Fig. 113.—Calder stove used as a lamp.
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294.—Lamp.—At heights between hills in wide valleys check levels may be taken from five to ten miles very well with a good 14-inch level in still clear weather in dark nights by the use of an oil lamp. Coincident points above datum being selected, the lamp is set upon the ground, or at a measured height at a calculated point, or raised or lowered to lantern signals, allowance being made for curvature and refraction. The wide band of light is read very easily by shifting the observer's position and raising or lowering his tripod. The "Calder" lamp stove answers very well as a lamp. It has a wick about 3½ inches wide, and by means of a masked chimney may be made to present a clear white line of light of 1 inch in depth, Fig. 113.
The heliostat is sometimes used for check levelling in sunlight. This will be described further on with the theodolite.
295.—Curvature Corrections of the earth and of Refraction to be made use of occasionally for check levelling. The rule for finding curvature is "That the difference between true and apparent level is equal to the square of the distance between two places or stations in miles—divided by the earth's mean diameter, 7916 miles"; consequently, by this rule the correction is always proportional to the squares of the distances. By proportioning the excesses of height to the squares of the distances, we may obtain a curvature table for corrections. This is, however, always in excess of the true curvature by the refraction caused by the increase of density of the air towards the earth's surface, which bends the visual ray. The curvature of the earth may be corrected for refraction one-fifth to one-sixth,[12] which varies according to the atmospheric pressure.
296.—The following table, which takes curvature minus refraction, will be found useful to have at hand: it may be written out and pasted inside the lid of the level case:—
| Distances in Chains. | Curvature minus Refraction in Dec. Ft. | Distances in Chains. | Curvature minus Refraction in Dec. Ft. |
|---|---|---|---|
| 1 | ·000089 | 14 | ·0175 |
| 2 | ·000358 | 17 | ·0258 |
| 3 | ·000804 | 20 | ·0357 |
| 4 | ·001435 | 22 | ·05 |
| 5 | ·002233 | 24 | ·06 |
| 6 | ·003216 | 26 | ·07 |
| 7 | ·00437 | 28 | ·08 |
| 8 | ·0057 | 30 | ·09 |
| 9 | ·0072 | 40 | ·14 |
| 10 | ·089 | 60 | ·31 |
| 11 | ·011 | 80 | ·56 |
Where great precision in levelling is required, as for important trigonometrical surveys, many precautions are required to be taken which would be quite superfluous, for instance, in railway work. Thus much greater exactness and freedom from personal error is secured by having two levellers to go over the same ground simultaneously. Errors by two persons in the same part of the track are very unlikely to occur, and by comparing books every part may be checked.