106 On the Depression of Mercury in the Tube of a Barometer. 
to considerable variations: it diminishes sensibly when the ba- 
rometer rises, and increases when it descends, the surface of 
the drop becoming more convex in the former case, and less 
convex in the latter. In order to restore the surface to its na- 
tural state, it is usual to strike the tube gently and repeatedly; 
but it is difficult to remove the irregularity altogether. For- 
tunately when the tube is very large, the variations of the angle 
of contact have but little effect on the depression of the sum- 
mit, though they sensibly alter the height of the convex part, 
The method above explained affords us the means of appreciat- 
ing this alteration. For, the depression remaining the same, it 
enables us to ascertain the addition 1made to the corresponding 
ordinates of the section of the surface in the last division of its 
length: and then, the angle of contact being supposed constant, 
it gives us the variations of the extreme corresponding ordinates, 
with reference to a given variation in the depression. It is easy 
to infer from these determinations, by the methods of the dif- 
ferential calculus, the variations of the depression of the sum- 
mit of the drop, and of its height, depending on a given varia- 
tion of the angle of contact ; and consequently the variation of 
the depression corresponding to an observed variation of the 
height of the drop. I find in this manner, that in a tube 11-4 
millimetres in diameter, a diminution of one-tenth of a milli- 
metre, in the height of the convex portion, produces in the de- 
pression depending on capillary action a diminution of 015; 
that is, about one-seventh as much as the diminution of the 
height. 
Table of the Depressions of the Mercury in the Barometer de- 
sived from its capillary Action, expressed in Millimetres. 
Diam. Depr. Diam. Depr. Diam, Depr. 
2 45599 9 5354 15 +1245 
3 = 2°9023 10 = *4201 16 +0970 
4 20388 BL) 3506"? 170754 
5 =-1°5055 [-3306] 18 -0586 
6~ 1°1482 12 2602 19 £430” 
7>* +8813) 13° +2047 [0450] 
§ "685 1 14 "1597 20 = -0352 
[Table calculated and interpolated from the preceding for Eng- 
lish inches, according to the method employed by the author, 
and compared with the Table published in NicHotson’s 
Journal, and there considered as generally accurate to the 
last place of decimals: the ultimate product of the depression 
and the bore being assumed +015, and the angular catent of 
the 
Rt ees sm 
