30S 



CATALOGUE. — PHYSICAL OPTICS. 



not greater than this, and tjiere couM scarcely have been 

 any material error in the observation. 



The situation of the lateral parhelia, without the halo, is 

 very satisfactorily explained by Mariotte : and the diversi- 

 fied forms of the tangent arches may" probably all be de- 

 duced from the suppositions laid down in the Journals of 

 the Royal Institution. As an instance, we may take the 

 ease there described by Sir Henry Englefield, where the 

 sun's altitude was about 1 5°. The horizontal prisms will 

 then cause an appearance of an arch with a contrary curva- 

 ture, exactly as Sir Henry has described it. 



The calculation is somewhat intricate : Its principal steps 

 are these, taking the refractive power ^. 



Deviation of transverse rays Qs" 37'. 



For rays inclined 20°, the inclination of the planes of the 

 raysisag" 32', the deviation 1<J° 12': the altitude being is", 

 the angle with the horizon is 25° 8' more than the altitude. 



For rays inclined 25°, the inclination of the planes is 34°, 

 the deviation 27° 47': the angle with the horizon 25° 47' 

 more than the altitude 15°. 



For rays inclined 30°, the inclination of the planes is 

 iao°, that is, the rays are in the planes of the surfaces ; the 

 deviation 39° 56'; the angle with the horizon a° 4' less 

 than the altitude 15°. 



When the altitude increases, the tangent arch descends 

 so as to approach considerably to the halo, as in the halos 

 observed by Halley and by Barker. For, calculating upon 

 the true refractive power of ice, the angles become these. 



For rays inclined 25°, the inclination of the planes 30° 

 Si', the deviation 25° 4o',=:2l'' 50' -f 3° 5o', the angle with 

 the horizon 50° 24'=:45°-hll° 24'. For altitude 15°, 38° 

 S7'=:i5»+23°S7'. 



It may also become double, the inferior arch being visi- 

 ble: thus the angle with the horizon becomes 21° is' or 

 45° — 23°42', as well as 56° 24'. 



The mode of calculation is this ; A being the inclination 



within the prism, and r the index. Sec. Bzz '—• for the 



incidence; S.C—r.S.B, D=C — B. As S.C : Sec. A :: S:D: t, 



^Ix^ly, 1 — y -.^x:: Had : T. E, 2 E is the mutual incli- 

 nation of the planes passing through the rays and the axis 



S. F ; 2 F is the whole de- 



T A 

 of the prism, — '• — '•: ij: : : Rad 



nation: 1- 



T.A 



— -—Ixx-^Lxx; z:^-^^^ ': : S. Altitude : S. G, the 

 y + T 



elevation of the plane of the incident ray ; G±: 2E=:H the 



T A 

 dcvatioD of the plane of the emergent ray ; -^ ■ z : : S. 



H : S. 1, the depression of the emergent ray. 



Mr. Cavendish has suggested, with great apparent proba- 

 bility, that the external halo may be produced by the re- 

 fraction of the rectangular termination of the crystals, rather 

 than by two successive refractions through the angles of 

 different crystals : which, with the index 1.31. would pro- 

 duce a deviation of 45° 44'. If this supposition is true, the 

 index cannot be greater than 1.31 : for 1.32 would give 47' 

 56' : which is more than appears to have ever been assigned. 



The mean of 4 accurate observations is about 45° 5o', that 

 of 4 of the best estimations 46". 



The lateral anthelia may be produced by the rays refract- 

 ed after two internal reflections, which will have a constant 

 deviation 60° greater than those which form the halo : these 

 anthelia ought therefore to be about 82° from the sun ; they 

 are however usually represented as much more distant. 



Glories, or coloured Anthelia. 

 See Colours from Interference, 

 Ulloa's Voyage. I. 



Mentions several coloured circles of different sizes, and a 

 white one 67° in diameter. 



Macfait. Etl. ess. I. 197. 



Halos with a glory. 



Mongez on a glory. Roz. XII. 223. 



8 June, by moonshine. 



Haygaith on a glory. Manch. M. III. 46S. 



In a cloud, which was probably icy. The shadow was 

 surrounded by coloured coronae, next to these were bright 

 arches, wider than those of a rainbow. 



Simple Rainbows. 

 I)e Dominis de radiis visus et lucis. 



Primary rainbow. 



Rainbows crossing each other, by the river, 



at Chartres. Ph. tr. 1665—6.1. 219. 

 fLinus on the rainbow. Ph. tr. 1675. X. 



386. 

 Mariotte on the rainbow. A. P. I. isg. 

 Lahire on a red iris seen at Angers in I69O. 



A. P. II. 53. 

 Cassini on a rainbow in the twilight. A. P. 



X. 275. 

 Halley on an iris by reflection. Ph. tr. I698. 



XX. 193. 



A very accurate account. ' 

 Halley de iride. Ph. tr. 1 700. XXII. 714. 



