May 24, 1838.
FRANCIS BAILY, Esq., V.P. and Treas., in the Chair.
His Imperial and Royal Highness Leopold II., 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 Principia, 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 communicated by Newton to Flamsteed. On this basis a table was computed and communicated to Flamsteed; but Newton subsequent-
