TRACT 33.

PROBLEMS.

375

foot in height on a square foot of base; hut the mediumpressure of the atmosphere is equal to the column of 29*75inches of the barometer; therefore 12 : 29*75 : : 13600 :33717 ounces pressure of the atmosphere on a square foot;hence 33717 ~ 144 = 234 ounces or 14|lb. is the mediumpressure of the atmosphere on a square inch.

Again, for the' height of a uniform atmosphere. Since33717 ounces is the pressure of the atmosphere on a squarefoot; and li ounces is the weight of a cubic foot of air, orits pressure on a square foot of 1 foot in height; thereforeIf. : 1 :: 33717 : 27600 feet the height the atmosphere wouldbe if it were all of the same uniform density as at the earth,being equal to 5~ miles in height very nearly.

PROBLEM XXXIII.

To show that the Density of the Atmosphere, at differentHeights above the Earth, Decreases in such Sort , that whenthe Heights Increase in Arithmetical Progression, the Den-sities Decrease in Geometrical Progression.

Let the indefinite perpendicular line ap,erected on the earth, be conceived to be dividedinto a great number of very small equal parts,

A, B, c, d, 8cc, forming so many thin strata ofair in the atmosphere, all of different density,gradually decreasing from the greatest at a:then the density of the several strata a, b, c,d, &c, will be in geometrical progression de-creasing.

For, as the strata A, b, c, &c, are all of equalthickness, the quantity of matter in each of them, is as thedensity there ; but the density in any one, being as the com-pressing force, is as the weight or quantity of all the matterfrom that place upward to the top of the atmosphere; there-fore the quantity of matter in each stratum, is also as thewhole quantity from that place upward. New, if from the