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Arrows and the Archer's Paradox
Part 2 of 4

The explanation of the archer's paradox was found by means of high speed spark photography which the writer undertook in 1932 to secure direct evidence of what the arrow does as it passes the bow. An electric circuit included a 9-uf condenser, charged to 5600 v. with rectified alternating current, and a spark gap of magnesium blocks mounted in a 12-in. reflector. The discharge of the condenser across the gap produced sufficient actinic light to give fully exposed negatives on the fastest photographic plate obtainable at that time. Two cameras were set up, one to photograph the arrow from directly above (Fig. 11), the other to obtain corresponding side views of the bow discharging the arrow. For any particular shot the discharge of the condenser was triggered by a small auxiliary spark gap within the larger one. The arrow penetrated a screen consisting of a sheet of waxed paper having tinfoil on both sides, thus closing a circuit that discharged the condenser through the primary of an air core transformer, to cause a secondary discharge across the trigger gap. Successive photographs of a given arrow shot from a given bow were obtained by placing the circuit-closing screen at increasing distances in successive shots. The pictures thus obtained, one set of which is reproduced in Fig. 12, show that as the string leaves the fingers the arrow is given a lateral impulse at its feathered end. At the same time the tip of the arrow is given a lateral impulse in the same direction by the side of the bow. These lateral forces are sufficient to start an oscillation of the arrow about two nodal points. The arrow oscillates not only while it is passing the bow for an appreciable number of cycles after it has left the string. An arrow which is properly matched to the bow has a period so related to the time required for it to pass the bow that it apparently "snakes" its way around the handle without once touching the bow after the first lateral impulse at the tip. Figure 13 will help in visualizing how this occurs. The oscillation of the arrow takes place about the line of aim, and since there is no interference to its passage by rubbing or striking the bow, it flies in the direction in which it was aimed. High speed motion pictures by Hickman bear out the findings from spark photographs.

Fig. 11. Speed-flash photograph in a series from which Fig. 12 was compiled. The camera pointed nearly vertically downward, with shutter open, in a darkroom. The arrow released the flash at a predetermined point of its path.
Fig. 11. Speed-flash photograph in a series from which Fig. 12 was compiled. The camera pointed nearly vertically downward, with shutter open, in a darkroom. The arrow released the flash at a predetermined point of its path.
Fig. 12. The archer's paradox explained by speed-flash photography. <br>Note the oscillation around the bow grip without touching the latter.
Fig. 12. The archer's paradox explained by speed-flash photography.
Note the oscillation around the bow grip without touching the latter.