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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 situation 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, &C. to 90 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 semicircle 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 180 to 360, and so completes an entire circle with the former semicircle.

The use of the protractor is to lay off angles, and to delineate or draw a map, or plan, of any ground from the field notes ; and is performed in the following manner.

To protract a field-book, when the angles are taken from the


PL. 6. fig. 9.

-..On your paper rule lines parallel to each other, at an inch asunder (being most usual), or at any other convenient distance; on the left end of the parallels put N. for north, and on the right S. for south; put E. at the top for east, and W at the bottom of your paper for West.

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Then let the following field-book be that which is to be protracted, the bearings being taken from the meridian, whether by a circumferentor, theodolite, or semicircle, and measured with a two-pole chain.

No. Bearing. Ch. L.
1 2833 55.20
2 3481

-3 317 29.20

266.55.20 5 193 40.00 6 124 76.00 ng 631 87.02 Close at the first station.

Pitch upon any convenient point on your paper for your first station, as at l, on which lay the centre-hole of your protractor, with a protracting-pin; then if the degrees be less than 180, turn the arc of your protractor downwards, or towards the west; but if more than 180, upwards, or towards the east.

Or if the right hand be made the north, and the left the south, the west will be then up, and the east down.

In this case, if the degree be less than 180, turn the arc of your protractor upwards, or towards the west; and if more, downwards, or towards the east.

By the foregoing field-book, the first bearing is 283 , turn the arc of your protractor upwards, keeping the pin in the centre-hole, move the protractor so that the parallel lines may cút opposite divisions, either on the ends of the scale, or on the degrees, and then it is parallel. This must be always first done, before you lay off your degrees.

Then by the edge of the semicircle, keeping the protractor steady, with the pin prick the first bearing 283 t, and from the centre point, through that point or prick, draw a blank line with the pin, on which from a scale of equal parts, or from the scale's edge of the protractor, lay off the distance 55C. 20L. so is that station protracted.

At the end of the first station, or at 2, which is the beginning of the second, with the pin place. the centre of the protractor, turning the arc up, because the bearing of the second station is more

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