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manageable motion. They reproach the instrument-maker's art as unchecked hydrophobia and cancer do that of medicine, or mercenary villany that of law, and should be supplanted by better practice.

9. Having thus completed the principal adjustments in their proper order, bring the telescope and its bubble-case as nearly vertical in the wye bearings as hand and eye can make them, and by reference to a plumb-line, or the corner of a well-built house, see if the vertical hair is out of true. If so, slightly loosen two opposite screws of the diaphragm, and correct the error by turning it. Try again the adjustment of the line of collimation before pinning up the wyes.

XI.

LEVELLING.

1. Suppose o he starting-point; 1, 2, 3, &c., the stakes of survey; and A the initial bench-mark. Wherever convenient the elevation of A above mean tide should be ascertained. It is to be regretted that this was not done from the outset,

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under statute provisions requiring maps and profiles also to be filed at the several State capitals. In that case, not only would much after labor and expense by way of duplicate surveys have been spared, but the older Commonwealths would now have in hand materials for the preparation of physiographical maps, the value of which to science, to the engineer, 2. For the purposes of a railroad-survey, however, such determination is not needful. Any elevation may be assumed for A, taking care only that it be large enough to avoid the possibility of having minus levels, which would be inconvenient. Zero of the datum should be below the lowest probable ground on the contemplated line.

3. Let the elevation of the initial bench-mark, A, in the figure, be taken at +200. Set the level at B, and suppose the rod on the B M to read 2.22. The “instrument height” then is 202.22. If the rod at sta. () reads 8.4, the elevation at that point is 202.22 — 8.4= 193.8. The rod being 1.9 at sta. 1, the elevation there is 202.2 - 1.9= 200.3. If desirable to turn at sta. 2, drive a pin nearly to the ground at that stake; suppose the rod on it to read 0.81. The elevation then is 202.22 – 0.81 = 201.41. Now move the instrument to C, and, sighting back to sta. 2, let the rod standing on the pin read 2.64. This makes the new “instrument height” at C=201.41, the height of sta. 2, + 2.64 = 204.05, and the elevations at 3, 4, 5, or other points observed from C are found by deducting the “rods” at those points from the ascertained instrument height at the new point of observation.

4. It thus appears how simple is the rule of levelling, namely: Find the “instrument height” by adding the “ backsight” to the elevation of the point upon which the rod stands for that purpose: from the “instrument height” thus found deduct the “foresights," severally, in order to find the elevations of the points at which such foresights are taken.

5. The foregoing example would appear in the field-book as follows:

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6. In levelling where great exactness is necessary, the rod at turning-points should be read to thousandths, and the reading

ing the target fast, it should be swayed slowly to and fro in the direction of the justrument to make suure of getting the full height. In foul weather the rodman should take care that the foot of the rod does not ball up with mud or snow. The leveller should have his cross-hairs free from parallax, the target in focus, and see his bubble true at the moment of observation. He should also set the instrument about half-way between turning-points when practicable, balancing largely unequal sights by subsequent ones similarly unequal in the opposite direction; and liis turning-points, even on favorable ground. ought not to be more than 600 or 800 feet asunder.

7. On ordinary railroad field work such nicety as is implied in most of these rules is not required. To read to the nearest tenth is sufficient, especially where the progress of the party depends in a good degree on ihe level; as, for example, in running grade lines on preliminary survey. The location levels are usually carried along more carefully; but even then the writer's practice has been to turn to hundredths only.

8. The Philadelphia Rod is the lest for our service. The sliding halves are unconnected except by brass sleeves or clips, which guide them, and are therefore not liable to bind in wet weather. They are made by William J. Young's Sons, who some years ago, at the writer's suggestion, supplied what seemed to be their only defect by adopting rivets for fastening the clips instead of wood screws: the screws had a tendency to work loose in the field, and cause the parts to chafe or jam. These rods are clearly figured, so as to be legible at a distance of several hundred feet; the leveller is thus enabled to take intermediate elevations rapidly, and, when necessary, to do his work with the aid of an wulettered rodman.

9. CORRECTION FOR THE EARTH'S CURVATURE AND REFRAC

TION.

The correction for a 100-feet “station” is .000215; for one mile, 0.6.

It is to be added to the calculated elevation of the point observed, or to be deducted from the “rod” before calculating the elevation, in the case of a long unbalanced sight. It varies as the square of the distance. Calling the required correction A, for any given distance D, then A .000215 X D ? if D is in “stations,” and A= 0.6 X D 2 if D .0215; for 50 stations, 0.5375; for 10 miles, 60 feet, and a spire or treetop apparently level with the instrument at that distance would really be 60 feet above it. Transposing the equation we have D=VA=0.6. In this forin it is applicable to the determination of distances at sea. The Peak of Teneriffe, for example, 16,000 feet high, should be just visible from the sea-level at a distance=V 10000 =-0.6= say 163 miles.

10. TO FIND DIFFERENCES IN ELEVATION BY MEANS OF TIIE

BAROMETER. Call the required difference D; the barometrical reading at the lower stand, L; that at the upper stand, U.

Then, D=((L-U): (L+U) | X 55000.

Example.

L=26.64; U=20.82.
Then, L-U= 5.82

L+U=47.46

0.1226

log. 0.764923

log. 1.676328 Diff. -1.088595

And 0.1226 X 55000=6743, the required difference of elevation in feet.

11. A closer approximation is thought to be attainable by using a thermometer in connection with the mercurial barometer. In that case, having found the difference as above, add ało of the result for each degree by which the mean temperaîure of the air at the two stands exceeds 55°; subtract the like proportion if the mean temperature be below 550. When the upper thermometer reads highest, for “subtract”

say “add,” and vice versa in the foregoing rule.

12. The naked formula, however, will usually be sufficient for the engineer. He can prescribe gradients by it for surveys, which shall develop the ground to be occupied, and can decide between summits well differenced in height. If not so differerced, questions of (letour, of approaches, and the like, will contribute to determine the expediency of making an instrumental examination.

13. HEIGHTS BY THE THERMOMETER. T= the difference, in degrees Fahrenheit, between 212°, the temperature of boiling water at the sea level, and that at the

II

the height of place of observation above or below the sea in feet.

H=513 T + T2.

Example.
T= 2120 - 2080 = 4o.
H= (513 X 4) + 4 = 2068 feet.

XII.

SETTING SLOPE STAKES.

1. Like swallowing, this is more easily done than described. To no detail of field service does the proverb more fitly apply, that “work makes the workman."

2. The problem is, to find where a formation slope of given inclination, beginning at the side of the road-bed, must needs intersect the ground surface. Formation slopes are usually stated in parts horizontal to one part vertical. Thus a slope of 45° is “1 to 1.” A slope of “2 to 1” has a horizontal reach of two feet to each foot vertical. The carriages of a stairway with twelve-inch treads and eight-inch risers would have a slope of “1} to 1."

3. To fix the point where any proposed formation slope must meet the surface on level ground, is quite simple; the distance from the centre line being obviously made up of half the width of road-bed added to the horizontal distance due from the slope, to the depth of cut or height of fill. Thus, with 20 feet road-bed, 9 feet cut, and slope of 14 to 1, the distance out would be 10 + 9 + 41 231 feet, as shown in the annexed diagram.

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4. On slant or broken ground, the solution is more difficult: recourse must then be had to the level, with a rodman, a tape

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