494 SCIENCE PROGRESS. 



not yet been found in nature, but those of which examples 

 are wanting are rapidly diminishing in number. 



Only during the last few months the observations of Rhine 

 ( 13) on scolecite, of Traube (14) on the antimonio-tartrates of 

 barium, strontium and lead, and on the double salt antimonio- 

 tartrate of lead with potassium nitrate, and of Penfield on 

 caesium mercuric iodide (15), have contributed examples of 

 four groups which were previously missing, while Traube 

 has also shown (16) that lactose does not, as appeared from 

 the early measurements of Schabus, present a symmetry 

 different from all of the thirty-two types. 



We may confidently expect that instances will shortly 

 be found of the four yet missing types which are predicted 

 by theory. 



Let us now review the position to which our survey of 

 the structural theories has brought us. 



It appears from the researches of Bravais that a lattice 

 structure accounts fully for the particular shape of crystals 

 (i.e., their subjection to the law of rational indices) ; from 

 the researches of Hessel and Gadolin, that crystals so defined 

 must belong to one or other of thirty-two symmetrical types ; 

 and, finally, from the researches of Sohncke, that the lattice 

 structure is only a special case of a homogeneous assemblage 

 of points, and that any such assemblage really implies a 

 compound lattice structure ; but that we cannot get the 

 thirty-two types out of a homogeneous assemblage without 

 assuming that the particles are of different kinds. 



So far, then, two courses are open : we may either 

 assume the law of rational indices as an empirical fact, and 

 deduce from it the thirty-two groups ; or we may start with 

 a structure theory, in which the constituent particles are of 

 different kinds. 



In either case it is impossible to establish fully the 

 varieties of form and symmetry of crystals by geometrical 

 reasoning alone from the simple principle of homogeneity ; 

 and yet it seems remarkable that Sohncke's theory only just 

 fails to do so ; is it not possible that, after all, something 

 may be lacking in Sohncke's treatment which deprives his 

 method of perfect generality, and that all the thirty-two 



