( ) 
At the Top, it fell to 29. 41. The Height of this Hill 
was found to be 507 Feet, 
Our Mathematicians do demonflrate, that theDenfity 
of the Air decreafes in a Geometrical Progreflion, as the 
Elevation encreafes in an Arithmetical one, and confe- 
quently, that the Logarithms oftheDenfities are as the 
Elevations reciprocally. But the Weight of the Air be- 
ing as its Denlity, and the Height of the Mercury in 
the Barometer being always proportional to the Air’s 
Weight, it follows, that the Logarithms of the Heights 
of the Mercury are, reciprocally, as the Elevations : 
Whence having found by Obfervation, what Elevation 
is requir’d to make the Mercury (land at any given 
Height, it will be eafy to determine, how much is re- 
quire to reduce it to any other Height propos’d. If 
we make 30 Inches the Standard Heigiit of the Mercury, 
equal to Unity, and fuppofe an Elevation of 85 Feet 
be requir’d to make it fall one Tenth of an Inch from 
that Height, as by thefe Obfervations it is very nearly j 
then as the Logarithm of is to 85, fo is the Loa 
29,9 
to the Number of Feet requir’d to make it fail 
29,5 1 
Half an Inch, and fo of the reft. When the Mercury 
ftands above 30 Inches, the Numbers will be negative, 
and fhew the Spaces defcendingj by which Method I 
computed the following Tables. 
The latter, which contains the Differences of the N um- 
bers in the former, was of very great Ufe to me, when, 
in thefe Experiments, the Mercury flood at any other 
Height in the Tube, belides 30 Inches, and fell 
any Number of Tenths, or Parts ofa Tenth, by adding 
the Numbers anfwering thereto, or proportionable Parts 
of them, to find the Elevation requir’d in the Table, to 
make the Mercury fall fo much, and thereby readily 
to 
