Jan. 17, 1889] 



NATURE 



279 



be expressed in the most general form possible, "and to 

 include all conceivable varieties of crystalline symmetry. 

 It has, however, recently been pointed out by Wulff ' 

 that the partial symmetry of certain crystals belonging to 

 the rhombohedral system— that, namely, of the minerals 

 phenacite and dioptase — is not represented among the 

 sixty-five arrangements of Sohncke. 



Other systems of points in space have also been studied 

 l)y Haag- and Wulfif, which do not exactly possess the 

 properties of a Sohncke system, and yet might reasonably 

 be adopted as the basis of crystalline structure, since they 

 lead to known crystalline forms/' These, however, and 

 all other systems of points which have been proposed to 

 account for the geometrical and physical properties of 

 crystals, may be included in the theory of Sohncke after 

 this has received the simple extension which is now added 

 by its author. 



In Bravais's network all the particles or structural 

 elements were supposed to be identical, and in Sohncke's 

 theory also there is nothing in their geometrical character 

 to distinguish one particle from another. 



In Fig. 2, the hexagonal series of dots may, as was said 

 above, be regarded as composed of a pair of triangular 

 webs, A and n; now these, although identical in other 

 respects, are not parallel, for the distribution of the 

 system round any point of A is not the same as that round 

 any point of B until it has been rotated through an angle 

 of 60'. 



It is possible, however, to conceive similar interpene- 

 trating networks which differ not only in their orientation 

 but even in the character of their particles. The centre of 

 each hexagon, for example, may be occupied by a particle 

 of different nature from A and B to form a new web, o. 

 The three webs are precisely similar in one respect, since 

 their meshes are equal equilateral triangles ; moreover, if 

 X\\& position of the points alone be taken into account, the 

 whole system would form a Bravais web,z>. if the particles 

 of o were identical with those of A and B. If, however, 

 as is here supposed, the set o consists of particles different 

 in character from A and B, the distribution round any point 

 of o is totally distinct from that round any point of A or 

 H. The points o are geometrically different from the 

 points A B. The web A is interchangeable with B,but O is 

 mterchangeable with neither. 



Now, it is precisely an extension of this kind which 

 must be given to Sohncke's earlier theory if it is to em- 

 brace all the crystalline arrangements which have been 

 alluded to above. The interpenetrating networks are no 

 longer to be regarded as consisting necessarily of identical 

 particles ; the structural units of a crystal may be of more 

 than one kind. 



The above figure represents a Sohncke system, A B, of 

 particles of one sort interpenetrated by a Bravais web, o, 

 of another sort ; but there is no reason why two or more 

 different Sohncke systems, no one of which is identical 

 with a Bravais network, may not interpenetrate to form a 

 crystal structure. 



In its most general form, then, the theory may now be 

 expressed — 



A crystal consists of a finite number 0/ interpenetrating 

 Sohncke systems which are derived from the same Bravats 

 network. The constituent Sohncke systems are in gene- 

 ral not interchangeable, and the structural elements of one 

 are not necessarily the same as those of another. 



Or, since each Sohncke system consists itself of a set 

 of interpenetrating networks, the theory may be thus 

 expressed — 



A crystal consists of a finite number of parallel inter- 

 penetrating congruent networks : the particles of any one 

 network are parallel and interchangeable ; the^e networks 

 ijroup themselves into a number of Sohncke systems in 



' Zeitschr.f Kry$t. xiii. (i8f7)p. soj. 



^ '' Die regularen Kryslallkiirper." (Rottweil, 1887.) 



3 Cf. VV. Barlow, Nature, xxix. (1834) pp. 186, 205. 



each of which the particles are interchangeable but ftot 

 necessarily parallel. ' 



The number of kinds of particles which constitute the 

 crystal may therefore be equal to the number of Sohncke 

 systems involved in its construction. 



The structural units are no longer, as they werfe in the 

 theory of Bravais, necessarily identical, but may repfesent 

 atoinic groups of different nature. 



The system in Fig. 2 consists of two sets of particles, 

 A B and ; and, if a large enough number of these be 

 taken, any portion of the system {i.e. any crystal con- 

 structed in this manner) consists of the particles united 

 in the proportion of two of the first group to one of the 

 second. Such an arrangeinent, then, may represent the 

 structure of a compound, o A,, 



" When, for example, a salt in crystallizing takes up 

 so-called water of crystallization which is only retained so 

 long as the crystalline state endures, the chemical molecule 

 salt -f water cannot be said to exist except in the 

 imagination, for the presence of such a molecule cannot 

 be proved. To obtain an easily intelligible example, 

 without, however, pronouncing any opinion as to whether 

 it may be realized, imagine the centred hexagons in the 

 figute to be constructed in such a way that each corner 

 consists of the triple molecule 3H2O, and each centre con- 

 sists of the molecule R. The chemical formula would 

 then be R -f- 6H2O, and yet a molecule of this constitution 

 would not really exist ; on the contrary, the structural 

 elements in the crystallized salt would be of two sorts — 

 namely, R and sHJo."! 



Hence it is geometrically possible that the structural 

 elements of a crystal may be different atomic groups which 

 are held in a position of stable equilibrium by virtue of 

 being interpenetrating networks. 



Whether such systems are chemically and physically 

 possible must be left for future criticism to decide.' 



Finally, we may call attention to a remarkable declara- 

 tion of faith which has recently been made in Germany 

 by one who is a recognized leader in crystallographic and 

 mineralogical science. 



Prof. Groth -^ has suggested that there may be something 

 more than a chance similarity between the theory of 

 Sohncke and the views of the eminent French crystal- 

 lographer Mallard, whose classical research upon the 

 optical anomalies of crystals has been the means of divid- 

 ing the students of this subject into two adverse cariips. 

 The explanation of Mallard has up to the present time 

 found little favour among those German mineralogists 

 who have made similar investigations. Prof. Groth has 

 now, however, declared himself in favour of Mallard, being 

 apparently induced to do so by the support which is given 

 to his views by the theory of Sohncke. 



Mallard has ascribed the optical anomalies of various 

 substances to a complete or partial intergrowth of two or 

 more crystals which combine in such a manner as to 

 simulate a symmetry of higher order than that which 

 naturally belongs to them. Now, since Mallard regards 

 each crystal as composed of a Bravais network, it is evident 

 that his views are not far removed from those of Sohncke, 

 whose system is based upon the possible intergrowth of 

 two or more networks. H. A. MiERS. 



THE EARTHQUAKE A T BAN-DAI-SAN, 

 JAPAN. 



A S it may interest our readers to know the present 

 -^*- state of matters at the scene of the great earthquake 

 which occurred lately at Ban-dai-san, Japan, we think it 

 well to publish the following narrative just received by Dr. 

 George Harley, F.R.S., in a private letter from his son, 

 who has recently visited the locality of the sad disaster. 



' Sohncke, Zeitsch. /. Kryst. xiv. p. 443. 



^ " I'eber die Molckularbesihaffenheit der Krystalle." (Festrede, Munchcn, 

 1888.) 



