78 Prof. Snell on the Theory of Halos, Sc. 
more or less perfectly formed, on an average one day in a week 
the year through. In the year 1839, in which I watched for this 
phenomenon with more than usual diligence, I recorded forty nine 
halos; of which forty four were formed about the sun, and five 
about the moon. And I cannot question that several, during the 
year, entirely escaped my notice. 
I have mentioned my reasons for believing that the colored 
band on the grass was nothing more or less than the lower limb 
of the common parhelion; and its peculiarities are explained, 
as soon as we attend to the circumstances of the case. ‘The va- 
rious prismatic colors were seen, not in regular succession, nor 
blended into white light, as in the halo of the sky, because the 
number of crystals was not sufficient,—there being only a single 
layer spread on the ground, instead of a stratum many feet or 
rods in depth, and filled with myriads of floating crystals. A 
cleam of yellow light, for instance, might come from a crystal in 
any part of the band, (except near the concave edge,) while no 
crystals were lying in exactly the same direction, and so turned 
in position, as to throw the other colors of the spectrum, to ob- 
literate or modify the yellow. 
The hyperbolic form of the halo is too plain a matter to need 
explanation. Yet itis not long since I saw an article in a scien- 
tific periodical, (I cannot now tell when or where, ) in which the 
writer seemed perplexed by a similar peculiarity of the bow form- 
ed in the mists of Niagara. From each end of the usual arch, he 
saw a band containing the same colors, extending horizontally in 
a straight line toward himself; and this appearance, if I mistake 
not, was regarded as something inexplicable. But had the mist 
been near enough, he might have traced these apparently straight 
lines to their place of meeting ina single curve, perhaps withina 
few feet of his station, and then he would have seen the entire 
bow. Ionce saw a bow formed in a dense morning fog, which 
filled the Connecticut valley, and could follow the curve from the 
for into the dew on the grass; and the nearest point was not 
more than four feet from the place where I stood; so that, witha 
wallking-staff, I could have extinguished the most beautiful part 
of the phenomenon. The higher and remoter part of the bow 
was circular, the lower and nearer part was hyperbolical. It is 
obvious, that in every such phenomenon, the light forms the sur- 
face of a cone, whose vertex is at the eye; and if the bow is 
