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 (0), fig. 21, p. 131, we find the maximum value of the differential quotient d I | d He = 400 (for 1 C.G.S.); from this follows d B❘de = 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 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 l', measured in amperes; by using all the 12 coils (n = 2400) [§ 72, equation (1)], it was

(30)

He =

2n I'

10r,

= 19.2 I'

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 portioned 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

E 4 π I d

A

t

Experiments were now made; I, for d = 1·13 cm. ; II, for d=2cm.; 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 1400 C.G.S. Taking as basis I = the formula for the demagnetising factor [§ 80, equation (111)]

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 . 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.

i

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.

1

CONFIRMATION OF THE THEORY

267

§ 172. Confirmation of the Theory. The agreement between observation and theoretical calculation is satisfactory, as seen in fig. 57, and affords the theory developed in Chapter V. an additional support, quite independent of the experim ntal confirmation there given. Curves I and II at first coincide; this is due to the fact that the reluctance of the air is then so great compared with the remaining reluctance, that virtually the entire magnetomotive force is engaged in overcoming the former, and hence, for a given value of it, the increase of potential in the gap is sensibly equal to it, and this independently of the width of the slit, provided this is not too small. The behaviour of the electromagnet when flat poles are used is defined by that quantity AT; the mean self-induced intensity in the air-gap is found by dividing ▲ T, by the width of the gap. Hence, from what has been said, up to semi-saturation that vector is sensibly inversely

proportional to the width of the gap. It does not follow that the field is infinitely great for infinitely narrow gaps, for then the above relation would not hold; the upper limit of the field is rather the maximum value of 4 n 3 attainable in practice—that is, about 20,000 C.G.S. (§ 103). If to this be added the relatively small intensity of the field of the coil, the total available intensity is obtained

It may be remarked that the results given are not to be

regarded as a simple confirmation of the experiments described in §§ 83-90, merely because here the toroid is relatively thicker (2/r0-200) than in the previous case (r2 / r = 0·112). The fact that the coefficients of leakage of fig. 22, applied to the present special case, give correct values, forms among others a farther support for the correctness of the view, firstly, that the gap as such determines the numerator, and secondly that the rest of the toroid rules independently the denominator of the demagnetising factor.

§ 173. Investigation of Leakage. In consequence of this, H. Lehmann's empirical formula for leakage [§ 90, equation (30)] acquires more general interest; it was

and held for the lower stage of magnetisation up to about semisaturation. Although it holds in the first place specially for a toroid of Swedish iron of circular section, the following assumptions hold approximately even more generally.

1. The number (v — 1) is proportional to the 'relative width of gap.'

2. The proportional factor will depend but little on the nature of the ferromagnetic material, as long as its permeability is sufficiently high, and can therefore generally be put = 7.

3. The result holds also approximately for gaps which are not circular in section. In order to transform the equation for the latter case we observe that

In this shape the equation may in many cases prove useful. In order to gain an insight into the leakage when flat pole-pieces are used, a compass was arranged in the second