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 : 



Atomic volume. 



Carbonate of Zinc, 175-33 



Carbonate of Magnesia, 181*25 



Mesitine, 186-26 



Carbonate of Iron, 188-50 



Carbonate of Manganese, 202-29 



Dolomite, 202-36 



Calc Spar, 231-20 



" 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 had 

 to Brewster's Philosophical Magazine for April, 1841, p. 255. 



" Since an increase of atomic volume is connected in the above min- 

 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 calc spar diminished by a heat of 180° F. 

 in the proportion 1 : t-tj"ot'S"BT' ar, d 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 coinci- 

 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 or 

 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, Rose 

 and others, to result in many instances from the different temperatures 



