5. Recording results in such a form and manner that a draughtsman may utilise the results without doubt or difficulty.

6. Astronomical observations for determining time, latitudes, longitudes, and azimuths.

The various means and appliances used in direct and angular measurement on surveys will be mentioned in the two next sections, the special principles involved in their construction and use, the limits of their application, and the preferable methods of manipulation and adjustment, occasionally entered into in detail; the corrections to be applied to results of instrumental observation, under various special conditions will also be fully explained and deduced; but definitions of terms, descriptions of easily visible instruments and appliances, and practical directions for commonplace manipulation, have generally been excluded from this work as unnecessary.

The two following sections will treat of the selection and demarcation of survey-points and lines in the field, and give a collection of formulæ commonly used in survey calculations; the less frequent or more special formulæ will be found attached to their appropriate subject or instrument. The subject of astronomical observations, the adjustments and corrections to be applied to the Transit instrument, and the necessary formulæ for all such purposes, are included in the Part devoted to Route-Surveys. The ordinary forms and modes of recording survey operations are fully exemplified in a series of practical field-records suited to surveys of every sort, which are collected at the end of the book, though their corresponding sketches or reduced plans are interspersed with the text bearing on the subject.

The modes of procedure and methods of operation adopted in surveying with various instruments are described in Chapter II.

Section 2. INSTRUMENTS FOR MEASURING DISTANCE.

The instruments and appliances most generally used in measurement of distance, also sometimes for height and depth, are the following:

1. Steel or iron chains of various patterns, plain, painted, or galvanized, used for all purposes.

2. Wooden rods or bars, now mostly used only in short distances, as offset staves or foot-rules, or in short measurements of height and depth, as graduated level staves, and vane staves.

3. Continuous steel tapes, and Woven tapes strengthened with wire, or otherwise.

4. Wheel pedometers.

5. Pacing, with or without the aid of passometers. 6. Direct telemeters for observation, with or without the aid of micrometers, on staves of known length whether graduated or otherwise.

7. Reflecting telemeters for observation to any fixed points, dependent on the length of the instrument as a base of triangulation.

1. The steel chain is the ordinary appliance of the surveyor for measuring long distances and for setting out on works of engineering. In large District Surveys the 100-feet chain is most convenient, more especially for measuring base lines; it also conduces to the advantage of keeping distances as well as heights in feet; in such work where accurate measurement is necessary,

the chain may be supported on planks or courses of brick, and in hot climates thermometrical observation is also necessary to enable some allowance to be made for expansion. In Parish Surveys the 66-feet chain, subdivided into 100 links, is used, as it is more easily handled by two men, and more convenient for calculating acreage; also in Railway Surveys, where miles and furlongs are sometimes obligatory under the Standing Orders of the Houses of Parliament, from its convenience in being the 80th part of a mile in length. In other surveys where these latter points are not of consequence the 50 feet chain is to be preferred.

Ordinary chain-measurement is generally far from being so exact as is usually imagined. Although the chain itself may be originally of correct standard length, and compared daily with some temporary standard marked on a building, or kerb-edge of a footway, or checked by comparison with level staves, and straightened or shortened as required; yet, even with chainmen practised in keeping the chain straight and level, putting the pins plumb, and holding the ends of the chain true to them, Mr. William Burt found the average error was th, and sometimes as much as th on using two sets of chainmen; though it was onlyth on using the same set of chainmen and same appliances at about the same time. (See Key to the Solar Compass, page 35.) In ordinary practice the amount of error must comparatively be higher, for inferior careless chainmen, as among men of every description, are the rule and not the exception; while in foreign countries there are additional natural difficulties with them; the surveyor himself, who attends to the recording, and perhaps to instrumental

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and other work also, cannot, after the first few starting chain-lengths, personally attend to all the minutia of the chaining, or see that each end of every chain, and its whole length, is correctly placed; he is hence dependent on his chainmen to a very great extent, and this must cause in addition to the above a high percentage of error, unless carefully guarded against. It is much to be wished that telemetrical observation should take the place of the greater part of the chain measurement in long distances, which is both laborious and rather uncertain, even when unaccompanied by hurry. In setting out, chaining cannot be dispensed with, it is true; but in ordinary surveys the only difficulty seems to be the expense and weight of an instrument. For soundings less than 100 feet the chain with a weight attached is generally used; there is however the liability to rust if it is not galvanised. Chains are marked with brass distinctive appendages at every 10 links or 10 feet, most frequently giving numbers 1, 2, 3, 4, from each end up to the middle where there is a round brass; this method of marking is liable to produce error: it is better never to let the same mark recur, but to number it from the beginning to the end with distinctive tallies. A description of the method to be adopted in ordinary chaining will be given in the paragraph on Chain-Surveys. For very special cases, where extreme exactitude in the measurement of a base line may happen to be necessary, a standard steel-chain, having a known rate of expansion for temperature, should be used, and the method formerly adopted in the Great Trigonometrical Survey, before compensating bars were used, imitated with more or less fidelity. In that practice the chain was

100 feet long, and consisted of 40 links, each half an inch square; it was kept constantly strained with a 56-lb. weight, and laid in coffers supported by trestles; at each chain's length a post, carrying a scale moved by a screw, was set up to obtain an exact mark from which to measure after removal of the chain onwards; thermometers were also used to ascertain the temperature of the chain during the work.

2. Wooden rods or bars were at one time used in the Great Trigonometrical Survey for base-measurement, and were also much used in ordinary surveying in measuring long distances; but as they expand or contract with damp, which renders them objectionable, and are cumbersome to manage, they are now superseded by the chain, except in cases where a chain cannot be readily obtained. The offset staff, having feet or links marked on it alternately painted black and white up to 6 feet or 10 links, used for measuring short offsets, is a useful remnant of this system. The level staff, with its various patterns, will be described in the chapter on levelling; it is a wooden staff painted and graduated to feet, tenths and hundredths, generally used either for giving heights or depths direct, or by observation on it with the horizontal wire of a levelled telescope; distances may also be obtained by its aid by observing on it with two fixed horizontal wires in a level-telescope, thus getting two readings, the difference between which is a measure of the distance. By exact setting of the wires the ratio may be made convenient for a rapid calculation of the required distance from the intercepted height, as, a chain to a foot, or 100 feet to a foot.

3. Tapes. The steel tape being continuous is slightly more accurate than the common land-chain,