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serve the object in the second station, and from the point, by the edge of the index, draw another line ; so is the angle laid down ; on that last line set ofl the distance to the second station, in chains and links : apply your instrument to the second station, taking the angle as before ; and after the like manner proceed till the whole is finished.

This method may be used in good weather, if the needle be well touched and play freely ; but if it be in windy weather, or the needle out of order, it is better, after having taken the first angle as before, and having removed your instrument to the second station, and placed the needle over the meridian line as before, to lay the index on the last drawn line, and look backward through the sights ; if

you then see the object in the first station, the table is fixed right, and the needle is true ; if not, turn the table about, the index lying on the last line, till through the sights you see the object in the first station : and then screw it fast, and keeping the edge of the index to the second station, direct your sights to the next; draw a line by the edge of the index, and lay off the next line; and prca ceed through the whole without using the needle, as you do with the theodolite.

If the sheet of paper on the table be not large enough to contain the map of the ground you survey, you must put on a clean sheet, when the other is full ; and this is called shifting of paper, and is thus performed.

Pl. 6. fig. 8.

Let ABCD represent the sheet of paper on the plane table, upon which the plot E, F, G, H, I,

K, L, M, is to be drawn; let the first station be E ; proceed as before from thence to F, and to G; then proceeding to H, you find there is not room on your paper for the line GH; however, draw as much of the line GH, as the paper can hold, or draw it to the paper's edge. Move your instrument back to the first station E, and proceed the contrary way to M, and to L ; but in going from thence to K, you again find your sheet will not holdit; however, draw as much of the line LK on the sheet as it can hold.

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Take that sheet off the table, first observing the distance oo of the lines GH and LK, by the edge of the table ; take off that sheet, and mark it with No. 1, to signify it to be the first taken off. Having then put on another sheet, lay that distance 00 on the contrary end of the table, and so proceed as before, with the residue of the survey, from o to H, to K, and thence to o; so is your survey complete.

In the like manner you may proceed to take off, and put on, as many sheets as are convenient; and these may afterwards be joined together with mouth glue, or fine white wafer, very thin.

If the index be fixed to the first centré, using the 360 side, it will then serve as a theodolite, and when to the second centre, using the 180 side, it will serve as a semicircle ; by either of which you may survey in rainy weather, when you cannot have paper on the table.

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1. To take an angle of altitude, by the circumferentor.


ET the glass lid be taken off, and let the instrument be turned on one side, with the stem of the ball into the notch of the socket, so that the circle may be perpendicular to the plane of the horizon; let the instrument be placed in this sitnation before the object, so that the top thereof may be seen through the sights; let a plummet be suspended from the centre pin, and the object being then observed, the complement of the number of degrees, comprehended between the thread of the plummet, and that part of the instrument which is next your eye, will give the angle of altitude required.



2. If an angle of altitude is to be taken by the theodolite, or semicircle, let a thread be run through a hole at the centre, and a plummet be suspended by it ; turn the instrument on one side, by the help of the ball and notch in the socket for that purpose, so that the thread may cut 90, having 360 degrees next you ; screw it fast in that position, and through the sights cut the top of the objects; and the degress then cut by the end of the index next you, are the degrees of elevation required. An angle of depression is taken the contrary way.


3. By the plane table an angle of altitude is taken in the like manner, by suspending a plummet from the centre thereof, having turned the table on one side, and fixed the index to the centre by a screw, so as to move freely, let the thread cut 90, look through the sights as before, and you have the angle of elevation, and on the contrary that of depression.





HE protractor is a semicircle annexed to a scale, and is made of brass, ivory, or horn ; its diameter is generally about five or six inches.

The semicircle contains three concentric semicircles at such distances from each other, that the spaces between them may contain figures.

The outward circle is numbered from the right to the left hand, with 10, 20, 30, &c. to 180 degrees; the middlemost the same way, from 180 to 360 degrees ; and the innermost from the upper edge of the scale both ways, from 10, 20, 30, XC. to yo degrees.

It is easy to conceive that the protractor, though a semicircle, may be made to supply the place of a whole circle ; for if a line be drawn, and the centre-hole of the protractor be laid on any point in that line, the upper edge of the scale corresponding with that line, the divisions on the edge of the se* micircle will run from 0 to 180, from right to left : again, if it be turned the other way, or downwards, keeping the centre-bole thereof on the aforesaid point in the line, then the divisions will run from

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