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SECTION II. ON DIVIDING LAND OF EITHER EQUAL OR VARIABLE

VALUE AMONG VARIOUS CLAIMANTS, IN PROPORTION TO

THEIR SEVERAL CLAIMS.

Prob. I. To divide a rectangular piece of land of equal value through-

out, either equally or unequally, among any given number of

claimants, by fences parallel to one of its sides

Prob. II. To divide a triangle of equal value throughout, either

equally or nequally, among several claimants, who shall all

have the use of the same watering place, situated at one of the

angles of the field

Prob. III. To divide a triangular field of equal value throughout,

either equally or unequally, among sundry claimants, by fences

running from a given point in one of its sides

Prob. IV. To divide an irregular field with any number of sides,

among sundry claimants, so that they may all have the use of

a pond situated at a given point within the field

Prob. V. To set out from a field or common of variable value, a

quantity of land, that shall have a given value, by a straight

fence in a given direction.-Cases I. to IV. (the last Case may

be solved by Prob. VI., Chap. VI., Part II.)

Prob. VI. Case I. To divide a common of uniform value, among

any number of proprietors, in proportion to the values of their

respective estates

Case II. To divide a common of variable value, among

any number of claimants, in proportion to the values of their

respective estates

Roads, quarries, watering-places, &c., required to be set out previous

to inclosing commons, wastes, &c.

The method of dividing and allotting the remaining part of the com-

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Prob. VIl. To lay out the Curve by offsets from its chord or chords,

when obstructions occur on the convex side of the Curve

166

Prob. VIII. To find the length of the Chord of a Curve

167

Prob. IX. To find the second Radius of a componnd Curve, the otho

radius, tangential points, and angles being riven

167

Prob. X. To find the second Radius of a compound Curve, the other

radius, tangential points, and angle of intersection being given 168

Prob. XI. To determine the reversing point and the common Radius of a

serpentine or reversed Curve, the tangent points, &c., being given 168

Prob. XI. To find the Chords and second Radius of a serpentine or

reversed Curve, the tangential points and first radius being given - 169

Prob. XIII. To find the common Radius of a serpentine or reversed

Curve, the tangential points being given

170

Prob. XIV. To find the common Radius of a reversed Curve, the length

of the common tangent and the angles of intersection being given 171

Prob. XV. To unite the Tangent Points by a parabolic vertical Curve,

the rate of inclination of gradients, number of stations, and tan-

gent points being given

172

Turnouts and Crossings

174

Prob. XVI. To find the Frog Angle and Chord of a Turnout, the radius

of a centre line being given

174

Prob. XVII. To find the Radius of the centre line of a Turnout, the

frog angle being given -

175

Prob. XVIII. To find the positiou of a given Frog practically on the

ground

175

Prob. XIX. To make a given deviation from a straight line of Railway

by three Curves, &c.

176

Examples of expensive severance of property by improperly setting cut

Railway carves

17;

The practice of Engineers in the adoption of Curves in various Railways 178

Careless Expenditure in the Construciion of Railways from the non-adop-

tion of Curves, from improperly laying out Gradients, Exactions of

Landowners, &c.

179

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No. 2. Correction of Levels for Parallax and Refraction

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LAND AND ENGINEERING SURVEYING.

PART I.

LAND SURVEYING.

CHAPTER I. Previous to commencing the various subjects of Land and Engineering Surveying, it will be necessary to give a clear view of Practical Geometry, which is especially requisite for those who are unacquainted with this branch, as well as those parts of the Mathematics which are equivalent to it.

PRACTICAL GEOMETRY.

as A B.

A

DEFINITIONS. 1. A point has no dimensions, neither length, breadth, nor thickness.

А
2. A line has length only, as A.
3. A surface or plane has length and

B breadth, as B.

4. A right or straight line lies wholly in the same direction, 5. Parallel lines are always at the same

B distance from each other, and never meet

D when prolonged, as A B and C D.

6. An angle is formed by the meeting of two lines, as A C, C B. It is called the angle ACB, the letter at the angular point C C being read in the middle. 7. A right angle is formed by one right

A line standing erect or perpendicular to an

D other; thus, ABC is a right angle, as is also A BE.

8. An acute angle is less than a right angle, as D BC. 9. An obtuse angle is greater than a right angle, as D'BE.

B

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