98 
Proceedings of the Royal Society of Edinburgh. [Sess. 
often only one per cent, or less, of the magnetism of saturation. Hence, 
whatever be the nature of the control, the range of stable deflection which 
the Weber element can undergo before instability occurs is very narrow, 
say about half a degree to either side of its initial position. It follows 
that in the old model the pivoted magnets had to be thought of as being 
placed near together with but little clearance between neighbouring poles.* 
As a result they form rows in which the poles of adjacent magnets in the 
row are very near together compared with the distance between adjacent 
rows, and consequently the equilibrium of the row, prior to rupture, is 
substantially unaffected by the existence of adjacent 
rows. Under these conditions the control of any one 
magnet is due almost wholly to the forces exerted 
by its next neighbours in the same row. In con- 
sidering the problem of stability it is therefore suffi- 
cient to deal only with a single row. 
3. Imagine an indefinitely extended row of mag- 
nets, uniform in length and moment, each free to 
turn about a fixed centre, and let the centres be 
spaced at a uniform distance 2a in a straight line. 
Let the length of each magnet be 2r and its pole 
strength m. In the absence of any deflecting field, 
the magnets will form a straight line with their poles 
2{a — r) apart. Suppose now a deflecting field H to 
act, everywhere of the same strength and inclined at 
a constant angle a to the direction in which the 
magnets lie when they are pointing along the line of 
centres 00 (fig. I). Except when a is not far from 
180° — within say 35° of that direction, a case which 
will be considered later — the effect of H is to deflect 
the magnets equally, so that they remain parallel to one another as in the 
fio'ure. At first, as H is increased, there is stability, and the action is 
reversible. The angle of deflection, d, has a single value for each value of 
H. But unless a is small, as will be shown immediately, instability occurs 
when 0 reaches a certain value d,. , and the magnets then swing irreversibly 
towards a new position of equilibrium. The angle of rupture d^ depends 
primarily on the ratio ajr which we shall call i. To some extent it also 
* In a paper by Honda and Oknbo on “ Ferromagnetic Substances and Crystals in the 
light of Ewing^s Theory of Molecular Magnetism,” Science Reports of the Tohoku University, 
vol. V, Aug. 1916, also Rhys. Rev., vol. x, p. 705, this point seems to have been overlooked. 
The distance l)etween centres is taken there as probably more than twice the length of each 
magnet, which gives a wider range of stable deflection than is admissible. 
