directrix corresponding to each width of the gap employed will thus be constructed. These directrices, or, as we shall call them for distinction, lines of demagnetisation, are drawn to the left of the axis of ordinates through a number of observed points, and are distinguished by the same numbers as the corresponding curves of magnetisation. Within the limits of experimental error, as will be easily seen, the points lie on straight lines about as far as the ordinate 3 875 C.G.S. (which corresponds to half the saturation value for the specimen of iron examined). The lines of demagnetisation express the relation between the mean magnetisation I and the mean demagnetising intensity $. Their approximately rectilinear form in the neighbourhood of the origin thus furnishes an experimental proof that the ratio of the ordinate to the abscissa, that is, the mean factor of demagnetisation N, remains constant until the magnetisation has reached about half its saturation value. The following are the values of the factor in question for those parts of the different curves over which it remains approximately constant : No. 1 2 We shall return to the consideration of these numbers in $ 89. II. Leakage-Coefficients So far we have confined our attention to the numbers contained in the first two columns of Table III. From the numbers in the last column, it follows that the leakagecoefficient, as determined by experiment, likewise remains constant until the magnetisation reaches about half its saturation value, but that for higher values of the magnetisation it slowly diminishes. The following table gives the mean values of the coefficient over its range of constancy, corresponding to the various widths of air-gap: Thus, the leakage-coefficient attains a value differing considerably from unity, even while the air-gap is still compara DISTRIBUTION OF LEAKAGE 133 tively narrow. In fig. 22 the leakage-coefficient v is plotted as a function of the mean magnetisation 3 (lower scale for abscissæ) for the gaps (2), (3), (4), (5); in the case of the narrowest gap, (1), no experiments on leakage were made. The initial constancy of here corresponds to the circumstance that the curves continue parallel to the axis of abscissæ until the magnetisation has reached about half its saturation value. As we pass to the higher values of the abscissæ, the curves begin to bend downwards. They are drawn as continuous lines as far as the experimental numbers extend, but if they are prolonged, as in the diagram, by the dotted parts, it appears that, as we approach the saturation point for the specimen of iron in question (about 0,10 020 100 200 300 400 500 600 700 800 500 1000 1100 1300 1.00 100 1300 1000 1200 1809 FIG. 22 1750 C.G.S.), they will all converge to the same point, whose ordinate corresponds to a leakage-coefficient equal to unity. III. Distribution of Leakage In the case of the three widest gaps employed, and for three values of the magnetisation (about 500, 1000 and 1500 C.G.S.), observations were made on the distribution of leakage along the circumference, using the movable auxiliary secondary coil mentioned in § 86. The results obtained are given in Table IV, p. 134, where the positions of the auxiliary coil on the circumference are entered as points of the compass, together with the corresponding values obtained for the flux of induction through this coil. From this table it follows that even for W NW N In the NE feeble magnetisations, for which the leakage is most considerable, the greater part of the leakage takes place within the short length which lies between NW and NE, and which contains the air-gap. case of the strongest magnetisation employed (the leakage-coefficient being considerably smaller), the property in question may be expressed by saying that up to the point NE or NW no considerable change occurs in the flux E of induction through the cross-section of the toroid. The distribution of the induction is therefore sensibly uniformperipheral over more than three-fourths of the circumference, and the uniformity of distribution will be the greater the higher the value which is reached by the induction. § 89. Comparison of Theory and Experiment. We are now in a position to compare the results of the experiments described above with the conclusions of the theory previously developed. In equation (III) (§ 80) SW FIG. 23 SE COMPARISON OF THEORY WITH EXPERIMENT 135 we have a relation between the mean factor of demagnetisation N and the function n, which is the reciprocal of the leakagecoefficient v. This last quantity, moreover, is represented graphically in fig. 22, p. 133, as a function of the magnetisation for the four widths of the gap (2, 3, 4, 5) which were employed. Again from (III) we easily obtain for the lines of demagnetisation the following equation: which now enables us to construct the lines in question from the curves v = funct. (3) of fig. 22. On the left-hand portion of fig. 21, p. 131, the lines of demagnetisation constructed in this manner are shown. The lines (2) and (3) are continued as far as the ordinate 3 = 1500, because for higher values of 3 the assumed reciprocity of n and v ceases to hold good with sufficient approximation (compare § 82). On the other hand (4) and (5) are only drawn for the range covered by the directly observed points.' As will be seen, these points lie approximately on the lines of demagnetisation. Thus, the theory leads to a satisfactory coincidence of the lines of demagnetisation plotted from measurements of the leakage with the curves of magnetisation which were determined by an entirely independent method. Fig. 21 also gives for the three narrowest air-gaps, (1), (2), (3), between the values = 1000 and 3 1750 C.G.S., the straight lines of demagnetisation whose equation is (29) where N H = N∞ I = denotes that factor of demagnetisation which is to be found from equation II (§ 76), and which, in accordance with the assumption there made, is, strictly speaking, only applicable for infinitely high values of .. From fig. 21, p. 131, it will now be observed how the values. of N, calculated from the measurements of leakage by means of 1 Fig. 22 does not give the function = funct. (3) for the gap (1), but, as we shall see in the next section, this can be found by interpolation. The line of demagnetisation (1) in fig. 21 was obtained in this manner. |