August ii, 1910J 



NATURE 



191 



valencies of the corresponding elements. Since the mole- 

 cules of nearly all the binary compounds which have been 

 crystallographically examined contain in the molecule one 

 atom each of two elements of the same valency, the poly- 

 hedral cells from which a crystalline binary compound must 

 be supposed built up are all, in general, of approximately 

 the same magnitude. The fact that most binary com- 

 pounds, like most elements, crystallise in either the cubic 

 or the hexagonal system, represents one of the simple 

 results of this law of valency volumes. 



The binary compounds thus, in general, affect crystal- 

 line structures which arc derived from the cubic or the 

 hexagonal closest-packed assemblage of equal spheres ; one- 

 half of the spheres, selected homogeneously, represent atoms 

 of the one element and the remainder atoms of the second 

 element. The mode in which the necessary homogeneous 

 selection may be made in the cubic assemblage, without 

 filtering the values of corresponding dimensions in three 

 rectangular directions, is shown in a model. 



The crystalline forms of the binary compounds are in 

 accordance with what has been above foreshadowed. 

 Table I. indicates that in geometrical respects the crystal- 

 line binary compounds closely resemble the elements ; 

 68-5 per cent, of those examined are cubic and 19-5 per 

 cent, hexagonal, the remaining 12 per cent, crystallising in 

 systems of lower symmetry than these. The axial ratios, 

 <x \ c, of all the hexagonal binary compounds known arc 

 stated in Table II. ; all approximate closely to the value, 

 a : c= I : 0-8165, for the model hexagonal closest-packed 

 assemblage of equal spheres. 



Table II. — Hexagonal Binary Compounds. 



Keryllium oxide ReO I:g*Si53 

 Zinc oxide ... ZnO i : o'8o39 

 Zmc sulphide.. ZnS l:o'8l75 



Cadmium sul- 

 phide Cd.S I : o'Sioq 

 Silver iodide. Agl I:0-Sic6 

 The ratio, I : ^'(5) I : 0-8165 

 In connection with the elements and binary compounds, 

 it' is noteworthy that the mode of treatment described 

 appears practically to eliminate molecular aggregation of 

 the atoms as a factor in determining the crystalline struc- 

 ture ; that is to say, the distance separating two neigh- 

 bouring atom centres is the same whether those atoms 

 belong to the same or to different molecules. Another 

 interesting fact is that, whilst the elements and binary 

 compounds for the most part crystallise in the cubic or 

 hexagonal systems, substances of greater molecular com- 

 ple.xity rarely crystallise in these highly symmetrical 

 systems ; thus, of a great number of organic compounds 

 examined, 2.5 and 4-0 per cent, only belong to the cubic 

 and hexagonal crystalline systems respectively (Table I.). 

 This observation is important as one of many indications 

 that the cells into which the crystal structure of a com- 

 plex compound are panitionable are not, in general, all 

 of the same volume. Further investigation shows that the 

 volumes of the polyhedral cells representing the atomic 

 domains of the several elements present in a complex 

 crystalline compound are governed by the law of valency 

 volumes, to which reference has already been made. The 

 correctness of this conclusion concerning the proportionality 

 between the numbers expressing the fundamental valencies 

 of the elements and the volumes of the corresponding 

 spheres of atomic influence has been abundantly verified, 

 not only by the laborious process of working out a large 

 number of cases, but in several other ways which may he 

 more rapidly indicated. The following are illustrations of 

 the latter kind of verification. 



Table III. states the composition and axial ratios, 

 a ; b : c. of a series of four crystalline minerals which differ 

 in composition by the increment, Mg„SiOj ; the sums of 

 liie valencies of the atoms composing the different mole- 

 cular aggregates .ire staled under the heading W. The 

 increment, Mg„SiO,, also occurs as the crystalline mineral 

 forsterite, of which the axial ratios have been determined. 

 It is evident that the ratio alb has approximately the same 

 value of i-oS for all four members of the series, and that 

 practically all differences in relative dimensions are ex- 

 pressed by the ratio c'b. On dividing the valency volume. 

 W, by the corresponding value for c'b in each case, the 

 quotients 11.7, 12. i, 12-3, 12-4, and 12-7 are obtained re- 

 snectively for the substances prolectite, chondrodite. humite, 

 (linohumite, and forst.ritp. The relative dimension, c'b. 

 NO. 2128, VOL. 84] 



is thus roughly proportional to the sum of the valencies 

 in this set of minerals. The comparison may, however, 

 be made more accuratelj' by including the changes in both 

 relative dimensions, a/b and cjb, in the calculation, in the 

 following manner. The " equivalence parameters " are 

 the rectangular dimensions, x, y, and s, of a rectangulzir 

 block having the volume W, and are in the ratio of the 

 axial ratios a : b : c. The parameters * and y preserve 

 almost constant values throughout the series, and addition 

 of the increment, Mg,SiO,, leads to a practically constant 

 increase of about 2-Sb in the dimension : on passing from 

 one mineral to the next in the series. The mineral 

 forsterite also gives nearly the same x and y values as 

 before, and its s value, 2. 87, is equal to the differences 

 between consecutive pairs of s values in the main series ; 

 these differences vary between 2-85 and 2-88. The axial 

 ratios and equivalence parameters of forsterite can, indeed, 

 be calculated with considerable accuracy from the data 

 available for the series of four minerals. 



T.^BLE III. — Tlie Humite Minerals. 

 Prolectite ... Mg.SiOj 2Mi;(F,OH) ... W = 22 



Chondrodite ... Mg.,{SiOj\„ 2M"g(F,OH) ... W = 38 



Humite Mg.lSiOj),, 2Mg(F,OH) ... W = 54 



Clinohumite ... Mgr(SiOj)j, 2Mg(F,OH) .. W = 70 

 The increment is Mg,SiOj, namelv, forsterite, with 

 W = i6. 



Axial Ratios Equivalence Parameters 



Prolectite 



I -0803 : I : I ■8S62 



59 : 2-210 : 4-169 

 Diff. = 2851 



Chondrodite ... 1-0863 ■ I '■ 3'I447 2-425 : 2-232 : 7-020 



Diff. = 2-877 



Humite 1-0802 : I : 4-4033 2'428 : 2247 : 9-897 



Difif. = 2-858 

 Clinohumite ... I -0S03 : I : 5-65SS 2-435 '■ 2-254 : 12-755 



Values for the increment, forsterite. 



Oberved '■0757 : I : I 2601 2449 : 2 277 ; 2-869 



Calculated 1-0823 : I : 1-2775 2-429 : 2245 : 2869 



The relations here displayed may be rendered more 

 obvious bv a series of models (Fig. 5). Rectangular blocks 

 h.iving as the horizontal dimensions the x and y values, 

 and as vertical dimension the z value, for forsterite, when 

 superposed upon a similar set of blocks having the corre- 

 sponding dimensions for prolectite, form a stack exhibit- 

 ing the equivalence parameters of chondrodite ; super- 

 posing on this a second set of forsterite blocks leads to a 

 stack .showing the equivalence parameters of humite, and 

 on again repeating the operation, a stack with the 

 dimensions of clinohumite results. From the numerical 

 data and the models exhibited, it must be regarded as 

 definitely proved that, in this series, the volumes appro- 

 priated by the constituent atoms are, in any one member, 

 directly proportional to the valency numbers of the corre- 

 sponding elements. 



.Another set of observations of a very convincing 



char.-ieter, although of a totally different kind, is laid out 



in Table IV. Experimental determinations of the mole- 



T.AHLE IV. — ^folecular Volumes of the S'ormal Paraffins 



at their Melting Points. 



Molecular volumes 



74 



92 



C,iH.,4 

 C,„H„„ 



c,;h;, 



C^H,., 



c.sH.,; 



C^Hjs ... 104 



Cis^^!^ ... no 



C,<,Hj„ ... 116 



C.,„Hj., .. 122 



C.,,H,, ... 12S 



C^Hj,, ... 134 



C.jjHj, ... 140 



C.,^H5„ ... 146 



C^H,^ ... 164 



CaiHfi, ... 188 



C:,.,HBrt ... 194 



C,;H-„ ... 212 



Melting point <° Observed Calculated 



at/' asW'xS 



-26-5 ... 201-4 --- 201-96 



-I2-0 ... 219-g ... 219-78 



... - 6-2 ... 237-3 ... 237-60 



... + 4-5 ••• 255-4 ... 255-42 



.. -noo ... 2732 .. 273-24 



,.. -f-i8-o ... 291-2 ... 29106 



4-22-5 ... 309-0 ... 30888 



.. -(-28-0 ... 326-9 ... 326-70 



.. -4-32-0 344-7 --- 344"52 



.. 4-36-7 ... 362-5 ... 362-34 



... -i-40-4 ... 380-3 ... 380-16 



... -f-44'4 -•• 398-3 -•- 39800 



.. 4-47-7 --- 4>6-2 ... 415-80 



... +51-1 ... 434'l •■• 433'62 



.. 4-59'5 --- 4S7'4 -•- 487'o8 



,.. 4-68-1 ... 558-4 ... 558-36 



,.. 4-70-0 ... 576-2 ... 576-lS 



... 4-74-7 ... 629-5 ••■ 629-64 

 ean value of S=^2'970. 



