35 INSTRUCTIONS TO MARINE METEOROLOGICAL OBSERVERS 



Tangent arcs. — Just as flat-topped crystals with vertical sides pro- 

 duce a circumzenithal arc when the altitude of the sun is l)etween 

 0° and 32°12', so, too, similar crystals whose axes are horizontal and 

 directed toward any point whose solar distance is between 90° and 57° 

 48', or between 0° and 32° 12', produce a colored arc — red next the 

 sun — about this directive point as a center. And as there are two 

 such points correspondino- to each solar distance, one to the right, the 

 other to the left, of the solar vertical, it follows that arcs formed in 

 the above manner are symmetrically situated with respect to this 

 vertical. Further, when the solar distance of the directive points is 

 6T°52' or 22°8', the resulting; arc is tangent to the halo of 46°. and 

 as always some, at least, of the imuunerable crystals are turned to- 

 ward this point, except when the altitude of the sun is greater than 

 these values, respectively, it follows, with the same exceptions, that 

 the blend of the numerous arcs produced by the various directed 

 crystals is always tangent to the halo of 46°, and also that except 

 near the point of tangency only the red of these blends is reasonably 

 pure. 



Infralateral tangent arcs of the halo of 46° are pi'oduced when the 

 altitude of the sun is less than 6T°52'. 



When the altitude of the sun is 57°48', or a little greater, the two 

 tangent arcs, springing from a connnon point on the solar vertical, 

 form a wide V. 



"When the solar altitude equals 67°52', the two arcs, now merged 

 into a smooth continuous curve, are tangent to the halo at its lowest 

 poiut. 



Finally, for altitudes of the sun greater than 67°52', the arcs, still 

 a])i)earing as a single curve, are slightly separated from the circular 

 halo even at its lowest and closest ])oint. 



When the altitude of the sun is less than 22°8' superlateral tan- 

 gent arcs similar to the infralateral are produced. 



Unusual halos. — Halos of various radii other than those already 

 given have occasionally been reported. They can readily be ac- 

 counted for on the assumption that the columnar ice crystals have 

 certain pyramidal bases that alford the appropriate refraction angles. 



Obviously, each bright spot of the primary halo phenomena, espe- 

 cially the upper and lower points of the 22° circle and its parhelia, 

 must in turn be the source of secondary halos. Doubtless, the 22° 

 halos of the lateral parhelia contribute much to the flaring vertical 

 column through the sun that occasionally has been seen; and, per- 

 haps, the brilliant upper and lower points of the halo of 22° may 

 ])roduce faint secondary parhelic circles. In general, however, very 

 few of the secondary halos are ever bright enough to be seen even 

 when carefully looked for. 



A few halos not included in any of the above classes have been 

 once reported. No satisfactory explanations of them have been 

 offered. Clearly, though, since the ice crystal appears in many 

 modified forms — with flat tabular, and pyramidal ends, for instance — ■ 

 and even in orderly clusters, it is obvious that although only a few 

 halos are Avell known, a great many are possible. 



