Feb. 2 1, 1884] 



NA TURE 



583 



instance of the lower portion of the erection being inclosed by 

 matting to form a "ground floor." Were these pile-dwellings 

 confined to the low, flat lands upon which the Bengali delights 

 to place his paddy-fields, it would be obvious that they were 

 adopted for the purpose of obtainirg a dry, wliolesome floor, 

 and security against unanticipated floods. But so far is this 

 from being the case that only very rarely is a Naga or Kuki 

 village to be found on low-lying ground, and generally they are 

 to be seen upon the slides and even the summits of considerable 

 elevations, where any danger from floods is quite out of the 

 question. Again, it might be supposed that these elevated dwell- 

 ings ^^ ere adopted as a protection against wild animals but for 

 a curious practice occasionally observable amongst the hill-men. 

 This is the habit of building upon the steep side of a hill in such 

 a manner that the back of the dwelling rests directly upon the 

 ground, while the front is supported upon piles which are of a 

 height sufficient to render the floor, throughout its length, hori- 

 zontal. Such a plan as this reduces the protection afforded from 

 vermin and wild animals to a minimum, and seems to justify the 

 belief that the fear of these creatures at least could have little or 

 no influence upon the architectural habits of the hill-tribes of 

 this part of India ; and I long ago came to the conclusion that 

 here at least the object of the pile-dwellings was simply to attain 

 in the easiest way a floor which should be exempt from the damp 

 exhalations of a tropical soil. James Dallas 



"Probable Nature of the Internal Symmetry of Crystals" 



Under this head Mr. Barlow has pulilished in Nature of 

 December 20 and 27, 1S83 (pp. 1S6 and 205) an interesting and 

 ingenious memoir. The subject being very important, but also 

 very difficult and intricate, a discussion of the new theory may 

 perhaps contribute to render our ideas a little more precise. 



Whilst Haiiy, Frankenheim, Delafosse, Bravais, and others 

 think a crystal built up of mere congruent particles, which may 

 be either the chemical molecules or rather certain aggregates of 

 them, Mr. Barlow considers the arrangement of the difterent 

 chemical atoms in the interior of a crystallised compound, and 

 illustrates some facts by this manner of viewing them. I pur- 

 pose in the following submitting some objections which arise 

 against the deductions of the author. These objections are of a 

 geometrical, chemical, and physical nature ; let us begin with 

 the geometrical ones. 



The first problem of Mr. Barlow is " to inquire what very 

 symmetrical arrangements of points or particles in space are 

 possible." He comes to this result : " It would appear that 

 there are but five." Then he describes these five arrangements. 

 What conditions are to be fulfilled by an arrangement of points 

 in space which is to be " very symmetrical,'' is nowhere said. 

 According to this indefiniteness of the fundamental notion, the 

 five kinds of very symmetrical arrangement seem to be found 

 rather by divination than by systematic reasoning. Therefore 

 the foundation of the theory appears somewhat arbitrary ; and 

 we may suspect that it is incomplete. We are in fact ccnfiimed 

 in this presumption if we consider the results of a geometric 

 research published in my " Entwickelung einer Theorie der 

 Krystallstruktur" (Leipzig: Teubner, 1879). In this book I 

 have specified all possible arrangements of points that are regular 

 and infinite, I have called a system of points ?r^?//a;- if the points 

 are disposed around every one point of the system in precisely 

 the same manner as around every other. There arc sixty-six 

 such regular systems of points possible. According to the pecu- 

 liarity of their symmetry they are subdivided into groups, which 

 correspond strictly to the known crystallographic systems. Many 

 of those arrangements of points have a hemihedric or tetarto- 

 hedric character ; others have the structure of a screw ; and 

 amongst the latter I could even suggest one particular system 

 which represents the internal structure of quartz. The latter 

 result was obtained {loc. cit. pp. 238-245) by comparing the 

 crystallographical and optical properties of quartz with those of 

 the known combination of thin laminae of mica arr.inged in the 

 manner of winding-stairs, described by Prof. Reusch fourteen 

 years ago. All sixty-six systems are in agreement w ith the prin- 

 cipal law of crystallography, the law of rational segments of the 

 axes (Wiedemann, Annalen der Pliysik, 18S2, vol. xvi. p. 4S9). 

 For example, if we have reason to suppose that a certain one of 

 these systems should represent the structure of a given substance 

 crystallising in hexagonal pyramids, then we derive geometrically 

 the same series of possible pyramids which nature actually 

 exhibits. 



Kour of Mr. Barlow's five kinds of "very symmetrical 

 arrangements " prove to be extremely particular cases of four 

 general systems of mine. The first, second, and third kinds of 

 Mr. Barlow's result from the systems which I have called the 

 "rhombendodecahedric, cubic, and octahedric system with 24- 

 points-aggregates" ("Entwickelung," pp. 165-168), if wesuppose 

 the twenty-four poiuts of the so-called " 24-punkter " coinciding in 

 one point, and if we identify this point with the centre of a 

 sphere of Mr. Barlow. Mr. Barlow's fourth kind of "very 

 symmetrical arrangements" results as a particular case from my 

 "3gangiges 6-punkt-schraubensystem " (loc. cit., Fig. 46), if 

 the sides of all hexagons are supposed to touch one another, and 

 the layers to have convenient distances. Mr. Barlow's fifth kind 

 of symmetry, not being regular in the sense defined above, can- 

 not be found amongst my sixty-six systems. Though every 

 point is surrounded by six neighbouring points at equal distances,, 

 the latter have not throughout an identical arrangement. Every 

 point of the first, third, fifth, &c., layers is situated at the centre 

 of a perpendicular prism (with regular triangular base) whose 

 angles bear the six neighbouring points of the system, but around 

 every point of the second, fourth, sixth, &c. , layers, the six 

 neighljouring points are situated at the angles of two regular 

 triangles, which do not lie parallel over one another as before, 

 one of them being turned round in its plane 60°. 



As my sixty-six systems cimprise four of Mr. Barlow's kinds 

 of symmetry, it maybe expected that they include other arrange- 

 ments besides, which may also pass as "very symmclrical." 

 For example, in a cubic aggregate of points, the centres of the 

 edges of all cubes determine a very symmetrical arrangement of 

 points, where every point has equal distances from the next 

 eight surrounding poiuts (cf. "Entwickelung," &c., p. 160). 

 From this I believe I have shown that the geometrical foun- 

 dation of Mr. Barlow's theory is somewhat arbitrary anj. 

 incomplete. 



I now come to the chemical objections, which I will explaiit 

 by an example. A chemical compound of two kinds of atoms, 

 present in equal number — for example NaCl — could, according 

 to Mr. Barlow, cry.-,tallise into the first or second of his five 

 kinds of symmetry, for either of these two kinds allows the 

 regular arrangement of two kinds of particles in equal number. 

 In the first kind of symmetry (for example) spheres are so 

 arranged that they constitute a cufjic system of points, in which' 

 the centre of each cube bears also a point of the system. By 

 putting atoms of one kind (Na) on the angles, and atoms of the 

 other kind (CI) on the centres of the cubes, we have built up the 

 structure of a crystal of NaCI. Thus eight atoms of Na .-.tanJ 

 in exactly identical manner around an atom of CI (and also eight 

 atoms of CI around an atom of Na). The atom of CI seems 

 consequently to be in equally close connection with eight atoms 

 of Na ; it has exactly the same relation to these eight atoms. 

 It appears therefore as octovalent, certainly not as univalent ; for 

 it would be entirely arbitrary to suppose any two neighbouring 

 atoms of NaCl in an especially close connection and to take this 

 couple for the chemical molecule of NaCl. By this example we 

 see that from Mr. Barloiu' s point of z'iezc both the notioJi of 

 chemical valency and of chemical molecule completely lose their 

 tresent import for the crystallised state. This objection, of 

 course, will not destroy the theory of Mr. Barlow, since chemical 

 valency does not yet belong to perfectly clear and fixed notions, 

 and since the idea of the chemical molecule in a crystal is also 

 not evident and clear. Tlie author, however, is at all events 

 obliged to show why these two notions, of such great moment 

 for substances in a gaseous state, should become completely in- 

 significant, as soon as crystallised bodies are in question. 



Finally for a physical objection. With respect to the fact 

 that most substances change their volume in congealing, Mr. 

 Barlow admits that the atoms themselves undergo an expansion 

 (positive or negative) in the act of crystallisation. Thus he 

 attributes to the atoms variability of volume, i.e. one of those 

 qualities, for the explanation of which the atomic theory has 

 been devised. Well, let it be so, but this hypothesis of atomic 

 expansion is not even found sufficient everywhere, but must be 

 assisted occasionally by auxiliary hypotheses. Thus for ex- 

 plaining the isomori'hisui of substances which contain atoms of 

 the same kind (e.g. CaCOj and FeCOj) Mr. Barlow supposes 

 that the expansion in the act of crystallising is confined to the 

 common atoms, whilst the different atoms in both substances 

 remain unaltered. 



All these objections do not overthrow the author's theory, but 

 they shake it. Perhaps they will induce Mr. Barlow to establish 



