he two sides, which will be found to
be about 12 inches and 8 inches long, and the third angle will measure
just 26 degrees. It doesn't make any difference on what scale we draw
the triangle, whether it be miles, yards, feet, inches or fractions of
an inch, the proportions will be the same. If the base line had been 6
half-inches, or 3 inches long, and the same angles were used, the other
two lines would measure 12 half-inches, or six inches, and 8
half-inches, or 4 inches. If the base line were 6 quarter-inches long,
the sides would be 3 inches and 2 inches long.

[Illustration: Fig. 84. Determining the Distance to the Tree.]

"Now, for example, I am going to measure the distance to that tree over
there. Get out your chain and measure off a straight line 10 feet long.
Now, I'll set the surveying instrument with the plumb-bob right over the
end of this line, and sight through the two sight holes until I bring
the two vertical hairs in line with each other and the tree. Look at the
compass needle. It points to the 173 degree mark on the cardboard ring.
Now, Bill, you hold the rod at the other end of our base line while I
swing this instrument around and sight it. There, the needle points to
92 degrees, and subtracting this from 173 the difference, 81 degrees, is
the angle at the right end of our base line. We'll do the same thing at
the other end of our line. See, the compass needle points to 189
degrees, and now sighting to the pole at the other end of the line we
find that the needle points to 268. The difference, 79 degrees, is
therefore the size of the angle at the left end of our base line. Now we
will draw this out on paper, as we did our first triangle, using
quarter-inches to represent feet. Our base line was 10 feet long, and we
will therefore draw a line 10 quarter-inches, or 2-1/2 inches long, on
our drawing board. On this line we will construct the triangle, using
the angles 81 and 79 degrees. There, that's how our triangle looks, and
the right hand side measures 7-1/4 inches, while the left hand side
measures 7-5/16 inches. That is, 29 quarter-inches for one side and
29-1/4 quarter-inches for the other. As each quarter-inch represents a
foot, you will find that the tree is about 29 feet from the right end of
our base line and 29 feet 3 inches from the left hand end. Of course,
our instrument is not perfect, neither is our drawing; but if you
measure it off with the chain you will see that I am not very far f