employment of Oblique Riders, 317 
with respect to the power of resisting a very rapid motion, 
which I have, on another occasion, ventured to call resilience. 
(Lect. Nat. Phil. I. p. 143. II. p. 50.) Now it appears to be 
extremely difficult to unite a number of parallel planks so 
firmly together, by pieces crossing them at right angles, as 
completely to prevent their sliding in any degree over each 
other : and a diagonal brace of sufficient strength, even if it 
did not enable the planks to bear a greater strain without giv- 
ing way, might still be of advantage, in many cases, by dimi- 
nishing the degree in which the whole structure would bend 
before it broke. 
The strength of a simple rectangular frame, firmly fixed 
at one end, is rendered somewhat less than double by per- 
fectly fastening the joints at the other (fig. 4,) and the stiff- 
ness is nearly quadrupled.* 
* When two horizontal bars are firmly fixed at one end only, and simply united at 
the other end by a vertical piece, their immediate joint force in resisting flexure re- 
mains unaltered ; but if the vertical piece is firmly fixed to the ends of the bars, it 
may be considered as a lever held in equilibrium by four forces, arising from the re- 
pulsive and cohesive powers of the separate bars ; and the sum of these forces must 
vanish when reduced to the same direction, while the sum of their actions, referred 
to any point as a fulcrum, vanishes also : and it is obvious that the total compression 
of the one bar will initially be equal to the total extension of the other, provided that 
their strength be equal. Hence, if the mean distance of the bars be a, and the depth 
b, reckoned between the centres of action of the respective forces, which in perfectly 
elastic bodies will be \ of the whole depth, the first force being or, and the second — y, 
the third will be y, and the fourth — .v, and, from the equilibrium with respect to the 
point of application of the first force as a fulcrum, we have the equation — by-\-ay—, 
(rt-f Z>) X — o, and x zz while the joint effect of all the forces in resisting the 
• • So 
pressure of the weight is 2 (y + ar) b : c, c being the length of the bars, or — . 
while the resistance of the two single bars would be the inclination of the elementary 
MDCCCXIV. T t 
