CONSTRUCTION X. THE ARCH LINE 155

suppose I will not give it to him, but only the two smaller stones at b, b; he will doubtless try to put them up, tilted against each other, as at d. Very awkward this; worse than card-house building. But if he cuts off the corners of the stones, so as to make each of them of the form e, they will stand up very securely as at B.

But suppose he cannot lift even these less stones, but can raise those at c, c, c. Then, cutting each of them into the form at e, he will doubtless set them up as at f.

§ 2. This last arrangement looks a little dangerous. Is there not a chance of the stone in the middle pushing the others out, or tilting them up and aside, and slipping down itself between them? There is such a chance: and if, by somewhat altering the form of the stones, we can diminish this chance, all the better. I must say “we” now, for perhaps I may have to help the reader a little.

The danger is, observe, that the midmost stone at f pushes out the side ones: then if we can give the side ones such a shape as that, left to themselves, they would fall heavily forward, they will resist this push out by their weight, exactly in proportion to their own particular inclination or desire to tumble in. Take one of them separately, standing up as at g; it is just possible it may stand up as it is, like the Tower of Pisa: but we want it to fall forward. Suppose we cut away the parts that are shaded at h and leave it as at i, it is very certain it cannot stand alone now, but will fall forward to our entire satisfaction.

Farther: the midmost stone at f is likely to be troublesome, chiefly by its weight, pushing down between the others: the more we lighten it the better: so we will cut it into exactly the same shape as the side ones, chiselling away the shaded parts, as at h. We shall then have all the three stones k, l, m, of the same shape; and now putting them together, we have, at C, what the reader, I doubt not, will perceive at once to be a much more satisfactory arrangement than at f.

§ 3. We have now got three arrangements; in one using

[Version 0.04: March 2008]