226 Proceedings of the Royal Society of Edinburgh. [Sess. 
the most powerful term in the zonal harmonic expansion is concerned. In 
the tetragonal system (C = B = A), the transverse component lies in a plane 
passing through the unique principal axis (*/). This condition also holds 
(§ 1 1) in the hexagonal system. Its value is then P = 3M/p 3 . (C — A) sin </> cos (p, 
which vanishes only when the magnetisation is in the direction of the 
greatest axis or lies in the plane of the two other principal axes. 
Therefore, although the parallel component of the internal force is zero in 
the directions given by a 2 — /3 2 = y 2 , magnetisation in these directions could 
only be maintained by the action of a transverse component of the external 
field balancing P= N /2M/p 3 . (C — A). In the more general case of the 
orthorhombic system (C>B>A), the formulae show that no direction of 
magnetisation is stable under the action of the internal forces of the first 
order alone except the direction of the greatest principal axis ; for, in 
every other case, the internal field has a component transverse to the 
direction of magnetisation. In fig. 3 values of P and Q are shown, for the 
value 7r/4 of 0 and <p, with the same numerical values of the constants as 
were assumed in § 9. 
