MECHANICS. 
tinflly the perpendicular pofition of the examen, by the 
fmall pointed index fixed above it. The firings by which 
the balance is fufpended, patting over two pulleys, one on 
each fide of the piece at A, go down to the bottom on the 
other fide, and are hung over the hook at v ; which hook, 
by means of a fcrew P, is moveable to about the difiance of 
an inch and a quarter backward and forward, and there¬ 
fore the balance maybe raifed or deprcfied fo much. But, 
if a greater elevation or depreflion be required, the Aiding 
piece S, which carries the fcrew P, is readily removed to 
any part of the fquare brafs rod V K, and fixed by means 
of a fcrew. 
The.motiorl of the balance being thus adjufted, the reft 
of the apparatus is as follows : H H is a (mail board fixed 
upon the piece D, under the fcales d and e, and is move- 
able up and dow n in a low Ait in the pillar above C, and 
fattened at any part by a fcrew behind. From the point in 
the middle of the bottom of each fcale hangs, by a Ane 
hook, a brafs wire ay, and ac; thefe pafs through two 
holes, m, m, in the table. To the wire af\s fufpended a 
curious cylindrical wire rs, perforated at each end for 
that purpofe : this wire rs, is covered with paper gradu¬ 
ated by equal divifions, and is about five inches long. In 
the corner of the board at E is fixed a brafs tube, on which 
a round wire hi is fo adapted as to move neither too tight 
nor too freely, by its fiat head I. Upon the lower part of 
this moves another tube Q, which has fufficient friction 
to make it remain in any pofition required ; to this is fixed 
an index T, moving horizontally when the wire lil is 
turned about, and may therefore be eafily fet to the gra¬ 
duated wire rs. From the lower end of the wire rs hangs 
a weight L ; and from that a wire p n, with a fmall brafs 
ball ^aboutone-fourth of an inch diameter. Ontheother 
fide from the wire ac hangs a large glafs bubble R, by a 
horfe-hair, in the vefiel N. 
Now', let us fuppofe the weight L taken away, and the 
wire pn fufpended from s; and on the other fide let the 
bubble R be taken away, and a weight, as F, fufpended 
at c in its room. This weight F we fuppofe to be fuffi- 
cient to keep the feveral parts hanging from the other 
fcale in equilibrium; at the fame time that the middle 
point of the wire p n is at the furface of the water in the 
vefiel O. The wire pn is to be of fuch a fize that the length 
of one inch (hall weigh four grains. Now, it is evident, 
fince brais is about eight times heavier than water, that, 
for every inch the wire finks in the water, it will become 
half a grain lighter, and half a grain heavier for every 
inch it rifes out of the water; confequently, by linking 
two inches below the middle point, or riling two inches 
above it, the wire will become in effeft one grain lighter 
or heavier. If, therefore, when the middle point is at the 
furface of the water in equilibrio, the index T be fet to the 
middle point of the graduated wire r s, and the difiance of 
r and of s from the index be eacli reckoned to contain 
100 equal parts; then, if in weighing bodies the weight 
is required to the hundredth part of a grain, it may be 
eafily obtained by proceeding thus : Let the body to be 
weighed be placed in the fcale e ; and let this be fo de¬ 
termined, that one grain more fhall be too much, and one 
grain lefs too little. Then the balance being moved gently 
up or down by the fcrew P till the equilibrium be nicely 
fhown at o, if the index T be at the middle point of the 
wire rs, it fhows that the weights put into the fcale e are 
juft equal to the weight of the body. But, if the index T 
Hand nearer to r than to s, as fuppofe 36 of the 100 parts, 
it fhows the number of grains in the fcale e were lefs than 
equal to the weight of the body in fcale d by 36 hun¬ 
dredths of a grain ; and if, on the other hand, the index 
had flood at the divifion 36 below the middle point of rs, 
then would the grains in the fcale e indicate more than tile 
real weight in d by 36 hundredths of a grain. 
Inftead of putting the body in the fcale d as before, 
let it be appended with the weight F at the hook c by a 
horfe-hair, as at R, fuppofing the vefiel N were away ; 
then obferve the equilibrium, and, as it hangs, let it be 
707 
immerfed in the water of the vefiel O, and it will become 
much lighter; the number of grains and parts of grains, 
determined as before, required to reltore the equilibrium, 
will (how the weight of water equal in bulk to the body 
immerfed. In practice, the wire p n (hould be oiled, and 
then wiped as clean as pofiible ; enough will remain to 
prevent the water adhering to it. The balance ought to 
be raifed very gently, and when brought to an equilibrium 
fhould be gently agitated, to fee whether it will return to 
the equilibrium again. 
The Hydrometer, or Aerometer, is an inftrument contrived 
to meafure the fpecific gravity of water and other fluids ; 
and, indeed, has fometimes been made life of to determine 
the fpecific gravity of folid bodies. The general princi¬ 
ple on which the conftruttion and pfe of the hydrometer 
depends is contained in Cor. 4- Prop. XII. from which it 
follows, that a body fpecifically lighter than feveral fluids 
will ferve to find out their fpecific gravities, becaufe ic 
will fink deepelt in the fluids whole fpecific gravity is the 
lead. Thus, if A B, fig. 11, be a fmall uniform glals 
tube, hermetically fealed, having a fcale of equal divi¬ 
fions marked upon it, with a hollow ball of about an inch 
in diameter at bottom, and a fmaller ball C under it, com¬ 
municating with the firlt; into the little bail is put mer¬ 
cury or fmall fiiot, before the tube is fealed, fo that it may 
fink in water below the ball, and float or Hand upright, 
the divifions on the fteni (bowing how far it finks. If 
this inftrument be dipped in common water, and fink to 
D, it will fink only to fome lower point E in fait water , 
but in port wine it will fink to fome higher point F, and 
in brandy perhaps to B. It is evident that an hydrometer 
of this kind will only (how that one liquid is fpecifically 
heavier than another; but the true fpecific weight of any 
liquid cannot be determined without a calculation for 
this particular infirumenr, the tube of which Ibould be 
truly cylindrical. Befides, thefe inltruments will not 
ferve for fluids whofe denfities are much different. 
Mr. Clarke conftrufled a new hydrometer, (bowing 
whether any fpirits be proof, or above or below proof, and 
in what degree. This inftrument was at firlt made of 
glafs, confilting of a Item AB, fig. 12, graduated by fmall 
beads of glafs of different colours, Ituck on the outfide ; 
a larger ball, B, quite empty as well as the Item, and a 
fmall ball, C, filled with quickfilver before the end A was 
hermetically fealed, in fuch manner, as to make the hy¬ 
drometer fink in rain-water as deep as m, the middle of 
the ftein. Such an inftrument does indeed fliow the dif¬ 
ferent fpecific gravity of all waters or wines, by linking 
deeper in the lighter, and emerging more out of the hea¬ 
vier, liquors; but, as it is difficult to have the Item ex¬ 
actly or the fame thicknefs all the way, which, if it could 
be had, the fame inftrument would not ferve for water 
and fpirits, finking quite over head in fpirits when made 
for water, and emerging in water with part of the great 
ball out, when made for fpirits. The hydrometer has 
only been ufed to find whether any one liquor is fpecifi¬ 
cally heavier than another; but not to tell how much, 
which cannot be done without a great deal of trouble, 
even with a nice inftrument. The hydroftatical balance 
has fnpplied the place of the hydrometer, and fhows the 
different fpecific gravity of fluids to a very great exaft- 
nefs. But, as that balance cannot well be carried in the 
pocket, and much lefs managed and underllood by per- 
fons not ufed to experiments, Mr. Clarke was relolved to 
perfect the hydrometer for the ufe of thofe that deal in 
brandies and fpirits, that by the ufe of the inftrument they 
may, by infpe&ion, and without trouble, know whether a 
fpirituous liquor be proof, above proof, or under proof, 
and exactly how much above or under; and thismuft be 
of great ufe to the officers of the cuftoms, who examine 
imported or exported liquors. 
After having made leveral fruitlefs trials with ivory, 
becaufe it imbibes fpirituous liquors, and thereby alters 
its gravity,he at laft made a copper hydrometer,reprefented 
by lig, 13. having a brais wire of about a quarter of. an 
inch 
