370 Review of Dana’s Mineralogy. 
* 
ranged axes. Dr. H. Kopp has lately shown that isomorphic bodies 
have equal atomic volumes, and draws the conclusion that isomorphism 
is owing to an equality in the volume of the atoms, or plesiomorphism 
to an approach to equality. Those bodies that replace one another 
without changing the crystalline form, have atoms of equal volumes, 
and their isomorphous compounds are also equal in atomic volume. 
He obtains the atomic volume by dividing the atomic weight by the spe- 
cific gravity, and thus shows for a great number of the acknowledged 
isomorphous or rather plesiomorphous minerals, a close approach to one 
another, in the volumes of their atoms. For example, for the carbo- 
nates of zinc and magnesia, mesitine, carbonates of iron and manga- 
nese, dolomite, and calc spar, he found the atomic volume as given in 
the following table : 
2 Atomic volume. Axis a. Angle 
Carbonate of Zinc, 175°33 0-807 107° 40 
Carbonate of Magnesia, 181°25 0-812 107 25 
Mesitine, 186°26 0815 107 14 
Carbonate of Iron, 188-50 0-819 107 0 
_ Carbonate of Manganese, 202-29 0-822 | 106 51 
Dolomite, ~ —_ 202°36 0-833 106 15 
Calc Spar, 231-20 0°854 105 15 
“The above table, which contains also the axis a, and the angle of 
the rhombohedron, of each of these minerals, illustrates the interesting 
fact, which he next deduces, that the axis increases, or the angle di- 
minishes, as the atomic volume increases. He also derives a formula 
for calculating the volume from the length of the axis, and finds it to 
give results coinciding very nearly with the above. ‘These principles 
are illustrated by numerous examples, for which reference may be 
to Brewster’s Philosophical Magazine for April, 1841, p. 259. 
“ Since an increase of atomic volume is connected in the above mil- 
erals with an increase of the axis a, and heat, by diminishing the den- 
sity, necessarily increases the volume of the atom, therefore the axis 
a must be lengthened by heat, as is actually the case. Mitscherlich 
found the specific gravity of cale spar diminished by a heat of 180° F. 
in the proportion 1: +.594g¢7, and Dr. Kopp, by calculation determines 
that for 180° F. the angle of the crystal should be changed 7 37", 
which is but 57” less than Mitscherlich’s observations—a near coinck 
dence, when we consider the difficulties which necessarily accompany 
the direct measurement of the dilatation and change of angles. 
‘These principles proceed on the hypothesis of simple spherical o 
spheroidal atoms for compound bodies, and the theory of atoms propo 
sed by the author receives from them strong confirmation. 
“ Dimorphism.—Dimorphism has been shown by. Mitscherlich, Rosé 
and others, to result in many instances from the different temperatures 
