EPOCH OF DE LISLE AND HAUY. 225 



height of the triangle might be one hundred, or 

 fifty, or twenty-five; but it would be found that if 

 the height were an intermediate number, as fifty- 

 seven, or forty-three, the edge of the wall would 

 become irregular ; and such irregularity is assumed 

 to be inadmissible in the regular structure of crys- 

 tals. Thus this mode of conceiving crystals allows 

 of certain definite secondary forms, and no others. 



The mathematical deduction of the dimensions 

 and proportions of these secondary forms; the 

 invention of a notation to express them ; the ex- 

 amination of the whole mineral kingdom in accord- 

 ance with these views; the production of a work 6 

 in which they are explained with singular clearness 

 and vivacity ; are services by which Haiiy richly 

 earned the admiration which has been bestowed 

 upon him. The wonderful copiousness and variety of 

 the forms and laws to which he was led, thoroughly 

 exercised and nourished the spirit of deduction 

 and calculation which his discoveries excited in him. 

 The reader may form some conception of the extent 

 of his labours, by being told that the mere geo- 

 metrical propositions which he found it necessary 

 to premise to his special descriptions, occupy a 

 volume and a half of his work ; that his diagrams 

 are nearly a thousand in number ; that in one 

 single substance (calcspar) he has described forty- 

 seven varieties of form ; and that he has described 

 one kind of crystal (called by him fer sul/ure pa- 



6 Traite de Miner alogie, 1801, 5 vols. 

 VOL. III. Q 



