404 Proceedings of the Royal Irish Academy. 



^ith. tte diagonals of tlie bases, thus presenting tlie appearance of pen- 

 tagonal plates. 



Some varieties of cirrus clouds, though, doubtless composed of fi'ozen 

 particles, do not exhibit halos. These are of a whitish colour', and 

 are probably more or less opaque ; sometimes, also, they may consist 

 of particles having a globular form (like small snow or hail), which 

 would explain the absence of coloured rings. During a balloon ascent 

 fi'om Paris in 1874, MM. Albert and Gaston Tissandier passed through 

 a zone of ice crystals which extended through a depth of 200 metres, 

 and presented the appearance of a " galaxy of Kttle hexagonal stars;" 

 yet as no colour-ed cii'cles are mentioned as having been seen, it is to 

 be presumed that they were not visible. In this instance, therefore, 

 the crystals must have been either partly opaque or irregularly formed. 



Ei-ight specks of halo appearing at a greater distance from the sun 

 than the parhelia above mentioned are called anthelia. These are of 

 rare occurrence, and though I looked for them on several occasions 

 which I thought favourable to their appearance, I have not discerned 

 them in any instance. Three positions are usually assigned to them, 

 the fii'st being about 90° from the sun. In reference to this appear- 

 ance Dr. Young says : •' The lateral anthelia may be produced by the 

 rays refi'acted after two intermediate reflections, which will have a 

 constant deviation 60° greater than those which fonn the halo. These 

 anthelia ought, therefore, to be about 82° from the sun. They are, 

 however, usually represented as much more distant." The explana- 

 tion here given is doubtless correct ; but there seems to be a mistake 

 in assigning 82° as the distance from the sun, that quantity being not 

 the greatest deviation, but its supplement. If x and z be the angles 

 made by the incident and emergent rays with perpendiculars to the 

 respective surfaces, and /= the refracting angle of the prism (not re- 

 garding the signs of the angles, and supposing also that in the progress 

 of a ray each change of direction is made from one sur-face of the prism 

 to the next in succession which is inclined to it at an angle equal to /), 

 then the deviation after two refi'actions and two reflections will be 

 ZI - (x + z). For hexagonal prisms this becomes 180° - {x ■\- %), the 

 maximum value of which (corresponding to index 1-31) is 98° 10'. The 

 part of the light which is cUfferently reflected does not form an anthelion. 

 at any deviation whatever. Hevelius and others have given 90° as the 

 distance of the anthelia observed by them ; but these instances are not 

 conclusive, as the elongations seem to have been merely estimated, and 

 not obtained by measuiTmlent. 



The other positions of the phenomena are mentioned in the follow- 

 ing statement : — '' The anthelia seem to be referrible to two refractions 

 and an intermediate reflection within the same crystal, causing a de- 

 viation of about 120 -f 22 = 142° ; and sometimes with two intermediate 

 reflections producing an angle of 60 + 22 = 82° only. It is not very 

 easy, however, to assign a reason for the appearance of an anthelion 

 exactly opposite to the sun, which is said to have been sometimes seen 

 in the horizontal circle." — {Encyclojic^dia Britannica, vol. vi., p. 645.) 



