Page:EB1911 - Volume 17.djvu/352

between the pole pieces. Two groups of observations were recorded, one giving the induction in the inner coil and the other that in the outer coil. The value of the residual induction which persisted when the bobbin was drawn out was added to that of the induction measured, and thus the total induction in the iron was determined. The highest induction reached in these experiments was 45,350 units, more than twice the value of any previously recorded. The corresponding intensity of the outside field was 24,500, but, owing to the wide angle of the cones used (about 2 × 63°), this was probably greater than the value of the magnetic force within the metal. The following table shows some results of other experiments in which H was believed to have sensibly the same value inside as outside the metal. Values of I are derived from (B − H)/4π and of μ from B/H.

Metal.	H	B	I	μ
Swedish Iron	1,490	22,650	1680	15.20
	6,070	27,130	1680	4.47
	8,600	30,270	1720	3.52
	19,450	40,820	1700	2.10
	19,880	41,140	1700	2.07
Cast Iron	4,560	20,070	1230	4.40
	13,460	28,710	1210	2.13
	16,200	30,920	1170	1.91
	16,900	31,760	1180	1.88
Tool Steel	6,210	25,480	1530	4.10
	9,970	29,650	1570	2.97
	12,170	31,620	1550	2.60
	14,660	34,550	1580	2.36
	15,530	35,820	1610	2.31
Hard Nickel	2,220	7,100	390	3.20
	4,440	9,210	380	2.09
	7,940	12,970	400	1.63
	14,660	19,640	400	1.34
	16,000	21,070	400	1.32
Cobalt	1,350	16,000	1260	12.73
	4,040	18,870	1280	4.98
	8,930	23,890	1290	2.82
	14,990	30,210	1310	2.10

These results are of extreme interest, for they show that under sufficiently strong magnetizing forces the intensity of magnetization I reaches a maximum value, as required by W. E. Weber’s theory of molecular magnetism. There appears to be no definite limit to the value to which the induction B may be raised, but the magnetization I attains a true saturation value under magnetizing forces which are in most cases comparatively moderate. Thus the magnetization which the sample of Swedish iron received in a field of 1490 was not increased (beyond the limits of experimental error) when the intensity of the field was multiplied more than thirteen-fold, though the induction was nearly doubled. When the saturation value of I has been reached, the relation of magnetic induction to magnetic force may be expressed by

B = H + constant.

The annexed table gives the saturation values of I for the particular metals examined by Ewing and Low:—

	Saturation Value of I
Wrought iron	1,700
Cast iron	1,240
Nickel (0.75% iron)	515
Nickel (0.56% iron)	400
Cobalt (1.66% iron)	1,300

It is shown in the paper that the greatest possible force which the isthmus method can apply at a point in the axis of the bobbin is

F = 11.137 I_s log₁₀ b/a,

I_s being the saturation value of the magnet poles, a the radius of the neck on which the cones converge, and b the radius of the bases of the cones.

Some experiments made by H. du Bois (Phil. Mag., 1890, 29, 293) with an electromagnet specially designed for the production of strong fields, confirm Ewing’s results for iron, nickel and cobalt. The method employed did not admit of the production of such high magnetizing forces, but was of special interest in that both B and I were measured optically—B by means of the rotation of a polarized ray inside a glass plate, as before described, and I by the rotation of a polarized ray reflected from the polished surface of the magnetized metal (see “Kerr’s constant,” Magneto-Optics). H(= B − 4πI) was calculated from corresponding values of I and B. Taylor Jones (Wied. Ann., 1896, 57, 258, and Phil. Mag., 1896, 41, 153), working with du Bois’s electromagnet and using a modification of the isthmus method, succeeded in pushing the induction B up to 74,200 with H = 51,600, the corresponding value of I being 1798, and of μ only 1.44. The diameter of the isthmus was 0.241 mm., and the electromagnet was excited by a current of 40 amperes.

Tractive Force of a Magnet.—Closely connected with the results just discussed is the question what is the greatest tractive force that can be exerted by a magnet. In the year 1852 J. P. Joule (Phil. Mag., 1852, 3, 32) expressed the opinion that no “force of current could give an attraction equal to 200 ℔ per sq. in.,” or 14,000 grms. per square centimetre, and a similar view prevailed among high authorities more than twenty years later. For the greatest possible “lifting power” of permanent magnets this estimate is probably not very far from the truth, but it is now clearly understood that the force which can be exerted by an electromagnet, or by a pair of electromagnets with opposite poles in contact, is only limited by the greatest value to which it is practically possible to raise the magnetizing force H. This is at once evident when the tractive force due to magnetization is expressed as 2πI² + HI. For fields of moderate intensity the first term of the expression is the more important, but when the value of H exceeds 12,000 or thereabouts, the second preponderates, and with the highest values that have been actually obtained, HI is several times greater than 2πI². If H could be increased without limit, so also could the tractive force. The following table shows the greatest “lifting powers” experimentally reached at the dates mentioned:—

Observer.	Kilos per  sq. cm.	℔ per  sq. in.	Date.
Joule	12.3	175	1852
Bidwell	15.9	226	1886
Wilde	26.8	381	1891
T. Jones	114.9	1634	1896

5. Magnetization in Very Weak Fields

Some interesting observations have been made of the effects produced by very small magnetic forces. It was first pointed out by C. Baur (Wied. Ann., 1880, 11, 399) that in weak fields the relation of the magnetization I to the magnetizing force H is approximately expressed by an equation of the form

I = aH + bH²,

whence it appears that within the limits of Baur’s experiments the magnetization curve is a parabola, and the susceptibility curve an inclined straight line, κ being therefore a known function of H. If these equations could be assumed to hold when H is indefinitely small, it would follow that κ has a finite initial value, from which there would be no appreciable deviation in fields so weak that bH was negligibly small in comparison with a. Such an assumption could not, however, without dangerous extrapolation, be founded upon the results of Baur’s experiments, which did not go far enough to justify it. In some experiments carried out in 1887, Lord Rayleigh (Phil. Mag., 1887, 23, 225) approached very much more nearly than Baur to the zero of magnetic force. Using an unannealed Swedish iron wire, he found that when H was gradually diminished from 0.04 to 0.00004 C.G.S. unit, the ratio of magnetization to magnetizing force remained sensibly constant at 6.4, which may therefore with great probability be assumed to represent the initial value of κ for the specimen in question. Experiments with annealed iron gave less satisfactory results, on account of the slowness with which the metal settled down into a new magnetic state, thus causing a “drift” of the magnetometer needle, which sometimes persisted for several seconds. Apart from this complication, it appeared that I was proportional to H when the value of H was less than 0.02.