242 On the Transverse Strain, 
ot! 
1 
Also sum of the $52 Bs oi x Ge et wy hae to 
a? 
vot2 
vi sba sbaz 
6. Co) ets) Te42 
by their distances = T XD ia the same rule. 
= sum of the forces X 
Also sum of the a yr , by a similar process, = a 
= the sum of the a of compression. 
rby ee b (d—a) 
ry jo 
Also sum of the (day in like manner = a = 
ihe sum of the products of those forces X their distances. 
Now by the nature of the centre of gra- 
vity: The sum of the products of any forces 
x by their distances, divided by the sum of 
those forces, is equal to the distance at which 
if they were all collected they would pr oduce 
rb (d—a)’* 
*the same effect. Hence ——— = —,> 
w+l 
(d-a)=Aa in the preceding formula. 
And the strength or Hel) —_— 
sba? sba a ; 
o+2 t =a Os 35 (da) sha a 
— LxC wa 75 i (srg 
ie ss \ . 
(v-F1)(w4+2) (d—a) ). And if a@ be taken in 
terms of d it will appear that the strength is 
as the square of the depth 
