VOL. XC.] PHILOSOPHICAL TRANSACTIONS. 66*7 



XII. On Double Images caused by Atmospherical Refraction, By Wm. H. 

 Wollaston, M. D., F. R. S. p. 23Q. 



In some of the last volumes of the Philos. Trans, there have been related many 

 instances of strong atmospherical refraction, by which, objects seen near the horizon 

 have appeared inverted, and the horizon itself either elevated or depressed. Mr. 

 Huddart first took notice of a distinct image, inverted beneath the object itself; 

 and, in the Philos. Trans, for 1797, has described several such appearances, accom- 

 panied with an optical explanation, where he shows that the lowest strata of the air 

 were at the time endued with a weaker refractive power, than others at a small 

 elevation. In the volume for 1799> Mr. Vince has given an instance, fig. 1, where 

 erect, as well as inverted images were visible above, instead of beneath, the objects 

 themselves; and, by tracing the progress of the rays of light, in a manner similar 

 to Mr. Huddart's, concludes that these phenomena arose from " unusual variations" 

 of increasing density in the lower strata of the atmosphere. In the volume for 

 1795, Mr. Dalby mentions having seen " the top of a hill appear detached, for the 

 sky was seen under it." In this case, as well as in the preceding, it is probable 

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

 inverted image of the upper, as the sky could not be seen beneath it, but by an 

 inverted course of the rays. 



Since the causes of these peculiarities of terrestrial refraction have not received 

 so full an explanation as might be wished, I have endeavoured, 1st. To inves- 

 tigate theoretically the successive variations of increasing or decreasing density to 

 which fluids in general are liable, and the laws of the refractions occasioned by 

 them. 2dly. To illustrate and confirm the truth of this theory, by experiments 

 with fluids of known density. And lastly, to ascertain, by trial on the air itself, 

 the causes and extent of those variations of its refractive density, on which the in- 

 versions of objects, and other phenomena observed, appear to depend. The 

 general laws may be comprised in three propositions. 



Prop. 1. If the density of any medium varies by parallel indefinitely thin strata, 

 any rays of light moving through it in the direction of the strata, will be made to 

 deviate during their passage, and their deviations will be in proportion to the incre- 

 ments of density where they pass. For each ray will be bent towards the denser 

 strata, by a refracting force proportioned to the difference of the densities above 

 and below the line of its passage; and as their velocities are the same, and there- 

 fore the times of action of the forces equal, the deviations will be as the refracting 

 forces, i. e. as the increments of density. 



Prop. 2. When 2 fluids of unequal density are brought into contact, and unite 

 by mutual penetration; if the densities at different heights be expressed by ordi- 

 nates, the curve which terminates these ordinates will have a point of contrary 

 flexure. For the straight lines da, rn, pi. 11, fig. 2, which terminate the ordinates 

 rx, dy, of uniform density, will be parallel, and, if not united by contrary curva- 



4a 2 



