The mathematical formulae in which the Messrs. Weber embody their results would hardly be instructive to most of our readers.  The figures of their Atlas would serve our purpose better, had we not the means of coming nearer to the truth than even their careful studies enabled them to do.  We have selected a number of instantaneous stereoscopic views of the streets and public places of Paris and of New York, each of them showing numerous walking figures, among which some may be found in every stage of the complex act we are studying.  Mr. Darley has had the kindness to leave his higher tasks to transfer several of these to our pages, so that the reader may be sure that he looks upon an exact copy of real human individuals in the act of walking.

[Illustration:  Fig. 1.]

The first subject is caught with his legs stretched in a stride, the remarkable length of which arrests our attention.  The sole of the right foot is almost vertical.  By the action of the muscles of the calf it has rolled off from the ground like a portion of the tire of a wheel, the heel rising first, and thus the body, already advancing with all its acquired velocity, and inclined forward, has been pushed along, and, as it were, tipped over, so as to fall upon the other foot, now ready to receive its weight.

[Illustration:  Fig. 2.]

In the second figure, the right leg is bending at the knee, so as to lift the foot from the ground, in order that it may swing forward.

[Illustration:  Fig. 3.]

The next stage of movement is shown in the left leg of figure 3.  This leg is seen suspended in air, a little beyond the middle of the arc through which it swings, and before it has straightened itself, which it will presently do, as shown in the next figure.

[Illustration:  Fig. 4.]

The foot has now swung forward, and, tending to swing back again, the limb being straightened, and the body tipped forward, the heel strikes the ground.  The angle which the sole of the foot forms with the ground increases with the length of the stride; and as this last surprised us, so the extent of this angle astonishes us in many of the figures, in this among the rest.

The heel strikes the ground with great force, as the wear of our boots and shoes in that part shows us.  But the projecting heel of the human foot is the arm of a lever, haying the ankle-joint as its fulcrum, and, as it strikes the ground, brings the sole of the foot down flat upon it, as shown in figure 1.  At the same time the weight of the limb and body is thrown upon the foot, by the joint effect of muscular action and acquired velocity, and the other foot is now ready to rise from the ground and repeat the process we have traced in its fellow.

No artist would have dared to draw a walking figure in attitudes like some of these.  The swinging limb is so much shortened that the toe never by any accident scrapes the ground, if this is tolerably even.  In cases of partial paralysis, the scraping of the toe, as the patient walks, is one of the characteristic marks of imperfect muscular action.