54 ‘PHYSICS. . 
the lower end of the tube, cd, a certain quantity of air of the same density 
as that external to it. Continuing this depression until: the mercury 
touches a point attached, similar to that described in the barometer of 
Fortin, the inclosed air becomes condensed, in a proportion dependent upon 
the dimensions of the instrument and the position of this point: If, for 
instance, the air were condensed to three fourths its original volume, the height 
of the mercury according to Mariotte’s law, would be one third of the actual 
height of the barometer, and for this proportion, as well as any other, the actual 
height of the barometer would be obtained by multiplication into a factor 
developed from the construction of the instrument. If now there be 
another point in the instrument, standing somewhat deeper or lower than 
the first, it can be brought in contact with the mercury by a change in the 
position of the piston, where then the factor would of course be different. 
Making observations in immediate succession, and at the same place, with 
the two points, the products of multiplication by the different factors must 
be equal; the two points therefore control each other. There must, of 
course, be attached to the tube, cd, as shown in the figure, two different 
scales for the two points. 
Upon the law of Mariotte depends an apparatus termed volumeter ( fig. 93), 
invented also by Kopp, for determining the volume of powders. ‘The tubes, 
k and i, correspond to those of the same name in the differential barometer, 
being likewise filled with mercury; from 7 passes a bent tube to the wide 
glass cylinder, n, whose upper broader end is carefully ground off for the 
purpose of placing a plate of glass upon it, and rendering it air-tight by the 
addition of a little tallow. Closing the cylinder, m, and depressing the 
piston, *, until the mercury touches the lower end of the ascending tube, 
a certain quantity of air will be inclosed in / and 2: pressing down the 
mercury to the point, a, the included air will be compressed, a corres- 
ponding column of mercury rising in the ascending tube. If, before laying 
on the glass plate, any body had been placed in the cylinder, x, then the 
mercury standing att c, less air would be included than before, and in forcing 
the mercury up to a, it would be more compressed, so that the ascending 
tube would contain a greater column of mercury than before. From the 
height of this column of mercury the volume of the body contained in the 
cylinder is to be calculated. The powder to be examined is introduced in 
a platinum vessel, of about the shape of x, and nearly the same size. The 
volume of air included when the empty vessel alone stands in 2, suppose 
it to be 15.07 cubic centimetres ; and also the volume between c and 6, 
say 2.5 cubic centimetres, to which the air is compressed, must be known. 
Now introduce the body whose volume is to be determined into n, and 
depress the piston again from its highest position, where c is closed by the 
mercury ; a quantity of air, z, is inclosed, and when the mercury comes in 
contact with the point a, the air is compressed to x—2.5. Let the column 
of mercury last obtained = 90 lines, and the actual height of the barometer 
== 336 lines, then the compressed air now experiences a pressure of 
336 + 90 = 426 lines, and 426:336::7:2—2.5; zx, therefore, = 11.72. 
As now, when 2 is empty, the volume included = 15.07 cubic centimetres, 
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