210 Ditermination of the Altitude of Great JiTiernside ^ 



this important subject, prefacing my own theories and obser- 

 vations by those of the iew yet enlightened authorities I have 

 been able to consult ? 



The strata or spherical shells of the atmosphere increasing 

 in density the nearer they approach the surface of the earth, 

 rays of light entering from above and not tending towards the 

 centre of these strata, which is also that of the earth, pass 

 with varying obliquity through media of increasing density, 

 ?ind, from the principles of optics, become curves convex 

 towards the eye of the observer. Hence the object is seen in 

 the direction of the inferior extremity of the curve, and the 

 observed elevation exceeds the true by an angular quantity 

 termed astronomical refraction. When these curves are in- 

 tercepted by a mountain or other object within the limits of 

 the atmosphere, the refraction is denominated terrestrial, and 

 bears a certain proportion to the angle formed at the centre 

 of the earth between the eye and the object. 



MM. Biot and Arago found from experiment that the re- 

 fringent force of dry air was directly as its pressure, and in- 

 versely as its temperature. The barom. being 29*922 inches, 

 and the therni. 32° ; the ratio of the sine of refraction to the 

 sine of incidence was constantly as 1 to 1-002943321, and the 

 correction for temperature equal to '00208 + for 1°. The 

 allowance for the moisture suspended in the atmosphere is con- 

 sidered too trivial to require notice. 



Experiments made with the barometer prove, that within 

 the limits of the observations the density of the atmosphere, 

 when of uniform temperature, diminishes in geometrical pro- 

 gression. Under such (unusual) circumstances, with a pres- 

 sure of 29"922, and temperature of 32°, Laplace calculates 

 the terrestrial refraction at ■g}j of the contained arc. 



Biot observes that when the altitudes are but small, the 

 densities of the air vary in arithmetical progression in propor- 

 tion to the difference of elevation, and determines the refrac- 

 tion in the ordinary condition of the atmosphere at ^i^ of 

 the arc ; to which, under such restrictions, it bears a constant 

 proportion. 



Dr. Maskelyne appears to have stated the refraction at yL. 

 An anonymous writer, who has treated the ray of light as a 

 projectile, deteni.ines the refraction, when nearly horizontal, 

 at y-j-.^ ; the barom. being 30 and the therm. 50, and the di- 

 minution of heat 1° in 300 feet. When the fall is about 1° 

 in 55 feet, the strata are of equal density, and the ray is un- 

 refracted or rectilinear. With a diminution still greater the 

 refraction becomes negative, the curve being co7icave towards 

 the eve of the observer. 



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