97 



magnetic field. The image f in P may, therefore, 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 

 direction of the current. 



From this it follows that the homogeneous magnetic field can 

 have neither planes of symmetry passing through its axis of isotropy, 

 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. J ) 



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

 symmetry perpendicular to its lines of force, and a centre of sym- 

 metry also. 



Thus we are compelled to attribute to the homogeneous magnetic 

 field the symmetry of the group Cg previously mentioned. 



It is worth while remarking here, that this result is essentially 

 dependent on the symmetry attributed above to the electric field, 

 or to the electric current (C<). Indeed, the connection between 

 the different physical phenomena, as proved by experience, makes 

 it necessary that definite relations must also exist between their 

 special symmetries, in the same way as between their dimensions. 

 If for some reason or other we had primarily attributed the sym- 

 metry Cg to the electrostatic field, we should have to give to the 

 magnetic field the symmetry previously attributed to the electric 

 field, i.e. C . The electromagnetic phenomena themselves determine 

 this reciprocal relation: and the whole question is, as closer exa- 

 mination shows, evidently settled, as soon as it has become clear 

 what one wishes properly to consider as the "mirror-image of an 

 electromagnetic field" 2 ). 



If it be postulated that also in "the mirror-image of the elec- 



1 ) Cf. also: A. Perrier, Archives des Sciences phys. et nat. Geneve, (5), 1, 

 124ieme annee, p. 243, (1919). 



2 ) On this side of the problem my attention was kindly drawn by Prof. 

 H. A. Lorentz, to whom I am indebted for some valuable remarks here; cf. also: 

 A. Perrier, Ann. des Sciences phys. et natur. Geneve, (4), 41, 493, (1916); 45, 

 73, (1918); 46, 243, (1919), who, from this general point of view, treats here the 

 pyro-inductive and pyro-electrical phenomena, and the transformation of heat 

 into electrical energy by periodical variations of temperature. 



7 



