212 Biographical Memoir ofM. Hauy. 



the molecules being once given, the angles and lines of all the se- 

 condary faces which the decrements might produce, ought to 

 be capable of being calculated beforehand. In a word, it was 

 necessary here, as in astronomy, and in physics, that, before 

 the theory could be admitted as certain, it should explain with 

 precision the known facts, and foresee with equal precision those 

 which were not yet known. 



M. Haiiy was sensible of this ; but in the last fifteen years, 

 during which he had passed the better part of his life in teach- 

 ing Latin, he had almost forgotten the little geometry that he 

 had acquired at college. He was not discouraged, however, 

 but sat down quietly to learn it again. He who so quickly 

 learned botany to please his friend, soon made himself master 

 of as much geometry as was necessary for completing his disco- 

 very, and from his first trials he found himself amply recom- 

 pensed. The hexahedral prism which he had inadvertently 

 broken, gave him, by an ingenious observation, and sufficiently 

 simple calculations, a value very near the angles of the mole- 

 cule of the spar. Other calculations gave him those of the 

 faces which were added to it by each decrement ; and on ap- 

 plying the instrument to the crystals, he found the angles pre- 

 cisely of the measurement afforded by calculation. The secon- 

 dary faces of other crystals were with equal ease deduced from 

 their primitive faces. He even discovered, that to produce 

 the secondary faces, it generally required only decrements in 

 proportions sufficiently simple, as are in general all the nume- 

 rical relations established by nature. It was then that, for the 

 third time, and henceforth without hesitation, he could say, / 

 have found all ; and it was then also that he took courage to 

 speak of his discoveries to his master M. Daubenton, whose 

 lectures he had hitherto attended modestly and in silence. It 

 may be judged with what favour they were received. M. de 

 Laplace, to whom M. Daubenton communicated them, insts^nt- 

 ly foresaw all their consequences, and hastened to encourage the 

 author to come and present them to the Academy *. 



• His first memoir, in which he treated of the garnets and calcareous 

 spars, was read there on the 10th January 1781. 



Daubenton and Bezout made the report of it on the 21st February ; but 

 it is easy to see, on reading this report, that they had not yet fully appre- 



