121-123] STRESS IN A BODY. 117 



forces acting in these lines on the particles on one side of the 

 plane be reduced to a resultant, at the centroid, A, of the area 

 within the curve, and a couple. Now let the curve, remaining in 

 its plane and similar to itself, be indefinitely contracted, so that 

 it tends to the point A at the original centroid. At any stage 

 of the process let R be the resultant, and a- the area in question. 

 Then a vector localised at the point A, of magnitude equal to 

 the limiting value of the ratio E/a; and in the direction and sense 

 which R takes in the limit when a- is indefinitely small, is called 

 the stress at A across the plane. 



The stress is conceived to be exerted by the part of the system 

 on one side of the plane upon the part on the other side of the 

 plane. Since the stress was compounded from internal actions 

 between particles on the two sides of the plane, there is an equal 

 and opposite stress exerted by the part of the system on the 

 second side of the plane upon the part on the first side. 



When the stress is normal to the plane it is called tension or 

 pressure according as it acts on the part of the system on one side 

 of the plane in the sense from that side towards the other side or 

 in the opposite sense. 



Now the method by which the general equations of motion, 

 for any part of a body, are applied to deformable bodies consists 

 in regarding the internal forces as always equivalent to stresses 

 across the elements of the surface of any part of the body. 



123. Reaction of bodies in contact realised as resultant 

 stress. To define stress at a point across a plane we began by 

 considering the forces exerted by particles on one side of the plane 

 upon particles on the other side, and the resultant of these forces 

 for a finite area of the plane. This resultant may be called the 

 resultant stress across the area. 



In the same way when two bodies are in contact over a finite 

 plane area we may define the resultant stress which either exerts 

 on the other across the area. 



If the area is indefinitely diminished, so that it is contracted 

 to a point, it is manifest that the resultant stress so defined ought 

 to be regarded as reducing to the reaction between the two bodies 

 described in Article 117. 



