230 On the Transverse Strain, 
equal forces,a = h. If v = 1, or the forces are 
: 8 i : 
as the extensions, a= yh, And this lastis 
a confirmation of the disputed assertion of 
Mr. Emerson, who, on the suppo ition of 
perfect elasticity in the fibres without their 
contraction, says, at page 114 of his Me- 
chanics, that if $1h of its height be ent from 
the top of such a beam, parallel to the base, 
the remainder will be stronger than the 
whole. 
Tt will however appear from the foregoing 
general value of a, that, if the bottom of the 
beam be incompressible, as is generally as- 
sumed, the assertion is true under every sup- 
position of force, except that of Galileo: 
And that is an hypothesis, which, when ap- 
plied to all kinds of bodies, cannot, it seems 
probable, be long considered sufficient to 
measure the forces of lateral cohesion. 
8. Now if we wish to obtain that point, at 
which, the top part being cut off parallel to 
the horizon, the remainder shall be as strong 
as the whole, we must equate the two values of 
the strength of ABCD and AhB, or put 
sb fh a* a3 ; ‘ 
PACES on a)= sbh GC Sei and from 
these, by reduction, we geta, or the height = 
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