[ 23 1 ] 
therefore at all heights above the furface ; and the 
denfities of the air muff decreafe, by a different law, 
from that which would obtain, if the force of gra- 
vity were uniform. This other law, however, is fuch, 
that, to a much greater height than is acceffible to 
man, the gradual variation of the compreffing force 
and denfities of the air, will befo little different, from 
what it would be upon the former hypothefis, that 
the error of that hypothefis, in the meafurement of 
heights, will be abfolutely infenfible. 
Let the point C [tab. IX. fig. i.] reprefent the 
center of the earth. CA the earth’s lemi-diameter. 
AB any height above the furface. At A, place a 
right line, AD, of any finite length, at right angles 
with AC. In the right line AC, towards C, take 
AjG, fuch that CA may bear to A/3 the propor- 
tion of CB to BA. In a right line drawn 
through /3, at right angles with AC, take /3E, of fuch 
length, as to bear to AD the proportion of the den- 
fity of the air at B to the deniity at A, or at the 
earth’s furface. The curve, which the point E 
always touches, is a logarithmic, of which AC is the 
afymptote-t A 
As I fall have frequent occafon to corf der the ' curve, 
which thus exhibits the relation between denjity and 
elevation , 1 JhcUl call it the atmospherical 
LOGARITHMIC, 
Imagine this curve deferibed, and take another 
height Ah, and take A£ r= ana draw Qe 
(?) Cotes’s Hydroftat. Le&ures, p. 261 — 167. Harmoiv 
Me;;('. p. 18. Phi!. Nat. Princip. Math, lib, ii. prop. 22. 
Brooke Taylor, Method, Increment, Prop. 26. 
parallel 
