130 ANNALS NEW YORK ACADEMY OF SCIENCES 



on mineralogy, now seriously offered to us in illustration of the fixed theo- 

 retical composition of each of those minerals. 



Nor is the certainty increased in very many cases by deduction of the 

 actual ratios existing between the components included in the chemical 

 analysis of a supposedly pure mineral. A chemical formula merely marks a 

 possible relationship and may be but a blind and even misleading guide. 

 The extraction of a formula is not confined to an independent mineral and 

 is not a certificate of homogeneity. Whatever the figures of an analysis 

 obtained from a pinch of soil or clay or from a fragment of brick, it would 

 go hard with any analyst if he could not devise therefrom some skeleton of 

 a formula. Yet these spectral shapes hover over all the early history of 

 mineral analysis, and their existence is often brought forward as the chief, 

 generally as the sufficient evidence to justify promulgation of new mineral 

 names or supposed new reactions in mineral genesis. 



It is obvious that the initial process in the calculation of a formula, i. e., 

 division of the percentage of each component by its molecular weight, is 

 one that tends to reduction of the comparative proportion of the minor 

 components, and thus to minimize and conceal the lack of homogeneity in 

 a substance subjected to analysis. An investigation of mineral material 

 therefore which ends with the presentation of the bulk analysis, even with 

 an annexed calculation of oxygen or molecular ratios and formula of the 

 crude aggregate, is surely incomplete. 



Constitution of Crystallized Minerals, 



The prevailing method of the analytical chemist, just discussed, seems 

 to have been founded upon two exaggerated views concerning the constitu- 

 tion of crystallized minerals: 



1. The assumption of their practical homogeneity and purity, an error 

 which has crowded the literature of the science with hordes of discordant 

 analyses and a series of poorly described and uncertain species. 



The revelations of the microscope, particularly by means of polarized 

 light, have long since established that a mineral, however well crystallized, 

 often even when limpid and free from visible enclosures, may be but an 

 aggregate, with one constituent in predominance in selected specimens, 

 enveloping a number of others. In the same association or vein, particu- 

 larly in vicinity of the matrix or vein-wall, phases of intermixture with 

 increasing amounts of the minor constituents commonly pass into less 

 perfectly crystallized forjns of the first predominant unit, and often into 

 earthy or massive aggregates in which one or another of the associates rises 



