106 



all determining causes of the effect .finally produced were fully 

 known, then of course the symmetry-elements appearing in the 

 complete set of causes must be characteristic also of the special 

 symmetry which is exhibited by the effects produced x ) . 



The group C^ is a common sub-group of the symmetry-groups 

 C , Cg , and D^ . If now two causes having the symmetry of two 

 of the groups mentioned, be superposed in the way stated, they 

 will act as a single cause having the symmetry C^ , and the effect 

 produced will have this symmetry or that of the higher symme- 

 trical group C . Some examples will make this clear. 



If a soft iron rod, through which an electric current (C ) is passed, 

 be placed simultaneously in a homogeneous magnetic field (Cg), 

 the lines of force of which are parallel to the direction of the rod 

 and of the current, the iron rod will show a torsion (D^ or C^), 

 produced by the cooperation of both causes. Indeed, with the ap- 

 paratus shown in fig. 100, this effect (Matteuci-Wiedemann) 2 ) 

 can be easily demonstrated, even as a lecture-experiment. The 

 thick iron-wire I, bearing at its one end a weight P of about 100 

 grams, can turn freely round a sharp steel-axis e, placed in the 

 mercury-cup Q. The current is introduced through the mercury 

 and the steel-axis e. The sudden magnetisation of the iron- wire 

 is brought about by means of a solenoid 5, and the resulting torsion 

 is demonstrated by the deviation of a light-beam reflected at 

 the small mirror a, which is fixed to the steel-axis. This deviation 



1 ) The theorem that a certain lack of symmetry-elements in the causes will 

 usually manifest itself by the lack of certain symmetry-elements of the effects , 

 needs some further comment. It holds only, if the causes be independent on 

 each other, if no one of them be preponderant in its influence, and if the 

 number of the governing causes be a limited and a relatively small one. If 

 this number, however, is very great, as e. g. in cases where merely statistic effects 

 are considered, the dissymmetry of one or more causes is, or at least need 

 not be manifested as a dissymmetry of the effects produced by their co- 

 operation (J. C. Kapteyn Skew frequency-curves in Biology and Statistics, 

 Groningen, 1916). In physical phenomena, however, the number of producing 

 causes is never a very great one; in such cases the considerations held here 

 will certainly be of use. 



2 ) C. Matteuci, Ann. de Chim. et Phys., (3), 53, 385, (1858); G. Wiedemann, 

 Pogg. Ann., 103, 571, (1858); 106, 161, (1859); Baseler Verh., 2, 169, (1860) ; 

 E. Villari, Pogg. Ann., 137, 569, (1869); G. Gore, Proceed. Roy. Soc. London, 

 22, 57, (1874); Transact, idem, (1874), 529. On the Wiedemann-effect in 

 the case of wires of cobaltum, cf. : K. Honda and T. Shimizu, Phil. Mag., 5, 650, 

 (1903); H. A. Pidgeon, Physical Review, 13, 209, (1919). 



