of the Problem of Atmospherical Refraction. 35 



a certain value is given to the indefinite index. Secondly, 

 Dr. Young was aware that the two solutions were a part of 

 my theory when he published them. For my paper was be- 

 fore the author in manuscript when he wrote the XlVth Num- 

 ber of the Astronomical Collections ; and when he speaks of 



the equation 3/ = s ^ the words imply that he had compared 

 it with other particular cases of my general formulae, havmg 



different exponents. The other formula, 3/ = f z 2 - ^z% he 

 never mentions without noticing that it belongs to a class ot 

 atmospheres which I had excluded; excluded, however, for 

 no other reason than that they did not seem to approach so 

 near nature as another class. Thirdly, Dr. Young has found 

 out no physical property of the two atmospheres he has 

 chosen which is not expressly developed in my paper. He 

 lays, indeed, great stress on the mathematical property, which 

 they possess, of exhibiting the refraction in a finite form. 

 But, besides that this consideration is really of no moment 

 and can weigh nothing in the balance against the least physi- 

 cal advantage, it is no discovery ; for the two assumptions of 

 Dr. Youno- are immediately deduced from my general for- 

 mulae, bv"choosing the particular value of the index that will 

 make the radical in the expression of the refraction a qua- 

 dratic trinomial. Fourthly, Dr. Young has nowhere inves- 

 tif^ated either of the two assumptions. It is easy to take the 

 expressions when they are found out, and, by substituting 

 them in the formula for the refraction, to show that the re- 

 sults are integrable; which is all that Dr. Young has done. 

 But the question is how he came by them. Mere conjecture 

 can hardly be supposed to lead to such particular formulae. 

 There must have been some train of thought which enabled 

 him to choose two individual expressions in an infinite variety. 

 But on this point we have no information. And we are as 

 little informed on what grounds he asserts that the equation, 



y _ 3 zl _ 1 s'^, belongs to an atmosphere which perfectly 

 i-epre^sents the true decrement of heat at the earth's surihce. 

 Tliere is no proof of this in his paper in the Philosophical 

 Transactions 1824, and he has nowhere else treated of the 

 same formula. But every thing that I have mentioned he 

 might find in my paper, which was in his hands, and to which 

 he had paid some attention. ,„«, r 



5 In the Philosophical Magazine lor September 1821, 1 

 made some observations on Dr. Young's method lor the re- 

 fractions ; and I shall now in(iuire whether, after so mucli dis- 

 1^ 2 tussion, 



