VOL. v.] PHILOSOPHICAL TRANSACTIONS. 45g 



obscurity. Whence it follows, that the angle of this cone BDE is that wliich 

 determines the diameter of the halo, which depends on the proportion the 

 opaque grain has to the transparent, in which it is inclosed. For if this dia- 

 meter is of 44 degrees, as is observed in most halos, the size of the opaque 

 grain will be to the transparent, as 40 to IQ. But he remarked that this pro- 

 portion was not always the same, and that the diversity of it was the cause that 

 sometimes there were seen many halos, one about the other, all having the sun 

 for their centre. 



He added, that it was easy to know why these halos were always of a round 

 figure, whether the sun be little or much raised above the horizon ; as also to 

 give the reason for their colours, which is the same with that in the triangular 

 glass-prisms ; as is evident by the tangents AC, drawn to the grain A, at the 

 points where the ray DA enters or comes out. He also noticed, that it was 

 manifest why the red colour is in the interior circumference of the halo. And 

 why the space which it takes in, and chiefly near the most lively coloured parts, 

 appears obscurer than the air about, viz. because it is there where most grains 

 are, which transmit no rays of the sun to our eyes, and so only darken the air, 

 as the drops of water when it rains. He farther noted, that M. Descartes, en- 

 deavouring to explain the cause of these halos, had committed a mistake, for 

 want of observations, truly relating to this last circumstance : Because he main- 

 tains that the space comprised within the halo is clearer than the air without ; 

 and to render a reason of it, he supposes certain grains, altogether transparent, 

 having the form of a lens, which supposition cannot therefore be true, because 

 what he deduces from it, is contrary to what is observed : Besides that the 

 roundness of the halo, in all the elevations of the sun, agrees not with it, as is 

 easily shown. 



As to the arch of the circle, which above touched the last halo seen May 1 2, 

 as also that the colours were more vivid in this place, and in that below, than 

 in the rest of the circle; he said, that these effects did not proceed from the 

 grains he had been speaking of, but from another cause, which also serves for 

 the production of the parhelia, and the circles which almost always accompany 

 them. Touching which circles and parhelias, he remarked, that besides the 

 round and semi-opaque grains, there were also formed in the air certain little 

 cylinders of the like nature, and of which M. Descartes himself declared, in his 

 Treatise of Meteors, he had observed some, not indeed with opaque kernels 

 within, but that the same cause which produces them in the round grains, 

 could also produce them in cylinders : Which being supposed to be such as 

 fig. 4 represents them, viz. oblong icy grains, and roundish at both ends, 

 having the inner kernel of the same shape, it was found, that from their differ- 



3m2 



