20 Proceedings of the 



The conditions necessary for these phenomena are : ist, 

 the presence of minute uniform crystals of frozen vapor in the 

 higher strata of the air, forming a light cirrus cloud over the 

 sun ) and 2d, comparative stillness of the atmosphere, that the 

 positions of the crystals in falling may remain nearly uni- 

 form. 



The most simple form of ice crystals is that of a hexag- 

 onal prism terminated by plane faces perpendicular to the sides. 

 Suppose an immense number of such crystals, in every possible 

 position, to be slowly falling in the air. Many of them will 

 be in or near the position of minimum deviation relatively to the 

 direction of the sun, and, unlike the others, will conspire to re- 

 fract the sunlight in the same direction ; as a prism, when near 

 the position of minimum deviation, can be rotated through a 

 considerable angle without sensibly affecting the direction of the 

 refracted ray. It is the combined action of the crystals in this 

 position which produces the visible result. All those prisms, 

 symmetrically situated with respect to the line through the eye 

 and sun, and at a proper angular distance from it, will conspire 

 to send the light to the eye, and the appearance produced is 

 symmetrical with respect to that line, namely, colored circles 

 with the sun as the center, the red (refracted least) marking the 

 inner border, and the other colors following in the order of the 

 spectrum. As the crystals within the circle can transmit to the 

 eye no light at all, while those without and not in the position of 

 least deviation may transmit some, the inner border is sharp and 

 distinct, but the outer border fades into a feeble white. 



The inclination of the lateral faces of a hexagonal prism is 

 60° and 120°; that of the ends with the sides is 90°. Taking 

 the refractive index of ice as 1.3 1, it is easily shown that the 

 mean deviation of light by passing through the angle of 60° is 

 about 22°, and by passing through the angle of 90° is 46°, thus 

 explaining the formation of the primary and secondary halos 

 which are found to be respectively at those distances from the 

 sun. The angle of 120° is too great for light to be transmitted. 



The two halos described depend for their formation on 

 the ice crystals having their axes at all angles. But as from 



