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



parallel lines and lines to a given point is the surface of a cone. 

 In this case, the eye is the apex, the axis the line of sunlight, 

 the angle at the apex is 2d. It will be seen at once that the 

 snow-snrface is a plane which cuts this cone. The conic sec- 

 tion produced depends upon the relation of the altitude of the 

 sun and o. In both cases, where d = 22° and 46°, the figure 

 on the snow is evidently a hyperbola. When the altitude of 

 the sun = d, the figure is at infinity; the sun has an altitude 

 of more than 22° till about the middle of the afternoon ; hence 

 before this time the inner hyperbola is invisible. As even at 

 noon the sun is not higher than 37°, the outer hyperbola is visible 

 at all times. The effect of the going down of the sun is 

 evidently to broaden the figures and bring them nearer. 



We have now proved inductively that d is constant, and de- 

 ductively that, o being constant, the figure is an hyperbola. 

 It remains to find a cause for the constancy of d. 



The light from the snow is evidently due either to reflec- 

 tion or refraction ; most of it is doubtless reflected. Several 

 facts already mentioned seem to prove, however, that the light 

 of the hyperbolas is not due to reflection. 



First, the only intrinsic law of reflection, that of the equality 

 of the angles of incidence and reflection, is seen to be no'path- 

 discriminating condition — for the facets of the snow-crystals 

 may be tilted at any angle. 



Second, reflection cannot account for the color. Therefore 

 this phenomenon must be due to refraction. The difference is 

 apparent between the light from the crystals lying in and out 

 of the path. As one turns his head, those crystals lying out- 

 side flash for an instant, and as quickly subside ; those in the 

 path, on the other hand, linger to run through their little life 

 of color. At noon the altitude of the sun is about 37° ; the 

 complement of the polarizing angle of ice is 37° 20'. Hence 

 at this time the reflected light near the vertex of the hyperbola 

 should be nearly all polarized. Experiments with Nicol's 

 prism and tourmaline prove that nearly all the general glim- 

 mer is cut off, while the light of the hyperbola is undisturbed. 



The problem is now simplified to that of finding a phenome- 

 non of refraction to correspond with the constancy of d. The 

 angle of minimum deviation seems to promise a solution ; it 

 will evidently give a maximum, for at this point the refracted 

 light is greatest. It will also give a sharp inside limit to the 

 path and an indefinite outside limit, which exactly corresponds 

 with observation. 



Now ice belongs to the hexagonal system ; it may form in 

 right hexagonal prisms. Consequently a snow-crystal may 

 offer to the light angles of 60°, 90°, and 120°. There will 

 evidently be no emergence in the case of the 120° angle. 



