103 



llu group TOP is a common sub-group of the symmetry-groups 

 ', and DQP- If now two causes having the symmetry of two 

 tin Croups last mentioned, be superposed in the way stated. 

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

 produced will have this symmetry or that of the higher 

 letrical group C^ . Some examples will make this clear. 

 It a soft iron rod, past which is sent an electric current 

 placed simultaneously in a homogeneous magnetic field 

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

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

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

 iratus shown in fig. 98, this effect (Matteuci-Wiedemann) ') 

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

 lick iron-wire /, bearing at its one end a weight P of about 100 

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

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

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

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

 demonstrated by the deviation of a light-beam reflected at 

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

 This deviation can be made visible to an audience by means 

 )f a divided scale on the wall of the lecture-room. 

 The dependence of the direction of the torsion on that of the 

 rent and the magnetic field (N == north, S = south pole), is 

 lown in fig. 99; this drawing needs no further comment. 

 Evidently we have to deal with the superposition of two causes 

 the symmetries C and **>, with their axes of isotropy 



iceds some further comment. It holds only, if the causes be independent of 

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

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

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

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

 not be manifested as a dissymetry of the effects produced by their 

 cooperation (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. 



i) C. Matteuci, Ann. de Chim. et Phys. (3). 58. 385 (1858); G. Wiedemann, 

 Pogg. Ann. 108. 571. (1858); 106. 161 (1859); Baseler Verh. 2. 169 (1860); 

 E. Villari, Pogg. Ann. 187. 569. (1869); G. Gore, Proceed. Roy. Soc. Lon- 

 don. 22. 57 (1874 ; Transact, idem, (1874). 529. 



