524 BESSEL ON BAROMETRICAL. 



2k 2t/T-r'\ 



[>- 



whence it follows that 



^^ ~ PV [4i«,'^PP' + u^'] + u ' 



and if we take the Briggs's logarithms of both numbers of the 

 equation, and develope fully to u^ inclusive, 



^-;y(r-r') = log p +;7^pp); 



but according to the relation between the temperatures and the 

 elevations in Art. 2, 



2k .H'-H 



i ^^ - '^)- 1 + A-T' 

 whereby we obtain 



, P _ 1 H'-H ^^ . . 



The integral occun-ing in the expression for u is found by deve- 

 loping the exponential quantity into a series 



= (^-'''{' + w'[(''-?i-''^'^)'--'^'']+^'=-}- 



In order to estimate in some measure the amount of the second 

 member of this series, we maj' assume that the centesimal ther- 

 mometer falls a degree for every 85 toises of elevation. Then 

 is this member for H' — H = » . 1000 toises, and for T = 0, 

 = n"^ . 0"0093 for small differences of elevation ; it is therefore 

 an inconsiderable part of the first member ; and even for the 

 greatest accessible elevations it does not amount to a tenth part 

 of it. The supposition as to the distribution of aqueous vapour 

 in the atmosphere, on which the present calculation rests, has 

 far more uncertainty ; on which account I think there can be 

 but little interest in adhering strictly to it by means of a compli- 

 cated calculation. I therefore simplify it by assuming 



^^^ 2a/3(l-</,)^(T-T^) ^Q.T-cr 

 V i 



According to Berzelius </^ = 0*62, and it has been snown above 

 that, 



