Page 700, line 8, for “Microphone,” read “Telephone.”

Page 700, 702, line 14, for “onset,” read “set.”

In taking my place this evening, I might reasonably be expected to say much about my unworthiness to fill the post, and the kindness of my friends in placing me here. All that I can trust myself to say is, that I feel too deeply everything that can be imagined of this kind to venture on giving it words. To be the successor of such men as the Duke of Argyll, Sir Robert Christison, and Sir Wm. Thomson, is an honour which the most ambitious man might covet, and the most self-conceited deem himself scarce worthy of. To myself that honour has come neither to gratify ambition nor to administer to self-conceit. It has descended on me all unsought through the kindness of the many friends who have sat with me for years in this room, and the only emotion it awakens is that of affection and gratitude. Just a month has elapsed since it became apparent to me that I should be called upon to address you to-night. That such would be the case had not till then crossed my thoughts. I had made no preparation for the address. The first month of the University session left me the very smallest amount of time and strength for the work. You will, therefore, pardon an address rather feebler in character than is fitted to the occasion.

Sect. I. It is well known that the movements of the iris are due to the stimulus of light, but I am not aware that any experiments have been hitherto made to determine the approximate quantity of that agent necessary to bring about this involuntary action. The usual way of observation precludes refined experimenting, it being customary to watch the iris of another person or animal whilst under the influence of varying amounts of light, or one's own iris by means of a mirror. Three methods will be described here, and I believe that one at least may afford a means of getting new data on this and other points.

If we look for a short time at any object, and afterwards turn the eye in another direction, we see a spectral image of the form of the object first looked at.

Again, if after we have looked at any coloured object we turn the eye in another direction, we see a spectral image of a colour complimentary to that first looked at.

In addition to these spectral forms and colours, I find there is another and distinct kind of ocular spectrum, which we may call a motion spectrum. It is seen when we look first at a body in motion and afterwards direct the eye towards an object at rest. The object at rest, when seen under these conditions, seems to be in motion, and the direction of its apparent motion is the opposite of that of the moving body first looked at.

In this memoir I examine the principles of the logical calculus of Boole, as laid down in his celebrated treatise on the “Laws of Thought,” and also the criticisms which have been published concerning these principles. I bring forward a new theory of the operation of the mind, founded upon an analysis of language and the nature of mathematical reasoning, which enables me to correct these principles, to place them on a clear, rational, and generalised basis, and to show that there is a logical algebra which coincides with the ordinary algebra when its symbols are integral, but is a generalised form of the ordinary algebra when its symbols are fractional.

While experimenting with an ordinary Bell telephone, of small resistance, I found that it was able to reveal the existence of electric currents produced by the mere friction between conducting substances. This was shown in the following way. Two files had wires firmly connected to them, and were thereby attached to the terminals of a telephone circuit in a distant room. When these files were rubbed against each other, a most distinct grating noise was heard in the receiving telephone. In order to find if this sound varied, when different substances were rubbed together, the following plan was adopted. A wire was firmly attached to a small table-vice, and led to one of the terminals of the telephone circuit, while the wire from the other terminal was attached to a clamp into which any substance, which it was desired to test, could be screwed. Different substances were then screwed into the vice and clamp, and rubbed against each other by an assistant, in each case, as far as possible, with the same pressure. By listening attentively in the receiving telephone, I endeavoured to detect any variation in the sound as the assistant passed from one substance to another. As far as I could judge, little or no variation was produced when the following substances were rubbed on themselves and on each other, viz.: steel, brass, iron, zinc, lead, gas carbon, copper, with possibly the exception of copper on iron, which, I thought, gave the sound a little louder.

In my former papers on the subject of Knots, I have provisionally measured Beknottedness by the smallest number of changes of sign at the crossings, which will render all the crossings nugatory.

Though I have not seen occasion to doubt the accuracy of this mode of measurement, there are two objections to it—(I) It is very difficult of application in complex cases; (2) It suggests no direct relation to the electrodynamic method which, except in the case of knots wholly or partially amphicheiral, gives results quite in accordance with it.

The object of the present paper is to describe a method which, while at least partially meeting these objections, very considerably simplifies some of the more important processes for the treatment of knots, which I have already given.

Last autumn I received from Mr Maclachlan of Lower Green, Mitcham, some specimens of india-rubber tape which had been for several years wound, under considerable tension, helically round copper Wire. At ordinary temperatures, after being peeled off, the material shows no tendency to contract; but Mr Maclachlan found that in hot water it almost instantly resumes its original dimensions.

I have recently reproduced almost exactly the same results by stretching sheet india-rubber, slightly warmed, helically round glass tubes, and immersing it for a short time in a freezing mixture.

The acetate is formed by treating the iodide of trimethyl-sulphinc with acetate of silver. On leaving the strong solution over sulphuric acid in vacuo for three weeks no crystallisation took place. The syrup on being heated in a small retort gave off water, and, without solidifying, sulphide of methyl, mixed with acetate of methyl. On redistilling the two latter, they went over at a temperature between 45° and 56° C. It was not possible to separate them by distillation, but on shaking the mixture with solution of chloride of mercury, the sulphide of methyl was removed, leaving a few drops of acetate of methyl, easily recognised by its fruity smell.

The following observations of the temperature of the water at different depths below the ice covering Linlithgow Loch were made with one of Messrs Negretti & Zambra's “half-turn” self-registering thermometers, which proved to be a useful instrument for this species of inquiry. It was necessary, however, to fit it with a suitable inverting contrivance, as this part of the apparatus supplied by the makers is quite useless. The temperatures have received a provisional correction for error of graduation, and they may still have to receive a further, though certainly very slight, rectification, when a thorough comparison with a Kew standard has been made.

The equation

x2 = x

expresses the condition that the symbol x be single and positive. The equation

x2 = −x

expresses the condition that the symbol x be single and negative. The principle of contradiction

x(1−x)=0

can be legitimately deduced with the help of the fundamental axioms of the science.

The Keith Prize for the biennial period 1875–77, which has been awarded to Professor HEDDLE, for his papers on the “Rhombohedral Carbonates,” and on the “Felspars of Scotland,” originally communicated to the Society, and containing important discoveries, was presented by the President (Professor Kelland) with the following remarks:—

Professor Heddle,—I am here to-night to exemplify a remark which is often made, that to insure success in an address such as I am about to deliver, the best way is to commit the charge of it to one absolutely ignorant of the subject. No false pride will then stand in the way of the best sources of information, nor will any undue admixture of half knowledge clog and darken the truth. For every particular contained in these remarks, then, I at once unhesitatingly acknowledge myself indebted to Professor Geikie.

In this chapter Dr Heddle considered the micas occurring in Scotland. These he found to be Muscovite or Muscovy glass, and margarodite—of the white micas; Biotite, lepidomelane, and a new species which he proposes to call Haughtonite, after Professor Haughton of Dublin—of the dark micas. He also finds the species pihlite, hitherto unrecognised in Britain, occurring in quantity in the central districts of Banffshire, and in the west of Aberdeenshire.

In connection with the first of these micas, the mode of formation of exfiltration veins, and the metamorphism of gneiss into the grey granite of Aberdeenshire, were considered.

In the introductory portion of the paper a sketch is given of the present state of opinion among Continental petrographers regarding volcanic rocks associated with palæozoic formations. The author points out that a relic of Werner's belief in the recentness of volcanic action may still be traced pervading the ideas of German geologists. In this paper he endeavours to show that, alike in their formation in the field and in their structure under the microscope, the basalts and tuffs of palæozoic time were as truly the products of volcanic action as the lavas and ashes of the present day.

Mr Dudgeon exhibited some specimens of auriferous quartz from Wanlockhead and Leadhills districts.

was found in July 1878, by Thomas Tennant in Wingate burn, Leadhills; it is a very rich specimen, and is now placed in the collection of Scotch minerals in the Museum of Science and Art.

was found by Eleanor Handcock in April 1878, on the banks of the Wanlock water, Duntercleuch.