brought over the driving pulley, or removed to some distance from it, so as to be able to bring the centre of suspension over the centre of gravity of the chain, whatever shape the chain may be caused to take. The chain so suspended, when in rapid motion, retains for a considerable time whatever form we please to give it. It may be moulded into a most complicated series of curves, and though it resists any effort made to alter these curves, it has itself but little tendency to do so. If we observe the chain closely, we will however find that the disturbing forces, which I have already referred to, are acting on the chain, tending to change its curvature. For instance, if we keep the point of suspension over the centre of gravity of the chain, we will find after some time that the chain will take up a circular form. This is caused by the friction in the chain, and other causes. Again, the effect of the varying rate of rotation of the link on its own axis is also well marked, but is quite different from what we get when the chain is hung over the driving pulley. When the chain is hung over the pulley, there is a tension due to the weight of the chain. This tension gives rise to the wave form which certain chains take up when in motion. The tension due to the centrifugal force has no such effect. When, therefore, the chain is suspended and gravitation removed, there is no tension preventing the chain from continuing to curve always in the same direction; and if we use a chain specially prepared to show this effect, such as the one already referred to, the chain goes on bending further and further round till it comes against the part of the chain coming in the opposite direction and stops the motion, even though the chain at that point is also bending out of the way on account of the resistance offered by the links to rotation on their axis.

Monday, 3d January 1876.

SIR WILLIAM THOMSON, President, in the Chair.

The following Communications were read:

1. On the Electrical Conductivity of Stretched Silver Wires. By J. G. MacGregor, M.A., B.Sc. Communicated by

Professor Tait.

The apparatus which I used in a few experiments on silver wires was as follows:-To a beam, supported in stonework, a plate of copper was fastened, upon which a smaller plate could be tightly screwed. Between the two plates a very thick copper wire was secured, vertically. Its lower end was provided with a small plate of copper, fastened by screws. This plate served to make fast one end of the silver wire under investigation. The other end was joined in the same way to a second thick copper wire; this was provided with a horizontal round brass plate, through the centre of which it passed, and which acted as weight-carrier. A length of about 8 mm. at the end of the part of the copper wire which projected below the weight-carrier was amalgamated, and, while hanging quite free, dipped into a glass cup containing mercury, which, by means of a long screw, could be elevated or depressed by any desired amount. When measurements of resistance were made it was always placed in such a position that the amalgamated part of the copper wire was just beneath the surface of the mercury. The glass cup served also to support the weight-carrier during the adjustment of the weights, that the silver wires might be subjected to no jerks. After putting on weights the cup was lowered very slowly and steadily until the weights hung free. A copper wire (47 mm. thick and 30 cm. long), dipping in the mercury, joined up the silver wire as one of the arms of a Wheatstone's bridge. At the upper end of the copper wire, which was fastened to the beam, two other copper wires were fastened by binding screws. One of them went to the galvanometer; the other was the standard wire, with whose resistance that of the silver wires was

compared. For all the observations on a single wire, it had, in all cases, as nearly as possible the same temperature. That it might not be affected by warm or cold currents of air it was defended by a coating of gutta percha, and made to pass through a tube of water whose temperature could readily be noted. By dipping into a mercury pool it was joined up as a second arm of the Wheatstone's bridge. A length of about 5 mm. of the end which dipped in the mercury was well amalgamated. Above that the wire was varnished by a nonconductor, so that contact began always at the same point of the wire. The other two arms of the bridge consisted of the segments of a German-silver wire,-Kirchhoff's form of the Wheatstone bridge being used exactly as described by Wiedemann in his "Galvanismus."* The galvanometer used was Wiedemann's mirror galvanometer,† the deflections of the mirror being observed by means of a telescope. The current employed was that of a Bunsen's cell of great internal resistance. The length of the wire was determined by a very delicate cathetometer, which could measure accurately to 02 mm. The lower end of the copper wire which was fastened to the beam, was smooth and flat, and cut at right angles to its vertical axis. The edge of the small plate was correspondingly cut, so that the exact point at which the silver wire was seized and compressed by the copper plate could be seen through the telescope of the cathetometer. The clamp which seized the lower end of the silver wire was arranged in the same way. The wires, of whose resistance measurements were made, were of pure silver, and were carefully drawn by M. E. Stöhrer, philosophical instrument maker of Leipzig. They were always raised to a red heat before being subjected to tension, care being taken that fusion did not occur in any part. In order to determine the effect of tension on the conductivity of the wires, it was necessary to know the relation of their diameter before to their diameter after being stretched. This was estimated by a careful measurement of lengths and specific gravities. For the latter purpose a chemical balance was employed, which could weigh accurately to 0001 grm. As the wires had to be rolled up to prevent their touching the sides of the vessel containing the distilled water in which they were weighed, the measured specific gravity was pro* "Galvanismus,” vol. i. pp. 251–255, 2d German ed., 1872. +"Galvanismus," vol. ii. pt. 1, pp. 227-230, 2d Ger. ed., 1873.

bably not exactly that of the wire of measured resistance. The error, however, must have been very slight.

The course of procedure was as follows:-The wire was heated red hot in an alcohol flame. After cooling, its specific gravity was determined. It was then fastened by the copper plates to the thick copper wires, and a slight weight was attached just sufficient to straighten the wire, that its length might be accurately ascertained (it was straightened as much as possible by being drawn between the fingers before being fastened in the apparatus). When straight enough for the determination of its length, its resistance was also measured by the method of double observation, as described in the "Galvanismus" (see above).* After the determination of resistance, weights were carefully piled upon the carrier, which during the operation was held fast from below. They were then allowed to stretch the wire gradually until it hung quite free, and its elongation had ceased. Then the length, the resistance, and finally the length a second time, were determined, the second measurement of length being made in order to be certain that there had been no further elongation. The weights were now carefully taken off, the carrier being again supported from below, and the specific gravity of the wire was measured as before, the compressed ends, however, having been cut off. A large number of experiments were rendered useless by the fact that too great weights were attached. Either the wires broke, or they were found on inspection to have too variable a diameter to be regarded as uniform. In the result given below such small weights were used that almost no difference of diameter throughout the whole length of the wire could be noticed by means of a magnifying instrument. Thus the wire could be treated as uniform, and the specific gravity method assumed to give its diameter.

The results of the examination of three wires are given in the following table:

* Instead of the formula given in "Galvanismus," the following was used:— s3+s2(3d12-dr- d2)+s(d ̧d+dąd ̧1⁄2 – 3d ̧d2) – d ̧dd12=0.

The length of the German-silver wire as found by this formula was 1108-795
As measured by the cathetometer its length was 1108.8 mm.

mm.

8

These results agree, as might be expected, with those which Mousson has published on steel, iron, and copper wires, in the fact that the resistance increases very much faster than the length. This must be the case unless there be a diminution of resistance, due to tension, sufficient to neutralise the increase of resistance due to decrease of the cross section of the wire. It is interesting to ask, then-Does the decrease in the diameter of the wire account for that part of the increase of its resistance which is not due to the increase of its length? The following table answers this question. The column headed "calculated resistance" contains the resistance as it ought to have been if its increase had been due only to change of dimensions:

The agreement of the figures in the observed and calculated columns is very close, notwithstanding the many sources of error to which the experiments were liable, such as the change in

*

See Wiedemann's "Galvanismus," vol. i. p. 255.

"Galvanismus," vol. i. p. 310; "Neue Schweizerische Zeitschrift," vol. xiv. (1855), p. 33.