221 
of Edinburgh, Session 1863 - 64 . 
developing the other, each inscribing and circumscribing the other, 
giving both as alternate forms, as the radius lengthens or shortens. 
The remaining polyhedron, viz., the tube or hexahedron stands 
out from all the others, and is, in fact, singular, inasmuch as it has 
no proper poles, and seems unsuited for polarized action. 
The author therefore fixes upon the dodecahedron and the 
icosahedron as the geometrical types of the molecules of bodies. 
He conceives that their molecules may possibly consist of 12 or 
of 20 chemical elements or units, either single units, binary units, 
ternary units, &c., as the case may be. And he proceeds to calcu- 
late solely from atomic weights, and without any reference what- 
ever to atomic volumes, the densities of liquids and solids on this 
hypothesis. 
But previously to entering upon details, he finds it necessary to 
allude to the law of molecular differentiation. Not that there is 
anything new in this law ; for it is merely the further operation, 
when the stability of a molecule is threatened by heat or otherwise, 
of the grand principle of all chemical synthesis, viz., the concur- 
rence and apposition of dissimilar particles ; hut it modifies the 
number of elements in a molecule according to the risks which that 
molecule has run ; and consequently it modifies also the specific 
gravity of the mass. Thus taking X to represent any chemical 
element ; instead of simple dodecatoms X^2 or icosatoms X20, both of 
which are isometrical as well as homogeneous, we may have a 
composite molecule, Xj2^2o=^32j consisting of both, the one diffe- 
rentiating the other, and thus securing a greater stability for both. 
Similarly single elements of X may differentiate both X^2 ^^4 X20, 
giving X X^2^ = Xj^ and X X2oX = X22. And these two, in their 
turn, may differentiate each other, giving X X^2 ^j ^ ^20^ = 36 X. 
And here one of the limits of the theory as a method of reaching 
the construction of molecules presents itself. Thus the compound 
undifferentiated dodecatom (Xj2)i2? occupying four volumes, must 
give the same specific gravity as X Xj2XX X2 qX = 36 X, occupying 
one volume; for 
12xl2X 
4 
= 36 X. 
To obtain densities in the familiar form of specific gravities the 
molecule or unit volume of water requires to be determined. And 
