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1. To convert Sidereal into Mean Solar Time
2. To convert Mean Solar into Sidereal Time
3. To convert Space into Time, and vice versâ
5. Contraction of semi-diameters of the Sun and Moon from Refraction
7. Augmentation of semi-diameter of the Moon, with her increase in
10. Parallax of the Planets in altitude
12. Dip of the Horizon at different distances
13. Reduction to the Meridian
9. Reduction of the Moon's equatorial horizontal parallax for any
14. Equation of equal altitudes
15. Length of a second of a degree of latitude and longitude
17. Reduction upon each chain's length for different vertical angles.
18. Ratio of slopes for different vertical angles
19. Comparative scale of Thermometers
Form for registering Meteorological Observations
Description of the "Pediometer" and "Computing Scale," for facilitating
No. 1. DIAGRAMS-to face page 36.
No. 2. DITTO.
No. 3. FIELD BOOK.
No. 4. CONTENT PLOT AND DIAGRAM-ditto.
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.
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
these points, either entirely by measurement with the chain and theodolite, or by partial measurement [principally of the roads], and by sketching the remainder with the assistance of some portable instrument. The degree of accuracy and minuteness to be observed in this detail, will of course determine which of these methods is to be adopted—the latter was practised on the Ordnance Survey of the South of England, which was plotted on the scale of 2 inches to 1 mile, and reduced for publication to that of 1 inch; but on the Survey of Ireland, and that of Scotland and the North of England now in progress, sketching has been entirely superseded by chain measurement, even in the most minute particulars, and the undulations of the surface of the ground are represented with mathematical accuracy by horizontal contour lines traced by actual levelling at equidistant vertical intervals, the whole survey being laid down to the scale of 6 inches to 1 mile. In the survey of only a limited extent of country, there does not exist the same absolute necessity for a triangulation, even though a considerable degree of accuracy should be required; this will appear evident, from the consideration that in every practical operation some amount of error (independent of the errors of observation) is to be expected-sometimes a definite quantity dependent upon the means employed; sometimes a quantity varying in amount with the extent of the operation.
In all angular measurements, the errors to be expected evidently depend upon the quality of the instruments made use of, and are altogether irrespective of the space over which the work extends. In linear measurements, on the contrary, the probable error is some proportional part (dependent upon the circumstances and the means employed) of the distances measured. So long, then, as the extent of the survey, and the scale upon which it is to be laid down, are such that the probable error attendant upon ordinary chain measurement of the largest figures would be imperceptible on the plan, no triangulation is necessary on the score of accuracy alone, though in many cases even of this nature it would be found in the end a saving both of time and expense.
In a new and unsettled country, particularly if flat and thickly wooded, the outlay that would be required, and the time that would be occupied by an accurate triangulation, would probably
prevent its being attempted, at all events in the first instance. If only a general map upon a very small scale is required, the latitude and longitude of a number of the most conspicuous stations can be determined by astronomical observations, and the distances between them calculated, to allow of their positions being laid down as correctly as this method will admit of, within which, as within a triangulation, the interior detail can be filled up. In surveying an extended line of coast, where the interior is not triangulated, no other method presents itself; and a knowledge of practical astronomy therefore becomes indispensable in this, as in all extensive geodesical operations. A topographical survey further requires that some of the party employed upon it should be practically versed in the general outlines of geology, as a correct description of the soil and mineral resources of the different parts of every country forms one of its most important features. The heights of the principal hills, and of marked points along the ridges, plains, valleys, and watercourses above the level of the sea, should also be determined, which, in a survey of no great pretensions to correctness in minute detail, may be ascertained with tolerable accuracy by means of the mountain barometer, or even by observing the temperature at which water boils at different stations.
A sketch of a certain tract of country, on a far larger scale than that of most general maps, is constantly required on service, for the purpose of showing the military features of the ground, the relative positions of towns and villages, and the direction and nature of the roads and rivers comprised within its limits. This species of sketch, termed a "Military Reconnaissance," approaches in accuracy to a regular survey, in proportion to the time and labour that is bestowed upon it. Having thus adverted briefly to the progressive steps in the different species of surveying, they will each be treated of more in detail in their proper order.
The system of forming the "net-work of triangles" alluded to, of as large a size as is consistent with the circumstances under which the survey is undertaken, within and dependent upon which the secondary triangulation and all the interior details are included, is to be considered as the working out of a general principle to be