BuETOx — On Salos and Anthelia. 



405 



Here it is evident that the deviation, 142°, has been calculated for 

 rays whose paths vrithin the crystals make equal angles with the sur- 

 faces, but no reason has been adduced to show that these could form 

 an anthelion or halo. When light is once reflected in any regular 

 prism (in the manner before mentioned), the deviation is 180° - 2/ + 

 {x + %), which, since in this case % is always equal to x, reduces to 

 180° - 2/+ 2x. Now, as this quantity must vary twice as fast as x, 

 it cannot tend to become constant for any successive values thereof ; 

 from which it follows that there cannot be at any point such a spis- 

 situde of the homogeneous rays as is always requisite to form hales. 

 Thus it appears that no halo or anthelion can be caused by light 

 which has been only once reflected. 



An anthelion not differing much from the assigned position would 

 be produced by two refractions and two reflections in quadrilateral 

 prisms having right angles. The deviation in this case is 270° -{x + z), 

 which, when a maximum, gives 134° 16', the elongation of the an- 

 thelion formed by such crystals ; hence it appears probable that the 

 phenomena seen near this position were produced by rectangular 

 prisms, or by the ends of the usual hexagonal ones. 



If the colours of these phenomena were observed, their order with 

 respect to the sun would sufficiently indicate whether they were 

 formed by rays directly transmitted, or after two reflections. In the 

 former case it is evident that the deviation must be a minimum, and 

 in the latter a maximum, and the colours of the reflected anthelion 

 will be the reverse of those usually seen in halos ; but I have not 

 found them described in any instance. 



The third anthelion which appears opposite to the sun has not 

 been explained ; but it seems possible that a phenomenon of this kind 

 may sometimes be produced by part of the light which has been twice 

 reflected in rectangular prisms. If at each change of direction a ray 

 passes from one surface of such a prism to the next, or again, if the 



reflections be made at the two opposite surfaces which are adjacent to 

 that at which the light was first incident, the deviation will be 

 3/- (a; + %) as before. But it is easily seen that a portion of the light 

 may be so transmitted that after the second reflection it will again fall 



2M2 



