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any perceptible armors discovered during the reconnaissance are On approaching a place by day, the officer should be diane, so is a tract ile amentica; bat supported at a distance by troops, hid from observaca by any cover that can be taken advantage of By night he should be accompanied by a strong party; and by advancing as near as possible towards daybreak, and rearing gradually, he would be enabled to make more correct coservaticos as to the outine and state of repair of the works than at any other time.
The anmerous conventional signs recommended in most continental military works are extremely puzzling, difficult to remember, and are mostly unintelligible. In a little work, the “Aide Mémoire Portatif," published in 1834, there are no less than ten pages devoted to these signs. Beyond the few that are absolutely necessary, and generally understood, it is far better to trust to references written on the face of the sketch, and the explanatory report, than by endeavouring to convey so much information by these conventional symbols and attempts at mathematical representations of the ground, to render a drawing so confused and difficult to comprehend that it really becomes of less value than an indifferent sketch with copious and clear remarks.
Below are given a few conventional signs, applicable only to military sketches:
On the following page are those of most general use in topographical plan-drawing: the boundary lines are those employed in the Ordnance Survey; a similar arrangement could of course be adopted to mark the divisions of any other country, however they may be designated.
Smithies. A small horse-shoe with the open side turned towards the road.
Turnpike roads. The side from the light shaded.
Cross roads. Narrower, and both sides alike.
Railroads. Both sides dark, very narrow, and perfectly parallel.
Canals. Distinguished from roads by the parallelism of the sides, the locks, and bridges, and by having the side next the light shaded like rivers. Canals and navigable rivers to be coloured blue.
the difference of level between staby means of reciprocal angles of has already been alluded to in page 32, unc can be taken in the same manner,
accurately as with a spirit level. It entering upon this subject, to explain os that must be applied to all vertical nose of obtaining relative altitudes - distance apart, which were referred iation. If they are only separated corrections are too trifling to have result.
here, any number of points upon centre are on the same true level;
course, the apparent altitude or two causes of error, curvature and
terrestrial retraction; the correction for the first of which depends upon the "are of distance," which is that contained between the two stations at the centre of the earth; and the second upon their comparative elevations above the horizon.
The effect of the curvature of the earth is to depress any object below the spectator's sensible horizon. Every horizontal line is evidently a tangent to the surface of the globe at that spot; and the difference between the apparent and true level at any distant point Reserving the effect of refraction for the present out of the most stance to the accompanying figure, to be the otvore, 267 & the spoun a "the are 1 D. above the radius
Whence x (2r+ x) = t2; and, owing to the small proportion that any distance measured on the surface must bear to the earth's radius, 2 may be substituted for (2r + x), and the arc a for the
tangent t; 2ræ then becomes = a3, and x = 2, which, assuming the mean diameter of the earth at 7916 miles, gives x = 8·004 inches or '667 of a foot for one mile; which quantity increases as the square of the distance. Or otherwise,
or 2r: a :: a: x, x being omitted in the expression (2r + x)
and a substituted for t; whence x =
A very easily remembered formula, derived from the above, for the correction for curvature in feet, is two-thirds of the square of the distance in miles; and another, for the same in inches, is the square of the distance in chains divided by 800*.
The second correction, terrestrial refraction, on the contrary, has the effect of elevating the apparent place of any object above its real place, and consequently, above the sensible horizon. The of light bent from their rectilinear direction in passing from a rare into a denser medium, or the reverse, are said to be refracted;
* The amount of the correction for curvature at different distances will be found by reference to the tables, and further remarks on Atmospheric Refraction in the chapter on the Definitions of Practical Astronomy.
and this causes an object to be seen in the direction of the tangent to the last curve at which the bent ray enters the eye, as in the last figure.
A is any station on the surface of the earth, the sensible horizon of which is AB; C and D are two stations on the summits of hills, of which C is supposed in reality to be situated on the horizontal line A B, and D above it, the angle of elevation of which is BAS. Owing, however, to the effects produced on the rays from these objects, in their passage to the eye, by the atmosphere through which they pass, they are seen in the directions A s and Ab, tangents to the curve described by the rays, and BA b, and SA s, are the measures of the respective terrestrial refractions.
Above eight or ten degrees of altitude, the rate at which the effects of refraction decrease as the altitudes increase (varying with the temperature and density of the atmosphere), is so well ascertained, that the refraction of the heavenly bodies for any altitude may be obtained with minute accuracy from any of the numerous tables compiled for the purpose of facilitating the reduction of astronomical observations; but when near the horizon, the refraction, then termed terrestrial refraction, is so unequally influenced by the variable state of the atmosphere that no dependence can be placed upon the accuracy of any tabulated quantities*. The rays are sometimes affected laterally, and they have been even seen convex instead of concave. Periods for observing angles of depression and elevation, particularly if the distances between the stations are long, should therefore be selected when this extraordinary refraction is least remarkable; morning and evening are the most favourable; and the heat of the day after moist weather, when there is a continued evaporation going on, is the least so.
It is a common custom to estimate the effects of refraction at some mean quantity, either in terms of the curvature, or of the arc of distance. The general average in the former case is of the curvature, making the correction in feet for curvature and refraction combined = D2, D being the distance in miles as before. In the latter the proportion varies consideraby†; and General Roy, * Puissant "Géodesie," vol. i. p. 342; and "Recherches sur les Réfractions Extraordinaires, par Biot." Also, the "Trigonometrical Survey," vol. i. p. 352.
Carr's "Synopsis of Practical Philosophy," articles Levelling,' and 'Refraction.'