On the Depression of Mercury in the Tube of a Barometer. 103 
face then becomes that of a hemisphere.” If, however, we boil 
the mercury for a very long time in a barometer tube, we at last 
so far diminish the thickness of the stratum of water, as to ren- 
der sensible the action of the glass on the mercury. It has 
been shown by the excellent experiments of Casbois the Bene- 
dictine, that by means of a long-continued ebullition, the sur- 
face of the drop becomes less and less convex, then plane, and 
at last concave; and in this case the capillary phenomena 
_ change their nature, and the depression is converted into an 
elevation. But in making barometers, the boiling is never car- 
ried so far; and the action of the glass on the mercury not 
being sensible, whatever differences there may be in the materials 
of the glass, they have no influence of the capillary effects of 
the tubes. We will suppose then, agreeably to experiment, that 
the angle of contact of the surface of the mercury with the sides 
of the tube is the same asin the open air. This angle, and the 
depression of the mercury in very narrow tubes, are very difficult 
to determine by experiment; they may be collected from dif- 
ferent phenomena, such as the thickness of a broad drop of 
mercury on a horizontal plane of glass; the difference of the 
level of the general surface of a quantity of mercury, and of the 
contact of this surface with the vertical side of a vessel of glass; 
the depression of mercury in very narrow tubes; and this same 
depression when the mercury is introduced into a tube of glass, 
so moist, that its surface is covered by a small column of water. 
I have inferred from the whole of these phenomena, observed 
with very accurate iustruments by M. Gay-Lussac, that the an- 
gle of contact of the surface of the mercury with the glass is 
*48 of a right angle [, or 43° 12']; and that the mercury, in a 
tube of glass of the diaméter of one ten-thousandth of a 
millimetre, would be depressed 94766 millimetres below the 
level, [or in a tube of a ten-thousandth of an inch, 146-9 inches]. 
The following table is deduced from these elements, according 
to which the action of mercury on itself is, for equal volumes, 
very nearly six times and one-third as great as that of mercury 
ou water. 
In order to form this table, it was necessary to integrate by 
approximation the differential equation of the second order be- 
longing to the surface of mercury contained ina cylindrical tube 
of glass.- This equation, which I have given in my Theory of 
eapillary action, furnishes a very simple expression of the radius 
of curvature of the generating curve of the surface, . Consider- 
‘ing this curye, therefore, as a series of small circular ares, de- 
scribed with these different radii, and joining each other at their 
extremities, we shall have the corresponding ordinates of the 
eurve, so much the more precisely as we employ a greater num- 
d ber 
