G3G 
PROFESSORS A. W. REUSTOLD AXD A. W. RUCKER 
Table I. 
R 
n 
2TJl/dT 
l 
V/ir 
v/ir 
(Y + v)P 
cm. 
2 
8+ %/63 
0-12 
cm. 
0-06116 
10-6660 
0-01529 
10-6813 
i 
4+ d 15 
0-25 
0-12232 
1-3323 
0-03058 
1-3629 
0-5 
2+ v3 
0 - 56 
0-24464 
0'16452 
0-06116 
0-22568 
0-286 
1-707 
+ co — 
0-42771 
0-02629 
0-10693 
0-13322 
0-271 
1-500 
0-45128 
0-02051 
011282 
0-13333 
0-256 
1-224 
— QO + 
0-47783 
0-01433 
0-11946 
0-13379 
0-250 
1-000 
0-98 
0-48930 
0-01042 
0-12232 
0-13274 
0-5 
2— d 3 
0-02 
0-24464 
0*00799 
0-06116 
0-06916 
00 
0 
0 
0 
0 
0 
0 
The importance of this table for our present purpose depends, however, chiefly on 
the figures in the first three rows. The radii are chosen to correspond with those of 
bubbles which Plateau used. As he does not mention the radius of the bubble on 
which he based his estimate of the superior limit of the radius of molecular attraction, 
it is impossible to estimate exactly the sensitiveness of his experiment. Probably it 
did not exceed 0*56. 
Limiting Sensitiveness of Ludtge’s Experiment. 
The expression for this quantity has been calculated by Van der MensbruggheA 
Let the radius of the tube at the extremities of which the films are formed be r, and 
let the sagittm of the two spherical segments be nr and nr respectively. Then from 
equation (2) 
8T?t _ 8TV 
r(l+n~) 
If the tensions alter, the change in the pressure exerted on the internal air must be 
the same for both films, so that 
ndT T(1—H 2 ) 1 _ n'dT 
l+7i 3+ (1 + h 2 ) 2 ( n ~l+n'~ 
T(l-n'z) 
(1+n'f 
tin'. 
If both films had at first the same surface tension, T=T' and n—n. Also, since 
the total volume is constant, dn— — dn. Hence 
2 Trdn/(dT-dT)=- nr( 1 + n 2 )/( 1 - nf 
In the following table we have taken r= 1, so that the sensitiveness for a tube of 
any given radius is obtained by multiplying the figures in the second column by the 
radius expressed in centimetres. 
* ‘ Bruxelles, Acad. Sci. Bull.,’ rol. 30, 1870, pp. 322-332. 
