368 On the PROGRESS of HEAT 
: 
cafes, as x is greater than r, 4* is lefs than 4, (b being a 
5 ig 
number greater than 1) and therefore )—4* is pofitive, fo 
that 4 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 « and r differ but little in refpe@ of 7, that is, in all 
the cafes to which our obfervations on the atmofphere can pof- 
fibly extend. 
fe 
Ir, in the term 47 we write r-+2z for x, x being the 
height of any ftratum of air above the furface of the earth, 
r r 
= a 
x = hrt+s 
we have J 
: r 
21. But, from the nature of exponentials, we know 47 = 
r* (Log 6)’ r> (Log 6)? 
1 + ~ Log b + —— ae are &e. 
r° (Log 8) 
tt pag OE airs) ee 
Now mG — es a = + = —, &c. And if we leave 
out the higher powers of z, we have nearly 
8 
bas 
+ 
R 
