The facts and deductions which are here presented are based on a large amount of experimental work carried on last winter and spring. One of the more important phases of this work was the taking of pictures of the arrow with extremely short time of exposure, as it was passing the bow. About 200 exposures have been made by this method; these have been carefully studied, and much information gained.
A review of the works on archery available to me discloses that Horace Ford was the first writer of a treatise on the subject to devote some attention to the manner in which the arrow passes the bow. Many writers since the days of Ford have undertaken to fathom the paradox, most of them unsuccessfully because they had no way of dealing with the forces and reactions set up during the very brief period in which the string accelerates the arrow from rest to its maximum velocity. We are dealing with a force, very large at its maximum value, acting on a non-rigid body, and varying continuously in magnitude and direction during its entire short period of action. It is this fact, and the impossibility of directly seeing the instantaneous positions and distortions of the arrow that have prevented our having more than a hazy understanding of the phenomenon of the paradox.
It will be of some value at this point to think in definite terms about the paradox of archery, in order that we may have something very tangible upon which to focus our attention. Why "paradox"? The word is derived from the Greek word meaning incredible; something seemingly absurd but perhaps really true. That the arrow should fly accurately along the line of aim, is paradoxical only if we think of its projection forward in terms of the string being let down slowly as illustrated in Ford's treatise, in Butt's revision of Ford, and in Badminton. The paradox is that the arrow flies on the line of aim, contrary to the expectation that it should fly far to the left. To most archers this is all very familiar ground.
The difficulty of the problem presented in the paradox— and by problem I mean the possibility of predicting the line of flight of an arrow, knowing the line of aim, weight of bow, stiffness, weight, and other characteristics of the arrow—is to be found in several causes. The first bears repetition, because of its importance: For any given bow and arrow we are dealing with a large force, acting on a non-rigid body, and varying in magnitude and direction during its entire short period of action. The other causes of difficulty are the large number of factors that affect the result. The fact that arrows can be selected to fly consistently, and behave properly, even when used with different bows, gives some hope that certain simple, fundamental relationships may be discovered which will help to an understanding of the paradox.
The first part of the problem is to ascertain exactly how the arrow gets by the bow. This must be done before we can say why it behaves as it does. In this case, high speed photography gives us the desired information.