BarLtow—A Mechanical Cause of Homogeneity of Crystals. 599 
_ extent, parallel to the variety of arrangement for the same balls 
_ in closest-packing thus shown to be possible when several different 
_ grouplets not identical with their own mirror-image are present. 
_ Thus Hantzsch, says' :—“ Bodies having two asymmetrical carbon 
atoms of the general formula Cabc, Cdef, possess the component 
rotations A and B, which can either of them be present in the 
positive or the negative configuration. Thus four combinations, 
and corresponding to these four optical isomers, are possible corre- 
_ sponding to the expressions — 
J. +:A4 Diecmuadis WA On <= Ab Ae OS A 
+B —B + B —-B 
Of these the first and fourth, and also the second and third have 
opposite and similar specific rotations, and thus correspond to 
compounds which show mirror-image isomerism. Consequently 
the first and fourth, and also the second and third, can together 
form inactive mixtures, but not so the first or the fourth in com- 
bination with either the second or third. Similarly, bodies with 
three asymmetrical carbon atoms of the structure formula Cadc, 
Cde, Cfgh, if they possess three component rotations Ey iwated by 
A, B, C, are possible in 2° = 8 isomerides. 
These conclusions are in a very striking manner borne out by 
facts. For example, when camphor is converted into borneol two 
isomerides, a dextro stable, and a laevo labile modification are 
produced, and these can be separated from one another by simple 
crystallization ; they both furnish on oxidation the same original 
camphor. The laevo-camphor, in its turn, in the same way fur- 
nishes means for the forming two complementary compounds, as 
appears in the following table :— 
Dextro-camphor, eae borneol. 
99 
Leevo-camphor, | Reehe labile * 
A difference of stability, and of some other properties such as, 
1“¢ Grundriss der Stereochemie,’’ p. 18. 
2“ Stéréochimie’’ par van’t Hoff u. Meyerhoffer, p. 54. Comp, Bischoff’s 
‘‘ Handbuch der Stereochemie,’’ p. 359. And also comp. ‘‘ Stéréochimie,’’ p. 57, as to 
Zincke’s observation respecting the glycols. Also ‘‘ Hantzsch’s Grundriss &c.,’’ p. 42. 
