648 Scientific Proceedings, Royal Dublin Society. 
equal, 1.e., to be isomorphous or isogonous ; (b) in addition to this to 
be capable of being intercalated in such a way that variously-shaped 
masses of the two assemblages have their corresponding planes of centres 
similarly orientated. 
We have already distinguished operative from inoperative balls 
in an assemblage,” operative balls being those on which the general 
form of the assemblage depends, and inoperative balls those which 
lie between the operative ones without doing anything towards 
regulating the relative situations of the latter. Bearing this in 
mind, the following proposition is evident :— 
If in two different assemblages the operative balls are the 
same, and, where more kinds than one are found, are present in 
the same proportions, the arrangement of the operative balls will, 
af the conditions are the same, be identical in both assemblages, and, 
unless a difference in the arrangement of the inoperative ones 
sufficient to produce a difference in the generic symmetry exists, 
the two assemblages will be completely isomorphous.*? They will 
also be capable of being intercalated in any proportions without 
any lessening of the closeness of packing. The inoperative balls 
may obviously be either entirely or partially different in the two 
assemblages. 
Far less resemblance than is here postulated will, however, 
suffice to make two assemblages practically isomorphous, and far 
less will too suffice to make them capable of becoming intercalated 
in such a way that the masses of different kinds have their corres- 
ponding planes of centres similarly orientated. 
For, on the one hand, they will be practically isomorphous if 
the inclinations of the planes of centres to one another in one 
assemblage be the same as the inclinations of corresponding 
planes to one another in the other assemblage, and that even 
1 The term isomorphous is sometimes applied to two crystals when one has hemi- 
hedral or tetartohedral symmetry and the other has not, so long as all corresponding 
angles are the same: e.g., dolomite and calcite. Compare Groth’s ‘‘ Physikalische 
Krystallographie,’’ p. 278. The term isogonism has been suggested to cover cases in 
which the resemblance is incomplete and only extends to some of the crystal zones. 
See Fock’s “‘ Chemical Crystallography,” Pope’s translation, p. 167. 
2 See p. 547. 
3 Thus, as Dumas puts it, one may in a building substitute one stone for another, 
and yet the building may retain its form and general properties. 
—_——s- =~ oo So 
