no 



KNOWLEDGE & SCIENTIFIC NEWS. 



[June, 1904. 



or definite aggregates of these. The molecules of such a 

 medium are either all of the same kind (of the same 

 size, shape, iSrc.) ; or else they are half of one kind and 

 half of another, the molecules of the two kinds being re- 

 lated in the same way as a right-handed and a left-handed 

 glove, that is, two molecules of different kinds may be 

 placed so that they are reflections of each other m some 

 plane. The two kinds of molecules are represented in 

 the diagrams liy the letters p and q. The molecules of 

 the medium are arranged according to certain laws of 

 " symmetry," that is, every molecule of the medium 



through a distance t parallel to the axis ; (4) a reflexion 

 in a plane called a " symmetry-plane " ; (5) a reflexion 

 in a point called a " centre of symmetry " ; (6) a gliding 

 reflexion, /.f., a reflexion in a plane (called a "gliding- 

 plane ") followed by a translation parallel to the 

 plane ; (7) a rotation through an angle a about a 

 line followed by a reflexion in a plane perpendicular 

 to the line. Each of these movements leaves un- 

 altered the distance between two given molecules ; 

 they may be considered as equivalent to only two 

 distinct movements, (i) and (2) being particular cases of 









cr 



a 



a 



7 



/O 



/^ 



/> 



A 



yO 



Fig. 2. 



(supposed of infinite extent in all directions) is brought 

 by certain so-called "mo\'ements" into the position pre- 

 viously occupied by some other molecule of the medium 

 (the medium is said to be " brought to self-coincidence" 

 by such a movement). These movements are of seven 

 different kinds:— (i) a translation, i.e., a shifting of each 

 point of the medium through the same distance in the 

 same direction ; (2) a rotation through an angle o, 

 about a straight line called a" rotation-axis" ; (3) a screw, 

 i.f., a rotation through an angle a, about a straight 

 line called a " screw-axis " followed by a translation 



(3) and (4), (5), and (6) of (7). The movements are 

 illustrated by figure i in which the molecule i is brought 

 into the positions now occupied by molecules 2, 4 by 

 reflexion in the planes B, A (perpendicular to the plane 

 of the paper) ; and into the position of molecule 3 by a 

 gliding reflexion in B. The molecule 2 is brought into 

 the position of molecule 3 by a translation, and of mole- 

 cule 4 by a rotation through iSo" about the intersection 

 of A and B. A medium may be brought to self- 

 coincidence by an indefinite number of different move- 

 ments, but the presence of certain symmetry-elements 



