93 



of that system, while C^ may be considered to be a "tetartohedral" 

 class of it. P. Curie pointed already in 1884 to this analogy of the 

 groups considered with those of the ordinary crystal-systems. l ) 



9. Now we must draw closer attention to the question: how 

 is it possible to speak of the "specific symmetry" of a physical phe- 

 nomenon, of a physical state, or of a physical medium? 



As long as an unlimited system is considered, built up by a very 

 great number of points deprived of all special qualities, such a system 

 as a whole can only possess the symmetry of the group Kg . 



But if every point P of the system under investigation has itself 

 vectorial properties, defined by magnitude and direction, the system 

 shall have the lower symmetry of one of the groups Dg, Cg, 

 C , Z)^ , or C^ , - - namely as long as the previously mentioned 

 condition is fulfilled, that the distribution of the points in space does 

 not show a lack of preference for some particular direction, because 

 in that case the vectorial qualities would become effaced in the 

 whole. As long as in P or in its immediate environment only scalar 

 properties (temperature, density, etc.) are concerned, which are 

 functions of the coordinates of P, the symmetry of the system will 

 also be no other than that of the group Kg . 



For determining the physical state in every point P of such a 

 system, it is necessary to consider an infinitely small volume-element 

 in the immediate vicinity of P. Such a volume-element can have 

 a certain symmetry; the parameters by which its momentary state 

 is characterised, can be the same or different in the various points 

 P, P', P" , etc. of the system, according as the system is a homo- 

 geneous or an inhomogeneous one. 



Now the vectorial qualities in a volume-element round every 

 point P can in most cases be represented by a certain suitable figure 

 /, which we shall call the "image" of the physical state in P. We 

 can consider in this way the "image" of a single molecule, or of a 

 group of molecules, or of a volume-element yet containing a very 

 great number of such molecules, which in this last case however 

 are not considered in it separately. Finally, it may be desirable to 

 consider the symmetry of a system or of a body as a whole. But 

 the "image" / must always be chosen in such a way that it really 

 describes the physical state to be investigated, as completely as 

 possible, and often it is by no means an easy matter to find out the 



l ) P. Curie, Bull, de la Soc. Miner. 7, 418, a. f., (1884). 



