406 HALO white, and deeper at the edges, and the semi- diameter of its internal edge was 36 50', that of its external edge being from 41 to 52 This fourth circle, commonly called the circle of Ulloa, or the white rainbow, is very seldom seen. Anthelia are explained upon the same principle as corona, with the single exception that the diffraction in this instance does not oc- cur during the direct transmission of the solar beams through the cloud, but during the retro- grade transmission of rays which, having pen- etrated to considerable depth in the cloud, un- dergo reflection, and are then diffracted by nearer globules while on their return to the eye. Halo* proper. In the commoner forms, one or two rings, formed in the thin, feathery cloud overspreading the sky at a great height, extend vertically about the sun or moon. The diameters of these vary somewhat, and some- times during the same display ; but when one only is seen, its distance from the sun is very near 22, or diameter 45 ; the latter number being also the radius or distance of the second, when seen. Of these rings, the color of the inner border, when obvious, is almost invari- ably red ; next to this comes green or blue ; the outer edge is one of the latter colors, violet, or white. Very rarely the outer border is red. The breadth is usually slightly less than that of the luminary ; sometimes a ring appears as if made up of two lying side by side, and crossing each other in very acute angles at certain points of their course. As in the rainbow, the red border is most defined, the opposite being lost in a diffused light; and the sky just within these rings usually appears more dark than elsewhere. The third and largest ring, having a radius of about 90, is usually white ; but it is seldom or never complete, even in the visible portion of sky. The same obvious atmospheric conditions that show these more ordinary forms, may also give rise to a white circle having the breadth of the solar disk, through which it passes, and extending completely around the sky in a plane parallel with the horizon. A second white band of the same breadth may pass through the sun's disk in a vertical direc- tion, while at the points in which this inter- sects the two ordinary rings above, tangent colored arcs may be seen curving away from the rings respectively, and tending to include the zenith. Parhelia and Paraselenes. A par- helion is an attendant image, more or less dis- tinct, of the sun's disk, which may appear with any halo, at one, two, or more points near the sun ; but which is more frequently formed in the course of the horizontal or vertical white bands, or in both, at or slightly without the in- tersection of these with the ordinary halos. Parhelia show the usual colors of halos, in the same order, but more brightly, and even when the latter are not perceptibly colored. They seldom appear at once at more than three or four of the intersections, and sometimes pre- sent a sort of tail in the direction opposite the luminary. Popularly, they are known as sun dogs, or mock suns. The corresponding ap- pearances about the moon are termed parase- lene. The more complicated phenomenon, showing both the halos and mock luminaries, although somewhat rare, is still much varied in form. Among the earlier clearly recorded ob- servations may be named an example of the solar observed by Schemer at Rome in 1629, and of the lunar by Hevelius of Dantzic in 1660. Very brilliant halos were seen about the sun for several days in succession at Moscow in 1812, during its occupancy by the French ; the most splendid instance on record occurred at Gotha, May 12, 1824. In high northern lati- tudes, halos and parhelia are very frequent; Capt. Parry always saw the former about the time of full moon. But whether in higher or lower latitudes, they are only seen when there intervene between the luminary and the ob- server those highest thread-like forms of cloud, the cirrus or cirro-stratus. The cold prevailing in the elevated regions occupied by these clouds renders it quite certain that their particles must be in the frozen condition a fine ice mist such as we experience in the coldest days of winter, and which, driven against the face by a wind, actually prick the skin. These crys- tals incline chiefly to the form of hexagonal prisms ; and to refraction and decomposition of light passing through certain angles of these, Mariotte was led to ascribe the production of halos. For any refracting angle of a prism there exists a minimum angle of deviation, de- pendent on the density and the angle. Now, the minimum deviation of a decomposed ray occurs when the angle of refraction is just half the refracting angle of the prism used. The refracting angle of the ice prisms being 60, the angle, of refraction giving the least deviation for the red ray from the original course of the light must be 30 ; and, the refractive index of ice being 1*31, the angle of incidence must be 41. Then the deviation, being equal to twice this angle less the refracting angle, or 2x41 60, is 22, a result very closely agreeing with that of observation for the smallest and most common form of halo. To produce this ring, then, it is only necessary to imagine the mi- nute prisms of ice floating or descending through the air in all positions, but, owing to the resis- tance presented by the air to the action of their weight, taking especially horizontal and verti- cal directions ; then, near to the position giving a minimum deviation of the transmitted rays, a considerable turning of the crystal about its axis gives only an insignificant change in the direction of the emergent light ; and hence, a far larger number of the crystals will transmit red rays deviating from their previous recti- linear course by exactly or nearly this angle of 22 than by any other. The rays from the sun or moon being in effect parallel, there should therefore be seen, at nearly this angle with the luminary, a dim circle, red and de- fined within, but beyond this having the colors overlapping one another, and indistinctly seen
