598 
HE. VIKTOE VON LANG ON THE 
we have the corresponding values, 
2=E ’” =0 ’1 (4) 
q=r, u=Vj 1 } 
U being the velocity of the water at the surface of the jet, given by 
W=Tr 2 U (5) 
By the equations (4) we get 
W log R— log; 
»r a log E-log r’ W 
and in consequence for the volume A of air flowing through the tube per second, 
A=f«2^=w[^ i |^__ 1 ] (7) 
In order to compare our observations with this formula, we have still to fix what 
numerical value we shall assume for the radius of the jet. The simplest way is of 
course to take for r the mean of its values at the top and at the bottom of the tube ; 
and, indeed, we get in this way a tolerably good result, as is shown by the following 
comparison of the observed values of A and of the calculated ones designated by A'. 
Asp. tube. 
- 
A’. 
A. 
A -A'. 
5 
0-1582 
14-20 
14-0 
-0-20 
6 
0'1 566 
15-56 
14-8 
-076 
7 
0-1392 
• 20-02 
20-0 
-0-02 
0-1708 
17-22 
17*5 
+ 0 28 
s 
0-1300 
24-57 
25-1 
+ 0-53 
0-1456 
24-77 
23-9 
-0-87 
0-1708 
22-71 
22-6 
-Oil 
9 
0-1392 
28-06 
25-7 
-2-36 
0-1512 
27-83 
25 6 
—2-23 
0-1708 
26-19 
24-9 
-1-29 
It is not before we come to tube 9 that the differences between the observed and the 
calculated numbers are greater than the possible errors of observation. But the radius 
of this tube is already beyond the limit within which our suppositions as to the motion 
of air hold good. 
A still better accord is got by supposing that there is a slipping between the air and 
the jet of water, and also between the air and the aspirating tube. We get, then, in 
lieu of the conditions (4) the following ones, 
-d i du 
i = E > u =-^Tq' 
du 
Tq’- 
( 8 ) 
