48 Colorado College Studies. 



Expanding this and neglecting, as before, all terms excejjt 



du 

 the first, we get — for the rate of inflow. 

 dx 



This shows that the lost forces obtained for two dimensional 



flow hold in the case where the inflow is over two faces. This 



could have been concluded without the above proof, for the 



amount flowing in is fixed, and it is immaterial whether the 



flow is all in the direction of z or partly in the direction of z 



and partly in the direction of y. 



The forces in the direction of the y and z axes can be ob- 

 tained in the same way. 



It is to be noticed that a force element of the second order 

 is neglected if, for example, there is a normal increase in the 

 velocity u, for in that case the inflow will be accelerated. 



Equating the forces found and writing the remaining two 

 symmetrical equations, we have 



dp _<hi .'J. Idhi d'u d'li 



pdx 'H p\dx^ dy^ dz' 



fj. Id'v d'^v 

 P Xdxr' dy^ 



dp _ dv /J. f'd'v _^ d'^v d^v\ 



pdy dt p xdx^ dy^ dz^J 



y. dp _ow /Ji/dhv d^iv d^w\ 

 pdz 8t p\dx^ dy^ dz'' J 



(To be Continued in Volume VIII.) 



