243.  Our lines are to be horizontal; then the roof must be as flat as possible.  We need not think of snow, because, however much we 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.

[Illustration:  Fig. 14.  Leading lines of Villa-composition.]

244.  Take a flat line of beauty, a d, fig. 14, for the length of the edifice.  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 parabolas with cycloids, etc.; but the use of curves is always the best mode of obtaining good forms.[55]

[Footnote 55:  [Compare Modern Painters, vol.  IV. chap. xvii.  Sec. 49, and Elements of Drawing, Letter III.]]

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 maximum of the great curve, to restore the balance), join r q, s b, and we have another modification of the same beautiful form.  This may be done in either side of the building, but not in both.

245.  Then, if the flat roof be still found monotonous, it may be interrupted by garret windows, which must not be gabled, but turned with the curve a b, whatever that may be.  This will give instant humility to the building, and take away any vestiges of Italian character which might hang about it, and which would be wholly out of place.

The windows may have tolerably broad architraves, but no cornices; an ornament both haughty and classical in its effect, and, on both accounts, improper here.  They should be in level lines, but grouped at unequal distances, or they will have a formal and artificial air, unsuited to the irregularity and freedom around them.  Some few of them may be arched, however, with the curve a b, the mingling of the curve and the square being very graceful.  There should not be more than two tiers and the garrets, or the building will be too high.

So much for the general outline of the villa, in which we are to work by contrast.  Let us pass over to that in which we are to work by assimilation, before speaking of the material and color which should be common to both.