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.
| Diameter in inches. |
Grains in
an inch. C. |
Mean depression
by calculation. Y. |
Central depression
by observation. C. |
Central depression
by formula. Y. |
Central depression
by diagram. Y. |
Marginal depression
by 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
