ARRANGEMENT OF ATOMS IN A CRYSTAL. 141 



CONCLUSIONS. 



In the preceding pages abundant stress has been laid 

 upon the difficulties which stand in the way of current 

 views upon the structure of the crystal molecule ; this has 

 been done not with any desire to detract from the interest 

 of these speculations or the great value of the accurate 

 observations upon which alone they can be based, but rather 

 in order to emphasise the difference which exists between 

 them and the geometrical conclusions described in the 

 previous article and at the commencement of the present 

 one. 



The latter are rigid, definite and final ; the former 

 cannot for the present be regarded as more than plausible 

 speculations ; if they represent anything approximating to 

 the truth then the atomic arrangement deduced from the 

 refractive equivalents should be the same as that deduced 

 from the topic axes ; this has not yet been tested. Again 

 such speculations should take into account the geometrical 

 laws of homogeneity, and therefore regard the possibility 

 of a given crystal having a structure corresponding to one 

 or other of 229 types now established; but at present the 

 crystals investigated have only been referred to one of 

 the fourteen simplest special cases of these types which 

 were established by Bravais ; and to one or other of these 

 types the symmetry of the molecule itself has also been 

 referred. Meanwhile, however, it is encouraging to note 

 that the problem of molecular structure has been attacked, 

 and that at any rate a firm geometrical basis has been 

 provided. 



In my own opinion the conclusions to be drawn from the 

 interesting memoirs mentioned in this article are not those 

 which have been suggested by their authors, but rather the 

 point which they implicitly assume. All these researches 

 appear to me to prove nothing regarding the arrangement 

 of atoms rigidly distributed in a crystal molecule, and 

 united by bonds having certain directions in a crystal, but 

 they do prove one very important fact which is equally 

 suggested by the geometrical treatment and by the experi- 



