222 J. D. Dana on the Isomorphism and 
pounds of unlike atomic proportions are heteromerous, whether 
isomorphous or no 
Without farther introduction I proceed with the details of the 
isomorphism among unlike compounds; and then giving the 
researches into the atomic volume of these and other species. 
I, CHRYSOBERYL, Be AI—CHRYSOLITE, (Mg Fe)? Si-SERPENTINE, 
2Meg* §i?-+3Mg H?—EPSOM SALT, Mg 8+7H—VILLARSITE, 
4(Fe, Mg)* Sit+-3H—PICROSMINE, 2Mg? Si?-+-3H. 
The magnesian minerals, Chrysolite, Serpentine and Villarsite, 
are well known to be isomorphous, and have been the subject of 
recent remarks by Hermann.* We now add the totally unlike 
mi se Chrysoberyl and Epsom salt. 
A brachydiagonal prism in Chrysolite has the angle 80° 53’, 
a corresponding one in mere inag 6% 119° 46’. The tangents of 
half these angles are nearly as 1:2; and a vertical prism ofthe 
former has the angle 49° 50’ and one of Chrysobery! 70° 40’, giv- 
ing the relation of 1: 14. The former planes, referred to the same 
fundamental form, are om Px and 2P x, and the latter 
2. sf pein a axes of these species as 
given by von Kobell a are as follows: 
: b. ; 
iy pmemereeryl, ge! gteey eat oof ache . 088 ts ott 
Chrysolite, 5 ‘ 723. cd. : Oe 
The -93 of Chrysolite it is seen is 's double of -A7 in Chrysobetie 
and 1:1733 is double of 0:58 showing a simple ratio. If w 
take for eeyen the vertical prism above roted to ( “49° 50’) 
as the prism o P, it gives b:c=1:0-465; which is almost identical 
with that ‘for chrysoberyl. We add farther, though other evi- 
dence is unnecessary, that the angles of the corresponding rhom- 
- octahedrons in each of the above Species, are given as fol- 
Chrysolite, ‘ * : 4 189955! 85°15! 108°31’ 
Serpentine, . ; : ‘ 189 34 88 26 105 26 
Villarsite, : é - 139 45 86 56 106 52 
Chrysobery], 139 53 86 
In Picrosmine, a brachydiagonal prism has the angle 117949”, 
which is near that of Chrysoberyl, and a vertical prism the angle 
53° U8’, the corresponding angle in Chrysolite being 49° 50’. 
pag prism being the prism cP, it gives b:c=1:0'5, while it 
s 1: 0:47 in Chrysoberyl, and 1: 0-465 in Chrysolite 
Epsom salt has the same axes as Chrysolite, except that for the 
assumed cemomontal form,+ the vertical axis is about one-half ei 
* J, f Pr. Chem., 1849, xIvi, 229. 
+ It may not be ‘understood by all my = that the axes of ES beac are not 
pon of fixed length for each erystal, vs only the axes ea peo a form ax 
in the crystal assumed as the fundamental form—a form of freque 
