Astronomical and Nautical Culleclions. 3{)C) 



nee 



dx 



- dti whence 2dr - d ( -^ - — ^ ) ; and si 

 V ydx yy dx J 



:.i:^-.z,dr==ld(^-^;) =f4^- 



dx 2 \ 7jy 2/? / 2 \ yy 



L±\ -2d± - i- di- - dl; butd" ± = dz - 



^ y J y K y ^ y 



1 d^ _ |dx __ |dz 

 dy - (I - dz, and - d — = -^ - -^^; "i;^ ' . 



_ 1 _ A Y Now we have found ^ in the present case= 1 .396, 

 m J 



and A = .0688 ; whence ^^ ^ ^^ (4-188 - 3.898 - I 

 m dz 2C 



_ 069 = - 779 — ; which being negative, it follows that t 



increases with the elevation, as z diminishes, and that the varia- 

 tion of temperature becomes greater in ascending. 



Mr. Plana has remarked, that " en suivant les consequences 

 de I'hypothese de M. de Laplace, Ton pourrait ajouter, que la 

 pressiou barometrique, qui en rhulte, est loin de s'accorder avec 

 celle observee par M. Gay-Lussac au point superieur de son 

 ascension aerostatique." I shall not undertake to criticize 

 Mr. Plana's Memoir, especially without having had time to read 

 it through with attention ; but I am utterly at a loss to conceive 

 by what witchcraft he has been able to compute the barometri- 

 ' cal pressure resulting from Laplace's hypothesis at the height 

 attained by Gay-Lussac, if that height was only deduced from 

 the actual observation of the barometer. Perhaps, indeed, the 

 aeronauts were able to measure, with their sextant, a variety of 

 angles, subtended by distant terrestrial objects : and if such 

 was the fact, my question is answered. 



I shall now proceed to discuss the second passage in which 

 Mr Plana has done me the honour to mention me. " Je crois 

 avoir reconnu," he observes, (p. 301), que le Dr. Young n'est 

 pas parti de la veritable equation du probl^me dans un de ses 



