small in comparison with those of the coil. But when one dimension preponderates, and is comparable with the length of the coil, the theory is rather complicated, and we are at present compelled to return to empirical investigation. § 163. Attractive Action of Coils on Iron Cores.-We possess numerous measurements on the attraction of short' or 'long' cores—that is, of such as are shorter or longer than the coil. We shall pass over the older researches of Hankel, Dub, von Feilitzsch, von Waltenhofen, &c.,1 and confine ourselves to the discussion of the more recent systematic ones of Bruger.2 His experimental arrangement will be sufficiently clear from fig. 47; the weight of the core in each case was compensated by one sliding weight, and the attraction was measured by another weight for various relative positions of the core and of the coil. Equilibrium is obtained, that is to say, the attraction ceases, when the middle of the core M, supposed to be symmetrical, coincides with the middle of the coil m. That follows from symmetry, as well as from the principle of least magnetic reluctance (§ 158). We determine, therefore, the relative position by the height. Y of the middle of the core over the middle of the coil. If the short or long core is moved downwards, the force of suction only attains an appre ciable value just before the lower end U of the core enters the upper opening o of the coil. It then rises to a maximum, and falls 1 G. Wiedemann, Lehre von der Elektricität, vol. 3, §§ 651–665, 1883. 2 Bruger, Action of Solenoids on Iron Cores of various Shapes. Inaugural Dissertation. Erlangen, 1886. [See also Mr. Mahon, the Electrician, vol. 35, pp. 293, 604; 1895. It would appear possible at present to give a theory describing these actions with more or less approximation.-H. du B.] POLARISED MECHANISMS 253 off again until the above position of equilibrium is attained. Bruger restricted himself to investigating long coils, and found, in agreement with older statements, that the maximum suction corresponds to about the position in which the lower end of the core U is just on the point of emerging from the lower opening u of the coil (as represented in fig. 47); and this holds for cores the length of which is twice that of the coil. Bruger used, among others, a coil with the following constants: length L, = 13 cm.; number of turns n = 266; field 5 in the middle of the coil, per ampere, He obtained, for example, with three cores of about 39 cm. (= 3 L) length the curves given in fig. 47. Y defines the position of the core, X gives the corresponding suction in gramme-weight. In the diagrams of the curve: A A, full curve: cylindrical core; Hm = about 180 C.G.S. m = about 180 C.G.S. Hm = about 250 C.G.S. Conical cores For the details we must refer to the paper. are used in some arc lamps. The moniliform core gave, as intended, a constant pull over a great range. As long as saturation is excluded, the attraction is roughly approximately proportional to about the square of the current in the coil. Bruger gives curves like those above for various currents. The phenomena for iron-clad coils, as represented in fig. 45, p. 247, are similar; the field then between the inner edges of the shell is more intense and more uniform than in a coil without shell, but outside the coil it diminishes so much the more rapidly, by which the character of the traction curve is somewhat but not materially altered. The case of coils without shells but with a lining of iron is quite different. These do not attract iron cores, but, on the contrary, repel them. Having regard to the principle discussed in § 158, this appears at once intelligible. § 164. Polarised Mechanisms. The phenomena are markedly simpler if the core of the coil is not previously magnetised by the current, but has from the outset permanent magnetisation (§ 46). This case we will discuss. We have seen in § 21 that a mechanical force is exerted on the single end of a magnet in a field, which is in the direction of the latter, and is equal to the product of the intensity of the field into the strength of the end. This may be experimentally realised by bringing one end of a long permanent magnet into the field of the coil, so that the action of the latter on the other end of the coil may be neglected. In fig. 47, p. 252, let UO be a powerful steel magnet, the lower end U of which would move in the direction of the field of the coil or against it, according as its sign is positive or negative. In the middle part of the coil, where the field is uniform, the mechanical force exerted on the end will also be invariable, while it decreases through the openings outwards in proportion to the intensity of the field. It is assumed that the field of the coil is so weak that it exerts no appreciable inductive action on the permanent magnetisation of the steel core. The arrangement described belongs to the group of what are called polarised mechanisms, in which permanent magnets may in any way be used. Two properties present themselves, which in certain circumstances it is desirable to develop as far as possible. In the first place, a 'bilateral' action, in consequence of which, with currents of opposite directions, actions about proportional to these currents and opposite to one another may be obtained, which is excluded in purely electromagnetic mechanisms. Secondly, the possibility of attaining greater sensitiveness of the attraction with weak currents-or rather with small changes of current d I-as results from the following consideration. According to Maxwell's law [§ 103, equation (12)] the attraction is From this it follows, by differentiation, that the sensitiveness Like the differential d B/d itself, the product B (d B / d H), and therefore the sensitiveness, attains (§ 154) a maximum for a definite value F1, which can from the outset be produced by permanent magnetisation, 3, 2/47. The magnetic circuit. is best made up of steel and soft iron; the former then furnishes the permanent induction, while the current is allowed preferentially to act on the latter, since the value of dB/d far greater. = for iron is In the third place, soft iron, with its high permeability and relatively small hysteresis, may be combined with steel—which, conversely, has low permeability-in such a manner that one of the two properties appears considerably less prominent. This method is analogous to that by which, in optics, pairs of prisms can be combined so as to have either no deviation or no dispersion; and just as achromatic systems can be constructed, it is clear that in the present case it is possible to construct arrangements so that they are almost devoid of hysteresis. Polarised mechanisms have for long been used, for example, in duplex telegraphy, in Hughes's printing telegraph, in many telephones, and other apparatus. Magnetic circuits consisting of steel and iron parts of various section (used as shunt) have been proposed by Abdank-Abakanowicz, Evershed and Vignoles, and John Perry to compensate or diminish hysteresis in the above manner, which, as is well known, forms a chief source of error in measuring instruments.1 § 165. Electromagnets with large Lifting-power.-After Sturgeon, in 1825,2 had constructed the first electromagnet, attempts were made to obtain great statical lifting power or rather load ratio. At the present day these attempts are of but subordinate importance, though machines have of late been constructed for instance, for welding iron plates, as well as for appliances for transmitting power, or for brakes-in which 1 Abdank-Abakanowicz, Electrician, vol. 32, p. 93, 1893. Vignoles, ibid. p. 166. Field and Walker, ibid. p. 186. 2 Sturgeon, Trans. Soc. of Arts, vol. 43, p. 38, 1825. electromagnetism is used exclusively for maintaining a statical attractive force. In Chapter VI. (§§ 109, 110) we have already drawn conclusions from Maxwell's law of magnetic stress which are to be considered as the bases for the construction of the kind of electromagnet here contemplated. As the attraction is, cet. par., proportional to the square of the induction, it is most important to increase that quantity to the value of 20,000 C.G.S. units, which is conveniently attained in practice, and which represents a pull of about 16 kg.-weight per square centimetre (§ 103). In order to attain this result with as small a number of turns as possible, the reluctance of the magnetic circuit, which, with such electromagnets, must always be closed, must be as small as possible-that is, its shape must be tolerably compact. As, moreover, with a given induction the attraction is proportional to the cross-section, the latter must be as great as possible. At the same time, it may in some circumstances be advisable to somewhat diminish the section in the neighbourhood of the bounding surfaces of the gap, from the principle laid down in § 109, according to which the attracting force for a given induction, apart from leakage, is inversely proportional to the section. This diminution of section, as was remarked (loc. cit.), is not, however, to be driven too far; in the first place, because the validity of that principle is ultimately restricted by leakage, and, in the second place, because any such 'throttling' of the magnetic circuit increases the reluctance. The ends, consisting of two or more separate surfaces, of each of the two parts of the magnetic circuit, must be carefully prepared, and ground or polished, so that the reluctance of the resultant joint is as small as possible (§ 151). The softest wrought iron, of high permeability, must be used. To divide it is for the present purpose not only without advantage, but is even injurious, owing to the increased magnetic reluctance. The question as to the possible load-ratio has been discussed in § 110, so that we need not here recur to it. § 166. Description of some Types of Electromagnets -The oldest form resembles the thin permanent horseshoe magnets then most in use (fig. 48). The coiling usually consisted of two long coils on each limb. From the considerations in the previous paragraph, a compacter form, such as fig. 49, deserves |