shown that for air at atmospheric pressure, a platinum wire at a red heat discharges positive electricity, but not negative. At a higher temperature both positive and negative electricity escape. Within certain ranges of temperature, therefore, other causes besides unequal velocities of the ions may lead to unequal values of the current with reversal of the electric field. Macdonald Physics Building, XVII. On a Model which Imitates the Behaviour of Dielectrics. By J. A. FLEMING, D.Sc., F.R.S., and A. W. ASHTON, B.Sc., 1851 Exhibition Scholar*. [Plate V.] has been shown by Profs. Ayrton and Perry, and by of dielectrics with regard to what are termed their "residual charge" effects is analogous to that of wires subjected to mechanical stress. If an iron wire be suspended by one end and a weight applied at the other, it is found that if the application of the weight has only lasted for a fraction of a second, the wire assumes its original length immediately the weight is taken off, provided the stress has not exceeded a certain limit. If the application of the weight is continued for a considerable time, it is found that the wire does not assume its original length immediately the load is removed; a small elongation still remains which slowly disappears, the wire very gradually decreasing in length to its original dimensions. In the case of the condenser, if the time of charge is very short, the whole of the charge disappears almost immediately on the condenser-plates being short-circuited. If, however, the charging pressure is kept on for a considerable time, we have first a discharge taking place immediately on short-circuiting the condenser; and this is followed by a slow giving-up of residual charge causing a continually decreasing current through the short-circuiting wire. The stress on the wire in the mechanical experiment is analogous to the electromotive force in the electrical experiment; the charge of the condenser corresponds to the elongation of the wire. The rate of variation of the charge, i. e. the charging or discharging current, is therefore analogous to the rate of change of displacement of the movable end of the wire, that is the velocity of that end of the wire. * Communicated by the Physical Society: read May 31, 1901. 2. A simple twisted wire is not, however, able to imitate all dielectric effects. Hence an endeavour has been made to follow up this analogy more completely, and has resulted in the construction of a model from which, by the application Front Elevation of Model, with Cylinder in section. of weights, curves of variation of velocity with time can be obtained strikingly similar to the curves of currentvariation with time given by condensers when charged and discharged. A simple form of the model can be made by taking two short lengths of spiral spring S1, S., and a metal cylinder slightly larger than the springs in diameter. To each spring is attached a piston P,, P, which just slides in the cylinder. The two springs with pistons attached are placed one above the other in the cylinder, which is then filled with oil. The top piston P1 must have holes drilled in it sufficiently large to allow the piston to slide very easily through the oil; let W be a weight just sufficient to compress S, and S, to half their original length. If the weight be applied momentarily, compression is produced in the upper spring S1; but provided the weight is immediately removed, the compression of S, is infinitesimal. If, however, the weight is kept on, the upper spring S, is soon compressed to its full extent; but the compression of S. proceeds very slowly and with decreasing velocity. If the weight is removed, S1 regains its original length almost immediately, but the piston P2 moves up to its original position very slowly. The variation of the displacement of P, is therefore very similar to the variation in the quantities absorbed and discharged by a condenser when both the charging and discharging are continued for a considerable time. 3. A simple apparatus such as that described above would draw curves somewhat similar to those obtained from the model about to be described; but it is evident that these curves would not completely represent the behaviour of a condenser. For the motion of P1 after the first few seconds of discharge is simply a copy of the motion of P.; also the motion of P, at any instant depends solely on the amount of compression in S, at that instant. Therefore it follows that, the springs having been compressed to a given extent and released, the motion of P, and therefore of P1 also after the first few seconds, depends only on the amount of the displacement, and not on the manner in which that displacement was produced. Thus it will be seen that only one velocitycurve could be obtained from this model, and the equation of the curve would not vary with the time of charge. It has been found that if as many as six pistons and springs are used the curves drawn by the model may be represented, at least approximately, by equations which are similar in form to those obtained by experiments on dielectrics. In the model now described the springs are 24 inches long, made of No. 12's S.W.G. brass wire, with a pitch of about 3 inches. To each spring is fixed a brass disk which forms the corresponding piston. The piston Pe fits fairly tight in the cylinder (see figure), and has no hole drilled in it. The second piston has no hole bored in it, but fits slacker in the cylinder than the first. The third piston has one hole 331⁄2 inch 6 1 in diameter, and each succeeding piston has a greater area cut away, the top piston having just sufficient metal left to make the spring come to rest without vibration after being compressed. The cylinder is filled with a mixture of machine. oil and vaseline. To the top piston is attached a brass tube to which is fastened a compound crossbar B. The latter is built up of two pieces of soft iron separated by a piece of sheet brass. The upper part of the crossbar forms the armature of an electromagnet M, the yoke of which has a hole drilled in it to form a guide for the rod R. Two electromagnets M, and M, carrying weights W, and W, can be attached to the lower plate of the crossbar, and can be instantaneously detached by breaking the circuit. The upper magnet M, by its attraction of the upper plate of the crossbar, keeps the top piston in its zero position. The magnets M1 and M, being attached, on breaking the circuit of M the crossbar moves downward under the action of the weights, and this corresponds to the charging of the condenser. the circuit of M and M, is now broken, the crossbar moves under the action of the springs alone, and its motion corresponds to the discharge of the condenser. In order to draw diagrams of the motion, a pencil which runs in a guide is attached to the crossbar. This pencil moves over the surface of a clockwork-driven recording-drum which runs in bearings attached to the back of the teak framework of the model. If 4. A typical diagram drawn by the model is shown in Pl. V., fig. 1; the ordinates represent displacement of the crossbar, and abscissæ represent time in arbitrary units. On applying the weight to the crossbar the latter first moves down very quickly, as shown by the steep initial portion of the curve in the diagram. This is followed by the more gradual compression of the lower springs, the crossbar moving with gradually decreasing velocity. At the point B on the curve the weights were detached from the crossbar, and the subsequent motion which is due to the springs alone corresponds to the discharge. It can be seen from the curve, that a large portion of the compression of the springs is given up almost immediately on releasing the weights; the crossbar then moves to its zero position with gradually decreasing velocity, due to the lower springs recovering their original length very slowly. In fig. 3 the velocity-curve obtained by differentiating curve I. is given. The general form of this curve is very similar to the current-curve one might expect to obtain when charging a condenser; but in the later parts of the curves the accuracy with which the model imitates the results obtained from actual dielectrics is very striking. In figs. 2 and 4 logarithms of the velocity are plotted to logarithms of the time of charge or discharge, and in each case the points so obtained are very nearly on straight lines, showing that the velocity of the pencil both when charging and discharging is a power-function of the time. Both these results have also been obtained by one of us in experiments on dielectrics. The three diagrams given in fig. 1 show the effect of varying the time of charge. From the equations obtained for the velocity of the pencil (see fig. 2) it appears that the exponent of t in the equations of discharge decreases as the time of charge increases, a result which has been shown to hold in the electrical case. The diagram in fig. 6 has been given to illustrate the action of the model in imitating the production of a second discharge which takes place when a charged condenser, after being once short-circuited and then kept insulated for a period, is short-circuited a second time. 5. The production of successive sparks from a charged leyden-jar is a very familiar fact. This can be imitated by the model. During the earlier part of the first discharge the upper springs extend to their full length, and while the lower springs are still considerably compressed and if the crossbar is then clamped, a state equivalent to insulation commences. The extension of the lower springs, however, still continues; but as the crossbar is fixed this results in the compression of the upper springs. When the crossbar is again released a second discharge takes place which is weaker than the first; if the operations be repeated, further discharges can be obtained until the crossbar returns to its zero position. In fig. 5 a diagram is given to illustrate the effect of decreasing the charging pressure of a condenser. This was obtained from the model by breaking the circuit of the magnet M1 only, and allowing the pencil to move under the action of M2. It will be seen that the effect of thus lowering the pressure is to cause a variation in the discharge to take place, similar in form to that in the corresponding electrical cases. It is interesting to consider also the effect of temperature on the discharge as given by the model. Increased temperature would make the mixture of oils in the cylinder become less viscous. This would cause the crossbar, when moving under the action of any given weight, to have a greater velocity, especially at the later portions of the discharge and discharge curves. This agrees with the fact that when the temperature of a cable increases, the charging and discharging currents as given by a galvanometer also increase. By freezing a portion of the oil, the effect of very low temperatures on dielectric constants could be imitated. It is evident, therefore, |