MY INVENTION AND IMPROV,
Year: 1813

page_text: TO ALL TO WHOM THESE PRESENTS SHALL COME, I, JOHN
DUNCOMBE, of Woolwich, in the County of Kent, Civil Engineer, send
greeting.
WHEREAS His present Majesty King George the Third, in and by His
Letters Patent under the Great Seal of Great Britain, bearing date at West-
minster, the Twenty-fifth day of November last, for Himself, His heirs and
successors, did give and grant unto me, the said John Duncombe, my exors,
adiñors, and assigns, His special licence, full power, sole priviledge and authority,
that I, the said John Duncombe, my exors, adñiors, and assigns, and every of
them, by myself and themselves, or by my and their deputy or deputies, servants
or agents, or such others as I, the said John Duncombe, my exors, adiñors,
assigns, should at any time agree with, and no others, from time to time and
at all times thereafter, during the term of years therein expressed, should and
lawfully might use, exercise, and vend, within England, Wales, and the Town
of Berwick-upon-Tweed, and also in all His Majesty's Colonies and Plan-
tations abroad, "MY INVENTION AND IMPROVEMENT, AS HEREAFTER DESCRIBED
AND APPLIED TO MATHEMATICAL AND ASTRONIMICAL INSTRUMENTS, IN ORDER TO
RENDER THEM MORE PORTABLE, ACCURATE, EASY, EXPEDITIOUS, AND CERTAIN IN
THEIR APPLICATION TO TOPOGRAPHICAL AND NAUTICAL SURVEYING, AND THE MEN-
SURATION OF CELESTIAL ANGLES ON LAND OR SEA, AND FOR ASCERTAINING THE DIRECT
DISTANCES OF INACCESSIBLE OBJECTS WITHIN A LIMITED EXTENT AT ONE STATION
ONLY, WITHOUT THE USUAL OR ANY OTHER CALCULATION. THESE INVENTIONS AND
IMPROVEMENTS CONSIST IN A NEW INDEX, WHICH ASCERTAINS THE MEASURED QUAN-
TITY OF AN AGLE TO ANY PROPOSED RATIONAL DEGREE OF PRECISION, BY RENDERING
THE DIVISIONS OF THOSE MINUTE PARTS HITHERTO IMPERCEPTABLE TO THE SENCES
TRULY CONSPICUOUS AND DISTINCTLY LEGIBLE BY THE COMMON NAKED EYE; AND AN

page_text: ATTACHED NEW PARALLEL MOVEMENT, BY WHICH THE NATURAL SINE AND COSINE OF
SUCH ANGLE ARE AT THE SAME TIME PRECISELY OBTAINED TO ANY ELIGIBLE RADIUS
WITHOUT TABULAR OR OTHER REFERENCE; AND ALSO A DETACHED NEW PARALLEL
MOVEMENT, FURNISHED WITH TELESCOPIC OR OTHER SIGHTS, BY WHICH THE DIRECT
DISTANCES OF INACCESSIBLE OBJECTS WITHIN A LIMITED EXTENT ARE ACCURATELY
MEASURED AT ONE.STATION WITHOUT TRIGONOMETRICAL OR OTHER CALCULATION; AND
A NEW IMPROVED COMPASS, WHOSE INDEX POINTS DUE NORTH AND SOUTH, AND WHICH
IS CAPABLE OF ADJUSTMENT ACCORDING TO THE KNOWN OR OBSERVED VARIATION OF THE
MAGNETIC NEEDLE;" in which said Letters Patent there is contained a proviso
obliging me, the said John Duncombe, by an instrument in writing under my
hand and seal, particularly to describe and ascertain the nature of my said Inven-
tion, and in what manner the same is to be performed, and to cause the same
to be inrolled in His Majesty's High Court of Chancery within two calendar
months next and immediately after the date of the said recited Letters Patent,
as in and by the same, reference being thereunto had, will more fully appear..
NOW KNOW YE, that in compliance with the said proviso, I, the said
John Duncombe, do hereby describe and ascertain the nature of my said, In-
vention, and in what manner the same is to be performed,, by the Plan or
Drawing hereto annexed, and the following description thereof, (that, is to
say):-
My Invention is an improvement, or improvements made in or added to
mathematical or astronomical instruments, in order to render them more
portable, accurate, easy, expeditious, and certain in their application, to topo-
graphical and nautical surveying, and the mensuration of celestial. angles, on
land or sea, and the direct distances of, inaccessible objects within a limited
extent at one station only. To which is also added an improved compass
whose index points due north and south, and which is capable of adjustment,
according to the known or the observed variation of the magnetic needle. The
table part of the surveying instrument represents the plane of the horizon, and
is adjusted thereto by the usual means, and has it circumference divided into
three hundred and sixty degrees, vide Figure No. 1; but it may consist of
some other number of equal divisions of a different denomination.. Its present
general index is a flat circular plate, four and a quarter inches radius, whose
center turns upon the common center of the instrument, but may be of any
other suitable radius, make, or form, vide Letter G, in Figure Nos. 1, 2, and 4.
A secondary index is also placed upon the same centre, vide m, in Figures 1, 2,
and 4, and is moveable thereon conjointly with the general index, or at pleasure
seperately without it, to a limitted extent, which it is prevented to surpass by a
suitable stop, and which, in the present instance, is one exact degree, but may

page_text: The
be some other extent and denomination, according to change, in existing
circumstances, viz, the change of extent and name of division on that limb of
the instrument. to which the said index refers or belongs. This index having
no greater width-nor thickness than necessary to prevent flexion, may have
its length equal to the radius or diameter of the general index, as occasion
requires. There is also a vernier index, vide n, in Figures Nos. 1, 2, and 4, which
immediately.connects with both the general and secondary indexes, and whose
assumed or given length is divided into two unequal parts, distinguished by an
axis passing perpendicularly or at right angles through it, and upon which it
is permanently and steadily fixed, vide (a), in Figures Nos. 1 and 2.
greater of these parts is the radius of the vernier index and scale, the:less.is
here termed the extended arm of the vernier. This extended arm having the
breadth, diminished in. a small degree at top by a gradual uniform slope from its
bottom of its parellel sides, passes as it were dovetailwise into a nicely fitted
groove in a short slide piece which moves very smoothly and regularly but
rather tightly thereon, vide a, in Figure Nos. 1 and. 2. Through this arm a
rectangular oblong aperture is made exactly along its meridian nearly to its
utmost extremity, and also a circular hole corresponding with the width of the
aperture, is drilled and tapped perpendicularly through the bottom of the slide
piece, which must be sufficiently thick to sustain. firmly the requisite screw pin
to be inserted therein, vide i, in Figures Nos. 1 & 2. This screw pin must be
perfectly straight, truly turned, and long enough to reach from the top of the
extended arm down to the bottom of the secondary index; its head on the under
side must be quite flat, and sufficiently wide. to extend a proper distance beyond
both sides of the aperture. That part of its length which protrudes below the
bottom of the slide piece, and which I term a cog, is of something less diameter
than the part above it, so as just to admit its passage through the hole in the
slide piece without injuring the tap thread therein, and that the screw on. the
upper part may everywhere tightly fit it. N.B. This slide piece and
Screw, pin are purposely intended as an easy and correct adjustment for
the maker, should any little inaccuracy occur in fixing the cog in the extended
arm at its true calculated distance from the permanently fixed axis of the
vernier index, and to remove the difficulty that might otherwise exist. For
example, should this distance be less than just,, the vernier index, during the
seperate movement of the secondary index through its present limitted extent of
one exact degree, will describe a greater angle or arc than is appropriated to the
vernier scale. On the contrary, should this distance be greater than just, the
vernier index during the seperate movement of the secondary index through
the same limitted extent of one exact degree will describe a less angle or are

page_text: than that appropriated to the vernier scale. Therefore in either case slack
the screw pin just to allow the slide piece to be moved further from or nearer
to the permanently fixed axis as the case requires, until by trial the
vernier index and scale are found precisely to agree with the seperate
movement of the secondary index through its constant limitted extent,
then tighten the screw pin and the thing is lastingly done. This slide piecė
may be moved by a small fine threaded screw, where required or judged
more eligible, but as it is not again to be disturbed, unless to renew
some part of the instrument, it was here deemed unnecessary. All the indexes
afore mentioned have such a meridian or middle line drawn or supposed to be
drawn direct throughout the whole of its length, and the center or centers of
each axis or pivot are respectively fixed therein. Each end of the permanently
fixed axis of the vernier has a conical termination; that on its under side passes
through a rectangular oblong transverse aperture in the secondary index, and
rests vertically as a pivot in a sole or counter-sunk center fixed on the meridan
of the general index; the end on the upper side is received by an opposite
center fixed in a cap or bridge united to the same index, so as firmly to confiné
the said axis always in a true perpendicular position and the extended arm of
the vernier index in a parallel position thereto, vide (c) in Figures No. 1 and
2. The afore-described aperture is also necessarily such as allows the seperate
movement of the secondary index across the pamanently fixed axis of the
vernier index to the full of its aforesaid limitted extent of one exact degree.
There is also another rectangular oblong aperture along the meridian of the
secondary index at the opposite end to the former, into which the lowest part
of the screw pin in the side piece on the extended arm of the vernier index
protrudes and connects as a cog, with its fiducial side being held in gentle
uniform contact thereto by a suitable spring on the general and the secondary
index. At the same end of each are two right lines struck from their center;
sce G, and in Figures No. 1 and 4, in the present instance, at the precise
angular extent or distance of one exact degree, viz, thirty minutes on each
side of the meridian, but may be some other extent according to the existing
circumstances before stated. That line on the general index precedes in its
regular motion, and that on the secondary index, which succeeds in the like
motion, are particularly distinguished, the first as indicating the intire degrees
or divisions on the limb of the instrument, and the last as exhibiting by the
vernier index the super parts of a degree or division which the measured
angle is found to contain. During the stationary position of the secondary
index at its fixed point of rest the lines at its ends continue in exact coinci-
dence with those on the general index, and then by the seperate movement of

page_text: the secondary index through its before-described limitted extent (that is until
the distinguished line thereon is in exact coincidence with the distinguished
line on the general index), the vernier index is caused at the same time to pass
through a certain augmented extent proportionate to the parts into which
the said index has been distinguished by its permanently-fixed axis. This
augmented extent, vide r, r, r, r, in Figures No. 1 and 2, is of the same name
or denomination with the limitted extent, and may be divided into other
inferior equal parts as occasion requires or circumstances allows; in the present
instance it is divided into sixty equal parts, representing the minutes of a
degree, and which are here subdivided at every tenth second by the index of the
vernier. When an observation has been taken and the operation finally ended,
the secondary index is then returned invariably to its former fixed point of
rest, by means of a suitable retaining spring, vide (w) in Figure No. 1, on the
general index, previous to the next succeeding observation. The work of this
index is neatly cased with brass, and has a glass over its vernier to prevent
injury from dust in summer, and rain and bad weather in winter. The com--
pound index above described, and which may be of any eligible material or
materials, make, form, or dimensions, is aptly applied to Hadley's quadrant, and
to instruments or machines of every description used for measuring astrono-
mical and other angles at sea or on land, and its theoretical principles put thus
into practice, constitute a part of my Invention or improvement. A vertical
arc, vide Figure No. 2, being the greater segment of a circle, is fixed upon.
the meridian of the general index, sufficiently high for the compass box, set on
the case of the aforesaid described compound index, to stand conveniently
under the middle of its horizontal diameter. Therefore, if (h) represents such
sufficient (allowed) height of. the said circle's center above the top of the.
general index, and R is the top radius of that index, R xh will be the
corresponding radius of such circle or rim of the vertical arc. The semicircular
part of this are represents that portion of the azimuth circle which is above.
the horizon, and is here divided both ways from its vertex or zenith into ninety
degrees, and which in the present instance are, by the nonius of a common
index, whereon the telescope is mounted, subdivided into minutes of a degree,
but may have the compound index before specified applied to it, and the degree
divided into such inferior parts as shall be required and circumstances admit.
In front of this arc, upon a regular platform, vide Figure No. 3, attached to
its. diameter, is fixed a parallel movement, vide F, A, and B, in Figures.
No. 1, 2, 3, and 4, as it were a rule of that description standing edgewise,
and which is everywhere at such an equal horizontal distance from it as allows
sufficient room for the telescope afore mentioned, to pass clearly along the

page_text: space between them. The upper limb of this movement consists of two straight
flat bars, every way similar and equal, about four tenths of an inch broad; and
sufficiently thick to prevent flexion; their length exceeds the inner diameter
of the vertical arc by their common breadth, but the distance between the
center carrying, the radial arm at one end of the bar, and the center carrying
the like arm at the other end of the same bar, is exactly equal to it. The
lower linib, for the sake of illustration,. may be supposed precisely of the
same form and dimensions as the upper, its real existence being dispensed
with, and its relative centers, which support the radial armis, put in' pedestals
fixed on the platform. These arms are, for a distance of about six-tenths of an
inch at each end, equally broad with the bars already described; the interme-
diate distance not being more than half that breadth, and are everywhere of
double their thickness. Their common length is less than the inner radius of
the rim of the vertical are by half the breadth of a single bar, and the distance
between the center at their one end and the like center at their other end is
also less than the same radius by the breadth and half breadth of such bar.
The centers in these arms connect at their one end with the centers in the
pedestals fixed on the platform, and at their other end with the centers in the
bars of the upper limb. The centers in the pedestals and the center of the
vertical arc are precisely of the same height from the platform; the distance of
those in the former from each other being exactly the same with the distance
between those in the bars, is equally divided into two parts, one on each side
the center of the vertical arc. In this central division of the distance between
the pedestals upon the platform is fixed an upright scale piece, vide S, in
Figures Nos. 1, 2, 3, and 4, of equal breadth and thickness with the afore-
mentioned bars, so as its front and the front of the radial arms all stand direct
in the same right line. This piecé passes perpendicularly between the bars of
the upper limb, and turning in a right angle at top connects with the under
edge of the rim at the middle of the vertical arc. The index to the vertical are
is placed behind it, vide I, in Figure No. 4, on the center of the semicircle,
and is joined to its vernier in front at a suitable height above the periphery of
the said arc, vide V, in Figure No. 2. On the top of this index, and. at right
angles to its radius, the telescope is fixed, see Figure No. 2. This index.is
connected to the parallel movement by a steady arm united to its radius at a
height above the center on which it stands, that is, precisely equal to the. radial
extent of the arms of the parallel movement (viz., the distance from the center
at their one end to the like center at their other end), and from thence pro-
duced to the back bar of its upper limb, into whose exact middle it is properly
fitted as a center. A compound nonius is nicely fitted to the scale picce (see

page_text: Figure No. 2 and 4, and which also receives the front bar of the upper limb of
the parallel, and as this nonius moves up and down upon. the scale piece. the said
bar passes at the same time to and fro transversely through the nonius;; an hori-
zontal line being drawn along the exact middle on the face of this bar, vide F,
in Figure No. 2, and in which line its afore-mentioned end centers are made a
second line at a propèr. equidistant space, as drawn below it ().
This space between the equidistant lines contains the smaller divisións of the
scale; that above the horizontal line is appropriated to the larger divisions with
their numerals. .A line is likewise drawn perpendicularly up the middle of
the front of the scale piece, see S, in Figure. No. 2, so as to be in exact coin-
cident position with a line drawn from the center of the index of the vertical
árc to the zero in the vertex of tlie samé arc. A second line on the right of
the former is also drawn, and the saine equidistant space preserved as on the
front bar of the parallell limb: This space, as there, contains the smaller
divisions, and that on the left of the perpendicular line, the larger ones, with
their numerals as before. From the exact middle of the aforesaid bar each way,
and also from a certain point on the scale piece, a distance precisely equal to
the radial extent of the arms between the limbs is here accurately divided into
one hundred equal parts as radius, but which may be one thousand or ten
thousand, &c, proportionate to any other eligible radial extent of the said
arms, and which are subdivided by the compound nonius thereon at every
second ténth, but may be at every tenth, as occasion requires and circum-
stances admits, .the index to the vertical arc being in coincidence with the
zenith line at its vertex. The index of the compound nonius at that time is
also.in. coincidence with zero or. O on the front bar of the parallel limb, and
with that point on the scale piece from which the distance aforesaid is
measured thereon. The divisions on the aforesaid bar are here numbered
froin its center (0) each way to one hundred; those on the scale-piece from O
at bottom to one hundred at top, but may all be extended to any other number
corresponding with radius,.as.before stated. These divisions on the front bar
of the parallel. limb to the right of its middle (0) contain the natural sine of
the. angle of depression, those to its left the natural sine of the angle of 'eleva-
tion, and those on the scale-piece the natural cosine of the agle either of
depression or elevation pointed out by the index or the vertical arc.
For
example, let the index of the vertical arc stand at the angle of thirty degrees
depression, the: compound nonius will then point out fifty parts on the right-
hand end of the parallel limb for the natural sine, and 86.5 parts on the scale-
piece for the natural cosine of that 'angle. From the above sines, by an
accompanying extended scale, the true lengths of their corresponding sides are

page_text: obtained in the terms of the measured hypothenuse by bare inspection. Not-
withstanding the afore-stated proportions and dimensions are very eligible, and
such as have in the present instance been adopted in the construction of the
parellel movement already described, they are by no means to be considered as
universally determinate, but may be varied as circumstances require or the
judgment directs, and the length of the radial arms, &c. be so far extended as
to carry the u
upper limb of the parellel above the vertical arc, and connect with
its index there instead of below; or the movement may be wholly transposed
to the back of the are, and made to take off and put on at pleasure. This part
of the instrument may also be made of any eligible material or materials, and
of any eligible dimensions, and in a detached state be advantageously applied
to the drawing board for correctly and readily laying down maps or charts and
traverses at sea. The theoretical principles of this part, put thus into practice,
constitute another portion of my Invention or improvement. To this instru-
ment is added a new improved compass, vide Figure No. 1, having a brass or
other non-magnetic index fitted to the cap of the magnetic needle, and which
is. capable of being always adjusted, thereto, according to its known or observed.
variation from the meridian, and thereby caused constantly to point due north
and south. This improvement is general to the compass of every description,
and useful in most cases, though a common compass may be annexed to and
used with my improvement. Also a detached new parallel movement, vide
Figure No. 5, on an extended scale, to be used independantly without the
instrument, or in conjunction with it at pleasure, for the purpose of measuring.
the direct distances of inaccessible or other objects within a limitted extent at
one station only, and without any calculation. This movement may be simi-
larly constructed with the one already described, having a telescope or plain
sights fixed upon each of its limbs, the one standing in a lineal direction, vide
(a), with the limb, and the other reclining inwardly from that direction, vide
(b), according to some, assigned permanent angle; or the parallelism of the
movement may be commodiously preserved by placing the angular telescope in
a relative position on a slide nicely fitted in a suitable stock-piece, in manner
of a sliding rule. Under this form the stationary telescope must be fixed at
right angles with the length of the stock-piece, at a convenient distance from
its left-hand end and the other on some proper part of the slide, in a transverse
oblique direction thereto, according to the permanent angle assigned. The
necessary length of the scale to be graduated on the stock-piece is determined
by this proportion, viz., as the tangent of the assigned permanent angle is to
the extreme distance, so is the limitted extent (beyond which this part of the
instrument is not intended to apply), in any appropriate. denomination of

page_text: measure, so is radius to the requisite length of the scale in the same measure.
The extent of the scale being thus found, the length of the stock-piece may be
determined at discretion. If the length of the scale be assumed in any appro-
priate denomination of measure, the permanent angle will be ascertained by
the following propórtion, viz., as the given length of the scale is to radius, so
is the extreme distance, in the same denomination of measure with the scale;
to the tangent of the permanent angle; for example, let the extreme distance
or limited extent be one mile, or one thousand seven hundred and sixty yards;
and the permanent angle comprehending it (that which the oblique télescope
forms with the length of the scale 89° 56', the length of the said scale is
required.
Here tang of the 89° 56'
Scale
rigut, commencing precisely at the axis of
the telescope, is now to be accurately divided into that exact number of
uniform parts (not exceeding one hundred and twenty to an inch) as is equal
to the number of units of the lowest sub-denomination of measure contained in
the limitted extent. N.B.-This sub-denomination is the measure that the
intermediate distances are accounted in on the scale. For the sake of
illustration, let the result of the preceeding example be taken, in which the
Yards.
Feet.
length of the scale, as there found, is 2.04783 × 3 = 6-1435 × 12 =
In.
Divisions.
73 722 x 120 = 8846 64; but as no divisional line can be, a fraction,
we must naturally conclude that 8846 are the greatest number of equal
divisions. Such scale admits of being resolved into by the vernier, to be dis-
tinctly legible by the naked eye, and therefore the number of units of any
chosen sub-denomination of measure contained in the aforesaid limitted extent
must not exceed it. Hence it appears, that inches in this instance cannot be
the chosen sub-denomination of measure, for the present limitted extent of one
mile contains 63360 of them, which are more in number than the equal
divisions (viz., 8846) admitted by this scale. Now, the same limitted extent,
one mile, contains one thousand two hundred and eighty feet, which are less
in number than the afore-mentioned equal divisions admitted by the scale, and

page_text: consequently the sub-denomination to be approved under these or similar cir-
cumstances. The scale may be actually divided,-first, into eight exact equal
parts, representing the furlongs of a mile; secondly, each of these into one
hundred and ten other exact equal parts, as the fathoms in a.furlong; and,
thirdly, each of these last divisions may be most legibly distinguished by the
vernier into six other equal parts, being the feet in a fathom. Hence, any in-
termediate.distance becomes ascertainable to a single foot. Again: or, supposing
the sub-denomination of measure to be links of a Gunter's chain, here one
hundred, links being contained in one chain, and eighty chains in a mile (the
foregoing. limitted extent), we have eight thousand for the number of units of
the sub-denomination contained in the limitted extent; and it being less than
the number of equal divisions admitted by the scale is consequently eligible.
Therefore, under this -circumstance, the scale may actually be divided,―
first, into eighty exact equal parts, representing the chains in one mile;
secondly, each of these parts into ten other exact equal parts, as the number
of marks on a chain-(being one at every tenth link); and, thirdly, each of
these last divisions may be most legibly distinguished by the vernier into ten
other equal parts, being-the-number of links between mark and mark. Hence,
any intermediate distance becomes ascertainable to a single link, and so of
any other limitted: extent and sub-denomination of measure whatever. The
limited extent, and any sub-denomination of measure, being given to find the
length of the scale, &c., reduce the limitted extent into units of the given
sub-denomination; divide the result by one hundred and twenty, and the
quotient will be the length of the scale in inches and decimal parts. N.B.-
This being known, the permanent angle may be found by the rule before
given. To. ascertain the distance of an object by this movement, turn it about
upon its stand until some distinct mark on the object is seen through the
telescope fixed on the end of the stock-piece, and there screw it fast; then
draw.out the slide until precisely the same mark is seen through-that telescope
thereon, and the distance will then be exactly pointed out by the vernier on
the scale. This part may also be made of any eligible material or materials,
and extended or contracted according to any eligible form or dimensions, as
occasion requires or the judgment directs. And all which Inventions and
improvements, are likewise.delineated in the Drawings or Plan thereof hereto
annexed.
In witness whereof, -I, the said., John Duncombe, have hereunto set
my hand and seal, the Nineteenth day of January, in the year One
thousand eight hundred and fourteen.
JOHN DUNCOMBE, C:E. (L.S.)

page_text: AND BE IT REMEMBERED, that on the Nineteenth day of January, in
the year of our Lord 1814, the aforesaid John Duncombe came before our
said Lord the King in His Chancery, and acknowledged the Specification
aforesaid, and all and every thing therein contained and specified, in form above
written. And also the Specification aforesaid was duly stamped according to
the tenor of the Statute made for that purpose.