148 Royal Society, 



the density of the lower part of the atmosphere which is reqiiired for 

 reconciling theory with observation. It becomes necessary, in par- 

 ticular, to investigate the law according to which the temperature 

 diminishes as the height increases. The initial value of the rate of 

 diminution has to be determined by experiment ; and the introduc- 

 tion of this new element into the equation of an atmosphere in equi- 

 librium must be an approach to the true solution of the problem of 

 the refractions, and is indispensable if arbitrary assumptions are to 

 be avoided. The author proceeds to notice Laplace's solution, 

 which, though highly ingenious, is nevertheless hypothetical ; and 

 he adverts to the want of precision exhibited in Biot's dissertation 

 on the influence which the presence of aqueous vapour in the air 

 has on the refractions : but refers to the paper which accompanies 

 his letter for the further explanation of his views on this subject. 



A paper was also in part read, entitled, " On the Theory of the 

 Astronomical Refractions," by James Ivory, Esq., K.H., M.A., 

 F.R.S., &c. 



May 10. — The reading of Mr. Ivory's paper " On the Theory of 

 the Astronomical Refractions," was resumed. 



May 24. — 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 



