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the strongest possible fields. The question as to the rational design of electromagnets for this purpose has, nevertheless, scarcely been considered. We shall discuss this question, therefore, somewhat more in detail than the electromagnetic arrangements hitherto mentioned, and the more so as we shall derive from it an interesting application, as well as a confirmation of the theory of Chapter V. (§§ 171–173).

Of the types of construction which have been empirically arrived at, perhaps those in most extensive use are copied from horseshoe magnets; like these (§ 166), they consist of two vertical coiled limbs, the lower ends of which rest on a massive iron yoke, while to the upper ends pole-pieces of suitable form

may be fitted. With vertical electromagnets the legs are usually very long, in order to bring in the requisite number of turns; owing to their being so near one another there is considerable leakage between them, which diminishes the available flux of induction between the pole-pieces.

The electromagnets of Ruhmkorff's construction are widely known, and are as effective as they are convenient to use (fig. 54). The two angular iron pieces OO and O'O' may be moved horizontally, and may be clamped in any given position, by which the space between the pole-pieces may be conveniently adjusted; to these may be screwed the horizontal cores, which for magnetooptical experiments are bored. The position of the coils M and M' is in any case far more rational than in the vertical

electromagnets (§ 173). The objection may be raised that the circuit Ō KO' is too weak magnetically as well as mechanically; the consequence of this is that, on the one hand, its magnetic reluctance is greater than necessary, and, on the other, the two angle pieces bend under the influence of magnetic tractive force, by which the distance of the poles is diminished. The magnetomotive force might moreover be considerably increased by coiling the lower connecting piece K.1

In this respect, the magnetic circuit of the electromagnet represented in fig. 55, and used by Ewing and Low in their

isthmus method (§ 217), is better arranged. It is true that this is at the cost of convenience of manipulation, which in Ruhmkorff's construction is unexcelled; this drawback might, however, be remedied by suitable mechanical arrangements. The electromagnet represented could be excited with 64,000 ampere-turns;

[These objections might be met by suitably designing connecting pieces of greater cross-section and rigidity; the adoption of modern 'cast steel' of high permeability would probably render such a type the best and cheapest for producing all but the very strongest fields.-H. du Bois]

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in this way Ewing and Low obtained an intensity = 24,500, and an induction B 45,350 C.G.S., the highest which had at that time been obtained in soft iron. As regards the field intensities observed in the air, it follows from the published statements that until recently values above 28,000 to 30,000 C.G.S. units had not been reached.

§ 168. Principles of Design.-There seemed no a priori reason why the production of still stronger fields should be impossible. The author accordingly attempted the construction of an electromagnet for this purpose, and in this attempt he was guided by the following considerations. The first point is to begin with the production of as high a value as possible of the flux of induction, which then, by 'throttling' the magnetic circuit by means of suitable pole-pieces, may, as it were, be concentrated as described below (§ 175). Accordingly the magnetic reluctance which, especially owing to the unavoidable air-space between such pole-pieces, cannot be indefinitely diminished, must be overcome by as great a number of ampere-turns as possible (§ 173).

In all the electromagnetic apparatus and machines we have hitherto discussed, and indeed in the great majority of such, it was sufficient from the nature of the case to consider only the first two stages of the process of magnetisation. But in the present problem the third, or stage of saturation, alone need be considered. In consequence of this, and of the circumstance that considerations of economy, certainty of working, facility of repair, and the like, are of less account in the present case, the conditions of construction are, to some extent, different. The discussion of § 95 showed that the field of the coil finally tends to completely direct and dominate the distribution of the vectors in the magnetic circuit; hence the coiling must be such that there is everywhere, and especially between the pole-pieces, a field in the desired direction-that is, tangential to the centroid of the magnetic circuit. In such an arrangement leakage will ultimately decrease as the saturation increases, and the inductiontubes so gained will be utilised; this result was confirmed by experiment (§ 173). As regards the shape of the ferromagnetic substance, the theoretical conditions already mentioned are best satisfied by a toroid divided radially. In other respects, the points discussed in § 141 for the construction of the frames of

they only hold, however, in Starting from the principles

electromagnets may be referred to; the present case mutatis mutandis. developed, the author has constructed an electromagnet which we shall proceed to describe.' The experiments made with this, to be discussed afterwards, must be considered as a confirmation of the validity of the principles followed in its design.

§ 169. Description of the Electromagnet.-As it was found that, with proper tooling appliances, the construction of a heavy iron toroid was neither more difficult nor more costly than building up a frame of several parts, the former was decided on. Fig. 56 represents the electromagnet in the

S the toroid is divided tangentially to the inner circle. A horizontal sliding motion is here introduced, so that the right side of the toroid can be displaced in reference to the left by means of a handle or wheel G, and thus the upper airspace Z be conveniently adjusted. The slide is so constructed that the

break of continuity of the ferromagnetic substance is as small as possible. However, with the preponderating magnetic resistance of the air-gap Z a few joints are not of much account (§ 152). In order to prevent any bending in consequence of the con

§ 169, du Bois, Wied Ann., vol. 51, p. 507, 1894; Elektrotechn. Zeitschrift, vol. 15, p. 203, 1894.

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siderable tractive force, a brass holder M, DM, is fitted, which, by means of a screw, can be adjusted to the width of the gap at any time. By using flat pole-pieces, separated by a narrow slit, the tractive force is so great that only discs of metal placed between can resist it.' The perforation L,, L, in the direction of the field allows of magneto-optical observations if desired, but iron plugs K, and K, are usually inserted, since an unnecessary increase of reluctance in this place is not desirable. The toroid rests on bronze bearings, which, in turn, are supported by a massive wooden tripod F1, F2, F3, provided with rollers R1, R2, R3 and levelling screws E1, E2, and E. The table TT serves for placing on it accessory apparatus. The axis of the field may, by tilting the whole apparatus, be set vertical, which is desirable for certain experiments.

§ 170. Coils of the Electromagnet. We have hitherto omitted to discuss general rules for winding and plans for connecting because in every special case this is simply determined by pre-existing conditions in a comparatively simple manner. It may perhaps be mentioned that the traditional rules for the use of batteries-that is, sources of current, whose electromotive force and internal resistance are assumed constant (which, however, seldom occurs)—have less interest at the present time. In most cases we are now concerned with self-regulating dynamo machines, street mains, or accumulators-that is, sources of current which furnish a more or less constant difference of potential, and in using which a definite limit of current may generally not be exceeded.

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1 Assuming a tension of 16 kg.-weight per sq. cm. (§ 103), the total pull is F38 16 × 78.5 1250 kg.-weight, whereas the entire weight of the whole electromagnet is 270 kg. Suitable discs are provided, 1, 1, 1, 2, 5, 10, 10 mm. thick like a set of weights.

2 When the air-space Z is not too small, it has little effect, as observation shows, whether the poles are filled with iron cores or not, as the reluctance of the air then preponderates (§ 175). Similar statements are made by Leduc (Journ. de Physique [2], vol. 6, p. 239, 1887). As to the properties of hollow iron cores in general, reference must be made among others to von Feilitzsch, Pogg. Ann., vol. 80, p. 321, 1850; Silv. Thompson, loc. cit., pp. 86, 184; Leduc, La Lumière électrique, vol. 28, p. 520, 1888; Grotrian, Wied. Ann., vol. 50, p. 705, 1893; du Bois, ibid., vol. 51, p. 529, 1894 (see also note 1, p. 235). Compare Silv. Thompson, loc. cit., chapter vi., where this question is thoroughly discussed for steady currents; in chapter vii. follows a discussion

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