444 Lieutenant Kenny on a new Barometric 



tude -f , of which g is the corresponding force of gravity {vide Definitions). 

 Then, according to Poisson's " Mecanique" (Paris edition, 1811, vol. i. book ii. 

 article 194), we have 



^"* ^'=Wg= M.G{l-^cos2^) = F&' (^ " ^ ^°' ^V^)"" == (^^ °°^i"i°g 

 second and higher powers of f, as too small to be usefully retained) 



^ (1 + f cos 2^). But K = jjT-, therefore Z", = ^. (1 + f cos 2f ). 



Substituting this value of Ki in our last equation, we have 

 i7.^.il + fcos2^|.jn-^j.jl + A^^ij 



. com. locr — x^ ^ ' ^ ; A 



° P\\^m{T-T)\-lV{fr) 



In this last equation .£" is a constant quantity corresponding to latitude 45°. 



Let us now compare this last equation with the similar one of Poisson's 

 "Mecanique" (Paris edition, 1811, vol. ii. book iv. chapter v.), viz. — 



z = 18336 . i 1 + 0-00287 cos2.|r! . jl+'Jo^j • [^ + ;} " \^°Sji + ^'^og(l +^ 



and recollecting that in Poisson's equation h and h' (which have the same sig- 

 nification as /3 and /3' of our equation) are supposed to be corrected for dilTer- 

 ence of temperatures, as shown by the attached thermometers ; consequently 



h f z\ ^i'^^, 



log 77 4- 2 log ( 1 + - ) = log II ' '' = (by omitting quantities too small to 



be usefully retained) log > < has the same signification as 



log 



'§!\l + m.T-T')\ 

 of our equation ; recollecting also, that in Poisson's equation the lower station 



