160 Royal Society, 



stant, by means of which the horizontal refraction is made to agree 

 with the true quantity. The author considers, with Dr. Brinkley, 

 that the French table, founded on La Place's investigation, is only a 

 little less empirical than the other tables, and that the hypothesis of 

 La Place does not appear to possess any superiority over other sup- 

 posed constitutions of the atmosphere in leading to a better and less 

 exceptionable theory. 



After eulogizing Bessel's tables of mean refractions, published in 

 his Tabulce RegiomontancE, the author refers to his own paper in the 

 Philosophical Transactions for 1823 *. In this paper the refractions 

 are deduced entirely from the very simple formula, — 



i:^,=i-fa-c ) 



in which /5 stands for the dilatation of air or gas by heat, r' and r" 

 for the temperature at the earth's surface, and at any height above 

 it, and c~" for the density of the air at that height in parts of its 

 density at the surface. If this formula be verified at the earth's sur- 

 face in any invariable atmosphere, by giving a proper value to the 

 constant/, it will still hold, at least with a very small deviation from 

 exactness, at a great elevation; and this is immediately shown. 



This manner of arriving at the constitution of the atmosphere is 

 contrasted with the procedure of M. Biot of transforming an alge- 

 braical formula, for the express purpose of bringing out a given re- 

 sult. As the problem in the 3Iecamque Celeste is solved by means 

 of an interpolated atmosphere between two others; as in Mr. Ivory's 

 paper of 1823, there is no allusion to such an atmosphere; and as 

 the table in that paper is essentially different from all the tables 

 computed by other methods, he contends that all these must be suf- 

 ficient to stamp an appropriate character on his solution of the pro- 

 blem. But if ingenuity could trace some relation, in respect of the 

 algebraic expression, between the paper of 1823 and La Place's cal- 

 culations, he considers that it is not difficult to find, between the 

 same paper and the view of the problem taken by the author of the 

 Principia in 1696, an analogy much more simple and striking. 

 Newton having solved the problem, on the supposition that the den- 

 sity of the air is produced solely by pressure, and having found that 

 the refractions thus obtained greatly exceeded the observed quantities 

 near the horizon, inferred, in the true spirit of research, that there 

 must be some cause not taken into account, such as the agency of 

 heat, which should produce, in the lower part of the atmosphere, the 

 proper degree of rarefaction necessary to reconcile the theoretical 

 with the observed refractions. The author's sole intention, in intro- 

 ducing the quantity y in his formula, is to cause the heat at the 

 earth's surface to decrease in ascending, at the same rate that ac- 

 tually obtains in nature, not before noticed by any geometer, but 

 which evidently has the effect of supplying the desideratum of 

 Newton. 



• Mr. Ivory gave an account of the theory of refractions enunciated in 

 his paper of 1823, in the Phil. Mag. First Series, vol. Ixiii. p. 420.— Edit. 



