THE

LONDON, EDINBURGH, AND DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FIFTH SERIES.]

NOVEMBER 1878.

XLIV. On the Experimental Determination of Magnetic Moments in Absolute Measure. By THOMAS GRAY*, B.Sc., Thomson Experimental Scholar in the University of Glasgow t.

SOME

[Plate V.]

(OME experiments on the intensity of the earth's magnetism were made by Gauss, and published, under the title "Intensitas Vis Magneticæ Terrestris ad Mensuram Absolutam Revocata," in the Commentationes Societatis Gottingensis, 1832, and in a paper on the General Theory of Terrestrial Magnetism, an English version of which is given in the second volume of ' Taylor's Scientific Memoirs.'

The results are given (according to the system the importtance of which was first seen, and which was first introduced, by Gauss himself) in absolute measure. The units of length, mass, and time employed by him are the millimetre, milligramme, and second. His results, when reduced to C.G.S. units, show that a steel magnet with which he experimented had a magnetic moment of 22.2 per gramme mass.

Gauss also calculated (Taylor's Scientific Memoirs, vol. ii. p. 225) the mass of steel which would have to be placed in each cubic metre of non-magnetic matter in order to make up

* Now Demonstrator in Physics and Instructor in Telegraphy in the Imperial College of Engineering, Tokei, Japan.

f Being the Essay to which the Cleland Gold Medal was awarded by the University of Glasgow in the Session 1877-78. Communicated by Sir W. Thomson to the Philosophical Magazine by permission of the Senate.

Phil. Mag. S. 5. Vol. 6. No. 38. Nov. 1878.

Y

a globe of the same magnetic moment as the earth. He found that this bar must contain 3.55 kilogrammes of the steel of which his magnets were made.

No experiments, however, have been made and published hitherto (so far as I know) having for their object the determination of the magnetic moments of steel magnets of different tempers and tempered by different methods, or which give information as to the permanence or non-permanence of the magnetism of such bars when left undisturbed for any considerable time. The experiments described below were undertaken with the view of supplying some approximately accurate information on these points, and also as to whether a hard or soft quality of steel gave the stronger magnets. They were performed in the Physical Laboratory of the University of Glasgow. The experiments on the effect of temper were all made on small bars cut from a wire of soft carbon steel.

The apparatus used is shown in the accompanying diagram (Pl. V.). M represents the magnetometer, which is a reflecting instrument consisting of a small mirror about one centimetre in diameter, carrying, cemented to its back, four small needles about 0-8 centimetre long, and suspended by a single silk fibre ten centimetres long, which passes down a narrow slit cut in the front of a wooden upright fixed to the base. This slit terminates in a small cell, in which the mirror hangs. The slit and cell being closed in front by a glass plate, a dead-beat arrangement is obtained similar to that of Thomson's reflecting galvanometer. BB is a bar of wood capable of turning round the vertical axis R, which, by means of a brass spring S is made to bear against two brass V's, one of which is fixed to the upper and the other to the under side of B B. AA are two arms of wood (shown in plan at the foot of the diagram), each of them fixed to BB by means of two thin wooden strips W. As will be seen from the plan of the arms, these strips were, in every position in which they were placed, in a vertical plane passing through the axis R.

The upper side of the bars AA was on a level with the centre of the mirror; and along the centre of them a small V-groove was cut, the line of which was arranged to pass through the centre of the mirror. The axis of a magnet placed in this groove could evidently, by turning the arms A A, be caused to make any desired angle with the magnetic meridian; and hence the instrument could be used either as a sine or tangent instrument. L is an ordinary galvanometerlamp, and M a scale of half-millimetres placed at a distance of one metre from the plane of the mirror.

The image of a fine wire, fixed vertically at F, was brought

to a focus on the scale by sliding L to the proper distance from the mirror, and served as an index by means of which the deflection was read. The distance of any point on either of the arms A A from the mirror was found by referring it to a fine line marked on the upper surface of each of the arms by a sharp point attached to a fixed support above in such a position as just to bear on the upper surface of the arms when they were turned under it. The distance of this line from the axis was evidently the same for each of the arms; and half the total distance between the two lines thus drawn gave the distance of either.

The plane of the magnetometer-needles was made to pass through the axis by first placing the magnetometer in such a position on the stand that this condition was approximately fulfilled, and then adjusting it by means of the levellingscrews at the base of the instrument until the deflections given on the scale by a magnet placed in the V-groove on one of the arms, when the arm was turned so that the magnet was alternately due east and due west of the centre of the mirror, were equal. In order that the magnetometer might be removed from the stand when desired, and replaced in exactly the same position, Sir William Thomson's geometrical arrangement was employed. One of the three rounded feet of the instrument was made to rest in a conical hollow cut in the upper surface of the stand, another in a V-groove cut with its axis in line with the centre of the conical hollow, and the remaining foot on the plane upper surface of the stand.

The mode of experimenting was as follows:-A large number of cylindrical steel bars were cut from the same bar, the diameter of which was 097 centimetre, its weight per metre 5.77 grammes, and its density 7.83.

Before being tempered the bars were carefully filed to a uniform length of five centimetres. Their lengths were compared with a scale of half-millimetres by means of a lens. About sixty of these bars, in order that they might be heated as nearly as possible to the same temperature, were spread on the bottom of a small thin iron tray, and the whole raised to a bright red heat in the heart of a glowing fire. To temper the bars glasshard, the tray with its contents was quickly removed from the

were then made up into parcels of five each, and placed in a vessel containing oil. was by means of a Bunsen lamp, and parcels of the bars removed at each of following temperatures-100°, 150°, 200°, 240°, 250°, 260, 270°, 280°, 300°, 310°. While this process was going on, the heated oil was taken advantage of to temper a number

the

of separate parcels by plunging them, after having been heated to a bright red heat, into oil of various temperatures. These bars were not again heated. All the bars were then magnetized by the current from ten of Thomson's Tray Daniells, flowing through a magnetizing coil, of the same length as the bars, made of insulated copper wire. This coil consisted of four layers of forty turns each, and had a resistance of 065 ohm.

Thus, taking the electromotive force of a Tray Daniell as 108 C.G.S. units, and its resistance as 1 ohm or 108 C.G.S. units, the current was, in absolute measure, approximately, 1 This was distributed over 160 turns of a solenoid five centimetres long; and therefore the magnetizing force was 1·0654π=377 nearly.

1.065*

1

160

Before the magnetic moments could be calculated, it was of course necessary to determine the horizontal component of the earth's magnetic force at the place where the magnetometer was to stand during the experiment. This was done by observing the period of oscillation, under the horizontal component of the earth's force, of five separate magnets, each suspended by a silk fibre about thirty centimetres long, and enclosed in a glass case placed on the magnetometer-stand. The magnetometer was then placed on its stand, and the deflection of its needle by each of these magnets, placed with its centre at a distance of twenty centimetres from the needle, observed. A reading was taken with the magnet resting in the groove on the arm A, which was placed in an east-and-west direction. The arm was then turned through 180°, and a reading taken with the magnet in its new position.

The same operations were repeated with the ends of the magnet reversed, and the arithmetic mean of these four readings taken as the deflection on the scale.

The formulas for deducing the horizontal component and the magnetic moment are easily obtained, as follows:

Let H horizontal component of the earth's magnetic force.

T=

period of vibration of magnet under H.

moment of inertia of magnet round an axis through its centre at right angles to its length. r = distance of centre of magnet from centre of needle.

a = virtual half-length of the magnet (that is, half the distance beteen its poles).

deflection of needle in degrees.

M = moment of magnet.

Substituting the value found above for M and squaring,

These formulas were used in preference to the approximate formulas which they become when a is struck out, and which are generally employed.

The distance between the poles of a magnet, or its virtual length 2a in the above formulas, may be determined by observing the deflections 0 and e' of the magnetometer-needle produced by the magnet when placed at distances r and from the centre of the needle.

The average of a number of determinations of a made by this method agreed almost exactly with the actual half-length of the magnet; and as the effect of a slight error in the value of a does not sensibly affect the value of M, the actual halflength was used in all the calculations.

The values found from each of the five magnets are given in the following Table. These results, as well as all those which follow, are given in C.G.S.