18 PHYSICS. 
extension, EH, may be expressed by the following general equation : —_ 
a5 ; where P” is the weight at which the wire would tear, and E’ the 
extension produced by it. 
However simple the theory of absolute or longitudinal strength may be, 
that of relative or transverse strength is exceedingly complicated. Here, 
not only the area of the transverse section is to be taken into account, but 
also the shape; and likewise, in addition to the resistance against fracture, 
that also to every bending of the body which may be produced by the 
pressure. 
If a prism be supported at the two extremities, or fastened at one, and be 
loaded in the middle, or at the free extremity in the latter case, there will 
be a bending of the prism. This will take place in such a manner, that 
while one set of fibres will be stretched, another set will be compressed ; in 
the interior. of the transverse section, therefore, a fibre can be imagined 
about which this bending takes place, without experiencing itself either 
extension or compression; this fibre is called the axis of flexion, or the 
neutral axis. 
Supposing the fibres of a beam to be absolutely incompressible, and the 
beam loaded as in pl. 17, fig. 8, at Q, then it must turn about its lower 
point in the line through AC, and every fibre in this direction will be in a 
state of tension ; if all the fibres were entirely unextensible, then the rotation 
would occur in the same manner, but every fibre in the lie would be ina 
condition of pressure. It is known, however, that all bodies may be both 
compressed and extended; therefore the rotation will be about neither the 
upper nor the lower point, but, as in fig. 6. about the point B, and the upper 
fibres will then be stretched, while the lower will be compressed ; those in 
the line AB will be in a condition of neutrality. Now, both above as well 
as below the neutral axis, a point may be imagined, in one of which the 
moments of compression, and in the other of extension, are united, these 
being the means of pressure and tension. In fig. 9, let the weights, P and 
Q’, represent the sum of this tension and compression, then the position of 
the neutral axis will be determined by the ratio of the moments, and will he 
in the middle when the moments are equal. The mean points of compres- 
sion and extension coincide with the centres of gravity of their respective 
surfaces. 
The mode of finding the neutral axis, and consequently the relative 
strength, for the case in which the body consists of extensible and com- 
pressible fibres, is explained in fig. 6. Imagine a body in the form of a 
parallelopipedon, whose breadth is b, and height #, and which is fastened in 
such a manner into the wall, CC, as to have in a natural condition the 
direction BB’. If, by a weight at A, it be bent into the position, BFA, then 
BFA is the neutral axis. Let EF = be asmaller part of this axis, so that 
GK is an element of the body ; then, in an uncompressed condition, this will 
everywhere be equal in length to». Draw JK parallel to GG’, and repre- 
sent the distance, ET, of a fibre, ST, from the axis by u= (FT) ; also make 
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