W = (V + lA)w1; or w1 = W/(V + lA),
w_p = W/(V + plA), and
w_n= W/(V + nlA),
or the densities of the several liquids vary inversely as the
respective volumes of the instrument immersed in them; and, since the
divisions of the scale correspond to equal increments of volume
immersed, it follows that the densities of the several liquids in
which the instrument sinks to the successive divisions form a harmonic
series.
If V = NlA then N expresses the ratio of the volume of the instrument
up to the zero of the scale to that of one of the scale-divisions. If
we suppose the lower part of the instrument replaced by a uniform bar
of the same sectional area as the stem and of volume V, the
indications of the instrument will be in no respect altered, and the
bottom of the bar will be at a distance of N scale-divisions below the
zero of the scale.
In this case we have w_p = W/(N + p)lA; or the density of the liquid
varies inversely as N + p, that is, as the whole number of
scale-divisions between the bottom of the tube and the plane of
flotation.
If we wish the successive divisions of the scale to correspond to
equal increments in the density of the corresponding liquids, then the
volumes of the instrument, measured up to the successive divisions of
the scale, must form a series in harmonical progression, the lengths
of the divisions increasing as we go up the stem.
The greatest density of the liquid for which the instrument described
above can be employed is W/V, while the least density is W/(V + nlA),
or W/(V + v), where v represents the volume of the stem between the
extreme divisions of the scale. Now, by increasing v, leaving W and V
unchanged, we may increase the range of the instrument indefinitely.
But it is clear that if we increase A, the sectional area of the stem,
we shall diminish l, the length of a scale-division corresponding to a
given variation of density, and thereby proportionately diminish the
sensibility of the instrument, while diminishing the section A will
increase l and proportionately increase the sensibility, but will
diminish the range over which the instrument can be employed, unless
we increase the length of the stem in the inverse ratio of the
sectional area. Hence, to obtain great sensibility along with a
considerable range, we require very long slender stems, and to these
two objections apply in addition to the question of portability; for,
in the first place, an instrument with a very long stem requires a
very deep vessel of liquid for its complete immersion, and, in the
second place, when most of the stem is above the plane of flotation,
the stability of the instrument when floating will be diminished or
destroyed. The various devices which have been adopted to overcome
this difficulty will be described in the account given of the several
hydrometers which have been hitherto generally employed.
The plan commonly adopted to obviate the necessity of inconveniently
long stems is to construct a number of hydrometers as nearly alike as
may be, but to load them differently, so that the scale-divisions at
the bottom of the stem of one hydrometer just overlap those at the top
of the stem of the preceding. By this means a set of six hydrometers,
each having a stem rather more than 5 in. long, will be equivalent to
a single hydrometer with a stem of 30 in. But, instead of employing a
number of instruments differing only in the weights with which they
are loaded, we may employ the same instrument, and alter its weight
either by adding mercury or shot to the interior (if it can be opened)
or by attaching weights to the exterior. These two operations are not
quite equivalent, since a weight added to the interior does not affect
the volume of liquid displaced when the instrument is immersed up to a
given division of the scale, while the addition of weights to the
exterior increases the displacement. This difficulty may be met, as in
Keene's hydrometer, by having all the weights of precisely the same
volume but of different masses, and never using the instrument except
with one of these weights attached.
[Illustration: FIG. 2.--Clarke's Hydrometer.]
The first hydrometer intended for the determination of the densities of
liquids, and furnished with a set of weights to be attached when
necessary, was that constructed by Mr Clarke (instrument-maker) and
described by J. T. Desaguliers in the _Philosophical Transactions_ for
March and April 1730, No. 413, p. 278. The following is Desaguliers's
account of the instrument (fig. 2):--
"After having made several fruitless trials with ivory, because it
imbibes spirituous liquors, and thereby alters its gravity, he (Mr
Clarke) at last made a copper hydrometer, represented in fig. 2,
having a brass wire of about 1 in. thick going through, and soldered
into the copper ball Bb. The upper part of this wire is filed flat on
one side, for the stem of the hydrometer, with a mark at m, to which
it sinks exactly in proof spirits. There are two other marks, A and B,
at top and bottom of the stem, to show whether the liquor be (1/10)th
above proof (as when it sinks to A), or (1/10)th under proof (as when
it emerges to B), when a brass weight such as C has been screwed on to
the bottom at c. There are a great many such weights, of different
sizes, and marked to be screwed on instead of C, for liquors that
differ more than (1/10)th from proof, so as to serve for the specific
gravities in all such proportions as relate to the mixture of
spirituous liquors, in all the variety made use of in trade. There are
also other balls for showing the specific gravities quite to common
water, which make the instrument perfect in its kind."
Clarke's hydrometer, as afterwards constructed for the purposes of the
excise, was provided with thirty-two weights to adapt it to spirits of
different specific gravities, and eleven smaller weights, or "weather
weights" as they were called, which were attached to the instrument in
order to correct for variations of temperature. The weights were
adjusted for successive intervals of 5° F., but for degrees intermediate
between these no additional correction was applied. The correction for
temperature thus afforded was not sufficiently accurate for excise
purposes, and William Speer in his essay on the hydrometer (Tilloch's
_Phil. Mag._, 1802, vol. xiv.) mentions cases in which this imperfect
compensation led to the extra duty payable upon spirits which were more
than 10% over proof being demanded on spirits which were purposely
diluted to below 10% over proof in order to avoid the charge. Clarke's
hydrometer, however, remained the standard instrument for excise
purposes from 1787 until it was displaced by that of Sikes.
Desaguliers himself constructed a hydrometer of the ordinary type for
comparing the specific gravities of different kinds of water
(Desaguliers's _Experimental Philosophy_, ii. 234). In order to give
great sensibility to the instrument, the large glass ball was made
nearly 3 in. in diameter, while the stem consisted of a wire 10 in. in
length and only (1/40)in. in diameter. The instrument weighed 4000
grains, and the addition of a grain caused it to sink through an inch.
By altering the quantity of shot in the small balls the instrument could
be adapted for liquids other than water.
To an instrument constructed for the same purpose, but on a still larger
scale than that of Desaguliers, A. Deparcieux added a small dish on the
top of the stem for the reception of the weights necessary to sink the
instrument to a convenient depth. The effect of weights placed in such a
dish or pan is of course the same as if they were placed within the bulb
of the instrument, since they do not alter the volume of that part which
is immersed.
[Illustration: FIG. 3.--Nicholson's Hydrometer.]
The first important improvement in the hydrometer after its reinvention
by Boyle was introduced by G. D. Fahrenheit, who adopted the second mode
of construction above referred to, arranging his instrument so as always
to displace the same volume of liquid, its weight being varied
accordingly. Instead of a scale, only a single mark is placed upon the
stem, which is very slender, and bears at the top a small scale pan into
which weights are placed until the instrument sinks to the mark upon its
stem. The volume of the displaced liquid being then always the same, its
density will be proportional to the whole weight supported, that is, to
the weight of the instrument together with the weights required to be
placed in the scale pan.
Nicholson's hydrometer (fig. 3) combines the characteristics of
Fahrenheit's hydrometer and of Boyle's essay instrument.[2] The
following is the description given of it by W. Nicholson in the
_Manchester Memoirs_, ii. 374:--
"AA represents a small scale. It may be taken off at D. Diameter 1½
in., weight 44 grains.
"B a stem of hardened steel wire. Diameter 1/100 in.
"E a hollow copper globe. Diameter 2(8/10) in. Weight with stem 369
grains.
"FF a stirrup of wire screwed to the globe at C.
"G a small scale, serving likewise as a counterpoise. Diameter 1½ in.
Weight with stirrup 1634 grains.
"The other dimensions may be had from the drawing, which is one-sixth
of the linear magnitude of the instrument itself.
"In the construction it is assumed that the upper scale shall
constantly carry 1000 grains when the lower scale is empty, and the
instrument sunk in distilled water at the temperature of 60° Fahr. to
the middle of the wire or stem. The length of the stem is arbitrary,
as is likewise the distance of the lower scale from the surface of the
globe. But, the length of the stem being settled, the lower scale may
be made lighter, and, consequently, the globe less, the greater its
distance is taken from the surface of the globe; and the contrary."
In comparing the densities of different liquids, it is clear that this
instrument is precisely equivalent to that of Fahrenheit, and must be
employed in the same manner, weights being placed in the top scale only
until the hydrometer sinks to the mark on the wire, when the specific
gravity of the liquid will be proportional to the weight of the
instrument together with the weights in the scale.
In the subsequent portion of the paper above referred to, Nicholson
explains how the instrument may be employed as a thermometer, since,
fluids generally expanding more than the solids of which the instrument
is constructed, the instrument will sink as the temperature rises.
To determine the density of solids heavier than water with this
instrument, let the solid be placed in the upper scale pan, and let
the weight now required to cause the instrument to sink in distilled
water at standard temperature to the mark B be denoted by w, while W
denotes the weight required when the solid is not present. Then W - w
is the weight of the solid. Now let the solid be placed in the lower
pan, care being taken that no bubbles of air remain attached to it,
and let w1 be the weight now required in the scale pan. This weight
will exceed w in consequence of the water displaced by the solid, and
the weight of the water thus displaced will be W1 - w, which is
therefore the weight of a volume of water equal to that of the solid.
Hence, since the weight of the solid itself is W - w, its density must
be (W - w)/(w1 - w).
The above example illustrates how Nicholson's or Fahrenheit's hydrometer
may be employed as a weighing machine for small weights.
In all hydrometers in which a part only of the instrument is immersed,
there is a liability to error in consequence of the surface tension, or
capillary action, as it is frequently called, along the line of contact
of the instrument and the surface of the liquid (see CAPILLARY ACTION).
This error diminishes as the diameter of the stem is reduced, but is
sensible in the case of the thinnest stem which can be employed, and is
the chief source of error in the employment of Nicholson's hydrometer,
which otherwise would be an instrument of extreme delicacy and
precision. The following is Nicholson's statement on this point:--
"One of the greatest difficulties which attends hydrostatical
experiments arises from the attraction or repulsion that obtains at
the surface of the water. After trying many experiments to obviate the
irregularities arising from this cause, I find reason to prefer the
simple one of carefully wiping the whole instrument, and especially
the stem, with a clean cloth. The weights in the dish must not be
esteemed accurate while there is either a cumulus or a cavity in the
water round the stem."
It is possible by applying a little oil to the upper part of the bulb of
a common or of a Sikes's hydrometer, and carefully placing it in pure
water, to cause it to float with the upper part of the bulb and the
whole of the stem emerging as indicated in fig. 4, when it ought
properly to sink almost to the top of the stem, the surface tension of
the water around the circumference of the circle of contact, AA',
providing the additional support required.
[Illustration: FIG. 4.]
The universal hydrometer of G. Atkins, described in the _Phil. Mag._
for 1808, xxxi. 254, is merely Nicholson's hydrometer with the screw
at C projecting through the collar into which it is screwed, and
terminating in a sharp point above the cup G. To this point soft
bodies lighter than water (which would float if placed in the cup)
could be attached, and thus completely immersed. Atkins's instrument
was constructed so as to weigh 700 grains, and when immersed to the
mark on the stem in distilled water at 60° F. it carried 300 grains in
the upper dish. The hydrometer therefore displaced 1000 grains of
distilled water at 60° F. and hence the specific gravity of any other
liquid was at once indicated by adding 700 to the number of grains in
the pan required to make the instrument sink to the mark on the stem.
The small divisions on the scale corresponded to differences of
(1/10)th of a grain in the weight of the instrument.
The "Gravimeter," constructed by Citizen Guyton and described in
_Nicholson's Journal_, 4to, i. 110, differs from Nicholson's
instrument in being constructed of glass, and having a cylindrical
bulb about 21 centimetres in length and 22 millimetres in diameter.
Its weight is so adjusted that an additional weight of 5 grammes must
be placed in the upper pan to cause the instrument to sink to the mark
on the stem in distilled water at the standard temperature. The
instrument is provided with an additional piece, or "plongeur," the
weight of which exceeds 5 grammes by the weight of water which it
displaces; that is to say, it is so constructed as to weigh 5 grammes
in water, and consists of a glass envelope filled with mercury. It is
clear that the effect of this "plongeur," when placed in the lower
pan, is exactly the same as that of the 5 gramme weight in the upper
pan. Without the extra 5 grammes the instrument weighs about 20
grammes, and therefore floats in a liquid of specific gravity .8. Thus
deprived of its additional weight it may be used for spirits. To use
the instrument for liquids of much greater density than water
additional weights must be placed in the upper pan, and the "plongeur"
is then placed in the lower pan for the purpose of giving to the
instrument the requisite stability.
Charles's balance areometer is similar to Nicholson's hydrometer,
except that the lower basin admits of inversion, thus enabling the
instrument to be employed for solids lighter than water, the inverted
basin serving the same purpose as the pointed screw in Atkins's
modification of the instrument.
Adie's sliding hydrometer is of the ordinary form, but can be adjusted
for liquids of widely differing specific gravities by drawing out a
sliding tube, thus changing the volume of the hydrometer while its
weight remains constant.
The hydrometer of A. Baumé, which has been extensively used in France,
consists of a common hydrometer graduated in the following manner.
Certain fixed points were first determined upon the stem of the
instrument. The first of these was found by immersing the hydrometer
in pure water, and marking the stem at the level of the surface. This
formed the zero of the scale. Fifteen standard solutions of pure
common salt in water were then prepared, containing respectively 1, 2,
3, ... 15% (by weight) of dry salt. The hydrometer was plunged in
these solutions in order, and the stem having been marked at the
several surfaces, the degrees so obtained were numbered 1, 2, 3, ...
15. These degrees were, when necessary, repeated along the stem by the
employment of a pair of compasses till 80 degrees were marked off. The
instrument thus adapted to the determination of densities exceeding
that of water was called the hydrometer for salts.
The hydrometer intended for densities less than that of water, or the
hydrometer for spirits, is constructed on a similar principle. The
instrument is so arranged that it floats in pure water with most of
the stem above the surface. A solution containing 10% of pure salt is
used to indicate the zero of the scale, and the point at which the
instrument floats when immersed in distilled water at 10° R. (54½° F.)
is numbered 10. Equal divisions are then marked off upwards along the
stem as far as the 50th degree.
The densities corresponding to the several degrees of Baumé's
hydrometer are given by Nicholson (_Journal of Philosophy_, i. 89) as
follows:--
_Baumé's Hydrometer for Spirits. Temperature 10° R._
+--------+--------+--------+--------+--------+--------+
|Degrees.|Density.|Degrees.|Density.|Degrees.|Density.|
+--------+--------+--------+--------+--------+--------+
| 10 | 1.000 | 21 | .922 | 31 | .861 |
| 11 | .990 | 22 | .915 | 32 | .856 |
| 12 | .985 | 23 | .909 | 33 | .852 |
| 13 | .977 | 24 | .903 | 34 | .847 |
| 14 | .970 | 25 | .897 | 35 | .842 |
| 15 | .963 | 26 | .892 | 36 | .837 |
| 16 | .955 | 27 | .886 | 37 | .832 |
| 17 | .949 | 28 | .880 | 38 | .827 |
| 18 | .943 | 29 | .874 | 39 | .822 |
| 19 | .935 | 30 | .867 | 40 | .817 |
| 20 | .928 | | | | |
+--------+--------+--------+--------+--------+--------+
_Baume's Hydrometer for Salts._
+--------+--------+--------+--------+--------+--------+
|Degrees.|Density.|Degrees.|Density.|Degrees.|Density.|
+--------+--------+--------+--------+--------+--------+
| 0 | 1.000 | 27 | 1.230 | 51 | 1.547 |
| 3 | 1.020 | 30 | 1.261 | 54 | 1.594 |
| 6 | 1.040 | 33 | 1.295 | 57 | 1.659 |
| 9 | 1.064 | 36 | 1.333 | 60 | 1.717 |
| 12 | 1.089 | 39 | 1.373 | 63 | 1.779 |
| 15 | 1.114 | 42 | 1.414 | 66 | 1.848 |
| 18 | 1.140 | 45 | 1.455 | 69 | 1.920 |
| 21 | 1.170 | 48 | 1.500 | 72 | 2.000 |
| 24 | 1.200 | | | | |
+--------+--------+--------+--------+--------+--------+
Carrier's hydrometer was very similar to that of Baumé, Cartier having
been employed by the latter to construct his instruments for the
French revenue. The point at which the instrument floated in distilled
water was marked 10° by Cartier, and 30° on Carrier's scale
corresponded to 32° on Baumé's.
Perhaps the main object for which hydrometers have been constructed is
the determination of the value of spirituous liquors, chiefly for
revenue purposes. To this end an immense variety of hydrometers have
been devised, differing mainly in the character of their scales.
In Speer's hydrometer the stem has the form of an octagonal prism, and
upon each of the eight faces a scale is engraved, indicating the
percentage strength of the spirit corresponding to the several
divisions of the scale, the eight scales being adapted respectively to
the temperature 35°, 40°, 45°, 50°, 55°, 60°, 65° and 70° F. Four
small pins, which can be inserted into the counterpoise of the
instrument, serve to adapt the instrument to the temperatures
intermediate between those for which the scales are constructed.
William Speer was supervisor and chief assayer of spirits in the port
of Dublin. For a more complete account of this instrument see
Tilloch's _Phil. Mag._, xiv. 151.
[Illustration: FIG. 5.--Jones's Hydrometer.]
The hydrometer constructed by Jones, of Holborn, consists of a
spheroidal bulb with a rectangular stem (fig. 5). Between the bulb and
counterpoise is placed a thermometer, which serves to indicate the
temperature of the liquid, and the instrument is provided with three
weights which can be attached to the top of the stem. On the four
sides of the stem AD are engraved four scales corresponding
respectively to the unloaded instrument, and to the instrument loaded
with the respective weights. The instrument when unloaded serves for
the range from 74 to 47 over proof; when loaded with the first weight
it indicates from 46 to 13 over proof, with the second weight from 13
over proof to 29 under proof, and with the third from 29 under proof
to pure water, the graduation corresponding to which is marked W at
the bottom of the fourth scale. One side of the stem AD is shown in
fig. 5, the other three in fig. 6. The thermometer is also provided
with four scales corresponding to the scales above mentioned. Each
scale has its zero in the middle corresponding to 60° F. If the
mercury in the thermometer stand above this zero the spirit must be
reckoned weaker than the hydrometer indicates by the number on the
thermometer scale level with the top of the mercury, while if the
thermometer indicate a temperature lower than the zero of the scale
(60° F.) the spirit must be reckoned stronger by the scale reading. At
the side of each of the four scales on the stem of the hydrometer is
engraved a set of small numbers indicating the contraction in volume
which would be experienced if the requisite amount of water (or
spirit) were added to bring the sample tested to the proof strength.
[Illustration: FIG. 6.]
The hydrometer constructed by Dicas of Liverpool is provided with a
sliding scale which can be adjusted for different temperatures, and
which also indicates the contraction in volume incident on bringing
the spirit to proof strength. It is provided with thirty-six different
weights which, with the ten divisions on the stem, form a scale from 0
to 370. The employment of so many weights renders the instrument
ill-adapted for practical work where speed is an object.
[Illustration: FIG. 7.--Atkins's Hydrometer.]
This instrument was adopted by the United States in 1790, but was
subsequently discarded by the Internal Revenue Service for another
type. In this latter form the observations have to be made at the
standard temperature of 60° F., at which the graduation 100
corresponds to proof spirit and 200 to absolute alcohol. The need of
adjustable weights is avoided by employing a set of five instruments,
graduated respectively 0°-100°, 80°-120°, 100°-140°, 130°-170°,
160°-200°. The reading gives the volume of proof spirit equivalent to
the volume of liquor; thus the readings 80° and 120° mean that 100
volumes of the test liquors contain the same amount of absolute
alcohol as 80 and 120 volumes of proof spirit respectively. Proof
spirit is defined in the United States as a mixture of alcohol and
water which contains equal volumes of alcohol and water at 60° F., the
alcohol having a specific gravity of 0.7939 at 60° as compared with
water at its maximum density. The specific gravity of proof spirit is
0.93353 at 60°; and 100 volumes of the mixture is made from 50 volumes
of absolute alcohol and 53.71 volumes of water.
Quin's universal hydrometer is described in the _Transactions of the
Society of Arts_, viii. 98. It is provided with a sliding rule to
adapt it to different temperatures, and has four scales, one of which
is graduated for spirits and the other three serve to show the
strengths of worts. The peculiarity of the instrument consists in the
pyramidal form given to the stem, which renders the scale-divisions
more nearly equal in length than they would be on a prismatic stem.
Atkins's hydrometer, as originally constructed, is described in
_Nicholson's Journal_, 8vo, ii. 276. It is made of brass, and is
provided with a spheroidal bulb the axis of which is 2 in. in length,
the conjugate diameter being 1½ in. The whole length of the instrument
is 8 in., the stem square of about 1/8-in. side, and the weight about
400 grains. It is provided with four weights, marked 1, 2, 3, 4, and
weighing respectively 20, 40, 61 and 84 grains, which can be attached
to the shank of the instrument at C (fig. 7) and retained there by the
fixed weight B. The scale engraved upon one face of the stem contains
fifty-five divisions, the top and bottom being marked 0 or zero and
the alternate intermediate divisions (of which there are twenty-six)
being marked with the letters of the alphabet in order. The four
weights are so adjusted that, if the instrument floats with the stem
emerging as far as the lower division 0 with one of the weights
attached, then replacing the weight by the next heavier causes the
instrument to sink through the whole length of the scale to the upper
division 0, and the first weight produces the same effect when applied
to the naked instrument. The stem is thus virtually extended to five
times its length, and the number of divisions increased practically to
272. When no weight is attached the instrument indicates densities
from .806 to .843; with No. 1 it registers from .843 to .880, with No.
2 from .880 to .918, with No. 3 from .918 to .958, and with No. 4 from
.958 to 1.000, the temperature being 55° F. It will thus be seen that
the whole length of the stem corresponds to a difference of density of
about .04, and one division to about .00074, indicating a difference
of little more than 1/3% in the strength of any sample of spirits.
The instrument is provided with a sliding rule, with scales
corresponding to the several weights, which indicate the specific
gravity corresponding to the several divisions of the hydrometer scale
compared with water at 55° F. The slider upon the rule serves to
adjust the scale for different temperatures, and then indicates the
strength of the spirit in percentages over or under proof. The slider
is also provided with scales, marked respectively Dicas and Clarke,
which serve to show the readings which would have been obtained had
the instruments of those makers been employed. The line on the scale
marked "concentration" indicates the diminution in volume consequent
upon reducing the sample to proof strength (if it is _over proof_,
O.P.) or upon reducing proof spirit to the strength of the sample (if
it is _under proof_, U.P.). By applying the several weights in
succession in addition to No. 4 the instrument can be employed for
liquids heavier than water; and graduations on the other three sides
of the stem, together with an additional slide rule, adapt the
instrument for the determination of the strength of worts.
Atkins subsequently modified the instrument (_Nicholson's Journal_,
8vo, iii. 50) by constructing the different weights of different
shapes, viz. circular, square, triangular and pentagonal, instead of
numbering them 1, 2, 3 and 4 respectively, a figure of the weight
being stamped on the sliding rule opposite to every letter in the
series to which it belongs, thus diminishing the probability of
mistakes. He also replaced the letters on the stem by the
corresponding specific gravities referred to water as unity. Further
information concerning these instruments and the state of hydrometry
in 1803 will be found in Atkins's pamphlet _On the Relation between
the Specific Gravities and the Strength of Spirituous Liquors_ (1803);
or _Phil. Mag._ xvi. 26-33, 205-212, 305-312; xvii. 204-210 and
329-341.
In Gay-Lussac's alcoholometer the scale is divided into 100 parts
corresponding to the presence of 1, 2, ... % by volume of alcohol at
15° C., the highest division of the scale corresponding to the purest
alcohol he could obtain (density .7947) and the lowest division
corresponding to pure water. A table provides the necessary
corrections for other temperatures.
Tralles's hydrometer differs from Gay-Lussac's only in being graduated
at 4° C. instead of 15° C., and taking alcohol of density .7939 at
15.5° C. for pure alcohol instead of .7947 as taken by Gay-Lussac
(Keene's _Handbook of Hydrometry_).
In Beck's hydrometer the zero of the scale corresponds to density
1.000 and the division 30 to density .850, and equal divisions on the
scale are continued as far as is required in both directions.
[Illustration: FIG. 8.--Sike's Hydrometer.]
In the centesimal hydrometer of Francoeur the volume of the stem
between successive divisions of the scale is always (1/100)th of the
whole volume immersed when the instrument floats in water at 4° C. In
order to graduate the stem the instrument is first weighed, then
immersed in distilled water at 4° C., and the line of flotation marked
zero. The first degree is then found by placing on the top of the stem
a weight equal to (1/100)th of the weight of the instrument, which
increases the volume immersed by (1/100)th of the original volume. The
addition to the top of the stem of successive weights, each (1/100)th
of the weight of the instrument itself, serves to determine the
successive degrees. The length of 100 divisions of the scale, or the
length of the uniform stem the volume of which would be equal to that
of the hydrometer up to the zero graduation, Francoeur called the
"modulus" of the hydrometer. He constructed his instruments of glass,
using different instruments for different portions of the scale
(Francoeur, _Traité d'aréométrie_, Paris, 1842).
Dr Boriés of Montpellier constructed a hydrometer which was based upon
the results of his experiments on mixtures of alcohol and water. The
interval between the points corresponding to pure alcohol and to pure
water Boriés divided into 100 equal parts, though the stem was
prolonged so as to contain only 10 of these divisions, the other 90
being provided for by the addition of 9 weights to the bottom of the
instrument as in Clarke's hydrometer.
The instrument which has now been exclusively used for revenue
purposes for nearly a century is that associated with the name of
Bartholomew Sikes, who was correspondent to the Board of Excise from
1774 to 1783, and for some time collector of excise for Hertfordshire.
Sikes's hydrometer, on account of its similarity to that of Boriés,
appears to have been borrowed from that instrument. It is made of
gilded brass or silver, and consists of a spherical ball A (fig. 8),
1.5 in. in diameter, below which is a weight B connected with the ball
by a short conical stem C. The stem D is rectangular in section and
about 3½ in. in length. This is divided into ten equal parts, each of
which is subdivided into five. As in Boriés's instrument, a series of
9 weights, each of the form shown at E, serves to extend the scale to
100 principal divisions. In the centre of each weight is a hole
capable of admitting the lowest and thickest end of the conical stem
C, and a slot is cut into it just wide enough to allow the upper part
of the cone to pass. Each weight can thus be dropped on to the lower
stem so as to rest on the counterpoise B. The weights are marked 10,
20, ... 90; and in using the instrument that weight must be selected
which will allow it to float in the liquid with a portion only of the
stem submerged. Then the reading of the scale at the line of
flotation, added to the number on the weight, gives the reading
required. A small supernumerary weight F is added, which can be placed
upon the top of the stem. F is so adjusted that when the 60 weight is
placed on the lower stem the instrument sinks to the same point in
distilled water when F is attached as in proof spirit when F is
removed. The best instruments are now constructed for revenue purposes
of silver, heavily gilded, because it was found that saccharic acid
contained in some spirits attacked brass behind the gilding.
The following table gives the specific gravities corresponding to the
principal graduations on Sikes's hydrometer at 60° F. and 62° F.,
together with the corresponding strengths of spirits. The latter are
based upon the tables of Charles Gilpin, clerk to the Royal Society,
for which the reader is referred to the _Phil. Trans._ for 1794.
Gilpin's work is a model for its accuracy and thoroughness of detail,
and his results have scarcely been improved upon by more recent
workers. The merit of Sikes's system lies not so much in the
hydrometer as in the complete system of tables by which the readings
of the instrument are at once converted into percentage of
proof-spirit.
_Table showing the Densities corresponding to the Indications of
Sike's Hydrometer._
+------------+------------------+------------------+
| | 60° F. | 62° F. |
| +---------+--------+---------+--------+
| Sike's | Proof | | Proof | |
|Indications.| Spirit |Density.| Spirit |Density.|
| |per cent.| |per cent.| |
+------------+---------+--------+---------+--------+
| 0 | .815297 | 167.0 | .815400 | 166.5 |
| 1 | .816956 | 166.1 | .817059 | 165.6 |
| 2 | .818621 | 165.3 | .818725 | 164.8 |
| 3 | .820294 | 164.5 | .820397 | 163.9 |
| 4 | .821973 | 163.6 | .822077 | 163.1 |
| 5 | .823659 | 162.7 | .823763 | 162.3 |
| 6 | .825352 | 161.8 | .825457 | 161.4 |
| 7 | .827052 | 160.9 | .827157 | 160.5 |
| 8 | .828759 | 160.0 | .828864 | 159.6 |
| 9 | .830473 | 159.1 | .830578 | 158.7 |
| 10 | .832195 | 158.2 | .832300 | 157.8 |
| 11 | .833888 | 157.3 | .833993 | 156.8 |
| 12 | .835587 | 156.4 | .835692 | 155.9 |
| 13 | .837294 | 155.5 | .837400 | 155.0 |
| 14 | .839008 | 154.6 | .839114 | 154.0 |
| 15 | .840729 | 153.7 | .840835 | 153.1 |
| 16 | .842458 | 152.7 | .842564 | 152.1 |
| 17 | .844193 | 151.7 | .844299 | 151.1 |
| 18 | .845936 | 150.7 | .846042 | 150.1 |
| 19 | .847685 | 149.7 | .847792 | 149.1 |
| 20 | .849442 | 148.7 | .849549 | 148.1 |
| 20B | .849393 | 148.7 | .849500 | 148.1 |
| 21 | .851122 | 147.6 | .851229 | 147.1 |
| 22 | .852857 | 146.6 | .852964 | 146.1 |
| 23 | .854599 | 145.6 | .854707 | 145.1 |
| 24 | .856348 | 144.6 | .856456 | 144.0 |
| 25 | .858105 | 143.5 | .858213 | 142.9 |
| 26 | .859869 | 142.4 | .859978 | 141.8 |
| 27 | .861640 | 141.3 | .861749 | 140.8 |
| 28 | .863419 | 140.2 | .863528 | 139.7 |
| 29 | .865204 | 139.1 | .865313 | 138.5 |
| 30 | .866998 | 138.0 | .867107 | 137.4 |
| 30B | .866991 | 138.0 | .867100 | 137.4 |
| 31 | .868755 | 136.9 | .868865 | 136.2 |
| 32 | .870526 | 135.7 | .870636 | 135.1 |
| 33 | .872305 | 134.5 | .872415 | 133.9 |
| 34 | .874090 | 133.4 | .874200 | 132.8 |
| 35 | .875883 | 132.2 | .873994 | 131.6 |
| 36 | .877684 | 131.0 | .877995 | 130.4 |
| 37 | .879492 | 129.8 | .879603 | 129.1 |
| 38 | .881307 | 128.5 | .881419 | 127.9 |
| 39 | .883129 | 127.3 | .883241 | 126.7 |
| 40 | .884960 | 126.0 | .885072 | 125.4 |
| 40B | .884888 | 126.0 | .885000 | 125.4 |
| 41 | .886689 | 124.8 | .886801 | 124.2 |
| 42 | .888497 | 123.5 | .888609 | 122.9 |
| 43 | .890312 | 122.2 | .890425 | 121.6 |
| 44 | .892135 | 120.9 | .892248 | 120.3 |
| 45 | .893965 | 119.6 | .894078 | 119.0 |
| 46 | .895803 | 118.3 | .895916 | 117.6 |
| 47 | .897647 | 116.9 | .897761 | 116.3 |
| 48 | .899509 | 115.6 | .899614 | 114.9 |
| 49 | .901360 | 114.2 | .901417 | 113.5 |
| 50 | .903229 | 112.8 | .903343 | 112.1 |
| 50B | .903186 | 112.8 | .903300 | 112.1 |
| 51 | .905024 | 111.4 | .905138 | 110.7 |
| 52 | .906869 | 110.0 | .906983 | 109.3 |
| 53 | .908722 | 108.6 | .908837 | 107.9 |
| 54 | .910582 | 107.1 | .910697 | 106.5 |
| 55 | .912450 | 105.6 | .912565 | 105.0 |
| 56 | .914326 | 104.2 | .914441 | 103.5 |
| 57 | .916209 | 102.7 | .916323 | 102.0 |
| 58 | .918100 | 101.3 | .918216 | 100.5 |
| 59 | .919999 | 99.7 | .820115 | 98.9 |
| 60 | .921906 | 98.1 | .922022 | 97.4 |
| 60B | .921884 | 98.1 | .922000 | 97.4 |
| 61 | .923760 | 96.6 | .923877 | 95.9 |
| 62 | .925643 | 95.0 | .925760 | 94.2 |
| 63 | .927534 | 93.3 | .927652 | 92.6 |
| 64 | .929433 | 91.7 | .929550 | 90.9 |
| 65 | .931339 | 90.0 | .931457 | 89.2 |
| 66 | .933254 | 88.3 | .933372 | 87.5 |
| 67 | .935176 | 86.5 | .935294 | 85.8 |
| 68 | .937107 | 84.7 | .937225 | 84.0 |
| 69 | .939045 | 82.9 | .939163 | 82.2 |
| 70 | .940991 | 81.1 | .941110 | 80.3 |
| 70B | .940981 | 81.1 | .941100 | 80.3 |
| 71 | .942897 | 79.2 | .943016 | 78.4 |
| 72 | .944819 | 77.3 | .944938 | 76.5 |
| 73 | .946749 | 75.3 | .946869 | 74.5 |
| 74 | .948687 | 73.3 | .948807 | 72.5 |
| 75 | .950634 | 71.2 | .950753 | 70.4 |
| 76 | .952588 | 69.0 | .952708 | 68.2 |
| 77 | .954550 | 66.8 | .954670 | 66.0 |
| 78 | .956520 | 64.4 | .956641 | 63.5 |
| 79 | .958498 | 61.9 | .958619 | 61.1 |
| 80 | .960485 | 59.4 | .960606 | 58.5 |
| 80B | .960479 | 59.4 | .960600 | 58.5 |
| 81 | .962433 | 56.7 | .962555 | 55.8 |
| 82 | .964395 | 53.9 | .964517 | 53.0 |
| 83 | .966366 | 50.9 | .966488 | 50.0 |
| 84 | .968344 | 47.8 | .968466 | 47.0 |
| 85 | .970331 | 44.5 | .970453 | 43.8 |
| 86 | .972325 | 41.0 | .972448 | 40.4 |
| 87 | .974328 | 37.5 | .974451 | 36.9 |
| 88 | .976340 | 34.0 | .976463 | 33.5 |
| 89 | .978359 | 30.6 | .978482 | 30.1 |
| 90 | .980386 | 27.2 | .980510 | 26.7 |
| 90B | .980376 | 27.2 | .980500 | 26.7 |
| 91 | .982371 | 23.9 | .982496 | 23.6 |
| 92 | .984374 | 20.8 | .984498 | 20.5 |
| 93 | .986385 | 17.7 | .986510 | 17.4 |
| 94 | .988404 | 14.8 | .988529 | 14.5 |
| 95 | .990431 | 12.0 | .990557 | 11.7 |
| 96 | .992468 | 9.3 | .992593 | 9.0 |
| 97 | .994512 | 6.7 | .994637 | 6.5 |
| 98 | .996565 | 4.1 | .996691 | 4.0 |
| 99 | .998626 | 1.8 | .998752 | 1.6 |
| 100 |1.000696 | 0.0 |1.000822 | 0.0 |
+------------+---------+--------+---------+--------+
In the above table for Sikes's hydrometer two densities are given
corresponding to each of the degrees 20, 30, 40, 50, 60, 70, 80 and
90, indicating that the successive weights belonging to the particular
instrument for which the table has been calculated do not quite agree.
The discrepancy, however, does not produce any sensible error in the
strength of the corresponding spirit.
A table which indicates the weight per gallon of spirituous liquors
for every degree of Sikes's hydrometer is printed in 23 and 24 Vict.
c. 114, schedule B. This table differs slightly from that given above,
which has been abridged from the table given in Keene's _Handbook of
Hydrometry_, apparently on account of the equal divisions on Sikes's
scale having been taken as corresponding to equal increments of
density.
Sikes's hydrometer was established for the purpose of collecting the
revenue of the United Kingdom by Act of Parliament, 56 Geo. III. c.
140, by which it was enacted that "all spirits shall be deemed and
taken to be of the degree of strength which the said hydrometers
called Sikes's hydrometers shall, upon trial by any officer or
officers of the customs or excise, denote such spirits to be." This
act came into force on January 5, 1817, and was to have remained in
force until August 1, 1818, but was repealed by 58 Geo. III. c. 28,
which established Sikes's hydrometer on a permanent footing. By 3 and
4 Will. IV. c. 52, § 123, it was further enacted that the same
instruments and methods should be employed in determining the duty
upon imported spirits as should in virtue of any Act of Parliament be
employed in the determination of the duty upon spirits distilled at
home. It is the practice of the officers of the inland revenue to
adjust Sikes's hydrometer at 62° F., that being the temperature at
which the imperial gallon is defined as containing 10 lb. avoirdupois
of distilled water. The specific gravity of any sample of spirits thus
determined, when multiplied by ten, gives the weight in pounds per
imperial gallon, and the weight of any bulk of spirits divided by this
number gives its volume at once in imperial gallons.
Mr (afterwards Colonel) J. B. Keene, of the Hydrometer Office, London,
has constructed an instrument after the model of Sikes's, but provided
with twelve weights of different masses but equal volumes, and the
instrument is never used without having one of these attached. When
loaded with either of the lightest two weights the instrument is
specifically lighter than Sikes's hydrometer when unloaded, and it may
thus be used for specific gravities as low as that of absolute
alcohol. The volume of each weight being the same, the whole volume
immersed is always the same when it floats at the same mark whatever
weight may be attached.
Besides the above, many hydrometers have been employed for special
purposes. Twaddell's hydrometer is adapted for densities greater than
that of water. The scale is so arranged that the reading multiplied by
5 and added to 1000 gives the specific gravity with reference to water
as 1000. To avoid an inconveniently long stem, different instruments
are employed for different parts of the scale as mentioned above.
The lactometer constructed by Dicas of Liverpool is adapted for the
determination of the quality of milk. It resembles Sikes's hydrometer
in other respects, but is provided with eight weights. It is also
provided with a thermometer and slide rule, to reduce the readings to
the standard temperature of 55° F. Any determination of density can be
taken only as affording prima facie evidence of the quality of milk,
as the removal of cream and the addition of water are operations which
tend to compensate each other in their influence on the density of the
liquid, so that the lactometer cannot be regarded as a reliable
instrument.
The marine hydrometers, as supplied by the British government to the
royal navy and the merchant marine, are glass instruments with slender
stems, and generally serve to indicate specific gravities from 1.000
to 1.040. Before being issued they are compared with a standard
instrument, and their errors determined. They are employed for taking
observations of the density of sea-water.
The salinometer is a hydrometer originally intended to indicate the
strength of the brine in marine boilers in which sea-water is
employed. Saunders's salinometer consists of a hydrometer which floats
in a chamber through which the water from the boiler is allowed to
flow in a gentle stream, at a temperature of 200° F. The peculiarity
of the instrument consists in the stream of water, as it enters the
hydrometer chamber, being made to impinge against a disk of metal, by
which it is broken into drops, thus liberating the steam, which would
otherwise disturb the instrument.
The use of Sikes's hydrometer necessitates the employment of a
considerable quantity of spirit. For the testing of spirits in bulk no
more convenient instrument has been devised, but where very small
quantities are available more suitable laboratory methods must be
adopted.
In England, the Finance Act 1907 (7 Ed. VII. c. 13), section 4,
provides as follows: (1) The Commissioners of Customs and the
Commissioners of Inland Revenue may jointly make regulations
authorizing the use of any means described in the regulations for
ascertaining for any purpose the strength or weight of spirits. (2)
Where under any enactment Sykes's (sic) Hydrometer is directed to be
used or may be used for the purpose of ascertaining the strength or
weight of spirits, any means so authorized by regulations may be used
instead of Sykes's Hydrometer and references to Sykes's Hydrometer in
any enactment shall be construed accordingly. (3) Any regulations made
under this section shall be published in the London, Edinburgh and
Dublin Gazette, and shall take effect from the date of publication, or
such later date as may be mentioned in the regulations for the
purpose. (4) The expression "spirits" in this section has the same
meaning as in the Spirits Act 1880. (W. G.)