &c., are almost wholly decomposed by a heat of 300° C., yielding acrolein, numerous hydrocarbons, &c.

2. 2. Distillation with dilute sulphuric acid, by which the volatile acids are separated from the non-volatile.

3. 3. Distillation in a current of superheated steam, when the glycerides are decomposed, the fatty acids being liberated.

4. 4. Saponification; oils and fats are decomposed by caustic alkalies into glycerine and a soap, the soap, when boiled with dilute sulphuric or hydrochloric acid, being decomposed into a sulphate or chloride of the alkali employed and the fatty acid set free.

The object sought to be gained by this tabulation may be best seen by considering a specific case. When we wish to produce, by help of toothed wheels, a certain ratio between the rotations of two axes, we must have that ratio represented by integer numbers, and these numbers must contain no prime factors exceeding the limit of the number of teeth which can conveniently be cut in any wheel. If, for example, we wish to represent the mean motions of the planets, we have to express the ratios of their periodic times by decomposable numbers; and as this, in general, can only be done approximately, we have to prescribe some limit of error on either side, and have to seek for all fractions between those limits, and then among these to search for those that are suitable.

In my treatise on wheel-teeth a solution of this problem is given, complete so far as the discovery of the fractions is concerned, but imperfect in this, that it does not place those fractions in the order of their magnitudes. I propose now to supply this deficiency by explaining an exceedingly simple process, which enables us to make a complete list, arranged in the order of their values, of all irreducible fractions whose denominators shall not exceed some specified number; and also to take up and interpolate any portion of the list. This process is founded on a general theorem flowing directly from the doctrine of continued fractions, but of which the following simple demonstration may be given.

Abundant as are the localities in which garnet is found in Scotland, there are but few which yield specimens such as can be analysed.

This is on account of an intermixture of quartz—for the most part in a granular form—the granules being promiscuously scattered throughout the mass of the crystals. In three localities the intermixture is not promiscuous, but has been governed by some intermittent crystalline action. These localities are Glen Skiag in Ross, where, around a central nucleus of leucitoidal crystals of garnet, translucent quartz is arranged in layers which alternate with those of the garnet, conformably to the figure of its crystal.

The two other localities are the first and third granitic veins to the east of Portsoy; in both of which garnet of a pale brown colour is laced with quartz, which is arranged in a graphic manner, as in the felspar from an adjacent vein. At no other locality do I know of such an occurrence. The appearance of a section of a rhombic dodecahedron is somewhat like the figure.

The determination by experiment of the thermo-electric relations of any one substance belonging to the electromotive series to all other such substances is sufficient to fix all mutual thermo-electric relations among these. The first endeavour of the experimenter is then to obtain as convenient a substance for this purpose as possible. In investigating charcoal and certain alloys, we have in almost all cases employed one or other of two alloys of platinum and iridium, which have been already used by Professor Tait for a like purpose. The wires we used were the same which he discusses in his “First Approximation to a Thermo-Electric Diagram,” under the names of M and N. Their complete freedom from oxidation, their elasticity, and the high temperatures of their fusing points, rendered them peculiarly suitable for thermo-electric investigations through long ranges of temperature.

Generally both the M and N wires were firmly bound, each by its one extremity to the end or ends of the wire or wires respectively which were under investigation, in a multiple junction. This triple or, as it was in some cases, quadruple junction constituted the “hot junction.” The free extremities of the wires thus united were each bound to a moderately thin copper wire by very thin wire of the same metal, and the copper wires were led from these “cold junctions” to a commutator, which was in connection with a galvanometer. The commutator consisted of an arrangement of small mercury pools, into which the galvanometer and circuit wires, carefully amalgamated to ensure contact, dipped. All the junctions were formed in the manner indicated above, namely, by tightly binding the extremities of the wires together by thin copper wire.

In the early part of the present century, when stratigraphical geology, starting from the clear succession of Secondary rocks of England, was groping its way among the older formations in this country and abroad, the Old Red Sandstone occupied a somewhat indeterminate position. The series of deposits comprised under that name had been recognised chiefly in the British Islands, hardly at all on the opposite mainland of Europe. By most geologists they were classed as a subordinate and inconstant portion of the Carboniferous system, while by some they were placed rather at the top of the yet unexplored “Transition” or “Greywacke “ series. Murchison first claimed for them the dignity and importance of a distinct system. On the whole, they had yielded comparatively few organic remains; they consequently seemed to lie as a thick red barren zone between the richly fossiliferous Silurian deposits below them and the equally fossiliferous Carboniferous limestone above. By degrees, however, as they brought forth a rich harvest of new and strange ichthyolites, they indicated their own right to recognition, and when they were found covering a vast space in Russia with many of the same types of fish as they had yielded in Britain, their claim to rank as a distinct and independent system was no longer contested.

Malacolite was first observed in Scotland by Dr Macculloch, who included it with the second sub-species, under the name of Sahlite.

He, in his different works, noted its occurrence—“near the church of Rodel in Harris,”- “in Tiree,”-“Glen Elg,”-“Glen Tilt,”-and “in Rannoch.” With his usual power he describes the occurrence, varieties, and even the crystalline form of the mineral,—the clearness and precision of his descriptions being only equalled by the utter want of precision and frequent mystifications as to their localities.

The above sentence conveys all the direct information which Dr Macculloch vouchsafes as to the five localities indicated by him, though in a vague manner he may occasionally lead one to conjecture that certain particular spots are meant.

By the time that the mineralogist, led by Dr Macculloch to Glen Elg, Tiree, or Rannoch, has walked some twelve or twenty miles in an unsuccessful search, he begins to think that if he be successful, he has some claim to be himself regarded as an independent discoverer.

The first experiment which I have to describe relates to an attempt to employ the telephone as a means of measuring the hearing power of the ear in different individuals, or in the same individual at different times. For this purpose a constant source of sound, driven by clockwork, is made to act upon the disc of a telephone in a distant room. In the circuit of this telephone are included two others, so placed on a stand, that they can be brought close to both ears of the person to be experimented on. Soft india-rubber rings are attached to these telephones so as to enclose both ears, and Serve the double purpose of avoiding any disagreeable pressure on them, and preventing, as far as possible, all extraneous sounds from entering. In the circuit of the telephones there is also included a column of slightly acidulated water whose length can be varied at pleasure, so as to introduce a greater or less resistance to the electric current. This is managed in the following way:—A pretty wide glass tube, about 24 centimetres long, closed at the lower end, and graduated to millimetres, is mounted vertically on a stand. Projecting through the lower end of the tube is a platinum wire melted into the glass and having its point inside opposite the zero of the scale.

Of the bases of the CnH2n—11N series, obtained from coal-tar and from the “acid-tar” from the distillation of shale, only three are known, viz., Leucoline, C9H7N; Iridoline, C10H9N; and Cryptidine, C11H11N. These are isomeric with the bases obtained by the distillation of cinchonine with caustic potash, and are described by their discoverer, Greville Williams, in “ Trans. Royal Society, Edinburgh,” vol. xxi. The leucoline series of bases, at first thought to be identical with the cinchonine series, Williams has shown to be isomeric, but otherwise having important differences, these differences chiefly being apparent in their boiling points, their slight tendency to form crystallisable salts, and their reaction with iodide of amyl.

The source of the leucoline bases of Greville Williams was “coal-oil of a very high boiling point, and a density greater than that of water;” his process of separation was to treat the oil with sulphuric acid, and distil the acid liquid with lime; that portion of the distillate which sinks in water is treated with nitrite of potash and hydrochloric acid to destroy phenols; the acid liquid is placed in an iron retort and a current of steam passed through it; the residue remaining in the retort, after being treated with caustic potash, is distilled, and the distillate, consisting of the mixed bases, purified by fractional distillation; the bases were then identified by converting the fractions into platinum and other salts. Proceeding in this manner, Greville Williams separated the three bases—leucoline, iridoline, and cryptidine; the last, cryptidine, C11H11N, being found in his highest fraction, that boiling 270°–275° C, and from what I can learn from other authorities, the isolation of the higher members of this series has not been attempted.

The analogies existing between elements belonging to one “family,” such, for instance, as the nitrogen family or the sulphur family, have long been recognised, and are pointed out and insisted upon even in elementary textbooks; but the very important analogies existing between substances of different quantivalence are apt to be forgotten or overlooked. For illustrations of such analogies we may point to boron and silicon, elements closely resembling one another in themselves and also in their compounds,—differing, indeed, in little else but that the one is triad and the other tetrad. A similar relation exists between gold and platinum.

The elementary substances, sulphur and phosphorus, have many points of similarity: both fuse at a comparatively low temperature, both are transformed by heat into amorphous insoluble modifications, and both have anomalous vapour densities.

Compounds of Ethyl-Thetine.—In the course of the investigations, the results of which are recorded in the preceding paper, Professor Crum Brown and I observed that sulphide of ethyl, like sulphide of methyl, forms a crystalline compound with bromacetic acid. This we called hydrobromate of diethylthetine, in conformity with the system of nomenclature we had proposed for such bodies—

Owing, however, to the extremely deliquescent nature of the substance, we did not at the time subject it to a closer examination, but devoted our attention to the methyl compound and its derivatives. The following are the results of an examination which I have since made of the hydrobromate of diethyl-thetine and its derivatives: —

Hydrobromate of Diethyl-Thetine.—50 grms. of sulphide of ethyl and 70 grms. of bromacetic acid were shaken together. The acid slowly dissolved, occasioning a fall of temperature in so doing from 20–14°. After about half an hour's standing, the mixture grew warm, and deposited a slightly brown, oily liquid. The reaction was very much less intense than in the case of the methyl compound, when the sulphide of methyl actually boils and the mixture has to be cooled to prevent loss of product.

(I.) It is proposed to consider determinants of the form

and of the same form as this with the top horizontal and last vertical rows removed, in connection with the two series of quantities

(II.) From the two given sets of quantities

two new sets are deduced

by means of the auxiliary quantities

viz.,

Then in like manner from the sets (c, d) two new sets

by means of the auxiliary quantities

The experiments to which I shall refer were carried out in the physical laboratory of the University during the late summer session. I was ably assisted in conducting the experiments by three students of the laboratory,—Messrs H. A. Salvesen, G. M. Connor, and D. E. Stewart. The method which was used of measuring the difference of potential required to produce a disruptive discharge of electricity under given conditions, is that described in a paper communicated to the Royal Society of Edinburgh in 1876 in the names of Mr J. A. Paton, M. A., and myself, and was suggested to me by Professor Tait as a means of attacking the experimental problems mentioned below.

The above sketch which I took of the apparatus in situ may facilitate tha description of the method. The receiver of an air-pump, having a rod capable of being moved air-tight up and down through the neck, was attached to one of the conductors of a Holtz machine in such a manner that the conductor of the machine and the rod formed one conducting system. Projecting from the bottom of the receiver was a short metallic rod, forming one conductor with the metallic parts of the air-pump, and by means of a chain with the uninsulated conductor of the Holtz machine. Brass balls and discs of various sizes were made to order, capable of being screwed on to the ends of the rods. On the table, and at a distance of about six feet from the receiver, was a stand supporting two insulated brass balls, the one fixed, the other having one degree of freedom, viz., of moving in a straight line in the plane of the table. The fixed insulated ball A was made one conductor with the insulated conductor of the Holtz and the rod of the receiver, by means of a copper wire insulated with gutta percha, having one end stuck firmly into a hole in the collar of the receiver, and having the other fitted in between the glass stem and the hollow in the ball, by which it fitted on to the stem tightly. A thin wire similarly fitted in between the ball B and its insulating stem connected the ball with the insulated half ring of a divided ring reflecting electrometer.

At the beginning of this session we proceeded to apply the method of measuring large differences of potential described in former papers, to the investigation of the disruptive discharge through liquid dielectrics. We have now obtained some results for oil of turpentine.

A vessel capable of holding the liquid, and at the same time of forming an electrode, was constructed by fixing on a metal plate to one end of a hollow glass cylinder of diameter slightly less than that of the receiver of the air-pump. The vessel was placed on a metallic support, so as to be in conducting connection with the metal parts of the air-pump, and with the earth. The other electrode, which was either a circular disc, a spherical ball, or a conical point, was screwed on to the brass rod passing through the stuffing-box on the top of the receiver, and was thus capable of being adjusted to various heights in the turpentine. The bottom of the vessel is 16·7 centimetres, and the brass disc, which commonly formed the upper electrode, is 10 centimetres in diameter, and 4 millimetres thick.

During the months of May and June of this session we have endeavoured to investigate certain questions suggested by our experience of the discharge of electricity through the gases and through oil of turpentine, for which purpose Dr Macfarlane had received a grant from the Royal Society of London.

When paraffin oil (the kind employed for illuminating purposes) was put into a glass vessel, in which were two brass plates arranged in the form of a condenser, and when the plates were charged by means of the Holtz machine, it exhibited the same phenomena as oil of turpentine. Gas bubbles were produced; they did not appear until after the passage of the spark. Once produced, they facilitated the passage of the spark through bringing the electrified surfaces virtually nearer to one another. Hence, when taking observations of the difference of potential required to pass a spark through layers of different thickness of the oil, it was always necessary to remove the bubbles generated by the passage of one spark before electrifying again. This was effected by bringing the discs into contact.