FRICTION BETWEEN WATER AND AIR. 
597 
1 Asp. tube. | E. | W. 
ii. m. 
IV. 
V ' 
VI. 
II.+III. 
A. 
5 0-238 26-0 
13-8 14-0 
14-1 
13-4 
12-6 
14-0 
14-0 
6 0-244 25-5 
j 14-7 | 14-8 
14-7 
13-8 
13-5 
14-8 
7 0-261 20-0 
20-5 19-5 
18-7 
17-8 
17-1 
20-0 
30-0 
17-9 17-0 
16-6 
16-3 
15-8 
17'5 
8 0-287 17-0 
24-5 25-6 
21-3 
17-9 
17-7 
25-1 
22-0 
24-0 23-8 
22-1 
19-6 
18-4 
23-9 
3°-0 
22-5 22-7 
20-7 
19-7 
19-5 
22-6 
9 0-303 20-0 
26-0 25-3 
21-4 
21-7 
23-7 
23-8 
23-5 25-2 
22-5 
21-8 
26-1 
25-6 
30-0 [ 
24-7 25-1 
22-6 
21-9 
24-9 
Approximate Theory of the Experiments. 
The exact theory of these experiments is rendered still more difficult by the fact that 
the water-jet has a different radius at different places. But to obtain at least an 
approximate solution of the problem we will assume a cylindrical form of the jet. In 
accordance with our smoke-experiments, we assume further that all particles of air flow 
through the aspirating tube in straight lines parallel to the tube’s axis, which we take 
for the axis of x. The velocity of the air-particles has therefore a finite value u only 
for this axis, it being zero for any direction perpendicular to this axis. 
In consequence of the last statement the pressure must be constant in each section 
of the aspirating tube. Now we have seen by the manometer that the pressure at the 
beginning of the tube is the same as at the end, viz. the pressure of the atmosphere ; 
this leads us to suppose that the pressure does not vary at all in the whole length of 
the tube. 
If we consider, further, that the motion of the air in the aspirating tube is a steady 
one and independent of time, and that no exterior forces exist, the hydrodynamical 
equations are reduced in the present case to 
dfu d 9 u „ 
U ’ 
( 1 ) 
the equation of continuity becoming 
dx 
( 2 ) 
In this last equation p denotes the density, which must be constant when the pressure 
is constant. This equation is therefore satisfied by our suppositions. As regards the 
equation (1) its integral is 
w=Llog#+M, (3) 
q denoting the distance from the axis of x. The constants L and M have to be deter- 
mined by the motion of the air next to the tube and next to the water-vein. If we 
assume that no slipping takes place, the air adhering to the glass as well as to the water, 
mdccclxxvi. 4 o 
