164 MEMOIR OF AUGUSTE BRAVAIS. 



it without explanation. His memoir has filled a gap in the labors of 

 the first masters of science. 



Tlie rainbow is not the only phenomenon which describes on the vault 

 of the heavens geometrical figures more or less brilliant, more or less 

 vividly colored. Parhelions and halos, less frequent, but not less strik- 

 ing than the rainbow, are formed under circumstances so visibly differ- 

 ent, that, fiir from appearing of good augury, they have been regarded 

 by tlie amazed populations as signs of divine wrath. Mariotte had pro- 

 posed to attribute these luminous apparitions to the action exerted on 

 the rays of the sun or moon by the frozen particles which remain, for 

 some time, suspended in the atmosphere before falling in the form of 

 snow or rain. But Huyghens had combated this explanation, and, for 

 more than a century, it had been left in abandonment. Brandes, Young, 

 Galle, Kiimtz, and other celebrated physicists, however, had recurred to 

 it with better success. But M. Bravais has removed all doubts by rep- 

 resenting by formulas, reduced with the ingenuity of which he possessed 

 the secret to great simplicity, the course of the reflected and refracted 

 rays, and by deducing from their discussion the forms, however strange, 

 of the observed phenomena. 



According to the greater or less depression of the temperature of the 

 elevated regions of the atmosphere, the vapor is there condensed into 

 water which gives rain, or into particles of ice which produce snow, sleet, 

 or hail. The ice crystallizes in regular hexagonal prisms, which, in their 

 most elementary form, are terminated by plane faces perpendicular to 

 the axis of the prism. The prism is sometimes much elongated, some- 

 times, on the contrary, extremely short. In the first case the frozen 

 l)articles formed in the air are small needles of microscopic diameter; 

 in the second they are small hexagonal or stellate plates, of a thickness 

 hardly measureable. In both cases these little crystals are very light. 

 They dance in the air like those grains of dust which are seen quivering 

 by myriads in a sunbeam. They fall, however, though slowly, in air 

 perfectly calm. Although microscopic, they have forms of the utmost 

 exactness, for the regularity of crystallizatiou is never more admirable 

 than in the smallest particles of matter. 



When the frozen particles are acicular prisms, the luminous rays pro- 

 ceeding from the sun or the moon, in being refracted across two faces 

 not contiguous of the prism, under the angle of minimum deviation, are 

 broken and pursue their route, by making with their first direction an 

 angle of about 22°. In this case, if the small prisms quiver in the air, 

 a colored arc is produced comparable to a rainbow, but of 22° only of 

 radius, of which the luminous body occupies the center and in which 

 the red band is situated on the inner side. This is the halo of 22°, the 

 most frequent of all. If the small prisms, or only a part of them, fall 

 gently through tranquil air, and take a vertical position, there is 

 formed, on each side of the sun and at the same height, an image of 

 that body which is called a parhelion, and which is distant from it, very 

 nearly as is the arc of the halo, about 22°. The rays of light which 

 are refracted, at the angle of minimum deviation, across a diedral 

 angle of 90°, like that which results from tbe rectangular incidence of 

 the faces of the hexagonal prism on its bases, are more strongly deflected 

 than in the preceding case and produce the halo of 40°. If the prisms 

 are vertical, they give rise to horizontal circles, decked with very lively 

 colors, which are tangents to the upper part or to the lower part of the 

 halo of 4GO. 



When the frozen particles have the form of small, very thin hexagonal 

 I)lates, the diedral angles of 90°, presented by the outUue of their base, 



