Koepsel has therefore recently modified the apparatus in the following manner :

A magnetising spiral contains a single test-piece, which is enclosed in a yoke (§ 218). The measuring coil is wound on an iron cylinder, which rotates in a suitable cavity in the yoke like an armature. Its deflection is not compensated by

F

F

FIG. 83

D

torsion, but is read off on a scale by an index. This gives directly the flux of induction in absolute measure; whereby, however, a definite value of the auxiliary current is assumed, and must be separately adjusted or measured.

An arrangement by Kennelly may, in conclusion, be mentioned, by which an approximate comparison of the magnetic reluctances of two specimens of iron is possible, as in the differential magnetometer described in § 213. Both specimens are placed in AF or FC respectively (fig. 83). If the reluctances are equalised, there will, from symmetry, be no induction in the central iron cross-piece FD. The criterion of this is the fixity of a copper disc D, traversed by a current in a radial direction, which can rotate in a suitable slit about the unifilar suspension OP, which conveys a current.

C. Induction Methods

§ 216. The Ballistic Method, notwithstanding its many disadvantages, is still undoubtedly the most important for experimental physics--chiefly on account of its universal applicability, and of the unlimited range within which it can be utilised by raising or lowering the sensitiveness. It is less suitable for practical measurements, owing to the considerable disturbance to which it is liable from external influences.

Its application to the measurement of the intensity of a field has been discussed in detail (§§ 195-197), and the way in which

1 Koepsel, Elektrotechn. Zeitschr. vol. 15, p. 214, 1894.

it is used for determining magnetic distributions has also been pointed out. In Chapter V we have elucidated by an example its application to the investigation of toroids, so that we may here dispense with further general discussion.' The present method is the only one which can be used with completely closed magnetic circuits. But as in this case it is not possible to pull away the exploring coil, the flux of induction actually existing at any time can never be ascertained, let alone measured, but its sudden variation can be determined. The ballistic method fails when the time required for such a variation exceeds about a second; in that case it is not possible to make the period of the galvanometer sufficiently long in comparison. With large electromagnets, and with high selfinduction, this order of magnitude is very soon reached (§ 170).2 This forms a chief objection to the ballistic method; in other respects it leaves little to be desired, especially for laboratory purposes.

§ 217. Isthmus Method. It only remains to mention the particular modification in which the ballistic method may be employed for special purposes. For measuring magnetisation at high intensities up to $25,000 C.G.S., Ewing and Low3 introduced what is known as the Isthmus method. The ferromagnetic substance to be examined-for example, a piece of iron-is turned on a lathe into the shape of an ordinary bobbin; its ends are either plane, or cylindrical about an axis at right angles to the principal axis. In the former case the iron can be suddenly withdrawn from the magnetic circuit of the electromagnet used in this method; a diagram of the latter form is represented in fig. 84. By means of a handle the whole iron bobbin can be turned about an axis at right angles to the plane 1 Further details are found in Ewing, Magnetic Induction, chapters iii. and iv.

• In cores of soft iron thicker than say 1 cm., of high magnetic permeability and electrical conductivity, eddy currents play a considerable part (§ 187). They seem, indeed, to diminish the self-induction, and therefore accelerate variations of current in the magnetising spiral (note, p. 282); but apparently, by their screening action, they produce a considerable time-lag of the vector B in respect of H, the amount of which is difficult to check or bring into calculation.

Ewing and Low, Proc. Roy. Soc. vol. 42, p. 200, 1887; Phil. Trans. vol. 180 A, p. 221, 1889.

of the figure, within the pole-pieces in which a corresponding cavity is bored, so that the direction of the field in respect of the bobbin appears suddenly reversed (see fig. 55, p. 260). A secondary coil is closely wound about the narrow neck of the

25

18

44 5

bobbin (the isthmus), by means of which therefore the flux of induction through the neck can be ballistically measured, and, on division by the value of the section, gives the induction. At a somewhat greater distance from the neck a second secondary coil is wound, so that between them is a narrow annular, indifferent space. The difference of the ballistic throws observed with each of the secondary coils, divided by the section of the space, is obviously a measure of the fieldintensity within this latter; and, from the tangential continuity of the vector in question, this may be regarded as identical with the intensity in the neck itself. In this way both the ordinates of the induction curves and also their abscissæ are determined.

FIG. 84

The latter can be increased far more than is possible with ordinary coils; by rightly shaping the conical part of the iron bobbin, and by using a powerful electromagnet, both the intensity and the uniformity of 5, and therefore also of B, within the neck are most favourably influenced, as discussed before (§§ 174, 175). With such a coil of annealed Lowmoor wrought iron, in which the section of the neck was 1,500 times less than that of the pole-pieces, Ewing and Low obtained the following values for the magnetic vectors:

If the two secondary coils--whose number of turns may be equal-are inserted so as to oppose each other, this field-intensity may be directly measured. In this way the correction for the thickness of the wire is also obtained. See also Ewing, Magnetic Induction, &c. chapter vii.

§ 218. Yoke Method. It is scarcely possible in practice that the ferromagnetic substance examined shall always have a specially prescribed form. Several methods have therefore been devised to use the material, which commercially is usually supplied in the shape of bars of various section or as wire, with the ballistic method without much trouble. J. Hopkinson' first endeavoured to diminish the considerable self-demagnetisation of a bar-shaped specimen by enclosing it in a simple or double closed yoke (fig. 85), AA, of large cross-section, and of the softest iron. The magnetisation curve is now much less sheared to the right than would be the case without such a closed yoke (§§ 17, 206). The directrix for a given closed yoke may be determined by means of a normal specimen, the magnetisation curve of which is known.

The induction in the test-piece within the yoke was determined ballistically by J. Hopkinson. In his original experiments the specimen bar consisted of two parts, CC (fig. 85), separated in the middle. By means of a handle the part on the right could be suddenly pulled out so far that, by means of a spring, the secondary coil D sprang out of the field between the primary coils BB. The momentary current then measures the flux of induction which had existed in the place in question. The surface of separation between the two halves is obviously in an unfavourable place, where the irregularities due to it (§ 151) directly influence the secondary coil. The two halves may, of course, be left in position, and, the secondary coil being fixed, step-by-step measurements may be made in the usual manner. Hopkinson's arrangement does good service, especially if a

1 J. Hopkinson, Phil. Trans. vol. 176, p. 455, 1885.

suitable shearing of the induction curve is not omitted, and the specimen bar is not of highly permeable soft iron like the yoke; for the magnetic reluctance of a 'harder' kind of iron or steel is, of course, far greater in comparison with that of the yoke.

§ 219. Various Forms of Closed Yoke. The arrangement is more favourable when, as proposed by Ewing,' two test bars are

FIG. 86

used, and their ends connected by two massive yokes (fig. 86, p. 336). The secondary coils are best arranged about the middle of each bar. One of the yokes is so arranged that when it is pulled off, the secondary coils come away with it.

In the apparatus represented in fig. 85 the test bars are inserted in the perforations in the yoke-in which case they must fit well, so as to avoid air-spaces; hence a very accurate form of section is necessary. In this respect, the simple connection at the ends, as in fig. 86, is more practical. The rods, strips, or Ewing, Magnetic Induction, §§ 60, 161.