For all such particles as are directed nearly towards the spectator will conspire in transmitting the light much more copiously titan it can arrive from any other part of the circle ; but such as are turned more obliquely will pro duce a greater deviation in the light, and at the same time a deflection from the original vertical plane. This may be easily understood, by looking at a long line through a prism held parallel to it : the line appears, instead of a right line, to become a curve, the deviation being greater in those rays that pass obliquely with respect to the axis of the prism; which are also deflected from the plane in which they were passing.
The line viewed through the prism has no point of con t•ary flexure, hut 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 in deed 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 uncommonly, that the forms of the luminous arches are so complicated as al most to defy all calculation. The coincidence in the mag nitude of the observed and computed 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 num ber of the prisms to assume a position nearly horizontal, which is all that is required for the explanation of the par belia with their curved appendages. Perhaps, also, the ef fect may sometimes 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 water, that such a form is accommodated to the production of an inverted arch of light, like that which is frequently ob served to accompany a parhelion.
The situation of the lateral parhelia without the halo is very satisfactorily explained by Mariotte; and the diversifi ed forms of the tangent arches may, probably, all be dedu ced from the suppositions laid clown in the Journals of the Royal Institution. As an instance, we may take the case there descrilied by Sir Henry Englelield, (see p. 615, so pra,) where the sun's altitude was about 15°. The hori zontal prisms will then cause an appearance of an arch with a contrary curvature, exactly as Sir Henry has de scribed it.
The calculation is somewhat intricate. Its principal steps are these, taking the Deviation of transverse rays 23° 37'.
For rays inclined 20°, the inclination of the planes of the rays is 29° 32', the deviation 26° 12' ; the altitude being 15°, the angle with the horizon is 8' more than the al titude.
For rays inclined 25°, the inclination of the planes is 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 the devi ation 38° 56', the angle with the horizon 6° 4' less than the altitude 15°.
When the altitude increases, the tangent arch descends so as to approach considerably to the halo, as in the halos observed by Halley and by Barker. For, calculating upon
the true refractive power of ice, the angles become these.
For rays inclined 25", the inclination of the planes 30° 55', the deviation 50' + 50', the angle with the horizon 56° 24'. For altitude 15°, 38° 57,±150+230 57'.
It may also become double, the inferior arch being visi ble. Thus the angle with the becomes 21° 18' or 45°-23° 42', as well as 56° 24'.
The mode of calculation is this : A being the inclination Sec. A within the prism, and r the index. Sec. B = for the incidence; S. C=r. S. 13, D =C — 13. Ac S. C: Sec. A :: S : H : .r, = y, 1 —y : Rad : T.E, 2 E is the mutual inclination of the plans frassing through the rays and the axis of the prism, x : : R S.F ; 2 F is T.A the whole deviation ; 1— ; z : —:: S. Al titude : S. CI, the elevation of the plane of the incident ray: the elevation of the plane of the emergent T.A z S.II : S I, the depression of the emergent ray.
Alr Cavendish has suggested, with great apparent pre bability, that the external halo may be produced by the re fraction of the rectangular termination of the crystals, rather than by two successive refractions through the angles of different crystals, which, with the index 1.31, would pro duce h deviation of 44'. If this supposition is true, the index cannot be greater than 1.31 ;* for 1.32 would give which is more than appears to have ever been as signed.
The mean of four accurate observations is about 45" 50', that of four of the best estimations 46°.
The lateral anthelia may be produced by the rays re fracted after two internal reflections, which will have a con stant deviation 60° greater than those which form the halo. These anthclia ought therefore to be about 82° from the sun. They are, however, usually represented as much more distant." In addition to the works referred to in the course of the preceding ticle, see Zahn Mundi Economia. Lycosthenis Chronicon Prodigiarum. Ft itsch On Meteors. Philosophi cal Transactions, 219. Id. 1669, iv. 953. Id. 1670, v. 1065. Id. 1699, xxi 107 and 126. Id. 1700, xxii. 535. Id. 1721, xxxi. 201, 212. Id. 1722, xxxii. 89. Id. 1727, xxxv. 257. Id. 1732, xxxvii. 357. Id. 1737, xl. 50, 54, 59. Id. 1740, xli. 459. Id. 1742, xlii. 47, 60, 157. Id. 1798, :dlr. 524. Id 1749, xlvi. 233. Id. 1761. 3, 94. Id. 1763, 351. Id. 1770, 129. I 1784, 59. Id. 17S7. 44. Mem. Acad. Par. ii. 208. Id. x. 47, 152, 168, 275, 411, 454. Id. 1699, 1 list. 82. Id. 1713, Iliht. 67. Id. 1721,231. Id. 1729, Hist. 2. Id. 1735, 87, 585. Id. 1743, Hist. 33. Id 1745, Hist, 19. Id. 1753, Hist. 75. Id. 1754, list. 32. Id. 1755, Hist. 37. Id. 1758, Hist. 23. Id. 1786, 44. Armoires de Berlin, 1734, iv. 64. Nov. Comment. Petrop. vi. 425. Id.
392. Id. x. 375. \Veidler, De Parheliis .4nni 1736. Irish Transactions, 1787, i. 23. Id. 1789, iv. 143. Edin burgh Transactions, iv. 174. Edinburgh Essays, i. 297. Rozier's Journal, xi. 377 ; xxxvii. 308. Dr Thomas Young's .Alitural Philosophy, i. 443 ; ii. 303-309 ; and our article GREENLAND.