250 
Proceedings of the Boy at Society 
lime in Aragonite is replaced by baryta, the angular elements of the 
latter are altered from 5S^ 5' and 40° 50' to 59° 25'-5, and 38° 39' 
respectively. 
Reasoning of a similar kind may be applied in a number of other 
cases. 
Hence, we conclude that the angular elements of a mineral vary 
when the normal constituents are replaced by isomorphous sub- 
stances. 
20. Again, all crystals, except those of the cubic system, expand, 
in general, differently in different directions under the action of 
heat. This is always the case in crystals belonging to the pris- 
matic, oblique, and anorthic systems. 
Hence a change of temperature alters the angles between the 
faces, and therefore the angular elements, of crystals belonging to 
these systems, and the angular elements will in general be per- 
manently altered if the temperature be sufficiently raised. 
Hence the angular elements of a mineral depend upon the tem- 
perature to which it is or has been exposed. 
21. We conclude, therefore, that the angular elements, instead 
of being constant in all specimens of the same mineral, vary within 
narrow limits, according to the amount of isomorphous replace- 
ment and the temperature to which it is or has been exposed;* and 
further, that the amount of this variation is quite as great as the 
differences which must be made in the angular elements, given in 
Miller’s “ Mineralogy,” in order to make the calculated agree with 
the observed angle between the optic axes. It is possible that, in 
a number of cases, the angular elements of the crystal employed 
^ Many apparent cases of dimorphism may possibly be hence explained. 
Thus, Aragonite is not pure carbonate of lime, but is always associated with 
variable quantities of the carbonates of strontia, lead, or manganese. Calcite 
sometimes contains a considerable quantity of foreign substances, — such as 
protocarbonate of iron, oxide of zinc, &c. Hence, if isomorphous replacement 
produces changes in the angular elements, these differences in the composition 
of Calcite and Aragonite would be sufficient to account for the differences in 
their angular elements (supposing tliem both referred to the prismaiic system) . 
Graphite sometimes contains as much as 10 per cent, of iron ; titanic acid is 
always associated in anatase, rutile, and brookite, with variable quantities oh 
sesquioxide of iron. Differences in the angular elements may also be due to 
differences in the temperature at which the crystals w'ere formed. 
