442 SCIENCE PROGRESS. 



(if not already accomplished) which will embrace these 

 seemingly anomalous cases, and establish the canon that 

 individuals of analogous constitution which are one in 

 crystallisation constitute a single species ; they are at least 

 so far identical as to pertain naturally to a common group, 

 whether we call it a genus or family or species or by any 

 other name." 



Tschermak in his Lehrbuch der Mineralogie, which is 

 perhaps more largely used for educational purposes than 

 any other text-book dealing with the subject, defines a 

 " Mineralgattung," which he substitutes for the word 

 species, as including all minerals which are identical in 

 chemical composition and in crystalline form. In an 

 isomorphous series of mixtures the division into species 

 is more or less arbitrary and is arranged so as to suit 

 practical convenience. 



The author who above all others has frankly accepted 

 this view of systematic mineralogy is Groth, who in 

 successive editions (1874, 1882, 1889) of his Tabellarische 

 Uebersicht der Mineralien nack ihrcu Krystallo-cheinischen 

 Beziehungen geordnet has attempted to frame a rational 

 classification in which only composition and form are taken 

 into account, and all minerals are described as simple com- 

 pounds or as isomorphous mixtures of the same. 



In this way minerals are brought together into 

 "groups" which include certain simple compounds and 

 their isomorphous mixtures. In the system of Groth there 

 is much that appears to be highly speculative ; in order to 

 secure the two features desired, (1) simplicity of constitution, 

 and (2) an isomorphous relationship between all the 

 members of a group, radicles are introduced in an arbitrary 

 manner, which is not always suggested by the results of 

 analysis. 



The assertion in the second edition that Fluorine is 

 replaceable by Hydroxyl, Ca 2 or Ca Mg by Na Fe and by 

 Li Al, Al 2 by Ca Si, and Si 2 by Ca Al, was not at that date 

 (1882) the enunciation of any generally accepted facts. 

 Subsequent study has, however, in many instances only 

 confirmed the remarkable insight which has led Groth to 



