108 CAUSE OF THE HALO, &c. CHAP. 2. 20. 



and impinging on A, should pass through the 

 cloud in a straight line, that is, perpendicular 

 to A B, it would appear to a spectator at D. 

 But it appears to a spectator at E ; therefore it 

 diverges from the straight line A D in the line 

 A E, making with it an angle DAE; join 

 M A and M E, and E D, making A D E M 

 a parallelogram, and A E its diagonal. Then 

 (Euc. i. 29.) the angle D A E, or angle of the 

 aberration of the ray, is equal to the alternate 

 angle A E M, or angle under which the semi- 

 diameter A M of the Halo A B appears. 



From the above, it appears then, that a Halo 

 of 48 diameter may be ascribed to a property 

 in the cloud of refracting certain of the rays at 

 an angle of 24. A double Halo, the exterior 

 ring whereof includes an area of 48, and the 

 interior ring whereof includes one of 10, must 

 be attributed to a property in the cloud of 

 refracting certain of the rays at an angle of 

 24, and certain other rays at an angle of 5, 

 and so on of triple ones. 



A Corona of 10 diameter appears to be the 

 consequence of a property in the cloud to refract 

 certain of the rays at every angle, from the 

 smallest, say an angle of \" to 5, beyond which 

 the rays are refracted in the cloud, in the usual 



