4 Dr. D. F. Comstock on the 
This can be readily shown by a consideration of the figure. 
When the velocity of the element is along (V) there is an 
Z A 
B. 
0' 
A' 
amount of work (v x . X x ) dy . dz done per second on the 
element by the tension (X x ) applied at the surface (O'A'), 
and this energy is instantly available at the surface (OA),. 
where it is given out. The distance over which the energy 
is transmitted being dx (the thickness of the 'element), the 
rate of energy-flow is 
— VaJLady dz dx = — v^X^dr, 
where (dr) is the element of volume. 
In like manner the velocity (vy) and the shearing stress 
(Y x . dy . dz) cause energy to be taken up at the surface (O'A') 
and given out at the surface (OA), and we have the rate of 
flow along the #?-axis 
— VyY x dj ; 
and finally the velocity (v z ) and the shearing stress (Z x ,dy . dz) 
give 
— v 2 Z x dr, 
Hence adding we have, if we call (fj) the density of flow 
along #, 
fjdr = - [v x X x + v y Y x + v,Zx) dr. 
Obtaining the corresponding equations in-similar way we 
have finally for the three components of the density of energy- 
flow along the constraints in any system 
fj = - (ffcX. + v,Y* + v z Z x ), * 
fy' = -(VvXy + VyYy + VzZy), L . . ■ (1) 
f z '^-(v x X g +v Sf Y e + v !S Z z ). . 
