776 
In order to calculate I we substitute for the body a fluid mass 
with perfectly the same motion as the body. The impulse of this 
fluid mass is to that of the body as @ to eo’; the total impulse of 
the fluid becoines therefore: 
vBti=eQvtl. . . 
This quantity can be calculated by means of formula (3). When 
the body has a rotatory motion it must be remarked that the sub- 
stituted fluid mass will contain vortex lines which must be comprised 
in the general sum. When the motion is a pure translation, all 
vortex lines lie outside the body. We have therefore: 
eQV+I=SJ=e02 CA... 7S ae 
from which follows 
I=o 2 Ci RY. ..o. 
and 
d dV 
We (ZCA) 08 .... . Uy 
This formula is the connection searched between the resistance and 
the vortex motion in the fluid. 
dV 
For a uniform rectilinear motion of the body Pie so that (11) 
is simplified into: 
d 
Wer Gh). . « +e Shean 
§ 4. Proof of formula (11). 
In the same way as above the body is replaced by a fluid mass which 
has the same motion as the body and zero pressure’). Let the 
following forces be acting on the fluid: 
a. on the part that has been substituted for the body: the forces 
dy ‘ 
X; which have the value X;= eee fe: unit of volume (v is the 
velocity of the fluid); 
5. on a thin layer that is always there where the surface of the 
body would have been: the forces Xj ;, equal to the force exerted 
by an element of the surface of the body on the fluid (pressure 
and frictional forces taken together). 
Then the fluid will have just the right motion viz. the inner 
1) This means that the pressure has the same value as at infinity. 
