Dr. G. T. Prior — P M :>j. 13 



worker-, of whom mention may be made of Becke, Fedorov, and 

 .tmost importance for the development of j-" 

 e been made in this direction that it wiil soon be 

 ble from the determination of the optical characters of any one 

 of these miLr; ren in thin-sections nnder the microscope 



make fairiv accurate deductions as to its other properties, including 

 the chemical composition. 



- towards the solution of the other branch of the problem 

 with which mineralog: b t - _ - been concerned, viz. the connexion 



reen irv - talline structure and chemical composition, had also been 

 take:: bef »re the period under review, in the study of isomorphous 



ips. More recently, series of brilliant researches, of which those 

 made bv Tutton on isomorphous groups of sulphates and selenates 



the most remarkable, have shown that the individual members of 

 such groups are not crystallographically absolutely similar, but that 

 quite definite and concordant, though minute, changes in the crystal 

 form and optical characters are produced by the replacement of one 



talby in ither. Host notable also in this connexion arePenfield's 



ac demonstration of the isomorphous replacement of fluorine and 



roxvl, and his investigation of the morphotropic relatior.5 :: the 

 members of the humite group of minerals. 



It was as far back ^ L850, however, that perhaps the most 

 striking advance was made towards the goal to "which mineralogy :- 

 were striving. In that year was published what might appear at 

 first nght to have little bearing upon the matter, viz. the mathe- 

 matical memoir of Bravais on the regular arrangement of points in 

 space. Bravais' work was a more complete development of the 

 geometrical investigations of Frankenheim on parallelepiped 

 networks of points known as space-lattices. In a space-lattice 

 points are arranged in snace for the most part at the intersections of 

 three sets of planes, the planes in each set being parallel and spaced 

 at equal distances apart. In such an arrangement space is divided 

 up by the points into parallelepiped cells, just as the space of a room 

 mav be regarded as divided up into so many cubic inches, the shape 

 of the cell depending upon the inclinations to each other of the three 

 sets of planes, and upon the distances apart of the parallel planes in 

 the three sets. It was assumed that as crystals are homogeneous 

 structures they must be built up of units occupying the position of 

 points in space-lattices; and according to the particular kind of 

 space-lattice, i.e. to the shape of its elementary parallelepiped cell, 

 crystals could be divided into the same seven systems into which 

 they had been grouped by the consideration of erystal-symi etry 



Since the publication of Bravais' memoir crystallographers have 



realized that crystals can be divided according to the degree of 



symmetrv they exhibit, i.e. according to the number of planes and 



: symmetry they possess, into thirty-two distinct classes, and 



: these may be regarded - it - m e extent mutually independent. 



although capable of being distributed through the seven larger 



- _ -terns according they have certain geometrical and physical 



tions in common. The fact that only thirty -two types of 



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