366 Astronomical and Nautical Colleciiuiis. 



ccrits, ayant pour litre Corrections for Refraction, Le D. Y. 

 apr^s avoir pris pour base cette equation tres exacte [dS :=: 



], donnee anterieurement par Lambert, suppose la 



perpendiculaire u, dans la courbe decrite par le corpuscule de 



lumi^re, telle que I'on a 21 ^ , b dtant un constant con- 



^ 1 + M^' 



venable." This value of u is inconsistent, he observes, with the 

 demonstration of Laplace and others, and he continues ; " Pour 

 redresser cette erreur, il faut supposer k la variable u une ex- 

 pression de la forme m = .. .Cette meprise du Dr. 



^ V (1 + ^h) 



Young est tellement singuliere, que je crois de mon devoir de 

 rapporter ici le raisonnement mfeme que ce physicien. . .a fait 

 pour fetablir son expression difFerentielle de la refraction." In 

 the passage quoted, I have called the refractive density 1 + pz, 

 " p being a very small fraction." 



Mr. Plana does not seem to be aware that, in the theory of 

 optics, which I have long since advanced, and which has of late 

 years begun to acquire some considerable popularity, the de- 

 monstration, to which he alludes, as deduced from the laws of 

 central forces, is wholly inadmissible, except as a mathematical 

 fiction : and he must show, that the refractive density does not 

 vary in proportion to the actual density multiplied by a very 

 small fraction, and increased by unity, before he can establish 

 this charge. But even supposing it established, that I ought 

 to have taken ^ (1 + Jlig) instead of 1 + p^, it is quite clear, 



that since aJ {I + iVig) = 1 + — M^ - — M^q^.. .and since 



2 8 



g is always less than unity, the error could only amount to 



— of the square of the coefficient M, that is, to the square of 

 8 



, and that such an error would have been wholly insensible. 



1700 ^ 



Believe me, dear Sir, yours, very sincerely, 

 9 June, 1823. ♦ * *. 



