experiment have convinced me that when a fish swims it never throws its body into a single curve, as represented at fig. 31, p. 67, but always into a double or figure-of-8 curve, as shown at fig. 32.[43] [43] It is only when a fish is turning that it forces its body into a single curve. [Illustration: FIG. 32.--Swimming of the Sturgeon. From Nature. Compare with figs. 18 and 19, pp. 37 and 39; fig. 23, p. 43; and figs. 64 to 73, pp. 139, 141, and 144.--_Original._] The double curve is necessary to enable the fish to present a convex or non-biting surface (_c_) to the water during flexion (the back stroke of authors), when the tail is being forced away from the axis of motion (_a b_), and a concave or biting surface (_s_) during extension (the forward or effective stroke of authors), when the tail is being forced with increased energy towards the axis of motion (_a b_); the resistance occasioned by a concave surface, when compared with a convex one, being in the ratio of two to one. The double or complementary curve into which the fish forces its body when swimming, is necessary to correct the tendency which the head of the fish has to move in the same direction, or to the same side as that towards which the tail curves. In swimming, the body of the fish describes a waved track, but this can only be done when the head and tail travel in opposite directions, and on opposite sides of a given line, as represented at fig. 32. The anterior and posterior portions of the fish alternately occupy the positions indicated at _d_ _c_ and _w_ _v_; the fish oscillating on either side of a given line, and gliding along by a sinuous or wave movement.