6G6 
PROFESSORS A. VY. REINOLD AND A. W. RUCKER 
But from (29) and (25) 
da x f cos 2(f) 1 sin 2(0 2 — £,) — cos 20 2 sin 2(0 : + _ 2YdT 
sin 2 L sin2(0 2 — £,) J T ’ 
and from the same equations and (22) 
d/3/ f cos 2(f)/ sin 2 %f) — cos 2 0/ sin 2(0/ + £/) ] 2Yr?T 
“cos 2 0ft sin2(0/+£/) J ““t - ’ 
whence, substituting for 0/, 0/, £/, and in terms of 0 1? 0 2 , and cla. l ——d^ 2 , 
and in like manner dot z = — d/3/. It follows that the maximum distances of the two 
parts of the film from the cylinder are the same whether the black covers l/'nth 
or 1 — 1/nth of the entire film, but that the maximum contraction in the one case is 
equal to the maximum bulge in the other, and vice versd. 
The following Table contains in the first column the fraction of the entire length of 
the film over which the change in surface tension is supposed to have extended. In 
the second and third columns are the corresponding values of 0 I and 0 2 , calculated 
for the case in which X= 1 ‘25/Y. The next four columns contain quantities from which 
&c., can be determined. In the last column is the ratio of the change of pressure 
caused by a partial change of surface tension to that produced by the extension of the 
change over the entire film. Throughout dT is considered positive. 
Table VII. 
&/(&+£*) 
0i 
02 
T dxJYdT 
TdpJYdT 
Tdx/YdT 
TdfaJYdT 
YdpfdT 
dpi dp' 
0 
o 
-23 
16 
o 
■90 
/ 
0 
0 
0 
2 
0 
0 
o 
0-2 
-21 
40 
100 
30 
0-037 
-0-234 
1-867 
-0-064 
0-197 
0-0985 ; 
0-3 
-20 
35 
103 
40 
0-069 
-0-489 
1-679 
-0-099 
0-420 
0-2100 
0-5 
-17 
54 
107 
54 
0-116 
— 1116 
1-116 
-0-116 
1-000 
0-5000 
07 
-13 
40 
110 
35 
0-099 
-1-679 
0-489 
-0-069 
1-580 
0-7900 
0-8 
-10 
30 
111 
40 
0-064 
-1-867 
0-234 
-0-037 
1-803 
0-9015 
1-0 
0 
113 
16 
0 
-2 
0 
0 
2 
1-0000 
Since, when dT is positive, d/3 1 and da.. z refer to parts of the two unduloids which 
do not lie between the rings, it follows from this Table that the greatest divergence 
of any part of the generating curves from the generating line of the initial cylinder is 
0T16YdT/T. 
If, therefore, as in most of our experiments, Y = 10 mm. (nearly), and if we take 
dT/T= 0'01, it follows that the greatest change in the diameter of the film caused by 
the gradual spread of a change of surface tension of 1 per cent, would be only a little 
greater than 0’02 mm., a quantity which certainly lies within the limits of the error 
of experiment. If, therefore, a film was half black and half coloured it would differ 
