192

Summary of sources of Error.

1. Unsteadiness of the stand, and dislevelment by wind or accidental motion.

2. Looseness of any attachment of the instrument; or of any screw not firmly set.

3. Settlement of the stand in the soil, or settlement of any part of the instrument.

4. Dislevelment by the sun, from unequal expansion during reading the sight.

5. Want of instrumental adjustment :

A. Focus error, or parallax.

B. Collimation error.

C. Level error.

6. Want of correction for curvature of the earth.
7. Result of atmospheric effect on the visual ray :
A. Refraction under the varying conditions.
B. Reflex refractive action.

c. Apparent depression of the distant point.
8. In connection with the level-staves:

A. Unequal, or unequally graduated staves.
B. Want of verticality.

c. Lateral and vertical motion at changing
points.

9. Inexactitude of datum or bench-mark used.

10. Personal errors:

A. In instrumental manipulation.

B. In bubble-reading.

c. In staff-reading.

D. From visual defect.

E. Simple mistakes from misconception.

Corresponding Remedies.

1. A heavy firm stand, permanently attached to the lower part of the instrument.

2. A well-made instrument; a thorough knowledge of it, its peculiarities and defects; care in removing and transporting it; repeated careful examination from time to time.

3. To invariably examine the bubble after reading on the staff. The bridge-reflector fails to be of much use for this purpose, as the length of the bubble is always varying. Piazzi Smyth's reflected bubble would guard against this.

4. Cover up the instrument when not in use. Set up the instrument alternately one way to the sun and the other.

5. Keep all in good adjustment. Have an arrangement for focussing the eye-lens as well as the objectlens.

6. Allow for curvature.

7. Note barometer and thermometer, and use a refraction table.

8. Use plummets; use discs or tiles; compare staves thoroughly; and employ good men as staff-holders.

9. Use three or four bench-marks for reference. 10. These are mostly unavoidable, although some may be reduced on noticing the cause of error.

General Remarks.

The system of equidistant sights should be adhered to as much as possible in long lines of levels: it eliminates errors due to curvature and constant refrac

tion, also any collimation error, and, if the bubble is brought into the centre of the run at each sight, the level error also. The error due to the earth's curvature and mean refraction is almost inappreciable in hundredths of a foot in sights less than 650 feet: it is hence better not to exceed this distance in ordinary work. See page 162.

It is absolutely necessary always to attend to parallax, that is, the object viewed should be in focus, and not appear to move when the eye is moved from side to side; observations should also be always made with the middle of the horizontal wire, which by the way is not always exactly horizontal. It is not strictly necessary to bring the bubble to the centre of the run; instead of this, the position of the bubble-ends may be read, and the correction applied from a small subtense table made for the instrument and its scale.

As measurements are sometimes on sloping ground, a small table for reduction of distances to their true horizontal value should be inserted in the level-book. As to level-books, their patterns are endless: the collimation form of record, explained on page 171 has several advantages; the results are so placed that they catch. the eye, independently of the side-work, and the reduced levels can be easily kept up while going along in the field. It is best to have a level-book that will go in the pocket, 7" x 4", and to have all its pages divided into little squares by ruling in pencil colour, pale grey; if these divisions are 100 to a foot, it makes it useful for sketches to scale; it also serves for tabular memoranda. These squares, any number of which can be marked off into a column-breadth, allow any number of columns to be made to suit any form.

No important levelling should be done when the wind is very high, nor when the air is so hot that the divisions on the staves seem to dance, and the bubble is so short that its motion is a comparatively useless indication; nor in very severe cold, when the fingers are stiff, benumbed, and incapable. A waterproof cloth should always be at hand to throw over the level in case of rain, which ruins an instrument; dust should be daily wiped off gently; screws occasionally washed in vinegar, well dried, and wiped with a clean oiled rag; staves should be wiped dry after being much wetted, laid horizontally to prevent warping, and occasionally compared with a standard length. Bench-marks should be made at distances of one or two furlongs on permanent objects; they can be painted (a bottle of red paint and a brush is easily carried) at the time, and chisel-marked afterwards. Permanent setting-out pegs should be two feet long and two inches square, distinct from survey pegs, which may be round. On recommencing work, always check over the last two pegs. Be careful that the pegs are always flush with the ground, especially in India, where simple-minded natives will cook their dinners with the marks of many miles' work, if they can find them.

As to the amount of accuracy with which levelling operations can be done with an ordinary set of instruments and appliances, and with ordinary chainmen, it is impossible to speak exactly; many and wild accounts of accurate levelling for long distances—100 and even 200 miles without any error, or next to none-have been frequently heard, though not often believed. Excessive good fortune may have occasionally produced such things in connection with good management, but not often; nor is the substantiation of this point so im

portant as at first appears. The best plan is to determine beforehand the maximum amount of error that will not affect, to any important degree, the object for which the levelling is done, and then working with ordinary care and precaution to make the error less than that for certain. Regularity of result or evenness of error is perhaps of more importance than being occasionally wonderfully correct; this is generally obtained by steady systematic persons, who thoroughly study the particular instrument they use and its defects, who keep to this one instrument, and one set of appliances, and have a set of chainmen whose habits are known, and on whom they can depend as far as small matters are concerned.

As to the amount of work that can be done by one observer in one day. This is a point over which endless difficulties have been made, and which will never be settled; levelling being of different sorts and for different purposes, and involving generally many things besides getting over the ground to ascertain the level of a single distant point. But when this latter is the sole object, a wonderful speed may be attained by an observer having instruments and appliances that he has often used, having excellent chainmen that are willing to run hard all day with the staves, etc., a long stretch of unbroken flat ground, and a powerful telescope. Results obtained this way cannot, however, be taken as a basis of amount for ordinary work; and hurrying observers is not an advisable proceeding under any circumstances.