[ 283 3 
to AF being given (by hypothefis), the length of 
AL will be given, from the fame analyfis as before. 
But D being given, and the right line AB given 
in pofition, LD is given in pofition and magni- 
tude ; and, AL being given, the proportion of 
LD to AC, and alfo to AF, is given (by logarithms). 
Therefore AC and AF are each given. 
The expreffion for the length of AL is the 
fame as before. And tab. log. LD ± =-L. 
In this expreffion the fecond term is politive, if the 
ordinate from A to the leffier curve is to be the 
greater of the two ; in the contrary cafe, negative. 
Now imagine CDE, FDG to be logarithmics 
of the atmofphere, in different temperatures 5 AC 
being the denlity at the earth’s furface in one 
temperature, and AF in the other; and let A B be 
the femi-diameter of the earth : let the two loga- 
rithmics meet in D, and draw D L perpendicular to 
AB. Now if the point L be any where in the line 
AB, between A, which is at the furface of the 
earth, and B, which is the center, the ordinate LD 
will reprefent the denfity of the air, in the fyfiem of 
both curves, at the diftance 
BAxAL 
BA-AL 
above the earth’s 
furface ; and therefore, at this height, the denfity 
is the fame in the one temperature as the other. 
If L coincide with B, D L reprefents the denfity at 
an infinite height ; but if L falls beyonds B, DL is 
not among the ordinates, of either curve, which re- 
prefent dcnfities any where exifting. The expref- 
O o 2 fion 
