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A manual of plane surveying : confined to work with the compass online

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UNIVERSITY OF CALIFORNIA
AT LOS ANGELES





TELESCOPE COMPASS.



A MANUAL



PLANE SURVEYING;



CONFINED TO



WORK WITH THE COMPASS.



WITH AN APPENDIX.



AMPLY ILLUSTRATED.
REVISED AND ENLARGED.



BY

THOMAS BAGOT,

SUPERINTENDENT OP RIPLEY COUNTY, INDIANA.



INDIANAPOLIS, INDIANA:

THE NORMAL PUBLISHING HOUSE.

J. E. SHERRILL, PROPRIETOR.

1889.



Entered according to Act of Congress in the year 1881,

BY J. E. SHEERILL,
In the office of the Librarian of Congress at Washington.



CARLON A HOLLENBECK,

PRINTERS AND BINDERS,

INDIANAPOLIS.



TA



I DEDICATE THIS BOOK TO MY MOTHER



THE AUTHOK.



356



PREFACE.



EVERY person who studies Surveying from the text-books in gen-
eral use, and afterward is called upon to discharge the duties of a
surveyor, must, in the course of time, become aware of two things :
(1) that he has spent time in learning much that he has never
had, and probably never will have, occasion to use, and (2) that a
great deal he needs to know, and must know, is not to be found in
the books.

This is the case particularly under the Rectangular System, and
the author's experience has led him to believe that a necessity ex-
ists for a book dealing directly with the problems continually
coming up before surveyors throughout the country, and that such
a book will be cordially received by every person who wishes to
understand the subject as it is comprehended in general practice.

And this, dear reader, accounts for the existence of this little
book. You will find it simply a brief treatise on Compass-Sur-
veying, shorn of everything superfluous, and yet embracing all
that is necessary to a good understanding of the subject. Very
few geometrical or trigonometrical terms are employed, and all
the problems may be mastered by any person having a moderately
good knowledge of arithmetic.

The author does not claim that the book is above criticism, but,
on the contrary, he is well aware of the fact that a person disposed
to criticise may find in it an ample field in which to exercise his
talents. He trusts, however, that a search for its faults will re-
sult in disclosing enough merit, even among so much demerit, to
excuse him for writing it, and so trusting, he submits it to the
public.

NEW MARION, INDIANA,
May, 1883.

(4)



CONTENTS.



CHAPTER I. INTRODUCTION.
No. of Art.

( 1). Surveying defined.
( 2). Branches.

1. Topographical surveying.

2. Geodetic surveying.

3. Plane surveying.
3). Measurements, how

1. Actual area nearly always greater than computed area.

2. Smooth surface conceived underneath.

3. Impossible in many instances to compute the area of

real surface.
( 4). Corners defined.
( 5). Surveying instruments used.
( 6). Transit and compass.

1. Remarks on the transit.

2. Remarks on the compass.
7). Chain and pins.

( 8). Chaining over hills.

( 9). Flag-staff, drawing instruments, etc.

(10). Assistants needed.

CHAPTER II. DESCRIPTION OP THE COMPASS.

(11). The compass circle, how divided.

(12). Magnetic needle and center pin.

(13). Degrees, how marked. and 90 points.

(14). Compass box, plate, sights, etc.

(5)



(15). Description of needle. Delicacy, how determine^.

(16). Horizontal angles, how measured.

(17). Letters "E" and " W" reversed on compass face.

(18). Eeason for this.

(19). Kule for reading bearings.

(20). Reverse bearing.

(21). Northerly and southerly bearings.

(22). Running lines east or west.

(23). Rules for measuring angles.

1. When both readings are in the same quadrant.

2. When one reading is in each of either the two north

quadrants or the two south quadrants.

3. When one reading is in each of either the two east quad-

rants or the two west quadrants.

4. When one bearing is in each of two opposite quadrants.
(24). Reasons for these rules.

(25). Glass cover to compass box. Electricity, how excited in it,

and how removed.
(26). Needle affected in other ways.
(27). Sight compass and telescope compass. Either may be either

a plain compass or a vernier compass.
(28). Description of the vernier.
(29). How used.
(30). Other kinds of verniers.
(31). Repairing the compass.

1. To re-magnetize the needle.

2. To sharpen the center pin.

3. To replace a spirit level.

4. To adjust a new sight.

5. To straighten the center pin.

6. To straighten the needle.

7. To put in a new glass.

8. To regulate the movement of the ball.
(32). The compass, how carried.

(33). Needle should be lifted from center pin when the compass is

not in use.
(34) Compass should be kept level when not in use, and the needle

allowed to assume its natural position.
(35). The telescope compass gradually growing in favor.



CONTENTS. 7

CHAPTER III. THE VARIATION OF THE MAGNETIC NEEDLE.

(36). Meridian defined.

(37). The true meridian.

(38). Methods of determining the true meridian.

1. By a shadow.

2. By Polaris.

(a). Polaris and Alioth.

(b). Pole between them.

(c ). The plumb-line.

(d). Greater accuracy.

(e ). When upper culmination occurs during the day.
(39). Table showing time of culmination of Polaris.
(40). Magnetic meridian.
(41). East variation and west variation.
(42). Agonic line.

(43). Isogonic lines. [variation of the needle.

(44). The north magnetic pole; the effect of its movement on the
(45). Secular change of variation.
(46). Diurnal change and annual change.
(47). Table showing diurnal change by hours.
(48). Diurnal and annual changes usually disregarded in practice.
(49). Electric disturbances.
(50). The "dip" or inclination of the needle.
(51). Many magnetic phenomena imperfectly understood.

CHAPTER IV. EFFECT OF CHANGE OF VARIATION ON OLD
LINES, AND METHODS OF CORRECTING BEARINGS.

(52). Bearings of lines subject to constant change.

(53). Illustration.

(54). Effect of re-surveying lines without considering the change.

(55). Area of tract not affected.

(56). To determine the present bearing of a line.

1. Bearing at time of a previous survey.

2. Date of previous survey.

3. Annual amount of secular change. This may be de-

termined in various ways.
(1). By comparison of bearings.
(2). By establishing a true meridian.
(3). By interpolation.



O CONTENTS.

(57). Table showing the variation of the needle at important sta-
tions.

(58). Table showing annual amount of secular change in certain
localities.

(59). Tables to be used in approximation.

(60). Determining variation for past times.

(61). Advantage of basing bearings on the true meridian.

(62). Magnetic meridian bearings subject to constant change.

(63). To determine the true bearing of a line from its magnetic
bearing.

1. When the variation is west.

2. When the variation is east.
(64). Bearings to be changed.

(65). When supplement is to be taken.

(65). Changing from the true meridian to the magnetic meridian.

CHAPTER V. METHOD OF RUNNING LINES.

(67). Finding a corner, etc.

(68). Determining position of corner from witnesses.

(69). Where trees are not available for witnesses, other things are
used.

(70). Method of describing witness trees.

(71). Starting the survey of a line.

(72). Course and distance of line must at least be known approxi-
mately before the line can be surveyed.

(73). Setting the compass and measuring the line.

(74). Setting off variation on the vernier.

1. When the variation is east.

2. W T hen the variation is west.
(75). Surveying the line.

(76). How chained.
(77). Pins, stakes, etc.

(78). Relative places on line of men engaged in the survey.
(79). Continuation of the line to the opposite corner.
(80). In case the line does not strike the corner.
(81). Illustration.

(82). Rules for correcting the stakes.

(83). Terminations of lines and starting point regarded as vertices
of an isosceles triangle.



(84). Examples in moving (correcting) the stakes.

(85). Abbreviations used.

(86). Errors caused by imperfection of instruments, etc.

(87). Correction of assumed bearing.

(88). Rules for correcting bearings.

1st method. Derivation of rule. -
(1). Trigonometrical lines.
(2). Sine and cosine defined.

(3). Study of relation of sine and cosine important.
(4). Application of these lines.
(5). -When the angle is large.
2d method.

(1). Modification of first method.
(2). Illustration.
3d method.
4th method.

(89). Examples of lines whose bearings are to be corrected.
(90). Is amount of correction to be added or subtracted?

1. Rule for north-east and south-west courses.

2. Rule for north-west and south-east courses.
(91). Examples under these rules.

(92). Thus far, all bearings have been based on the true meridian.
(93). Bearings of lines based on the magnetic meridian.

1. Rule for correction.

2. Demonstration of the rule.

(94). Rule good while the needle moves westward.

(95). Bearings to be corrected.

(96). Abbreviations, etc.

(97). Completion of the survey.

(98). Assistants generally sworn.

(99). Instruments should be tested frequently.

(100). Backsights.

CHAPTER VI. UNITED STATES RECTANGULAR SURVEYING.

(101). Public lands, how divided.

(102). Townships, how divided.

(103). These provisions sufficient.

(104). Fundamental lines and initial point.

(105). Some imperishable mark chosen for the initial point.



10 CONTENTS.

(106). Survey of range lines or meridians, etc.

(107). Survey of parallels, etc.

(108)". Convergence of meridians. Correction lines.

(109). Auxiliary meridians, etc.

(110). Survey of townships north of the base-line and east of the

principal meridian.
(111). Survey of townships north of the base-line and west of the

principal meridian, etc.
(112). Excesses and deficiencies.
(113). Congressional township and civil township.
(114). Survey of sections.

1. Preliminaries.

2. How to obtain bearings.

3. Sections, how numbered.

4. Survey of section 36.

5. Survey of the rest of eastern tier of sections.

6. Completion of the township.

(115). Full sections and fractional sections. The "double frac-
tional."

(116). Meander corners and meander lines.

(117). Making up the field-notes.

(118). Monuments adapted to the country surveyed.

(119). Work of Government deputy extends only to the division of
the township into sections.

(120). Advantages of the Rectangular system, etc.

CHAPTER VII. THE DIVISION AND SUBDIVISION OF THE
SECTION.

(121). Subsequent surveys must be made in accordance with the

original.

(122). The ideal section and the real section.
(123). The divisions and principal sub-divisions of the section.
(124). Names of these divisions and sub-divisions.
(125). Descriptions of land generally qualified by the words "more

or less."
(126). Corners, how named.

1. Section corners.

2. Quarter-section corners.

3. Half-quarter corners.

4. Fourth-quarter corners.



CONTENTS. 11

(127). Section lines and center lines.
(128). Position of corners, how determined.

1. Section corners and exterior quarter-section corners.

2. Center corners, methods of setting.

(1). By crossing the center lines.

(2). By bisecting east and west center line.

3. Half-quarter corners.

4. Fourth-quarter corners.

5. Other corners.

(129). Examples in setting corners.

(130). Survey of the divisions and sub-divisions of the section:

1. Quarter section.

2. Half-quarter section.

3. Fourth-quarter section.
(131). General rule.

(132). When some of the boundary lines are known.

(133). Tracts to be surveyed.

(134). Independent corners, lines, and tracts.

(135). Illustration of independent corners, etc.

(136). Dependent corners, lines, and tracts.

(137). Dependent lines, etc., how surveyed.

(138). Examples of dependent tracts.

(139). Description by "metes and bounds."

(140). Rules for setting corners, etc., in full sections, generally

apply to fractional sections.
(141). When a tract of land lies partly in one section and partly

in another.

CHAPTER VIII. FIELD-NOTES.

(142). Field-notes of sectional survey by the Government deputy.
(143). Contents of full section, supposition regarding it, etc.
(144). Plot of township.
(145). Explanation of the plot.
(146). List of witnesses to corners.

1. Exterior corners.

2. Interior corners.
(147). Other particulars.

1. Area of fractional quarters.

2. Creeks, etc.

3. Offsets.



12 CONTENTS.

(148). Surveyor needs copy of original field-notes.
(149). What surveyors' records should contain.
(150). Pocket record.
(151). Description of pocket record.

1. Left-hand page.

2. Right-hand page.

(152). Instructions regarding bearings.
(153). Representation of surveys on the plot.
(154). Approximating the bearing of a line.
(155). Illustration.

(156). Principles underlying the method.
(157). The field-book.

(158). Method of keeping the field-book in independent surveys.
(159). When new witnesses should be taken.
(160). Method of keeping the field-book in dependent surveys.
(161). Names of stations, witnesses, etc.

(162). Records by authorized surveyors taken as prima facie evi-
dence in favor of surveys recorded.
(163). Other methods of keeping field-notes.

CHAPTER IX. RE-LOCATION OF CORNERS.

(164). Trouble caused by lost corners.

(165). Nature of this trouble. Means of re-locating corners.

1. Remains of missing corner or witnesses.

2. By course and distance from some other corner.

3. By retracing old line by marks on trees, etc.

4. By projecting lines.

(1). Illustration of this method.

(2). The reverse of the method by which the corners

were established.
(3). Another illustration.
(4). Examples for practice.

5. A last resort.

(1). Setting S. } corner.

(2). 'May not agree in position with corner lost.

(S). A case illustrated.

(4). Lost section corner.

(5). Case of disagreement illustrated.

(6). When a quarter corner can not be found.



CONTENTS. 13

(166). Re-locating original corners to the variable quarters of

fractional sections.

(167). To set a quarter corner between two fractional sections.
(168). To set an exterior corner to a fractional section, or to any

exterior section.

1. When there is an offset.

2. When there is no offset.
(169). Examples.

(170). He-location of subsequent corners, etc.

CHAPTER X. DESCRIPTIONS OF LAND.

(171). Necessity of a good description.

(172). Length of lines and area of tracts should be given in sur-
veyor's measure.

(173). Tables of equivalents.

(174). Examples for reduction.

(175). Fractions of a chain expressed in links.

(176). General rule for reduction.

(177). Area of tracts, how expressed.

(178). Description of independent tract.

(179). Examples of errors in descriptions.

(180). Examples for correction.

(181). Erroneous descriptions.

(182). Use the words " more or less."

(183). In describing dependent tracts the course and distance of
each boundary should generally be given.

(184). The description should state whether the bearings are based
on the true meridian or on the magnetic meridian.

(185). Lines running north, etc.

(186). Surveys generally made in accordance with the description.

CHAPTER XL OBSTACLES TO ALIGNMENT AND MEASUREMENT.

(187). Obstacles met on line.

(188). Two classes of obstacles.

(189). Methods of spanning obstacles of first class.

1. By perpendiculars.

2. By an equilateral triangle.

3. By a right-angled triangle. [urement.

(1). When an obstacle both to alignment and meas-
(2). When an obstacle to measurement alone.



14 COXTENTS.

4. By symmetrical triangles.

5. When a fence is built on or near the line.

(1). When offset line terminates on the opposite side.

(2). When the offset line terminates on the same side.

(a). When the distance missed is greater than

the offset.

(b). When the offset is greater than the distance
missed.

6. Surveying over hills.

(190). Methods of spanning obstacles of the second class.

1. By a right-angled triangle.

2. By symmetrical triangles.

3. By similar triangles.
(191). Other methods, etc.



CHAPTER XII. COMPUTATION OP AREA.

(192). Advantage of expressing dimensions of tracts in chains and

links.

(193). Special rules deduced.
(194). Examples in computation.
(195). Every tract of land a polygon in shape.
(196). Rectangles.
(197). Parallelograms.
(198). Trapezoids.
(199). Triangles.

1. With base and altitude given.

2. With no altitude given.
(200). Trapeziums.

(201). Any figure.

(202). Computation of area by latitudes and departures.

(203). Latitude and departure, as applied to courses, defined.

(204). North and south latitudes, and east and west longitudes.

(205). Signs of latitudes and departures.

(206). Relation of sine and cosine to departure and latitude.

(207). Table of natural sines and cosines explained.

(208). Examples in computing latitudes and departures.

(209). Columns marked differently at top and bottom.

(210). Traverse tables.



CONTENTS. 16

(211). Sum of latitudes and sum of departures in every cor-
rect survey.

(212). A trial survey.

(213). Explanation.

(214). When a discrepancy exists.

(215). Initial line or meridian.

(216). Difference between longitudes and departures.

(217). How to determine the longitude of a course.

(218). Algebraic sum must be used.

(219). Simplification of the rule.

(220). Computation of area by longitudes.

(221). North products and south products.

(222). Double longitudes.

(223). Method of keeping the data.

(224). General rule for computing areas by double longitudes.

(225). To determine the most westerly corner.

(226). Examples in computation.

(227). Courses without departures, etc.

(228). Not absolutely necessary that the meridian be drawn
through the most westerly station.

CHAPTER XIII. LAYING OUT AND DIVIDING UP LAND.

(229). No general rule can be given.

(230). What are known in problems to be considered.

(231). To lay out a square.

(232). To lay out a rectangle.

(233). To lay out a parallelogram.

(234). To lay out a right-angled triangle.

(235). To lay out a trapezoid.

(236). To lay off any figure.

(237). Things to be considered in making partition.

(238). Nature of problems chosen.

(239). To divide a rectangle into equal parts.

(240). To divide a rectangle into unequal parts.

(241). Problems.

CHAPTER XIV. SURVEYING TOWN LOTS.

(242). Description of town lots, blocks, etc.
(243). Survey of town, how based.



16 CONTENTS.

(244). Usual shape of lots, etc.

(245). What the plot of a town should show.

(246). Particulars respecting Figure 58.

(247). Illustration of a town in which the lots vary in size.

(248). Method of surveying lot number 11 in the figure.

(249). Examples for practice.

(250). Chain or tape used in surveying should be tested frequently.

CHAPTER XV. PLOTTING.

(251). Plotting defined.
(252). Instruments used.

1. Drawing board.

2. T-square.

3. Euler.

4. Drawing pen.

5. Dividers or compasses.

6. Protractor.

7. Diagonal scale of equal parts.

(253). Units of the scale may have various equivalents.

(254). Plotting bearings.

(2551. Examples for practice.

(256). Plotting rectangular tracts.

(257). Plotting tracts in general.

(258). A particular case. When a survey does not "close."

(259). The pantograph.

(260). Locating objects on the plot.

(261). Coloring plots and maps.

CHAPTER XVI. SURVEYING WITHOUT A COMPASS.

(262). The compass nearly always necessary.

(263). Setting corners.

(264). Establishing lines.

(265). Setting out perpendiculars.

(266). Survey of rectangular tracts.

(267). Measurements.

APPENDIX.
Land Decisions.
Table of natural sines and cosines.



MANUAL



PLANE SURVEYING.



CHAPTER I.

INTRODUCTION.

ART. ( 1 ). SURVEYING is that branch of applied mathematics
which embraces operations for finding, (1) the relative positions
of points on the earth's surace, (2) the area of any portion of its
surface, and (3) the contour or shape of any part of its surface, so
that it may be represented in maps and plots.

( 2 ). It is divided into three branches :

1. Topographical Surveying, or Topography, includes operations for
determining the contour of portions of the earth's surface and re-
presenting it on paper.

2. Geodetic Surveying, or Geodesy, takes into consideration the
curvature of the earth's surface and is employed in extensive sur-
veys.

3. Plane Surveying does not regard the curvature" of the earth's
surface and all lines are measured as on a plane. It is used in lo-
cal work.

(3). All measurements in surveying are made as nearly hori-
zontally as possible, and the area of a tract of land is not its ac-
tual surface measure, unless the tract be perfectly level, but the
amount of land enclosed by its boundaries measured horizontally,
instead of with the inclinations of the surface over which they run.
2 (17)



18 MANUAL OF PLANE SURVEYING.

1. The actual area, therefore, is nearly always greater than the
computed area, and increases in proportion to the inequality of
the surface.

2. We may conceive a smooth surface at the level of the ocean
underlying the surface of the land; then the area of a tract of
land is equal to the contents of a figure formed by projecting the
boundaries of the tract on the horizontal surface below.

3. Were the real surface considered, it would be impossible in
many instances either to compute its area or represent its figure
on paper.

( 4 ). The extremities of lines in surveying are called corners,
and each corner marks the vertex of an angle formed by the meet-
ing of two lines. The corner is a mathematical point, and may
or may not be marked with a monument.

( 5 ). Lines are surveyed either with a solar or a magnetic in-
strument. With the former, where more precision than expedi-
tion is required ; and with the latter, where expedition is of more
importance than precision.

( 6 ). The principal magnetic instruments in use are the transit
and compass.

1. The transit is provided with a telescope, and at the present
time is so constructed as to be adapted to the measurement of
both horizontal and vertical angles. It serves many important
purposes independent of the assistance of the magnetic needle, and
is not strictly a magnetic instrument.

2, The compass is either supplied with sights or a telescope,
and is strictly a magnetic instrument. It is not usually adapted
to measuring vertical angles. The lightness, simplicity, and con-
venience of the compass have brought it into almost general use
in common surveying, and the following chapter is devoted to a
description of it. The transit may be found described in almost
any comprehensive work on Surveying.

( 7 ). Measurements of lines in surveying are made with an
iron or steel chain* usually 33 feet or 2 rods long and divided
into 50 links. It has a handle at each end by which it is carried
during the survey, and the successive chain-lengths are maked

*For convenience in counting the links, this chain is divided into five
parts of ten links each by four brass or copper tags. The real chain is 100
links or 66 feet in length, and called a Gunter's chain, from its inventor.
Ihe half-chain of 50 links is used for convenience. A link is 7.92 inches in
length. In Government surveys, a chain 66.06 feet in length is used. The
M foot being added to make up for " slack," etc.



MANUAL OF PLANE SURVEYING. 19

with pins of iron or steel wire, generally 10 or 12 inches in length,
sharpened at one end and bent into the form of a ring at the'other.

In the ring is sometimes tied a bright ribbon or piece of cloth to
render the pin more conspicuous, in order that it may be easily
found by the person who carries the rear end of the chain, and
such colors should always be chosen as will contrast most with
the surface to be surveyed.

( 8 ). In chaining up and down hill, the chain must be kept taut
and horizontal, as on a level surface. In order to do this, it is
sometimes necessary to drop the pin from the front end of the chain,
or elevate the rear end of the chain to a point exactly over the
pin that sticks in the ground.

(9). A straight staff, about 1 inches in diameter and 8 or 10
feet high, surmounted by a small flag of brilliant color, is used in
alignment; and a good set of drawing instruments, drawing board,
t-square, triangle, protractor, ruler, etc., are necessary in drawing
and plotting.

(10). In field-work the surveyor generally needs four assist-
ants ; two chain-men, one flag-man, and a marker. The first two
measure the line with the chain, the third carries the flag, and
the fourth assists the chain-men by marking the line with stakes
at the proper distances. To this force it is sometimes necessary
to add one or more ax-men, as bushes may have to be cut out of


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