A Third Lecture, much to the same purpose, I read, May, 1699. in the same place, before the present Grand Duke of Tuscany, who honoured the University with a Visit, and me with his Presence at that Lecture. After which, he was pleased very particularly to consider both the Delineation and Model, and declared himself very well pleased with it,

The contrivance is obvious to the Eye. The outsides represent the Walls of the Building on which this Flat Floor or Roof is to be laid. The Beams next adjoyning to the sides, have one end lodged on those Walls; the other end sustained by another Beam, lying cross; both ends of which, are in like manner sustained by other cross Beams; and those again by others; till they reach the other Walls. So that no one of them can fall, unless the Walls fail, or the Beams break: all mutually sustaining each other without any Pillar or Prop to support them, besides the outer Walls.

The Models I caused to be made, and that of the Royal Society in imitation thereof, are in Breadth, about four times as much as the Length of the longest Beam. But may be continu'd, at pleasure, to farther breadth, as shall be thought fit. With this Caution: That the farther the Work is continu'd, the greater Weight will be charged on every Joynt; especially near the middle. And though in this Model, no one Beam is charged with so much as seventeen times its own weight: yet if the Work be continu'd to a greater breadth, the proportional Weight will be thereby increased. And therefore must be limited, according to the strength of Timber, able to bear more or fewer times its own weight.

I do not know, that yet it hath been reduced to practise, in more than four Pieces, in this Form. Such is one of the Floors in the Tower of the Publique Schools at Oxford: the Breadth whereof, to the Length of the Beams, is as three to two. But may doubtless be continu'd much further: especially in such a Roof or Floor, as is not to bear much more than its own weight.

Thus, for instance, a Bowling-Green of near an Acre of Ground, may be cover'd with a Frame of long slender pieces, without any other Prop than on the sides, for Vines, or other like Plants to run upon, so as to shade the whole.

Note here, That whereas the ends of the several pieces are to lie upon those that cross them, about the middle thereof; it will be necessary at every Joynt to abate both pieces half way, or near it; that one may be thus let into the other, and the whole reduced to a Flat. But whether such piece, so abated doth end even with that on which it lies, or doth lie over somewhat beyond it; is indifferent. And though That may seem more elegant; This, perhaps, may be fitter for use.

Each piece, I say, must be so abated half way, or near it. For, whereas those Beams, especially if of a considerable length, will, with the weight, bow a little; if this abatement be somewhat less than half way, (whereby without such bowing, the whole would somewhat rise in the middle) it will by such bowing be reduced to a Flat.

Note also, That a Frame thus contriv'd, needs neither Nail nor Pin; the several pieces fastening, as well as supporting one another. Yet, if it be to bear a great weight more than its own; it will be convenient to fasten each Joynt with Pins; and, if need be, to strengthen it with Iron-Plates, or line it with other pieces of Timber, to be fasten'd with Iron- Bolts; to make amends for what is weaken'd by the abatements at the Joynts: which will make the whole Frame exceeding strong.