The following paper contains, in a compact form, the substance of several somewhat bulky communications laid before the Society during the present session. The gist of each of these separate papers will be easily seen from the abstracts given in the Proceedings. These contain, in fact, many things which I have not reproduced in this digest. Nothing of any importance has been added since the papers were read, but the contents have been very much simplified by the adoption of a different order of arrangement; and long passages of the earlier papers have been displaced in favour of short general statements from the later ones. With the exception of the portion which deals with the main question raised, this paper is fragmentary in the extreme. Want of leisure or press of other work may justly be pleaded as one cause; but there is more than that. The subject is a very much more difficult and intricate one than at first sight one is inclined to think, and I feel that I have not succeeded in catching the key-note. When that is found, the various results here given will no doubt appear in their real connection with one another, perhaps even as immediate consequences of a thoroughly adequate conception of the question.

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 construction of the toothed wheels used in machinery gives rise to some very interesting investigations in the geometry of motion. The general problem is so to shape the contours as that they shall remain in contact while the wheels turn on their centres with uniform angular velocities.

The inquiry becomes more extensive when the velocities of the wheels are to be variable; as, for example, when we seek to imitate the revolutions of the planets round the sun, and for that purpose introduce the equation of the centre.

In these cases the wheels are supposed to turn on fixed centres; but we may still farther extend the scope of our researches by removing the centres and subjecting the discs to the single condition that they roll upon each other.

If two discs A and B touch at the point S, and if they so move as that the point of contact shifts equally along the two boundaries, they are said to roll on each other; that is to say, if we measure equal distances ST, SV along the two boundaries, the points T and V will come together in the course of the movements.

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.

Before submitting the results of my examination of the silicates, it is incumbent upon me to give an outline of the processes adopted for their analysis, seeing that the amount of confidence which is to be placed in the results must rest very immediately thereupon.

1. Determination of the Water. — In all silicates which were found, after thorough drying, to give out moisture when heated in the closed tube, the amount of loss upon ignition was calculated as water. About 2 grammes, crushed in the diamond mortar, were first merely heated throughout in the air-chamber of a water-bath, the contact temperature of which was 212° Fahr., the temperature of the air-space being never below 199°. The weight after this heating was taken; and, except in the case of a mineral functioning in any peculiar way, the loss in weight was estimated as hygroscopic moisture. The mineral was now continuously heated in the bath until the weight was found to be constant. It was then exposed for the space of one hour to a full red heat, in the flame of a Bunsen burner, after which it was re-weighed. Finally, it was exposed for ten minutes to a heat approaching whiteness, in a three-jet Griffin blast-furnace, again re-weighed, and again heated in this furnace, until the weight was constant.

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.

If light, emanating from a fixed source, be reflected to the eye, also fixed, from the surface of a polished cylinder, which cylinder changes its position in some definite manner, the point of reflection moves in some curve or locus whose nature may be made the subject of investigation.

In the present paper I propose to examine that case in which an indefinitely thin cylinder is restricted to pass through a fixed point. The locus of the point of reflection is then a curved surface, For the present I shall still farther restrict the polished line to the plane passing through the vertex, the source of light, and the eye ; the locus being then a plane curve.

Let then a fine polished straight line, extended indefinitely both ways, turn on the vertex O, while light emanating from the source A is reflected to the eye at B; it is required to investigate the locus of the point C at which the reflection takes place.

The reflection is only possible while the polished line passes outside of the angle AOB. When the wire lies along AO, the point of reflection is at A ; when along OB, at B; and when it is equally inclined, outwards, to OA and OB, the reflection occurs at O, wherefore the curve must pass through the three points O, A, and B.

(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.

In preparing a specimen of diamond boron by Wöhler and Deville's method, the idea struck us of substituting silver, gold, or some other metal in place of the aluminium. We thought that by so doing we might be able to save considerable expense if the silver would dissolve the boron; because in the case of aluminium the byproducts are useless, whereas in the case of silver the byproducts are easily reconverted into metallic silver. On making an experiment with silver in place of aluminium, we found that it did dissolve boron, and that on dissolving the silver away with nitric acid a slate-grey powder was left behind. This powder, on being examined after purification, was found to be boron, and to contain nothing but boron; under the microscope, it presented a complex composition, some being transparent and some opaque,—the opaque portion consisting of hexagonal prisms exactly like those of graphite; the transparent portion being composed of plates and a few small tetrahedra. The quantity obtained was but small, so we repeated our experiment several times, at last obtaining sufficient to examine the properties of these crystals.

Having occasion at one time to require a quantity of methylamine, I tried a number of the best methods given in text-books and books of reference, but the smallness of the yield and the great trouble involved in the processes drew my attention to the fact that there was room for a good method of preparing the primary monamines. Hofman's method, viz., heating the iodides of the alcoholic radicals with ammonia, is of little use, as the trouble of separating the diamines and triamines formed at the same time is so great as to make the process practically useless if the primary monamines alone are required.

Keeping this fact before me, I tried for some years, in the intervals of more systematic work, to find the solution of this problem, and I think I have now found a process which, at the same time simple and inexpensive, gives a large yield of the primary monamines. This result has not been arrived at without several failures, and as I think that even negative results are often useful, I shall briefly refer to them. In the first place, together with Professor E. A. Letts, I tried to obtain methylamine from oxamate of methyl. As oxamate of methyl has the following constitutional formula, viz.—

While working at an investigation (about to be published), relating to the flow of liquid through capillary tubes, it was thought that the cohesion of a liquid might influence the rate of its flow, and a method was sought for, which would enable the cohesion of any liquid to be determined; the ordinary method of calculating the cohesion from observations of the flattening of a drop of the liquid resting upon a plane surface not being applicable to all liquids. The method which seemed most likely to yield results was that of observing the drops of a liquid so arranged that they fell from the end of a column of the same liquid, and accurately measuring the width of the neck of the drop at the instant of breaking, and the weight of the fluid which caused the rupture. It is easily seen that before this could be done a complete knowledge of the nature of drops would be required, and as the phenomenon of dropping has been made the subject of a long investigation by Professor Guthrie, an examination of his results was undertaken. They show that the drop increases in weight as the growth-time decreases, that is, the quicker the rate of flowing the larger the drop. Many experiments were made, which, agreeing with Professor Guthrie's numbers pretty closely, need not be quoted here. While, therefore, his experimental numbers may be taken as quite correct, they do not seem to prove the theory he has put forward in their explanation. The following is from his paper:—“The most prominent fact is that, on the whole, the drops undergo a continuous diminution in weight or size as G.t. increases. To such an extent is this the case, that the most rapidly falling drops of the above table are nearly twice as heavy as the most slowly falling ones. The cause of this is probably to be sought for in the circumstance that when the flowing to the solid is more slow, the latter is covered with a thinner film of liquid, so that, as the drop parts, the solid reclaims by adhesion more of the root of the drop than is the case when the adhesion of the solid to the liquid can satisfy itself from the thicker film which surrounds the drop in the case of a more rapid flow.”