60 



May 24, 1838. 



FRANCIS BAILY, Esq., V.P. and Treas., in the Chair. 



His Imperial and Roj^al Highness Leopold 11. , Grand duke of 

 Tuscany, was elected a Fellow. 



The reading of the paper by Mr. Ivory, " On the Theory of the 

 Astronomical Refractions," was concluded. 



In this communication, the author, after stating that the mean 

 refractions are the object of investigation, and fully defining what 

 he understands by this term, gives an historical review of what has 

 been done up to the present time on this very important subject. 

 Having stated that the foundation of the theory of astronomical re- 

 fractions was laid by Dominique Cassini, he deduces on Cassini's 

 hypothesis (that of an homogeneous atmosphere) a formula for the 

 refraction, which agrees exactly with that of La Place, employed in 

 computing the first part of the table of mean refractions, published 

 by the French Board of Longitude. 



The labours of our immortal countryman Newton, in this vast 

 field of inquiry, are next reviewed. As the density of the atmo- 

 sphere in ascending decreases gradually, the path described by a ray 

 from a star, in its passage through the atmosphere, is not a straight 

 line, as it would be on Cassini's hypothesis, but is a curve more and 

 more inflected towards the earth's centre. In the Principia there is 

 found whatever is necessary for determining the nature of this curve, 

 and, consequently, for solving the problem of the astronomical re- 

 fractions, which consists in ascertaining the difference between the 

 direction of light when it enters the atmosphere, and its ultimate 

 direction when it arrives at the earth's surface. 



On the principles established in the second section of the Prin- 

 cipia, the author deduces equations requisite for the solution of the 

 problem of astronomical refractions, and remarks that these equations 

 are perfectly general, and will apply in any constitution of the at- 

 mosphere that may be adopted. In this investigation, in preference 

 to employing functions with peculiar properties to express the mole- 

 cular action, the manner in which the forces act has been consider- 

 ed. When the light, in passing through the atmosphere, arrives at 

 a surface of increased density, it receives an impulse which may be 

 considered as instantaneous; and this impulse being distributed over 

 the breadth of a stratum of uniform density, ascertains the centripetal 

 force tending to the earth's centre, by the action of which the tra- 

 jectory is described. 



It appears, that Newton himself was the first to apply this new 

 method to the problem of the astronomical refractions. In his first 

 attempt he assumes that the densities decrease in ascending, in the 

 same proportion as the distances from the earth's centre increase. 

 On this supposition the author investigates a formula, which M. Biot 

 has also obtained, and which is equivalent to the construction com- 

 municated by Newton to Flamsteed. On this basis a table was 

 computed and communicated to Flamsteed; but Newton subsequent- 



