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Drive a picket 3 or 4 feet long at H, and another at L, where the top of a long rod FD is in a line with the object S from the point A (the heads of these pickets being on the same level); mark also the point C, where the head of the rod is in the same line with S, from the top of any other picket B, and measure AF and BC; lay off the distance BC from F to b, and the two triangles ADb and
PS AB HI
and ASB are evidently similar, whence =
AP==HPS therefore DF. H; and APAF. HI
АР АВ HI
A few other methods of ascertaining distances and heights, more particularly connected with military reconnaissances, will be found in the next chapter.
Where angles can be taken between three inaccessible objects, the relative positions of which are known, and can be laid down on paper; the place of the observer can be ascertained either by calculation, by construction, or by means of an instrument used for that purpose, called a "station pointer;" or, what is better still, a piece of thin tracing paper, with the observed angles plotted upon it, can be shifted about until the point falls into the only spot from whence the lines containing these angles pass through the three fixed stations. The case is a very common one in maritime surveying, where the two first methods of solution, calculation and construction, are seldom thought of; and the last, which is the most simple, and sufficiently correct for the purpose, generally adopted. In a trigonometrical survey, of course, this method would never be thought of for fixing a station, but the calculations for the different cases that may occur of the three points being in one line, or forming a triangle within or without which the observer may happen to be, will be found, with a mass of other information on such subjects, in "Adam's Geometrical Essays," pp. 169 to 177.
The following is the mode of obtaining the position of the observer by construction, in the case that most commonly occurs, viz. when the three points form a triangle, without which the place of observation lies :-O, P, and Q represent the three points on shore whose positions have been determined by interior triangulation, and S a rock or anchorage, whose place is to be determined with relation to the stations above mentioned. Suppose
the angle QSP is observed 35°, and PSO-40°, describe a circle
passing through Q, S, and P, which is thus done :-Double the angle QSP which=70°; subtract this from 180, leaving 110°; lay off half of this, or 55° at PQR and QPR, and the angle at R is evidently 70°, or double QSP; now the angle at the centre being double that at the circumference, a circle described from R as a centre with the radius RQ, or RP, will pass through the point S. In like manner a circle described from V, with the radius VP, will also pass through S, and their intersection gives the spot required.
For the analysis of the calculation of this problem, vide "Puissant, Géodesie," vol. i. p. 233.
The method of surveying any tract of country through which a line of railway is projected or has been determined upon is so similar to that of measuring roads or other continuous lines by traversing" with the chain and theodolite, that it does not require any peculiar directions. The lines, however, being generally very long, must be measured with the greatest exactness, and the angles be observed with proportionate care. Where practicable also, the work should, whilst in progress, be tested by reference to known fixed points near which it passes, which can in most cases be obtained from good maps. The existing Standing Orders of Parliament regulate the scale upon which these surveys are required to be plotted in England; and the lateral deviation
allowed from the proposed line of rails, with other local causes, determine the breadth required to be embraced in the survey.
For the methods of laying out the lines of railways; the levels of the different portions; determining the curves, gradients, and slopes of embankments and cuttings, &c., every information can be obtained from the works of Mr. Hascoll and many others; and it would be out of place here to attempt any description of subjects which belong to a most important branch of civil engineering, and embrace such a multitude of details. A few remarks, however, upon the method of taking sections for railways, and the scales upon which they should be plotted, will be found in the chapter upon Levelling.
MILITARY RECONNAISSANCE, AND HINTS ON SKETCHING GROUND.— OF DELINEATING
GROUND.-HORIZONTAL CONTOURS.-GEOLOGICAL MAPS.-CONVENTIONAL SIGNS.
THE sketch of any portion of ground for military purposes should, in all cases, be accompanied by an explanatory statistical report, and the combination of these two methods of communicating local information constitutes what is termed a Military Reconnaissance, in which the importance of the sketch, or the report, predominates according to circumstances.
The object for which a reconnaissance is undertaken naturally suggests the points to which the attention of the officer should be principally directed; if for example, it is merely to determine the best line of march for troops through a friendly or undisputed country; the state of the communications, the facilities of transport, and possibility of provisioning a stated number of men upon the route, are the first objects for his consideration. If the ground in question is to be occupied either permanently, or for temporary purposes, or if it is likely to become the seat of war; his attention must be directed to its military features, and a sketch of the ground, with explanatory references, together with a full and correct report of all the intelligence he can collect from observation, or from such of the inhabitants as are most likely to be well acquainted with the localities*, and most worthy of credence, will demand the exertion of all his energies: upon the correct information furnished by this reconnaissance may depend, in a great measure, the fate of the army.
* It is almost needless to point out the incalculable advantages of being a good modern linguist to an officer employed on duty of this nature in an enemy's country.
The principal points for observation in a military sketch and report are―
ROADS. Their direction; nature; liability to injury; facility of repair; practicability, in what seasons, and for what species of troops; exposure to, and means of security from, enfilade; whether bordered or not by hedges, ditches, or banks, &c.
CANALS.-Means of destruction, or of rendering them of use; construction; depth of water, size of locks, &c.
RIVERS. Their sources, width, depth, velocity of current; fords for infantry and cavalry, whether permanent, or only passable at certain periods of tide, or seasons of the year, and if exposed to fire; means of passage; profile of banks; size and nature of vessels and boats employed in the navigation; tributary springs and rivulets; bridges, with their dimensions, materials, and construction, and means of destroying or repairing them.
MILITARY FEATURES.-Inclination of slopes, and all irregularities of ground; accessible or not for cavalry or infantry; description of country, open or inclosed; relative command of hills †; ravines; forests; marshes; inundations; barriers; plains; facilities for landing, if on a sea coast; military posts, and fortified towns, &c.
STATISTICAL INFORMATION.-The population and employment of the different towns, villages, and hamlets, contained within the limits of the sketch. Agricultural and other produce; commerce; means of transport; subsistence for men and horses, &c.; with a variety of minute but important details, for which the reader is referred to the excellent essay on this subject, in the fourth volume of the "Mémorial Topographique et Militaire;" to the "Aide Mémoire des Officiers du Genie;" Macauley's "Field Fortification;" &c.
The degree of accuracy of which a sketch of this nature is susceptible depends upon the time that can be allowed, and the means that may be at hand. If a good map of the country can
* A ford should not be deeper than three feet for infantry, four feet for cavalry, and two and a half for artillery and ammunition waggons.—Macauley's "Field Fortification." The nature of the soil at the bottom should always be ascertained, and also if it is liable to shift, which is the case in a mountainous country.
† If actual differences of level cannot be determined for want of time, still relative command may be obtained, and numbered 1, 2, 3, &c., accordingly.