at the right-hand side of the diagram, the greatest error introduced by neglecting H/41r not exceeding 0-6 %. A study of such curves as these reveals the fact that there are three distinct stages in the process of magnetization. During the first stage, when the magnetizing force is small, the magnetization (or the induction) increases rather slowly with increasing force; this is well shown by the nickel curve in the diagram, but the effect would be no less conspicuous in the iron curve if the abscissae were plotted to a larger scale. During the second stage small increments of magnetizing force are attended by relatively large increments of magnetization, as is indicated by the steep ascent of the curve. Then the curve bends over, forming what is often called a “ knee, ” and a third stage is entered upon, during which a considerable increase of magnetizing force has little further effect upon the magnetization. When in this condition the metal is popularly said to be “ saturated.” Under increasing magnetizing f0rces, , greatly exceeding those comprised Within the limits of the diagram, the magnetization does practically reach a limit, the maximum value being attained with a magnetizing force of less than 2000 for wrought iron and nickel, and less than 4000 for cast iron and cobalt. The induction, however, continues to increase indefinitely, though very slowly. These observations have an important bearing upon the molecular theory of magnetism, which will be referred to later. The magnetic quality of a sample of iron depends very largely upon the purity and physical condition of the metal. The presence of ordinary impurities usually tends to diminish the permeability, though, as will appear later, the addition of small quantities of certain other substances is sometimes advantageous. A very pure form of iron, which from the method of its manufacture is called “ steel, ” is now extensively used for the construction of dynamo magnets; this metal sometimes contains not more than 03% of foreign substances, including carbon, and is magnetically superior to the best commercial wrought iron. The results of some comparative tests published by Ewing (Proc. Inst. CE., 1896) are given in the accompanying table. Those in the second column are quoted from a paper by F. Lydall and A. W. Pocklington (Proc. Roy. Soc., 1892, 52, 228) and relate to an exceptional specimen containing nearly 99-19% of the pure Low hysteresis is the chief requisite for iron which is to be used for transformer cores, and it does not necessarily accompany high permeability. In response to the demand, manufacturers have succeeded in producing transformer plate in which the loss of energy due to hysteresis is exceedingly small. Tests of a sample supplied by Messrs. Sankey were found by Ewing to give the following results, which, however, are regarded as being unusually favourable. In a valuable collection of magnetic Limits of Ergs per c.cm. Watts per lb. Induction. per cycle. Frequency, 100.

2000 220 0-129

3000 410 0-242

4000 640 0-376

5000 910 0-535

6000 1200 0-710

7000 1520 0-S90

8000 1900 I'I2O

9000 2310 I-360

metal.

Magnetic Magnetic Induction.

FOFCE- Pure l Low Moor 1 Steel Steel

Iron. Iron. Forging. Casting.

5 12,700 10,900 12,300 9,600

IO 14,980 13,120 14,920 13,050

I5 15,800 14,010 15,800 14,600

20 16,300 14,580 16,280 15,310

30 16,950 15,280 16,810 16,000

40 17650 15,760 17,190 16.510

50 16,060 17,500 16,900

60 .. 16,340 17,750 17,180

70 16,530 17,970 17,400

80 16,800 18,180 17,620

Q0 . . 17,000 18,390 17,830

100 . . 17,200 18,600 18,030

data (Proc. Inst. C.E., cxxvi.) H. F. Parshall quotes tests of six samples of iron, described as of good quality, which showed an average hysteresis loss of 3070 ergs per c.cm. per cycle at an induction of 8000, being 1-6 times the loss shown by Ewing's specimen at the same induction.

The standard induction in reference to determinations of hysteresis is generally taken as 2500, while the loss is expressed in watts per lb at a frequency of IOO double reversals, or cycles, per second. In many experiments, however, different inductions and frequencies are employed, and the hysteresis-loss is often expressed as ergs per cubic centimetre per cycle and sometimes as horse-power per ton. In order to save arithmetical labour it is convenient to be provided with conversion factors for reduc4 ing variously expressed results to the standard form. The rate at which energy is lost being proportional to the frequency, it is obvious that the loss at frequency 100 may be deduced from that at any other frequency n by simply multiplying by 100 n. Taking the density of iron to be 7-7, the factor for reducing the loss in ergs per c.cm. to watts per lb with a frequency of 100 is 0-000589 (Ewing). Since 1 horse-power=746 watts, and I ton= 2240 lb, the factor for reducing horse-power per ton to Watts per lb is 746/2240, or just 1/3. The loss for any induction B within the range for which Steinmetz's law holds may be converted into that for the standard induction 2 500 by dividing it by B1'°/2500". The values of this ratio for different values of B, as given by Fleming (Phil. Mag., 1897), are contained in the second column of the annexed table. The third column shows the relative amount of hysteresis deduced by Ewing as a general mean from actual tests of many samples (foufn. Inst. Elec. Eng., 1895). Incidentally, these two columns furnish an undersigned test of the accuracy of Steinmetz's law: the greatest difference is little more than 1 %.

To secure the highest possible permeability it is essential that the iron should be softened by careful annealing. When it is mechanically hardened by hammering, rolling or wire-drawing its permeability may be greatly diminished, especially under a moderate magnetizing force. An experiment by Ewing showed that by the operation of stretching an annealed iron wire beyond the limits of elasticity the permeability under a magnetizing force of about 3 units was reduced by as much as 75 %. Ewing has also studied the effect of vibration in conferring upon iron an apparent or spurious permeability of high value; this effort also is most conspicuous when the magnetizing force is weak. The permeability of a soft iron wire, which was tapped while subjected to a very small magnetizing force, rose to the enormous value of about 80,000 (Magnetic Induction, § 85). It follows that in' testing iron for magnetic quality the greatest care must be exercised to guard the specimen against any accidental vibration.

Induction BW Observed relative

B. 25001'°' Hysteresis.

2000 0-700 0-702

2500 1 -000 1 -000

3000 1-338 1 340

4000 2-118 2-128

5000 3-031 3-000

6000 4-058 4-022

7000 5-193 5-129

8000 6-430 ~ 6-384

Curves of Permeability and Susceptibility.-The relations of it (=B/H) to B, and of lc (=I/H) to I may be instructively exhibited by means of curves, a method first employed by H. A. Rowlandf The dotted curve for, u and B in fig. 18 is copied from Rowland's paper. The actual experiment to which it relates was carried only as the point marked X, corresponding to a magnetizing force of 65, and an induction of nearly 17,000. Rowland, believing that the curve would continue to fall in a straight line meeting the horizontal axis, inferred that the induction corresponding to the point B-about 1 7, 500-was the highest

1Phil. Mag., 1873, 46, 140.