(Note: As many readers — and the article's author, Richard Reed — have pointed out, "How to Catch Carp With a Longbow", MOTHER EARTH NEWS NO. 33, contains a major error. The diagram on page 101, which illustrates the compensation for refraction needed when shooting into shallow water, shows the fish's actual location above its image. Actually, the reverse is true and the hunter must aim low, not high. The mistake was mine, and I apologize . . . both to Richard and to any beginning bowmen who may have returned frustrated from a day of misdirected archery. Among those who called my attention to the goof was Herm Fitz of Blue Riper, Oregon, who sent along the following valuable information on the optics of wetland bow-hunting. — MOTHER.)
In MOTHER EARTH NEWS NO. 33, Richard Reed ably described hunting carp with bow and arrow in shallow water ... and his article has no doubt inspired many readers to take up this sport, which involves shooting across an air-water interface. A single — but flagrant — inaccuracy in MOTHER's presentation will, however, inevitably lead to the failure of any beginner's attempts to pursue the intended prey.
Reed states on page 102, "To shoot at even a clearly visible fish only 8 inches under the surface. . . you must compensate for the refraction of light at the water's surface." This is quite true, but the novice who compensates according to MOTHER EARTH NEWS instructions will miss every shot! The diagram which illustrates the author's point (reproduced here as Figure 1in the image gallery) contains a serious error: The image of the fish should be shown directly above the creature's actual location — not below and beyond, as in the drawing — and the hunter should therefore aim low, not high (see the corrected version in Figure 2 in the image gallery). Moreover, the archer hunting carp is given no idea of just how much too low to direct his arrow. Since we don't want a bunch of carp-hunters coming home empty-handed, let's look more closely at the phenomenon of shooting into water.
Here's what happens when you peer through the lake's surface at the fat carp you hope to bag: The light rays reflected from the fish under water reach the air-water interface and, upon crossing that boundary, are bent. This phenomenon — known as the refraction of light — results from the light's speeding up as it enters the air. The amount of bending depends on the angle at which the original ray hit the interface; The greater the angle of incidence, the more deviation from its original direction. Thus, when one looks directly down (perpendicular to the surface) on a fish, there is no deviation in the line of sight . . . although the object will appear closer than it actually is. As the horizontal distance from hunter to quarry increases, the deviation gradually increases also, so that the prey seems to be higher and higher above its actual position (see Figure 3 in the image gallery).
You may have heard of the old hunting rules, "Kentucky windage" (whereby a rifle hunter on land aims into the wind) and "Tennessee elevation" (whereby he aims higher at more distant targets). Let's coin a new term to describe the technique of shooting across the air-water interface. Since the aim in such cases must be lower than appears proper, how about calling the corrective lowering "swamp depression"?
Now, the actual amount of "swamp depression" required for a true shot depends on one factor: the angle between the line of sight to the fish's image and the horizontal (call this the "sighting angle"). If the hunter can estimate the sighting angle fairly accurately — within 10 degrees — and learn how much to alter his aim in each case, he'll be almost guaranteed a hit with every arrow.
Table 1 lists a series of probable "sighting angles" with their corresponding "swamp depression" angles and approximate distances from hunter to fish. In composing this table I've assumed that the archer is 6 feet tall, wading in water 14 inches deep (so that his eye is 54 inches above the surface), and aiming at a fish through 8 inches of water . . . the maximum depth at which Reed recommends shooting. (My calculations — involving the use of Snell's law of optical refraction and relevant trigonometric functions — are likely to be of little concern to the general reader and aren't included here. Figure 4 in the image gallery presents the data of Table 1 in graphic form.
The results summarized in the table and graph are grounds for a few simple generalizations that may assist those who stalk the marshes for carp, or other hunters in related aquatic situations:
 "Swamp depression" is always negative: that is, the hunter always aims slightly lower than the image of the fish.
 The proper amount of "swamp depression" is never great. It ranges from zero for "straight down" shots to a maxim mum of less than 2 degrees for a sighting angle of approximately 25 degrees (the fish is then about 10-1/2 feet away), and falls off to zero as the distance between hunter and prey lengthens. Thus, the archer should gradually increase the "swamp depression" as the range approaches 10-1/2 feet and gradually decrease the angle of compensation as the quarry moves farther away.
 If you believe that your prey is swimming at a depth of less than 8 inches, use a correspondingly smaller "swamp depression" angle . . . since the distance between reality and image decreases as the fish approaches the surface (at the interface, fish and image are coincident).
Meanwhile, don't forget those other hunting rules I mentioned. Let's suppose you're trying for a distant carp on a windy day. In that case, "Kentucky windage" dictates that you shoot slightly into the wind so that the arrow will be blown true (the correct adjustment varies with distance to the target and windspeed). At the same time, the "Tennessee elevation" principle requires you to aim slightly above the object to compensate for the downward curve in the arrow's flight path . . . yet according to the rule of "swamp depression" you must aim slightly low to allow for the refraction of light at the surface! That may sound complicated, but with some experience a good hunter may learn to make all three compensations simultaneously and accurately. Happy hunting!