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 = 5 natural size, partly in outline, and partly in section. In the notation of fig. 15, p. 109, r1 = 25 cm., cm. ; hence L= 157 cm., and S=78.5 sq. cm. At 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). 1 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. COILS OF THE ELECTROMAGNET 263 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, R, R, and levelling screws E, E, 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. We have hitherto § 170. Coils of the Electromagnet. 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.3 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. 1 Assuming a tension of 16 kg.-weight per sq. cm. (§ 103), the total pull is F = 38 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 In the present case the former amounted to 108 volts, and the latter to about 50 amperes. Each individual coil comprises a sector of the circumference of 20°; its 200 turns have about 0.2 ohm resistance when warm. If the 12 coils are arranged in series, they have, accordingly, 2-4 ohms resistance, and they cover 210° that is, two-thirds of the circumference. With that total resistance the difference of potential, 108 volts, produces a current of 45 amperes; this corresponds to a magnetomotive force of 108,000 ampere-turns, or 136,000 C.G.S. units. Dividing the latter number by the perimeter L 157 cm., we get 860 C.G.S. for the mean intensity of the field of the coils. Of these only about 380 C.G.S. is to be considered as a direct inductive agent. With the iron actually used' the magnetisation attained is 1600 C.G.S. The excess of intensity (480 C.G.S.) serves exclusively for counteracting the demagnetising action. If the value of magnetisation given is to be maintained, a demagnetising factor up to is admissible. This, in fact, is its value with the widest airspaces which occur in use-that is, with pointed pole-pieces. The power necessary for exciting the maximum effect of the electro-magnet is 108 x 45 volt-amperes = 4860 kilo-watts = 6.5 HP Its greatest self-inductance, with closed magnetic circuit, if we disregard the demagnetising action of the sliding guides, as well as of other joints, which, however, may scarcely be neglected, may by § 153 (eq. 8) be calculated as follows: of the winding and connecting of coils for variable currents as required in electromagnetic mechanism, when as rapid an action as possible is an essential requirement. 'This was the same brand as that from which the toroid described in § 83 was turned, and the normal curve of which is represented in fig. 21, p. 131. 2 From the curve of ascending reversals (o), fig. 21, p. 131, we find the maximum value of the differential quotient dI / d He = 400 (for H = 1 C.G.S.) ; from this follows d Bd He = 4 πd I | d He 5000 [§ 154, equation (9)]. = = = METHOD OF INVESTIGATION 265 The corresponding maximum value of the time-ratio is then 0 A/R 180/2.4 75". = For instance, the time was observed with the magnetic circuit closed for various values of the steady current I-that is, of the field of the coil 5-which elapsed after making the (variable) current I' until it attained 90 per cent. of its steady value; firstly when the apparatus was previously demagnetised (T1), and secondly when there had been a previous magnetisation (T) in the opposite direction: I=0.1 amp.; = 2 C.G.S. | I'=0·09 amp.; T1=98′′; T2=185" These numbers speak for themselves (compare fig. 40, p. 242).' With high self-induction a sudden break or even reversal of the current is out of the question, for the extremely high electromotive force which would thereby be produced would endanger the insulation, or at least produce too strong a spark on breaking. In the present case the simplest remedy was adopted -that is to say, a' carbon switch.'2 Ballistic experiments were obviously out of the question, owing to the great self-induction, and recourse was therefore necessary to another method of investigation. 2 § 171. Method of Investigation. The electromagnet has a number of flat poles like P, in fig. 56, p. 262; if these are screwed in on each side, the apparatus represents a divided toroid with adjustable air-gap. The author has made measurements, in order to test experimentally by another method the conclusions of Chapter V.3 In the first place, the mean intensity of the field of the coil 1 With a non-inductive resistance of about 40 ohms in circuit, the above time amounted, on the contrary, ceteris paribus, to only fractions of a second; this depends on the fact that the impressed electromotive force in the sense of § 153 is then not constant, but at the beginning assumes a far higher value than corresponds to the steady current. 2 There are a number of other methods of avoiding injurious sparking, or perforation of the insulation. Silv. Thompson, loc. cit., devotes a special chapter (xiv.) to this subject. 3 There exist in addition the following more or less extended series of measurements on electromagnets of Ruhmkorff's form (fig. 54, p. 259), which, however, have been made according to other principles and methods: Stenger, Wied. Ann. was calculated from the current I', measured in amperes; by using all the 12 coils (n = 2400) [§ 72, equation (1)], it was The total difference of magnetic potential AT, between the flat poles provided with narrow bore-holes was determined by a magneto-optical method to be described in the next chapter (§ 199). If d is again the width of the slit, the potential difference AT, is obtained by subtracting from the above that portion 5d which arises from the direct action of the coil; hence the value deduced from the observations is On the other hand the theory of Chapter V. [§ 80, equation (19)] gives (32) d = E 4π Id ΔΥ = Υ = Experiments were now made; I, for d = 1·13 cm. ; II, for 2 cm.; corresponding to dr2 = 0·226 and 0.400 respectively; that is to say, two values which are also found in Table V, § 89. Hence the corresponding curves (4) and (5), fig. 22, p. 133, could be used, which, according to Lehmann, represent v as a function of I; only so far, it is true, as his observations extend, and the reciprocity of v and n holds with sufficient approximation—that is, up to values of about 3 1400 C.G.S. Taking = as basis the formula for the demagnetising factor [§ 80, equation (111)] (33) N = = 2 d d 2 π the magnetisation curves for the two gaps could be obtained, and from them, according to equation (32), the dotted curves which in fig. 57 theoretically represent AT, as a function of H. The observed values of AT, are moreover plotted, and the individual points connected by straight lines; for further details the paper quoted must be referred to. vol. 35, p. 333, 1888; Leduc, Journal de Physique [2], vol. 6, p. 238, 1887, and La Lumière électrique, vol. 28, p. 512, 1888; Czermak and Hausmaninger, Wiener Berichte, vol. 98, p. 1142, 1889. |