The subject of the address with which I am to open the present session of the Royal Society has been announced in your notices as the ‘Dawn of the Constitutional Principle.” Such, indeed, was the general tenor or complexion of the thoughts which led me into the field of inquiry on which I intend to dwell to-night, and such the topic round which I propose to weave a very fragmentary and imperfect excursus or dissertation. I had long thought that the rise and growth of the constitutional principle in this island,—a plant nurtured in many storms and watered by the best blood of the land,—might be worth tracing in these more stable and peaceful times. It might also be interesting to recall the gradual progress and direction of opinion in the two ends of the island, and of the conflict or concord out of which so powerful and thorough a fabric has been consolidated. But my theme to-night is necessarily less ambitious than its title indicates. I am limited both by the place in which and the audience to which I speak, and also by the time which it would be reasonable for me to occupy.

§ 1. In my previous papers on this subject I used the relationship terms, not in a representative but in a class sense; for instance, cA was employed to denote the children of the man A, and U was employed to denote the total assemblage of mankind, or a limited portion of that assemblage. I have found it useful for the purpose on hand to analyse these symbols into their component elements. Let U denote a man representatively, that is, any man, then mankind is appropriately represented by ΣU, where Σ has its ordinary mathematical meaning of taking the sum. Also UA is the appropriate mathematical expression for the man who has the name A, and A standing by itself is to be regarded as a contraction for UA. This notation is useful where, as in the present case, the universe of the investigation is composed of individuals; but since the universe may be continuous in its nature, by taking U to denote the whole, a more general basis is given to the Algebra of Logic, and accordingly I adopted that notation in my work on the subject.

The following problem presented itself to me nearly thirty years ago. I cannot find any notice of it in books, though it must have occurred to every one who has studied the oscillations of a balance:—

Two equal masses are attached to the ends of a cord passing over a smooth pulley (as in Attwood's machine). One of them is slightly disturbed, in a vertical plane, from its position of equilibrium. Find the nature of the subsequent motion of the system.

The interest of this case of small motions is twofold. From the peculiar form of the equations of motion, it is of exceptional mathematical difficulty. This is probably the reason for its not having been given as an example in Kinetics. And from the physical point of view it presents a very beautiful example of excessively slow, but continued, transformation of mixed potential and kinetic energy into kinetic energy alone.

In 1877, my father, Mr David Stevenson, communicated to the Society a notice of earthquake shocks in Argyllshire (see Proceedings, vol. ix.) from observations made by the keepers at several lighthouses, which the late Dr Bryce undertook to use in his intended visit to the west of Scotland, to trace the source of the earthquake waves of 1877, an intention which, however, was suddenly terminated by his lamented accidental death at Inverness.

Another earthquake shock, which visited Scotland and the north of Ireland on the 28th November 1880, has afforded the means of acquiring further observations, of which I think (in connection with those formerly given) the Society may consider it not unimportant to have a record in their Proceedings.

The present note is a continuation of a short paper which appeared in the Proceedings of the Royal Society of Edinburgh for session 1876–77. The problem in question is that referred to in Professor Tait's “Memoir on Knots,” viz.:—To find the number of possible arrangements of a set of n things, subject to the conditions that the first be not in the last or first place, the second not in the first or second place, the third not in the second or third place, and so on.

In this paper the action of permanganate of potash on ferrous salts in hydrochloric acid is studied, and a satisfactory method of titrating such solutions is indicated. Further, a short study is made of the action of chlorates, perchlorates, and nitrates on acid ferrous salts under various conditions. The results have a certain interest for the analytical chemist.

The class of problems treated is one to which considerable attention has been paid of late, as for instance by Glaisher and others in this country, and by Mannheim, &c, abroad.

Two years ago (Proc. 1879, p. 200), in connection with Minding's Theorem, I investigated the space-locus of the feet of perpendiculars from the origin on the rays of a complex. These were found to fill the space bounded by the two sheets of the reciprocal of a Fresnel's wave-surface. The method I employed is capable of very extended application in the same direction, and the following general process is applicable to all the problems I have seen treated by the authors above referred to.

While at work during the past session in the Berlin Laboratory, it was suggested to me by Professor Hofmann, that I should examine the behaviour of thioformanilid when submitted to various degrees of heat. The thioformanilid employed was prepared by heating formanilid with penta-sulphide of phosphorus, the resulting mass was treated with dilute caustic soda, and the alkaline solution of thioformanilid thus obtained was mixed with excess of hydrochloric acid, when impure thioformanilid separated out; this was purified by crystallisation from hot dilute alcohoL The crystals thus prepared melted at 137°–138° C., the melting-point of pure thioformanilid being 137.5° C. (Hofmann).

In 1872 I wrote a paper on galvanic currents, which continue for a long time in an electrolytic cell, under the influence of an electro-motive force, too feeble to effect electrolytic decomposition. I tried at that time to prove that the long duration of these currents was caused by oxygen dissolved in the water of the electrolyte, combining with the hydrogen, which is carried by the electrolytic motion to the cathode. So the oxygen, which existed formerly near the surface of the cathode, is taken away, and instead of it the same amount of oxygen is liberated at the anode. This can return by diffusion to the cathode, and so the same action can go on without end. It appears as a current producing no electrolytic action. I called it “Electrolytic convection.”

In the course of my examination of the “Challenger” thermometers, I was once surprised by a sudden bell-like vibration of the massive iron cylinder (nine inches thick) in which the apparatus to be tested was enclosed. This was due to the giving way of the protecting-sheath of one of the thermometers, at a pressure of a little over four tons weight on the square inch. When the pressure was let off, the bulb of the thermometer was found to have been crashed to an almost impalpable powder. I then determined to make a set of experiments with the view of finding under what amount of distortion glass gives way. For this purpose I employed the smaller compression apparatus which I have already described to the Society. Its capacity is about ten cubic inches only, so that a couple of strokes of the pump produce a pressure of three to four tons weight.

In the microphone, or loose contact receiver, we have two or more small blocks of carbon resting lightly against each other, through which the interrupted current from the transmitter is passed. At the points of contact, a strong heating and cooling effect must take place every time the current is interrupted or otherwise varied. This heating and cooling will cause corresponding expansions and contractions of the air or other medium surrounding the points. These produce undulations in the medium, which, striking against the sides of the containing vessel, set them also into a state of vibration, and so reproduce the sounds of the transmitter.