Page:Philosophical Transactions - Volume 095.djvu/88

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74
Dr. Young's Essay

divided by the diameter of the tube: and in tubes less than half an inch in diameter, the curve is very nearly elliptic, and the central depression in the tube of a barometer may be found by deducting from the corresponding mean depression the square root of one-thousandth part of its diameter. There is reason to suspect a slight inaccuracy towards the middle of Lord Charles Cavendish's Table, from a comparison with the calculated mean depression, as well as from the results of the mechanical construction. The ellipsis approaching nearest to the curve may be determined by the solution of a biquadratic equation.

 Diameterin inches. .mw-parser-output .hanging-indent{margin-left:2em;text-indent:-2em}Grains inan inch. C. Mean depressionby calculation. Y. Central depressionby observation. C. Central depressionby formula. Y. Central depressionby diagram. Y. Marginal depressionby diagram. Y. ⁠.6 972 .025 .005 (.001) .005 .066 ⁠.5 675 .030 .007 .008 .007 .067 ⁠.4 432 .037 .015 .017 .012 .069 .35 331 .043 .025 .024 .017 .072 .30 243 .050 .036 .033 .027 .079 .25 169 .060 .050 .044 .038 .086 .20 108 .075 .067 .061 .056 .096 .15 ⁠61 .100 .092 .088 .085 .116 .10 ⁠27 .150 .140 .140 .140 .161

The square root of the rectangle .01, or .1, is the ordinate where the curve would become vertical if it were continued; but in order to find the height at which it adheres to a vertical surface, we must diminish this ordinate in the proportion of the sine of 25° to the sine of 45°, and it will become .06, for the actual depression in this case. The elevation of the mercury that adheres to the lower horizontal surface of a piece of glass, and