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CONSTRUCTION. 
Find the point (3 (by corollary of preceeding pre- 
problem) fuch that the ordinate /3HE being drawn, 
(3 E, /3H, may be reciprocally as the fubtangents ; 
or that jQE may be to /3H as the fubtangent of the 
curve GHK to that of DEF : and the thing propofed 
is done. 
Now imagine the curves GQK, DQF, to repre- 
fent the logarithmics correfponding to different given 
temperatures of the air, A being at the furface of 
the earth, and C at the center. And having found 
'A/3 x C A 
the point /3, take AB = then B is the place 
where the barometer will Rand at the fame height, 
in both conditions of the atmofphere. 
LIMITS. 
Draw the ordinates, AGD, CFK, and QR. [f 
the point Q be any where below the ordinate 
through A, it is evident, the point (3 will lye above 
the point R. And if the fubtangents /3L, (3M, be 
reciprocally as the denfities AD, AG, the points 
(3 y A, and confequently B, A, coincide, and the 
preffure, at the level of the fea, remains unchanged. 
If the greater fubtangent (3M. be greater than to 
bear to the lefs /3L, the proportion of the greater 
denfity AD to the lefs AG, {3 will fall above A, and 
B confequently will be below it ; for A/3 becoming 
4 negative. 
