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In the foregoing table, we have the allowance to be made for every chain-length, from 1° to 45°. To reduce an inclined field to a level, let it be required to find the deduction on 10 chain-lengths, upon a declivity of 24°. Against 24° in the column of degrees, we have 8 in the column of deductions; that is, 92 links on the level, which, multiplied by 10, gives 920 links; and so on of the rest.
The straightest line that can be measured by the chain is, for various reasons, longer than the true quantity. All decimals of links should, therefore, be neglected; and, indeed, a moderate and judicious allowance should be made on integers themselves, except when the ground is smooth and plain.
The area of the above figure is computed as follows: Fig. 3.
To find the off-sets on the first station-line AB.
To find the area of the off-sets on the second line BC.
2)2250 100 I 20 1152)4000 2)5670 109 08 60 20 49
2000 2835 2)6000 2)240r 2)4600
2 4360 2)5880
145550 The triangles, 3117000
2000 6750 2100 8120 4400 7750
The plain table consists of a plain rectangular board of any convenient size, fitted in a frame of wood, so as it can be taken out or put in at pleasure for the convenience of putting a sheet of paper upon it.
One side of the frame is divided into degrees for the purpose of taking angles ; the other is usually divided into equal parts for drawing lines on the table, either parallel or perpendicular to the sides.
The plain table is provided with an index, either with open fights, or a small telescope: And that edge of the index, which is in the same plane with the fights, is called the fiducial edge.
A magnetic needle and compass is fixed in one side of the plain table, to point out the direction. It is fixed to a stand of a convenient height, and moves upon an universal joint, by which means it will incline in any direction, and, being screwcd fast in the socket, it will retain any situation given it.
The plain table is one of the most expeditious instruments surveyors ufe ; for no sooner are the different angles taken, and
the distances marked on the plain table, than a plan of the field is obtained ; and this may be done by,taking a station within , the field, or by choosing one of the corners for a station, or otherwise by going round the field.
I. By taking a station within the field Let ABCDE, Fig. 4. be a field, and O an eminence within the field. Plant the table at O, and screw it with the needle north. Mark, O upon your paper, and apply the index to O, directing it to the corner A, till through the fights you see A, then draw an obfcure line along the fiducial edge of the index to represent the direction OA. Then turn the index, till through the fights you fee B, and draw an obscure line from 0 along the fiducial edge of the index to represent the direction OB. In like manner, apply the index successively to O, turning it round with the fghts to the remaining angles C,D,E, drawing the obscure lines OC, OD, OE; then with the chain measure the straight lines OA, OB, OC, OD, OE, and mark the results upon the corresponding lines on the table. Join their extremities AB, BC, CD, DE, EA, and the thing is done.
When the plain table has degrees marked on it, the quantity of the angles may be marked immediateiy when taken; otherwise they may afturwards be measured from a line of chords or protractors—and the area found, as taught above.
2. When from one of the angles all the rest may be seen, let the point A be an angle from whence the rest may be seen; there fix the station. Turn the table till the middle point to the flower-de-luce ; screw your instrument fast; then turn the index till through the fights you see the corner B, and draw an obscure line along the fiducial edge of the index, to represent the direction AB : again turn the index, till through the sights successively you see the corners C, D, E, and to each of these draw obfcure lines : Then with the chain measure the lines