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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.
THE 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-hole 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 8. for south; put E, at the top for east, and W. at the bottom of your paper for west. .
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
No. Bearing. Ch. L.
193 40,00 6 124 76.00
631 87.02 Close at the first station,
Pitch upon any convenient point on your paper for your first station, as at 1, 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 cut 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 2834, 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
than 180, viz. 3481, Place your protractor parallel as before, and by the edge of the semicircle, with the pin prick at that degree, through which and the end of the foregoing station, draw a blank line, and on it set the distance of that station.
In the like manner proceed through the whole, only observe to turn the arc of your protractor down, when the degrees are less than 180.
If you lay off the stationary distances by the edge of the protractor, it is necessary to observe, that if your map is to be laid down by a scale of 40 perches to an inch, every division on the protractor's edge will be one two-pole chain ; ; a division will be 25 links, and of a division will be 12 links.
your map is to be laid down by a scale of 20 perches to an inch, two divisions will be one twopole chain ; one division will be 25 links; • a division 12, links, and • of a division will be 6. links.
In general, if 25 links be multiplied by the number of perches to an inch, the map is to be laid down by, and the product be divided by 20 (or which is the same thing, if you cut off one and take the half), you will have the value of one division on the protractor's edge, in links and parts.
1. How many links in a division, if a map be laid down by a scale of 8 perches to an inch?