108 



DYNAMICAL THEORY OF SOUND 



distance, by an amount proportional to this distance. This 

 kind of strain is called a " shear," from the fact that it is of the 

 type which tends to be set up by the action of the two edges 

 of a pair of shears. The " amount " (77) of the shear is specified 

 by the relative displacement per unit of mutual distance, i.e. by 

 the ratio DD'/AD, or 2e, in the first part of Fig. 39. Again, 

 by moving B'C' into coincidence with BC, we might prove that 

 the strain is also equivalent to a shearing of planes parallel to 

 BC and the axis 3, in the direction of BC. This is shewn in 

 the second half of the figure. 



D D' 



C C A A 



D D 



A B B C 



Fig. 39. 



41. Stresses. 



The name " stress " is applied to the mutual action which 

 is exerted across any ideal surface S drawn in a body, between 

 the portions of matter immediately adjacent to $ on either side. 

 We are here concerned with molecular actions sensible only over 

 an exceedingly short range, so that the portions of matter in 

 question are confined to two exceedingly thin strata, whose 

 common boundary is S. The resultant force on a small portion 

 of either stratum may then be taken to be ultimately pro- 

 portional to its area, and the intensity of the stress is 

 accordingly specified by the force per unit area. This force 

 may be of the nature either of a push or a pull, and may be 

 normal or oblique, or even tangential to the area. 



For simplicity, it is usual to begin with the notion of a 

 state of uniform or " homogeneous " stress, i.e. the stress over 

 any plane is assumed to be uniform, and the same in direction 

 and intensity for any two parallel planes. It will of course in 

 general be different for planes drawn in different directions. 

 It may be shewn that there are then three mutually perpendic- 



