AL; afterwards point the index to the steeple I, and then to the points M, O, P, N, H, E, G, then draw a line on the table parallel to the north and south of your compass, to represent the magnetic meridian.

Remove the plain table to C, planting a staff at A, measure A C, and set off that measure by your scale from A upon the line AC, and fix the needle at C; then set the index upon the line A C, and turn the table till the line of sight coincides with A, fasten the table, point the index to F, and draw C F, intersecting AF in F, and determining the position of the windmill F; from C draw the indefinite lines CM, CK, CL, &c. which will determine the points M KL, &c. draw K L and mn parallel thereto, to represent the line of cavalry.

Remove the table from C to D, setting up a staff at C, measure CD, and set off the distance on CB from your scale, place the needle at D, the index on CD, and turn the table till C coincides with the sights, and take the remarkable objects which could not be seen from the other stations.

Staves should be placed at the sinuosities of the river, and lines drawn at the stations A, C, D, B, to these staves, which will give the windings of the river.

Having thus determined the main objects of the field, sketch on it the roads, hills, &c.

PROBLEM 43. To take a plan of the trenches of an attack, fig. 1, plate 29.

The plan of trenches, taken with accuracy, gives a just idea of the objects, and shews how you may close more and more upon the enemy, and be covered from their enfilade fire, and also how to proceed in the attack without multiplying useless works, which increase expense, augment the labour, and occasion a great loss of men.

Measure a long line A B, parallel to the front o the attack D F, place the table at A, and set- up f

staff at B, point the index to B, and draw a line to represent AB, fasten the table, and fix a needle at the point A, direct the line of sights to the flanked angle of the ravelin C, and draw AC; proceed in the same manner with the flanked angles D, E, F, G, to draw the lines at the opening of the trenches, plant staves at H and R, from A draw a line on the table in the direction A H, measure AH, and set off that measure from your scale upon the line A H on the table.

Remove the plain table from A to B, set up a staff at A, lay the fiducial edge of the index against the line AB, and turn the table about till the staff at A coincides with the line of sight, then fasten the table, direct the sights to C, and draw B C, intersecting A at C; in the same manner ascertain the flanked angles D, E, F, G, draw a line in the direction BR, and set off the measure thereof from your scale.

Remove the table from B to R, and set up a staff at B where the plain table stood, lay the index upon the line corresponding with RB, then turn the table about till the line of sight is in the direction BR, srew the table fast, direct the sights towards P, and draw on the table the line RP, and by the scale lay off its measure on that line.

Remove the plain table from R to P, lay the index upon the line PR, and turn the table about till the line of sight coincides with R, screw the table fast, and draw a line upon it in the direction PQ; measure PQ, and take the same number of parts from your scale, and set it off on the line, and so on with the other station Q.

Having removed the table to the station S, and duly placed it with regard to Q, from the point S, draw the lines SV, ST, SU, setting off from your scale their lengths, corresponding to their measures on the ground.

Having thus taken the zigzags RPQ, STW,

and the parts UUWZ of the parallels, you remove the plain table to H, and proceed in like manner to take the zigzags HIK, &c. as above, which will represent on your plain table the plan of the attack required.

OF LEVELLING, fig. 48, plate 28.

Levelling is an operation that shews the height of one place in respect to another; one place is said to be higher than another, when it is more distant from the centre of the earth than the other; when a line has all its points equally distant from the centre, it is called the line of true level; whence, because the earth is round, that line must be a curve, and make a part of the earth's circumference, as the line ABED, all the points of which are equally distant from the centre C of the earth; but the line of sight AG, which the operation of levelling gives, is a right line perpendicular to the semi-diameter of the earth CA raised above the true level, denoted by the curvature of the earth, and this in proportion as it is more extended; for which reason, the operations which we shall give, are only of an apparent level, which must be corrected to have the true level, when the line of sight exceeds 300 feet.

Suppose, for example, that AB was measured upon the surface of the earth to be 6000 feet, as the diameter of the earth is near 42018240 feet, you will find B F by the following proportions.

* 42018240: 6000 :: 6000 BF equal to 0.85677 f. which is 10.28124 in. that is to say, between two objects A and F, 6000 feet distant from each other, and in the same horizontal line, the dif

As the arc AB = 6000 feet is but very small, it may be considered equal to the tangent A F, and in this respect, AF is a mean proportional between the whole diameter, or twice the Tadius BC, and the exterior part B F.

ference B F of the true level, or that of their distance from the centre of the earth, is 10.28124 in.

When the difference between the true and apparent level, as of B F, has been calculated, it will be easy to calculate those which answer to a less dis tance; for we may consider the distances BF, bf, as almost equal to the lines AI, Ai, which are to cach other as the squares of the chords, or of the arcs AB, ab, because in this case the chords and the arcs may be taken one for the other.

Thus to find the difference fb of level, which answers to 5000 feet, make the following proportion; 6000 f.: 5000 f. :: 0.85677 : fb, which will be equal to 0.71399 f. or 8.56788 in.

The point F, which is in the same horizontal line with A, is said to be in the apparent level A, and the point B is the true level of F; so that BF is the difference of the true level from the apparent.

PROBLEM 44, fig. 49, plate 28. The above positions being supposed to know the difference of level between points B and A, which are not in the same horizontal line; then at A make use of an instrument proper to take the angle BCD, and having measured the distance CD, or CI, by a chain which must be kept horizontal in different parts of it on the ground ALV B, you may in the triangle CDB, considered as rectangular in D, calculate BD, to which add the height CA of the instrument, and calculate the difference of level DI, as we have shewn above.

But as this method requires great accuracy in measuring the angle B CD, and an instrument very exact, it is often better to get at the same end with a little more trouble, which is shewn by the following method.

PROBLEM 45. Use of the spirit or water level, fig. 50, plate 28.

Place the level at E, at equal distances from B and G, fix one station staff at B, the other at G;

your instrument being adjusted, look at B, and let the vane be moved till it coincides with the line of sight; then look at the staff G, and let the vane be moved till it coincides with the line of sight H, and the difference in height shewn by the vanes on the two staves, will be the difference in the level between the two points B and G. Thus, suppose the vane at G was at 4 f. 8 in. and at B 3 f. 9 in. subtract one from the other, and the remainder 11 inches, will be the difference in the level between the two points B and G; you may proceed in the same manner with the other points; but more need not be said on this head, as I have already treated this subject very fully in the foregoing part of this work.

AN

ESSAY ON PERSPECTIVE;

AND A DESCRIPTION OF

SOME INSTRUMENTS,

FOR FACILITATING THE PRACTICE OF THAT USEFUL

ART.

DEFINITIONS.

Definition 1. Perspective is the art of delineating the representations of bodies upon a plane, and has two distinct branches, linear and aerial.

Definition 2. Linear perspective shews the method of drawing the visible boundary lines of objects upon the plane of the picture, exactly where those lines would appear if the picture were transparent; this drawing is called the outline of those objects it represents.

Definition 3. Aerial perspective gives rules to fill