|oo On tht douke Images caufed by Almofphcrical RefraElion. 



fomc judgment of its nature ; for, whether the denfities depend on different fpecific 

 gravities of different fluids, or on unequal temperatures of different portions of the fame 

 fluid, the curves will be nearly alike. 



In each of thcfe cafes, to whatever fmall dillance p c. Fig. 2, the mutual attra£lion is 

 fufficient to occaGon intimate union of the fluids, the denfity m n of the mixture will be 

 an arithmetic mean ; and, for the fame reafon, at any intermediate fmaller dillances, there 

 will be a feries of arithmetic means efy g h-, &c. interpol'ed, and the line a 0, uniting the 

 ordinates, will be ftraight. 



By progreffive cffedl of this attraftion, and fucceffive interpolations, In Fig. 1, curves 

 d efnit r s t m, will be formed, of which the ftraight lines w/>, t qt &c. are tangent. 



The attra£ling denfities « />, e j, &c. are fubtangents ; and if it be admitted that thefe 

 are every where equal, the curves fo produced are logarithmic, and the increment of the 

 ordinate greateft at m, where they meet. 



Prop. 3. If parallel rays pafs through a medium varying according to the preceding 

 propofition, thofe above the point of contrary flexure will be made to diverge, and thofe 

 below the fame point will converge, after their paffage through it. 



For fince the deviation of each ray depends on the increment of denfity where it paffes, 

 and fince the increment of denfity is greateft at the point of contrary flexure, any rays, as 

 a b. Fig. 3, paflSng near to that point, will be refrafted more towards the denfer medium 

 than thofe at c d, which move in a higher ftratum, and will diverge from them, but 

 will be refra£led towards and meet thofe ^t ef, which pafs nearer to the denfer medium, 

 where the increments of denfity are alfo lefs. 



Cor. Hence adjacent portions of the converging rays will form a focus, beyond which 

 they will diverge again ; and the varied medium will produce effects fimilar to thofe caufed 

 by a medium of uniform denfity * having a furface fimilar to the curve of denfities, fince 

 convergence or divergence will be produced, according as the curve of denfities is convex 

 or concave ; confequently, by tracing backwards, to the extremities of an obje£l, the 

 progrefs of the vifual rays (or axes of the pencils received by the eye) it will be 

 manifeft that, 



Any objedl feen through the inclined concave part r m, Fig. 5, would appear elevated, 

 creft, and fomewhat diminiftied. 



An obje£l feen through m d, where it is convex and inclined, would be elevated ; and, 

 if fituated beyond the focus of vifual rays from the eye, it would appear inverted. The 

 magnitude would depend on the relative diftances of the eye and obje£t. 



* In the varied medium, b c and b m. Fig. 4, the correfponding increments of the abfcifla and ordinate, 

 are to each other as radius to the tangent of the angle c. Therefore, the tangent of deviation, which is as 

 the increment of the ordinate, varies as the tangent of the angle c. 



So alfo, in the uniform medium, fince the fines of refraction and incidence are in a given ratio, then 

 differences will bear a given r.itio to either of them } and, when the angles are fmall, the tangent of de- 

 Ttation will vary at the tangent of incidence, or as the tangent of the angle e, which is e^ual to it. 



Below 



