368 On the PROGRESS of HE J? 



r 



cafes, as x is greater than r, b~ is lefs than b, (b being a 



r 



number greater than i) and therefore b — b* is pofitive, (6 

 that h is lefs than T, as it ought to be. 



20. We may obtain an approximate value of this formula, 

 without exponential quantities, that will apply to all the cafes 

 in which x and r differ but little in refpect of r, that is, in all 

 the cafes to which our obfervations on the atmofphere can pof- 

 ubly extend. 



r 



If, in the term b * we write r -f- z for x, z being the 

 height of any ftratum of air above the furface of the earth, 



we 



have b * = b r + % - 



21. But, from the nature of exponentials, we know b* zz 

 ^L r'(Log»)- ^IXLog^ &c> = 



1 ~ X 6 2 X ' 2.3 # J ' 



I + -4-Log^+ r \ (L ? S ?,' +. &* ' 



1 ^ r + z 6 2 (r + z) 1 



vr ow — ! — — j — - — &c. And if we leave 



r -\- z r r 



out the higher powers of z, we have nearly 



r 



r -f % 



