and Strength of Materials. 227 
strength or utmost tension of a fibre at dis- 
tance a=s, and let the tension of a fibre be 
designated by any power v of its extension. 
SL" 
We have then a’: 2°::s: > the forceex- 
erted by a particle at a, which multiplied 
by y, gives oe = the force of all the parti- 
cles in de; and this multiplied by z, its dis- 
v+} 
“4 SYX 
tance from b, gives —~— = the momentum 
of cohesion of de: and the sum of the mo- 
menta of all the de will be equal to the weight 
hung at D, or the whole strength of the 
beam. 
4. For example: Suppose the beam to be 
arectangle, as a common joist; then de will be 
constant, and equal to 5, and the expression 
: het 
of its strength will be —,— ; andthestrength 
~ b \ 
of the joist = 5 X sum of all the er If then 
the distance, ba, be supposed to be divided 
into an infinite number of parts of equal 
breadth, the line de may be considered one of 
those parts, and » will assume all the various 
values 1, 2, 3, &c. to infinity, or a. The 
foregoing expression for the strength will then 
ofl ofl 0-1 ort) 8 
sb 
become = x(1'42°4 34&.toa )=> 
