362 Of Things relating to Mathematical Part 1 V 0 
A Third Lefiure, much to the fame purpofe, I read, 
May, 1 699. in the fame place, before the prefent Grand 
Duke of Tufcany, who honoured the Univerfity with a 
Vifit, and me with his Prefence at that Lefture. After 
which, he was pleafed very particularly to confider both 
the Delineation and Model, and declared himfelf very well 
pleafed with it, 
The contrivance is obvious to the Eye. The outrides re- 
prcfent the Walls of the Building on which this Flat Floor 
or Roof is to be laid. The Beams next adjoyning to the 
fides, have one end lodged on thofe Walls 5 the other end 
fuftained by another Beam, lying crofs$ both ends of 
which, are in like manner fuftained by other crofs Beams • 
and thofe again by others 5 till they reach the other Walls. 
So that no one of them can fall, unlefs the Walls fail, or the 
Beams break : all mutually fuftaining each other without 
any Pillar or Prop to fupport them , befides the outer 
Walls. 
The Models I caufed 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 longer!: Beam. But may be 
continu d, at pleafure,to farther breadth, as fhall be thought 
fit. With this Caution: That the farther the Work is 
continu'd, the greater Weight will be charged on every 
Joynt; efpecially near the middle. And though in this 
Model, no one Beam is charged with fo much as feventeen 
times its own weight : yet if the Work be continued to a 
greater breadth, the proportional Weight will be thereby 
increafed. And therefore muft be limited, according to 
the ftrength of Timber, able to bear more or fewer times 
its own weight. 
I do not know, that yet it hath been reduced to practife, 
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 
maydoubtlefs be continu'd much further: efpecially in 
fuch a Roof or Floor, as is not to bear much more than its 
own weight. 
Thus, for inftance, a Bowling-Green of near an Acre of 
Ground, may be cover d with a Frame of long flender 
pieces, 
