﻿110 Prof. 0. Henrici on 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 informa- 

 tion 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 w r ell 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. 



Svdney, 13th July, 1893. 



VIII. On a new Harmonic Analyser. 

 By Prof. 0. Henrici, F.R.S* 



§ 1. A CCORDING to the theory of Fourier's Series any 

 J\. function y of x 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 # = to x — c (fig. 1). For this interval the 

 curve may be drawn perfectly arbitrary as long as it gives 

 for every x 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 x the ordinate changes 

 suddenly from a value y l to a value y 2 , as from C to C in 



* Communicated by the Physical Society : read March 9, 1894. 



