216 PROCEEDINGS OF THE AMERICAN ACADEMY 



those of 60° made by alternate faces, and those of 90° made by the 

 faces and ends of the prisms. The inner halo is caused by refraction 

 through an angle of 60°, the refracting edges being parallel to the tan- 

 gents to different parts of the halo. The outer halo is caused by refrac- 

 tion through an angle of 90°, the refracting edges of different prisms 

 being parallel to different tangents. Both halos require that the prisms 

 should be scattered at random, so that a sufficient number would be found 

 in the required positions. The white parhelion circle is produced by 

 reflection from the sides of the prisms when their ax;es are vertical. 

 These same prisms, acting through the angle of 60°, would produce the 

 mock suns whenever they stood in the position of minimum deviation ; 

 while others, not in the position of minimum deviation, would produce 

 the colored appendages to the mock suns. These same prisms, acting 

 through the angle of 90°, would cause the tangent curve to the larger 

 halo of 46°. If the luminary were above the horizon, reflection from 

 the upper end of these prisms would produce an uncolored image of the 

 luminary underneath the real luminary ; but this image would not be 

 visible unless the observer were elevated to a great height above the 

 surface of the earth. If the luminary were a little below the horizon, 

 reflection from the lower end of these prisms would produce a similar 

 image above the luminary, and above the horizon, which would be visi- 

 ble ; and hence the luminary might appear to have risen again after set- 

 ting. When the axes of the prisms are horizontal, refraction by the 

 angle of 60° would cause the tangent curve to the inner halo of 22°. 

 If large numbers of prisms were floating contemporaneously in all three 

 positions, all these phenomena might coexist ; otherwise, only a portion 

 of these various features would be displayed. It is evident, therefore, 

 that both halos might be wanting, and yet one or both of the curves 

 which are tangent to them might appear. If the tangent curve to the 

 larger halo of 46° is seen, generally the mock suns and the parhelion 

 circle are also seen, even in the absence of the halo itself. In other 

 words, all which vertical prisms are capable of producing would gen- 

 erally, though not necessarily, be seen at the same time. 



These general features are somewhat changed by the altitude of the 

 sun, or other luminary, above the horizon. When the sun is in the hori- 

 zon, the parhelia are at the same distance from it as the inner halo, and 

 rest upon it. As the sun rises they go outside of the halo, and become 

 impossible when the altitude of the sun exceeds 60° 45'. The lengths 

 of the tails affixed to the mock suns increase as the sun rises, until the 



