282 Mr. Ivory on the Theory of the Astronomical Refractions. 



agreeing exactly with Laplace's formula employed in com- 

 puting the first part of the table of mean refractions published 

 by the French Board of Longitude. 



2. The publication of Newton's Principia enabled geome- 

 ters to take a more enlarged view of the astronomical refrac- 

 tions, and one approaching nearer to nature. According to 

 Cassini, the atmosphere is a spherical stratum of air, uniform 

 in its density throughout, diffused round the earth to the 

 hei'fht of about five miles; in reality the density decreases 

 gradually in ascending, and is hardly so much attenuated 

 as to be ineffective to refract the light at the great elevation 

 of fifty miles. The path described by the light of a star in 

 its passage through the atmosphere is therefore not a straight 

 line, as it would be in the hypothesis of Cassini, but a curve 

 more and more inflected towards the earth's centre by the 

 successive action of air of increasing density. Now in the 

 Principia there is found whatever is necessary for determining 

 the nature of this curve, and consequently for solving the pro- 

 blem of the astronomical refractions, which consists in ascer- 

 tainino- the difference between the direction of the light when 

 it enters the atmosphere, and its ultimate direction when it 

 arrives at the earth's surface. In the last section of the first 

 book of his immortal work, Newton teaches in what manner 

 the molecules of bodies act upon the rays of light and retract 

 them; and as the atmosphere must be uniform in its condi- 

 tion at all equal altitudes, its action upon light can only be a 

 force directed to the centre of the earth ; so that the trajec- 

 tory in which the light moves, being described by a centripetal 

 force, the determination of its figure will fall under the pro- 

 positions contained in the second section of the same book. 



Conceive that light falls upon an atmosphere A G K, con- 

 stituted as Cassini supposed, spherical in its form, concentric 



to the earth, of the same 

 density ^ throughout; and 

 suppose that the attractive 

 force of the molecules of air 

 situated in the surface A G K 

 extends to ?« n on one side, 

 and to ni' n' on the other. 

 Every molecule of light when 

 K it arrives at m 7i will be at- 

 tracted by the air in a direc- 

 tion perpendicular to the sur- 

 face A G K, and tending to 

 C the centre of the earth ; it 

 will continue to suffer a varied attraction till it penetrates to 



