little practice, and one great advantage of it is that the area of the cross sections and cubic contents of earthwork may be calculated from the figures in Fig. 238 without plotting the cross sections. The areas and cubic contents of earthwork are usually entered in special columns on the opposite page of the cross-section book, which page is reserved for that purpose. To calculate the area of the cross section shown in Fig. 237 and booked in Fig. 238, proceed as follows:-The area of the trapezium abgh is the mean of the depths ah and bg multiplied by gh, i.e., 1⁄2 (1.00 + 1.50) × 1.20 = 1.50. Similarly the area of bcfg is the mean of the depths bg and cf or (1.50 +0.90) multiplied by fg, i.e., § (1.50 +0.90) × 2.15. The distance gh is 1.20 as indicated by the denominator of the first fraction to the left, Fig. 238, and the distance fg hf-hg=3.35-1.20 = 2.15, or the difference between the denominators of the two fractions to the left of the central column, Fig. 238. It now remains to deduct the triangle fxc, of which the area is (1.35 × 0.90). The area of the left hand part of the cross section is therefore (1.00 +1.50) x 1.20+ (1.50 +0.90) x 2.15 (1.35 × 0.90) = 3.47 superficial metres.

The other half of the cross section is treated similarly, and the total result is the area of the whole cross section.

Cubic contents are then got by adding up the superficial areas of the cross sections and multiplying by the common distance apart of the cross sections in the usual manner. Thus there is no necessity for any plotting, and as the quantities are calculated from the actual levels and measurements taken in the field, errors of plotting and scaling for the areas are obviated. With a little practice both the field work of cross sectioning and the calculation of the areas is very rapid.

II. Surveys of a Limited Area of Country.-As a rule all survey work of very large areas is conducted by Government, the primary triangulation of the country being taken as the basis of the work. The surveyor may, however, in his private capacity be called upon to make surveys of considerable area abroad for private individuals, syndicates, or companies. In this chapter we shall confine ourselves to surveys of moderate extent, reserving for Chapter XII. larger surveys necessitating triangulation from an accurately measured base.

Methods to be Adopted.-After making a careful examina

tion of the ground, in most cases the surveyor will decide to run a traverse round the boundaries of the property. At convenient points on this traverse he will leave marks from which to run lines throughout the interior, which he will divide up into well-conditioned triangles, the most convenient for picking up all interior detail. From these interior lines and subsidiary chain lines he will survey all the details of the property. The traverse round the boundary will form the basis of the work, and all other lines will "check in" upon it. Whether or not a complete traverse is first made round the whole property, or whether it is divided up by smaller traverses partly along the boundaries and partly through the interior, will be decided by the circumstances and local conditions of each individual case. In other cases it may be found better to project lines right through the property as bases from which to survey the ground. Tacheometry or stadia work is much used for the details or topography of surveys abroad (see Chapter VI.). In any case the main principles to be observed. are precisely those set forth in Chapters I., II., III. The essential difference is that the bearings must be referred by astronomical observations to true north, and thus checked and corrected about every mile, as already explained for a long line of communication, while the chaining must be executed with the greatest care and every allowance made.

Steel Tape Measurements.*-As regards chaining, the steel band will be found the best to use, and it may be from 1 chain to 10 chains in length, according to the character of the country. On sloping ground more accuracy is attained by measuring on the slope and reducing to horizontal distance by calculation. When the range of temperature is considerable, allowance must be made. In the colony of Victoria, Australia, for instance, the measurement of a line 1 mile long measured with a steel band 66 ft. long in winter may vary nearly 5 links from the measurement of the same line with the same band in summer, from the effect of change of temperature only. The increase of length of a steel band per degree Fahr. is 0.000006886 ft. per foot of steel band. Thus for a 66 ft. steel band the increase of length is 0.000006886 × 66 ft. per degree Fahr. Error due to unequal tensile strain on the steel band should be provided against.

* See also page 443.

The extension in 1 mile with a 66 ft. steel band having an effective sectional area × 16 in. is 0.667 link when a stress of 30 lbs. is used, and the extension will vary with the stress put upon the steel band, which should therefore be uniform. This is effected by means of a spring attachment to indicate the pull on the chain. When measurements are made on inclined ground by "stepping" and holding up the chain, an error of considerable amount is introduced. "A steel tape weighing 6 lbs., used with a tensile

stress of 30 lbs., will give an error of 13.44 links per mile due to 'sagging' or curvature of the tape."

In practice, of course, some of the errors in chaining counterbalance and neutralise each other to a greater or less extent.

As a survey of this kind must close in on its starting point, great care must be taken with the chaining and all sources of error as above guarded against. In a long line of communication such as a railway, there is no necessity to close in to a nicety on any given point, neither does the line return to its starting point as

in a survey of an area of country whose exact superficial area is required. The chaining, therefore, on a railway survey need not be conducted with excessive care. See Chapter XII. for accurate steel tape measurements.

Example of Survey.-Fig. 239* is an example of a survey of 320 acres in the heart of steep, scrubby, and heavily timbered ranges in Australia. The survey was made with a Cooke's 5 in. theodolite and a 66 ft. steel band. The check line kl which was projected through it showed the "closing error" to have been 30" in angle and o.1 link in linear measurement. This great accuracy was no doubt due to errors of chaining and angular measurement counterbalancing each other. The following is the calculation of the latitudes and departures or northings, southings, eastings, and westings of the survey, and also of the check.

2 639.72503

A 319.86251

R

3.45004

Р

18.00160

6070 6070.0 7707.9 7707. I

The area is calculated from the latitudes and departures as described in Chapter II.

Area, 319 acres 3 roods 18 poles.

Note. The bearings marked on Fig. 239 are measured from o° round to 180°. The bearings recorded above are measured from N. to 90° E. and W., and from S. to 90° E. and W., this being more convenient for calculation as it is the sines and cosines of these bearings which are used to calculate the latitudes and departures.

* Minutes of Proceedings Inst. C. E., vol. xcv., "The Practice of Surveying in the Australasian Colonies." By S. K. Vickery, Assoc. M. Inst. C.E.

The original traverse consisted of the distances and bearings abcdefgha. The check was made by measuring the distance ak, distance and bearing kl, and distance f, the remaining distances and bearings fg, gh, and ha being taken from the record of the original traverse. The angle at a was measured and compared with the difference between the original bearings of ha and ab, which gave the "closing error" in angle.

Regulations of the Victoria Survey Department, Australia. The regulations of the Victoria Survey Department are that the dimensions furnished on the plan must close geometrically, i.e., they must have been adjusted to do so as described in Chapter II., and the maximum difference between the plan and the actual field measurements is not to exceed 2' in arc or the tangential equivalent on the length of any line. Chaining by stepping is allowed, but when the slope exceeds 5° it is recommended that the angle of slope should be measured on the vertical arc of the theodolite and the distance measured on the slope and reduced to its horizontal projection.

With a 5 in. or 6 in. theodolite and a steel band the above limits of error may be easily complied with.

Surveying Regulations in the Australian Colonies. In the Australian Colonies almost every branch of the civil engineer's profession is practised directly under the control of the State, and more especially those branches in which surveying plays an important part.

Surveys under the control of the Departments of Lands and