magnetic force, bears a somewhat larger ratio to that of the whole section (fig. 1) than in the case of the alternating force.
The conclusion is, however, that with an alternating magnetic force having a direction parallel to the longitudinal axis of a cylinder of given diameter, the effects of induced currents examined in this paper are more severe than in the same cylinder, of length equal to diameter, when rotated about its longitudinal axis in a magnetic force whose direction is at right angles to the axis of rotation for corresponding values of the frequency and the surface-induction density.
It should be remembered that in the case of alternating magnetic force, the electromotive force of a coil embedded in the iron is due to a true reversal of magnetism in the iron, and all the magnetic forces can be referred to a given cross-section of the iron cylinder. With a rotating field, the magnetic forces are referred to position in space.
Table III gives the values of the intensity of magnetic induction at different points of the 12-inch cylinder under alternating magnetic force. It also gives the relative phase-displacement of the electro- motive-force curves obtained from the exploring coils.
III. Phase-dixplacancnt. The preceding remarks have dealt with the maximum intensity of induction experienced each half-period at different points along a radius of the cylinder. In Table II are given the phase-displacement of the electromotive-force curves for coils 1, 2, and 4 with regard to the electromotive force of No. 3 coil. Referring to fig. 6, we saw how very sensitive the induction density at the centre of the cylinder is to changes at the surface in the region of 16,000, and this is when the maximum phase-displacements are experienced. For a very small change in the intensity of magnetic induction at the surface, when of the order 16,000, the interior of the cylinder experiences variations ranging from 738 to 7830. The phase- displacements change very abruptly, for when the induction density at the surface is 18,500, the phase between the electromotive-forces of coils 1 and 3 has dropped to 15 from 122 at 16,400. For very high induction density the curves are practically in phase. With the smallest value of induction density at the surface (180), the phase- difference between the electromotive forces of Nos. 1 and 3 coils is 44.
The phase-displacements in Table II have been judged from the points at which the respective electromotive-force curves cross the axis of time. This can be done with a good deal of certainty, but with the alternating magnetic force (Table III) this is not always the case. If reference be made to the electromotive-force curves,[1] it will be seen how different in character they may be when compared with those obtained with the rotating cylinder. In Table III the phases have been judged from the centre of gravity of the area inclosed by the electromotive-force curve and the axis of time per half-period.
- ↑ See Wilson, 'Roy. Soc. Proc.,' vol. 68, p. 218.
