94 The Rev. J. Challis on Capillary Attraction 
equation. Hence this equation cannot in general be satisfied 
except for a very small value of ¢. If the surface were hori- 
zontal, we should have * = 0, cos¢ = 0, and therefore 
2q' = q. This relation appears to be nearly satisfied be- 
tween mercury and glass, since the experiment of Casbois 
shows, that by merely boiling the mercury, its upper surface 
in a capillary glass tube may become horizontal, or even con- 
cave. The reasoning by which ¢ was shown to be in general 
a very small angle, does not apply to mercury, which is inca- 
pable, like water and oils, of adhering to a solid. The small- 
ness of the angle of actual contact, seems to be a condition 
always satisfied, whenever a fluid moistens a solid*. 
It is not possible to determine theoretically the form of the 
curve A N Q near the solid, because the laws of the mole- 
cular forces are unknown. Considering, however, the small 
extent of their sphere of activity, we may say that for a small 
distance the curve will be the same, whether the fluid rise 
against a plane surface or in a capillary tube. Let N bea 
point of the fluid surface situated just beyond the sphere of 
sensible action of the solid, let N R be drawn vertically, and 
the angle QN R =. It is proved, on the supposition of 
incompressibility, (see Poisson’s New Theory of Capillary 
Action, art. 18,) that the quantity of fluid raised in a given 
tube varies as cos w. Now, as it is shown above that the an- 
gle ¢ of actual contact is constant, and very small, it follows 
that the angle w, and consequently the heights of ‘ascent, may 
be different for different relative positions of A and N. If 
the fluid ascend ina tube not previously wetted, the points A 
and N will be nearest each other, » will have its greatest value, 
and the height of ascent be least. As A and N are more re- 
moved from each other by wetting more of the solid surface, 
the rise of the fluid may be expected to be greater, and to 
attain its maximum value when the moistening is carried to 
such a degree, that the solid can retain no more fluid attached 
to it. In this case the influence of the solid on the form of 
* The views which this communication is intended to explain are stated, 
in part, at the close of my Report on Capillary Attraction (contained in 
the Fourth Report of the British Association), to which I take this oppor- 
tunity of referring for the sake of pointing out an error in the remarks 
(p. 273.) on an equation of Laplace’s theory, equivalent to that obtained 
above, excepting that gravity is not taken into account. It is not true, 
as there stated, that Laplace neglects the superficial variation of pressure. 
The strictures of Dr. Young upon it, adduced at p. 266 of the Report, 
will appear to be inapplicable from the reasoning above, which it is hoped 
will serve to place the inferences to be drawn from this equation, and its 
importance in the capillary theory, in a true point of view. 
