G 30 
PROFESSORS A. W. REINOLD AND A. W. RUCKER 
that he was evidently aware that other causes might affect the result, and that the 
differences of surface tension given by different experiments varied considerably. 
Thus, if we attempt to compare the surface tensions of two spherical films by 
measuring their sagittse, the question of the real magnitude of their circular bases 
becomes important. The fact that a film adheres to its solid support by means of a 
ring of comparatively thick liquid makes it uncertain whether the dimensions of the 
film can be directly inferred from those of the solid. 
In one of Van der Mensbrugghe’s experiments the films were formed on a ring 
4 cm. in diameter, and their sagittte were 16'55 and 17'70 mm. respectively. If, 
therefore, the bases of both segments had the same diameter as the ring, the radii of 
the spheres, of which they were parts, were 2'03G and 2’015 cm. This might indicate 
that the surface tensions differed by about 1 per cent. The inequality can also be 
accounted for by supposing that the films had the same surface tension, but that, 
owing to some little difference in the size of the thick liquid rings which united them 
to the solid, the radii of their bases differed by 0'18 mm. This calculation, at all 
events, proves that small errors of this kind might produce differences of the same 
order as those ascribed to changes in surface tension. 
The experiments of previous observers were all made with comparatively thick films. 
We have had considerable experience in producing films which display the black of the 
first order. Their thickness, the measurement of which we have described in a previous 
communication, # is about one-tenth of that ascribed by Plateau to the bubble on 
which he based his conclusion. It was quite possible that the two surface layers might 
be separate in his experiment and yet give evidence of mingling in a film ten times 
thinner. 
[t A preliminary objection may be taken to the observations of Plateau and 
Ludtge, as it may be urged that, if the tension of a film alters as it becomes thinner, 
it must break when it has become thin enough for the tensions of the thicker and 
thinner parts to differ by an appreciable amount. We have elsewhere^ expressed an 
opinion that the possibility of the existence of a film in such a state depends on the 
relative magnitudes of its viscosity, and of the difference of tension in question. As 
the matter has an important bearing on the subject of this paper, it may be well to 
discuss it a little more fully. 
There can of course be no doubt but that a difference of surface tension in two parts 
of the same film must produce motion. Is it therefore a priori certain that, if large 
enough to be measured, it must either produce rupture or motion so violent as to 
prevent the measurements being made ? 
In considering this question, it must be observed that no calculations had been 
made previous to our own as to what difference of surface tension is measurable by 
* ‘Phil. Trans.,’ vol. 174 (Part 2, 1883), p. 645. 
f The paragraphs within these brackets were added Nov. 10, 1886. 
f ‘ Phil. Trans.,’ vol. 172 (Part 2, 1881), p. 489. 
