OF ARTS AND SCIENCES: MAY 10, 1870. 215 



Professor Lovering made the following communication : — 



" Optical Meteorology has been developed mathematically with great- 

 er success than any other department of this complex science. The 

 principal features of a fully developed halo are : 1. The inner circle, 

 concentric with the luminary, and having a radius of about 22°. 2. The 

 outer circle, also concentric with the luminary, and having a radius of 

 about 46°. Both of these circles, called the smaller and larger halos, 

 are tinged with the colors of the spectrum, the blue being the outermost 

 color. 3. The parhelion circle which passes through the luminary and 

 is parallel to the horizon. This circle is white. 4. Upon this circle, and 

 at a distance of 22° or more from the luminary, are two mock suns, 

 the edges towards the sun being reddish and the opposite edges bluish. 

 5. A sort of tail stretching from these mock suns horizontally, and op- 

 posite to the line which connects them with the sun, to the distance of 

 43° 28', or more, from the sun. 6. The tangent curve to the inner halo. 

 7. The tangent curve to the outer hald. 



All these features of the halo are satisfactorily explained by refrac- 

 tion and reflection, produced by hexagonal prisms of ice, floating or 

 sinking in the higher region of the atmosphere. These particles may 

 be so situated as to present three independent cases. 1. They may be 

 indiscriminately in all possible positions. 2. The axes of the prisms 

 may be parallel and vertical, the sides of the prisms facing all azimuths. 

 3. The axes of the prisms may be horizontal, but in all possible azimuths. 

 The Jirst case would exist when the particles of ice were newly formed, 

 and had not accumulated so much velocity that the resistance of the air 

 would bring the surface of least resistance to the front. If the three 

 dimensions of the crystal were nearly the same, there would be no sur- 

 face of least resistance, and the air would exercise no directing influ- 

 ence. The second case would arise, as the consequence of increasing 

 velocity and resistance, if the minimum section of the prism was parallel 

 to the base. The third ca.se would arise, under similar circumstances, if 

 the minimum section was perpendicular to the base. All three cases 

 might coexist at the same moment, because some of the prisms were 

 long and others short, and because some of the prisms had had less 

 time than others to fall, and accumulate velocity and resistance, since 

 their first formation. 



Of the various angles formed by the sides and ends of these prisms, 

 some would exceed the limit of transmission, others would be zero and 

 produce no refraction. There would remain, of the available angles, 



