B18 Mr Watts’ Observations on the Resistance of Fluids. 
P = l ih {u + vf 
hnt p:=zgm, where represents the mass of matter actuated 
by the force of gravity g ; 
Therefore, m =: ^b 4)^ 
If, therefore, the small surface o be immersed to the depth h 
below the upper surface of the water, and moved through it 
with the velocity v, it will sustain on the one side the dead pres- 
sure gb j 
- 
is. 
dp — 
( 2 ). 
4 1 b^h X .... 
This equation exhibits the ultimate sensible pressure, or 
resistance ; or, which is all one, the element of the quantity 
of motion communicated to the fluid in an unit of time ; 
and therefore, differential of the 
quantity of motion communicated to the fluid during the in- 
stant d t. 
Let M, therefore, be the mass of the body which the surface 
h presents to the direct impulse of the fluid, and dv the instan- 
taneous diminution of the velocity v, caused by the resistance of 
the fluid, then, because the impulse of the resisting surface 
causes it to lose a quantity of motion equal to that which it com- 
municates, we shall have the equation. 
Mdv — ^^bv X s/ 
bat the force 
( 3 ). 
whence we conclude that the force opposed to the resistance, is 
dv 4<ghv 
Tt'~~W 
That is to say, that the resistance is in the sub-duplicate ratio 
of the depth immersion^ and the simple ratio of the velocity 
(f the_ resisted surface^ jointly. 
