may slope the roof, it will not slip off from the material which, here, is the only proper one; and the roof of the cottage is always very flat, which it would not be if there were any inconvenience attending such a form. But, for the sake of the second contrast, we are to have gracefulness and ease, as well as horizontality. Then we must break the line of the roof into different elevations, yet not making the difference great, or we shall have visible verticals. And this must not be done at random. Take a flat line of beauty, a d, Fig. 45, for the length of the edifice.
Fig. 45.
Strike a b horizontally from a, c d from d; let fall the verticals; make c f equal m n, the maximum; and draw h f. The curve should be so far continued as that h f shall be to c d as c d to a b. Then we are sure of a beautifully proportioned form. Much variety may be introduced by using different curves; joining paraboles with cycloids, &c.: but the use of curves is always the best mode of obtaining good forms. Further ease may be obtained by added combinations. For instance, strike another curve (a q b) through the flat line a b; bisect the maximum v p, draw the horizontal r s (observing to make the largest maximum of this curve towards the smallest maxi-
