[In practice, the dotted line may conveniently be drawn with a coloured pencil or crayon.] A little consideration shows that 1. Of the four angles at each crossing, one is enclosed between full lines, and its vertical angle by dotted [coloured] lines. These will be called the symmetrical angles. 2. The crossing is electrodynamically positive if it is over to the right in the symmetrical angles, and vice versa. [In the figure the two interior crossings alone are positive.] 3. If the knot be cut through along a line dividing the symmetrical angles at any crossing, and the pairs of ends on either side of that line be reunited, the whole remains a knot, with one crossing less than before (Proc., 1877, p. 322). If the line divide the unsymmetrical angles, the whole becomes a link. [Dividing the figure at the upper crossing, it becomes either the twist of five-fold knottiness, or the trefoil knot once linked with a simple ring.] These methods are in practice very much superior in convenience of application to those I have already given, especially when the knot to be reduced is complex. The paper contains rules for the calculation of the beknottedness of the original knot, in terms of the beknottedness and belinkedness of these reduced forms; so that knottiness n is made to depend upon n-1. I have not yet succeeded in obtaining from these a general expression such as will take account of all the successive reductions of a knot to zero of knottiness. 3. Preliminary Note on the Measurement of the Thomson Effect by the Aid of Currents from the Gramme Machine. By Professor Tait. 4. On the Disruptive Discharge of Electricity. By Alexander Macfarlane, D.Sc., and P. M. Playfair, M.A. (Abstract.) During the months of November and December of this Session we have investigated certain questions suggested by the results already communicated to the Society. Difference of Potential required to pass a spark between (1) two equal spherical balls at different distances, (2) a plate and ball at different distances, and (3) a plate and point at different distances. A series of observations was taken for each of these, and on three successive days, without altering the arrangement of the apparatus or the charge of the electrometer. The couple of small Leyden jars were attached to the conductors of the Holtz machine, as we had previously found that it was impossible to observe the discharge between a plate and point with any degree of accuracy when the capacity was small. Two Balls, each of inch diameter.-The series of observations for the two balls is a more minute and extended investigation of a problem we took up and solved approximately before. We have observed more minutely the values of the readings at the smaller distances, and also noted the cause of the irregularity at the ends. We found that at 80 mm. small violet sparks began to pass before the principal white spark, and that the reading was then more ambiguous than for smaller distances. Escape from the conductor was first noticed at 120 mm. * Plate and Ball.-We employed a tin plate 8 inches diameter, and one of the brass balls used in the previous experiment. The curve obtained is not very different from that for the two balls; it is somewhat more circular. Small sparks passing before the large one were observed to begin at a shorter distance than in the previous case. Another irregularity at the end was due to the passing of two large sparks. Finally, the electricity began to escape from the insulated wires. Plate and Point.-The plate used was the tin plate of the pre Hence the irregularity previously observed is not due to the escape of electricity into the air, but to the passage of small sparks between the electrodes. vious experiment; the point was conical and of brass. From 1 to 5 mm. the discharge was in the form of a white spark; for higher distances nothing was visible excepting a glow at the point. The series was continued up to 200 mm., as there was no difficulty due to escape of the electricity into the air. Discharge through a Solid Dielectric.-We obtained, by favour of Mr Calderwood, of Addiewell Chemical Works, a quantity of a pure solid paraffin of low melting point. The plate electrodes were separated to a distance of inch inside a glass vessel, the liquefied paraffin poured in so as to cover the plates completely, and then allowed to solidify for twenty-four hours. When the plate electrodes were charged the first spark which passed was large and illuminated the whole of the paraffin; but the succeeding discharges were much smaller, and of equal amount. The first spark produced a deflection 3-6 times as great as the succeeding sparks. When the plate of paraffin was examined afterwards, it was found to be perforated in a zigzag manner, the hole being surrounded by char. We found that Thus the electric strength of this substance, when in the solid state, is to its electric strength when in the liquid state as 2 to 1. As an instance of how these experiments may be made directly useful, I may mention that we obtained two samples of liquid paraffin from Mr Calderwood to compare their electric strength. We found the ratio to be 16. It is, however, extremely difficult to effect the comparison unless we have a considerable quantity of each specimen. It is best to have a dish of the above form, where we can have broad plates, the lower one slightly raised above the glass bottom, and the upper one well immersed in the liquid. The former of these conditions helps to prevent solid particles getting in between the plates, and the latter prevents the rising of the liquid up the stem, and consequent splashing about of liquid particles. Discharge through Paraffin Vapour.-We put the discharging vessel, with a quantity of one of the pure liquid paraffins, inside the receiver of an air-pump, exhausted the air, and allowed the paraffin vapour to accumulate. When the barometer-gauge indicated 50 mm, pressure, the distance being inch, we took sparks through the vapour. The spark was of a broad section, green at either end, but of a deep violet between. When a quantity of air was let in, white jagged sparks were observed in the midst of the coloured spark. From the readings obtained at 50 mm. pressure, we infer that this paraffin vapour is 17 times as strong as air. 5. Laboratory Note. By Professor Tait. 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. Some of the specimens thus produced in a few minutes compared favourably in their after behaviour in hot water with those of Mr Maclachlan. Even without the use of a freezing mixture the effect may be produced, though not so perfectly, by drawing out the heated indiarubber to the point at which its intensibility begins to diminish very rapidly. If it be held for a few seconds in that state of extension, it shows very little tendency to contract till it is immersed again in hot water. Then it is instantly reduced to one-fourth or one-fifth of its previous length, but remains permanently stretched to three or four times its original length. This operation may be performed many times in succession on the same specimen with the same results. Professor Clerk-Maxwell informs me that similar results are to be obtained with gutta-percha, drawn out when cooled, after being boiled in water. The subject is especially interesting as an exaggerated example of the Elastische Nachwirkung, which has recently been discussed at great length by Boltzmann and others. The following Gentlemen were duly elected Fellows of the Society : J. B. BROWN MORRISON, of Finderlie and Murie, Perthshire. JAMES LAMBERT BAILEY, Ardrossan. ROBERT COX, Gorgie, Murrayfield. JOHN HISLOP, Sec. to the Dep. of Education, New Zealand. JAMES COSSAR EWART, M.D., 12 Alva Street. GEORGE WM. BALFOUR, M.D., 17 Walker Street. Monday, 20th January 1879. DAVID STEVENSON, Mem. In. C.E., Vice-President, in the Chair. The following Communications were read :— 1. On the Action of Heat on the Salts of Trimethylsulphine. No. III. By Professor Crum Brown and J. Adrian Blaikie, B.Sc. I. Acetate of Trimethyl-Sulphine. The acetate is formed by treating the iodide of trimethyl-sulphine. 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° VOL. X. H |