che 
fluid will move with the prescribed velocity and with zero pressure; 
and the outer fluid moves in the same way and experiences the 
same pressure, as if the body were present. For the sake of 
continuity the forces XX ,; will also be treated as volume forces 
(with finite derivatives with respect to w, y, 2) acting on a very 
thin layer *). 
We now have: 
» 7 dV 
[fae ay dex = fff de dy de x, + f [ate dy de X= 9 + WOS 
When on the other side we put 
sE [ffasdyderxw . O13 NO AB 
ee ffe ana ae 15 
aa |p fee ELKE oi. ter Te ee (HO) 
where according to the well-known formula: 
we have 
Ow 
a ON V)v—e(v- V)wtpAw. . (16) 
(u is the coefficient of friction of the fluid). 
Substituting this in (15), we find by working out the integrals, 
that according to (1) (these conditions suffice for this) all terms 
vanish except that with X, so that: 
d © Es Ow a du d EX 
—_—=— ; =d TR r = 
os w dy zx 8 if edy de fr X ro 
4 dV 
=| ftearaermor g+ 5 de Os) 
C 
d dV 
W = 0.= ("Gi dy pe sens ATS) 
dt dt 
Therefore: 
which is in agreement with (11). 
§ 5. Remarks. 
I. Applying (15) and (16) not to an unlimited fluid, but to a 
fluid bounded by a fixed surface S, along which both w and its 
first derivatives are zero, we find 
1) This layer is not the boundary layer from the theory of PRANDTL; it must 
_ still be thin compared with the latter. Outside this layer no external forces act 
on the fluid. 
2) The place and therefore the radius vector r of each element dx dy dz are 
regarded as fixed; then we must take the local differential quotient of w. 
