1. In a book, with accompanying descriptions of the points; as for example, in a list of bench marks, or in a level-book.

2. On a plan or map, the exact points being marked and the levels recorded close to them.

3. On a plan, by a series of contour lines, or lines of equal elevation, whose levels are recorded; so that the level of any intermediate point may be approximately determined by interpolation.

4. On a section, or series of sections, taken in various directions, showing the relative heights to scale of any points in that section. A plan is frequently necessary as a guide to show the direction or course of the sections, which may either be straight or circuitous in any direction, while again the section may comprehend levels of two or more sets of objects, and these necessitate reference to more than one plan.

A section generally not only shows by scale the position of various detached points in a vertical plane with reference to some convenient datum level or datum line, but also the position of continuous objects or surfaces, such as ground surfaces, water levels, lines of pipes, road levels, rail levels, edges of strata, mine adits, galleries, shafts, tunnels, bed levels, formation levels, etc., according to the special purposes for which it is intended.

The actual datum level need not occur in the section-any horizontal line of known level may be used for convenience in scaling the relative heights; these latter are frequently also recorded in figures.

Sections being generally short in comparison with a great circle of the globe, horizontal levels and surfaces are represented by straight horizontal lines, and curvature is neglected; the heights and depths indicated on

sections being also small in comparison both with the lengths of the sections and with the radius of the sphere, natural sections, in which the same scale is used both for horizontal distances and vertical heights, are less often used than exaggerated sections, in which the vertical heights are on an exaggerated scale, and differences of height more easily distinguished.

480

1200

As a general rule, it is most convenient to exaggerate sections 10 times, that is, with a horizontal scale of 4800th, a vertical scale of th could be conveniently used to indicate variation of surface; special circumstances may, however, require any amount of exaggeration. For Parliamentary sections of proposed public works, two vertical sets of scales are fixed as the smallest allowed: the one is th, or 100 feet to an inch, in combination with a horizontal scale of not less than 20 chains to the inch, for longitudinal sections; the other,th, or 40 feet to an inch, combined with a horizontal scale of 5 chains to the inch, for cross sections showing alterations; but they may for convenience be used in combination with any horizontal scale used in the plan accompanying them. Engineers' working sections are drawn to larger vertical scales; and in natural sections taken at the sites of intended large works in masonry, iron, and timber, the scales used are still larger.

Instruments and Appliances used in Levelling.— Apart from the instruments and appliances used in preliminary surveying, and in the measurement of distances required for levelling (which have been already referred to in Chapter I.), the following are more specially used in the operations of levelling, or the measurement or determination of relative heights and depths.

Ist. For direct measurement of height or depth : the surveyor's chain and tape before mentioned, with plummet attached; sounding-cords or lead-lines for depths exceeding 100 feet; permanent and temporary tide-gauges and sounding-rods; graduated level-staves, and sliding vane-staves of various patterns.

2. Angular instruments: the sextant, clinometer, and theodolite.

3. Boning staves.

4. The water level.

5. Spirit-levelling instruments of various patterns. 6. Reflecting levels of various patterns.

7. The barometer.

8. The thermometer, or hypsometer.

Appliances for direct measurement should in the first place be correct to standard; failing that, all such various appliances as may be used in any one set of levelling operations should be correct by inter-comparison, so that one percentage of error alone may have to be applied; or at the worst, all discrepancies should be known.

The special appliances intended for soundings and subaqueous depths should be invariably kept for those purposes; for however convenient it may occasionally be to the surveyor to use his chain or the level-staff as a sounding-chain or sounding-rod, it must be remembered that he may thus rust the former or distort the latter.

In direct measurement of lofty heights, several chains may be used, firmly bound together, and the level-staff in addition; care should then be taken by those managing the upper end that it may not slip away, as its weight, directed by accidental bias, might cause severe injury to those below. Cords and tapes

being liable to stretch and shrink, require frequent verification. Wooden level-staves and vane-staves are liable to warping and distortion. Telescopic level-staves, though convenient for transport, are liable to stick, and thus become useless for a time; they are also liable to slide gradually this, when it occurs in the middle of a series of observations, and is unperceived by the staff-holder, may vitiate an unknown number of them. To guard against this contingency, the author has sometimes had a large-headed screw applied to the catch when the staff is extended, which retains it in position, and can be unscrewed on closing the staff. In very accurate levelling operations, telescopic staves should not be used: 10-foot staves, of equal breadth and thickness, with an arrangement for fixing one above another when required, are preferable, as errors are reduced, and the readings and graduations are more distinctly visible to a greater distance. Papered level-staves are seldom very correct, as the paper stretches on application to the staff; painted staves are to be preferred generally. But as surveyors like to use graduations and marks to which they are accustomed, and frequently keep their own level-papers and apply them themselves, the former thus possess advantages in this respect.

As to patterns for graduation of level-staves, they are exceedingly various. The following three patterns, for use in short, intermediate, or long sights respectively, were devised by the author in 1861, a few being then made for the Government of India. The angular figures are intended to enable the graduated bar-scale to be done away with, the middle of each figure being the exact point of reading for tenths of a foot, the angularities indicating hundredths.