MECHANICS. 17 
duce motion the applied force must be considerably greater than what is 
necessary for equilibrium, and this increase of power required will be in 
proportion to the number of obstacles to motion. Of these, the principal is 
friction, which requires a greater or less increase of power, when an actual 
motion of the machine is demanded. On the other hand, friction admits a 
diminution of power when equilibrium is to be restored after motion has 
taken place, or when motion is to be prevented. In the investigation of the 
action of machines, therefore, reference must be had ‘o friction and similar 
hindrances, the rigidity of cords, &c., for example. 
c. On the Strength and Stress of Materials. 
When a solid body is exposed to any stress whatever, whether in the 
direction of its fibres, or perpendicular or obliquely to them, and this stress 
be continued until a fracture results, before this last circumstance occurs, 
there must be a moment in which there is an equilibrium between the 
resistance of the fibres of the body or its strength, and the stress to which 
it is exposed; by strength being meant the power resisting fracture, and 
stress the power tending to produce fracture. By reason of this equilibrium 
the theory of the strength of bodies comes under the head of statics. 
This strength of bodies may be considered under three points of view: 
first, with regard to the absolute or longitudinal strength, or the resistance 
presented by a body to a force acting in the direction of its fibres, and 
tending to tear them apart, as in pl. 17, fig. 5; secondly, with regard to 
their relative, respective, or transverse strength, or the force with which a 
body supported or fastened at one or both ends, resists a force acting trans- 
versely, that is, perpendicularly or obliquely to the direction of its fibres; 
thirdly, the strength of resistance, or the force with which a body resists a 
pressure tending to crush or crumble it. By strength of torsion is meant 
the resistance of a body to a force striving to twist it about its fixed axis. 
The absolute strength of two beams or rods—the form is indifferent—is in 
direct proportion to the area of their transverse sections. Thus if the body 
fastened to A (fig. 5, pl. 17) have at B a transverse section of one square 
inch, and be just capable of supporting the weight applied to C, then a body 
three inches square or nine inches in area will sustain nine times that 
amount. The weight of the body itself, however, must be taken into 
account, as acting at its centre of gravity. A rod or pole may be made so 
long as to break or tear asunder with its own weight, as soon as its weight 
acting at the centre of gravity exceeds the absolute strength of the trans- 
verse section. On this account, this centre of gravity should be brought as 
near as possible to the point of support, and such bodies should always be 
made stronger above, as in fig. 5. 
If to a wire or any elastic body weights be suspended, not enough, how- 
ever, to produce a rupture, and the extension suffered by the operation be 
measured, it will be found that the relation between the weight, P, and the 
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