Improvements in or relating to Mathematical Instruments for Use in Drawing Arcs of Circles.
Year: 1895

page_text: Date of Application, 14th Mar., 1895
Complete Specification Left, 16th Dec., 1895-Accepted, 25th Jan., 1896
PROVISIONAL SPECIFICATION.
Improvements in or relating to Mathematical Instruments for Use
in Drawing Arcs of Circles.
I, THOMAS CLARKSON, of Grove Villa, Carshalton Grove, Sutton, in the
County of Surrey, Engineer, do hereby declare the nature of this invention to be
as follows:-
This invention relates to mathematical instruments for use in drawing arcs of
circles whose diameters are too great to permit the ares to be drawn by ordinary
compasses.
Hitherto a long wire or rod or a trammel has been used as a radius arm in
drawing such arcs, but these devices are unwieldy and cumbrous and frequently
need two operators; moreover the curved lines produced by such means are more
or less wavy or otherwise inaccurate owing to the absence of rigidity from the
apparatus. Another common device consists in bending a thin piece of spring
steel, or wood so that it will approximately correspond with three points previously
determined upon the required curve, the said spring then constituting a ruler for
completing the curve. It is well known however that this device does not give a
true circular arc, for the established reason that a straight spring when bent either
by end pressure, or by pressure applied to the middle whilst the ends are supported
yields more in the centre than towards each end, so that its curve approximates
more to a parabola than to a circle.
The object of my invention is to construct a compact and simple instrument
wherein a novel form of flexible template or flexible ruler and means for enabling
it to be easily given the desired curvature are combined in such a manner that one
operator alone is enabled to draw arcs of great radius with accuracy and facility.
The flexible template or flexible ruler is of resilient material so formed and so
held by holding and operating devices that it can readily be caused to bend and
become an are which will vary in radius with the movement of the adjusting
devices but will always be circular.
According to my invention I construct the flexible template or flexible ruler of
a strip, preferably of metal with one edge plain and the other shaped; this strip
is widest at the centre and tapering off towards the ends. It may be formed as
two right-angled triangles with their bases meeting at the centre of the plate or
joined by a parallel sided strip and the apex of each triangle at or towards
the end of the plate. This would be approximately correct as a theoretical
construction, but as minute differences in temper at different parts of the plate or
in thickness or in quality of the metal or material may affect the result, I find
it desirable to slightly hollow the edge of the plate so that it becomes not a true
triangle; this however would depend very much upon circumstances and the
above illustration will serve to indicate the broad principle of the construction.
As an alternative the template or ruler may be a thin flat strip so tapered or
reduced from the middle of its length towards its ends that successive parallel
measurements of its width taken parallel with the intended axis of curvature
would if plotted perpendicularly to a straight line be ordinates of a symmetric
hyperbolic segment; or instead of a plate reduced in width I may employ a strip
or bar whose cross section is varied in such a manner as to constitute it the
equivalent of such a tapered flat strip.
When the triangulated template is employed I support the ends thereof upon

page_text: a rigid bar or equivalent and curve the plate by forcing its centre out of a straight
line. Various means may be employed for carrying this form of my invention into
effect I will describe two of them.
A convenient means of bending the plate in this manner is to employ a couple
of pins or plungers passing through the before-mentioned bar or beam and
operating the plungers by any convenient lever and screw or equivalent mechanism.
Conveniently the lever may be pivoted to the beam and provided with adjusting
pins or equivalents arranged to engage with two plungers arranged in a plane
perpendicular to the base of the plate, but I may use any desired number of
plungers or equivalent say for example one with a T-head formed as a knife edge
or rounded where it engages with the plate. A screw bolt and thumb nut may be
employed to operate the lever the free end of which I may use as an index
travelling over a graduated scale so as to indicate the curve of the plate when the
lever is in any particular position. To reduce the compass of the instrument when
packed 1 may pivot the scale so that it may be folded up on the beam.
I prefer
to carry the plate in two sockets, one at each end of the beam and to provide stops
so that when the plate is dropped into these it will not fall entirely through;
however, other means may be employed for fixing the plate which if desired may
be permanently secured to or connected with the beam.
In the second arrangement I employ a beam and plate as before, but instead of
pressing the plate from the centre, 1 press it from two points, practically dividing
it into three equal lengths. I may press it in more than two points, but two will
be sufficient to illustrate my meaning. In this case I may adopt any arrangement
of screw and levers for forcing out the plungers or otherwise curving the plate, but
I find a convenient arrangement to be to place a screw at the centre of the beam
and hinge or pivot two levers towards the end of the beam, their free ends coming
substantially together so that one nut upon the screw may operate both levers
simultaneously. The plungers or other forcing devices may be passed through the
beam at the desired parts and operated by the levers as before. One of the levers
may be employed to indicate upon a graduated scale as before described, but I
wish it to be understood that in this and other arrangements I may dispose the
scale and index in any other convenient manner.
The plate in this instance is substantially the same as before, the triangular
construction before observed being adopted, but as the plate is moved from two
points instead of one the base of each triangle would be approximately at the point
where the power is applied, the piece of the plate between these two points being
of substantially the same width throughout.
As regards the principles involved in the shaping of the plates it will le
sufficient for present purposes to say that they are substantially those well
understood in connection with the bending strains of girders, it being remembered
that in this instance the object is not to prevent the plate from bending but to
cause it to bend but always in a true circular arc.
It will be readily appreciated that the form or construction of the beam or
frame-work carrying the plate can be greatly varied and that any suitable materials
may be employed for that or for the plate though hitherto I have found a high
quality of steel for the plate to give excellent results.
As a matter of convenience in constructing these instruments I prefer to make
the plates of fixed lengths commonly useful so that they may serve for purposes
of measurement and to make the flat edge true so that it may be used as a straight
edge and if desired to let the plate bear a scale so that it may be used as a rule,
trammel or for other similar purposes.
As it is desirable to avoid the possibility of undue strain being placed upon the
plate by bending it too much, and also to prevent bending or straining the levers
I prefer to provide a stop for this purpose. A convenient way of effecting this is
to provide that portion of the lever through which the screwed rod passes with a
boss, collar extension or equivalent so arranged that at the extreme limit allowed
in the bending of the plate it comes in contact with the beam and thus stops further

page_text: movement. The same result would be obtained if this arrangement were reversed
and the projection or equivalent provided upon the beam; other stop devices
however may be employed.
Where a strip or template with one edge hyperbolic is employed, I curve the
template by applying pressure to its ends which are specially shaped for a purpose
hereinafter stated. To hold the template and bend it I employ compressors
pivoted to each other and provided with jaws to engage with the ends of the
resilient template; to facilitate this engagement the ends of the plate are squared
and made of sufficient width to prevent it from tilting in the jaws which are of
V form so as to put no undue restraint upon the bending of the plate into arcs,
a screwed rod which has a milled nut thereon is operatively connected with both
the compressors in such manner that when the nut is rotated by means of its milled
head the compressors will move about their pivot relatively to each other so as to
bend the plate into a circular arc or conversely to permit it to partly or wholly
unbend. The operative connection of the screwed rod with the compressors is
effected at one end by a head having a V-face or knife edge, which rests in a
correspondingly shaped recess in one compressor. A spherical collar formed on
the nut bears against a correspondingly shaped seating on the other compressor.
The screw upon the rod is preferably of limited length so that only a limited
endwise movement of the nut on the rod is possible this arrangement is designed
in order to prevent over-compression of the template. The instrument comprises
a scale marked along one compressor. An index lever is pivotted to the other
compressor and coupled to a link which is pivotted to the compressor carrying the
scale. The length of the link and of the arms of the index lever and the distances
between the several connections are so chosen and the parts so disposed that when
the compressors are opened out to allow the plate to be flat the link and one arm
of the index lever are nearly in line with each other. The result of this arrange-
ment is that the ratio of the angular movement of the index lever scale to equal
increments of the angle between the compressors increases rapidly as the compressors
open out from one another into their extreme positions consequently it is possible
for the small angular movement of the compressors near these extreme positions
effecting great variations of the radius of the plate to be measured by wider spaced
graduations on the scale, and this is very greatly conducive to case and accuracy
in the use of the instrument.
Or I may employ a screwed adjusting-rod connected by pivoted nuts to each
compressor, and pivot to one compressor an index arc operated by the other.
In another modification in which the template with curved edge is employed the
ends of that template are provided with collars and the instrument has a base
part of which is segmental. Upon this base is pivoted a lever the end of one arm
of which travels along the edge of the segmental portion of the base and engages
therewith by means of a pawl. The exact adjustment of the lever is provided for
by means of a vernier and micrometer device carried on one arm thereof and a
scale graduated on the segment. The other arm and an extension of the base
carry pins which engage with the collars on the template so that by adjusting the
lever the template is bent into a circular arc of the desired curvature.
In a further modification of the instrument in which the curved-edge template
is used the compressors are blocks one of which is fixed at one end of a tube. The
other compressor block slides upon the opposite end of the tube and part of it
enters the interior thereof through a slot provided in the wall of the tube; a screw
with a milled head is screwed through the end of the tube which is plugged and
internally threaded to receive it, and it engages with the sliding compressor block
which it moves along the tube to compress, as required, the resilient plate. A semi-
circular scale graduated on one edge is attached to the tube and an index lever
is pivoted to the scale and connected by a link to the movable compressor. The
connections of the index lever and the link with the movable compressor are so
arranged that when the compressors are moved apart from each other to allow the
template to become flat the link and the shorter arm of the index lever are more

page_text: nearly in line than when the compressors are moved to buckle the plate; this
arrangement is to enable clear readings of the values of the arcs of larger radii to
be obtained on the scale and is similar to the devices for a like purpose previously
described.
To prevent back-lash which might produce error in the indications of the several
sorts of indicating-apparatus I provide springs to connect the ends of the links
with the compressors and the scale or index in such a manner as to take up the
slack in the connections.
As an alternative to the indicating-mechanism hereinbefore described I may
attach a suitable scale to one compressor so that it will move past an index on the
other compressor.
The indicating-apparatus in these improved instruments is calibrated by
comparison with standard curves and graduated accordingly, preferably to
indicate the radii of the arcs assumed by the template.
The indicating mechanism may be dispensed with if the instrument is to be used
for the production of circular ares and it is not desired to know their radius.
The instruments are made so as to lie flat and steady on a level surface such as
that of a drawing.
To ensure the obtainment of an accurate template or ruler I put it in compression
with its straight edge downward so that its curvature corresponds approximately
with a circular arc of convenient radius which has been carefully drawn upon a
sheet of paper. If the plate does not exactly correspond with the drawn arc those
parts of the plate where the curvature is too flat are narrowed by removing part
of the metal from the angular or curved edge for example until the plate exactly
corresponds with the drawn arc at all points excepting only for the short distance
at each end where the small portions of the plate are allowed to remain outside
the angular or curved edge to be engaged by the compressors as before stated, but
this may be compensated for by removing a small portion of the metal at the
adjacent part of the plate. I have found by trial that a plate made and operated
in the manner described will always spring into a circular are whether the bending
be much or little, that is to say if a plate is made so as to bend exactly to a twelve
inch circle, it can be also made to exactly correspond with any circular arc of say
larger radius by simply allowing its. extremities to move apart or its centre to
approach the chord of the arc.
An alternative construction embodying the triangulated plate is one in which the
two ends of the plate are pivotted to arms the opposite ends of which are carried by
a sleeve, which latter encircles a screwed rod.
By adjusting the rod in the sleeve the centre of the template is thrust in or out,
the ends being held by the pivots and arms before referred to. To ensure the
maintenance of the rod centrally between the two arms those arms are connected
by links to another sleeve free to slide on the rod.
Dated this 14th day of March 1895.
BOULT & & WADE,
Agents for the Applicant.
Improvements in or relating to Mathematical Instruments for Use
in Drawing Arcs of Circles.
I, THOMAS CLARKSON, of Grove Villa, Carshalton Grove, Sutton, in the County
of Surrey, Engineer do hereby declare the nature of this invention and in what
manner the same is to be performed to be particularly described and ascertained
in and by the following statement :-
This invention relates to mathematical instruments for use in drawing arcs of

page_text: circles whose diameters are too great to permit the arcs to be drawn by ordinary
compasses.
Hitherto a long wire or rod, or a trammel, has been used as a radius arm in
drawing such arcs, but these devices are unwieldy and cumbrous and frequently
need two operators; moreover the curved lines produced by such means are more
or less wavy or otherwise inaccurate owing to the absence of rigidity from the
apparatus. Another common device consists in bending a thin piece of spring
steel or wood, so that it will approximately correspond with three points previously
determined upon the required curve, the said spring then constituting a ruler for
completing the curve. It is well known however that this device does not give a
true circular arc, for the established reason that a straight spring when bent either
by end pressure, or by pressure applied to the middle whilst the ends are supported,
yields more in the centre than towards each end, so that its curve approximates
more to a parabola thau to a circle.
The object of my invention is to construct a compact and simple instrument
wherein a novel form of flexible ruler and means for enabling it to be easily given
the desired curvature are combined in such a manner that one operator alone is
enabled to draw arcs of great radius with accuracy and facility.
The flexible ruler is of resilient material, so formed, and so held by bending and
retaining devices, that it can readily be caused to bend into an arc which will
vary in radius with the movement of the adjusting devices but will always be
circular.
According to my invention I construct the flexible ruler of a strip, preferably of
metal, with one edge plain and the other shaped; this strip is widest at the centre
and tapering off towards the ends. It may be formed as two right-angled triangles
with their bases meeting at the centre of the plate or joined by a parallel-sided
strip, and with the apex of each triangle at or towards the end of the plate. This
would be approximately correct as a theoretical construction, but as minute
differences in temper at different parts of the plate or in thickness or in quality of
the metal or material may affect the result, I find it desirable to slightly hollow
the edge of the plate so that it differs a little from the true theoretical form; this
however would depend very much upon circumstances and the above illustration
will serve to indicate the broad principle of the construction.
As an alternative the flexible ruler may be a thin flat strip so tapered or reduced
from the middle of its length towards its ends that successive parallel measurements
of its width, taken parallel with the intended axis of curvature would if plotted
perpendicularly to a straight line be ordinates of a symmetric hyperbolic segment;
or instead of a plate reduced in width I may employ a strip or bar whose cross
section is varied in such a manner as to constitute it the equivalent of such a
tapered flat strip.
When the triangulated ruler is employed I support the ends thereof upon a rigid
bar or equivalent and curve the plate by forcing its centre out of a straight line;
or equivalently I adopt mechanism whereby I am enabled to hold the centre still
and bend the ends out of a straight line.
Where a strip or template with one edge hyperbolic is employed, I curve the
template by applying pressure to its ends which are specially shaped for a purpose
hereinafter stated.
As regards the principles involved in the shaping of the plates it will be sufficient
for present purposes to say that they are substantially those well understood in
connection with the bending strains of girders, it being remembered that in this
instance the object is not to prevent the plate from bending but to cause it to bend
always in a true circular arc.
It will be readily appreciated that the form or construction of the retaining and
bending devices carrying the plate can be greatly varied and that any suitable
materials may be employed for them or for the plate though hitherto I have found
that for the plate a high quality of steel gives excellent results.
As a matter of convenience in constructing these instruments I prefer to make

page_text: the plates of fixed lengths commonly useful so that they may serve for purposes of
measurement, and to make the flat edge true so that it may be used as a straight
-edge, and if desired, to let the plate bear a scale so that it may be used as a rule,
trammel or for other similar purposes.
In the accompanying drawings
Figures 1 to 7 illustrate constructions of my instrument wherein the triangulated
form of flexible ruler is employed, and
Figures 8 to 15 illustrate constructions wherein a flexible ruler having one edge
straight and the other edge hyperbolic is used. In these drawings
Figure 1 is a plan,
Figure 2 a front elevation and
Figure 3 a rear elevation of one construction of instrument according to my
invention;
Figure 4 is a plan and
Figure 5 a rear elevation of another construction.
Several further alternative constructions are illustrated in succeeding figures,
one construction in
Figures 6 and 7 which are plan and front elevation respectively, another in
Figures 8 and 9 which are rear elevation and plan respectively, another in
Figures 10 and 11 which are respectively plan and front elevation, another in
Figures 12 and 13 which are respectively plan and transverse section (the latter
on the line 13, 13, of Figure 12), and another in
Figures 14 and 15 which are respectively plan and rear elevation.
Like letters indicate like parts throughout the drawings.
With reference first to Figures 1, 2 and 3, A. is the resilient triangulated ruler
that is to say it has one edge A¹ straight and the opposite edge A2 tapered off
towards the ends as shown. The form of this triangulated ruler is indicated
clearly in Figure 2 in which it is seen quite flat. B is a rigid bar provided at each
end with jaws B₁ B2 which engage with the ends of the resilient ruler A ; to
facilitate this engagement the ends A³ of the ruler are squared and made wide
enough to prevent the ruler from tilting in the jaws which are sufficiently open to
put no undue restraint upon the bending of the ruler into arcs.
D is a skeleton arm pivotted at B3 to lugs on the bar B. Two plungers E pass
through the bar B and engage at one end with the flexible ruler A and at their
opposite ends with a pair of pins D₁ in the arm D; the pins D¹ are screw-threaded
to facilitate the setting or preliminary adjustment of the plungers relatively to the
ruler A and to the arm D.
F is a screw-bolt. F¹ is a milled nut thereon, engaging with a hemispherical
bearing D2 on the arm D, and F is a knife-edged head engaging with a corre-
spondingly shaped recess B4 in the bar B.
The nut F is used to operate the arm D, the free end G of which is used as an
index with reference to a graduated scale H hinged at B5 to the bar B. By
moving the arm D the plungers E are operated to bend the flexible ruler, and
simultaneously the index G indicates upon the scale H the curvature of the ruler A
corresponding to the position into which the arm D is adjusted. In Figure 1,
-chain lines indicate the position taken up by the several parts when the ruler A is
bent. In this and allied constructions of my apparatus I may use any desired
number of plungers or their equivalent, say for example one with a T-head formed
as a knife-edge or rounded where it engages with the ruler. To reduce for
packing, the compass of the instrument, the scale H may be folded into the
position indicated by dotted lines in Figure 1.
I prefer to provide stops B6 in the jaws B1 B2 to prevent the ruler A when
dropped into the jaws from passing entirely through them, but one or both ends of
the ruler A may if desired be permanently secured to or connected with the bar B.
The ruler A in all the apparatus herein described automatically unbends itself
when the action of the bending or compressing device is reversed.
In the alternative construction illustrated in Figures 4 and 5 I employ a ruler A

page_text: and bar 1 as before, but instead of pressing the ruter A from the centre,
press
from two points A practically dividing it into three equal lengths. I may press it.
at more than two points, but two will be sufficient to illustrate my meaning. la.
this case I may adopt any arrangement of screw and levers for forcing out the
plungers E or otherwise curving the plate, by pressure applied at points inter--
mediate between the ends of the ruler, but I find a convenient arrangement to be
to fix the screw F in the centre of the beam and hinge two levers D towards the
ends of the beam by hinges at B³, their free ends coming substantially together so
that one nut F¹ upon the screw F may bear upon both the levers as shown, so as to
be able to operate them simultaneously. The plungers E are passed through the
beam at the desired parts and operated by the levers as before. One of the
levers D may if desired be employed to indicate upon a graduated scale as before.
described, but I wish it to be understood that in this and other arrangements I may
dispose the scale and index in some other convenient manner.
The ruler A in this instance is substantially the same as in Figures 1, 2 and 3,
the triangular construction before observed being adopted, but as the ruler is.
moved from two points instead of one the base of each triangle would be
approximately at the points A* where the power is applied the portion of the ruler-
between these two points being of substantially the same width throughout, as
at A³ Figure 5.
Chain lines in Figure 4 show the ruler A bent and the levers and nut in.
corresponding positions.
As it is desirable to avoid the possibility of undue stress being placed upon the
ruler by bending it too much, and also to prevent bending or stressing the bending-
devices I may if necessary provide a stop for this purpose. A convenient way of
effecting this is to provide that portion of the bending-device through which the
adjusting-screw passes with a boss or a collar extension or equivalent so arranged
that at the extreme limit allowed in the bending of the ruler A it comes in contact.
with a stationary part of the instrument and thus stops further movement. The
same result would be obtained if this arrangement were reversed and the projection
or equivalent provided upon the said stationary part; other stop devices however
may be employed in any of the instruments herein described.
The alternative construction illustrated in Figs. 6 and 7 and embodying the
triangulated ruler is one in which the two ends A³ of the ruler are pivotted by
lugs A fixed thereon, to arms T, the opposite ends of which are pivotted to a
nut T which latter engages with and can travel upon a screwed rod J to which is.
fixed a milled head J.
By adjusting the rod J in the nut T' the centre of the ruler A is thrust into or
out by that rod so that the ruler is bent into a circular arc its ends being held by
the lugs A and arms T before referred to. To ensure the maintenance of the
rod J centrally between the two arms T, those arms are connected by links T' to a
sleeve K free to slide on the rod.
In the instrument illustrated in Figs. 8 and 9 I employ to hold the ruler A and
bend it, compressors LL' pivotted to each other at L' and provided with jaws B¹ B
to engage with the ends A³ of the ruler A; these jaws are of V form so as to put
no undue restraint upon the bending of the ruler A into arcs; a screwed rod M
which has a milled head M' thereon is connected with both the compressors L L'
in such manner that when the screwed rod M is rotated by means of its milled
head M¹ the compressors L L will move about their pivot L' relatively to each
other so as to bend the plate in the manner indicated in Fig. 9 by chain lines or
conversely to permit it to partly or wholly unbend. The connection of the
screwed rod M with the compressors L L' is effected by sleeves N N¹ both of
which are pivotted to the compressors. Collars O fixed on the rod M bear against
the sleeve N so that the rod can rotate in the latter but cannot move end wise in
it; the sleeve N¹ is screw-threaded internally to engage with a threaded portion of
the rod M. H is a segmental scale graduated along its arc H'; it is pivotted
at L to the compressor L' and coupled at L' to a link P which at L is pivotted

page_text: to the compressor L. L' is an index on the compressor L₁; this index is
employed with reference to the graduations of the arc H to indicate the radius
or other dimension of the circular arc into which the ruler A is bent.
The length of the link P, the distances between the points L³ and L L³
and L are so chosen and the parts H and P so disposed relatively to each
other that when the compressors L L' are opened out to allow the ruler A to
be flat as in Figure 8 the link P and the points L³, L and L' are nearly in
line with each other. The result of this arrangement is that the ratio of the
angular movement of the segmental scale H to equal increments of the angle
between the compressors L L decreases rapidly as the compressors approach each
other, and conversely increases rapidly as the compressors open out from one
another into the extreme position indicated in full lines in Figure 9; consequently
it is possible for a small angular movement of the compressors near this extreme
position (effecting great variations of the radius of the arc of the ruler A) to
be measured by graduations on the scale H which are not necessarily cramped
as they would have to be if variations in the curvature of the ruler had to
be indicated directly by the angular movement of one compressor relatively to
the other.
The instrument shown in Figures 10 and 11 is similar to that which is shown in
Figures 8 and 9 except that the adjusting screw M by which the compressors can
be drawn together has on one end a milled nut N¹ with a hemispherical end
adapted to seat itself in a hemispherical seat on one compressor L' and has also
a knife-edged nut N on the other end engaging with a correspondingly-shaped
recess L in the other compressor. The screw-thread upon the rod M is of
a limited length so that only a limited end-wise movement of the nut N is
possible; this arrangement is designed in order to prevent over-compression of
the ruler A.
The indicating mechanism is slightly different from that shown in Figure 9,
the scale H being marked along the compressor L and the index lever G being
pivotted to the compressor L' and coupled to a link P which is pivotted to and
operated by the compressor L in the movement of the two compressors relatively
to each other.
Chain lines in Figure 10 show the compressors brought towards each other, the
ruler A bent and the indicating mechanism in a corresponding position.
In the modification illustrated by Figures 12 and 13 the compressors LL
instead of being hinged arms are blocks one (L) of which is fixed at one end of a
hollow beam or tube Q. The other compressor block L' slides upon the opposite
end of the tube and part of it enters the interior thereof through a slot Q
provided in the wall of the tube; J is a screw with a milled bead J'; it is
screwed through the end Q3 of the tube which is plugged and internally threaded to
receive it, and it engages with the compressor block L' which it moves along the
tube to compress as required the ruler A. H is a semicircular scale graduated on
one edge as shown at H. G is an index lever pivotted at H2 to the scale H and
connected by a link P to the movable compressor L'. The connections of the
index lever Ġ and the link P with the movable compressor L' of Figures 12 and 13
are so arranged that when the compressors L and L' therein shown are moved
apart from each other to allow the ruler A to become flat, the link P and the
shorter arm of the index lever G are more nearly in line than when the com-
pressors are moved to buckle the ruler A; this arrangement is to enable clear
readings of the values of the arcs of larger radii to be obtained on the scale and
is similar to the devices for a like purpose herein before described with reference
to Figures 8 and 9. In Figure 12 the ruler A is shown fully extended in chain
lines, with the compressors and indicating mechanism in corresponding positions.
In the instrument shown in Figure 14 and 15 the ends of the ruler A are
provided with small cylindrical sleeves A which have saw-cuts along one side into
which the ends of the ruler are passed.
This instrument has a flat base L which may be regarded as a stationary

page_text: compressor; one edge of this base is segmental. Upon the base is pirotted at L
a lever constituted by the two arms L' and G; the arm L' forms a movable
compressor and the outer end of the arm G travels along the edge of the
segmental portion H of the base and may be moved to bend the ruler A as shown
by chain lines; it is made to engage with the ratchet teeth H³ of the base by
means of a spring detent or thumb lever G¹ pivotted to an intermediary lever G
which in turn is pivotted on the arm G. The exact adjustment of the arm G is
provided for by means of a vernier G³ and micrometer screw G₁ which latter is
carried in the end of the arm G and adapted to act through the intermediary
lever G2 upon the detent G¹ in a manner which may be well understood by
reference to the drawings.
The other arm L' and the part L of the base carry pins L7 which enter and
engage with the sleeves A so that by adjusting the lever L' G the ruler A is
bent into a circular arc, the curvature of which is indicated by a scale H¹ marked
in contiguity to the teeth H³.
To prevent back-lash which might produce error in the indications of certain of
the indicating-apparatus herein before described I provide springs R to connect the
ends of the links P with the compressors and the scale or index, in such a manner
as to take up the slack in the connections.
As an alternative to the indicating-mechanism hereinbefore described I may
attach a suitable scale to one compressor so that it will move past an index on the
other compressor.
The indicating apparatus in these improved instruments is calibrated by com-
parison with standard curves and graduated accordingly, preferably to indicate the
radii of the arcs assumed by the template.
The indicating mechanism may be dispensed with if the instrument is to be
used for the production of circular arcs and it is not desired to know their
radius.
The instruments are made so as to lie flat and steady on a level surface such as
that of a drawing.
To ensure the obtainment of an accurate template or ruler I put it in com-
pression with its straight edge downwards so that its curvature corresponds
approximately with a circular are of convenient radius which has been carefully
drawn upon a sheet of paper. If the plate does not exactly correspond with the
drawn are those parts of the plate where the curvature is too flat are narrowed by
removing part of the metal from the angular or curved edge for example until the
plate exactly corresponds with the drawn are at all points, excepting only for the
short distance at each end where, the small portions of the plate are allowed to
remain outside the angular or curved edge to be engaged by the compressors as
before stated, but this may be compensated for by removing a small portion of the
metal at the adjacent part of the plate. I have found by trial that a plate made
and operated in the manner described will always spring into a circular arc
whether the bending be much or little, that is to say, if a plate is made so as to
bend exactly to a twelve inch circle, it can be also made to exactly correspond
with any circular are of say larger radius by simply allowing its extremities to
move apart or its centre to approach the chord of the arc.
Having now particularly described and ascertained the nature of the said inven-
tion and in what manner the same is to be performed I declare that what I
claim is;-
1. A resilient ruler reduced in width or varied in cross-sectional area in a
hyperbolic curve from the middle of its length towards each end substantially as
and for the purpose described.
2. A resilient ruler of triangulated or of hyperbolic outline substantially as and
for the purpose described.
3. In an instrument for use in drawing arcs of circles the combination with a
resilient ruler which is reduced in width or varied in cross-sectional area from
B

page_text: the middle of its length towards each end, of retaining and bending devices
substantially as described.
4. In an instrument for use in drawing arcs of circles the combination with a
resilient ruler which is reduced in width or varied in cross-sectional area from
the middle of its length towards each end, of retaining bending and indicating
mechanism, substantially as and for the purpose described.
5. In an instrument for use in drawing arcs of circles the combination with a
resilient ruler such as A (Fig. 2) of a beam such as B having retaining devices
such as B1 B2 and a bending device such as the plungers E arranged to act on the
middle portion of the ruler substantially as and for the purpose described.
6. In an instrument for use in drawing arcs of circles the combination with a
resilient ruler such as A (Fig. 5) of a beam such as B having retaining devices
such as B1 B2 and bending devices such as the plungers E arranged to act on
the ruler at different points such as A substantially as and for the purpose
described.
7. In an instrument for use in drawing arcs of circles the combination with a
resilient ruler such as A (Fig. 7) of a rod such as J, nut such as T' adjustable
thereon, and means such as arms T whereby the ends of the ruler are linked to
the nut substantially as and for the purpose described.
8. In an instrument for use in drawing arcs of circles the combination with a
resilient ruler such as A (Figs. 8 and 15) of pivotted compressors such as L L'iu
operative connection with each other and with the ends of the ruler substantially
as and for the purpose described.
9. In an instrument for use in drawing arcs of circles the combination with a
resilient ruler such as A (Figs. 8 and 13) of a beam such as Q (Figs. 12 and 13)
and retaining and bending devices such as B' B2 so arranged that the distance
between them is variable substantially as and for the purpose described.
10. In an instrument for use in drawing arcs of circles such as is herein before
described, indicating mechanism so constructed and arranged that the ratio of its
movement to that of the compressors to which it is coupled, varies, substantially
as and for the purpose described.
11. In an instrument for use in drawing arcs of circles the combination with
indicating-mechanism of the kind claimed in the last preceding claiming-clause, of
springs to prevent "back-lash" substantially as described.
12. The combination and arrangement of parts constituting a complete instru-
ment for use in drawing arcs of circles substantially as described and illustrated in
Figs. 12 and 3 or Figs. 4 and 5 or Figs. 6 and 7 or Figs. 8 and 9 or Figs. 10
and 11 or Figs. 12 and 13 or Figs. 14 and 15 of the accompanying drawings.
Dated this 14th day of December 1895.
THOMAS CLARKSON.
Boult & Wade,
Agents for the Applicant.