264 THE STRENGTH AND ELASTICITY OF IRONBARK TIMBER 
Let = oe of elasticity. 
Let v = deflect: 
M 
Then it can be act that —- = #7 = 3 = nearly. 
Jf ¢ is the circular measure te the slope at a distance x from the 
origin, since 7 = tan ¢ = d ae 
Po M 
dw #I 
i + = al ae 
ar 
Fis a constant, and if the beam is of uniform section J will 
also be a constant, an we may write 
i= Sf Maz; vagy ff Maw 
In the case of a beam supported at each end and loaded in the 
centre as in the experiment. Assume the origin at the left hand 
support, then we have I = ~ w, if x is taken to left of centre’ 
; 
of beam, and If = = (7-), when # is taken to right of centre 
of beam. 4 
Therefore we nae by integrating ne 3° Ya) the qual 
i W x 
for Sees =eT futeas SET (2) x C 
When x = 4 then 7 = 0. 
Wis 
16HI 
fei = TET (#—Z) 
W hg Pz 
= lf ae a a 
rat (* z) ¢= a7 (S- T) xe 
When z = 0, v = 0, oe ee 
Wo fe Pp; pci a 
0 es Ose ~~) which is equal to a maximum 
Noeea =~ 
we 
v= SET = @ maximum when z = o 
