§ XII. Suppose, then, instead of taking so much trouble with the member Yb, we save time and labor, and leave it a square block. Xb must, however, evidently follow the pillar, as its condition is that it slope to the very base of the wall veil, and of whatever the wall veil becomes. So the corners of Yb will project beyond the circle of Xb, and we shall have (Fig. XII.) the profile _d_, the perspective appearance _e_, and the plan _f_. I am quite sure the reader likes _e_ much better than he did _b_. The circle is now placed, and we are not afraid of its rolling away. The foot has greater expansion, and we have saved labor besides, with little loss of space, for the interval between the bases is just as great as it was before,--we have only filled up the corners of the squares. But is it not possible to mend the form still further? There is surely still an appearance of separation between Xb and Yb, as if the one might slip off the other. The foot is expanded enough; but it needs some expression of grasp as well. It has no toes. Suppose we were to put a spur or prop to Xb at each corner, so as to hold it fast in the centre of Yb. We will do this in the simplest possible form. We will have the spur, or small buttress, sloping straight from the corner of Yb up to the top of Xb, and as seen from above, of the shape of a triangle. Applying such spurs in Fig. XII., we have the diagonal profile at _g_, the perspective _h_, and the plan _i_. § XIII. I am quite sure the reader likes this last base the best, and feels as if it were the firmest. But he must carefully distinguish between this feeling or imagination of the eye, and the real stability of the structure. That this real stability has been slightly increased by the changes between _b_ and _h_, in Fig. XII., is true. There is in the base _h_ somewhat less chance of accidental dislocation, and somewhat greater solidity and weight. But this very slight gain of security is of no importance whatever when compared with the general requirements of the structure. The pillar must be _perfectly_ secure, and more than secure, with the base _b_, or the building will be unsafe, whatever other base you put to the pillar. The changes are made, not for the sake of the almost inappreciable increase of security they involve, but in order to convince the eye of the real security which the base _b_ _appears_ to compromise. This is especially the case with regard to the props or spurs, which are absolutely useless in reality, but are of the highest importance as an expression of safety. And this will farther appear when we observe that they have been above quite arbitrarily supposed to be of a triangular form. Why triangular? Why should not the spur be made wider and stronger, so as to occupy the whole width of the angle of the square, and to become a complete expansion of Xb to the edge of the square? Simply because, whatever its width, it has, in