88 THE CONSTITUTION OF ^HE SILICATES. [bull. 125. 
quadrupled, and iu that way a relation with the garnet group was 
brought out. For spodumene, regarding it also as a mixed silicate, a 
sixfold multiplication of its formula indicates its greater density, and 
its splitting up into eucryptite and albite, with partial replacement of 
lithium by sodium, is representable as follows: 
Li 2 Li 
II I 
/Si 3 8 — Al=Si0 4x 
Al=Si 3 O a — AV \A1— Si0 4 EEAl 
^Si 3 8 =Al— SiO/ 
I li 
Li Li 2 
From this grouping of atoms the transition into Al 3 (Si 3 8 ) 3 Na 3 4- 
Al 3 (Si0 4 ) 3 Li 3 is hardly more than a simple case of cleavage, and the 
relations between the three species are intelligibly expressed. Acmite, 
which yields pseudomorphs of analcite, and jadeite also, probably fol- 
low the same rule, the formula of one being typical of the others. The 
ferric molecule in babingtonite should be still another instance of the 
same kind, with Fe" 3 in place of Li 6 , and Fe'" instead of Al. 
If the formula just developed for spodumene should be sustained, it 
would seem necessary to adjust the other pyroxenes with it. In the 
case of Tschermak's aluminous constituent of augite this adjustment 
is easily made by taking the formula Al 2 MgSiG 6 six times, as in the 
case of spodumene. The parallelism between the two species is then 
representable as follows : 
Spodumene Al 6 (Si 3 8 ) 3 (Si0 4 ) 3 Li 6 
Al. augite Al 6 (Si0 4 ) 3 (Si0 4 ) 3 (A10 2 Mg) 6 
the univalent A10 2 Mg having been recognized among the micas. This 
formula serves to explain the well-known alterability of augite into 
epidote and into mica, and so far at least is useful. I do not, however, 
feel inclined to put very much stress upon it, for as yet it is only an 
expression of analogy, which may or may not prove to be valid. It 
would seem to require the recognition of all the pyroxenes as pseudo- 
metasilicates, in which case the normal series, containing only dyad 
bases, would become 
R R 
H II 
Si 3 8 — R— Si0 4x 
< >R 
\Si 3 8 — R— SiCV 
II II 
R R 
with four atoms of R given linking functions, while the other four are, 
so to speak, replaceably combined. On this basis we should write 
Diopside Mg 4 Ca 4 (Si 3 8 ) 2 (Si0 4 ) 2 
Hedenbergite Fe 4 Ca 4 (Si 3 8 ) 2 (Si0 4 ) 2 
