2 REPORT—1862. 
On Capillary Attraction. By the Rey. F. Basnrortu, B.D. 
The theories of capillary action brought forward by Laplace, Young, and Poisson 
lead to the same form of differential equation to the free surface of a drop of fluid. 
During the last fifty years many attempts have been made to compare theory and 
experiment, but the results arrived at seem to be quite unsatisfactory. The expe- 
riments have generally been made by measuring the heights to which fluids rose 
in capillary tubes. The smaller the diameter of the tube, the greater is the 
elevation or depression of a fluid; but at the same time it becomes more difficult 
to secure a bore of a perfectly circular section and a surface perfectly clean. Laplace 
attempted to test his theory by comparing the measured thickness of large drops of 
mercury with their theoretical thickness obtained by an approximate solution of his 
differential equation. 
After duly considering all the circumstances of the case, it appeared to the author 
that the forms assumed by drops of fluid, of small or moderate size, afforded the 
best means for testing the theory of capillary action. The drops of fluid may rest 
on horizontal planes which they do not wet, or they may hang below horizontal 
surfaces which they do wet. Extensive tables have been calculated, which give 
the exact theoretical forms of all drops of fluid resting upon horizontal planes, as 
mercury on glass, within the limits of size to which it seems desirable to restrict 
experiments. 
n order to determine the exact forms of drops of fluid, a microscope has been 
mounted so that it can be moved horizontally or vertically by micrometer screws 
provided with divided heads. In th2 focus of the eyepiece are two parallel hori- 
zontal and two parallel vertical lines, .orming by their intersections a small square 
in the centre. The lines are purposely made rather thick in order that they may 
be seen without difficulty, and before reading off the screw-head divisions, care 
is taken to cause the image of the outline of the drop to pass through the middle 
point of the square caused by the intersection of the cross lines. Thus the co- 
ordinates are obtained of as many "a as may be thought necessary, and after- 
wards the form of a section of the drop, passing through the axis of its figure, may 
be drawn by a scale of equal parts. By trial, a theoretical form must be fitted to 
this experimental form, using the tables. When this is satisfactorily accomplished, 
the value of Laplace’s a is known, as well as the value of 6, the radius of curvature 
at the vertex: a determines the theoretical form of the drop, and 0 its size. 
Only one or two satisfactory measurements have been made at present, but suffi- 
cient has been done to show that such values may be assigned to the constants as 
to secure a most exact agreement of the theoretical with the experimental form of 
the free surface of a drop of fluid resting on a horizontal plane. It remains to he 
seen whether a is constant for drops of all sizes of the same fluid at the same tem- 
perature. If experiment be found to agree with theory, then the effect of a variation 
of temperature upon a must be determined. 
' This method of proceeding affords the means of determining with great accuracy 
the angle of contact, because the tables calculated from theory give the coordi- 
nates for points, where the inclination of the tangent to the horizon is known, at 
intervals of one degree, and parts of a degree can be calculated for by proportional 
arts. 
If the experiments on mercury appear to confirm theory, it will be desirable to 
complete the tables for the forms of pendent drops of fluid, because it will be very 
difficult, if not impossible, to find supporting planes which such fluids as oils, water, 
spirit of wine, &c. do not wet or adhere to. In such case it appears to be possible 
to make use of pendent drops alone for the determination of a. When a has been 
determined for each of two fluids, as spirit of wine and oil, it will be desirable to 
examine the mutual action at their common surfaces, which may be done by 
measuring the forms of drops of one fluid immersed in a bath of the other fluid con- 
tained in a cell having parallel and transparent vertical sides and horizontal planes 
at the top and bottom. 
_ Since the differential equations of Laplace and Poisson are the same in form, it 
‘is evident that the above measurements for a single fluid cannot decide the difference 
between them. It seems, however, manifest that the constitution of the surface 
is very different from the interior of a fluid, But the thiclmess of this surface of 
