92 



A velocity, a force, etc., may thus be represented by a heteropolar 

 vector (arrow) in P, determined by direction and magnitude, and 

 having the symmetry C< . But there are a number of physical pheno- 

 mena for which the choice of the "image" in every point P of the 

 system is not so simple : in the case of a liquid endowed with optical 

 activity e.g., the symmetry may be represented by a portion of a 

 small screw, with its axis varying in direction from one point to the 

 other. 



In this connection it may be remarked that a body or a medium 

 in which all kinds of physical phenomena can take place, may be 

 considered with respect to its symmetry-properties from several 

 standpoints : we can speak of the symmetry of the medium itself, 

 in as far as that symmetry is attributed to it regarding its molecular 

 arrangement (crystals e.g.), or with respect to the whole complex 

 of phenomena observed in it ; or we can more particularly draw 

 attention to the symmetry of the medium with respect to a certain 

 group of phenomena, or finally with respect to a special phenomenon 

 only. In a similar way we can speak of the symmetry of a group of 

 phenomena, or of the symmetry of a special phenomenon. In all 

 such cases we must know either the effects produced, or the causes 

 which produce these effects; and the above mentioned image/ must 

 represent certain elements of symmetry which we attribute to the 

 effects, or to the causes, if it should be considered really to fulfil 

 the condition that it gives a complete description of the peculiarities 

 of the phenomenon under investigation. If this be the case, the image 

 / is indeed suited to its purpose; and then it will be possible for us 

 to bring the considerations on symmetry-properties, as developed 

 in the previous chapters, into the range of the phenomena inves- 

 tigated. 



10. With respect to the connection of the symmetry of causes 

 and of the effects produced by them, we can now conclude from the 

 facts observed up till now, that differences of symmetry in the causes, 

 or in the special circumstances, can generally be manifested also 

 in the effects produced, but that this is not absolutely necessary in 

 every case. On the other hand : differences of symmetry in the effects 

 observed can only be possible, if they are present likewise in the deter- 

 mining causes or circumstances. 



A pencil of polarised light travelling in the ether, has undoubtedly a 

 lower symmetry (Z)f) than the ether itself (R^), which lower 

 symmetry is of course connected with the absence of certain symme- 



