On the Formation of Hail. 93 
here. They first found series (2), and then derived series (1) 
from it. But the analysis given here seems to have the advan- 
tage of greater simplicity. 
The series (2) is more convenient for calculation, and likewise 
more convergent; and, in order to find the result given in the 
Mécanique Céleste, vol. iv. p. 257, we have only to substitute 
the values of 7, 8, A, found at p. 167 of the Magazine for Sep- 
tember last. After all, there are few physical problems of any 
difficulty, that admit of a more direct and satisfactory solution, 
or that can be brought to a calculation so easy and commo- 
dious. 
Although the case of the horizontal refraction has alone been 
considered, yet the same analysis will apply to the general state 
of the problem : : but, as this is attended with no difficulty, any 
further explanation will be unnecessary. 
Feb. 4, 1822. JaAMEs Ivory. 
XX. On the Formation of Hail. By A Nauticat Corre- 
SPONDENT™*. 
Tue absence of hail generally remarked by sailors navigating 
the Arctic regions, which observations during the late Polar ex- 
peditions have confirmed, seems to invalidate the commonly re- 
ceived theory of its forination from rain, precipitated by the up- 
per regions of the atmosphere, being frozen on passing through 
a cold stratum of air in its descent. For were this the case, it 
Sond be but just to suppose, that instead of hail being unknown 
within the Arctic circle, it would bear nearly the same proportion 
to the rain there, that the hail bears to the rain in this country. 
And indeed, from the circumstance of the sea in those high la- 
titudes being nearly covered with ice, we might reasonably infer, 
that a stratum of air sufficiently cold to congeal rain deposited 
by the higher strata of the atmosphere, would more frequently 
occur there than it does in this parallel. 
But it will appear that this theory is contrary to general ana- 
logy; for, in ascending hills, we find the atmospliere gradually 
decrease in temperature, and it is well known that the summits 
of many mountains are covered with perpetual suow. Though 
currents of air of varied temperatures do occasionally eccur as 
exceptions to this general rule, | cannot suppose the ordinary 
ceconomy of the atmosphere to be so completely inverted as is 
gratuitously assumed to account for the formation of hail, unless 
the sudden influence of some powerful auxiliary be admitted, to 
produce a phenomenon so contrary to general observation. 
* From the Gentleman's Magazine, vol. xci. p. 628, 
If, 
