which continued for some time after the experiment was made. The effect of this rotating apparatus might form an interesting study in connection with the important investigation at present conducted by Professor Alex. Crum Brown on the function of the semicircular canals of the ear.

3. On the Principles of the Logical Algebra; with Applications. Part I. By Alexander Macfarlane, M.A., D.Sc.

(Read 16th December 1878.)
(Abstract.)

In this memoir I examine the principles of the logical calculus of Booie, 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. Hence all the theorems in ordinary algebra when generalised properly are true in the logical algebra. I show the analytical meaning of the axioms of logic and their relation to the algebraic axioms of operation. By means of this algebra I investigate the theory of immediate inference, and also the conclusions and numbers of conclusions of different kinds which can be deduced from premises of certain given forms. The memoir also professes to prove a great number of new theorems in the theory of necessary and probable inference.

4. Note on Ulodendron and Halonia. By Mr D'Arcy Wentworth Thompson. Communicated by Sir Wyville

Thomson.

Monday, 6th January 1879.

Professor KELLAND, President, in the Chair.

The following Communications were read:

1. Notes on some Experiments with the Telephone.
By James Blyth, M.A.

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.

It was different, however, when two pieces of antimony and bismuth were rubbed together. In this case the sound was decidedly louder. I tried also, with a very distinct effect, antimony rubbing on gold, and antimony on silver.

VOL. X.

In order to augment the currents, and consequently the sounds produced in this way, I took a large iron fly-wheel mounted on an axis which ran in centres. By a wire attached to one of the centres this wheel was connected to one of the terminals of the circuit, while a file was connected to the other terminal. The wheel was then driven rapidly round, and the file held hard on to its rim,—so hard that sparks of fire were produced by the friction. In this way a very distinct noise was heard in the receiving telephone. I have also made a variety of the above experiment by mounting a small cylinder of antimony in a turning-lathe, and driving it round against a bar of bismuth. This produces the loudest and most distinct noise of anything which I have yet tried.

These experiments demonstrate, without doubt, the existence of currents produced in conducting substances by friction alone, but it becomes a question whether they are to be regarded as merely thermo-electric, or whether they are not the very currents referred to by Sir William Thomson as the probable cause of friction, and by Professor Tait, in his "Thermo-dynamics," where he says, "it is possible that all friction, not excepting that caused by actual abrasion, is due to the production of electricity."

Instead of rubbing the substances together, I next proceeded to try the effect of knocking the one against the other. For this purpose a small anvil was put into metallic connection with one of the terminals of the circuit, and a hammer similarly connected to the other. Each stroke of the hammer on the anvil was very faintly heard in the distant telephone. As a variety of this experiment I put a small quantity of detonating powder on the anvil, and came down upon it with a blow from the hammer. I thought that it might be possible to hear something of the sharp snap produced by such a blow. The sound, however, heard in the telephone was not appreciably louder than before. Another variety of this experiment was made by driving a wheel, with large teeth, rapidly round in the turning-lathe, and holding against it a strong metal spring. The rapid clicks produced in this way were heard even when the telephone was a short distance from the ear. Here, however, it is plain that we have a mixture of the effects produced by rubbing and knocking.

In my next experiment I took a phonograph, and so arranged it

that a telephone circuit was completed through the spring which carries the pricker, the pricker itself, and the cylinder. When the pricker was allowed to press hard into the groove, and the cylinder turned, a faint grating noise was heard in the telephone, unless at those points where there happened to have been regular serrate markings left by the tool in cutting the groove, and then, as the pricker passed over these, a sound more or less resembling a feeble attempt at an articulation was heard. I then put a sheet of tinfoil on the phonograph cylinder, and spoke a sentence loud and distinct into the mouthpiece, and, for the purpose of increasing the sound, as heard in the telephone, I also included two Bunsen's cells in the circuit. When the phonograph was now turned, so as to reproduce the sentence, the articulation was heard in the receiving telephone, loud enough certainly, but considerably marred by the mere rasping of the pricker on the natural inequalities of the tinfoil.

It is obvious that, in this experiment, the articulation, such as it is, heard in the telephone must be caused by the variation in the resistance to the current, which arises from the unequal pressure of the pricker upon the tinfoil as it follows its indentations. This has, I think, an important bearing upon the character of all curves got by different processes of enlargement from the tinfoil record. Such curves could only accurately correspond to the movements of the disc which produced the indentations, provided the style attached to the lever, for producing the enlargement, pressed exactly on the tinfoil as the pricker did. Now, seeing that the pricker does not press equally at all times on the tinfoil, it would be very difficult, if not impossible, so to arrange a style and enlarging lever as to press in a manner so exactly similar.

The telephone can be employed to illustrate, in a very pleasing way, the incipient stage in the breaking-up of a liquid vein into globules. For this purpose a vein of acidulated water is made part of a telephone circuit, which also includes one or two Bunsen cells. This is easily managed by attaching a metallic can, having a small orifice in its bottom, to one of the terminals of the circuit, and a shallow metallic basin to the other. The first vessel, being now filled with acidulated water, is held over the basin, so that the column of water from the orifice flows into it, and so completes the electric

On

circuit. By gradually raising or lowering the upper vessel, a longer or shorter column of liquid can be made part of the circuit. listening in the telephone, so long as the liquid vein is short and limpid, no sound whatever is heard. This shows that the electric current has uninterrupted circulation. On gradually lengthening the liquid vein, a point is reached when a rattling noise is heard in the telephone. This arises from the altered resistance caused by the liquid vein beginning to break up into globules. On still farther lengthening the vein, a point is very soon reached when all sound in the telephone again ceases. This corresponds to the stage when the liquid vein has actually separated into detached drops, and so broken entirely the electric circuit.

2. On the Measurement of Beknottedness. By Professor Tait. (Abstract.)

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-(1) 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.

In this abstract a very simple example will suffice to indicate the method. Take the following six-fold knot

and modify the sketch, as on next page, the dotted line being traced always on the right-hand side of the full line as we go round the curve.