veniently high temperature. The toroid was therefore placed in a circular glass tank filled with pure petroleum, and was supported at a certain height above the bottom by wooden wedges. A block of ice was placed in the middle of the toroid, and served to keep the petroleum cool; while the water which accumulated from the melting of the ice was drawn off by a siphon. This simple device was found to answer perfectly.

The primary wire of the toroid was placed in circuit with a battery of accumulators, a commutator, a reliable ampèremeter, as well as rheostats, both metallic and liquid, by means of which the current could be brought either suddenly or gradually to any value up to 20 ampères. Before the commencement of each series of measurements the iron was demagnetised as far as possible by continually and rapidly reversing the commutator, while at the same time the adjustable fluid resistance was slowly increased, so that there was an exciting field rapidly alternating in direction, and gradually diminishing in intensity. Experience shows that by means of this method it is only possible to approximate more or less closely to the condition of the ferromagnetic substance previous to its first magnetisation. For complete demagnetisation, heating and subsequent slow cooling would be necessary; but, generally speaking, such an operation is of course impracticable.

The so-called 'curves of ascending reversals' (aufsteigende Kommutirungskurven) were determined by proceeding in a somewhat analogous manner; that is, by passing gradually from weaker to stronger values of current (and therefore of magnetising field), while for each value of the current (or of intensity of field) the direction of the current was reversed. The corresponding magnetisation was found from half the throw of the ballistic galvanometer as follows. Half the throw in question was multiplied by the constant of the galvanometer (which was determined in the manner mentioned above), and also by the total resistance of the secondary circuit. On dividing the product so obtained by 613, the number of turns in the secondary coil, we have the flux of induction & in the toroid. Let the quotient then be further divided by the cross-sectional area S=2.52 cm.2, and the result is the resultant induction F. Subtracting from this

ARRANGEMENT OF THE SLIT

127

5. (which, in the case of a closed toroid, is identical with 5'), and then dividing by 47, the magnetisation 1

In this manner a determination was made of twenty-five points on the normal curve of magnetisation 3 = funct. (5.) (§ 13), each being deduced as a mean from ten readings [see Table II. and fig. 21, p. 131, curve (0)]. The curve so obtained characterises the specimen of iron examined, and constitutes a basis for the subsequent investigation.

TABLE II.-CURVE OF ASCENDING REVERSALS FOR A

§ 86. Arrangement of the Slit.-After the normal curve of magnetisation had been duly determined, the continuity of the toroid was interrupted. By means of a circular saw about 0.1 cm. thick a radial cut of corresponding width was made in the place left free for the purpose between the two cheeks b, and b (fig. 18, p. 124). In sawing, care was taken to leave the faces of the slit as plane and parallel and the edges as clean and sharp as possible. In order to render it possible to work with a narrower gap, a flexible brass hoop was fixed round the toroid, which could thus be bent together more or less closely by means

1 For various small corrections, which must be introduced into this formula for a closed or divided toroid, as well as for other experimental details, we may refer to pp. 420, 434 of Lehmann's work already cited.

of the screw-clamp shown in fig. 19. A small disc, of magnetically indifferent brass, and of known thickness, was placed between the two faces, and then the toroid was bent together as far as this disc would allow (fig. 19).1

Further measurements were made with wider gaps, which were cut out by saws about 0.20 and 0.35 cm. in thickness respectively. In each case a special brass disc was fixed between the cut ends, so that the two faces bounding the air-gap could be held at a determinate distance apart. The rim of the little disc (which had been turned in a lathe) was then overwound with several turns of very fine copper wire, so as to form a small secondary coil completely filling the gap. Care was taken to make the mean diameter of these windings equal to

that of the cut faces of the toroid, so that the current impulse induced in them directly measured the flux of induction 6, through the gap. The ends of this small auxiliary coil were carefully insulated, and then the portion of the toroid between the cheeks b1 and b2 (fig. 20) was on each occasion re-wound with nine turns of the primary wire, so that the magnetic field produced had, as before, a uniform peripheral distribution.

The width of the gap was taken to be the mean between the thickness of the little separating disc, as determined by a micrometer, and the distance between the cut ends of the toroid,

The slight distribution of stress thus produced in the ferromagnetic substance has so small an influence on its magnetisation that the effect may certainly be neglected. (Compare § 167.)

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129

as measured by means of a dividing engine. The latter was, for obvious reasons, always somewhat in excess of the former.

Finally, it should be mentioned that, in order to determine the flux of induction through any given cross-section of the toroid, a movable secondary coil of seven turns was introduced, which embraced the toroid, and could be moved along the circumference from one part to another. It should be remarked that the large secondary coil surrounding the whole toroid measured the mean flux of induction & in the iron, while the small auxiliary coil, wound on the rim of the separating disc, measured the flux 6, through the gap. In accordance with the definition already given (§ 78), the former of these quantities, divided by the latter, gave directly the leakage-coefficient :

V =

§ 87. The Curves of Magnetisation.-Lehmann's observations were made with five different widths of the gap:

and the corresponding results are set forth in five tables, of which we will here reproduce only one relating to measurements made with gap (3) (d = 0·103 cm.). In the first column of Table III, p. 130, is given the intensity of field H. due to the primary coil; in the second the magnetisation I; in the third the mean flux of induction ; in the iron; in the fourth the flux 6, through the gap. Then follow the leakage-coefficient v = 6/6, in column 5, and its reciprocal 1/ 6,/6, in column 6. As we have already shown, the latter quantity is very nearly equal to the function n introduced above.

We may be content to omit the other tables, since Lehmann has plotted curves to represent graphically the first two columns of each. To the right of the axis of ordinates (fig. 21, p. 131) the curves of magnetisation

I = funct. (H.)

are drawn; first the normal curve (0) for the complete toroid, then the five other curves corresponding to different widths of

K

the gap. 3, 4, 5.

These are distinguished by the numbers 0, 1, 2,

It must be noticed that for the abscissæ e three different

avoid unduly extending the The first scale for abscissæ

scales had to be used, so as to height of the diagram (fig. 21). corresponds to ordinates ranging from 30 to 3= 1000; the second scale, one-fifth of the former, from 31000 to 3 1300; and the third scale, one-twentieth of the first, from 3 1300 upwards. Thus, the inclinations of the curves to the axes of reference are throughout kept within convenient limits. The diagram shows at a glance how the influence of the gap gradually increases as its width is made greater.

=

§ 88. Discussion of the Principal Results.-The experimental data may be considered from three different points of view :

I. Lines of Demagnetisation

If we suppose each of the curves 1, 2, 3, 4, 5 (fig. 21) to suffer separately a shear parallel to the axis of abscissæ until it is brought into coincidence with the normal curve (0), the