{ 200

ti

gives us the required corrections to the readings of the constant-pressure gas-thermometer. The value of t, which we require for the purpose of calculating these corrections, is only known approximately; but an approximate value is sufficient for our present purpose.

The following table gives us the corrections required for the constant-pressure thermometer in the case of the gases hydrogen and nitrogen. The values are calculated for every 10 degrees between the freezing-point and the boiling-point of water, and the constant pressure is supposed to be 1 atinosphere.

It will be readily seen that the corrections for a gasthermometer when the pressure is kept constant and equal to 1 atmosphere are considerably larger than the corrections for a thermometer employing the same gas on the constantvolume method with an initial pressure of 1 atmosphere. We also notice that two gas-thermometers constructed with two different gases will differ in their readings more when used according to the constant-pressure method with a constant pressure of 1 atmosphere, than when used according to the constant-volume method with an initial pressure of 1 atmosphere. This result is quite in accordance with the experiments of Regnault on the subject.

VIII. On the Magnetic Effect of Electric Convection, and on Rowland's and Cremieu's Experiments. By HAROLD A. WILSON, D.Sc., M.Sc., B.A., Clerk-Maxwell Student, Cambridge University *.

HE object of this paper is chiefly to point out that Cremieu's failure † to observe both the magnetic effect of electric convection and its converse, the electrostatic effect of magnetic convection, is to be attributed rather to the methods employed than to the non-existence of these effects.

So many phenomena are known of which these effects afford a simple explanation, that it is very difficult to believe that their non-existence is possible. The magnetic deflexion of cathode-rays and the Hall-effect in gaseous electrolytes may be mentioned as examples of such phenomena.

I shall first consider Cremieu's experiment for detecting the electrostatic effect of a varying magnetic field. In this experiment (fig. 1) a circular disk AB attached to a rectangular frame ACDB was suspended by a wire E. The disk surrounded a vertical bar-electromagnet NS, and was charged by means of a battery through the wire E. During an expek riment, the magnetizing current and the charge on the diswere alternately reversed; and it was expected that the electrostatic effect of reversing the magnet would cause the charged disk to turn against the torsion of the suspending wire E. No such rotation, however, was observed; and Cremieu concluded that the effect in question does not exist.

It is easy to calculate the impulsive couple on the disk when the magnet is reversed. If dQ is an element of the

Communicated by Prof. J. J. Thomson.

+ Comptes Rendus, cxxx. pp. 1544-1549 (June 5, 1900); cxxxi. pp. 578581 (Oct. 1900), pp. 797-800 (Nov. 12, 1900).

charge on the disk at a distancer from the centre, and H the total magnetic induction through the magnet, then the impulsive couple on the disk when the magnet is reversed is

where Q is the total charge on the disk and Ho the total induction through the magnet when the current is steady in either direction.

When the charge on the disk is reversed, there is a current through the suspending wire and frame; and since these are in the magnetic field of the magnet, there will be an impulsive couple on the frame when the charge is reversed *.

Consider an element of the frame of length dS anywhere in ACDB. Let dH be the number of magnetic lines of force cut by this element when the frame and disk are turned through one complete revolution.

Then since the magnet is symmetrical about the vertical

I am indebted to Dr. Larmor, F.R.S., for the suggestion to take into account the effect of the charging current.

Phil. Mag. S. 6. Vol. 2. No. 7. July 1901.

L

axis the element will be in a field of strength

to itself. The force on the element is therefore

CdH
2πr

where C is the current in the element. But C=

1 dQ

2 dt'

Q being the charge on the disk, and half the current going down each side of the frame.

The impulsive couple on the frame when the charge is reversed is therefore

(For all the lines of force going through the middle section of the magnet are cut by the frame when it makes half a revolution.)

This effect therefore is equal and opposite to the impulsive couple when the magnet is reversed.

Consequently, when the charge and magnet are alternately reversed the total average couple on the disk should be zero, as Cremieu found.

Since the force on a current in a magnetic field is well known to exist, it follows that this experiment of Cremieu's may be regarded as indirectly proving the existence of the equal and opposite electrostatic effect of the reversal of the magnet, for if the latter effect did not exist then Cremieu ought to have observed the former.

I shall now consider Cremieu's experiments made with the object of detecting the magnetic field due to electric convection.

In these experiments a charged ebonite disk, coated with gold-leaf divided into sectors, was rotated inside a brass drum. The ends of the drum which were parallel to the disk were lined with mica, also coated with gold-leaf divided into sectors. With this arrangement no external magnetic field could be detected, but on removing the ends of the drum, but leaving the mica in position, a small effect was detected, which was attributed by Cremieu to impulsive currents induced in the sectors on the mica by the passage of the sectors on the disk.

It is, however, easy to show that the brass ends of the drum ought to cut off the desired effect, for currents will be produced in the sectors and drum-ends by the rotation of the

disk which will amount to a current equal and opposite to that carried on the disk. Also, if the drum-ends are removed, the full effect will not be observed unless the insulation of the sectors on the mica and on the disk is good. Rowland, with a similar apparatus, obtained the full effect, whilst Cremieu obtained only a small part of it. This may be taken to indicate that the insulation of Rowland's sectors was good enough, whilst Cremieu's sectors were not well insulated.

In fig. 2, A is the drum-end, B1, B2, &c. are the sectors on the mica, and C1, C2, &c. the sectors on the rotating disk. Some of the lines of force are also drawn. Consider the

sectors C1, B1, and B. As C1 moves along from left to right, the lines of force have to get across the gap between B, and B. To do this, each line will curl upwards and join on to the drum-end A, so that two lines will be formed, one starting on C, and ending on A, and another starting on A and ending on B1. The line from C1 to A will then move on and form two more, one from C1 to B, and another from By to A. The short lines from A to the sectors B1, B2, &c., will move along between the sectors B1, &c. and the drumend A, and those from the one end of a sector will neutralize those from the other end.

The motion of these short lines will not produce any magnetic field, because their positive and negative ends move along together. Also the positive and negative ends of the long lines from A and B, &c., to C1, &c., move along together, so that they constitute two equal and opposite parallel currents, and should produce very little magnetic disturbance outside the drum. Thus in this case there should be no magnetic field outside the drum, which is what Cremieu found to be the case.

Now consider the case where the drum-ends are removed (fig. 3). In this case the lines of force can only get across the gaps by leaving short lines, e. g. from B2 to B1. These short lines will disappear by neutralizing each other behind