94 



of certain dimensions and with its axis of isotropy parallel to the 

 ternary axis of the crystalline medium. The symmetry of the image 

 f is now, as already stated, Z)^ , while that of the crystalline medium, 

 as concluded from its molecular structure, or from its cohesion- 

 phenomena, is only that of the group Z)f . The last group is a sub- 

 group of Z)g , - - a fact to be remembered in what follows. 



In the same way, if we ask: what symmetry is to be attributed 

 to the homogeneous electric field, as e. g. it may be produced between 

 two parallel, infinitely extended, condensor-plates, - - the answer 

 is that we can attribute to it the symmetry of the group C, 

 the parallel lines of force of the field having the direction of the 

 axis of isotropy A^ . 



If now the last mentioned symmetry is given to the image /"which 

 describes the physical state in every point P of the electric field, 

 the question may rise, whether the special symmetry of the image/ 

 describing the physical state in every point P of the homogeneous 

 magnetic field be the same, or perhaps another? 



Now it is a well-known fact that the action of a magnetic field 

 in each point P can be imagined to be produced by an electric current 

 of a definite direction, flowing in a circular circuit round P as its 

 centre, and with its plane perpendicular to the lines of force of the 

 magnetic field. The image f in P therefore may be suitably taken 

 as a circle with P as centre, with its plane perpendicular to the 

 parallel lines of force of the field, and with a heteropolar vector 



(arrow) indicating in every point 

 of the circuit the intensity and 

 - - -V_ direction of the current. 



From this it follows that the 

 homogeneous magnetic field can 



- . have neither planes of symmeti 



~ JT ~ passing through its axis of isotro- 

 py, nor binary axes perpendicular 

 to the lines of force. Moreover, if 

 the field is reflected in a mirror 

 perpendicular to the lines of force, the direction of the current in 

 the mirror-image so obtained is evidently the same as in the original 

 field. The action of the field remains therefore unchanged by the 

 reflection. 



In other words: the magnetic field must itself possess a plane of 

 symmetry perpendicular to its lines of force, and a centre of symmetry also . 



Fig. 93- 



