The degree, therefore, may be more or less, but it is always the 360th part of the circumference of a circle. Let it be quite understood that, whether an angle is to be on a sheet of paper, or in the skies, the divisions do not change.
This must be well grasped, it is of the utmost importance for the explanations which follow. It is therefore settled: the measure of the angles has nothing to do whatever with a measure of length.
We have shown how to measure an angle. Let us examine now what is a triangle, without pondering too much over this geometrical figure, which every one knows. The essential property of this three-cornered figure is that the sum of its three angles is always equal to 180 degrees.
In other words, the protractor placed successively at each angle will give three numbers, which, added, make up 180 degrees. Keep this property well in mind, as it will serve us hereafter.
Now, to what distance does a degree correspond? For example, take a yardstick, and with the graphometer (an instrument by which angles are measured), in readiness, carry it from the latter instrument to a certain distance, till the two extremities of the yardstick measure one degree; this yard is then said to subtend an angle of one degree.
Now, measure the distance which divides the yardstick from the instrument, and you will find it to be 57 yards. Therefore, one degree corresponds to an object being at a distance of 57 times its height. A man two yards high at a distance of 57 times his height, or 114 yards will measure one degree.
One minute will be represented by a piece of cardboard of a hundreth part of a yard long seen from a distance of 34 yards; and finally, a second will be given by a card a hundreth part of a yard seen from a distance of 2062 yards.
A hair seen at 20 yards about represents a second. This perhaps, you think to be too small to be seen by the naked eye.
Suppose that you to measure the distance of a church situated on a height, and from which you are separated by a river (see fig.) Choose on the river’s bank two spots from which the steeple C can be seen, say A and B. At B plant a surveying-staff, and with the graphometer, go to A and find the angle formed by B A C.