ARISING FROM INEQUALITIES OF TEMPERATURE. 697 



We begin with an element of volume moving with the velocity-com- 



ponents U, V, W t then by the ordinary investigation of the "equation of 

 continuity " 



If after performing the differentiations we make U=u, V=v, Ww, the 

 equation becomes for an element moving with the velocity (u, v, w) 



u dv dw\ d , ~. ,., d , ~ . d , ,.,.,. S ._ 



(8) Equation of Density. 



Let us first make Q=l, then, since the mass of a molecule is invariable, 

 the equation becomes 



d + p ( d ^ + ^ + <^\ = Q . ,..(39) 



ri/ V ft or Citi dz / 



which is the ordinary "equation of continuity." 



Eliminating by means of this equation the second term of the general 

 equation (38) we obtain the more convenient form 



>P% (>). 



(9) Equations of Motion. 

 Putting Q = u + g, this equation becomes 



where any combination of the symbols , 17, is to be taken as the average 

 value of that combination. 



Substituting their values as given in (28) 



which is one of the three ordinary equations of motion of a medium in which 

 stresses exist. 



VOL. u. 88 



