A . W. Whitney — Refraction of Light upon the Snow. 391 

 The formula, d=2 sin -1 (n sin — j —A, gives for the angles 



2. 



of minimum deviation, where n, the refractive index of ice, is 

 1-31, and A is first 60° and then 90°, the angles 21° 50' and 

 45° 44', which correspond very closely with observation. 



The greater brilliancy of the 22° hyperbola corroborates the 

 theory also, for evidently less light is transmitted through a 

 90° prism, than through one of 60°, owing to the greater 

 obliquity of the incident rays in the former case. 



To sum up, in a field, of snow crystals tilted at all possible 

 angles, not one can send a refracted ray to the eye unless, first, 

 it lies in the path of the hyperbola, and, second, it is tilted at 

 just the right angle. 



The resemblance of this theory to that of halos, or, in fact, 

 the real unity of the two, is manifest. The halo and the snow- 

 hyperbola are respectively the aerial and terrestrial portions of 

 the same phenomenon ; the comparison in detail is very inter- 

 esting. 



Some rays of light doubtless experience internal reflection. 

 Hence other conic sections are within the range of possibility. 

 The simplest such case, that of one internal reflection, where 

 the maximum is given by the critical angle, would give angles 

 corresponding to d of about 87° and 116°. Some color may be 

 seen throughout this region, but I have not been able to detect 

 anything definite enough to be called a path. 



The perspective of these snow-hyperbolas forms concentric 

 circles upon a plane normal to the path of the sun's rays, which 

 is also evident from the fact that they are the completion of 

 the halos. On a vertical plane the perspective forms ellipses. 



Another interesting fact concerns the relation of the other 

 limb of the hyperbola to that upon the snow. If the observer 

 walks so as always to keep one certain point in the path of 

 light, his track will be an hyperbola ; if now, from the apex of 

 the hyperbola which he has traced, he advances a distance 

 equal to his height multiplied by the cotangent of the angle, 

 the altitude of the sun plus o, the figure which he now sees and 

 the figure which he has traced upon the snow are the two limbs 

 of the same hyperbola. 



The difference between the refractive indices for red and 

 violet light gives theoretically a dispersion of 46' in the case 

 of the hyperbola of 22°, and of 2° 10' in the case of the hyper- 

 bola of 46°. It may be noticed that the colors in the nearer 

 figure are more conspicuous. I do not understand, however, 

 why the arrangement of color is not more regular. It may be 

 due to an inability of the eye to sum up this discrete color. 

 The hyperbola is produced by a single layer of crystals, the 



