MOLECULES IN A CRYSTAL. 497 



The newer theory shows, for the first time, that these 

 two essential features can be deduced by purely geometrical 

 reasoning from a purely geometrical definition ; the arbitrary 

 assumptions which mar the theories of Bravais and Sohncke 

 are no longer necessary. It cannot be denied that this is 

 an extremely interesting result, whether the theory have any 

 physical meaning or no. 



The new theory is, of course, more complicated than 

 Sohncke's system, just as the latter was more complicated 

 than the early theories of Wollaston and Hauy, or than that 

 of Bravais ; there are, for example, no fewer than thirty 

 different structures possible, according to Schonflies and 

 Fedorow, for a holohedral orthorhombic crystal, as com- 

 pared with nine in Sohncke's theory, and four in that of 

 Bravais ; much more research is naturally required before 

 we can determine which of these thirty is the most probable 

 for a given orthorhombic crystal, such as barium sulphate. 



On the other hand, it must not be forgotten that certain 

 groups, such as the anorthic, and one mode of tetartohedrism 

 in the hexagonal system, have only one corresponding 

 molecular structure, even in Schonflies' theory ; it is in 

 these that the structure theories are to be most easily 

 tested. 



A great advance has been made, if we can dismiss from 

 our structures all molecules of a definite form, like the poly- 

 hedral molecules of Hauy, the ellipsoidal molecules of 

 Wollaston and Dana, the pear-shaped molecules of Kekule, 

 and the other fantastic devices which have been introduced 

 to account for crystal symmetry. It is also an advantage 

 to escape the necessity of assuming any difference in the 

 nature of the structural emits^of a crystal; there is no direct 

 evidence of any such difference. It remains to be seen 

 how far the physical and chemical characters demand that 

 such a difference should be recognised. Barlow and Sohncke 

 have insisted upon the necessity of doing so, and Lord Kelvin 

 introduces something of the sort into the structure which he 

 has devised to account for the piezo-electricity of quartz. 



It must be pointed out, however, that even a purely 

 structural theory like that of Schonflies, although it supposes 



