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 Geodesie," vol. 1, p. 233.

No allusion was made when explaining the different methods of obtaining the contents of irregular figures, to the instrument lately invented termed a Pediometer, by which the contents of fields (reduced or divided into triangles or trapeziums) are very easily ascertained. The description and application of this instrument will be found at the end of the tables; it is in constant use at the Tithe Commission Office for the purpose of calculating and checking the contents of plans surveyed under the Tithe Commutation Act; and, independently of the saving of time gained by its introduction, it almost prevents the possibility of error. The principle of its construction depends upon the following equation combined of the sum and difference of a diagonal of the trapezium and the two perpendiculars :—

Let a represent the diagonal, and 6 the sum of the two perpendiculars, then the area = ab = ( a + 1 b) 2 − ( a − 1 b) 2 - 2

CHAPTER V.

'MILITARY RECONNAISSANCE, AND HINTS ON SKETCHING ground.

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 any 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.

The principal points for observation in a military sketch and report are

ROADS. Their direction; nature; liability to injury; facility of

*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.

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 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 enclosed; relative command of hills ;t 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 "Memorial Topographique et Militaire;" also to the last "Aide Memoire 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 be procured (which is generally the case), the positions of several conspicuous points, such as churches, mills, &c., can be taken from it and laid down on the required scale; or a rough base may be measured, carefully paced, or

* 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 commands may be obtained, and numbered 1, 2, 3, &c., accordingly.

obtained from some known distance, such as that between milestones, for instance, and angles taken with a sextant or other instrument from its extremities, to form a tolerably accurate species of triangulation, which may be laid down without calculation, and within this the detail can be sketched more rapidly and with far more certainty than without such assistance. No directions that can possibly be given will render an officer expert at this most necessary branch of his profession, as practice alone can give him an eye capable of generalizing the minute features of the ground, and catching their true military character, or the power of delineating them with ease, rapidity and correctness.

The instruments used in sketching ground have already been alluded to when describing the mode of filling in the detail between measured lines on a regular survey. In addition to the advantages there ascribed to the azimuth compass, it will be found peculiarly well adapted for sketching on a continuous line, such as the course of a road or river, or a line of coast, which reflecting instruments are not; and the angles with the magnetic meridian measured by the compass, can be read off with quite as much accuracy as they can be laid down by the small protractor used in the field. This should have a scale of six, four, or three inches to one mile (or whatever other proportion may be preferred) engraved on the other bevelled side, and with a sketching portfolio* and compass, together with a small sextant and field telescope, comprise all the instruments that can be required by an officer employed on a reconnaissance; and as they can always be carried without inconvenience about his person, or strapped in front of his saddle, he need never be driven to the necessity of sketching entirely without their assistance, though the practice of doing so occasionally is decidedly of service, as it teaches him to make use of

*The present "Sabretache" is of little use as a sketching case on horseback, and on foot it is a mere incumbrance. It is most desirable that Officers of Engineers, and those attached to the Quarter-Master-General's department, on service, should be equipped with one of an improved pattern, which might easily be arranged so as to answer for a portfolio and sketching case, and at the same time contain such scales and drawing instruments as are required by an officer employed upon an extensive reconnoissance.

The introduction of a well-contrived sabretache to answer these purposes, with which

his eyes, and tends to make him a good judge both of linear and angular measurement.*

Sketching such parts of the interior detail as have a decidedly marked outline is comparatively easy; but the delineation of ground, so as to represent the various slopes of the hills and irregularities of the surface, is far more difficult; and methods have been proposed, and partially adopted on the Continent, as systems for expressing these features, not merely giving a general idea of their character, but even a mathematical representation of their various complicated inclinations; so that the angle of every slope might be evident from a mere inspection of the drawing, or measured from a scale; and, consequently, furnishing data for constructing sections of the ground in any required direction. This degree of perfection would of course be most desirable in military sketches, as well as in finished topographical plans, but the labour and difficulty attending the execution will always prevent its general application in surveys or sketches of any

extent.

The two methods in general use for representing with a pen or pencil the slopes of the ground, are known as the vertical, and the horizontal. In the first of these the strokes of the pencil follow the course that water would take in running down these slopes; in the second (which is comparatively of late introduction) they represent contour or level lines traced round them; and are such as would be shown on the ground by water flooding the country at the different stages of its progressive altitude. This last is now generally the mode in which ground is etched, and it certainly produces a more correct representation of its general character and features than the vertical method.† Neither of these styles of representing ground, however, aspires to

it should be imperative that every officer of Engineers should provide himself, would be a real benefit to the service.

45

60

30

90

* A protractor (for want of a better) can be made by folding a square or rectangular piece of paper into three, which, when doubled, divides the edge into six portions of fifteen degrees each; these can be again divided into three parts, by which angles of five degrees can be laid down, or even ap- 15 proximately observed, the intermediate degrees being

judged by the eye.

Very good specimens of both these styles of sketching hills are to be found in Mr. Burr's" Practical Surveying."