Dec. 2-j, 1883] 



NATURE 



207 



Surely the fact thus established, that each term of a series of 

 relative altitudes of the hexagonal pyramids in which a particular 

 .-ulistance crystallises always has to some term of the series ihu-^ 

 theoretically derived a particular ratio peculiar to the substance, 

 constrains us to conclude that the above fourteen "root" forms 

 are tho=e to which all crystal forms involving regular six-sided 

 pyramids are referable, and that the actual forms are produced 

 from the " root " forms by difference in the degree of expansion 

 in the direction of the axis of the crystal as compared with other 

 directiiin~ at the time of crystallisation. 



Other allied forms, as allied octahedra or rhombohedra, can be 

 in the same way connected with some one of the five kinds of 

 internal symmetry. 



The peculiarities of (r;y'i/ij/-^™«/'»;^ displayed in twin crystals 

 can be shown to favour the supposition that we have in crystals 

 symmetrical arrangement rather than symmetrical shape of 

 atoms or small particle-. Thus if an oct.ahedron be cut in half 

 liy a plane parallel to two opposite faces, and the hexagonal 

 faces of separation, while liept in contact and their centres coin- 

 cilent, are turned one upon the other through 60°, we know 

 that we get a familiar example of a foiTn found in some twin 

 crystals. And a stack can be made of layers of spheres placed 

 triangularly in contact to depict this form as readily as to depic' 

 a regular octahedron, the only modification necessary being for 

 the layers above the centre layer to be placed as though turned 

 bodily through 60° from the position necessary to depict an octa- 

 hedron (compare Figs. 7 and 8). The modification, as we see, 



Fig. 7. Fig. 8. 



involves «o diparttire from the condition that each particle is 

 equidistant from the twelve nearest particles. 



Before closing, a few words may l^e said on the bearing of the 

 conclusions of this paper on isomorphism and dimorphism . 



First, as to isomorphism. 



The conclusion that there are but five kinds of internal sym- 

 metry possible, three of w hich indicate a cubic form, evidently 

 accords with the fact that not only the simplest combinations — 

 those in which two kinds of atoms are present in equal propor- 

 tions — but also many very complicated compounds crystallise in 

 cubes. 



Out of the regular system we generally find that for the angles 

 of crystals of different compounds to be the same there nrast be 

 some resemblance in their atom-composition, and the explanation 

 suggested is that the atoms which are common to two iso- 

 morphous compounds, e.g. the carbon and oxygen atoms in calc- 

 spar and spathic iron ore, have similar situations in the two 

 different crystals, and that the change of bulk which occurs when 

 crystallisation takes place is due to a change in these atoms only, 

 the atoms not found in both remaining /(TmjVv. 



There are, however, some cases which do not at first seem to 

 be met by this view — cases in which the atom composition of 

 isomorphous compounds has only a very parlial similarity. Am- 

 monia compounds may be specially mentioned. Thus, ammonic 

 sulphate, (NH3)2H„S04, is isomorphous with potassic sulphate 



The following suggestion would seem to enable us to suppose 

 that in this, as in other cases of isomorphism, the phenomenon 

 i< referable to the passivity of s >me of the atoms in the change 

 of bulk which accompanies crystalli-ati on. Let us write am- 

 monic sulphate 'hus (NH:j)2H„S04, and let us suppose that the 

 symmetrical arrangement is such that the groups, (NHj), just 

 occupy places which might, without altering the .symmetry, be 

 filled by additional groups H^SO^ ; that, in other words, the 

 relative position of the groups H.^S04 which are present in the 



symmetrical arrangement is precisely the same as it would be if 

 the entire mass consisted of these groups instead of consisting 

 partly of NUa groups. If now, in a^ldition to supposing that 

 in both compounds the active atoms in the process of crystallisa- 

 tion are the sulphur and oxygen atoms, and these only, we sup- 

 pose that the expansion of some of the atoms of the active kind 

 checks the expansion of others ; that only a certain proportion 

 of these atoms expands, we perceive that we may have both the 

 same amount and kind of atom expansion in the two cases, and, 

 as the natural result, isomorphism. 



Next, as to dimorphi.sm. 



It is evident that a very small change is requisite to convert 

 one kind of internal symmetry into another. Thus we have 

 already had occasion to notice that the only difference in depict- 

 ing the third and fourth kinds of ,symmeti-y is that for the former 

 the centres of the spheres in the first and fourth layers, those in 

 the second and fifth, and so on, range vertically, while for the 

 latter the centres in the first and third, in the second and fourth, 

 and so on, range in this way. 



In the ca-e of a dimorphic compound consisting of two kinds 

 of atoms in the proportion of 2 : i, e.g. water, H.,0, we 

 have only Jto suppose therefore that the same layers of atoms 

 which under one set of conditions produce hexagonal prism-, are 

 by some alteration in conditions arranged in the slightly difierent 

 way necessary to produce rhombohedral forms. Other cases ot 

 dimorphism are probably to be accounted for much in the saoic 

 way. 



Thus the following interpretation of the fact that calcic 

 carbonate, which we have seen crystallises in obtuse rhombo- 

 hedra as calc-spar, sometimes crystallises in six sided trimetric 

 prisms as aragonite may be offered. 



We have already endeavoured to show that the first or second 

 l.ind of internal symmetry is that proper to calc-spar. We will 

 now endeavour to show that the fifth kind of internal symmetry 

 (Fig. 6) is proper to aragonite. 



Alternate layers of spheres (plan b) will represent the oxyten 

 atoms, and the other alternate layers the calcium and carbon 

 atoms ; the central layers of the triplets above alluded to, viz. 

 the second, the fourth, the sixth, &c., being the o.xygen layers ; 

 tbe calcium and carbon atoms in the remaining layers will be 

 symmetrically arranged (plan/). From the fact of the crystals 

 being trimetric, the layers containing the last-named atoms, 

 which, considered apart from the o.xygen layers, are in the fourth 

 kind of symmetry, probably have the arrangement above de- 

 scribed, in which the less numerous spheres form zigzags, the 

 stack in this case having a different symmetry about three axes 

 at right angles to each other (Fig. 6). 



The fact that the dimorphic varieties of the same substance 

 have different densities is in harmony with the supposition that 

 different sets of the atoms are concerned in the different cases ; 

 that the active atoms which produce one form are not those, or 

 those only, which produce the other. 



It is not always necessary to refer two incompatible crystal 

 forms of the same .substance to two different kinds of internal 

 symmetry : for example, from the third kind of internal sym- 

 metry we can produce square-based octahedra, and we can also 

 produce right-rhombic prisms, and in accord with this we have 

 the well-known fact that right-rhombic prisms of sulphate of 

 nickel, N2S047H.,0, when exposed to sunlight are molecularly 

 transformed, and, though they neither liquefy nor lose their form, 

 when they are broken are found to be made up of square-based 

 octahedra several lines in length. William Barlow 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE 



Cambridge. — The following awards (among others) have 

 been made at St. John's College on the results of the examina- 

 tion for candidates who have not yet commenced residence : — 



For Mathematics: H. F. Baker (Perse Grammar School, 

 Cambridge), Foundation Scholarship, raised for two years to 

 75/. a year ; A. W. Flux (Portsmouth Grammar School), Minor 

 Scholarship of 75/. a year ; P. T. Fagan (Highwood School, 

 Weston), Exhibition of 50/. a year ; H. R. Norris (University 

 College School), Exhibition of 30/. a year. 



For Natural Science : G. S. Turpin (Nottingham High School 

 and Owens College, Manchester), Foundation Scholarship raised 

 for two years to 75/. a year ; P. Lake (Newcastle College of 

 Science), Minor Scholarship of 75/. a year; W. Harris (Brad- 

 ford Grammar School), Exhibition of 50/. a year ; W. M. Mee 



