FLUIDS AND THE DETERMINATION OF THE CRITERION, 155 
The integral equation of energy of relative-mean-motion becomes 
Nae oee=— Mo fray + Joelle Cc) +) + Co) 
/dw’ dv’ dw dw'\2 dv if 
+(e+e) +(Gete) +(etG) lave... (2) 
lz dz | \dx 
If the mean-mean-motion is steady it appears from equation (41) that 


_— dp 
= [J ieay ae, 
the work done on the mean-mean-motion w, per unit of length of the tube, by the 
constant variation of pressure, is in part transformed into energy of relative-mean- 
motion at a rate expressed by the transformation function 
<7 [fe (we yr = + ww za) dy dz, 
and in part transformed into heat at the rate 
oil) + El) 
While the equation (42) for the integral energy of relative-mean-motion shows 
that the only energy received by the relative-mean-motion is that transformed from 
mean-mean-motion, and the only energy lost by relative-mean-motion is that 
converted into heat by the relative-mean-motion at the rate expressed by the last 
term. 
And hence if the integral of E’ is maintained constant, the rate of transformation 
from energy of mean-mean-motion must be equal to the rate at which energy of 
relative-mean-motion is converted into heat, and the discriminating equation becomes 
[[p (we dy sett 7) ue= -»({l2 ia) + (7) a esi 
dw’ dv'\2 du’ dw! \2 fdv’ du’\2 
ve (re ar a) a CG ag dy ) a5 (GE au dy ) Jy cae (43). 


The Conditions to be Satisfied by u and wv’, v’, w’. 
31, If the mean-mean-motion is steady wu must satisfy :— 
x2 
