first to note those which regard the actual shell of the arch, and then we shall give a few examples of the superseding of such expedients by Mont-Cenisian masonry. § III. What we have to say will apply to all arches, but the central pointed arch is the best for general illustration. Let _a_, Plate III., be the shell of a pointed arch with loose loading above; and suppose you find that shell not quite thick enough; and that the weight bears too heavily on the top of the arch, and is likely to break it in: you proceed to thicken your shell, but need you thicken it all equally? Not so; you would only waste your good voussoirs. If you have any common sense you will thicken it at the top, where a Mylodon's skull is thickened for the same purpose (and some human skulls, I fancy), as at _b_. The pebbles and gravel above will now shoot off it right and left, as the bullets do off a cuirassier's breastplate, and will have no chance of beating it in. If still it be not strong enough, a farther addition may be made, as at _c_, now thickening the voussoirs a little at the base also. But as this may perhaps throw the arch inconveniently high, or occasion a waste of voussoirs at the top, we may employ another expedient. § IV. I imagine the reader's common sense, if not his previous knowledge, will enable him to understand that if the arch at _a_, Plate III., burst _in_ at the top, it must burst _out_ at the sides. Set up two pieces of pasteboard, edge to edge, and press them down with your hand, and you will see them bend out at the sides. Therefore, if you can keep the arch from starting out at the points _p_, _p_, it _cannot_ curve in at the top, put what weight on it you will, unless by sheer crushing of the stones to fragments. § V. Now you may keep the arch from starting out at _p_ by loading it at _p_, putting more weight upon it and against it at that point; and this, in practice, is the way it is usually done. But we assume at present that the weight above is sand or water, quite unmanageable, not to be directed to the points we choose; and in practice, it may sometimes happen that we cannot put weight upon the arch at _p_. We may perhaps want an opening above it, or it may be at the side of the building, and many other circumstances may occur to hinder us. § VI. But if we are not sure that we can put weight above it, we are perfectly sure that we can hang weight under it. You may always thicken your shell inside, and put the weight upon it as at _x x_, in _d_, Plate III. Not much chance of its bursting out at _p_, now, is there? § VII. Whenever, therefore, an arch has to bear vertical pressure, it will bear it better when its shell is shaped as at _b_ or _d_, than as at _a_: _b_ and _d_ are, therefore, the types of arches built to resist vertical pressure, all over the world, and from the beginning of architecture to its end. None others can be compared with them: all are imperfect except these.