172 Prof. Everett on the Optics of Mirage, 



the reflected sky. The sky itself, and its reflection in water, so 

 far exceed in brightness all other objects in an ordinary land- 

 scape, that when this gleam is seen in a place where the sky 

 cannot be, the observer feels irresistibly compelled to ascribe it 

 to water. 



IX. In the transmission of rays through a medium of conti- 

 nuously varying index, no proper distinction can be taken between 

 refraction and reflection. They shade insensibly into one an- 

 other ; or rather, I should perhaps say, both names are equally 

 inappropriate in this application. 



X. The following are some of the mistakes which have fre- 

 quently been made by writers on mirage : — 



1. The mistake of supposing that a ray in air can be bent at 

 an angle — in other words, can have a point of infinite curvature. 

 This would imply an absolutely abrupt change of index. 



2. The mistake of supposing that a ray can pursue a straight 

 course parallel to planes of equal index in a continuously vary- 

 ing medium. The contrary was pointed out so long ago as 

 1799 and 1800 by Vince and Wollaston in the Philosophical 

 Transactions, but appears to have since dropped out of mind. 



3. The mistake of supposing that rays which first ascend and 

 then descend, or which first descend and then ascend, must pro- 

 duce inverted images, or an appearance as of reflection. If all 

 the rays of a system are circular arcs in vertical planes, with the 

 same radius of curvature, and everywhere nearly horizontal, the 

 images which they present to the eye will be neither inverted 

 nor distorted, but simply elevated or depressed; for such a 

 system can be converted into a system of straight rays by a pro- 

 cess of bending which will not alter their distances apart. Let 

 such of them as lie in one vertical plane be represented by a dia- 

 gram drawn upon one face of a prismatic rod ; then if the rod 

 be bent in the plane of this face with a uniform curvature op- 

 posite to that of the lines of the diagram, all these lines will 

 become straight; and it is clear that this process does not sen- 

 sibly alter the distances between the lines, nor the angles at 

 which they intersect each other. 



Some further consequences of the law of ray-curvature, of 

 theoretical rather than practical interest, are reserved for a second 

 paper. 



