TABLE XVII.-Air-gap Reluctance. General Table. A. Bar 921 cm. diameter ; 63 cm. long. Air-gap Reluctance. Air-gap in Air-gap Reluctance. B. Bar 1.165 cm. diam. ; 63 cm. long. terms of the terms of the Induction Induction Induction Induction Induction Induction Air-gap diameter of the diameter of the pole-face. pole-face. C. Bar 2.8595 cm. diameter; 91.5 cm. long. Air-gap in terms Air-gap Reluctance. Air-gap Reluctance. Air-gap Reluctance. Induction-density Induction-density Induction-density Mean of Reluctances at all Inductions. Mean Reluctances Mean Reluctances of Bar B at distances given in Table B. Mean Reluctances of Bar C at distances given in Table C. of Bar A at distances given in Table A. § 19. We can make a comparison between the work done by a ring magnet when it is divided at one point with the work done when the ring is divided at two points. The reluctance data show that though the mean air-gap reluctance may be larger than that of the iron, it is not very greatly so in any practical case, and we can therefore obtain no information by supposing that one is much greater or less than the other; but must proceed by actual trial from the curves to find out which is the most efficient arrangement. 20. In the case of a mechanism represented by a ring divided at one point only, we must remember that the closure of the induction curves involves a "sliding" magnetic contact, and if friction on the bearings is to be avoided this practically ties us down to iron of symmetrical form. § 21. Incidentally I had occasion to observe the change of reluctance caused by cutting a bar, and then grinding and polishing the ends. This was not done quite so well as in our most successful attempts. The reluctance corresponded to a separation of the bars by about 20 wave-lengths of sodium light, but I am certain that the bars could not have been half so far apart as this, so the surface reluctance is still unaccounted for. Sydney, 13th July, 1893. § 1. VIII. On a new Harmonic Analyser. By Prof. O. HENRICI, F.R.S.* CCORDING to the theory of Fourier's Series any A function y of a can, under certain restrictions, be expanded in a series progressing according to cosines and sines of multiples of x. This function may be represented graphically by a curve, x and y being taken as rectangular co-ordinates, or it may be defined by aid of such a curve. Anyhow, we shall suppose this curve_given, and also that it extends from x=0 to x=c (fig. 1). For this interval the curve may be drawn perfectly arbitrary as long as it gives for every one single finite value of y. This implies that if a point moves along the curve the corresponding value of x always increases. The curve may, however, be discontinuous, so that for a particular value of a the ordinate changes suddenly from a value y, to a value y2, as from C to Cin * Communicated by the Physical Society: read March 9, 1894. |