166 MEMOIR OF AUGUSTE BRAVAIS. 



of the s,,-stems niiglit be bleuded in a single one, and after him all crys- 

 tallo<irai)liers had admitted six crystaUine fii/stcms only. M. Bravais 

 demonslmtcs that it is necessary to retnrn to the number seven, and this 

 demonstration, accompanied by all the light which results from a ge- 

 ometric analysis so profound as his, is no slight addition to the immor 

 tal creation of Haiiy. Lagrange and Laplace had foHowed, in 1784, the 

 lessons of the ingenious investigator of crystals, but had been content 

 with simply admiring them. The grounds of the beautiful science due 

 to his genius had never been studied from so high a point and with so 

 much generality as in the memoir of M. Bravais on the systems formed 

 by points ; a memoir to wliicli our illustrious Cauchy has, in a remarka- 

 ble report, given liis most unreserved sanction. 



You do not expect me, gentlemen, to enter here into the detail of pro- 

 ceedings, though simple, yet rigorous, by which in a second memoir, en- 

 titled Mudes crystallognqjhiques, replacing empirical rules by the theo- 

 rems of geometry, M. Bravais deduced from his fundamental results 

 all the formulas of crystallography with tliat marvellous facility which 

 denotes almost infallibility in the radical vsolution of the difficulties of 

 a subject. Being limited as to time I shall restrict myself to the state- 

 ment that in the second part of this memoir, ceasing to regard the mo- 

 lecules as points and considering them as small bodies, which he calls 

 atomic polyhedrons, he throws light upon the relations which exist be- 

 tween these latter and the various crystalline systems. He reduces to 

 simple laws the phenomenon, until then almost unknown, of the hemi- 

 hedral, upon which our learned fellow-member, M. Delafosse, in a justly 

 celebrated memoir, has diffused unexpected light. M. Bravais demon- 

 strates that he could exhibit twenty-live cases of hemihedral forms, of 

 which only eleven had before been discovered, though these were for a 

 long time amply sufficient to exercise the sagacity of crystallographers. 



Not forgetting dimorphism, one of the claims of Mitsoherlich to dis- 

 tinction, nor the curious discoveries previously made by our ingenious 

 fellow-member, M. Pasteur, M. Bravais, in a third memoir, gives the 

 results of his equally successful labors on the peculiar form of crystal- 

 lization exhibited in a mineral called made and hemitropes, which had 

 been in their turn a stumbling-block to the crystallographer. About this 

 time he was also at work upon investigations relative to the connection 

 of atmospheric optics and crystallization, as well as composing various 

 memoirs upon subjects entirely different, but relating for the most part 

 to meteorology, some of which are not the less remarkable from being 

 6ntside of this branch of physical geography. 



He was endowed with a remarkable facility for all kinds of intellect- 

 ual labor, and he possessed the rare faculty of occupying himself at the 

 same time with the most varied subjects : hydrography, navigation, 

 astronomy, atmospheric optics, physics, properly so called, geometry, 

 crystallography, pure analysis, and natural sciences, were at once the 

 subjects of his investigations. It might be said of him, notwithstand- 

 ing the apparent opposition of words, that the universal was his spe- 

 cialty. 



All his memoirs have received honorable notice in our " Comptcs- 

 Rendus,'^ and met with merited success by their publication in the most 

 esteemed scientific transactions of the day. They continually present 

 ingenious and frequently profound conceptions, which are well worthy 

 of special attention, but which, for want of time, I am not at present 

 able to specify. The works of Bravais, taken in their totality, are of 

 immense extent, and 1 am forced to limit myself to a sketch of the prin- 

 cipal treatise. . As an astronomer, called upon to give an abridged idea 

 of the firmament, can only speak in detail of the stars of the first mag- 



