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the field notes for the plan were wanting, and as the subject-matter was otherwise very defective, and as the former omission could not be supplied, or the latter defects corrected, without an actual survey of the ground, -conditions almost wholly impracticable,—it was considered advisable to make this change, as preliminary surveys of the kind in question are frequently demanded for reasons that will be found in the section to which we refer.

In this branch of land-surveying it is a standing rule that the measure of every line and angle shall be determined both by linear and angular instruments; and when an error or an omission is detected in any of the field books open, the error must be corrected, and the omission supplied in the field. The reason of this is, because the exceptions are few where a single line in a survey can be accurately measured with the chain ; consequently, if a continuous check is not kept upon linear measure by angular, the field notes, both for plotting and setting out curve lines and inclinations or gradients, cannot be obtained with that degree of accuracy which the nature of the survey demands. If the station poles are accurately ranged, then the lines in the field close ; and in plotting either plan or section, the only proof of accuracy admissible is when the lines formed by the station-points also close, for unless they do so, the subsequent operations of the survey cannot be correctly performed.

W. B.

CONTENTS.

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Geometrical Definitions

1

Geometrical Problems .

7

PROB. 1. To bisect a given line

7

2. To bisect a given angle

8

3. To draw a line parallel to a given line

8

4. To erect a perpendicular from a given point, near the middle of a

given line.

8

5. To erect a perpendicular from a given point, near the end of a

given line

6. From a given point, to let fall a perpendicular upon a given line

7. To construct a triangle of three given lines.

9

8. Having given the base and perpendicular, to construct a triangle 10

9. To describe a square whose side shall be equal to a given right line 10

10. To describe a rectangular parallelogram whose length and breadth

shall be equal to two given lines

10

11. Upon a given right line to construct a rhombus .

11

12. With two given right lines, as sides, to construct a rhomboid

11

13. With a given base and two given perpendiculars, to construct a

trapezoid

12

14. With four given sides, to construct a quadrilateral figure which has

one right angle

12

15. With given transverse and conjugate diameters, to construct an

ellipse.

12

16. To reduce a given trapezium to a triangle of equal area

13

17. To reduce an irregular polygon of five sides to a triangle of equal

14

18. To raise a perpendicular by a scale of equal parts

14

19. To make a right angle by the line of chords on the plane scale 15

20. To make an acute angle

15

21. To make an obtuse angle

15

22. To find the number of degrees contained in a given angle

16

23. To lay down a line making a given angle with the meridian line 16

Geometrical Theorems .

17

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METHOD I. .

A table for reducing hypotenusal to horizontal lines

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