449 



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 cry- 

 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. 



The results thus obtained from theory, and verified by experiment, 

 with reference to an amorphous ellipsoid, were compared with the 

 results obtained from the observation of crystals, and manifested a 

 complete agreement. According to this theory, the magnetic induc- 

 tion within a crystal is, like the elasticity of the luminiferous ether, 

 determined by means of an auxiliary ellipsoid. As there are three 

 rectangular axes of optical elasticity, so there are three principal 

 axes of magnetic induction, characterized by the property that if a 



