SPECIAL COLLECTIONS RESEARCH CENTER

A Treatise on Engineering Field-Work by Peter Bruff. 1838

[Front Free Fly Leaf]

[Half Title]

A TREATISE
ON
ENGINEERING FIELD-WORK.

[Title Page]

A TREATISE
ON
ENGINEERING FIELD-WORK:
CONTAINING
PRACTICAL LAND SURVEYING FOR
RAILWAYS, &c.
WITH THE THEORY, PRINCIPLES, AND
PRACTICE OF LEVELLING,
AND THEIR
APPLICATION TO THE PURPOSES OF CIVIL ENGINEERING.
ALSO
PARISH AND SUBTERRANEAN SURVEYING,
WITH SECTIO-PLANOGRAPHY,
AND
EVERY INFORMATION NECESSARY TO BE KNOWN IN THE
ELEMENTARY PARTS OF CIVIL ENGINEERING;
WITH DESCRIPTIONS OF THE BEST INSTRUMENTS EMPLOYED IN SURVEYING AND
LEVELLING, THEIR ADJUSTMENTS AND METHODS OF USING IN THE FIELD.
Illustrated by numerous Plates and Diagrams.
BY
PETER BRUFF,
SURVEYOR. &c. LONDON:
SIMPKIN, MARSHALL, & CO., STATIONERS' HALL COURT
SOLD BY
HEBERT, CHEAPSIDE; TAYLOR, WELLINGTON STREET, STRAND; WEALE HIGH
HOLBORN; AND WILLIAMS, GREAT RUSSELL STREET, BLOOMSBURY
1838.

---

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[Preface]

PREFACE

THE idea of writing this Treatise suggested itself
to me a considerable time since, from knowing
the repeated inquiries that had been made for such
a book; and after perusing, I believe, every work
that has been published on the subject, I was fully
convinced of the necessity of such a work, adapted
to the present improved practice. Of the works
on Surveying, I may say, they are all elementary,
and of ante-date, no treatise, that I am aware of,
having been published since the fine mathematical
instruments at present in use have been considered
a necessary adjunct to the successful prosecution of
land surveying. Of the treatises published on
levelling, there is only one of recent date, by Mr.
Sims, that can be referred to, and I consider that
does not supply the wants of persons seeking in-
formation on the subject.

The few rules and suggestions that I have
thrown in at the end of the volume, I hope will be
found of service.

[page vi]

Many facts and suggestions that I wished to
embody in these pages, I have been compelled to
omit, from not having time to put them in an
intelligible shape. I have transcribed but little
from other works, although, where the subjects
are the same, there is necessarily a similarity.

In the Theory of Levelling, I have extracted
portions from Playfair's Philosophy, and Hutton
and Barlow's Philosophical Dictionaries; the article
on Refraction, from Robson's Marine Surveying;
some facts connected with the tides, from the En-
cyclopædia Britannica; a portion of Subterranean
Surveying, from Fenning's work on that subject.
I have also carefully looked over Mr. Sims's work
on Levelling, and his Treatise on Mathematical
Instruments, to which the reader, requiring more
detailed accounts of, is referred.

The method of laying out Curves is adapted
from the Railway Magazine, to which publication
I feel indebted. I would have added further exam-
ples in Surveying, but for want of time, am unable
to prepare them for the press.

P.B.
22, Charlotte Street, Bloomsbury,
April, 1838.

[Table of Contents]

[page ]

[B]

THE
PRACTICE OF SURVEYING.

SURVEYING in a general sense, denotes the art of
measuring the angular and linear distances of objects,
so as to be able to delineate their several positions
on paper, and to ascertain the superficial area, or
space between them. It is a branch of applied ma-
thematics, and supposes a good knowledge of arith-
metic and geometry. In the erection of extensive
buildings; the forming of new roads, or altering of
old ones; in the sale or purchase of property; or, in
fact, in any alteration of, or change in, landed pro-
perty, a survey is required.

It is most essential that the survey when made
should not only contain the correct area, but also
that every part should occupy its proper and true
position, otherwise serious evils will result. The
importance then of a survey being admitted, it
becomes the student's duty to make inquiry for
the most accurate method. It is admitted, when a
survey is made with the chain only, that numerous

[page 2]

[B2]

GENERAL OBSERVATIONS,
WITH DIRECTIONS TO BE OBSERVED ON COMMENCING
A SURVEY.

SURVEYING may be performed in various ways with
the chain only, or by means of angular instruments
with the chain. In the first place, it should be
observed, that the base or principal line of a survey,
from which all the other lines diverge, should,
if practicable, be carried through the greatest extent
of property to be surveyed, so as to intersect the
principal or most intricate parts of the work; it is
also as well to carry your base line near midway
through the property, so as to leave nearly the same
quantity of work on the one side the base, as on the
other. Then your tye-lines in filling in, crossing
your base, and tying into the opposite line, will be
a satisfactory test of the accuracy of the work, and
will ensure the exact positions of the different objects
to be delineated in the survey. Chain surveying is
much more limited in its capabilities than survey-
ing with an instrument, and certainly not so
correct. In surveying with a chain you are, in
every case, limited to one figure, a triangle; and
the correctness of the survey, and relative position
of all objects to be delineated, entirely depend on

[page 4]

[page 5]

[page 6]

[page 7]

[page 8]

[page 9]

Of the Method of Taking Offsets.

A, c, d, e,f, g, h, being a brook or crooked hedge.

From A measure in a straight direction along the
side of it to B; and in measuring along the line
A B observe when you are opposite any bends or
corners of the hedge, as at i j k, &c., and from thence
measure the perpendicular offsets, i c, j d, &c., with a
tape or offset staff. When these offsets are marked
off from the distances on the line A B, a line drawn
through their extremities will represent the crooked
hedge A c d, &c.

To Survey a single Field with the Chain only.

Having carefully read the general observations,
and the method of taking offsets, directions will now
be given for surveying a single field with the chain
alone. As before observed, in a chain survey you
are confined to one figure, a triangle; and the
correctness of every part depends on the extreme
accuracy with which its relative parts are measured,
as well as the judgment displayed in the arranging
or laying out the sides of this figure on the ground,
which should always, as near as possible, be an

[page 10]

[page 11]

The preceding sketch shows at once the method
of procedure in surveying a single field: A B
being the diagonal or base line, E D the false
stations, left when measuring the diagonal; B C one
side of the triangle, commenced from the termina-
tion of the diagonal, and C A the remaining side of
triangle, which finishes the figure; having arrived
at the point from whence we set out. We have
now to measure the line C D, which verifies the
measurement of the triangle A C B. The same
method of procedure is adopted on the other side of

[page 12]

[page 13]

To Survey the same Field, without a Diagonal,
by means of Chain Angles.

This method is not at all advisable, although
practised to a considerable extent; there is a little
time saved, but the chances of error are con-
siderably multiplied. Commence, as previously
directed, at one corner of the field; but instead of
measuring to the opposite corner, go down the
longest side, and within 200 links, or some con-
venient number, of the end of the line leave a
mark. Now commence a new line, as before
observed, without regard to the angle it makes
with the preceding; and at the same distance
on the new line from the station or point at the
end of the last line leave a similar mark. Now
measure the distance between these two marks,
noting exactly the measurement, even to half a link;
or continue the line to the end of the fence, and
measure it afterwards. The same method may be
pursued at the other angles of the field, although
not absolutely necessary.

The following diagram will illustrate the pre-
ceding method of surveying a field and the manner
of plotting it: --Commence at the angle A, and
measure down one side of the fence towards B, and
at 200 links, or some convenient number, before
arriving at B, leave a mark, a; when arrived at B

[page 14]

[page 15]

The Method of Surveying a Field with a
Theodolite or Sextant.

Commence on the longest side of the field, and
measure quite round it, as in the preceding example,
taking offsets at all bends in the fence as before.
In the diagram (see last example) commence at A,
and measure to B, leaving a mark at the point A,
whence you started. When arrived at B, with the

[page 16]

To Survey a Road with the Chain only.

Suppose A B C D to be a piece of road re-
quiring to be surveyed, commence at A, and if no

[page 17]
[C]

To Survey a Coppice of Wood with the Chain only.

Let A, B, C, D, represent a coppice of wood,
very much overrun with brushwood, so that it cannot
be measured through. In that case take an angle
with the chain by measuring 100 links from A to e,
keeping in a line with A D, and put in a mark at e;
then measure 100 links from A to f, in a line with
A B, and measure the distance from f to e; then

[page 18]

To plot the work draw a line at pleasure, to
represent the line e A D, then put one foot of the
compasses in A, and sweep an arch from e to f, after
having taken off 100 links from a large scale. Then
take off the distance, e f, from the same large scale,
put one foot of the compasses in e, and bisect the line
at f; then lay a straight edge on the point of inter-
section at f and the angle of the wood at A, and
draw the line A B, and lay off the distance A B,
with any scale you like to plot your work with,
which may be much smaller than the scale used for
laying down the angle. Then take the distance
from A to D, which lay off upon the line from
A to D by the same scale you used from A to B.
If the angle is taken at B, which should be done, the

[page 19]
[C2]

To take any Inaccessible Distance with the Chain,
as the Width of a River, &c.

Suppose in the annexed sketch you brought
your survey up to the river, the width of which

[page 20]

If you wish to lay these lines on paper so as to
show the method pursued in crossing the river, it
will be necessary to measure either of the diagonals
A C or D B, which will divide the figure into two
triangles; plot these triangles by intersection, as
before directed, then produce D A and C B, until
they intersect at E, apply your scale to A E, and it
will give you the width of the river.

To Measure over a Steep Hill with the Chain, so as
to reduce it to Horizontal Measurement.

The method adopted in measuring over a hill
to reduce the line to horizontal measurement, is by
taking short lengths of the chain. lithe hill is not

[page 21]

Example in Surveying, with different Methods of
Keeping the Field-book.

To survey the annexed three fields the same
method should be observed, whether an instrument
was used or the chain only. You will commence at
A (see Plate 5 where you must set up a mark, that

[page 22]

Of the field-books we need only to refer to them,
and leave the reader to make his choice. The field-

[page 23]

If an instrument had been used in the above
survey, the angles A B D, B D A, would have been
taken; also D A C, or B A C, and A C B. The
angles formed by the internal lines need not be
taken, as their positions would be correctly deter-
mined by the outer lines. But without an instru-
ment, if an error of 20 or 30 links was committed
in measuring the line A C it would not be detected,
the point C being determined by intersection, except.
by measuring a line from the apex of the triangle at
C to some part of the base, and the same on the
other side; or a line should be measured from
C to D, (see Parish Surveying) which would occupy

[page 24]

EXAMPLE IN RAILWAY SURVEYING,
Showing in what manner the Survey for the Rail-
way was performed, and an Explanation of the
Field-book.

The base-line A B C was first carefully measured,
of which the portion, A B, is only given in the field-
book. At the commencement of the base, at station
A, was set up a flag, natural mark being visible at
C, in a line with the intended base. Before arriving
at the first fence a false station was put down a, and
the exact chainage (540) was entered in the field-
book, and also at the crossing of the fence; farther
on another false station b (1,330), was put down, the
crossing of the fence being noted as before; and in
a similar manner were put down the other false
stations c (2,240), d (3,380), e (4,080), and, lastly,
that at B (4,720).

[page 25]

[page 26]

Now you may either measure the angle formed
by the line j n, off the line j f, or you may proceed
to c, and take it off the base,--which would, perhaps,
be advisable; then from c (2,200 on the base), take
the angle A c j (79° 40'), extend the line a conve-
nient distance to o, so as to command the line o p q,
and measure from o to n, noting the chainage at j
and c; when you come to n you will find yourself
in a line with m and l, the two stations you had
previously left. Measure n, m, l, noting the chain-
age very exactly at m and l. Now return to o, take
the angle n o q (83° 18'), and measure the line o p q,
leaving a mark at p (1,135), proceed on to q (2,535),
and at q take the angle o q a (88° 15'), measure
q s, noting the chainage, cutting the base at B:
leave a mark at r (675), so as to form a line r e t,
and proceed on to s (1,000).

[page 27]

When the student becomes conversant with the
above method much of the labour would be abridged,
as he would run his lines backwards and forwards,
in several instances, without walking to a distant
point to resume his work. Neither is it absolutely
necessary that so many angles should be taken, as
those at h, i, and c, might have been omitted, the

[page 28]

Suppose the false station at i moved forwards
20 links to the black line, the distance i b would
appear to be correct, and the line produced through
b to * would be also assumed as correct, in conse-
quence of the measurement, i b, answering to the
position of i on the plan, on reference to which it
will be seen how much the position of m would be
altered: it is true the line m l would correct this,
but suppose the error of 20 links to be committed at
h, the station at l would then be as much in error as
that at m, and the line m l would plot correctly as
to length; but it would be said the measured
distance, k g, would ensure the accurate position of
k, but in the general method of surveying; the dis-
tance, k g, would be necessary to fix the point g,
which would consequently be as much out of its
proper position as the other stations, therefore k g

[page 29]

We do not mean to assert that a person making
the above survey without an instrument would lay
out his lines in the same manner; therefore the
inference drawn of an error committed at i, extend-
ing back to g, may by many persons be set down
as erroneous; but, although the same distribution
of lines would not be observed, the consequences
pointed out would ensue wherever an error was
committed, which, if of small amount, it would be
almost impossible to detect.

The field-book is a sketch made as the work
progressed; the several lines being entered as they
were measured, and the offsets in the order they
were taken. The same method is observed, as in
the common system, by commencing at the bottom
and writing upwards.

This survey was made with a sextant--if the
angles had been taken with a theodolite, the first
thing determined would have been the angle formed
by the base line with the magnetic meridian (for the
method of doing which see directions for observing
with the theodolite) which it is always desirable to
ascertain, as your theodolite being set to this read-
ing at any subsequent station on your base will point
out its direction; also when arrived at the end of
your base, if of any considerable extent, it would be
desirable to bisect the beck station, and note the
bearing, the difference would be exactly 180° if you

[page 30]

It will also be found of great advantage in
measuring a base line to have its bearing, otherwise
(except in a very open country) it will be almost
impossible to measure it straight, without first
ranging it out with poles, as in passing through
a plantation or orchard you are pretty certain to
lose sight of your marks, you have then nothing
but your bearing to satisfy you that you are in the
right line.--For further directions in measuring a
base, and in general surveying, see observations on
parish surveying.

[page 31]

Of Parish Surveying

Previous to appending any remarks or instruc-
tion of our own on parish surveying, we think it right
to direct attention to the following extracts on ties
subject from Captain Dawson's invaluable Report
to the Tithe Commissioners: it is necessary, he
observes, to determine the area of the whole parish
by some means, which make the correctness of that
area independent of the result obtained by summing
up the contents of each enclosure, minute errors in
many of which would escape observation, if not
checked by comparison, with the correctly ascer-
tained whole, It is essential, in fact, to arrive at the
total area of the pariah by direct admeasurement
of the apace included within its external boundary;
and the simplest and cheapest means by which a
survey and plan may be made for effecting this
object appear to me to be as follows:--

1st. To measure two straight lines through the
entire length and breadth of the parish.

2nd. To connect the ends of those lines by
means of other measured lines: and

3rd. From those connecting lines (by measured
triangles and offsets) to determine the entire pariah
boundary.

The true area of the parish may then be ob-
tained by calculation from the measured distances,

[page 32]

Lines of the description herein proposed to be
measured are ordinarily used by surveyors in the
construction of their plan, but are not always shown
on the finished map; I propose to retain them per-
manently for purposes which will presently appear.

The object and application of these lines will
be better seen by reference to the diagram beneath,
which is a rough sketch of a parish to be surveyed.

The two main lines which I should recommend
to be measured through it are marked A B and
C D; A C, C B, B D, D A are the connecting
lines, a a a, are the offsets, or perpendicular

[page 33]
[D]

Now, if the main lines A B and C D be mea-
sured accurately, and their true lengths from the
point (O), at which they cross one another, be laid
down upon the plan, it will be seen that the connect-
ing lines A C, C B, &c. will form an efficient check
on the general direction of the two main lines with
reference to one another. A satisfactory check on
the lengths of the several lines will, by the same
meant be afforded; for as the points A, C, B, D, are
in each case determined by the intersections of three
lines, an error in any one of these lines must im-
mediately be discovered.

Thus the true relative position of four extreme
points (A, C, B, D), in the parish boundary will be
obtained, and such portions of the boundary as fall
within the ordinary range of offset-distances from
the connecting lines (A C, C B, &c.) will also be
determined, and may be laid down in their true
positions.

The more remote parts of the parish boundary
may be determined by means of the triangles
(T, T, T), the sides of which (E F, G H, K I, &c.)
being prolonged on the ground to intersect the
main lines A B, C D (as they do at M, N, P, &c.),
may be laid down correctly in position and direction
upon the plan. By this simple process the whole
boundary will be determined, and the total area
may then be ascertained.

[page 34]

Among the objects to be particularly attended
to in practice, is that of reducing the lines, mea-
sured over steep slopes in hilly districts, to the
horizontal plane.

This demands especial mention, because anise
inattention to it is not unusual, though the necessity
for such reduction is well known to practised sur-
veyors, and all should be alive to the importance of
using a theodolite, spirit-level, or other assured
means, in the measurement of lines over hilly
ground, for determining the exact allowance to
be made. Without this reduction of the lines
they cannot be laid down in plan upon a flat
surface, and distortion of the outline must inevitably
result.

Care, of course, most be taken in all cases to
measure the lines straight to the points desired;
sad this will require more particular care in a
mountainous, rocky, marshy, wooded, or thickly
inhabited country. The expedients in use among
practical surveyors will of course be resorted to for
overcoming any difficulties which may attend the
measurement of these main lines, and the theodolite
offers a never failing resource in all cases where a
departure from the direct line is inevitable.

[page 35]
[D2]

Observations

The lines which have been described as essen-
tial to be surveyed, should, in all cases, be marked
upon the plans. They should he drawn in red ink,
in order to distinguish them from, and prevent
their interfering with the lines of fences, &c. and
the length of each line in links should be marked
in red figures upon it. Lines measured in the
direction of external objects, should be drawn out
to the margin of the plan, and the name of the
external object should be written upon the line
thus:-

[page 36]

The main lines should be selected, as much as
possible, with reference to permanent well-defined
objects, such as churches, &c. In other cases it
will be desirable that the extremities of the lines (or
of some of them at least) should be marked, and
preserved on the ground by stones or posts, or by
trees, planted there so as to admit of the points
being referred to at a future time.

The parish boundary should be shown, in all
cases, by a dotted line; and when it passes along
the middle of a fence, the dots should be drawn on
both sides of the fence, thus:-

When a road forms part of the boundary of a
parish, both fences of the road should be shown;
and it will be desirable also to mark the abutments
of other fences upon the outer fence of the road.
The same remark will apply to rivers generally; and
in Lincolnshire and other fen districts, to droves
and the drains by which they are bounded, &c.

When a parish boundary passes through a field
or other enclosure, without being defined by a fence,
the whole of such field or enclosure should be shown
on the plan, with the parish boundary, marked by
a dotted line, passing through it. The area of the
included portion only of such field or inclosure will
appear in the schedule; but the area of the excluded

[page 37]

In all cases of fences, the actual boundary line
of the adjacent properties should be marked upon
the plan, whether it be the central line or the side
of a hedge, ditch, wall, bank, &c.; and when the
fence belongs entirely to one property or the other,
that should be indicated by the proper mark.

The plans are to be drawn to the scale of three
chains to one inch, to admit of the correct com-
putation of the contents of the several lands. And
the ordinary usage should be observed with regard
to placing the north towards the top of the plan;
writing the name of the parish, as a title, with that
of the county in which it is situated, and adding
the name and address of the surveyor, the date of
performance, the scale, and the total contents.

The extracts we have made from Captain
Dawson's Report are so much to the point, as ne-
cessarily greatly to abridge our remarks, which will
be confined simply to the guiding and directing
persons in the measurement of such lines as are
therein recommended. In the first place, then, we
will endeavour to point out the best and most
correct method of measuring the principal base
through the entire length of the parish. Previously
to commencing or arranging the work, the surveyor
should, if possible, procure an old map of the parish,
which, however incorrect it may be, will still serve

[page 38]

We will suppose, then, the surveyor to have
decided on the point of commencement and direc-
tion of the base, which, if possible, should be on,
with some conspicuous permanent mark, without
the bounds of the parish, as a church, windmill,
house, or such like. At this point set up your
theodolite, and ascertain very exactly the angle
formed by this line with the magnetic meridian;
then take angles to several conspicuous objects
around, which would serve hereafter very accu-
rately to determine the point. At this spot erect a
pole, very perpendicular, and commence the mea-
surement of the line; but before proceeding further,
it cannot be too strongly enforced on the surveyor's
mind the absolute necessity of extreme exactness in
this part of the operation; for which purpose a
much longer chain is recommended than that
usually adopted.--(See remarks on the chain.)

At about every 5 or 10 chains, it would be

[page 39]

The roads, rivers, brooks, fences, &c. as they
are crossed, should be very carefully noted; but in
this stage of the proceedings it would be quite
useless putting down false stations at nearly all the
fences, as in common surveying. Offsets, if within
distance, should be taken to all conspicuous objects.
At certain prominent points, as you pass along, set
up poles; these will serve to keep you in a direct
line, even if you entirely lose your forward object.
Your forward chainman must at each chains length
plumb back to those poles you have erected, and by
keeping them exactly in a line, you need not fear of
departing from your true course.

If you come upon a house, or gentleman's
pleasure ground, through which it is impossible to
measure a line (but this always should be avoided,
if possible:) the means of overcoming the difficulty
will be found by referring to a chapter on the sub-
ject, in the section devoted to levelling; but the
most ready and correct method would be, very
carefully to measure an angle with the theodolite,
either to the right or left of your line, of exactly
60°, and measure out any length until clear of the

[page 40]

We will now suppose the surveyor arrived at
She extremity of his base, where he must set up his

[page 41]

[page 42]

In throwing out triangles to enclose any part
of the parish that may be without these aide lines, if
an instrument be used, there will be no occasion to
extend them back to the base, without the figure
should be very large, or the internal lines can be
used for other purposes, than merely to verify the
position of the figure; but where a chain only is
used, it is indispensable to the correct fixing of
the figure that those lines should be so extended
to one of the bases. From the extremity of the
transverse base very accurately observe the angles
of the tye-lines to the extremities of the principal
base, and measure these tye-lines in the same
accurate manner as the bases, leaving stakes at
intervals, and taking offsets to the parish boundary
and conspicuous objects wherever within distance.
When these angles and tye-line are measured and
protracted, there will be four principal stations in
the parish very accurately determined; and by
these stations being correctly fixed, each stake on
the lines connecting the stations, may be consi-
dered as a correctly determined station, and used as
such.

It would be advisable, before filling in any por-
tion of the work, to get the boundary of the parish,
and all the work laying outside the lines; but if not
all the boundary, at least the part on that side from

[page 43]

deter-

---

[page 44]

mined

If the surveyor is expert in the use of the
sextant, it would be very desirable to have the
angles taken of all the lines, except where well tied;
but where only determined by their extremities, the
angle should in every case be taken. Particular
care is necessary in reducing lines measured over
steep ground to the horizontal plane; for the method
of doing which see description and use of theodolite,
also the method of correction with the chain only.
The surveyor is advised to lay down his work as he
proceeds, if done every day it would be best; he
will then, in the event of committing an error be
able immediately to rectify it. The sextant may be
used with advantage in filling in, but on no account
should any other instrument than the sextant and
theodolite be employed.

With regard to computing the aggregate quan-
tity of land in the parish, the principal measured
lines, as suggested by Captain Dawson, may be used
for that purpose, equalizing and arranging into tri-
angles what may be without; and for the separate
enclosures within they may be equalized and arranged
in a similar manner. But it would appear to us

[page 45]

The contents of the whole, computed by the
measured lines, might be used as a check on the
preceding method. The lines forming the parallelo-
grams should be permanent; either in faint red or
blue; but probably blue would be the best, so as to
be distinguished from the measured lines, which
Captain Dawson desires to have retained. All the
entire squares must be numbered consecutively, and
the broken figures (as where a fence crosses), calcu-
lated separately; and it will be evident that, in this
separate calculation, the ascertained contents must
be correct; for, having the contents of the whole
square, its parts added together must of course be.
the same.

[page 46]

On Subterranean Surveying, with Directions for
Procedure in Surveying Coal Pits, Mines, &c.

The instrument usually employed in all subter-
ranean surveys is the circumferenter, or a modified
instrument, which is half circumferenter, half theo-
dolite, having the large compass of the farmer, with
the limb and vernier of the latter; by which means
the bearing can be obtained with much greater
accuracy than with the common circumferenter.
The method of procedure is to plant your instru-
ment where the survey is intended to commence,
and take the bearing to a lighted candle placed at
as great a distance in the required direction as can
be seen; the distance must then be measured; to do
which, remove the instrument, and let a person
stand on the exact spot where it stood, holding in
his hand one end of the chain, while another person
takes the other end with a lighted candle in the
same hand, being directed by the former until that
hand which holds the candle and the chain is in a
direct line with the light whose bearing was taken;
there mark the first chain, to which mark the hind-
most man comes, the other advancing another chain
forward as before; this is repeated until the dis-
tance of the light to which the bearing was taken is
determined. The instrument is now fixed where
the light stood as an object, or at the termination of

[page 47]

As surveys of pits or mines are generally made
for the purpose of ascertaining if the workings ex-
tend into adjoining property, or for sinking shafts,
either for ventilation, or convenience for mining the
produce--it is essential, in either case, to mark on
the surface the extent of the workings, or the exact
spot at which the shaft is to be sunk, so as to open
on a precise spot in the pit previously determined
on; or it is often the case, that you may have to di-
rect the miner as to the bearing and distance from
the extremity of some working to another pit: in
either case it is essential to trace the survey on the
surface, to do which, plant the instrument as near
the pit as convenience will allow, so that when the
foresight is put in the direction of the first bearing
you may, by looking backwards, cut exactly the
centre of the pit; if it does not do so, the instrument
is not placed in a proper position, which must be
obtained by shifting the instrument to the right or
left, until it is in the situation beforementioned; after
this is found, measure out the distance of the first
bearing from the centre of the pit, remove the in-
strument to the end of the line, and take the various
bearings, and measure the distances, the same as
below; or, instead of the above manner, choose any
spot near the pit, as the point of commencement,
and from this point take the first bearing and dis-

[page 48]

It will be frequently found necessary, where
only particular points are to be determined so the
surface, to reduce the intermediate bearings and dis-
tances into one bearing and distance; the most easy
and practicable method of doing whish, into apply a
good protracter to the meridian line, with its centre
no the angular point--accurately noting the angle
subtended, and measure the distance with the scale
by which the survey was plotted; during the time
of making the survey, care should be taken not to
admit any iron within three or four feet of the in-
strument, for fear of attracting the needle, although
a large mass of iron will attract it at a much greater
distance. The tram plates or rails generally laid
down in pits do not seem to attract the needle, if
elevated from two to three feet above them; but we
have ourselves found the needle very sensibly affected
by a large clasp-knife in our breast packet. As
these surveys from records which are being continu-
ally referred to from time to time, and additions
made thereto, it is necessary to lay down the work

[page 49]
[E]

A different method of using the circumferenter,
from what we have just now described, is sometimes
adopted: it is to plant the instrument at alternate
angles, and take back and foresights; thus, in place
of setting up the instrument at the commencement
of the survey, it is done at the extremity of the first
line, and its bearing taken, but with the instrument
reversed, that is, you apply your eye to the opposite
sight vane to that when a forward bearing is taken:
it should be noticed in this case, that the angle is
read off from the South end of the needle, which
angle is easily reversed and laid off, as if taken from
the North end--the forward bearings are taken in

[page 50]

ON THE PROTRACTING AND PLOTTING OF SUR-
VEYS; THE REDUCING AND COMPUTING OF
AREAS, &c.

It is usual with practical surveyors to plot their
work daily, which, if possible, should always be
done; otherwise, if left alone for a few days, and an
error should have been committed in the first day's
work, it will be very troublesome to correct, besides
a great loss of time: but by plotting daily, any
mistake that may have occurred can be easily
rectified. There is also another advantage in so
doing, which is, that you are enabled to lay down
your work with the most scrupulous exactness, every
part being fresh in your memory; and in all sur-
veys there are particular parts which can only be laid

[page 51]
[E2]

The method of laying down a survey made
with a theodolite or sextant, will, therefore, only be
given here; to do which, with any degree of ac-
curacy, a circular metallic protracter is indispensable.
This instrument, for the general purposes of survey-
ing, should be of about 5 or 6 inches diameter,
divided on silver in a similar manner to a theodolite,
with two projecting arms carrying verniers, and a
third by which the other two are moved round the
circle, either with a rack and pinion, or clamp and
tangent-screws; but where great accuracy is re-
quired, the latter is preferable. The projecting
arms carrying the verniers have each a branch, with
a fine pricker at its extremity. The inner part of
the circle is chamfered off at each quadrant to an
edge, and the divisions brought down to it. A
small circular space of metal in the centre of the
instrument is removed, and a circular disc of glass
inserted in its place, on which are drawn lines cross-
ing each other at right angles, and dividing the
small circle into four quadrants, the intersection of
the lines denoting the centre of the protracter.

[page 52]

[page 53]

ON THE REDUCING OF FIGURES AND EQUALIZING
OF BOUNDARIES.
To Reduce a Parallelogram to a Triangle of
equal Area.

Suppose the parallelogram A B C D, is to be
reduced to a triangle, whose area will be the same.

Produce or extend one of the sides, suppose A B,
then lay a parallel ruler on the diagonal D B, and

[page 54]

To Reduce a Trapezium to a Triangle of equal area.

Let A B C D be the trapezium. Draw the
diagonal A C, and extend the base from A to E;
draw B E parallel to A C; from C draw C E,
and the triangle E C D will be equal to the trape-
zium A B C D, which may be proved by scaling
the figures.

To Reduce a Figure of Five Sides to a Triangle.

Let A B C D E be the given figure; extend
the base each way; draw C A, and C E, and B G,
and D F, parallel thereto. C F G will be the re-
quired triangle.

[page 55]

To Reduce or Equalize an Irregular Side or
Boundary to a Mean Line.

Suppose the side of a field to be of the irre-
gular form below. Draw the line A B, and at A

draw a transverse line, which is usually at right
angles thereto, except when the equalizing line of
the adjoining fence passes through that point. Lay
a parallel ruler from A to the third point at c; slide
the ruler up to b, and draw in the dotted line to the
transverse line, or, without drawing it, mark where
it cuts it; from which point lay the ruler to d, slide
it down to c, and draw in the dotted line as before;
from the point at which it cuts the transverse line
lay the ruler to e, and slide it up to d, and draw in
the dotted line from d; lay the ruler from the point
bisection to f, and slide it down to e, draw in this
line, and, from the point of bisection, lay the ruler
to B, slide it up to f, draw in the dotted line; and
from the point of bisection at C, draw the line C B,

[page 56]

This method is rarely adopted in practice; too
much time being taken up in the operation, and
equally as accurate results being arrived at by a
much shorter process, which is to equalize those
irregular boundaries by the eye, and by a little
practice it may be done with the greatest exactness.
A thin piece of transparent horn, or a strip of glass,
is recommended for this purpose, by which means
you can very exactly judge if you include as much
new space as you exclude of the original; or a bow
of whalebone, or any elastic substance, strung with
horse-hair, will suit as well. But the method gene-
rally adopted is to draw an equalizing line, in pencil,
with a parallel ruler or straight-edge, which, on
being removed, if the line is found to exclude a
greater portion of the original than it includes of
new space, is rubbed out, and fresh lines drawn,
until the eye judges it correct.

[page 57]

ON THE METHOD OF COMPUTING
AREAS.

In computing ,the contents of any piece of land,
whether it be one enclosure or a great number, it is
done quite independent of the several lines mea-
sured in the field, except in some cases where the
base line and a few others, from their position on
the plan, may be used with advantage; otherwise
new lines are drawn, dividing each separate enclo-
sure into trapeziums and triangles, the bases and
perpendiculars of which are measured on the plan
by means of the scale from which it was plotted,
and so multiplied, and added together for the total
contents. After all the separate quantities are thus
computed, and added together in one sum, calculate
the whole estate, independent of the fields, by dividing
it into large triangles and trapeziums, and