that in many ways the characteristic properties of dielectrics can be illustrated by experiments with a model of this kind, which will, it is hoped, afford valuable help in illustrating the behaviour of dielectrics.

The question may be asked, In what respect the action of this model differs from that of a simple twisted wire as an illustration of dielectric effects? The answer is that experiment has shown that although the current flowing out of a charged condenser is a simple power-function of the time, yet the exponent varies with the time of charging.

In the case of the simple twisted wire, whether the wire is twisted quickly or slowly, the twist per unit of length of the wire is approximately the same.

In the case of the model here described, it is evident that the effect on the compression makes itself felt first on the top piston; and hence that the amount of total compression depends not only upon the compressing force, but upon the time during which this acts, and that this compression is propagated gradually down the chain of pistons. In this respect the model imitates closely the electrical behaviour of dielectrics such as indiarubber when subjected for various times to different electromotive forces.

In the above model the velocity of return of the upper piston to its zero position is very approximately represented in terms of the time t reckoned from the instant of release by an equation of the form

V=Ae-Bt,

where A is a constant, and B is a function of the time T during which the operation of compression lasted.

In the case of the charge and discharge of a condenser, an equation of the above form has been shown by one of us to connect the value of the discharge-current and the times of discharge and charge.

XVIII. Note on the Electrification of Dielectrics by Mechanical Means. By A. W. ASHTON, B.Sc.*

THE HE apparatus used consisted of two brass plates P1 and P2, the upper one, P1, being 6 inches diameter and 25 inch thick. These two plates were connected to a quadrant electrometer, E. The electrometer gave a deflexion of 4.72 cms. for one volt. The sheet of rubber was laid on P, and P1 was laid gently on top of the sheet. The first sheet tested was pure Para rubler, which had been rolled to a thickness of 012 inch, and

1

* Communicated by the Physical Society: read May 31, 1901.

had not previously been electrically treated. The deflexion of the electrometer was about 5 cms., but on joining P1 to P2 this disappeared. A 2-lb. weight was then dropped on P1 from a height of three inches. The spot of the electrometer

moved very quickly off the scale to the right, but immediately returned and settled down to a fairly steady deflexion to the left. The electrometer thus appeared to receive two impulses, of opposite sign, one quickly following the other. It appeared probable that the first impulse might be due to the compression of the sheet, and the second to the extension of the dielectric when it recovers its original thickness. To test this, the sheet was stretched transversely and the effect on the electrometer noted. A fresh sheet of rolled Para rubber was taken, 022 inch in thickness, and placed on the plate P2. The top plate P, was then gently placed on the sheet of dielectric. The electrometer showed a deflexion of 50 cms. to the right, and the deflexion was slowly increasing. This was due either to the compression produced by the top plate, or to the mechanical stress to which the dielectric had been subjected during manufacture. The two edges of the rubber sheet were then grasped gently in the hands, and the sheet stretched until its length increased about 30 per cent. This caused the electrometerspot to fly off the scale to the right, showing a difference of potential of at least 7 volts established between the plates, the top plate being negative. The condenser and electrometer were then discharged for an instant, the sheet being then released and allowed to return to its original dimensions. This caused the electrometer-spot to fly off the scale to the

left, showing the top plate to be positive, the E.M.F. being more than 10 volts. The sheet of dielectric was then reversed, and exactly the same effect produced, viz. extension made the top plate negative, and vice versa. It appears, therefore, that polarization of a dielectric may be produced by simple pressure or extension, and hence some part of the mechanical energy expended on the indiarubber during manufacture may remain in the dielectric as electric energy.

XIX. Reply to Mr. Harold A. Wilson's Article entitled “On the Magnetic Effect of Electric Convection, and on Rowland's and Crémieu's Experiments." By V. CREMIEU, Dr. ès Sciences *.

MR.

R. WILSON has brought forward two objections of an experimental nature to the results obtained by me. The first of these bears on the experiment regarding the effect which is the converse of the magnetic effect of electric convection.

It may be briefly stated thus: Owing to the construction of the apparatus, the field of the magnet NS, which is excited at

*Communicated by the Author.

the moment of charging the disk AB, would produce on the charging current circulating in ABCD an electromagnetic effect precisely equal and opposite to the effect of the ponderomotive induction which the rupture of the circuit of the magnet should produce on the charged disk AB.

The objection would be valid had I used an arrangement corresponding to Mr. Wilson's diagram, reproduced above. In this it is, in fact, assumed that a vertical magnet NS is employed for acting on the charged disk AB.

But in the various forms of apparatus which I have used, and especially in the last one, of which I have given a detailed drawing, a closed electromagnetic solenoid was always employed.

Now it is known that the external field of such a solenoid

is zero. Hence no electromagnetic effect on the charging current of the disk AB is possible in my experiment. Mr. Wilson's objection on this point thus falls to the ground.

The second objection relates to my first repetition of Rowland's experiments, in which I used an arrangement closely resembling his.

Mr. Wilson thinks that he has traced the cause of my failure to observe the magnetic effect of electric convection to the fixed sectors, which he concludes were insufficiently insulated in my experiments, and well insulated in Rowland's.

To this I may in the first place reply that since the above experiments I have carried out two others †, in which the fixed sectors were completely suppressed, and the results of which have confirmed those of the preceding experiments.

Mr. Wilson's second objection has therefore no foundation. But this objection is further based on an altogether gratuitous assumption.

In studying the papers of Rowland, Rowland and Hutchinson, and finally Himstedt, I was led to suspect that they had not paid sufficient attention to the insulation of their sectors, either fixed or movable. I therefore used especial care in this connexion. The insulation of each sector was separately tested. In the case of the movable disk, it was tested when the disk was both at rest and in motion. I thus made sure that no charge was transferred from the previously charged sector to the neighbouring sectors on account of rotation.

Besides, the distance between the sectors was from 8 to 20 millimetres, according to the experiment; and the ebonite or mica which separated them had been carefully cleaned and varnished with shellac dissolved in absolute alcohol.

*Comptes Rendus, vol. cxxxi. p. 578 (1900).
+ Ibid. vol. cxxxii. p. 1108 (1901).

In taking my experiments one by one, it is possible to point out in each some defect which might account for the negative result of that one experiment. But the general conclusions which I have stated are based on the ensemble of four widely different experiments, and are confirmed by a fifth, a very conclusive one, regarding the existence of open currents.

Each of these experiments has, besides, been subjected to numerous criticisms. Up to the present I have always met a criticism by an experiment, and this latter has always confirmed my conclusions.

While thanking Mr. Wilson for drawing my attention to a point in connexion with my first experiment which might have been unnoticed by me, I think myself justified in replying to him that: :

(1) Electric convection produces no magnetic effect.

(2) There is no electrostatic effect on a charged conductor due to a variable magnetic field.

I cannot conclude without tendering to Professor H. Poincaré my best thanks for the suggestions received from him in the preparation of this brief note.

IT

XX. Note on the Potential of a Symmetrical System.
By T. J. I'A. BROMWICH †.

T was proved by Legendre that if the potential of a system (symmetrical about Oz) is known at all points of the axis of z, then the value of the potential can be expressed at any point of space in terms of zonal harmonics. But it does not seem to have been remarked that this method may lead in some cases to an apparent discontinuity in the potential functions when so expressed.

To illustrate the point, let us examine the potential of a circular disk for all points of space; this is, of course, a stock example of Legendre's method, given in all the ordinary text-books. From Thomson and Tait's 'Natural Philosophy' (1890 edition), Art. 546, we find

V1 = 2mp (a— rP1 + c1 = P2+cs ~ Pot...)
V1=2πp(a—rP1+ci

a

p2

a3

* V. Crémieu, Thèse de Paris, Gauthier-Villars, 1901.
+ Communicated by the Author.

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