[ 2 3 ° ] 
at all heights, the denfities would decreafe geo- 
metrically as the height increafed arithmetically. 
This is an obvious confequence from a known 
property of air, that it expands itfelf through 
a greater or a Iefs fpace, in proportion as the 
force, by which it is compreffed, is iefs or greater; 
that is, that the denfity of air, is always as the com- 
preffing force (?). And from hence it would follow, 
that the difference of the elevation of any two places, 
would be as the logarithm of the ratio of the den- 
fities of the air, at each: and the denfity being 
every where as the compreffing force, and the com- 
prefling force as the length of the column of quick- 
iilver fuftained by it in the barometer, the difference 
of elevation would be, as the logarithm of the 
ratio of the altitudes of the quickfilver in the baro- 
meter, at the fame time, at the different ftations ; that 
is, as the difference of the tabular logarithms of the 
numbers, by which thofe altitudes would be ex- 
preffed in any given meafure (/). But the accele- 
rative force of gravity diminishes, in the fame pro- 
portion, as the fquare of the diftance, from the 
earth’s center, is increafed. It is not the fame 
(e) Cotes’s Hydroftat. Leftures, left. ix. 
(/) See Philoi'opb. Tranfaft. n. 1 8 1 . Phil. Nat. Princip. 
Math. lib. ii. prop. 22. Scholium. Cotes’s Hydroftat. Leftures, 
left. ix. H.umon. Menf. p. 17. 
Of all thefe demonftrations, that given by Mr. cotes, in 
the hydroftatical leftures, will be the moft perfpicuous to the 
generality of readers. It is very difrufe, and he hath been 
at great pains to reduce it to the moft ftmple principles. 
Mathematicians will find the fubftance of his argument well 
fummed up, by M. de la lande, in the Connoiftance for 
the year 1765, p. 21 1, 212. who, I am perfwaded, would not 
have produced it as a new aemonftration, had he known it 
had been given before. 
therefore 
