At the same time, there is a downward motion of the bow hand, brought about in part by the downward push of the arrow, but probably to a greater extent by the elastic reactions of the muscles in the bow-arm. The downward motion is clearly shown in the spark-tracer photographs.

It is probable that the vertical component of force on the arrow, and reaction on the bow, are a partial cause for the rotation of the latter about a horizontal axis at right angles to the direction of shooting, when the "California Style" of shooting is employed. In part, this can also be accounted for by limbs that are dynamically unbalanced, i.e., one limb moving faster than the other.

Two avoidable causes of vertical jump are unbalanced limbs, which contribute to "kicking" in a bow, and failure to nock at the proper point. By finding the proper nocking point in a bow that has well-balanced limbs, vertical jump from any cause can be reduced if not altogether eliminated.

In all this I have mentioned some things with immediate practical applications, but have said nothing about that much talked-about quality of an arrow called "spine". Although this is a study in itself, it is so closely related to the paradox that a very brief statement about it should be made. Stiffness alone isn't spine. Writers on the subject have correctly pointed this out, and have suggested that it is stiffness combined with a quick return to straightness. This is not altogether a correct statement, since the arrow, as we have seen in the photographs, does not return to straightness after a single bend, but continues to oscillate more or less rapidly for perhaps a second, i.e., somewhere between 20 and 50 times before the oscillations die out and it remains straight. If, instead of saying "stiffness combined with a quick return to straightness" we say that spine may be measured by quickness of recovery from a deformation or bend, in relation to a certain amount of mass or weight, we shall come much closer to a usable definition. For example, a 5/16 rod of steel would have great quickness of recovery from being bent, but it would be far too heavy to be usable as an arrow. A 5/16 dowel of pine would be enormously less stiff, but, because of its lighter weight, might have the same quickness of recovery as the rod of steel; at the same time, its light weight makes possible its propulsion by the bow with a velocity that is practicable and serviceable.