104 
Proceedings of the Eoyal Society of Edinburgh. [Sess. 
These values of are plotted in relation to a in the curve ABC of 
fig. 4, which also shows by a dotted continuation of the curve (to E) how 
F^, if calculated in the same way, would continue to change as the angle a 
increases towards 180°. 
9. But the manner in which the row of magnets becomes ruptured 
when a approaches 180° is entirely different from that shown in fig. 1, and 
consequently the values of F^ calculated from the equations that have been 
given above have no relevancy to that part of the curve. We have then 
to consider a different type of instability, namelj^, that in which neighbour- 
Fig. 4.— Values of Fr calculated for a row of magnets, for ^ = I'l and for various values of a. 
ing poles break away to the same side of the centre line. In that type the 
row of magnets assumes a serpentine form before instability sets in, with 
one pair of poles to the right of the centre line, the next pair to the left of 
it, the next to the right, and so on. 
That the manner of rupture is different will be obvious when the condi- 
tion of instability for a = 180° is considered. The externally applied mag- 
netic force is then directly opposed to the magnetic force with which each 
pole is attracted by its next neighbour, and a state of neutral equilibrium 
is reached when these oppositely directed forces are equal, namely, when 
TT^^r 1 
4?•2L(^•-l)2_ 
or 
( 6 ) 
