1918, | On a New Theorem in Elasticity. 423: 
(X, Y, Z)=force bese on the particle which occu- 
pies the point (2, y;2 
4. A number of interesting applications are at once 
suggested. 
Suppose the motion to be vibratory. Then if the body 
forces be nil, the average kinetic energy will be equivalent to 
the average potential energ 
(i) the surface tractions be nil, or constant, as in the 
case of the vibration of a supported rod, or plate 
ends, 
(ii the surface deplevcnens be zero, 
(iii) If part of the surface be under zero or constant 
stress and part under varying stress with no sur- 
face cepacia (e.g. the case of a clamped rod, 
or string stretched between two points). 
These theorems are of course well known, and can be 
deduced in other wa ys. ' 
PROVE OOP 
