ARRANGEMENT OF ATOMS IN A CRYSTAL. 139 



Not only do A, B, C, give the relative molecular intervals 

 along three directions in crystals of the first substance, and 

 A 2 B 2 C 2 along three corresponding directions in the second, 

 but the ratio A t : A 2 represents the relative molecular se- 

 paration along corresponding directions in the two different 

 substances. Hence in a series of isomorphous substances 

 we are enabled to express the increased or diminished 

 separation of the molecules along a given direction which 

 results from the replacement of one element or radicle by 

 another in the series. 



Thus, as regards the first series examined by him, 

 Muthmann found that in the tetragonal phosphates and 

 arsenates the replacement of an atom of phosphorus by an 

 atom of arsenic causes a separation of the molecules which 

 is almost uniform in all directions ; when, on the other 

 hand, in either the phosphate or the arsenate the potassium 

 atom is replaced by the ammonium radicle, the molecules 

 are again separated, but now almost entirely in the direction 

 of the principal axis. 



From this interesting result he concludes that . the 

 metallic elements occupy such a position in the molecule 

 that lines uniting them to the acid radicles are parallel to 

 the principal axis. 



With the further assumption that the symmetry of the 

 crystal molecule is tetragonal like that of the crystal, and 

 therefore that it must contain at least eight chemical mole- 

 cules, Muthmann finally proposes a scheme of the structure 

 of the crystal molecule, in which eight K O radicles are 

 placed vertically above and below four pairs of P O (O H) 2 

 radicles arranged at the corners of a square. 



In a similar manner Tutton proposes as the structure 

 of the orthorhombic group of alkaline sulphates an arrange- 

 ment of four chemical molecules, and suggests the relative 

 positions of the metallic atoms. 



It will be evident that in these speculations again we 

 are confronted by a long series of assumptions ; we do not 

 know that the volume of the elementary parallelepiped is 

 the equivalent volume of the substance ; we have no con- 

 vincing evidence to indicate the form of the elementary 



