“How comes it that a stick, loaded with a weight at the upper extremity, can be kept in equilibrio, on the point of the finger, with much greater ease than when the weight is near the lower extremity, or, for instance, that a sword can be balanced on the finger much better when the hilt is uppermost?” “That is indeed strange. I should have thought,” replied Louisa, “that the higher the weight was placed above the point of support, the more readily would the line of direction have been thrown beyond the base.” “In that respect you are perfectly right; but the balancer will be able to restore it more easily in one case than in the other; since, for reasons which you will presently discover, the greater the circle which a body describes in falling, the less will be its tendency to fall. Look at the sketch which I have prepared for the explanation of this fact, and I think you will readily comprehend the reason of it. [Illustration: Man balancing a sword in each hand, hilt up in one, hilt down in other, showing arc of centres of gravity for each.] “When the weight is at a considerable distance from the point of support, its centre of gravity, in deviating either on one side or the other from a perpendicular direction, describes a larger circle, as at _a_, than when the weight is very near to the centre of rotation or the point of support, as at _b_. But, in a large circle, an arc of any determinate extent, such as an inch, for example, describes a curve which deviates much less from the perpendicular than if the circle were less; as may be seen by comparing the positions of the sword at _d_ and _e_; and the sword at _d_ will not have so great a tendency to deviate farther from the perpendicular, as that at _e_; for its tendency to deviate altogether from the perpendicular is greater, according as the tangent to that point of the arc, where it happens to be, approaches more to the vertical position. You see then that it is less difficult to balance a tall, than a shorter pole; and it is for the same reason that a person can walk with greater security on high than on low stilts.” “That is very clear,” said Louisa, “although, before your explanation, I always associated the idea of difficulty with their height.” “I suppose,” added Tom, “that the whole art of walking on stilts may be explained by the principles you have taught us.” “Undoubtedly it may; for the equilibrium is preserved by varying the position of the body, and thus keeping the centre of gravity within the base.” “It must be a great exertion,” observed Louisa.