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. 
Diameter 
in inches. 
Grains in 
an inch. 
C. 
Mean depres- 
sion by cal- 
culation. Y. 
Central depres- 
sion by ob- 
servation. C. 
Central de- 
pression by 
formula. Y. 
Central de- 
presson by 
diagram. Y. 
Marginal de- 
pression by 
diagram. Y. 
.6 
972 
•02 5 
.003 
(.001) 
.003 
.0 66 
•5 
6 75 
.030 
.007 
.OOB 
.007 
.067 
•4 
43 2 
•037 
.013 
.017 
.012 
.0 69 
•35 
33 1 
•°43 
.023 
.024 
.017 
.072 
.30 
243 
.030 
.O36 
•°33 
.027 
•°79 
.25 
1 69 
.060 
.030 
.044 
.038 
.086 
.20 
108 
•0 75 
-O 67 
.061 
.036 
•0 9 6 
•15 
61 
.100 
.092 
.088 
.085 
.11 6 
.10 
27 
.150 
.140 
.140 
. 14 ° 
.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 23 0 to the sine of 43 0 , 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 
