and the Theory of Halos. 75 
direction than 21° 50’, can transmit a ray to the eye of the ob- 
server; otherwise the deviation would be less than 21° 50’, 
which, according to the above calculation, is the minimum. But 
those crystals, which are about 22 or 23 degrees from the sun, 
may, as already stated, be revolved on their own axes, so as to 
change the angle of incidence 10 or 15 degrees, and yet send 
their transmitted ray to the eye. Some of these positions are 
represented at B, in the figure. 
That I might render my own ideas of the case as definite as 
possible, I constructed the following table, for every five degrees 
of incidence. 
Angle of incidence. Angle of emergence. Angle of deviation. 
13° 27’ 90° 43° 27’—maximum. 
15° Poeey 34° 19’ 
20° 66° 40’ 26° 40’ 
25° 59° 37" 24° 37’ 
30° 53° 23° 
35° aa a Ze Oot 
40° Ao ae 21°51" 
40° 55’ AQ° 55’ 21° 50’—minimum. 
A5? 36° 59/ 21°59’ 
50° 32° 30’ 22° 30’ 
55° 28° 22/ 23° 22’ 
60° 24° AZ! 24° 43’ 
65° 21° 287 ere? mor 
70° 18° 42/ 28° 42' 
15° 16° 287 31° 28’ 
80° 14° 487 34° 48’ 
85° te 49' 38° 49’ 
90° 13° 27’ 43° 27’—maximum. 
This table shows that no crystal can transmit light, unless so 
situated that the angles of incidence are between 13° 27’ and 90°, 
on that side of the perpendicular most remote from the refracting 
angle. This range equals 76° 33’. It shows, also, that if the 
angles of incidence are between about 29° and 55°, (a range of 
26°, or one third of the whole,) the emergent ray will vary but 
about one degree and a half from the minimum deviation. 
Hence, of all the light which can come from the sun by trans- 
mission through crystals of 60°, one third is refracted by those 
