ON THE GRADUATING OF HYDROMETERS. 
311 
directions, by which a careful workman will be enabled to gra- 
duate his instruments without being obliged to resort to standards, 
the accuracy of which he has no means of determining. 
1st. For liquids lighter than water. 
According to the well-known hydrostatic law, " A floating body 
always displaces its own weight of the liquid in which it swims," 
the weight of any liquid which the hydrometer displaces is, there- 
fore, equal to the weight of the hydrometer. From this fact the 
following proportion is deduced : As the weight of the liquid on 
trial is to that of water or unity, so is the original weight of the 
hydrometer to its required weight. The sp. grav. corresponding 
to 20° B. Pese esprit, being '93333, we have, as -93333 : 1 : : 
weight of hyd. : required weight of hyd.=r( lX %j£ hjd - -) = weight 
ofhyd. X 1*071428, and by subtracting the original weight of 
hyd. from this amount, there remains weight pf hyd. X '071428 
(.071 nearly) as the weight required to be added to sink the hydro- 
meter to 20° B.j and the same amount for every other ten degrees 
successively. This is conveniently done, and the instrument gra- 
duated in the following manner : Having fastened in the stem of 
the hydrometer a slip of paper of the exact weight of the in- 
tended scale, and divided accurately for its whole length, into 
spaces as small as possible and numbered, immerse it in pure 
water at the temperature of 60° Fahr. ; then add mercury or fine 
shot until the instrument sinks to the place intended for the com- 
mencement of the scale. Next dry the hydrometer carefully, and 
weigh it. Then immerse it again in the water and observe the 
division on the scale where the surface of the water cuts the stem 
— this will be the zero point or 10° Beaume. For each succeeding 
10 p Beaume drop into the hydrometer a quantity of mercury, 
found by multiplying the original weight of the hydrometer by 
•071, as above shown, and reading off the divisions to which the 
stem sinks successively. If the stem was perfectly cylindrical, the 
70 Q Beaume could be ascertained at once by adding the requisite 
weight (wt. ofhyd. X .071 X 6) and the intermediate space divided 
equally into 60 parts. The hydrometer is, lastly, to be emptied 
and its original weight made up ; the true scale is then to be 
finished by withdrawing the graduated slip and marking off the 
observed numbers for every ten degrees ; the intermediate degrees 
are then divided off, the scale fastened in its correct place and the 
stem hermetically sealed. 
