Measuring the Height of a Tree

There is a very easy way to measure the height of a wall, or a tree, or a church spire, that any boy or girl can use if he or she can do a sum in simple proportion. It is necessary that the sun should be shining at the time - that is all. Suppose that we have a tree, and the sun is shining, then the shadow of the tree is cast on the ground.

We must measure the distance from the extreme point of the shadow to the place right under the top of the tree. If the top point of the tree is right above the middle of the trunk, then we must calculate half the diameter of the trunk in making our measurements. Suppose that the distance from the point of the shadow to the trunk of the tree is 40 feet, and that the tree is 2 feet thick, then the total distance is 41 feet (40 feet plus half the diameter of the tree).

Now we take a stick, of which we know the exact length. Suppose that it is three feet long. We hold this upright with one end on the ground and notice how far its shadow extends. Then we measure the length of the stick's shadow, and perhaps find that it is 6 feet long. Now we multiply the length of the tree's shadow (41 feet) by the length of the stick (3 feet), and divide by the length of the stick's shadow (6 feet). The answer we get is 20 1/2, and we know that the tree is 20 1/2 feet high.

If we get odd inches in our measurements, we can work the sum out in inches instead of in feet. We can also get the answer - though not quite so correctly - by seeing how many steps it takes to go from the edge of the shadow to the tree, being careful to make our steps as nearly uniform as we can. Then, by measuring the length of one step, we can multiply its length by the number of steps, and find the distance. But in any measurement, whether it be a tree, or a church, or a wall, we must make sure that we take the distance to a point immediately under the highest point, so that if it be a church spire, for instance, we must make allowance for the distance between the wall up to which we measure and the centre of the church tower.

from the 1911 Book of Knowledge: The Children's Encyclopedia (Grolier)
page 1927