REPORT OF THE DIRECTOR I917 I5I 



inevitably thrust upon him the key to the mystery of the mathe- 

 matical interrelation of these forms. But without a mind prepared 

 to interpret this chance occurrence, without the imagination reaching 

 out to its interpretation, the incident would have meant no more 

 to him than to his friend who stood beside him. Bergman, although 

 unknown to Hauy, had had an almost identical incident called to 

 his attention by his pupil Gahn, without fully realizing its signifi- 

 cance. Bergman did not voice the cry, which on the lips of his 

 illustrious successor has become historic, "Tout est trouve." 



Returning to his cabinet, Hauy lost no time in verifying the 

 principle which was thus revealed to him. Under his hammer 

 were sacrificed successively a scalenohedral crystal of calcite of the 

 form known as " dog tooth spar," and another of a low rhombo- 

 hedral habit; in each case the primitive cleavage rhombohedron 

 appeared from the fragments as he expected that it would. With 

 the idea of developing the " primitive form " from other species he 

 ruthlessly attacked the other treasured specimens of his little collec- 

 tion and his sacrifice was fully justified by the results, for the cleav- 

 age fragments in many instances furnished him with the basis, 

 significantly termed by him le noyau, upon which the complicatedly 

 modified crystal combinations were, as it were, built up. He con- 

 ceived the theory of modified forms, built up from the primitive 

 by diminishing layers of crystal particles (dicroissements) , each 

 successive layer having a definite relation to the preceding one and 

 to the primitive nucleus. 



But the Abbe Hauy had spent fifteen years of his life in teaching 

 Latin and had, like so many of us, forgotten what little geometry 

 he had acquired at the College of Navarre. He sat himself assidu- 

 ously but tranquilly to master enough mathematics to enable him 

 to proA^e his law. In the introduction to his Traite de Cristallo- 

 graphie we find this very illuminating paragraph which represents 

 his experience during these days. He says: 



" In the solution of analytical problems, the object of which 

 is to represent the progress of nature, we are led by very rapid 

 methods to results which are often overlooked and which now and 

 then excite our surprise by the paradoxical form in which they are 

 presented. But when, guided by simple reasoning, we return st^p 

 by step OA r er the course which was so quickly bridged by calculation, 

 we end by perceiving the action of the principles which have given 

 birth to these results." 



The researches of the Abbe Hauy communicated to his master 

 in science, Daubenton, and through him to Laplace, won for him 



