On the double hnagts catifedby AtmoJ^herkal ReJraBion, *t^ 



In tlie volume for 1799, Mr. Vince has given an inflance* (tab. i. fig. 1.) where cre£t 

 as well as inverted images were vifible above, inftead of beneath, the objefts themfelves } 

 and by tracing the progrefs of the rays of light, in a manner fimilar to Mr. Huddart's, 

 concludes that thefe phenomena arofe from " unufual variations" of increafing denfity in 

 the lower ftrata of the atmofphere. 



In the volume for 1 795, Mr. Dalby mentions having feen " the top of a hill appear 

 " detached, for the fky was feen under it." In this cafe, as well as in the preceding, it is 

 probable that reverfion took place, and that the lower half of the portion detached was an 

 inverted image of the upper, as the iky could not be feen beneath it, but by an inverted 

 courfe of the rays. 



Since the caufes of thefe peculiarities of terreftrial refra£tion have not received fo full 

 an explanation as might be wifhed, I have endeavoured, 



ift. To inveftigate theoretically the fucceflive variations of increafing or decreafing denfity 

 to which fluids in general are liable, and the laws of the refradlions occafioned by them. 



2dly. To illuftrate and confirm the truth of this theory, by experiments with fluids of 

 known denfity. 



And laftly, to afccrtain, by trial upon the air itfelf, the caufes and extent of thofc 

 variations of its refradlive denfity, on which the inverfions of objefts and other phenomena 

 obferved, appear to depend. 



The general laws may be comprized in three propofitions. 



Prop. 1. If the denfity of any medium varies by parallel Indefinitely thin ftrata, any 

 rays of light moving through it in the direSlion of the ftrata, will be made to deviate during 

 their paflage, and their deviations will be in proportion to the increments of denfity where 

 they pafs. 



For each ray will be bent towards the denfer ftrata, by a refradling force proportioned 

 to the difference of the denfities above and below the line of its paflage ; and as their 

 velocities are the fame, and therefore the times of aftion of the forces equal, the deviation* 

 will be at the refrafting forces, /'. e. as the increments of denfity. ' 



Prop. 2. When two fluids of unequal denfity are brought into contaft, and unite by 

 mutual penetration ; if the denfities at different heights be cxprefTed by ordinatcs, the 

 curve which terminates thefe ordinates will have a point of contrary flexure. 



For the ftraight lines J ^, r 71 (Plate XIII.) Fig. I. which terminate the ordinates r at, 

 dy^ of uniform denfity, will be parallel, and, if not united by contrary curvature, fome 

 ftraight line of union, as a muft be fuppofed. But, from whatever caufe the firft line 

 fl is inferred, by the fame caufe other intermediate lines m p, t q, Sec. will be produced, 

 and curves d e f tn, m t s r, will be ultimately formed, having a point of contrary 

 flexure at m. ; 



The form of the curve does not appear to admit of accurate inveftigation, nor is it of 



importance to the fubfequent reafoning, if wholly unknown. We may, however, forni 



...... / 



* Ibid. II. 140. 



Q^q 2 forac 



