132 REPORT—1840. 
of the radii of the principal halos, which indicates a uniformity 
of cause incompatible with Huyghens’s assumption. The theory 
of Huyghens is alluded to by Newton, though without any ex- 
press approbation, at the close of his Theory of the Rainbow* ; 
and in another part of his Optics} the principle of refraction 
through ice-prisms of 58° or 60° is distinctly stated as the pro- 
bable cause of halos of 221°, which appears to have been New- 
ton’s own view, as he gives a reason for it (the oval form of some 
halost{), and does not quote Mariotte. 
281. So little reason, then, is there for supporting Huyghens’s 
theory on the ground that it was maintained by Newton, as M. 
Biot has done §, even since Mariotte’s theory has been revived 
by Young, who published it in the second volume of the Royal 
Institution Journal||, where he states that he had adopted 
the principle before he knew of Mariotte’s application of it ; 
and he had even inferred from it that the refractive index of 
ice is less than that of water, a fact then doubted, but after- 
wards confirmed by Dr. Wollaston. M. Babinet has therefore 
no ground for affirming ** that M. Arago was the first to revive 
Mariotte’s explanation. 
282. The most obvious facts in support of Mariotte’s theory 
of icy prisms are, 
(1). That the imperfect crystals of ice which alone we can 
obtain, have a tendency to rhombohedral crystallization, amongst 
the forms of which are three- and six-sided prisms ; and the 
minimum deviation of light through an ice-prism of 60° would 
give the halo of 223°. 
(2). The constancy of the effect gives a probability to a con- 
stant cause, such as a crystalline angle. 
(3). The fact that halos occur most frequently in cold cli- 
mates and after a sudden fall of temperature, when the moisture 
of the air is evidently and palpably deposited in icy spicule or 
hoar frost. In the excellent observations made in the United 
States, the relation between the sudden fall of the thermometer 
and the occurrence of halos is very clearly traced{}. 
* Optics, book i. part ii. prop. 9. + At the end of the second book. 
t It is rather singular that the same reason which was urged by Newton in 
favour of the theory of refraction by ice-prisms, should be stated by Arago 
(Annuaire, 1836, p. 8303; 1840, p. 303) as an anomaly which, on that theory, 
still requires explanation. It is plain that Newton had some theoretical opinion 
on the subject which he has not explained, and according to which the upper 
radius of the halo should be shorter than the lower. 
§ Traité de Physique, iii. 476. || See his Lectures, ii. 306. 
q Ibid. ** Comptes Rendus, iv. 639. 
+t Annual reports made to the legislature by the Regents of the Universities 
of the State of New York. 
