CHAPTER IX.

COLONIAL SURVEYING.

Difference between the Objects in view in the Survey of a Cultivated

and that of a new Unsettled Country.-First Operations.—Preliminary Ex-

ploration. Objects to be principally considered.-Sites of Townships,—

Main Lines of Communication.—Guides for marking on the Ground the

Divisions of Properties.-Size of these Divisions.-Precautions to be ob-

served to secure to the Public Rights of Road, &c.-Necessity for Extensive

Surveys on the First Settlement of a New Colony.-Deviations from Gene-

ral Rules in laying out Sections.-Frontages on, and Access to Rivers and

Main Roads.-Sectional Roads.-Monopoly of Water to be guarded against,

-Sections laid out in Broken Irregular Ground.-Statistical and other In-

formation to be fully afforded to Settlers.-Marking Boundaries of Sec-

tions and Roads.-Reservation of Rights of Road.-Natural Features of

Ground. Geological and Mineralogical Specimens, and Meteorological

Register, &c.-Usual Method of marking Regular Figures upon the Ground,

-Necessity for a Triangulation to conduct these Operations with any degree

of accuracy when upon an extended Scale.-Advantage of Carrying it on

rather in advance of the Sectional Surveys.-Other Uses of the Triangula-

tion.-District Surveyors.-Surveying by Contract.-Rate of Progress and

Cost per Acre of the Sectional Survey and Marking out Roads.—Cost of

the Triangulation. Method of Survey pursued in the Canterbury Settle-

ment, New Zealand.-Temporary Division of Land for pastoral Purposes,

-Territorial Division of Counties, Hundreds, &c.-Remarks on Exploring

Expeditions.-Method of Proceeding.-Objects in View, and collateral In-

formation to be obtained

Page

118

CHAPTER X.

GEODESICAL OPERATIONS CONNECTED WITH A TRIGONOMETRICAL

SURVEY.

Figure of the Earth.-Measurement of an Arc of the Meridian.—Of a

Parallel.-French Standard of weights and measures obtained from the

measurement of an Arc of the Meridian between Dunkirk and Barcelona.

-Popular Account of the method of conducting these Measurements.-

Correct determination of distance between two points whose latitude and

longitude are known.-Convergence of Meridians.—Radius of Curvature.—

Calculation of Azimuths as practised on the recent Survey of the North

American Boundary.-Latitude and Longitude of Stations with reference

to those of places already determined.—Variation of the Compass, and

marking out a Meridian Line.-Projections of the Sphere.-Projection

adapted to limited portions of the Globe

138

CHAPTER XI.

PRACTICAL ASTRONOMY.

Sextant and Repeating Circle, &c.-Definition of Terms.-Division of

Time.-Solar and Sidereal Day.-Observations of the Sun and Stars .

162

b

PROBLEMS.

Page

I.-TO CONVERT SIDEREAL TIME INTO MEAN SOLAR TIME, AND THE REVERSE 173

II. TO DETERMINE THE AMOUNT OF THE SEVERAL CORRECTIONS FOR

REFRACTION, PARALLAX, &c.

III. TO DETERMINE THE LATITUDE.

1. By Observations of a circumpolar Star at the time of its Upper and

Lower Culminations.

2. By Meridional Altitudes of the Sun, or a Star whose declination is
known, involving the Reduction to the Meridian.

3. By the Altitude of the Pole Star at any time of the day.

4. By an Altitude of the Sun, or a Star, out of the Meridian, the correct

time of Observation being known.

5. By two observed Altitudes of the Sun or a Star, and the interval of time

between them; or the difference, or sum of their Azimuths.

6. By Transit Observations on the Prime Vertical

IV. TO FIND THE LOCAL TIME.

1. From single, or absolute, Altitudes of the Sun, or a Star whose declina-

tion, as also the latitude of the place of observation, are known.

2. By equal Altitudes of a Star, or the Sun, and the Interval of Time be-

tween the Observations

V. TO DETERMINE THE LONGITUDE.

1. By the Comparison of local Time with that shown by a Chronometer from

which the Time at some fixed Meridian is known.

2. By Signals.

3. By the Transmission of Chronometers between Stations.

4. By the Eclipses of Jupiter's Satellites, and the Eclipses of the Sun and

Moon.

5. By Lunar Observations.

6. By the Method of Moon-culminating Stars.

7. By Occultations of fixed Stars by the Moon

. 175

VI. TO FIND THE DIRECTION OF A MERIDIAN LINE, AND THE VARIATION

OF THE COMPASS.

1. By the Azimuth of any Celestial Object.

2. By the Amplitude of the Sun at his rising or setting.

3. By equal Altitudes and Azimuths.

4. By a Transit Instrument when properly adjusted in the Plane of the

Meridian

180

. 195

199

219

TABLES OF USE IN THE FOREGOING PROBLEMS.

1. To convert Sidereal into Mean Solar Time

2. To convert Mean Solar into Sidereal Time

Page

. 228
229

. 230

3. To convert Space into Time, and vice versa

4. Table of Refractions

5. Contraction of semi-diameters of the Sun and Moon from Refraction

6. Semi-diameter of the Sun

7. Augmentation of semi-diameter of the Moon, with her increase in

altitude

8. Parallax of the Sun

9. Reduction of the Moon's equatorial horizontal parallax for any

latitude

15. Length of a second of a degree of latitude and longitude

16. Corrections for curvature and refraction

17. Reduction upon each chain's length for different vertical angles

18. Ratio of slopes for different vertical angles

19. Comparative scale of Thermometers

20. Comparative scale of Barometers .

Form for registering Meteorological Observations

. 231

234

234

235

248

. 252

Description of the "Pediometer" and "Computing Scale," for facilitating

the computation of areas .

Form of Report on the Military Reconnaissance of a Road .

No. 5. SCALE OF SHADE FOR REPRESENTING SLOPES OF Ground,

-to face page 60.

No. 6. ANAGLYPTOGRAPH ENGRAVING FOR TOPOGRAPHICAL DRAW

ING-to face page 117.

No. 7. SPECIMENS OF THE VERTICAL AND HORIZONTAL STYLE OF SKETCHING GROUND-to face page 59.

No. 8. METHOD OF TRACING CONTOURS

No. 9. SPECIMEN OF CONTOURING

to face page 95, &c.

AND 113 WOOD-CUTS.

TRIGONOMETRICAL

ETC.

CHAPTER I.

SURVEY,

GENERAL OUTLINE OF THE SYSTEM OF CARRYING ON A TRIGONOMETRICAL SURVEY.

THE basis of an accurate survey, undertaken for any extensive geodesical operation, such as the measurement of an arc of the meridian, or of a parallel, or the formation of a geographical or territorial map, showing the positions of towns, villages, &c., and the boundaries of provinces and counties, or a topographical plan for military or statistical purposes, must necessarily be an extended system of Triangulation, the preliminary step in which is the careful measurement of a base line on some level plain :—at each extremity of this base, the angles are observed between several surrounding objects previously fixed upon as trigonometrical stations; and also, when practicable, those subtended at each of these points by the base itself. The distances of these stations from the ends of the base line and from each other are then calculated, and laid down upon paper, forming so many fresh bases from whence other trigonometrical points are determined, until the entire tract of country to be surveyed is covered over with a net-work of triangles of as large a size as is proportioned to the contemplated extent of the survey, and the quality and power of the instruments employed. Within this principal triangulation secondary triangles are formed, and laid down in like manner by calculation; and the interior detail is filled up between

B