TIN. m.LVl'loN OF MINKUAI.S To TIIK KI.KMF.NTS 231 



: 



:m- chlorine, iodine, and bromine, which are completely isomor- 



phous in such simple salts as those of silver. Fluorine enters as an 

 i-;omorphous element with them only when the molecule becomes 

 complex. MS iii the silicates, when hydroxyl (OH) may also replace 

 them, as in topax. 



From a consideration of the above isomorphous groups of ele- 

 cnts which may replace each other in the simple mineral mole- 

 cule, not only will the number of elements in each isomorphous 

 group increase with the complexity of the mineral molecules, but 

 in the more complex silicates whole groups of elements replace 

 each other. In the amphiboles such groups as Naa, H 2 , (A1 2 OF 2 ), 

 (FejOF 2 ), (A1 2 O(OH 2 ) 2 ), (Fe 2 O(OH 2 ) 2 ) are considered to be isomor- 

 phous. It is readily appreciated that mineral species are with 

 rare exceptions never pure chemical compounds, constant in their 

 percentage composition, where such replacements are possible. In 

 the attempt to deduce from the percentage analysis of any min- 

 eral its formula, and thus its relation to other mineral species, it is 

 always necessary to group the equivalent elements, or those which 

 belong to the same isomorphous groups, under the same head. 



Thus the formula of garnet is written R 3 " R 2 '"(SiO 4 )3, where R" 

 stands for all those bivalent elements or groups of elements which 

 may replace each other in the garnet molecule ; R" usually is Ca, 

 Mg, Fe, Mn ; and R'" is usually Al, Fe, Cr, Ti, and Mn. TiO 2 may 

 also replace SiO 2 . In the analysis of a garnet the following per- 

 centages were found ; the formula would be calculated as follows : 



The general formula will then be: 

 3(R"0)R*'"03(R""Q2) or 



'0 2 ) 3 



by substituting the elements actually present for R, the for- 

 lula for this garnet is (Mg . Ca . Fe . Mn)(Al . Cr . Fe) 2 ((Si . Ti) O 4 ) 3 ; 



