158 



lives of tfn'valent carbon (as triphenylmethyl, etc.) and of the specific 

 nature of the "aromatic" nucleus with its "paralysed" valencies. 

 Something of the same kind was found in the case of bivalent and 

 tetravalent tin. 



It is highly probable, indeed, that the phenomena of the "allo- 

 tropy" of the elements is intimately connected with the variation 

 of their "valency", as defined by means of chemical investigations. 

 In the same way the case of "polymorphism" in chemical compounds 

 might have its deeper cause in real "desmotropic" changes within 

 the chemical molecule, as was already suggested on former occasions 1 ). 



27. Without going into further details of these highly important 

 investigations or into the discussions and problems which they entail, 

 we may bring to the fore the following salient points from the above : 



a). Direct experimental proof is given of the correctness of the view 

 that the component particles in crystals are arranged in space- 

 lattices, as was already foreshadowed by crystallographers some 

 sixty years ago. 



b). Direct proof is given of the correctness of the other view 

 (Sohncke, Groth 2 ), that the unlimited regular structures we call 

 crystalline substances, may be considered as being built up by the 

 regular interpenetration of such space-lattices, each of which con- 

 sists of one and the same kind of atoms. These atoms preserve, 

 therefore, apparently their individuality as constituents of such 

 crystalline substances. 



c) . Because of the periodical character of these unlimited regular 

 systems, it is from a mathematical and crystallographical point 

 of view absolutely arbitrary, in which way we wish to imagine these 

 atoms to be combined into larger units, although we have at present 

 no idea, wether and in what way or by what forces the "chemical 

 molecule" is preserved in such structures 3 ). 



The notion of "crystal-molecule" as a structural unit has, there fore, 



!) F. M. Jaeger, Zeits. f. Kryst., 40, 131, 371, (1905); Proceed. Ron. Acad. v. 

 Wet. Amsterdam, 20, 282, (1917). 



2 ) P. Groth, Ber. d. d. Chem. Ges., 47, 2063, (1914); Zeits. f. Kryst., 54, (1915). 

 According to this author, the interatomic connections must remain, even if from a 

 crystallographical point of view the chemical molecule as such seems to have lost its 

 significance. Many crystals have symmetry-elements, the special nature of which 

 is obviously closely related to the atomic structure of the chemical molecule itself. 

 This can only have real significance, if the latter remains present in the crystal. 



3 ) In 1916 Smits and Scheffer (Proceed. Kon. Acad. v. Wet. Amsterdam, 

 19, 432, (1916) and in 1917 J. Beckenkamp (Centralbl. f. Miner., (1917), p. 



