318 iMr. Ivoi'y on the Theory of the Astronomical Refractions. 



ihat Halley's table is no other than the one which Newton 

 computed on the sup})osition that the densities in the atmo- 

 sphere are proportional to the pressures. The discrepancies, 

 amounting in every instance to a small part of the whole 

 quantity, are such as might be expected to occur unavoidably 

 in the intricate and laborious methods of calculation followed 

 by Newton. Some part of the differences may also arise from 

 the elements of the formula, which, being deduced from only 

 two numbers of the table, may not exactly coincide with the 

 fundamental quantities which Newton assumed. M. Biot, by 

 a method different from Kramp's, has found other elements, 

 which make the horizontal refraction 8"*3 less than in the 

 table; but these small variations, which proceed from cal- 

 culating in different ways, only confirm more strongly that 

 Hallev's table is the same which Newton constructed by his 

 second hypothesis, and communicated to Flamsteed. 



It appears from what has been said, that, as far as the ma- 

 thematics is concerned, the problem of the astronomical re- 

 fractions was fully mastered by Newton. It would be strange 

 indeed to suppose that the author of the theories in the Prin- 

 cipia would find difficulty to apply them in a case to which 

 he bent the whole force of his mind. But he was embar- 

 rassed bv the suppositions he found it necessary to make 

 respecting the physical constitution of the atmosphere. His 

 first hypothesis is evidently contrary to nature, in admitting 

 that air at all altitudes exerts the same power to inflect the 

 licrht to the earth's centre; his second method made the re- 

 fractions too great near the horizon, thereby proving the ne- 

 cessity of searching out some new cause for the purpose of 

 reconcilin"- the theory with observation. Averse from hypo- 

 theses, he seems, on these accounts, to have declined inserting 

 in his works a problem which had cost him so much labour, 

 and upon his solution of which he evidently set some value. 



If the different attempts to solve this problem are to be 

 tried with the same rigour that Newton judged his own, it 

 must be decided that they are all liable to objections. They 

 all involve some supposition that has no foundation in nature; 

 or thev leave out some necessary condition of the problem. 

 It is allowed that the variation of heat at different altitudes is 

 unknown ; that we are equally unacquainted with the manner 

 in which is diffused the aqueous vapour that is always found, 

 more or less, in the atmosphere ; that the law of the densities 

 has not been ascertained. But besides these capital points, 

 the accurate M. Poisson will suggest other properties that 

 must be attended to in an atmosphere in equilibrium : the 

 conducting power of heat varying with the condilicn of the 



