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the temperature fuppofed ; or, which is the fame 
thing, as the fpace occupied by a given quantity of 
air, at an infinite height, to the fpace occupied 
by the fame quantity, at the furface. This root 
I call the radical number. Then, imagining the 
earth’s femi-diameter, divided into ioo equal parts, 
and numbering thofe parts i, 2, 3, &c, down- 
wards, towards the center, I compute the heights, 
above the furface, correfponding to thofe parts 
fucceffively, according to the conftrudtion of the 
atmofpherical logarithmic, §. 2 ; and, writing the 
refulting numbers in the fecond column, in the third, 
I write the powers of the radical number, increafirig 
by unit, in regular fucceffion down-wards. 
The proportion in which the atmofphere will be 
rarefied, at given heights above the furface, will be 
very different, in different temperatures. It may 
always be exhibited by a table of this form, but 
every different temperature will have its own radical 
number. The radical number, in the temperature 
-q- 40, is 3069 ; and, for any other given tem- 
perature, may be thus found. Call the tabular loga- 
rithm of 3069, y ; and let n be the number of 
degrees of bird's Fahrenheit, in the difference 
between the given temperature, for w r hich the ra- 
dical number is to be found, and 4- 40. Then 
y rh — y will be the tabular logarithm of the 
y 449 =F n J 0 
radical number, for the temperature afilgned : ob- 
ferving, that n is to be pofitive or negative in the 
denominator of the coefficient — — , according as 
Vo l. LX IV. N n 49 ~ ” the 
