Encyclopaedia Britannica > Volume 3, Anatomy-Astronomy

392
A R iE
A R
ty of li
quid.
Arseome- because the value of x is divided by z2, which is the square
ter. of a very small quantity.
When the araeometer is immersed in a liquid of
Sensibility mother specific gravity g1, then the equation is a;1 =
tiO tlflG SpG- /" j \
cific gravi- _vf • subtract the value of x1 from that of x, and
IvnfU- g^TZ2
there results x — x1 = This is the diminution
99^
in the length of the immersed part of the stalk, which
takes place when the araeometer is transferred to a liquid
of a greater density. By this formula it is seen, that the
sensibility of the araeometer, that is, the length of the
portion of the stalk which emerges upon transferring the
araeometer to a denser liquid, is augmented, in the first
place by increasing w (the weight of water displaced by
the araeometer), that is, by increasing the volume of the
body of the araeometer; secondly, by diminishing z (the
diameter of the stalk), which is in the denominator of the
value of a? xl; consequently, the faculty of the arae¬
ometer to show the different densities of liquids is in
w
general expressed by the fraction
With regard to the vertical mobility of the araeometer,
when put in motion by placing a small weight s in its ex-
, . , „ . , 4(w + 5—gv)
tenor cup,substitute w+siorw; then,xl = ——2*7^2 *
Take the difference between this and x — :
Zg’xz1
this difference is xl — x = 5; which shows that the
9VZ
length of the portion of the stalk that a small weight
causes to immerge is proportional to or in the direct
ratio of the small weight, and in the inverse ratio of the
square of the diameter of the stalk.
When the small weight, the density of the liquid, and
the length of that part of the stalk which is submerged
on adding the small weight, are known, then this equation
will give the diameter of the stalk in known quantities
2—2*/ 1 .
gv^x1—x)
When the weight of the whole araeometer is known in
ounces, &c., and the specific gravity of one of two liquids
(water, for instance) is known, the difference of specific
gravity between that liquid and another liquid may be
had in known quantities.
g is the specific gravity of water.
gl is the specific gravity of the second liquid, which is
here supposed more dense.
w is the weight of the volume of water displaced by
the araeometer.
5 is a small additional weight placed on the exterior
cup to keep the araeometer, when placed in the denser
liquid, at the same point of immersion as when it floated
in water.
w + s is the whole weight of the apparatus when float¬
ing in the denser liquid.
The equation gl = ~ ~j~2 is obtained by substi¬
tuting g1 for g, and w -f s for w, in the equation g =
w ...
v q- lxff22’ w llch was glven above. Divide by ^ =r
w qx w "I" s
—-j-j—£, and there results - ^ , which gives the
proportion of the density of the second liquid to the den¬
sity of water. By subtraction there results ^ — -1
and o1 — n — —; that is, the difference between the Arseostyle
w . . . U
density of the second liquid and the density of water is Arafat.
found by multiplying the small weight by 1000 ounces,
and dividing this product by the number of ounces, &c.
which denote the weight of the araeometer uncharged.
Small bodies, whose specific gravities are known, serve Bead artt
to indicate the specific gravity of a liquid in which they ometer.
just remain suspended. In this way beads of glass three
or four tenths of an inch in diameter are employed, each
of which remains suspended in spirit of a certain specific
gravity. The density of each of these beads, or rather bub¬
bles, is regulated by the proportion between the quantity
of glass and the cavity which the glass incloses. A piece
of bees-wax, whose specific gravity, by the addition of
lead, is such that the body is just suspended in brine of a
known density, is used as an araeometer in some salt
works. The fresh egg of a common fowl is just sustained
by brine of a certain specific gravity, and is employed as
an araeometer.
The araeometer of Homberg consists of a phial with a Hom-
slender neck and glass stopper, so made that it may be filled berg’s,
with the same volume of different liquids. It is employed
in finding the specific gravity of liquids in the following
way : ls£, The phial is filled with distilled water, and then
weighed in a balance; 2dly, the phial is emptied, and
again filled with the liquid whose specific gravity is
sought, and weighed in a balance: the proportion of the
weight of the contents of the phial in the second process
to the weight of its contents in the first, is the specific
gravity required. The inconveniences which have pre¬
vented this method from being generally used are, the
difficulty of completely cleaning the phial from the liquid
which it previously contained; the difficulty of filling the
phial exactly with the same volume of each liquid; and
the variation of the volume of the phial from changes of
temperature.
The pressure of the atmosphere supports columns ofFump
different fluids, whose height is inversely „ arseome-
as the densities of the fluids. An araeome- ■ ter’
ter has been constructed on this principle.
It is a curved tube, one leg of which has
its extremity immersed in water, and the
other in the spirit whose density is to be
tried. On rarefying the air in the tube,
by means of a pump fixed at the upper
part of the tube, the water ascends in one
leg, and the spirit in the other; the height
of the column of each liquid being mea¬
sured by a scale of equal parts applied to
each branch of the tube. This instrument
has never come into use, probably on ac¬
count of the difficulty of ascertaining with precision the
points at which the surfaces of the columns are termi¬
nated. (w.A.c.J
ARiEOSTYLE (dpaios and crrvAos), in Architecture, a
term used by Vitruvius to signify the greatest interval which
can be made between columns.
ARiEOSYSTYLE (compounded of the Greek words
dpaios, crw, orvAos), in Architecture, an arrangement of co¬
lumns in pairs, with an interval, usually equal to half a dia¬
meter, between the coupled columns, and an interval of three
diameters and a half between the pairs.
ARAIOTICS (dpcnamKa), in Medicine, remedies which
rarefy the humours, and render them easy to be carried off
by the pores of the skin.
AR AFAH, the ninth day of the last month of the Arabic
year, named Dhoulhegiat, on which the pilgrims of Mecca
perform their devotions on Mount Arafat.
ARAFAT,a mountainnear Mecca in Arabia,held in high
w