SURVEYING, AND RECONNOITRING.
HEIGHTS, AND DISTANCES.
The accurate determination of heights, and distances of objects being required in various military operations, especially for the position of batteries, the following methods for their attainment will be found useful when the requisite instruments are at hand; by frequent practice, the eye should, however, be enabled to determine, nearly, either the height of, or distance from any object.
HEIGHTS.
1.—BY MEANS OF A “POCKET SEXTANT,”
to ascertain the height of an object.
When the sextant is used for taking the height of objects, it is to be held vertically, and the quicksilvered part of the horizon glass will be on the left hand of the observer, or on the left part of the transparent glass. Altitudes are measured in the same manner as horizontal angles, for if we conceive the horizontal triangle A B C (vide [Plate 2, Fig. 2]), to be raised on its base A C with the angle C next to the observer, then the perpendicular A B becomes the height of the object B; and supposing the object to stand on a horizontal plane, then the ground and the object form the right angle at A; therefore, if the object is accessible, the sextant need only be set at any of the angles mentioned for distances (vide Art. [Distances]), and walking backward on the line A C until the top of the object is brought down to the height of the observer’s eye from the ground, then the distance from where the observer stands to the object will be in the same proportion to its height as the base was to the distance. Then add the height of the eye from the ground, and the height of the object will be ascertained. If the object is not accessible, the angle must be taken, and calculated by trigonometry.
2.—BY MEANS OF A PORTABLE BAROMETER, AND THERMOMETER,
to ascertain the height of an object.
Observe the altitude (B) of the mercurial column in inches, tenths, and hundredths, at the bottom of the hill, or other object, the height of which is required.
Observe, also, the altitude (b) of the mercurial column at the top of the object. Observe the temperature on Fahrenheit’s thermometer at the times of the two barometrical observations, and take the mean between them. Then 55000 × B - b B × b = the height of the hill in feet, for the temperature of 55 degrees on Fahrenheit. Add 1 440 of this result for every degree which the mean temperature exceeds 55 degrees, and subtract as much for every degree below 55 degrees. This will be a good approximation when the height of the hill is below 2000 feet.
3.—BY MEANS OF THE RECONNOITRING PROTRACTOR,[51]
to measure the height of an inaccessible object.
[Plate, Surveying, and Reconnoitring, [Fig. 1].]
Place yourself at a convenient distance from the object whose height is required, taking care to have a good base line to the second station. Hold the protractor vertically, with a steady hand, the tube side uppermost, and bring the top of the object in a line with the centre of the tube. Allow the arm (or index) to vibrate freely, and, when steady, note the angular height of the object (shown by the edge of the index on the marginal scale of degrees). By the aid of points taken through the tube, or by pickets, then pace, or measure a base in a direct line from the object; and, when arrived at the second station, again note the angular height of the object.
Construction—
Set off the angles, and draw the respective lines, which, by their intersection, will determine the height of the perpendicular, to which the height of the protractor above the ground must be added for the altitude of the object. By using the scale of the measured base line, the height required will be ascertained, or it may be calculated by “Trigonometry, without logarithms.”—[Page 303].
To measure the height of an accessible object.
[Plate, Surveying, and Reconnoitring, [Fig. 2].]
At an appropriate distance from the object, take its angular height and measure the distance to its base.
Construction—
Draw a line representing this distance, at one end of which draw another line at the angle found, and at the other erect a perpendicular; the intersection of these lines will determine the altitude of the object.
To measure the vertical height of a hill, or mountain.
[[Fig. 3], Plate, Surveying, and Reconnoitring.]
From a station a short distance from the hill, take, and note down its angular height; then select a rear position for a base line, using the tube of the protractor to insure a straight direction; proceed to the requisite distance on the base, and again note the altitude of the hill.
Construction—
The intersection of lines drawn from each end of the base line, at the angles found, will determine the altitude; the perpendicular height of which, added to that of the protractor above the ground, will give the altitude required.
To measure the altitude of a tower, &c., on a height.
[[Fig. 4], Plate, Surveying, and Reconnoitring.]
From the first station, near the base, take the altitude of the hill, and also that of the tower above it, and note down these angles; proceed to another station in a straight line with the former one, measuring its length, and again observe the angular height of the hill, and also that of the top of the tower.
Similarly to the previously described mode, ascertain, first, the height of the hill; second, the height of the hill, and tower; deduct the first calculation from the second, which will leave the height of the tower.
In all the foregoing cases the heights may be correctly ascertained by trigonometrical calculations (vide [Trigonometry], without logarithms, [page 303]).
4.—BY THE SHADOW OF THE OBJECT,
to ascertain the height.
Set up vertically a staff of known length, and measure the length of its shadow upon a horizontal, or other plane; measure also the length of the shadow of the object of which the altitude is required. Then, by the property of similar triangles,
As the length of the shadow of the staff
is to the altitude of the staff,
so is the length of the shadow of the object
to the altitude of the object.
5.—WHEN THERE IS NO SHADOW,
to ascertain the height.
Place a staff (equal in length to the height of the observer’s eye) vertically at such a distance from the foot of the required altitude, that the observer, having laid himself upon his back, with his feet against the bottom of the stick, may see the top of the staff, and object in the same line. Then, by similar triangles, the height may be readily ascertained.
6.—BY MEANS OF THE TANGENT SCALE OF A GUN,
to ascertain the height of an object, the distance being known.
Lay the gun for the top of the object the height of which is required, then raise the tangent scale until the top of it, and the notch on the muzzle are in line with the bottom of the object: then, by similar triangles,
As the length of the gun
is to the length of the raised part of the tangent scale,
so is the distance from the gun to the object,
to the height required.
Plate 2.
Heights.
Fig. 1. Fig. 2.
Distances.
Fig. 3. Fig. 4. Fig. 5.
Practical Geometry.
Fig. ½. Fig. 21. Fig. 22.
7.—BY MEANS OF TWO PICKETS,
to ascertain the height of an object.
[Vide 2nd Plate, Heights, and Distances, [Fig. 1.]]
Let two pickets C D (4 feet), E F (6 feet), be placed with their bases in the line C A passing through A the height required, and move them nearer to, or farther from each other, until the summit B of the object is seen in the same line as D, and F, the tops of the rods. Then, by the principles of similar triangles,
As D H (= C E) : F H :: D G (= C A) : B G.
To which add A G = C D for the whole height A B.
Thus, supposing C E to be 6 feet, F H 2 feet, and C A 150 feet, the proportion will be,
As 6 : 2 :: 150 : 50 feet.
Then 50 + C D will be the altitude required.
DISTANCES.
1.—BY MEANS OF THE SEXTANT,[52]
to find the distance from an object, whose height is known.
Let A B represent the height of the object; C your station; and C B the distance to be found.
Take the angle B C A with the sextant,[52] and note it in minutes; then A B, in feet × 573 ÷ B C A, in minutes = A C in fathoms. Or A B in feet × 573 ÷ B C A, in minutes × 2 = A C in yards.
573 is a constant multiple.
This method requires no table of sines, &c., the number of minutes in the angle being used instead of the sine.
2.—BY MEANS OF A POCKET SEXTANT,
to measure inaccessible distances.
When used for taking the distance of objects, the sextant is to be held horizontally, and the quicksilvered part of the glass will be uppermost, or above the transparent part.
To ascertain the distance A B (vide Plate 2, [Fig. 2]), obtain, by observation, the direction A C perpendicular to A B, which is thus performed:—Set the instrument at 90°, and place yourself at the point A, with your right towards the point B; then look through the sextant, and direct a picket to be placed in the line A C at 100 yards, or feet, from you, so that the point B will appear right above it. Then set the sextant at 45°, and walk along the line towards C until you bring the points A, and B to coincide; the base and perpendicular will then be of equal length, and A C being known, or measured, the distance A B will also be ascertained. But if you cannot walk far enough to find angle C 45°, find it equal to 63° 26′, and then A C = ½ A B; at 71° 34′ = ⅓ A B; at 75° 58′ = ¼ A B; at 78° 41′ = ⅕ A B; at 80° 32′ = ⅙ A B; at 82° 52′ = ⅛ A B; and at 84° 17′ the distance will be ⅒ A B.
Should the object be far distant, it will be necessary to take a long base, and the side A B must be calculated, therefore, by trigonometry.
3.—BY MEANS OF THE PRISMATIC COMPASS,
to measure inaccessible distances.
Having fixed the instrument to the stand, place it over the station-point, spreading the legs so as to give sufficient firmness, and observing that the card is level enough to allow it to play freely; raise the prism by means of the slide, until the divisions of the compass-card are distinctly seen; then look through the slit, and turn the box round until the thread bisects the object whose distance is required; allow the card to settle, and the division on it, which coincides with the thread of the vane, will be the azimuth, or bearing of the object, reckoned from the north, or south point of the needle, when the card is divided into twice 180 degrees. The angular distance between any two objects will, of course, be the difference of their bearings; thus, suppose one to bear 15° N.E., and the other 165° S.E., the angular distance between them will be 150°.
In military sketching, the compass is often supported merely by the hands, using the little spring to check the vibrations of the card. In windy weather, the mean of these vibrations must be taken for the bearing sought.
The directions for surveying, &c., &c., by means of “The Reconnoitring Protractor,” apply similarly to the “Prismatic Compass.”
4.—BY MEANS OF “THE RECONNOITRING PROTRACTOR,”
to ascertain the distance from inacessible objects.
[Plate, Surveying, and Reconnoitring, [Fig. 6].]
Select a good position for a base line; fix the protractor on the tripod at the first station, placing the instrument in a direct line between the first station and the point selected for the second station. Direct the index consecutively at the objects, the relative distances of which are to be ascertained, and note correctly their respective angles. When the object is above the horizontal line, the sliding-sight must be sufficiently raised to take its bearing; and, should the object be below the level of the protractor, its angle may be taken by observation through the upper holes of the near sight; or the feet of the tripod may be adjusted, by raising, or sinking them in the ground, so that the index may be correctly directed to the object. Then proceed to the second station, measuring, or carefully pacing the base line, at the end of which fix the protractor in a straight line between the two stations; direct the index at the objects previously noted at the first station, taking their respective angles as before.
Construction—
Draw the base of the length required, according to the scale; from each end of which set off the angles found, and draw the lines required; the intersection of these will determine the position of the several objects, and their relative distances may be ascertained by measurement on the scale of the base line; or they may be calculated trigonometrically.
5.—BY MEANS OF TWO PICKETS,
to ascertain the distance from an object.
Take two pickets of unequal lengths, drive the shortest into the ground, say close to the edge of a river; measure some paces back from it, and drive in the other, till you find, by looking over the tops of both, that your sight cuts the opposite bank. Pull up the first picket, measure the same distance from the second in any direction the most horizontal, and drive it as deep in the ground as before. Then, if you look over them again, and observe where the line of sight falls, or terminates, you will have the distance required. This method is only applicable to short distances.
6.—To ascertain the distance of the object A from B.
[Vide Plate 2, [Fig. 3.]]
Place a picket at B, and another at C at a few yards’ distance, making A B C a right angle, or B C perpendicular to A B.[53] Divide B C into 4, 5, or any number of equal parts, make another similar angle at C in a direction from the object, and walk along the line C D until you bring yourself in a line with the object A, and any of the divisions (say O) of the line B C. Then (having measured C D) as C O : C D :: B O : B A.
Or, as 10 : 53 :: 30 : 159 yards.
7.—To find the distance between two objects, C, and D.
[Vide Plate 2, [Fig. 4.]]
From any point A, taken in the line C D, erect the perpendicular A E, in which set off from A to E 40 yards, set off from E to G, in the prolongation of A E, 10 yards, at G raise the perpendicular G F, and produce it towards I, plant pickets at E, and G, then move with another picket on G F, till F is in a line with E, and D; and on the prolongation of the perpendicular F G place another picket at I in the line with E, and C: measure F I (54 yards), then—
as G E : A E :: F I : C D;
Or, as 10 : 40 :: 54 : 216 yards.
8.—To find the inaccessible length, A, B, of the front of a fortification.
[Plate 2, [Fig. 5.]]
Plant a picket at C, from whence both points may be seen; find the lengths C A, C B (by the method in No. 5); make C E one-fourth, or any part of C B, and make C D bear the same proportion to C A: measure D E; then
as C D : D E :: C A : A B.
Nearly in the same manner the distance from B to A may be ascertained, when the point B is accessible; for having measured the line C B, and made the angle C E D equal to C B A, the proportion will be as C E : D E :: C B : B A.
9.—BY MEANS OF THE TANGENT SCALE OF A GUN,
to ascertain the distance, the height of the object at the required distance being known.
Lay the gun by the line of metal for the top of the object; then raise the tangent scale till the top of it and the notch on the muzzle are in line with the foot of the object, and note what length of scale is required.
Then,—by similar triangles—
As the length of the raised part of the tangent scale
is to the length of the gun;
so is the height of the distant object
to the distance required.
Thus, supposing the height of the object to be 9 feet, the length of that part of the tangent scale which is raised, 3 inches, and of the gun 6 feet, the proportion will be—
As 3 : 72 :: 108 : 2592 inches, or 216 feet.
10.—BY MEANS OF THE PEAK OF A CAP,
to measure the breadth of a river.
Place yourself at the edge of one bank, and lower the peak of your cap till you find the edge of it cut the other bank, then steady your head by placing your hand under your chin, and turn round gently to some level spot of ground on your side of the river, and observe where your eyes, and the edge of the peak again meet the ground; measure the distance, which will be nearly the breadth of the river.
11.—BY THE REPORT OF FIRE-ARMS, TO ASCERTAIN THE DISTANCE
OF ANY OBJECT, vide [Sound], [page 316].
To estimate distances, in the field.
Good eyesight recognises masses of troops at 1700 yards; beyond this distance the glitter of arms may be observed. At 1300 yards infantry may be distinguished from cavalry, and the movement of troops may be seen; the horses of cavalry are not, however quite distinct, but that the men are on horseback is clear. A single individual detached from the rest of the corps may be seen at 1000 yards, but his head does not appear as a round ball until he has approached up to 700 yards; at which distance white cross-belts, and white trousers may be seen. At 500 yards the face may be observed as a light coloured spot; the head, body, arms, and their movements, as well as the uniform, and the firelocks (when bright barrels) can be made out. At between 200 and 250 yards all parts of the body are clearly visible, the details of the uniform are tolerably clear, and the officers may be distinguished from the men.
Vide “United Service Magazine.”—No. CCCXXXI.
BY MEANS OF THE RECONNOITRING PROTRACTOR,
to traverse roads.
[Plate, Surveying, and Reconnoitring, [Fig. 5].]
Fix the protractor on the tripod at the first station, placing it so that the side tube may be in a direct line with the intended second station. From each end of the tube observe the objects in sight (or place pickets) in order to secure a straight line in pacing, or measuring, from the first to the second station. Mark the distance between the stations, and place the protractor, by means of the tube, in a direct line with the first station. Then select the third station, and direct the arm or index correctly to it (using the upper holes of the near sight for a declivity, or raising the sliding-sight for an ascent); note the angle thus found, and notice the objects in front, and rear (if any, if not, place pickets) for points to enable you to pace towards, and work with accuracy at the third station. Select station 4, place the tube in line with the third, and second stations; note the bearing of No. 4, and pace the distance to it. Proceed thus from station to station, entering the angles, and distances in your note-book, as well as the offsets (which must also be carefully measured) from the lines taken, until the survey is completed.
Construction—
The day’s work will be easily plotted on paper, by setting off the angles found, and drawing lines for the measured distances, according to scale.