Subsection of Mechanical Sciences applied to the Arts. 69 
in a popular manner, that if the internal cross section of the baro- 
meter tube at its upper part were made equal to the cross section of 
the pillar or stem of the hydrometer, the sensibility of the instru- 
ment would be too great for practice; the scale in that case would 
be lengthened out indefinitely, since the hydrometer could never 
sink sufficiently to attain a position of equilibrium upon a fall of the 
barometer, and vice versd. But if the cross section of the stem or 
pillar of the hydrometer be made twice as great as the internal cross 
section of the upper part of the barometer, the rising and falling of 
the cistern would be exactly equal to the rising and falling of the 
common barometer ; and therefore the scale of this instrument would 
then be equal to the scale of the common barometer; and between 
these limits any desired scale, however long, may be obtained. A 
scale shorter than that of the common barometer may also be had 
by increasing the cross section of the stem of the hydrometer be- 
yond the above limit ; but this is not likely to be ever desired. When 
it is desirable to save expense, the hydrometer may be made to float 
in water; but of course its dimensions will require to be much 
greater in that case: or the cistern may be counterpoised, and a 
cylinder like the stem of the hydrometer, dipping into the mercury, 
may, by its varying buoyancy, be made to restore the equilibrium. 
The exact mathematical formula which gives the relation of the 
scale to that of the common barometer, whatever be the dimensions 
of the parts of the instrument, is of the form 6h = dh' x C, where 
6h is the variation of the height of the common barometer, 2h! is 
the corresponding part of the scale of this instrument, and C a con- 
stant depending for its value upon the dimensions of the several parts 
of the instrument. 
Professor Stevelly also described a very simple and cheap instru- 
ment for weighing hydrometrically, the sensibility of which is very 
remarkable,—a hydrometer-ball with a stem of steel wire, having 
upon it one or two dots of gold, and a scale-pan attached to it, either 
above as in Nicholson’s, or below as in Ronchetti’s modification of 
the hydrometer. An index, or a microscope with a horizontal wire, 
is attached to the side or cover of the vessel in which the hydro- 
meter floats in such a way that it may be steadily and slowly raised 
or lowered to mark the position of the gold-dot, instead of taking the 
indications from the surface of the fluid, as in the common method. 
The weight of the substance to be weighed is then had by placing 
it in the seale-pan, bringing the index or wire of the microscope to 
mark the position of the gold-dot, then removing the substance and 
substituting for it known weights until the dot is again brought to the 
same position. Since the adjustment takes place at the instant of 
using the instrument, it becomes almost incapable of being deranged, 
and thus a very correct balance may be had by a common apothe- 
cary’s phial, with a little mercury to steady it, and a knitting-needle 
pushed down through its cork, and a scale-pan placed above. Every 
person knows the difficulty of adjusting the common hydrometer, and 
its liability to derangement. 
The same principle may be readily conceived to apply to the con- 
struction of a self-registering rain-gauge. 
