‘ 
va Mariotte, vol. i. p. 272.9 
“A theo 
be shewn by an experiment on two prisms.” See 
Traité des Couleurs, Paris 1686, or Quvres de 
of halos has recently been given by Mr 
Wood in the Manchester Transactions. He assumes, 
with Dr Halley, that r consists of hollow spheri- 
cles of water, filled with an elastic fluid, and having a 
thickness. equal to +}, of their diameter ; and he sup- 
es the halos to'be produced by-refraction, and reflec- 
Flot from: these, in the same manner as the rainbow is 
produced by solid drops. See Manchester Memoirs, 
vol. iii,-p. 336. » A similar opinion seems to be enter- 
tained by M. Brande. See Gilbert's Journal, vol. xi. 
} 414, — 5. ax i 1¥i OSE (ma ire 
s eT he subject of halos has recently been examined with 
much attention by our learned countryman Dr Thomas 
Young, who, before he was acquainted with the expla- 
nation of Mariotte, had adopted the.very same theory. 
Our readers will no doubt be gratified with an account 
of Dr Young’s theory and calculations in his own words, 
-» “It is well known, that the crystals of ice and snow 
tend always to form angles of 60°; nowa 
ter or ice of 60°, produces a deviation of about 233°, for 
rays forming equal angles with its surfaces, and the an- 
gle of deviation varies at first very slowly as the incli- 
nation the variation amounting to less than 3°, 
while the inclination changes 30°. 
. Now if such prisms were placed at all possible angles 
of inclination, differing y from each other, one 
half of them would be so situated,:as to be incapable of 
_ transmitting any light regularly by two-successive re- 
fractions directed the same way ; and of the remaining 
two-fourths, the one would refract all the light within 
these 8°, and the other would disperse the light in a 
space of between 20° and 30° beyond them. 
In the same manner, we may. imagi ntort immense 
number of prismati icles of snow to be disposed in 
Dipkedblairessions and a considerable proportion of 
them to be so situated, that the plane of their transverse 
section may pass within certain limits of the sun and 
the tor. . Then half of these only will appear il< 
: luminated; and the greater part of the light will be trans- 
mitted by such as are situated at an angular distance of 
4°, or, within 3? of it, the limit being strongly mark- 
pang but the light being externally more — 
dually lost. And thisis precisely the appearance of the 
most common halo, When there is a sufficient quanti- 
of the prismatic particles, a considerable part of the 
ht must fall, after one refraction, on a second parti- 
3 so that the effect will be doubled: and, in this 
ease, the angle of refraction will become sufficient to 
present a faint appearance of colour, the red. being in- 
ternal, as the least refrangible light, and the external 
part having a tinge of blue. a 
These concentric halos of 23}° and 47°, are therefore 
sufficiently explicable, by particles of snow, situated pro- 
miscuously in al} possible directions. If the prisms be 
so short as to form ae plates, these plates, in: 
falling through the air, will tend to assume a vertical 
_ direction, and a much greater number of them will be 
in this situation than in any other. The reflection from 
their flat surfaces will consequently produce a horizon~ 
tal circle of equal height with the sun ; and their re« 
fraction will exhibit.a bright 
the sun, with an appearance of wings or horns, diver- 
upwards from the parhelion.. 
or all such particles as are directed nearly towards 
the spectator, will conspire in transmitting the mens 
much more copiously than it can arrive from any other 
VOL. X, PART Il. 
- 
Moe 1 ’ 
HALO. 
prism of wa-. 
pavhelion immediately over: 
617 
| rie sre but such ee 
» will , and at 
So ee eT deviation in the light 
the same time a deflection from the ovighnal vértieal 
lane. This may be easily understood, by looking at a 
ong line through a prism held parallel to it: the line 
appears, instead of a right line, to become a curve, the 
eviation being in those rays that pass oblique- 
ly with respect to the axis of the prism ; which are al- 
so defle from the plane in which they were passing. 
The line viewed through the prism has no point of 
contrary flexure, but if its ordinates were referred to a 
centre, it would usually assume a form similar to that 
which has often been observed in halos, 
The form of the flakes of snow as they usually fall, is 
indeed more complicated than we have been supposing; 
but their elements in the upper regions of the air are 
probably more simple. It happens however not un- 
commonly, that the forms of the luminous arches are so 
complicated, as almost to defy all calculation. The co- 
incidence in the magnitude of the observed and com- 
puted angles is so striking, as to be nearly decisive with 
respect to the cause of halos, and it is not difficult to 
imagine that many circumstances may exist, which may 
cause the axes of the greater number of the prisms to 
assume a position nearly horizontal, which is all that 
is required for the explanation of the parhelia with their 
curved appendages. Perhaps also, the effect may some- 
times be facilitated by the partial melting of the snow 
into conoidal drops; for it may be shown, by the light 
of a candle transmitted through a wine glass full of wa- 
ter; that such a form is accommodated to the ues 
tion of an inverted arch of light, like that which is fre- 
quently-observed to accompany a parhelion. 
The situation of the lateral parhelia without the halo, 
is very satisfactorily explained by Mariotte; and the 
diversified forms of the tangent arches, may 
all be deduced from the suppositions laid down in the 
Journals of the Royal Institution. Asan instance, we 
may take the case there described by Sir Henry Engle- 
field, (see p. 615, supra,) where the sun’s altitude was 
about 15°. The horizon “ee prisms will then cause 
an appearance of an arch with a contrary curvature, 
exactly as Sir Henry has described it. ar 
The calculation is somewhat intricate. Its principal 
are these, taking the refractive power +. 
eviation of transverse rays 23° 37’. 
For rays inclined 20°, the inclination of the planes of 
the rays is 29° $2’, the deviation 26° 12’; the altitude 
being 15°, the angle with the horizon is 25° 8! more 
than the altitude. : 
For rays inclined 25°, the inclination of the planesis 
34°, the deviation 27° 47’, the angle with the horizon 
25° 47' more than the altitude 15°. 
. For rays inclined 30°, the inclination of the planes is 
120° ; that. is, the rays are in the planes of the surfaces, 
the deviation 38° 56’, the angle with the horizon 6° 4” 
less than the altitude 15°. -~- 
When the altitude increases, the tangent archdescends 
so as to aj considerably to the as in the ha- 
los observed by Halley and by Barker. For, calcula- 
ting upon the true saheeaive power of ice, the angles 
become these. : ug 
For rays inclined 25°, the inclination ‘of the planes 
30° 55’, the deviation 25° 40’ = 21° 50/4 8° 50’, the 
angle with the horizon 56° 24 = 45° 411° 24/; ~ For 
altitude 15°, 38° 57/=15°+428° 57". ; 
It may also become double, the inferior arch being 
visible, Thus the angle with the horizon becomes 24° 
18’ or 45°—23° 42’, as wellas 56° 24’. 
At 
Halo, 
—— 
