478 Royal Society ~ 
which he was thereby led. With reference to the form in which he 
enunciated the law regulating the action of a magnet on a uniaxal 
cerystal—that the optic axis is attracted or repelled by the poles of 
the magnet—he disclaims any intention of assigning a physical cause 
to the phenomenon, or doing anything more than expressing the 
results of observation, which are as if such a force existed. In the 
case of crystals of a more complicated character, he was led, in the 
first instance, to assume the existence of two magnetic axes, possessing 
a similar character as to attraction and repulsion with the one axis of 
optically uniaxal crystals. But finding that the proposed law did 
not hold when the crystal was examined in all directions, and not 
solely along peculiar axes, he abandoned, nearly two years ago, a 
hypothesis respecting which serious doubts had arisen long before. 
For the hypothesis of one or two axes acted upon by the magnet, 
he substituted another similar hypothesis. In the case of uniaxal 
crystals he now conceived an ellipsoid of revolution, consisting of 
an amorphous paramagnetic or diamagnetic substance, and having 
within the crystal its principal axis coincident with the principal 
crystallographic axis. It is easy to verify that both crystal and 
ellipsoid, the poles of the magnet not being too near each other, 
will be directed between them in exactly the same way. In the 
generalization, an ellipsoid with three unequal axes, having a deter- 
minate direction in the crystal, must be substituted for the ellipsoid 
of revolution. In this hypothesis too, two “magnetic axes”’ are 
met with, that is, according to the new definition, directions which 
possess, in common with the single crystallographic axis of uniaxal 
crystals, the property that if the crystal be suspended so that either 
of these axes is vertical, and the body is at liberty to turn freely 
round it, no extraordinary magnetic action is exhibited, but the ery- 
stal behaves like an amorphous substance. 
According to observation, a crystal under favourable circumstances 
is directed in the same way as the smallest of its fragments. Hence, 
according to the new hypothesis, each of its particles may be regarded 
as acted on like an amorphous ellipsoid. But such an amorphous mole- 
cular ellipsoid, when influenced by a magnetic pole at a finite distance, 
will be directed like an ellipsoid of finite dimensions under the in- 
fluence of an infinitely distant pole. Here Poisson’s theory presented 
itself for the verification of the hypothetical conclusions and their 
consequences, to which the author had been led by considerations of a 
different kind. This verification had the most complete success. But 
before proceeding to it, it was found necessary to confirm Poisson’s 
theory itself (or rather the results following from it), with respect to 
an ellipsoid of finite dimensions influenced by an infinitely distant 
pole. . By means of a beautiful theorem lately published by Professor 
Beer, by which the results relating to the influenced ellipsoid are 
simply and elegantly expressed by means of an auxiliary ellipsoid, 
the author was enabled to deduce immediately the analytical expres- 
sions. These were afterwards compared with experiment, by obser- 
vations made on two carefully worked ellipsoids of soft iron, executed 
by M. Fessel of Cologne. 
