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and renders the smallest divisions on the staff distinct to be read at a moderate distance. Every distinct part of this level has a distinct means of adjustment.
The adjustments of this instrument may be examined and rectified in the same manner as described for Troughton's level, but much more correctly as described by Mr. Gravett himself.
The geometrical demonstration of this adjustment may be of some use to the student, and as I have not met with it as yet in any work, I will give it here.
To correct the line of collimation. On a level piece of ground drive in three stakes, at two chains from each other, (Fig. 19,) as at A, B, D. Now place the instrument half way between the stakes A and B as at n, and read the staff placed on the stakes A and B, their differenee will give BQ (having A Q a horizontal line.) Again, place the instrument in the middle between the stakes D and B as at C, read off the staff B and also the staff placed on D; take their difference and you get the true difference of the level between B and D, this added to BQ will give DR. Now it has been proved this to be the case whether the instrument is in perfect adjustment or not.
Again, place the instrument at any short distance beyond D, as at H; bring the bubble to the centre of the tube, get a reading from each of the stakes, D, B, A. Now if the line sight goes parallel to the horizonal line A Q, Pr suppose, the cut Ar will be the cuts from B and D move BQ and D R. But if the line of sight takes any other position as P K, take the cut R z from both Q s and A K and if the line of collimation be correct the difference Ky will 2 the difference st.; but if not, alter the screws which adjusts the horizontal wire, until such be the case; and the instrument will be adjusted for collimation.
To adjust the spirit-level, without removing the instrù
Adjust the instrument by means of the parallel platescrews, until you read Ar, Qv, and Ro=. Now, by the screws attached to the bubble-tube, bring the bubble to the centre of its tube.
The next adjustment is that which makes the spirit-bubble preserve its position in the centre of its run, while the instrument is turned round; this is done by correcting half the error by the screws which attach the telescope to the bar, and the other half by the parallel plate-screws. The instrument will now be in complete practical adjustment.
Among the advantages, as peculiar to this instrument, is a cross level, placed at right angles to the principal level; which affords very great facility in setting up the instrument, and adjusting it for observation.
The operation of collimating, when once performed upon this instrument, will scarcely ever need being repeated: unless to correct the horizontal wire from time to time. Almost all levels have a compass box and needle.
The wire-plate in all levels, are generally furnished with three threads, two of them vertical, between which the station staff may be seen; and the third is placed horizontally, by which the observation is made.
There are many descriptions of staves for levelling; sometimes divided into feet and inches, and sometimes into feet and decimals of a foot. Length generally from 12 to 21 feet; which consists of three sliding pieces, graduated on the face, with a sliding vane.
Mr. Gravett, the inventor of the Dumpy Level, has invented a staff graduated into feet, tenths, and hundredths; and can be read distinctly at any distance not exceeding ten chains. This staff requires no vane this staff is composed of three pieces, or slides, to draw out
like a telescope, a spring catch retaining each joint in its place.
Mr. Gregory, C. E., has contrived a staff, obviating the objections to some others. It consists of two pieces, which are joined by a peculiar sort of a hinge, not very unlike a carpenter's rule: when closed, the gratuated face is concealed, and ... protected from injury: when unfolded, its face presents one uniform surface, which makes it as easy to read the smallest division at the bending joint as at any other part of the staff, which is not the case when the graduated face is not in the same plane. As one part do not slide in a groove within another, like others, it is of uniform strength. It turns round freely upon an iron plate attached to its lower end. The assistant holds it upright by means of a plumb, which is inserted in its side. If the figures on the staves are turned upside down, so that when viewed through the telescope they may appear upright, by this contrivance they may be read as if the telescope did not invert the object at all; this is, however, a matter of little consequence, as after a little practice, the figures can be as easily read in one position as another.
Rectangular staff and a small circular vane, attached to it, which can be moved from end to end. This vane will be moved up or down to meet the height of the apparent level.
The vane is divided into 4 = parts, by two straight lines, cutting each other at right angles. Two opposite parts of the face are painted white, and the other two black; thus they are easily distinguished. A screw is used to clamp the vane in any position required.
This staff is composed of two bars, about five or six feet long, placed side by side. They are so connected that one,
which is about 2 inches shorter than the other, may be made to slide along the other, and thus increase the whole length.
ON LEVELLING OPERATIONS.-IN THE FIELD.
Having explained the instruments employed in levelling operations, we shall next give an example to illustrate their
Let it be required to find the difference of level between the points A and B, (Fig. 20.)
Set up the level at H, and the staff at A; level the instrument, and direct the telescope to the staff at A; read the division on the staff as at m; (having Km the line of sight,) write this number in the column, headed B. sight. This number we will suppose to be 5. 40 feet. Next set up the staff at C and read off the cut c g, which cut you will write in the column headed F. sights. The height shown on this staff we shall suppose 3. 24 feet. The dif ference between the points A and C is evidently 2. 16 feet, which shows that there is a rise from A to C, of 2. 16 feet. Again, set up the staff at D, note the reading as Dh, put the last cut 3. 24 in the column of B. sights; and Dh which we shall suppose to be 3. 90 feet, in the column of F. sights. The difference between C and D is evidently 0.66 feet this last difference taken from 2. 16 feet, gives 1. 50 feet Df, the reduced level at the point D. Hence it appears that when the back sight exceeds the fore sight, there is a rise, so far, by the difference of both cuts: but when the back sight is less than the fore sight, there is a
fall, by their difference. Again, take the last cut 3. 90 feet to the column of B. sights; and put up the staff at the point T, and turn the telescope to cut said staff in the point C, which you read, as before, and write in the column of F. sights. This height we will suppose to be 4. 60 feet: the difference between the points D and T is 0. 70 feet, which is a fall. Take this from the last reduced level Df = 1. 50 feet, and you get 0. 80 feet for te; which is the reduced level at the point t. Again, take the last cut into the column of back sights; and set up the pole at the point E, read off the cut as E P, note this reading in the column of F. sights. Let us suppose this to be 8. 10 feet; the last cut from this gives a fall of 3. 50 feet, the fall from T to E. Take 0. 80 from. 3 50 and you get 2. 70 feet, the reduced level at the point E. It is evident this last reduced level is a depression, below the horizontal line A B. If you wish to find the point O, where the horizontal line cuts the surface. Say as the fall at E. is to the filling Ex, so is the distance T E to E O.
Next remove the spirit-level from H to R, the assistant remaining at E, who turns the face of the staff round, without moving it off the ground. Level the instrument as before, direct it along the line of sight towards Q, note the reading in the column of B. sights. Let us suppose this to be 7.02 feet: remove the staff to the point F; then
rning the telescope about, you intersect the staff in the point S, and note the reading in the column of F. sights. Let us suppose this to be, 1. 70 feet: the difference be
tween the points E and F is 5. 32 feet rise, which taken from Q E-Ex is BF = 5. 32-2.70 = 2. 62 feet the rise at F. Now it is evident that the difference, 2. 62 feet, shows the amount of raise from A to F; which may be found otherwise, by adding all the back sights together, and also all the fore sights, and the difference of these