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portant object: in the latter case the sketching may be aided by measurements.

As all such work must be done on the spot, and generally also in pieces, tracings of the original survey-plan must be used, and the resulting work transferred back on to the original. The finished work being of value in accordance with its accuracy, the latter must be vouched for by inscribing in figures on the plan the level of every point that has been actually observed. See Plate VIII. Hill-sketching.--Such work very much resembles the interpolation of contours just described; the difference being that the intermediate contours are very numerous, and are simply sketched in without the aid of level or measurement, while the principal contours are very few, far between, and roughly determined.

Hill Reconnaissances. In this work even principal contours are dispensed with; a few detached levels of principal points, peaks and passes, etc. are given, and the general form of the ground is shown on the plan by hill-shading, or a close-hatching of broken contour-lines sketched on the spot-the utility of this work is confined to representing the extent of the hilly ground, and giving some notion of the comparative steepness of the hill-sides. It is suited to rough surveys in unexplored countries, and to military purposes.

Section 4.

SOURCES OF ERROR IN LEVELLING
OPERATIONS.

The foregoing explanation is intended to apply to ordinary levelling in the ordinary practice of the surveyor, most of which is carried out with the 14-inch or 16-inch Gravatt level. When a higher amount of accu

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racy is necessary, as for instance on canals having a fall of only four inches per mile, it becomes necessary to use an 18-inch level, and besides to guard against all possible sources of error-at least such is the author's opinion, forced on him by experience in 1869; others may prefer to persevere in their ordinary practice, and make up for deficiencies by solemn asseverations of wonderful results.

In order to guard against all possible sources of error, these must be investigated, and always kept in view.

During a careful examination of this subject,, it occurred to the author that the levelling operations of the Indian Trigonometrical Survey might, as well as those of others, throw considerable light on this subject; he consequently extracted the following notes from their reports, as well as the account of the instruments used by them and the errors they acknowledge, and followed up the same by a list of errors to be guarded against in very accurate canal-levelling, and their corresponding remedies. The whole was published in the Appendix to the author's Curve-Book, dated Calcutta, March 25, 1870, a copy of which was forwarded to the Library of the Institution of Civil Engineers in London. The matter referred to is here reprinted :

In adding this to the Curve-Book, it is necessary to mention that it is from no love of intense exactitude, nor with any hope that it can be obtained, or wish that it should be attempted; but it is important, as in the case of angular observations and their errors treated in the first chapter, that all sources of error should be known, and hence also the means of avoiding them to a certain extent understood; and that a guide to the

ordinary limits of error, both in angular and in levelling observations, should be forthcoming to the engineer or the surveyor, whenever he thinks fit to refer to it.

Neither in angular observations nor in levelling does the railway engineer or even the canal-engineer use very exact instruments: the more exact instruments of both these classes are the altitude and azimuth instrument of the astronomer, and large theodolites of the Great Trigonometrical Surveyor, and the levelling instruments and appliances used in determining heights by the Great Trigonometrical Survey Department. From the former the principles of correction for angular error have been taken and applied to the surveying engineer's wants; from the latter, and their system, we can judge in what respect and to what amount the ordinary results of levelling of the engineer are deficient.

General sources of Error thus indicated.

Ist. When a series of levelling operations are united in a circuit, or when the same ground is levelled by successive parties, the lengths of the staves are sometimes found to vary, sometimes as much as '05 of a foot in a 10-foot staff; thus eventually causing discrepancy of height. The discrepancies of height thus due to dif ferences of unit should be corrected, the corrections being made proportional to the height actually measured by the staves whose units are incorrect; such discrepancies being treated distinct from those due to cumulative or accidental error, which again should have their corrections distributed over each station of the line of levels in proportion to its distance from the station

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of junction with the absolutely correct or accepted starting level.

2nd. In continuing to level, along a long line that is really level, the further end constantly appears from the observation to be the lower end, and the amount of this depression appears to increase with the distance, the result of one's work showing the distant point to be always lower than it actually is. The difference arising from this cause is never considerable, but is always in the same direction, and in the same series of operations is greater in proportion as the distance levelled is greater. The causes of this error are as yet unassignable, as they take place in an instrument shaded from the sun, and on hard ground as well as on soft, where sinking might take place in the interval between observation of the back and fore staves. There are probably several causes of different sorts which are minute and variable, and again sometimes accumulate rather than cancel. The only way to eliminate this error to a certain extent is to level the whole line twice over in opposite directions, and accept the mean of both results.

The following amounts of error due to this cause are recorded, and are useful to show in what distance this error is serious when the instruments and appliances are of a very perfect description.

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It is probable that the greater error in the levels by Mr. Bunt on behalf of the British Association were due to his using only one staff, and that a vane-staff.

3rd. The dislevelling effect of the sun's action, which tends to raise the end of the telescope towards itself, and to depress the opposite end. The amount of this was proved by the surveyors of the Indian Great Trigonometrical Survey by adding together algebraically the respective level-corrections of each instrument for a whole season, when the negative corrections were found to predominate in every section worked from south to north, and the positive corrections in the opposite sections. Their amounts, when referred to a common origin, were as follows at the end of 310 miles :

No. 2 Level Interchanged between

No. 4
No. 3

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J1.51 feet.

two of the observers 1.60 feet. used by the same observer 3:55 feet.

All three instruments were always carefully shaded from the sun by large umbrellas while set up for observation, and by blankets over their boxes while being carried. Being all of the same pattern, they were pro

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