:^53 



Art. XVI. ASTRONOMICAL AND NAUTICAL COL- 

 LECTIONS. No. VI. 



i. A Postscript o)i Atmospherical Refraction. By Thomas 

 YouMG, M.D., F.R.S. i^rom ^Ac Philosophical Trans- 

 actions yb;- 1819. With a parenthetical Correction. 



1. A SIMPLE and convenient method of calculating the pre- 

 cise magnitude of the atmospherical refraction, in the neighbour- 

 hood of the horizon, has generally been considered as almost 

 unattainable ; and Dr. Brinkley has even been disposed to 

 assert the " impossibility of investigating an exact formula," 

 [that should represent all its variations], notwithstanding the 

 " striking specimens of mathematical skill, which," as he justly 

 observes, " have been exhibited in the inquiry." We shall find, 

 however, that the principal difficulties m.ay be evaded, if not 

 overcome, by some very easy expedients. 



2. The distance from the centre of the earth being repre- 

 sented by X, and the weight of the superincumbent column by 

 y, the actual density may be called z, and the element of y will 

 vary as the element of x and as the density conjointly ; conse- 

 quently, dy = — mzdiX ; the constant quantity m being the re- 

 ciprocal of the modulus of elasticity. The refractive density 

 may be called 1 -f pz, p being a very small fraction ; and it is 

 easy to see that the perpendicular u, falling on the direction of 

 the light, will always vary inversely us the refractive density, 

 since that perpendicular continually represents the sines of the 

 consecutive angles, belonging to each of the concentric surfaces 

 at which the refraction may be supposed to take place (Nat. 



Phil. II. p. 81 :) and u = — ! — , s being a constant quantity. 

 \+pz 



The angular refraction at each point will obviously be directly 



as the elementary change of this perpendicular, and inversely as 



the distance v from the point of incidence ; whence the fluxion 



of the refraction will be -?^ = dr, as is already well known. 



V 



3. For the fluent of this expression, which cannot be directly 



