374

MISCELLANEOUS

TRACT 38,

which is about half an inch more than the greatest fall ob-served by Mr. Labelye.

And, for Blackfriar’s-bridge, the fall will be much thesame as that of Westminster.

*** See other solutions at pa. 87, 8cc, vol. 1.

PROBLEM XXXII.

To determine the Circumstances relating to the Pressiire ofthe Atmosphere on a given Space on the Earth , with theHeight of a uniform Atmosphere, He,

It is a fact, and may easily be shown, that the height is aconstant quantity, or always the same, of a uniform atmo-sphere above any place, which shall be all of the uniformdensity with the air there, at any time, and whatever thervcight of it then be as measured by the barometer. Thisproperty happens from the circumstance of the density ofthe air, at the earth’s surface, always varying in propor-tion as indicated by the barometer; in fact, the height oftile barometer at once shows both the density of the air andits weight, at the time. So that, as the density varies inexact proportion to the weight of the column, it thereforerequires a column of the same height, in all cases, to makethe respective weights or pressures; when the temperatureor heat of the air is the same. Thus, if w and w denote theweights of atmosphere above any places, d and d their re-spective densities, and h, h the heights of the uniform co-lumns, of these densities and weights: Then, each densitymultiplied by the height being equal to the weight, viz.

h x d = W, and hx d= w ; hence = h, and ~ = h;but, as the weight is always proportional to the density,therefore — = that is, h = h, or the heights are equal.

The general height of the uniform atmospheric column isthus easily found. The weight of a cubic foot of mercuryis 13600 ounces, or the pressure of a column of mercury 1