employment of Oblique Riders. 31^ 
It is well known, that if the planks were firmly united into 
one mass, their strength would be rendered 12 times as great 
by the union, and their stiffness 144, times: but this is not the 
greatest resistance of which the materials are capable, even 
without any extension of their base of support ; for if the 
planks were connected in pairs at half the distance of the 
whole depth, and allowed to move freely round fastenings 
perfectly secure, their strength, speaking theoretically, would 
be greater by nearly one half than if they formed a compact 
mass, while their stiffness would be only about one fourth as 
great: and an effect nearly similar might be produced if the 
respective pairs were united by oblique braces, extending over 
half the depth of the whole structure, although it would be 
very difficult, in practice, to make the strength of an arrange- 
ment of this kind even equal to that of a compact mass, since 
the fastenings could never be so perfect, as to bring every 
fibre of each plank into its full action at once, as the theory 
supposes. If the planks were already united into a compact 
mass, so as to be incapable of bending except as a whole, it is 
of importance to inquire W’hether any advantage would be 
of elasticity m, the depression d, and the force applied at the end equal to the weight 
45* 4 ^* 
of a similar plank of the length g, we have m = g, and d — g; but, for a 
simple frame of two equal pieces, the force being g, the longitudinal extending force 
g . g . 
will be the weight of — and the actual extension ■— . — , and the depression 
half as great as that of a plank of the same dimensions, when g is given, or supposing 
the weight on the frame sextuple, so as to be equal to that supported by the plank 
of six times the depth, three times as great; but by taking 12 planks together, we 
increase their stiffness only 12 times, while that of the frame is rendered 144 times 
as great by a similar extension of the base, so that it becomes in this case 4 times as 
great as that of the 12 planks. 
T t 2 
