171 Reply to Mr. Brooke. 407 



and sufficient to justify us in considering 2 and 3 as the stand- 

 ard values of the second and third columns, from which 

 values the deviations are comparatively inconsiderable. 



It appears then that all the above discordant analyses are 

 nearly represented, and most of them very nearly, by this 

 law: — that the atoms of the ingredient S, those of A and 

 Fes taken together, and those of Fe, Mn, C and M, taken 

 together, are respectively as the numbers 4, 2, 3. If we put 

 this law into a formula, according to the notation explained 

 elsewhere, it will stand thus : 



Garnet = 4 S + 2 A, Fes + 3 Fe, Mn, C, M ; 

 which may also be put in this form, 



2(S + A, Fes) + 2S + 3Fe, Mn, C, M. 

 Or this, 2(S + A) + 2S + 3C: 



where, in the latter formula, it is understood that a portion 

 of A may be replaced by Fes, and a portion of C by M, Mn 

 or Fe. ' 



Since we can include the above analyses under a simple 

 arithmetical law by supposing such replacements, while we 

 can exhibit no such law without this supposition, this example 

 appears to prove the usefulness of the doctrine that ingre- 

 dients do thus replace each other; and this is the doctrine of 

 isomorphism. Such is the kind of evidence on which the 

 establishment of this doctrine must rest; and its certainty 

 will depend on the exactness with which it will thus reduce 

 to a common formula a number of analyses of minerals, agree- 

 ing in crystallographical and physical character. The above 

 case is taken unfavourably for the doctrine of isomorphism; 

 for if several different chemical formulae ever meet under one 

 crystalline form, this is perhaps most likely to occur in 

 crystals of the tessular system, like garnet. It has however, 

 I think, been shown, that in the case thus taken, the formula 

 includes all the analyses, at least within 4 or 5 per cent. ; 

 wliile the doctrine of essential constitution is absolutely inl 

 applicable, inasmuch as silica is the only ingredient common 

 to all the cases. 



A similar examination of a number of analyses of amphi- 

 bole, with a similar result, is given by Bonsdorf in the Ann. 

 de Chim. torn, xx., and a similar discussion of pyroxene, by 

 Rose, in the Aim. de Chim. tom. xxi. Undoubtedly in various 

 other minerals the true constitution remains still to be dis- 

 covered, and can be oi)tainc(l only by the laborious process 

 of making or collecting many good analyses of the mineral, 

 well ascertained and pme, and then conijiaring these in a 

 manner somewhat similar to that employed above, so as to 



discover 



