FRICTION BETWEEN WATER AND AIR. 
599 
where ip is the coefficient of slipping for the water, and f this coefficient for the glass 
tube. These conditions give for u and L, 
W 
7JT 2 
l°gR-log? + ^ 
logR- 
l 4 * £ 
- lo gr + s + - 
( 9 ) 
L=W 
(R 2 — r 2 ) — Rr 2 (log R — log r) 
Rr 2 (log R — log r) + Rr£ + r 2 p 
( 10 ) 
The last formula applied to the former observations gives ten linear equations for £ 
and from which one finds, by the method of least squares, |=4'=0 - 029. With these 
numbers we now get the following differences between the observed values of A and the 
calculated ones : — 
+0-23 -0-26 +0-87 +0-85 +1-69 
+0-20 +0-71 -1*86 -1-18 -0-40 
One sees that the accord is of the same degree as before, although the sum of the 
squares of the errors is now a little smaller, 10-01 against 17-46 as before. The equality 
of £ and \p could easily be explained, as the tube was always wet inside ; but the 
values of i and ip cannot be relied on at all, because they become even negative when 
the first seven observations only are used for their determination. The real values of 
£ and ^ can only be found by taking into account the conical form of the jet. 
I have also calculated the first series of observations by aid of the equation (7). The 
calculated values are of course all too great, as the measuring tube with which the obser- 
vations were executed was too small ; but still one can see that the calculation goes 
parallel to the observation as long as the limit is not passed within which our theory 
holds good. 
Asp . tube . 
I- 
r . 
A . 
A ’. 
| A_A ' 
l 
47*2 
0-1393 
17-1 
18-5 
- 1-4 
38-2 
0-1408 
16-6 
17-8 
- 1-2 
26-9 
0-1435 
15-1 
16-9 
— 1-8 
16-0 
0-1463 
140 
16-1 
- 2-1 
2 
47-1 
0-1393 
22-3 
25-1 
- 2-8 
37-3 
0-1410 
21-8 
24-3 
- 2-4 
26*5 
0-1434 
19 1 
23-4 
- 4-3 
3 
49'8 
0-1389 
28-1 
45-1 
- 18-0 
42-6 
0-1400 
25-8 
44-4 
- 18-6 
36-5 
0-1412 
22-6 
43-9 
— 21-3 
4 
50-5 
0-1391 
25-2 
57-2 
— 32-0 
44-0 
0-1398 
23-1 
56-2 
— 33-1 
31-7 
0-1422 
17-5 
54-8 
— 37’3 
