250 On the Transverse Strain, 
Cor. 2d. If v —w —1, or the forces are 
as the extensions and compressions. 
Xax : 
Ik = xf «Xe = — x section of ten- 
a 
ay ah, a 
sion X g, where g is the distance of the centre 
of gravity of that section from the neutral line. 
Yy"y : ; 
And J/—* = * xJ yy = = x section of 
compression x g’, g’ being the distance of its 
. s 
centre of gravity as before. Hence — x see- 
ie : Cc - 
tion of tension x g = ah section of com- 
pression x g’; .*, section of tension x g : sec- 
tion of compression x g’:: ¢: s,* a constant 
'* From the application of those principles which we 
have controyerted in the preceding note, Mr. Barlow has 
obtained a rule for finding the position of the neutral line 
when the centres of tension and compression coincide with 
those of gravity, and which is the same as the second 
corollary. Butin Mr. B.’s case v and w in the textareeach 
=o; and if what we have done there be correct, the sur- 
faces, (not the surfaces multiplied by the distances of their 
centres. of gravity,) must be in a constant ratio, as in 
Cor. Ist. 
Ii may further be stated, that the very disputable conclu- 
sions which that gentleman has arrived at of the effect being 
the same as if all the fibres resisted with equal forces (or that 
the centres of tension and compression are the same as the 
centres of gravity of the sections) seem wholly to rise 
from the false theory which he has adopted since they 
were derived from the application of that theory. 
