In this figure (54) the conditions represented at fig. 53 (p. 107) are exactly reproduced, the only difference being that in the present figure the wing is applied to the air in a more or less horizontal direction, whereas in fig. 53 it is applied in a more or less vertical direction. The letters in both figures are the same. The insects whose wings tack upon the air in a more or less horizontal direction, have an extensive range, each wing describing nearly half a circle, these half circles corresponding to the area of support. The body of the insect is consequently the centre of a circle of motion. It corresponds to _x_ of the present figure (fig. 54). When the wing is seized by the hand at _a_, and the root made to travel in the direction _n e_, the body of the wing travels in the direction _j f_. While so travelling, it flies upwards in a double curve, kite-fashion, and elevates the weight _l_. When it reaches the point _f_, it reverses suddenly to prepare for a return stroke, which is produced by causing the root of the wing to travel in the direction _m a_, the body and tip travelling in the direction _i b_. During the reverse stroke, the wing flies upwards in a double curve, kite-fashion, and elevates the weight _k_. The more rapidly these movements are repeated, the more powerful the wing becomes, and the greater the weight it elevates. This follows because of the reciprocating action of the wing,--the wing, as already explained, always drawing a current of air after it during the one stroke, which is met and utilized by it during the next stroke. The reciprocating action of the wing here referred to is analogous in all respects to that observed in the flippers of the seal, sea-bear, walrus, and turtle; the swimming wing of the penguin; and the tail of the whale, dugong, manatee, porpoise, and fish. If the muscles of the insect were made to act at the points _a e_, the body of the insect would be elevated as at _k l_, by the reciprocating action of the wings. The amount of tractile power developed in the arrangement represented at fig. 53 (p. 107), can be readily ascertained by fixing a spring or a weight acting over a pulley to the anterior margin (_a b_ or _e f_) of the wing; weights acting over pulleys being attached to the root of the wing (_a_ or _e_).