IMPROVEMENTS IN APPARATUS POR MEASURING OR ASCERTAINING WEIGHTS OR PRESSURE
Year: 1839

page_text: TO ALL TO WHOM THESE PRESENTS SHALL COME, I, JOHN
LOTHIAN, of Edinburgh, in the Kingdom of Scotland, Geographer, send
greeting.
WHEREAS Her present most Excellent Majesty Queen Victoria, by Her
Letters Patent under the Great Seal of Great Britain, bearing date at West-
minster, the Tenth day of October, in the third year of Her reign, did, for
Herself, Her heirs and successors, give and grant unto me, the said John
Lothian, Her especial licence, full power, sole privilege and authority, that I,
the said John Lothian, my exors, adñiors, and assigns, or such others as I, the
said John Lothian, my exors, adiñors, or assigns, should at any time agree
with, and no others, from time to time and at all times during the term of
years therein expressed, should and lawfully might make, use, exercise, and
vend, within England, Wales, and the Town of Berwick-upon-Tweed, my
Invention of "IMPROVEMENTS IN APPARATUS POR MEASURING OR ASCERTAINING
WEIGHTS OR PRESSURE;" in which said Letters Patent is contained a proviso
that I, the said John Lothian, shall cause a particular description of the
nature of my said Invention, and in what manner the same is to be per-
formed, to be inrolled in Her said Majesty's High Court of Chancery within
six calendar months next and immediately after the date of the said in part
recited Letters Patent, as in and by the same, reference being thereunto bad,
will more fully and at large appear.
7

page_text: NOW KNOW YE, that in compliance with the said proviso, I, the said
John Lothian, do hereby declare the nature of my said Invention, and the
manner in which the same is to be performed, are fully described and ascer-
tained in and by the following statement thereof, reference being had to the
Drawings hereunto annexed, and to the figures and letters marked thereon
(that is to say):
My Invention consists, first, in combining against each other spiral or
eccentric wheels situated in different places, but united so as to move simul-
taneously on one axis, or situated in the same plane, and thrown into one
wheel, in which the curves may be made to merge into one another, said
combination giving rise in the progress of the revolution of the wheels to
a continuous power of equilibrium or self-adjustment, and said power of
equilibrium being obtained by causing the weights, strains, or pressure to be
ascertained to exert their effect by a cord or chain acting in a groove on the
circumference of the wheel (or of both wheels when two are used), in which
the leverage decreases as the wheels revolve, while the counterpoise is made in
like manner to operate on the increasing leverage of the remaining wheel, said
changes of leverage continuing and combining their effect until the counter-
poise is placed on terms of mechanical equality or equilibrium with the
weights, strains, or pressure to be ascertained; the movement of the wheels
and their appendages in their progress to equilibrium affording means of
indication by a pointer on a dial or scale suitably situated; and said dial
having once been graduated by causing. a correct set of weights to produce
their respective effects on the machine, the amounts of such other weights,
strains, or pressure as are afterwards applied, and as come within the range
for which particular machines may have been constructed to indicate, become
known on inspection. This opposing combination of spiral or eccentric, wheels,
more particularly exhibited hereafter in its parts, but formed and used in the
manner and for the ultimate purposes here specified, is the subject of my first
claim.
t
The second part of my Invention relates to an improvement on the pen-
dulum balance by combining with the lever rod of the balance an eccentric
grooved wheel for the cord or chain of the scale to act on, said wheel being so
formed as to render the self-adjusting power of the loaded pendulum more
equable, and to distribute its power as an adjusting counterbalance over an
effective movement of a quadrant in extent.
i
My third claim is for a peculiar construction of axis, which may be used or
not as may be wished with the machines above described; said axis being

page_text: intended for the machines to revolve upon, while itself is suspended at each
end a little above its centre on knife-edge rests, and fitted by means of a
tongue attached to it, to shew by the departure of the tongue from a vertical
position when friction on the round part of the axis is interfering to prevent a
correct indication, and thus enabling the experimenter, on his assisting the
adjustment of the machine, to perceive, by the perpendicular position of the
tongue, when the indication of the ordinary pointer of the machine may be
Figure 1 represents two spiral or eccentric wheels united by an intermediate
axle, so as both may move round simultaneously. Each end of the axle termi-
nates in an axis of reduced diameter, and rests in steel bearings inserted in the
two uprights which rise from the bracket here shown. A scale S is attached to
the extremity of the one wheel, and the cord or chain by which it is attached
passes in a groove round the circumference of the wheel, and is fixed towards
the origin of the wheel's curve, near the axis. A counterpoise W is suspended
from the other wheel, and hangs not from the extremity, but from near the
origin of its curve, where the cord or chain which suspends it is fixed; a groove
in the wheel receives the cord when the wheels are moved round, and the
weight of the counterpoise should be made sufficient to preserve the wheels in
equilibrio when in the position shown in the Figure. A dial (omitted in the
Drawing for the sake of distinctness) is screwed to the upright A, aud a
pointer is fixed to the projecting end of the axis. The dial may then be
graduated by planing a succession of correct weights in the scale, and marking
the movement made by the pointer at each additional ounce or pound, &c.,
which is placed in it. The bracket may be fixed either to a stand or against
a wall, observing that its position be such as allows the pointer to stand at
zero when the scale is empty. The machine is then ready for use, and will
indicate the weight of such articles, not exceeding the extent of its range, as
may be placed in the scale. In this form of the machine the counterpoise
may be removed to any required distance from the scale by increasing the
length of the intermediate connecting axle. If a machine capable of weighing
to double the extent be wanted, the weight of the counterpoise and scale may
each be doubled, and the dial graduated in manner foresaid; and if a machine be
wanted to weigh to half the extent, the respective weights of the counterpoise and
scale should be halved, and so on for other ranges greater or less than the one
thus found. Two spiral. or eccentric wheels or scrolls of one size and shape

page_text: may he used for the scale to act on, and may be fixed one on each side of the
counterpoise wheel, both being placed in the same direction with respect to it,
and the whole three united by a common axle, so as to move simultaneously
upon it. Figure 4 represents a front plan of such a machine, and Figure 5
a side plan, partly sectional; the same letters of reference indicating similar
parts of the Figures, and the letters W and S being here used (as they are also
in all the Figures referred to in this Specification, to point out respectively the
cord or chain for the counterpoise (denoted by the letter W), and the cords or
chains for the scale (denoted by the letter S). Here the two wheels for the
scale are used in order to distribute the varying weight of the scale and its
contents equally on each side of the counterpoise wheel, in order that the
machine may preserve a perpendicular position when the wheels are suspended
by their axis in a frame, as shewn in the Drawing.
In the Figures above described the wheels occupy different planes. In
Figure 6, the opposing curves are represented as thrown into one plane, and
forming a single compound wheel, the groove for the scale's cord being made
along the upper half of the wheel, and that for the cord of the counterpoise
being made long the lower half of the wheel. The axis passes through C, and
is supported by a frame in a manner similar to the fulcrum of a common balance,
and the dial, which may be fixed to one of the arms of the frame, may be
graduated as before described. When the weight to be measured is con-.
siderable, it (viz, the weight) may be made to act in part as its own counter-
poise. In Figure 2, B represents the cord for the scale as passing under a
moveable pulley P to a wheel similar to that from which it first proceeds, but
of smaller leverage, and which is fixed to move simultaneously with the others.
To this wheel the remaining end of the cord is fixed at H, and the scale in
this case hangs as shewn from the pulley P. The scale now acts partly
against itself, but not so much as to keep it from descending when pressed
downwards, and therefore turning the wheels. The counterpoise having thus
less to resist may be diminished in weight, and should as formerly be made of
such weight as to keep the wheels in equilibrio when in the position repre-
sented in the Figure, after which a dial may be added and graduated by placing
a succession of known weights in the scale."
Having thus described the combination of spiral or eccentric wheels as
affording a general means of procuring a self-adjusting power without
reference being had to the extent of movement made by the wheels at
each additional ounce or pound, &c., put into the scalé, I shall now describe
the manner in which these opposing wheels are formed of a shape to

page_text: distribute the self-adjusting power arising from their mutual changes of lever-
age in a nearly equal degree throughout their revolution, and thus causing them
to move through nearly equal successive angles on a succession of equal weights
being placed in the scale.
To construct a machine of this kind, I divide a circuit into a number of
equal angles. In Figure 3 there are forty-eight of such angles; let the
weight of the counterpoise be now represented by 160, and that of the scale by
64, and let 14 represent the increase in weight which the scale is to acquire
at each angle, and let 700 represent the length of a constant lever to be suc-
cessively divided in the inverse proportion of the weight of the counterpoise to
the weight of the scale at each successive angle. When the scale is empty
the arithmetical statement of the first question will run thus, 160 + 64-224:
160 700: 500. From a scale of equal parts of which the constant lever
is 700, make Qa equal to 500. The second question arithmetically exhibited
will stand thus, 224+14=238: 160: 700: 470-5, which will be the length
of Q. The next proportion will stand thus, 238+14=252 160: : 700,:
444 4, which will be the length of Qc, and so on throughout the circuit. In
this manner the lengths of each of the radients to be used in the construction
of the scale's wheel are ascertained, and for the sake of distinctness are marked
on the Figure at their respective lengths. The points a, b, c, d, &c., being thus
determined, the lines a A, b B, c C, &c., are each made equal to 700, being the
number representing the whole length of the constant lever. The lines forming
the sides of the equal angles are then crossed by perpendiculars, in the
manner shewn in the Figure at all the points so formed. If curves were now
projected within these perpendiculars, so that the perpendiculars should form
a circuit of tangents to them, these would be the true curves for the wheels, if
the cord or chain to be used has no thickness. When chain is used, the wheels
should, therefore, be reduced by half the thickness of the chain all round; in
other words, the bottom of the groove in which the chain lies should be as
much sunk in the substance of the wheel as is necessary to keep the middle of
the chain in the line of the true curve; when cord is used, the wheels may be.
a little more reduced, particularly near the shorter rdiants. The wheels, with
their cords or chains attached, may now be balanced so as to remain at rest on
their axes in any part of the revolution in which they may be placed. This
balancing may in most cases be effected in the manner represented in Figure 4,
viz, by forming the wheels more solidly towards the shorter than the longer
radiants. When thus balanced, a counterpoise and scale proportioned to each
other in weight, as 160 64, may now be attached to their respective cords,

page_text: and the dial graduated in the manner already described. Returning again to
the calculations, it will be found that on pursuing them through the 48 angles
of the circuit, the first term of the proportion will have accumulated by the
successive additions of 14 to 896, which, if diminished by 224 (being the sum
of the weights of the counterpoise and scale, with which sum the calculations
commenced), there remain 672, as representing the effective range of the
machine. To adjust the weights of the counterpoise and scale so that the
wheels may perform about a revolution on 20 lbs. being placed in the scale,
the question will run thus, as 672: 160: 20 to 4.761 lbs. for the weight
of the counterpoise, and again as 160 64: 4,761 to 1-9044 for the
weight of the scale, and so on for other ranges greater or less than 20 lbs.
which it may be wished the machine should-indicate. Figure 7 represents the
construction of a wheel in which the curves for the counterpoise and scale are
thrown into a single wheel in one plane. The weight of the counterpoise
is here represented by 300, that of the scale by 180, the accumulation at each
of 16 equal angles by 20, the range by 320, and the constant lever by 400;
the lengths of the radiants are found in a manner similar to that already
described; and these, after being laid down in their proportions and lengths, as
shewn in the Figure, a A, B, C, &c., are each made equal to 400, and the
radiants crossed by perpendiculars at their extremities, and the curve
thereafter formed agreeably to the directions already given.
Figure 6 exhibits a wheel in which the counterpoise and scale are pro-
portioned to each other in weight, as 618 382, while its effective range
towards the end of a half revolution amounts to the same as the counterpoise,
and is therefore represented by 618. If the counterpoise be therefore 5 lbs.,
and the scale 3 lbs. 1 oz. 192 grains, the range of weights indicated in the
course of about a half revolution will also be 5 lbs.
Figure 8 shews the construction of a wheel to have a revolution of about
3 quadrants or a little more. Here the weight of the counterpoise is supposed
to be 8, that of the scale 3. The circuit is divided into 16 equal angles, the
additional weight added to the scale at each angle is 17. The radiants
numbered in the Figure as the 9th, 10th, 11th, 12th, and 13th, are respectively
assumed and laid down from a scale of equal parts at the lengths there marked,
viz', 53, 52, 49, 45, and 41. Those opposite to them in the same diameters,
and numbered 1st, 2nd, 3rd, 4th, and 5th, are then calculated by a series of
proportions thus, as 8: 353 to 19.8, for that numbered the 1st; again,
as 83+17=4-7: 52 to 30.5,. for that numbered the 2nd, and so on to
the 5th. The 6th, 7th, and 8th radiants are then assumed to lead gradually

page_text: into the 9th. The lengths are now therefore determined as far as the 13th.
To find the 14th, say, as the weight of the scale and its contents, which at that
point will have accumulated to 11.5: 8:53 (viz, the length of the opposite
radiant numbered the 6th): 36-8 for the 14th; and again, as 11.5+17=13.2:
8: 54: 32-7 for the 15th, and so on to about the 22nd radiant. Beyond
this the calculations need not be carried, as the revolution of the wheel is here
terminated by the cord of the scale coming in contact with the curve for the
counterpoise. The calculated lengths of these levers are now crossed by per-
pendiculars, and the curve formed in the manner before described. The wheel
is cut out as shewn in Figure 9, which brings it nearly to balance. The cord
or chain of the counterpoise is attached at i, and allowed to hang down, and is
left long enough to go round about three-fourths of the wheel. The cord or
chain for the scale is fixed at e, and laid round its groove in the wheel. An
annular dial is fixed to the wheel, and kept at a little distance from it by
screws and bushes at 9, 9, 9, (Figures 9 and 10). The balancing of the wheel
with its cords or chains is now completed by slightly loading the dial at the
light side of the machine. The axis of this machine will be understood by
referring to Figure 10, where the wheel is shewn as resting by sharpened steel
bushes N, N, on a round axis, about which the wheel revolves. On each end
of this axis is screwed a steel collar Q, secured in its place by a pin through
the screws, and having a protruding part above at K, L, which is saddle-shaped;
each end of the axis is thus made, by means of its protruding collar, to spread
over and be supported (a little above the centre of its section) by a steel knife y
edge rest set in each arm of the frame, the letter L in both plans shewing
the apex of the steel rest, in this manner the wheel revolves about a round
axis, which is itself hung upon knife-edge rests. An index K, V, is fixed at
K. to the protruding collar in front of the machine; the movement of the collar
round the apex of the rest is limited by the rectangular openings cut in
the frame of the machine for the protusion of the collars.
The index
attached to the collar is thus permitted to move only to a small extent on each
side of V. V, Z, are two sharpened ends of a pointer set in the front arm of
the frame, the point at Z being intended to indicate on the dial of the machine
as it revolves past it, and the point at V being intended to shew when the
upper index departs from the perpendicular. When it does so it shews that
the friction of the wheel in its self-adjusting movement about the round axis
interferes, and that the wheel has not moved far enough about the 'round
axis, or that it has gone too far and is unable to return; the upper index
will therefore move to the one side or the other of the point V, according

page_text: to which of these two suppositions is the true one for the time being. The
machine liaving thus done all it could do on a round axis towards its self-
adjustment, and the experimenter perceiving from the upper index that
friction is interfering, and perceiving, by the position of the index on the one
side or the other of V, which direction to assist the movement of the wheel in,
he gives the slight assistance which is thus needed until the upper index points
to the apex V. When it does so the machine is in its proper position; and
the point Z giving a right indication. A counterpoise and scale being now
attached to their cords, and proportioned in weight as 8:3; or (as in the
present machine shewn in the Drawing) as 4 pounds to 1½ pounds, the
machine may be graduated as before described, observing during the gradua-
tion that at each additional ounce, pound, &c., put into the scale the upper
index is adjusted to its vertical position before the indication of the lower one
is marked on the dial.
Figure 11 represents a pedulum balance combined with a groove eccentric
wheel for the scale, so projected as to render the self-adjusting power of the
loaded pendulum more equable, and distribute it over an effective movement
of a quadrant (or a little more if wished) in extent. In constructing the
curve, I divide the two opposite quadrants in Figure 12 into four equal angles,
and take one of the radiants at which the centre of the weight is to be placed
equal to 48; perpendiculars are drawn from this point, as shewn in the
Figure, to the sides of the four adjoining angles. These radiants are respec-
tively equal to 18.3, 33.9, 44.3, and 44.3, as marked in the Figure. The
weight being thus supposed to be 26, the scale 24 and the increase at each of
the opposite anglés 23, the lengths of the opposite radiants are found by
proportion as before, viz., 24: 26:: 18.3 to 19-8 for the first radiant of the
scale; then 24+23=47:26:33.9 to 18-7 for the second radiant of the
scale, and so on. These calculated levers are then crossed at their extremities
by perpendiculars, and the curve drawn, and allowance made for the thickness
of the chain or cord, as before. The rod of the pendulum, with its combined
wheel and attached chain, are thén adjusted (by means of a loaded lever behind
the dial when necessary), so as to be nearly balanced. The counterpoise and
scale are then proportioned in weight to each other, as 26 to 24. The coun-
terpoise may be a cylinder or globe, and should have a projection at B equal
to that at C, by which it is screwed into the end of the rod, and should
likewise have its centre W at the distance W, D, from the middle of the
axis. The machine may be supported on its axis in a frame (of which the
front arm is shewn in the Figure), and the scale attached to its chain or cord,

page_text: a pointer having been fixed to the axis, and a dial to the front arm of the
frame, as shewn in the Figure. The graduation may be accomplished by
placing a succession of correct weights in the scale, and marking the place.
of the pointer at each additional weight used for a range of ten pounds: The
weight of the counterpoise should be 2 pounds 13 ounces 94 grains, and that
of the scale 2 pounds 94 ounces 99% grains; or the rod may be lengthened,
and along with its wheel and cord or chain for the scale balanced, so as to
remain inert on the axis of movement, and a counterpoise of half the weight
here named attached to the rod, observing in this case to make the distance
W, D, from the centre of the counterpoise to the centre of the axis twice
the length shewn in the Drawing. In the same manner, if the distance
W, D, be trebled, a counterpoise of a third of the weight will answer, and so
on för a range of 20 pounds, videlicet, double the extent; the counterpoise
and scale should each be doubled in weight, and for a range of half the
extent, each halved in weight, and so on in like manner for other ranges.
The Figure explanatory of the construction of the eccentric curve is on half
the scale on which the machine itself.is presented in the Drawing.
Figure 13 shews one of the single wheels already described supported in
a stand and frame, the counterpoise and scale being proportioned to each
other in weight, as 15 to 9, and its range being 16.
In cases where it is particularly wished that any of the machines already
described should have great exactness in the equality of the movements made
by them on a succession of equal weights being placed in the scale, this
may
be attained by dividing the dial equally between the extremes of the machine's
range, and deepening the groove at parts where on trial the leverage may
prove too powerful until the pointer stands successively at the equal divisions
of the dial on the successive additions of weight being placed in the scale. A
machine where this equal movement is presumed is shewn at Figure 14;
where W is a counterpoise, 82.81 grains weight; S is a ball, here substituted
for the scale, 49.68 grains weight; B is a bollow ball, 2 cubic inches in capa-
city, and of the specific gravity of water. at 62°, and weighing 505 grains.
The weight of 2 cubic inches of spirit at 790 specific gravity being taken at
399 grains, the difference of weight, videlicet, 106 grains, has been here
regarded as a supposed range for the machine, and for this range the weights
of the two smaller balls have been calculated. The extremes of the range of
the machine, before the largest hollow ball is attached, are now marked on
the dial, videlicet, when S is without load and when it is loaded with 106
grains, and the intermediate arc is divided into 210 equal parts, which are

page_text: numbered, as shewn on the dial, from .790 to 1.000. If the large ball be now
attached, as shewn, by a thin wire or hair, and immersed in water, the wheel
and balls will take the position shewn by the colored parts, the figure and
the pointer stand at 1,000, the ball, being less supported by spirit, will con-
tinue to fall in proportion to the relative lighter weight of the fluid in which it
may be immersed, until the wheel and balls take the dotted positions shewn
in the Drawing, in which case the fluid used will be the lightest in relative
weight, for which the machine has here been arranged, videlicet, to shew the
relative weights of fluids between water and spirit of 790 specific gravity. In
the same manner, other extremes of specific gravity may be assumed to obtain
what I have above called a supposed range, and this range then used as the
basis for calculating the weights of the counterpoise and scale balls, which,
when the same wheel is used, should be in the proportions above observed for
a range of 106.
I would remark, that altho' I prefer the dial plates to be equally divided,
and have given the best means of construction of the wheels or opposed
spiral or eccentric surfaces for that purpose, I would have it understood that
the same may be varied, and have the divisions of the dial unequal; and
although I have described the apparatus generally as fitted with scales, it will
be evident that if the cord or chains of the scale's wheel be attached to any
apparatus for producing strains, the result will be indicated on the dial.
What I would be understood to claim is, first, the mode of combining
opposing spiral or eccentric wheels acting in different planes, as described.
Secondly, I claim the mode of combining of spiral or eccentric curves or
surfaces thrown into one wheel, and made to act in the same plane, as above
described.
Thirdly, I claim the combining with the rod of the pendulum or lever balance
an eccentric wheel formed to equalize its indications, and extend its effective
movement to a full quadrant, as described.
Fourthly, I claim the mode of constructing the axis of such weighing
machines, as above described in respect to Figures 9 and 10.
In witness whereof, I, the said John Lothian, have hereunto set my hand
.and seal, this Tenth day of April, in the year of our. Lord One thousand
eight hundred and forty.
JOHN (L.s.) LOTHIAN.

page_text: AND BE IT REMEMBERED, that on the Tenth day of April, in the
year of our Lord 1840, the aforesaid John Lothian came before our said
Lady the Queen in Her Chancery, and acknowledged the Specification afore-
said, and all and every thing therein contained and specified, in form
above written. And also the Specification aforesaid was stamped according
to the tenor of the Statute made for that purpose.
Inrolled the Tenth day of April, in the year of our Lord One thousand
eight hundred and forty.