MEMOIR OF AUGUSTE BRAVAIS. 165 



concur in the formation of the halo of 46^; and should their fall through 

 tranquil air render one of their diagonals vertical, the parhelion of iG^ and 

 the anthelion make their appearance. The rays reflected, without disper- 

 sion of cok^rs, on the vertical faces of the i)risms and hexagonal tablets 

 produce the parhelic circle of M. Babinet, which is brilliant but colorless. 



Other combinations may be conceived, almost all realized in nature ; 

 moreover, the microscopic crystals of ice, besides their principal faces, 

 sometimes present secondary tacets, which also give rise to refractions 

 and reflections, the effect of which is to break the ray of light, in each 

 case, under a special angle. The analysis of all the possible cases of 

 this kind, and the complete explanation which results therefrom of all 

 the phenomena observed, even the most singular and most rare, fur- 

 nished M. Bravais the subject of the consummate memoir which is fresh 

 in the admiration of learned Europe. 



Considering the phenomenon under all points of view, M. Bravais 

 completes the study which M. Arago had given to the polarization of 

 light in halos properly so-called, by extending it to all the parts of me- 

 teors of this nature. 



Equally skilled as an experimenter, and versed in the management 

 of analytic formulas, he conceives an ingenious apparatus which, by the 

 rapid rotation of a transparent prism with vertical axis, represents with 

 much exactness the multitude of needles or vertical flakes of ice sus- 

 pended in the atmosphere, whose horizontal movement, dispersed in all 

 directions, produces the greatest number of atmospheric illuminations. 

 By means of this new instrnment, and of artificial light, we are able to 

 reproduce in a cabinet of physics most of the phenomena of meteoro- 

 logical optics. 



In Lapland and on Mont Blanc M. Bravais had had numerous oi)por- 

 tunities of observing the crystalline forms of sno\v. He had often met 

 with admirable crystallizations of congealed water, and had always de- 

 srfL-ribed them with a peculiar predilection. In his memoir on halos he 

 employs the notations and formulas which represent the crystalline sys- 

 tem of the ice, as one perfectly conversant with them and thoroughly 

 master of their principle. But he did not stop there, and his studies 

 eventually extended to the whole science of crystallography-. 



In his view crystals are assemhlages of molecules, identical as regards 

 one another, and similarly oriented or arranged, which — being reduced 

 in thought to a single point, their center of gravity — are disposed in 

 rectilinear and parallel rows, in each of which the distance of two points 

 is constant. 



The points of an assemblage are aligned in rows, corresponding to an 

 endless number of different directions ; but the knowledge of three rows 

 not parallel and not comprised in the same plane is sufficient completely 

 to determine the assemblage of which they form a part. An infinitude 

 of assemblages entirely different may be conceived. By a profound 

 mathematical study M. Bravais had succeeded in discovering the de- 

 grees of syumietry, more or less great, of which they are susceptible. 

 He finds the axes and the planes of symmetry which they may present, 

 and establishes that according to the number and arrangement of these 

 axes i\in\ planes of symmetry, the rt6'se/»6/«^e.s- possessing them are divided 

 into six elasscs. By adding-^ to these the asymmetrie assemblages, in 

 which there exist neither axes nor planes of symmetry, we have seven 

 classes of assemblages. Thus are evolved the most simple and general 

 laws of the symmetry observed in crystals, and the adoption, in crys- 

 tallography, of secen erystalUne systems is a necessary conse(iuence. Of 

 this Haily had had an indistinct percejJtion j but he concluded that two 



