3i8 
Dr, Young’s Remarks on the 
The comparative security, obtained by the addition of a dia- 
gonal brace, is almost without limit. Supposing any number 
of planks of equal dimensions to lie simply on each other 
without any adhesion, and to be firmly fixed at one end, their 
aggregate strength will be very little greater than that of a 
single plank of one sixth part of the common depth or thick- 
ness of each, supported by a brace a little stronger, in the 
direction of the diagonal of the whole, (fig. 5); and the stiff- 
ness of the parallel planks will be as many times less than that 
of such a frame, as there are planks in one third of the whole 
series. Thus if we had twelve planks, six inches deep, and 
one thick, with friction rollers interposed, it is demonstrably 
true, however surprising, that they would be very little stronger 
in supporting a weight at the end, than a single tie an inch 
square in its section, assisted by a diagonal brace of equal 
relative strength : and also that this apparently slight struc- 
ture would be nearly four times as stiff as the 13 planks, being 
depressed only one fourth as much, with a given weight, as 
the planks with a similar force acting on them.^ 
forces being here reduced to : and since the magnitude of y at the instant of break- 
ing is given, the force will be augmented by the firmness of the connexion in the 
ratio of 2a to a -\-b, which is always less than that of 2 to i. The stiffness may be 
nearly quadrupled by the fastenings, since the depression at the moment of breaking 
is reduced to little more than one half. 
* “ If one of the surfaces of a beam were incompressible, and the cohesive force 
of all its strata collected in the other, its strength would be six times as great as in 
the natural state.” Lect. Nat. Ph. II. 50. Art. 335. Hence a plank of -i of the actual 
depth, acting simply as a tie, supported by a brace fixed at the distance of the depth, 
would be as strong as the original plank: and by increasing the distance of the point of 
support of the brace in the ratio of the number of plafiks, the strength of the two ar- 
rafigements will remain equal, without altering the dimensions of the tie. The length 
of a plank being e, (Lect. II. 48. Art. 326.) the depth h, the height of the modulus 
