VOL. LXXXIX.] PHILOSOPHICAL TRANSACTIONS. 441 



draw the tangents Ea', ed', and a' b' will be the image of the object, as usually 

 formed. Now if we take the case represented in fig. 4, let a" b" represent the in- 

 verted image, and a'" b'" the erect image ; join a' 7 E, the a"'E, and Me, d'"e, and 

 these lines must respectively be the directions of the rays entering the eye from a 

 and b, in order to produce the images a" h" and a"" b'" ; hence these lines must be 

 tangents at e, to the curves which are described by the rays of light ; let therefore 

 anE, amE, bvE, bwE, be the curves described. We have therefore to assign a 

 cause which may bring rays passing above the rays arE, bsE, to the eye at e. Now 

 if there were no variation of the refractive power of the air, a ray of light passing 

 through it would describe a straight line ; therefore the curvature of a ray of 

 light passing through the atmosphere, depends on the variation of the refractive 

 power of the air. If therefore we suppose the air lying above arE, to vary quicker 

 in its refractive power than the air through which arE passes, the curvature of a 

 ray proceeding above that of arE, will be greater than the curvature of ars ; and 

 on this principle we may conceive that a ray may describe the curve anE : and, in 

 like manner, if a quicker variation of refractive power should take place above the 

 curve anE, than in that curve, a 3d ray may describe the curve amE. The same 

 may be said for the rays bvE, bwE, diverging from b. The alterations of the re- 

 fractive power may arise, partly from the variations of its density, and partly from 

 the variations of its moisture ; and the passage of the rays through the boundary 

 of the fog may there suffer a very considerable refraction ; for, from the motion 

 of the fog, and that of the images above-mentioned, I have no doubt that the fog 

 was a very considerable agent in producing the phenomena. When all the causes 

 co-operate, I can easily conceive that they may produce the effects which I have 

 described. If the cause should not operate in the tract of air through which the 

 curves anE, bvE pass, but should operate in the tract through which amE, bwE 

 pass, an erect image would be visible, but there would be no inverted image ; and 

 should it operate in the latter case, but not in the former, there would be Only an 

 inverted image. 



As the phenomena are very curious, and extraordinary in their nature, and have 

 not, that I know of, been before observed, I have thought proper to lay a descrip- 

 tion of them, with all the attending circumstances, before the r. s. They appear 

 to be of considerable importance ; as they lead us to a knowledge of those changes 

 to which the lower parts of the atmosphere are sometimes subject. If, when these 

 phenomena appear, a vessel, furnished with a barometer, thermometer, and hygro- 

 meter, below, and also at the top of the mast, were sent out to pass below the 

 horizon and return again, and an observer at land, having like instruments, were 

 to note, at certain intervals, the situation and figure of the images, it might throw 

 further light on this subject, and lead to useful discoveries respecting the state of the 

 atmosphere, from a conjunction of the causes which affect these instruments. 



vol. xvm. 3 L 



