igo 



NATURE 



Table I. — Relation betii'een Crystal Form and Molecular 

 Complexity. 



Number of atoms in molecules of 

 T., compound inorganic substances Organic 

 „,. ^ < com- 



[AUGUST II, I9IO 



Crystal system 



Cubic 



Hexagonal 



Tetragonal j 



Orthorhombic 5 



iNIonosymmetric ... 5 



Anorthic o 



Numberof cases sum- 1 

 marised in each . 40 

 vertical column ... ) 

 The proportion of substances 



50 68-5 



35 19-5 



5 4-5 



5 3-0 



s 4-5 



42 



pounds 

 - man 5 



5 12 58 2-5 



35 3« 14-6 40 



567 5-0 



5 50 36 27-3 34-0 



; 5 6 37-3 47'S 



5028 7'o 



67 63 20 50 673 585 



crystallising I 



s stated abov 



Of the elements which have been crystallographically 

 examined, 50 per cent, are cubic ; their crystal structure 

 is simulated by the cubic closest-packed assemblage of 

 equal spheres. Another 35 per cent, belong to the 

 hexagonal system, and that these are correctly represented 

 by the hexagonal closest-packed assemblage of equal spheres 

 is indicated by the fact that for the hexagonal elements 



NO. 2128, VOL. 84] 



the ratio of corresponding dimensions in the horizontal 

 and vertical directions approximates to the value a : c = 

 I :0'8iOs, deduced for the model assemblage. 



The task of accounting for the 15 per cent, of the 

 crystalline elements which have been examined and found 

 to crystallise in systems other than the cubic or hexagonal 

 still remains. A little inspection show's that the crystal 

 forms of these elements in every case approach very closely 

 to one or other of the two of highest symmetry, namely, 

 the cubic or the hexagonal ; one example of this will now 

 suffice. The values of corresponding dimensions in three 

 directions in space for the monosymmetric form of the 

 element sulphur are given by the axial ratios a :b : c — 

 0.9058 : I : o-qqqS, /3 = q5° 46'. The slight departure of 

 these dimensions from the corresponding values for the 

 cubic closest-packed assemblage, in which a : b : c=i : i : i, 

 i8 = qo°, at once suggests that the monosymmetric modifi- 

 cation of sulphur is derived from the 

 latter assemblage by some minute 

 distortion. Such a distortion in- 

 dicates a very trifling departure 

 from uniformity in the influence 

 exerted in different directions from 

 each atomic centre, and may either 

 arise from some want of symmetry 

 in the individual atoms or in a re- 

 duction of the syiTimetry <!aused by 

 some grouping of the atoms; two or 

 more atoms might thus be more 

 closely connected in some way with 

 one another than with other next 

 neighbouring atoms. 



Having shown that the crystalline 

 forms of the elements are in com- 

 plete harmony with the conception 

 that crystal structures can be homo- 

 geneously divided into similar cells 

 of polyhedral shapes approximating 

 closely to the spherical, reference 

 may now be made to some simple 

 compounds, those, namely, in which 

 the molecule consists of two dis- 

 similar atoms. 



The conception of the equilibrium 

 of centred forces which has been 

 shown fertile in the case of the 

 crystalline elements can be immedi- 

 atelv applied to the binary com- 

 pounds ; as before, each atom will 

 be represented by forces emanating 

 from a centre, and equilibrium will 

 demand closest packing of the 

 spheres used, just as in the previous 

 case. The atomic centres will now, 

 however, be of two kinds, and the 

 question arises as to whether the 

 domains of atomic influence to be 

 described about them will be all of 

 the same magnitude or whether two 

 magnitudes of spheres must be 

 employed, one for each element pre- 

 sent. This question is difficult to 

 answer by reference to the facts 

 already reviewed above ; probably the 

 only indication which the latter 

 afford in this connection is that 

 closest packing of a considerable 

 variety of different magnitudes would 

 certainly be most unlikely to lead to 

 the close, similarity of crystal form 

 observed as between the elements 

 and the binary compounds. A 

 direct answer is, however, provided 

 as the result of investigating the 

 crystalline forms of organic sub- 

 stances, to which reference will presently be made ; 

 this investigation has led to the discovery of a 

 definite law which governs the magnitudes of the several 

 kinds of atomic domain concerned in any crystalline com- 

 pound substance. It is found that the magnitudes of the 

 atomic domains in any crystalline coinpound are very 

 approximately in the ratio indicated by the fundamental 



