Similar movements occur in the arms, which, as has been explained, are articulated to the shoulders by ball-and-socket joints (fig. 26, _x_ _x_´, p. 55). The right leg and left arm advance together to make one step, and so of the left leg and right arm. When the right leg advances the right arm retires, and _vice versâ_. When the left leg advances the left arm retires, and the converse. There is therefore a complementary swinging of the limbs on each side of the body, the leg swinging always in an opposite direction to the arm on the same side. There is, moreover, a diagonal set of movements, also complementary in character: the right leg and left arm advancing together to form one step; the left leg and right arm advancing together to form the next. The diagonal movements beget a lateral twisting of the trunk and limbs; the oscillation of the trunk upon the limbs or feet, and the oscillation of the feet and limbs upon the trunk, generate a forward wave movement, accompanied by a certain amount of vertical undulation. The diagonal movements of the trunk and extremities are accompanied by a certain degree of lateral curvature; the right leg and left arm, when they advance to make a step, each describing a curve, the convexity of which is directed to the right and left respectively. Similar curves are described by the left leg and right arm in making the second or complementary step. When the curves formed by the right and left legs or the right and left arms are joined, they form waved tracks symmetrically arranged on either side of a given line. The curves formed by the legs and arms intersect at every step, as shown at fig. 19, p. 39. Similar curves are formed by the quadruped when walking (fig. 18, p. 37), the fish when swimming (fig. 32, p. 68), and the bird when flying (figs. 73 and 81, pp. 144 and 157). [Illustration: