claeke.] THEORY OF THE SILICATES. 15 
and the latter class offers the most serious difficulties. A basic ineta- 
silicate, for example, may have the same empirical composition as an 
orthosilieate; so that its ratios, studied apart from other evidence, tell 
nothing as to the class in which it belongs. Take for instance the 
formula Al 2 Si0 5 , which represents the composition of three distinct 
minerals, andalusite, sillimanite, and kyanite, and it admits of several 
different structural expressions. As a basic metasilicate it may be 
written 
AI \ 
A \ 
>sio 3 
•SiO^ 
Al Al 
vo/ 
and as an orthosilicate it becomes either 
Q=Al-Si0 4 =Al, or Si0 4 ^f ^>0 
If its molecular weight is a multiple of that indicated by the formula 
Al 2 Si0 5 , then the possibilities of isomeric structure become still more 
complicated. Its composition alone does not give its molecular struc- 
ture, and other evidence, as shown in the introduction to this memoir, 
must be brought to bear before the problem can be even approxi- 
mately solved. This evidence is sometimes available, sometimes not, 
as will be seen in the systematic discussion of the individual species 
later. 
A hasty glance over the entire field of the natural silicates will show, 
first, that many of them are most easily interpreted as orthosilicates, 
and, secondly, that by far the greater number are salts of aluminum. 
As regards both abundance and variety the aluminous silicates out- 
rank all the others, and from the wide range of composition which 
they exhibit we can obtain clews to their constitution. In other words, 
they furnish the most evidence, and some of it is of the highest import. 
Their relations to one another are oftentimes clear and unmistakable, 
so that the constitution of one salt is the key to that of a second; and 
thus generalization becomes possible. 
If we consider first the orthosilicates of aluminum, one general rela- 
tion is easily made apparent. By a general relation I do not mean a 
universal relation, for exceptions are possible; but only that many of 
the salts are connected by a simple regularity, or even a law. To make 
this apparent it is necessary to recognize the fact that aluminum is 
now properly regarded as a trivalent metal, its formerly supposed 
quadrivalency being no longer admissible. Formuhe in which alumi- 
num appears as a tetrad are not valid; and ferric iron, which replaces 
aluminum, follows the same rule. This point has been made clear by 
the vapor density and cryoscopic investigations of recent years, and is 
