RECENT PROGRESS IN CRYSTALLOGRAPHY in 



systems, with similar " coincidence movements " (Deckschie- 

 bungen), the first being of sulphur or selenium atoms, the second 

 of four times as many oxygen atoms, and the third of twice as 

 many alkali metallic atoms — the three systems interpenetrating 

 in such a manner as to produce equilibrium, and being so 

 mutually arranged that the sulphur or selenium system lies 

 centrally with respect to the other two, and the metallic system 

 in such wise as would affect chiefly the vertical direction. 

 Barlow's type S7 3 -! would appear to fulfil these conditions, and 

 such a supposition is in accordance with a friendly communi- 

 cation recently made to the writer by Mr. Barlow, who hopes 

 shortly to publish his views on the geometrical structure of 

 the alkali sulphates. 



That these facts, and others which have been adduced by 

 Prof. v. Groth — such as the case of ammonium iodide NHJ, in 

 which the replacement of the hydrogen atoms by CH 3 radicles 

 causes equal increases along two parameters, but no increase 

 along the third — are pregnant with meaning as to the positions 

 of the atoms or their spheres of influence in the molecule, admits 

 of no doubt. 



One further highly interesting result with regard to topic 

 parameters has been revealed by the investigation of the 

 ammonium salts — namely, that the replacement of potassium by 

 ammonium in either series is only accompanied by about 

 the same amount of separation of the molecular centres as is 

 observed when rubidium is substituted for potassium. Thus 

 two atoms of the alkali metal are replaced by ten atoms of two 

 ammonium radicles NH 4 , without more extension of the structure 

 than if merely two rubidium atoms had been introduced instead 

 of two potassium atoms. The amount is far less than when two 

 caesium atoms are introduced. Hence there has been room 

 in the structure for eight additional hydrogen atoms without 

 pushing the molecules farther apart, and the writer has therefore 

 concluded that the space defined by the topic parameters is not 

 filled with matter, but that relatively large interatomic and inter- 

 molecular spaces occur. There appear to be only two other 

 alternatives possible. One is that, owing to the different sizes 

 and shapes of the atoms of the different elements composing 

 the'molecule, it is just possible to pack into the crannies eight 

 extra atoms of hydrogen. The other is that room is made 

 for the NH 4 groups by the sulphur-oxygen layers being thrust 



