finds that it is sensible to 1/1000 of a grain when loaded with ten
grains. It is necessary, however, where accuracy is required, to
employ a scale-pan. This may be made of thin card paper, shaped as in
_fig. 191._
A thread is to be passed through the two ends, by tightening which they
may be brought near each other.
The most convenient weights for this beam appear to be two of one grain
each, and one of one tenth of a grain. They should be made of straight
wire; and if the beam be notched at the divisions, they may be lodged
in these notches very conveniently. Ten divisions on each side of the
middle will be sufficient. The weight of the scale-pan must first be
carefully ascertained, in order that it may be deducted from the
weight, afterwards determined, of the scale-pan and the substance it
may contain.
If the scale-pan be placed at the tenth division of the beam, it is
evident that by means of the two grain weights, a greater weight cannot
be determined than one grain and nine tenths; but if the scale-pan be
placed at any other division of the beam, the resulting apparent weight
must be increased by multiplying it by ten, and dividing by the number
of the division at which the scale-pan is placed; and in this manner it
is evident that if the scale-pan be placed at the division numbered 1,
a weight amounting to nineteen grains may be determined.
We have been tempted to describe this little apparatus, because it is
extremely simple in its construction, may be easily made, and may be
very usefully employed on many occasions where extreme accuracy is not
necessary.
_Description of the Steelyard._
The steelyard is a lever, having unequal arms; and in its most simple
form it is so arranged, that one weight alone serves to determine a
great variety of others, by sliding it along the longer arm of the
lever, and thus varying its distance from the fulcrum.
It has been demonstrated, chapter xiii., that in the lever the
proportion of the power to the weight will be always the same as
that of their distances from the fulcrum, taken in a reverse order;
consequently, when a constant weight is used, and an equilibrium
established by sliding this weight on the longer arm of the lever, the
relative weight of the substance weighed, to the constant weight, will
be in the same proportion as the distance of the constant weight from
the fulcrum is to the length of the shorter arm.
Thus, suppose the length of the shorter arm, or the distance of
the fulcrum from the point from which the weight to be determined
is suspended, to be one inch; let the longer arm of the lever be
divided into parts of one inch each, beginning at the fulcrum. Now
let the constant weight be equal to one pound, and let the steelyard
be so constructed that the shorter arm shall be sufficiently heavy
to counterpoise the longer when the bar is unloaded. Then suppose a
substance, the weight of which is five pounds, to be suspended from the
shorter arm. It will be found that when the constant weight is placed
at the distance of five inches from the fulcrum, the weights will be in
equilibrium, and the bar consequently horizontal. In this steelyard,
therefore, the distance of each inch from the fulcrum indicates a
weight of one pound. An instrument of this form was used by the Romans,
and it is usually described as the Roman statera or steelyard. A
representation of it is given at _fig. 192._
The steelyard is in very general use for the coarser purposes of
commerce, but constructed differently from that which we have
described. The beam with the scales or hooks is seldom in equilibrium
upon the point F, when the weight P is removed; but the longer arm
usually preponderates, and the commencement of the graduations,
therefore, is not at F, but at some point between B and F. The common
steelyard, which we have represented at _fig. 193._, is usually
furnished with two points, from either of which the substance, the
weight of which is to be determined, may be suspended. The value of
the divisions is in this case increased in proportion as the length
of the shorter arm is decreased. Thus, in the steelyard which we have
described, if there be a second point of suspension at the distance of
half an inch from the fulcrum, each division of the longer arm will
indicate two pounds instead of one, and these divisions are usually
marked upon the opposite edge of the steelyard, which is made to turn
over.
This instrument is very convenient, because it requires but one weight;
and the pressure on the fulcrum is less than in the balance, when the
substance to be weighed is heavier than the constant weight. But,
on the contrary, when the constant weight exceeds the substance to
be weighed, the pressure on the fulcrum is greater in the steelyard
than in the balance, and the balance is, therefore, preferable in
determining small weights. There is also an advantage in the balance,
because the subdivision of weights can be effected with a greater
degree of precision than the subdivision of the arm of the steelyard.
_C. Paul’s Steelyard._
A steelyard has been constructed by Mr. C. Paul, inspector of weights
and measures at Geneva, which is much to be preferred to that in
common use. Mr. C. Paul states, that steelyards have two advantages
over balances: 1. That their axis of suspension is not loaded with
any other weight than that of the merchandise, the constant weight of
the apparatus itself excepted; while the axis of the balance, besides
the weight of the instrument, sustains a weight double to that of
the merchandise. 2. The use of the balance requires a considerable
assortment of weights, which causes a proportional increase in the
price of the apparatus, independently of the chances of error which it
multiplies, and of the time employed in producing an equilibrium.
1. In C. Paul’s steelyard the centres of the movement of suspension, or
the two constant centres, are placed on the exact line of the divisions
of the beam; an elevation almost imperceptible in the axis of the beam,
destined to compensate for the very slight flexion of the bar, alone
excepted.
2. The apparatus, by the construction of the beam, is balanced below
its centre of motion, so that when no weight is suspended the beam
naturally remains horizontal, and resumes that position when removed
from it, as also when the steelyard is loaded, and the weight is at
the division which ought to show how much the merchandise weighs. The
horizontal situation in this steelyard, as well as in the others, is
known by means of the tongue which rises vertically above the axis of
suspension.
3. It may be discovered, that the steelyard is deranged if, when not
loaded, the beam does not remain horizontal.
4. The advantage of a great and a small side (which in the other
augments the extent of their power of weighing) is supplied by a very
simple process, which accomplishes the same end with some additional
advantages. This process is to employ on the same division different
weights. The numbers of the divisions on the bar, point out the degree
of heaviness expressed by the corresponding weights. For example, when
the large weight of the large steelyard weighs 16 lbs., each
division it passes over on the bar is equivalent to a pound; the small
weight, weighing sixteen times less than the large one, will represent
on each of these divisions the sixteenth part of a pound, or one ounce;
and the opposite face of the bar is marked by pounds at each sixteenth
division. In this construction, therefore, we have the advantage
of being able, by employing both weights at once, to ascertain,
for example, almost within an ounce, the weight of 500 pounds of
merchandise. It will be sufficient to add what is indicated by the
small weight in ounces, to that of the large one in pounds, after an
equilibrium has been obtained by the position of the two weights, viz.
the large one placed at the next pound below its real weight, and the
small one at the division which determines the number of ounces to be
added.
5. As the beam is graduated only on one edge, it may have the form of
a thin bar, which renders it much less susceptible of being bent by
the action of the weight, and affords room for making the figures more
visible on both the faces.
6. In these steelyards the disposition of the axes is not only such
that the beam represents a mathematical lever without weight, but in
the principle of its division, the interval between every two divisions
is a determined and aliquot part of the distance between the two fixed
points of suspension; and each of the two weights employed has for its
absolute weight the unity of the weight it represents, multiplied by
the number of the divisions contained in the interval between the two
centres of motion.
Thus, supposing the arms of the steelyard divided in such a manner
that ten divisions are exactly contained in the distance between the
two constant centres of motion, a weight to express the pounds on each
division of the beam must really weigh ten pounds; that to point out
the ounces on the same divisions must weigh ten ounces, &c. So that the
same steelyard may be adapted to any system of measures whatever, and
in particular to the decimal system, by varying the absolute heaviness
of the weights, and their relation with each other.
But to trace out, in a few words, the advantages of the steelyards
constructed by C. Paul for commercial purposes, we shall only observe,--
1. That the buyer and seller are certain of the correctness of the
instrument, if the beam remains horizontal when it is unloaded and in
its usual position. 2. That these steelyards have one suspension less
than the old ones, and are so much more simple. 3. That by these means
we obtain, with the greatest facility, by employing two weights, the
exact weight of merchandise, with all the approximation that can be
desired, and even with a greater precision than that given by common
balances. There are few of these which, when loaded with 500 pounds
at each end, give decided indication of an ounce variation; and the
steelyards of C. Paul possess that advantage, and cost one half less
than balances of equal dominion. 4. In the last place, we may verify at
pleasure the justness of the weights, by the transposition which their
ratio to each other will permit; for example, by observing whether,
when the weight of one pound is brought back one division, and the
weight of one ounce carried forward sixteen divisions, the equilibrium
still remains.
It is on this simple and advantageous principle that C. Paul has
constructed his universal steelyard. It serves for weighing in the
usual manner, and according to any system of weights, all ponderable
bodies to the precision of half a grain in the weight of a hundred
ounces; that is to say, of a ten-thousandth part. It is employed,
besides, for ascertaining the specific gravity of solids, of liquids,
and of air, by processes extremely simple, and which do not require
many subdivisions in the weights.
We think the description above given will be sufficiently intelligible
without a representation of this instrument. An account of its
application to the determination of specific gravities will be found in
vol. iii. of the Philosophical Magazine.
_The Chinese Steelyard._
This instrument is used in China and the East Indies for weighing
gems, precious metals, &c. The beam is a small rod of ivory, about
a foot in length. Upon this are three lines of divisions, marked by
fine silver studs, all beginning from the end of the beam, whence the
first is extended 8 inches, the second 6-1/2, and the third 8-1/2. The
first is European weight, and the other two Chinese. At the other end
of the beam hangs a round scale, and at three several distances from
this end are holes, through which pass so many fine strings, serving as
different points of suspension. The first distance makes 1-3/5 inches,
the second 3-1/5, or double the former, and the third 4-4/5, or triple
the same. The instrument, when used, is held by one of the strings,
and a sealed weight of about 1-1/4 oz. troy, is slid upon the
beam until an equilibrium is produced; the weight of the body is then
indicated by the graduated scale above mentioned.
_The Danish Balance._
The Danish balance is a straight bar or lever, having a heavy weight
fixed to one end, and a hook or scale-pan to receive the substance,
the weight of which is to be determined, suspended from the other
end. The fulcrum is moveable, and is made to slide upon the bar, till
the beam rests in a horizontal position, when the place of the fulcrum
indicates the weight required. In order to construct a balance of this
kind, let the distance of the centre of gravity from that point to
which the substance to be weighed is suspended be found by experiment,
when the beam is unloaded. Multiply this distance by the weight of the
whole apparatus, and divide the product by the weight of the apparatus
increased by the weight of the body. This will give the distance from
the point of suspension, at which the fulcrum being placed, the whole
will be in equilibrio: for example, supposing the distance of the
centre of gravity from the point of suspension to be 10 inches, and
the weight of the whole apparatus to be ten pounds; suppose, also, it
were required to mark the divisions which should indicate weights of
one, two, or three pounds, &c. First, for the place of the division
indicating one pound we have (10 × 10)/(10 + 1) = 100/(10 + 1) = 9-1/11
inches, the place of the division marking one pound. For two pounds we
have 100/(10 + 2) = 8-1/3 inches, the place of the division indicating
two pounds; and for three pounds 100/(10 + 3) = 7-9/13 inches for the
place of the division indicating three pounds, and so on.
This balance is subject to the inconvenience of the divisions becoming
much shorter as the weight increases. The distance between the
divisions indicating one and two pounds being, in the example we have
given, about seven tenths of an inch, whilst that between 20 and 21
pounds is only one tenth of an inch; consequently a very small error
in the place of the divisions indicating the larger weights would
occasion very inaccurate results. The Danish balance is represented at
_fig. 194._
_The Bent Lever Balance._
This instrument is represented at _fig. 195._ The weight at C, is
fixed at the end of the bent lever A B C, which is supported
by its axis B on the pillar I H. A scale-pan E, is suspended from
the other end of the lever at A. Through the centre of motion B draw
the horizontal line K B G, upon which, from A and C let fall
the perpendiculars A K and C D. Then if B K and B D
are reciprocally proportional to the weights at A and C, they will be
in equilibrio, but if not, the weight C will move upwards or downwards
along the arc F G till that ratio is obtained. If the lever be so
bent that when A coincides with the line G K, C coincides with
the vertical B H, then as C moves from F to G, its momentum will
increase while that of the weight in the scale-pan E will decrease.
Hence the weight in E, corresponding to different positions of the
balance, may be expressed on the graduated arc F G.
_Brady’s Balance, or Weighing Apparatus._
This partakes of the properties both of the bent lever balance and of
the steelyard. It is represented, at _fig. 196._ A B C
is a frame of cast iron having a great part of its weight towards A. F
is a fulcrum, and E a moveable suspender, having a scale and hook
at its lower extremity. E K G are three distinct places, to
which the suspender E may be applied, and to which belong respectively
the three graduated scales of division expressing weights, _f_ C,
_c d_, and _a b_. When the scale and suspender are applied at
G, the apparatus is in equilibrio, with the edge A B horizontal,
and the suspender cuts the zero on the scale _a b_. Now, any
substance, the weight of which is to be ascertained, being put into
the scale, the whole apparatus turns about F, and the part towards B
descends till the equilibrium is again established, when the weight
of the body is read off from the scale _a b_, which registers to
ounces and extends to two pounds. If the weight of the body exceed two
pounds, and be less than eleven pounds, the suspender is placed at K;
and when the scale is empty, the number 2 is found to the right of the
index of the suspender. If now weights exceeding two pounds be placed
in the scale, the whole again turns about F, and the weight of the
body is shown on the graduated arc _c d_, which extends to eleven
pounds, and registers to every two ounces.
If the weight of the body exceed eleven pounds, the suspender is hung
on at E, and the weights are ascertained in the same manner on the
scale _f_ C to thirty pounds, the subdivisions being on this scale
quarters of pounds. The same principles would obviously apply to
weights greater or less than the above. To prevent mistake, the three
points of support G, K, E, are numbered 1, 2, 3; and the corresponding
arcs are respectively numbered in the same manner. When the hook is
used instead of the scale, the latter is turned upwards, there being a
joint at _m_ for that purpose.
_The Weighing Machine for Turnpike Roads._
This machine is for the purpose of ascertaining the weight of heavy
bodies, such as wheel carriages. It consists of a wooden platform
placed over a pit made in the line of the road, and which contains the
machinery. The pit is walled withinside, and the platform is fitted to
the walls of the pit, but without touching them, and it is therefore
at liberty to move freely up and down. The platform is supported by
levers placed beneath it, and is exactly level with the surface of the
road, so that a carriage is easily drawn on it, the wheels being upon
the platform whilst the horses are upon the solid ground beyond it. The
construction of this machine will be readily understood by reference to
_fig. 197._, in which the platform is supposed to be transparent
so as to allow of the levers being seen below it.
A, B, C, D, represent four levers tending towards the centre of the
platform, and each moveable on its fulcrum at A, B, C, D; the fulcrum
of each rests upon a piece securely fixed in the corner of the pit.
The platform is supported upon the cross pins _a_, _b_, _c_, _d_,
by means of pieces of iron which project from it near its corners, and
which are represented in the plate by the short dark lines crossing the
pins _a_, _b_, _c_, _d_. The four levers are connected under the centre
of the platform, but not so as to prevent their free motion, and are
supported by a long lever at the point F, the fulcrum of which rests
upon a piece of masonry at E: the end of this last lever passes below
the surface of the road into the turnpike house, and is there attached
to one arm of a balance, or, as in Salmon’s patent weighing machine, to
a strap passing round a cylinder which winds up a small weight round a
spiral, and indicates, by means of an index, the weight placed upon the
platform.
[Illustration: _Captn. Kater, del._ _H. Adlard, sc._
_London, Pubd. by Longman & Co._]
Suppose the distance from A to F to be ten times as great as that from
A to _a_, then a force of one pound applied beneath F would balance
ten pounds applied at _a_, or upon the platform. Again: let the
distance from E to G be also ten times greater than the distance from
the fulcrum E to F; then a force of one pound applied to raise up the
end of the lever G would counterpoise a weight of ten pounds placed
upon F. Now, as we gain ten times the power by the first levers, and
ten times more by the lever E G, it follows, that a force of one
pound tending to elevate G, would balance 100 lbs. placed on the
platform; so that if the end of the lever G be attached to one arm of
a balance, a weight of 10 lbs. placed in a scale suspended from
the other arm, will express the value of 1000 lbs. placed upon
the platform. The levers are counterpoised, when the platform is not
loaded, by a weight H applied to the end of the last lever, continued
beyond the fulcrum for that purpose.
_Of Instruments for weighing by means of a Spring._
The spring is well adapted to the construction of a weighing machine,
from the property it possesses of yielding in proportion to the force
impressed, and consequently giving a scale of equal parts for equal
additions of weight. It is liable, however, to suffer injury, unless
the steel of which it is composed be very well tempered, from a want
of perfect elasticity, and, consequently, from not returning to its
original place after it has been forcibly compressed. This, however,
must be considered to arise, in a great measure, from imperfection
of workmanship, or of the material employed, or from its having been
subjected to too great a force.
_The Spring Steelyard._
The little instrument known by this name is in very general use, and
is particularly convenient where great accuracy is not necessary, as
a spring which will ascertain weights from one pound to fifty, is
contained in a cylinder only 4 inches long and 3/4 inch diameter.
This instrument is represented at _fig. 198._ It consists of a
tube of iron, of the dimensions just stated, closed at the bottom,
to which is attached an iron hook for supporting the substance to be
weighed; a rod of iron _a b_, four tenths of an inch wide and one
tenth thick, is firmly fixed in the circular plate _c d_, which
slides smoothly in the iron tube.
A strong steel spring is also fastened to this plate, and passed round
the rod _a b_ without touching it, and without coming in contact
with the interior of the cylindrical tube. The tube is closed at the
top by a circular piece of iron through which the piece _a b_
passes.
Upon the face of _a b_ the weight is expressed by divisions,
each of which indicates one pound, and five of such divisions in the
instrument now before us occupy two tenths of an inch. The divisions,
notwithstanding, are of sufficient size to enable them to be subdivided
by the eye.
To use this instrument, the substance to be weighed is suspended by the
hook, the instrument being held by a ring passing through the rod at
the other end. The spring then suffers a compression proportionate to
the weight, and the number of pounds is indicated by the division on
the rod which is cut by the top of the cylindrical tube.
_Salter’s improved Spring Balance._
A very neat form of the instrument last described has been recently
brought before the public by Mr. Salter, under the name of the Improved
Spring Balance. It is represented at _fig. 199._ The spring is
contained in the upper half of a cylinder behind the brass plate
forming the face of the instrument; and the rod is fixed to the lower
extremity of the spring, which is consequently extended, instead of
being compressed, by the application of the weight. The divisions, each
indicating half a pound, are engraved upon the face of the brass plate,
and are pointed out by an index attached to the rod.
_Marriott’s Patent Dial Weighing Machine._
The exterior of this instrument is represented at _fig. 200._, and
the interior at _fig. 201._ A B C is a shallow brass
box, having a solid piece as represented at A, to which the spring
D E F is firmly fixed by a nut at D. The other end of the
spring at F is pinned to the brass piece G H, to the part of which
at G is also fixed the iron racked plate I. A screw L serves as a stop
to keep this rack in its place. The teeth of the rack fit into those
of the pinion M, the axis of which passes through the centre of the
dial-plate, and carries an index which points out the weight. The brass
piece G H is merely a plate where it passes over the spring, and
the tail piece H, to which the weight is suspended, passes through an
opening in the side of the box.
_Of the Dynamometer._
This is an important instrument in mechanics, calculated to measure
the muscular strength exerted by men and animals. It consists
essentially of a spring steelyard, such as that we first described.
This is sometimes employed alone, and sometimes in combination with
various levers, which allow of the spring being made more delicate,
and consequently increase the extent of the divisions indicating the
weight.