AN IMPROVED METHOD OF AND INSTRUMENT FOR TAKING AND PLOTTING LEVELS
Year: 1883

page_text: LETTERS PATENT to Frederick Low of 17 King Street, Cheapside, in the city
of London, Solicitor for an Invention of "AN IMPROVED METHOD OF AND
INSTRUMENT FOR TAKING AND PLOTTING LEVELS" communicated to him
from abroad by Alexander Thomas Fraser, Major in the Corps of Royal
Engineers, Madras Presidency in the East Indies
PROVISIONAL SPECIFICATION left by the said Frederick Low at the Office
of the Commissioners of Patents on the 8th February 1883.
FREDERICK LOW of 17, King Street, Cheapside in the city of London, Solicitor
"AN IMPROVED METHOD OF AND INSTRUMENT FOR TAKING AND PLOTTING
LEVELS," [communicated to him from abroad by Alexander Thomas Fraser, Major
in the Corps of Royal Engineers, Madras Presidency in the East Indies]
This invention relates to the construction of a surveying instrument on a
principle that has not hitherto been attempted; in which by means of two equal
perambulator wheels, connected at their centres by a bar, moving a sheet of
drawing paper and an arm carrying a style, a section of ground or of a surface is
repeated on any reasonable scale that may be required from the pole of the
instrument, which is kept vertical by an inertia pendulum. The use of two equal
perambulator wheels, a moving roll of drawing paper, an arm fixed to the
pole of the instrument carrying a style and a special curve to regulate its motion,
with the pole kept in place by an inertia pendulum and a bar to give the tangent
to the surface, is a combination different from any that has hitherto been employed
in levelling operations.
The instrument is based on the mathematical principle of the differential
calculus, that, where is the angle between the radius vector of a curve at the
point whose polar coordinates are r and 4, and the tangent to the curve at that
point; then Cos
that is, that when an arc S is increasing at the rate d 8 in
a given brief space of time, the corresponding rate of increase of the radius vector
is dr = Cos ds.
=
dr
The present invention has for object to apply this principle in a practical

page_text: manner as follows. A surface, say of ground, to be levelled over may bo
considered to form a curve line having a pole situated anywhere in space, from
which radii vectores may be imagined to be drawn so as to describe the curve.
The length of the curve is ascertained from the running of the perambulator
wheel, and it only remains to influence the style of a tracing arm by the
inclination of the tangent, between feasible limits, for the curve of the ground, or
section to be described to scale on a sheet of paper carried by the instrument.
Seeing that the pole of the instrument travels along with the perambulator wheels
in a path always at the same distance from the curvature of the ground and is
sustained vertically, the instrument can be made to trace on paper the curves, to
any particular scales for which it may be constructed, that the surface run over
possesses. For this plane curvature has at any point only two elements; its own
length taken infinitesimally, and the rate of increase of the radius vector given in
position, determined by the angle it makes with the tangent at the point.
A suitable instrument for carrying out the invention is constructed as
follows:-
Two perambulator wheels of any convenient diameter, according to the size of
section required, are taken, similar in make by preference to bicycle wheels, and
their axles are connected by a bar in the journals at the end of which the axles
are free to turn. The bar may be of any suitable length and of any suitable
metal or substance; but the shorter it is the less discrepancy between the actual
curvature of the ground and the section in the instrument. In any case it must be
a minute difference.
It is obvious that when two wheels of exactly the same diameter are connected
by a bar at their centres and rolled along the ground, the bar will be as nearly as
may be in the direction of the tangent to the curvature of the ground at the
moment.
Any convenient distance may be taken for the pole of the instrument to
stand at.
The pole is on the vertical bar which swings freely upon the axle of one of the
wheels and has a heavy mass at top and bottom; such masses are inversely
proportional to the squares of their distances from the point on which the bar
swings. This arrangement is the inertia pendulum, which prevents swaying
motion of the pole, when the instrument is moved along the ground. The radius
vector is an arm of steel or other substance such as vulcanite, turning on a pin at
the polar point. There is a fixed slider on the tangent bar at the forty five degree
point within which the radius vector arm slides freely, so as to alter its position
as the inclination of the tangent bar varies. The arm is so adjusted on a pin at
the pole as to work clear of the inertia pendulum and between the tangent bar and
the wheels.
The radius vector arm is fitted with a slider containing a style or pencil, which
is impelled by an endless wire, or other simple means, and circulates from end
to end of the radius vector backwards or forwards, as the curve of cosines
dictates.
Immediately behind the radius vector arm and below the style or tracing point,
is a sheet of metal or other suitable substance, truly even and fixed to a frame
which again is firmly attached to the tangent bar and moves with it. Over the
sheet or table, a web of paper or similar material wound and unwound from two
cylinders is drawn at a speed proportionate to the rate of the instrument's moving,
by toothed gearing attached to one or both, and connected with the axle, so as to
move at such a rate with reference to the circumference of the perambulator wheel
as the scale requires. The style is arranged so as to touch the paper and mark it
after the manner of a self-registering apparatus.
It is apparent that the motion of the paper on the table will represent the
differential element ds of the curve S of the ground. The angle between the
radius vector and the tangent will vary from forty five degrees to ninety degrees
as the tangent moves into the vertical position and from forty-five degrees to 0°
•

page_text: as it moves perpendicularly downwards. Consequently Cos will vary with the
slope of the ground.
To delineate a section it only remains by suitable mechanism, while the paper
or web on the table is kept moving at the rate of d 8, to move the style along the
radius vector arm at the rate dr that is at the rate of Cos à 8. This is
accomplished by means of a cam of metal, or other substance, which is fastened
to the axle revolving in it and by a connecting piece to the upper inertia mass.
The cam is thus always vertical. It has on one edge a curve of Cosines whose
equation appears to be r = a (1-Cos 45° + The pole of the cam coincides
with that of the instrument; the difference between the distance of the pole from
the axle and the radius vector of the cam, being in the proportion of the Cosine
of the angle throughout.
The tangent bar is bent in the most convenient manner into a support which
carries an axis or pin secured to it only at the inner end. A conical metal or other
wheel slides on this axis and a spiral spring keeps the cone steadily up to the cam.
The height of the cone is the same, or proportional, as the case may be, to the
length of the cam and the diameter from the cone's base to its apex varies according
to the Cosine of the angle . The conical wheel is driven by toothed or other
gearing from the axle by the perambulator wheel at a rate proportional to ds.
There is a revolving disc of suitable diameter on a fixed axis, with sufficient
adhesion to the cone under which the conical wheel slides. The axis of the disc
has play in a vertical direction so as to move up or down as the conical wheel
slides out and in. The disc having a knife edge is turned by the revolving cone
against which it rests and communicates motion by a double Hooke's joint, or
other ordinary expedient, to a spindle at the pole of the instrument which by bevel
gearing turns a drum on which the wire of the radius vector bar is wound carrying
the style round the radius vector arm. The object of this mechanism is to change
the rate of motion ds of the web simultaneously into the rate Cos ds for the
style on the radius vector arm.
8
The driving mechanism is so proportioned that when the front wheel moves
vertically down a precipice the pinion revolving then over the diameter of the
cone's base, the same rate of motion that the paper has, or d s, is communicated to
the tracing point or dr = d s. The rate of motion of the tracing point will
obviously diminish compared with that of the web of paper in proportion to Cos o,
as the tangent bar moves through the entire arc of one hundred and eighty
degrees when the instrument is taken down a precipitous slope on one hill and up
another.
The style will therefore describe on the web a series of curves agreeable to those
of the ground run along by the instrument.
As long as the inclination of the ground remains the same for any appreciable
time, the direction of the radius vector arm does not change; while the tracing
point continues running till it turns round the end of the arm. The angle will be
forty five degrees when the instrument is moving on a level, and what may be
termed its datum line representing the horizon will be diagonal to the web. A
handle with rack and pinion gearing is to be provided, so that the operator may
shift the web and table in a direction at right angles to the tangent bar so as to
get within reach of the style and when the run of the latter is exhausted, the
instrument is stopped by a bell till a fresh adjustment is made of the style and a
new sheet of levelled section commenced. When the survey has been completed
the sheets are cut and pasted together in their correct places

page_text: SPECIFICATION in pursuance of the conditions of the Letters Patent filed by
the said Frederick Low in the Great Seal Patent Office on the 4th August
1883.
FREDERICK LOw of 17 King Street Cheapside in the city of London, Solicitor
"AN IMPROVED METHOD OF AND INSTRUMENT FOR TAKING AND PLOTTING
LEVELS (A communication to me from abroad by Alexander Thomas Fraser,
Major in the corps of Royal Engineers, Madras Presidency in the East Indies)
"
This invention relates to the construction of a surveying instrument on a
principle that has not hitherto been attempted, in which by means of two equal
perambulator wheels connected at their centres by a bar, moving a sheet of
drawing paper and an arm carrying a style, a section of ground or of a surface is
repeated on any convenient scale that may be required from the pole of the
instrument which is kept vertical by an inertia pendulum.
The use of two equal perambulator wheels, a moving roll of drawing paper, an
arm fixed to the pole of the instrument carrying a style and a special curve to
regulate its motion, with the pole kept in place by an inertia pendulum, and a bar
to give the tangent to the surface, is a combination different from any that has
hitherto been employed in levelling operations.
In order to enable the invention communicated to me to be fully understood I
will proceed to describe the same by reference to the accompanying drawing in
which figure 1, is a side elevation and figure 2, an end view of an instrument for
taking and plotting levels constructed according to this invention; figure 3, is a
part plan and figure 4, is a diagram serving to explain the principle of the
invention. Similar letters in figures 1, 2 and 3 are used to represent similar
parts.
The instrument is based on the mathematical principle of the differential
calculus, that where is the angle between the radius vector of a curve at the
point whose polar co-ordinates are r and 0, and the tangent to the curve at that
point; then Cos
that is that when an arc S is increasing at the rate d 8
in a given brief space of time, the corresponding rate of increase of the radius
vector is dr Cos ø d 8.
==
dr
The present invention has for object to apply this principle in a practical manner
as follows. A surface, say of ground, to be levelled over may be considered to
form a curve line A B (see diagram figure 4, on the accompanying drawing)
having a pole O, situated anywhere in space, from which radii vectores may be
imagined to be drawn A, a, b, c d, e and f, so as to describe the curve.
The length
of the curve is ascertained from the running of the perambulator wheel and it only
remains to influence the style of a tracing arm by the inclination of the tangent,
between feasible limits, for the curve of the ground, or section, to be described to
scale on a sheet of paper carried by the instrument. Seeing that the pole of the
instrument travels along with the perambulator wheels in a path always at the
same distance from the curvature of the ground and is sustained vertically
the instrument can be made to trace on paper the curves to any particular scales
for which it may be constructed that the surface run over possesses. For this
plane curvature has at any point only two elements; its own length taken
infinitesimally and the rate of increase of the radius vector given in position,
determined by the angle it makes with the tangent at the point.
A suitable arrangement for carrying out the invention is constructed as
follows:-

page_text: Two perambulator wheels of any convenient diameter, according to the size of
section required E, B, D and B C D in the drawing are taken similar in make by
preference to bicycle wheels and sufficiently rigid and their axles are connected
by a bar OA in the journals at the end of which the axles are free to turn. The
bar may be of any suitable length and of any suitable metal or substance, but the
shorter it is the less discrepancy between the actual curvature of the ground and
the section in the instrument. In any case it must be a minute difference.
It is obvious that when two wheels of exactly the same diameter are connected
by a bar at their centres and rolled along the ground the bar 0 A will be as
nearly as may be in the direction of the tangent to the curvature of the ground at
the moment.
Any convenient distance may be taken for the pole of the instrument to stand
at, the distance O Q being laid off at right angles to the bar OA supposed to be
standing on level ground, and the distance OZ taken along the direction O A
equal to O Q.
The pole is on the vertical bar in the line P R which swings freely upon the
axle of one of the wheels at O. The points P and R are the centres of gravity of
heavy masses P', and R' such masses are inversely proportional to the squares of
their distances OP and OR from O. This arrangement is the inertia pendulum,
which prevents swaying motion of the pole, when the instrument is moved along
the ground.
The radius vector is an arm of steel or other substance such as vulcanite,
turning on a pin at the polar point Q and whose length may be about twice the
distance QO or Q g = say 2 QO. There is a fixed slider on the tangent bar O A
at the forty five degree point Z, within which the radius vector arm slides freely,
so as to alter its position as the inclination of the tangent bar varies. The arm is
so adjusted on a pin at the pole Q as to work clear of the inertia pendulum and
between the tangent bar OA and the wheels.
The radius vector arm is fitted with a slider containing a style or pencil which
is impelled by an endless wire or other simple means and circulates from end to
end of the radius vector Qg, backwards or forwards as the curve of Cosines
dictates.
Immediately behind the radius vector arm and below the style or tracing
point h, is a sheet of metal or other suitable substance, truly even and fixed to a
frame c, d, e, f, which again is firmly attached to the tangent bar OA and moves
with it. Over the sheet or table a web of paper or similar. material wound and
unwound from two cylinders U X V Y, is drawn at a speed proportionate to the
rate of the instrument's moving along the ground by toothed gearing attached to
one or both, and connected with the axle O so as to move at such a rate with
reference to the circumference of the perambulator wheel B E D as the scale
requires. The style h, is arranged so as to touch the paper and mark it after the
manner of a self registering apparatus.
It is apparent that the motion of the paper on the table will represent the
differential element ds of the curve S of the ground. The angle QZO between
the radius vector and the tangent O A, will vary from forty five degrees to ninety
degrees as O A moves into the vertical position, and from forty five degrees to 0°
as OA moves perpendicularly downwards. Consequently Cos will vary with
the slope of the ground.
To delineate a section it only remains while the paper or web on the table is
kept moving (by the arrangement hereinafter described) at the rate of ds to move
the style along the radius vector arm at the rate dr that is at the rate of Cos
ds. This is accomplished by means of a cam of metal or other substance OTQ
which is fastened to the axle O revolving in it and by a connecting piece p, q, to
the inertia mass P'. The cam is thus always vertical. It has on one edge a curve
of Cosines whose equation appears to be r= a (1— Cos 45° + The pole of the
cam coincides with that of the instrument; the difference between the distance

page_text: OZ of the pole from the axle O and the radius vector of the cam, being in the
proportion of the Cosine of the angle throughout.
The mechanism by which one of the cylinders U X may be made to revolve at
an equable rate so that the web of paper may move proportionally to the element
"d8" of the curve of the ground consists of a bevel wheel v on the axle of the
front wheel B D C driving a pinion w. This pinion is at the end of a shaft w, A x,
which is mounted in bearings and on a collar at the axle, so as to be retained in
its position while the axle revolves. The opposite end of the shaft at x, is attached
to a pin which slides in a circular groove situated near and within the rim of the
perambulator wheel E B D so as to be trammelled. To the same pin is fastened
a chord bar y, x, the extremity of which at y, is attached to another trammelled
pin travelling in the same groove. Two slightly inclined rigid supports z, and at x,
receive within bearings at the top of each a shaft having a bevel pinion at either
end. One of these pinions takes its motion from a bevel wheel near x, on the
shaft x A w. The other at the end z, acts on a bevel wheel fixed on the extremity
of the axis of the cylinder U X to be turned. The pitch circles of the bevel
wheels and pinions are to be so proportioned that the same rate of motion (or a
proportional rate if the scale requires it) is given to the web of paper as the pencil
has when is equal to nothing or in other words a proportional rate to "d 8."
It is apparent that the three points OA and x, being fixed relatively the
mechanism which they support will not be dislocated as the curvature of the
ground alters.
The tangent bar OA is bent back into the support Ou, t, L, j, k, l, and carries
an axis or pin G sliding on which there is a conical wheel of polished metal driven
by the same mechanism as that hereinbefore described for driving the cylinder UX
carrying the. web of paper by bevel wheels not shewn in the drawing from the
axle of one of the perambulator wheels at a rate proportional to ds. A spiral
spring G with the ordinary accessories keeps the cone steadily up to the
cam On, T. The height of the cone is the same, or proportional as the case may
be, to the length of the cam OQ or OZ and the diameter from the cone's base to
its apex varies according to the Cosine of the angle ; the diameter H I, being
to OZ as the diameter at the point K which is the point of the cone in the
drawing where the instrument is level to the distance n, Z.
There is a revolving disc of suitable diameter M N on a fixed axis with sufficient
adhesion to the cone, under which the conical wheel slides. The axis of the disc
has play in a vertical direction so as to move up or down as the conical wheel
slides out and in.
The wheel M N which has a knife edge revolves on an axis m, a, and is turned
by the revolving cone HF I the friction being increased if wished by application
of a vulcanized india rubber band (not shewn in the drawing). The wheel MN
communicates motion more or less approximately either by a double Hooke's joint
between a, and b, or preferably (as shewn in the drawing) to a spindle at the
pole Q. The simplest mode of imparting a rate of motion proportional to dr to
the style h, is by a bevel wheel on the axle m, a, of the fixed disc turning a
horizontal bevel wheel which carries a small drum on its axle which is at right
angles to the tangent bar O A. At the centre O there is a pair of loose pulleys
with flanges. A corresponding pair of loose pulleys are fixed by a strut to the
radius vector bar near the pole. The spindle at the pole which turns with the
radius vector bar bears a pulley and an endless wire or fine chain is taken round
the pulleys and crossed in direction at O and the pulleys are so arranged that the
length and motion of the wire are not altered by the movements of either the
radius vector bar or the tangent bar.
.
The driving mechanism is so proportioned that when the wheel B C D moves
vertically down a precipice, the pinion M N revolving then over the diameter H I
of the cone's base, the same rate of motion that the paper has or d 8 is communi-
cated to the tracing point h, or d r = d 8. The rate of motion of the tracing point
will obviously diminish compared with that of the web of paper in proportion

page_text: to Cos, as the tangent bar moves through the entire arc of one hundred and
eighty degrees when the instrument is supposed taken down a precipitous slope on
one hill and up another.
The style h, will therefore describe on the web a series of curves agreeable to
those of the ground run along by the instrument.
As long as the inclination of the ground remains the same for any appreciable
time, the direction of the radius vector arm does not change; while the tracing
point continues running till it turns round the end g, of the arm. The angle at Z,
will be forty five degrees when the instrument is moving on a level and what may
be termed its datum line representing the horizon will be vertical to the web.
A handle H', with rack and pinion gearing not shewn in the drawing is provided
so that the operator may shift the web and table in a direction at right angles to
the tangent bar so as to get within reach of the style and when the run of the
latter is exhausted, the instrument is stopped by a bell till a fresh adjustment is
made of the style, and a new sheet of levelled section commenced. When the
survey has been completed the sheets are cut and pasted together in their correct
places.
Having thus described the nature of the said invention and the manner of per-
forming the same as communicated to me by my foreign correspondent I wish it to
be understood that what is claimed is :-
Firstly. A surveying instrument constructed to measure its own distances and
heights and simultaneously to plot a section of the ground it is run over to n
suitable scale on a web of drawing paper the operation of the instrument being
based upon the ratio which subsists between a curve its tangent angle and its
radius vector as hereinbefore described.
Secondly. The combination of parts forming the improved instrument for taking
and plotting levels arranged and operating substantially as hereinbefore described
and represented in the accompanying drawing.
Thirdly. The two perambulator wheels connected by a bar to give the tangent
direction of the curve of the ground as herein before described.
Fourthly. The inertia pendulum to reduce to a minimum the communication of
motion and to keep the pole vertical as described.
Fifthly. The gearing to impart the same rate of motion the perambulator wheels
have to the web of paper and the differentiating cone as herein before described and
represented in the accompanying drawing.
Sixthly. The endless wire and pulleys to give the corresponding differential
motion to the pencil as described.
Seventhly. The radius vector bar fixed to the pole on the inertia pendulum and
running in a slider attached to the tangent bar, operating by a style upon a sheet
of paper for tracing a curve proportional to the curve of the ground thereon and
thus taking and plotting a section in the manner and by the means substantially
as set forth.
Eighthly. The curve of Cosines held vertical by the pendulum to regulate the
motion of the style as hereinbefore described
Ninthly. The differentiating cone (or its equivalent) and its mechanism, substan-
tially as described and for the purpose set forth
In Witness whereof I the said Frederick Low have hereto set my hand
and seal this third day of August in the year of our Lord one thousand
eight hundred and eighty three
FRED LOW (L.S.)