lit) Proceedings of the Royal Society of Edinburgh. [Sess. 
We are concerned only with a narrow range of stability ; the expression 
may be simplified when it is applied to cases in which 0 is very small 
and a is not small. Under these conditions sin (a — 0) may be treated as 
sensibly constant, and the criterion for rupture becomes 
/y* 
which gives x = — ^ as in § 8. 
V 2 
The deflection ceases to be stable when 
the angle OPT becomes tan or 35° 16'. The criterion is a geometrical 
one ; it is independent of the strengths of the poles. Hence a narrow 
range of stable deflection is secured by set- 
ting the fixed poles near to those of the 
pivoted magnet W, though the resultant 
controlling force due to them may become 
vanishingly small. It will be evident that the 
strength of the control may be adjusted to any 
desired value, say by making the attracting 
fixed pole rather stronger than the repelling 
fixed pole, or by bringing it rather nearer. 
Or again, if P and P' are exactly equal, and 
are placed equally near, W may have some 
stability given to it from another source, but 
the action on it of P and P' will still deter- 
mme the limit of its stable deflection. 
23. When the Weber element breaks away from one position of 
stability it turns into another which is more favourably inclined to the 
impressed field H. Accordingly the outer group of electrons furnishes 
the equivalent not only of one pair of fixed magnets A and B, but of 
other pairs such as C and D (fig. 12), providing alternative stable positions 
into which W may be turned. The model photographed in fig. 13 (PI. I) 
illustrates this action for movements in one plane. There the four 
fixed magnets are held in supports which allow their distances from W 
to be adjusted. When the clearances as well as the pole strengths are 
made equal, it is found that W has some stability in any one of the four 
positions in which it ma}^ be placed ; this is an obvious consequence of the 
fact that the magnets of the model are not magnetically rigid, but 
influence one another by induction, with the effect of drawing unlike 
poles a little closer together and driving like poles further apart. Thus 
W in turning round from one position to another disturbs the magnetic 
