Catalogue. — physical optics. 



307 



these proportions should be constantly such, as always to 

 produce a halo at the distance of 23" or 24° from the sun 

 OF moon. We may explain all these phenomena in a much 

 more simple and natural mariner, by reverting to the theory 

 long ago proposed by Mariotte, but of late years almost en- 

 tirely abandoned and forgotten. 



It is well known, that the crystals of ice and snow tend 

 always to form angles of 60"; now a prism of water or ice, 

 of Oo", produces a deviation of about 23"i, for rays forming 

 equal angles wiih its surfaces, and the angle of deviation 

 varies at first very slowly, as the inclination changes, the 

 variation amounting to less than 3", while the inclination 

 changes 30°. 



Now if such prisms were placed at all possible angles of 

 inclination, diffeiing equally from each other, one half of 

 them would be so situated, as^to be incapable of transmit- 

 ting any light regularly by two successive refractions di- 

 rected the same way ; and of the remaining two fourths, 

 the one would refract all the light within these three de- 

 grees, and the other would disperse the light in a space of 

 between 20° and 30° beyond them. 



In the same manner, wc may imagine an immense num- 

 ber of prismatic particles of snow to be disposed in all pos- 

 sible directions, and a considerable proportion of ihem to 

 be so situated, that the plane of their transverse section may 

 pass within certain limits of the sun and the spectator. 

 Then half of these only will appear illuminated, and the 

 greater part of the light will be transmitted by such as are 

 situated at an angular distance of 23°i, or within 3° of it : 

 the limit being strongly marked internally, but the light 

 being externally more gradually lost. And this is precisely 

 the appearance of the most commorv halo. When there is 

 a sufficient quantity of the prismatic particles, a consider- 

 able part of the light must fall, after one refraction, on a 

 second particle ; so that the effect will be doubled : and, 

 in this case, the angle of refraction will become sufficient 

 to present a faint appearance of colour, the red being in- 

 ternal, as Che least refrangible light, and the external part 

 having a tinge of blue. 



These concentric halos of 23°^ and 47°, are therefore suf- 

 ficiently explicable, by particles of snow, situated promis- 

 cuously in all possible directions. If the prisms be so shoi't 

 as to form triangular 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 con- 

 sequently produce a horizontal circle of equal height with 

 the sun: and their refraction will exhibit a bright parhelion 

 immediately over the sun, with an appearance of wings, or 

 homs, diverging upwards from the parhelion. 



For,' all such particles as are directed nearly towards the 

 spectator, will conspire in transmitting the light much 

 more copiously than it can arrive from, any other part of the 

 circle ; but such as are turned more obliquely, will produce 

 a greater deviation in the light, and at the same timo a de- 

 flection from the original vertical plane. This rr.ay be 

 easily understootl, by looking at along line through aprism 

 held parallel to it : the line appears, instead of a right line, 

 to beQome a curve, the deviation being greater in those rays 

 that pass obliquely with respect to the axis of the prism.j 

 which are also deflected from the plane in which they were, 

 passing. 



The line viewed through the prism has no point of con- 

 trary flexure, but if its ordinates were referred to a centre, 

 ir 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 uncommonly, that the 

 forms of the luminous arches are so compUcatedasalmostto 

 defy all calculation. The coincidence in the magnitude 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 ex- 

 ist, which may cause the axes of the greater number of the 

 prisms to assume a position nearly horizontal, which is all 

 thatis required for the explanation of the parhelia with their 

 curved appendages Perhaps also, the effect may sometimes 

 be facilitated by the partial melting of the snow into co- 

 noidal 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 observed to ac- 

 company a parhelion. 



If the refractive power of ice were precisely es4ual to that 

 of water, the angle of deviation of an equilateral prism 

 would be 23° io', but the average of 22 of the most accu- 

 rate observations gives 22° 29', and that of 20 less accu- 

 rate ones 22° 16'. Now an angle of 22°i corresponds 

 to a refractive power of 1.32. Lahire found the refrac- 

 tive power of ice less than that of water, but Krafft in 

 his oration on northern climates makes it greater. It was 

 therefore desirable to ascertain its powers by direct expe- 

 riment, and Dr. Wollaston was so good as to try it by his 

 excellent method, which showed that the refractive power 

 was in fact no greater than 1.3 1, giving a deviation of 21° 

 50'. Perhaps a partial melting of crystals may sometimes 

 cause a difference in the actual magnitude of the deviation. 

 In the lunar halo, which I observed, the angle was certainly 



