ilarke.1 CONSTITUTION OF TOURMALINE. 27 
The two analyses by Penfield and Foote, however, conform sharply 
30 their formula, thus: 
De Kalb, white Ho 9 .g.,B;,.,i.;Si t iO:u. ,s 
Haddam Neck, green H. J .,.. 1 sB:;. l »;Sir,0 .-,,. .-, „ 
The Gouverneur and Hamburg tourmalines represent the extreme 
range of variation; a variation which is too large to be safely set aside 
is due to analytical errors or to impurities in the material analyzed. 
Some of the formulae approximate to mine, some to that of Penfield 
ind Foote, and hence it seems probable that neither formula, without 
some qualification, can safely be taken as final. 
In order to be satisfactory, a constitutional formula must fulfill several 
•onditions. First, it must adequately express the composition of the 
jompound in question, covering all of its variations. Second, it must 
}e readily applicable to the full discussion of analyses, so that the dif- 
ferent isomorphous salts which are commingled in a mineral species 
;an be separately identified and given reasonable expressions. Finally, 
t should indicate the relations between a species and the other min- 
erals with which it is allied, or into which it commonly alters. A 
brmula can be fully adopted only when all of these conditions are 
satisfied. The third condition, which relates to function, is equally 
mportant with the other two. 
With the tourmalines, the micas seem to be most nearly akin. In 
>ach group we have to consider comminglings of isomorphous niole- 
snles, and when tourmaline alters, a mica is commonly the product of 
he reaction. In composition, also, the two groups show an apparent 
parallelism. With the lithia mica, lepidolite, lithia tourmalines occur; 
nth muscovite and biotite, the common iron tourmaline is associated; 
i.nd the magnesian tourmalines, which show the minimum of alumina 
q their composition, are similarly allied to phlogopite. This relation- 
hip, if it is real, should be suggested in the formula' assigned to the 
everal species. 
To the commoner micas a simple series of formulae can be easily 
iven, thus : 
Muscovite AlKSiO^KH,, 
Biotite Al 2 (SiO ( ) ;! Mg>KH, 
Phlogopite Al,(SiO.,)3Mg : ,KH 2 ; 
i id to these types, or mixtures of them, most micas are referable. The 
uiations and exceptions have been considered elsewhere, and need 
)t be discussed here. 
With these fundamental molecules the corresponding salts of the 
< urmaline acid H 29 B :i Si (j 3 i, or H I4 Al5B3Si c O; n are structurally corre 
I ted. The subjoined formula' are sufficient to make this point clear; 
» id to render the splitting up of tourmaline, its alteration into mica, 
< mewhat intelligible. 
