23 
dicular section of the capillary surface was a parabola, from 
which a second approximation furnishing a small correction of 
the first was easily obtained. In tubes of small caliber a like 
method shewed the section of the capillary surface by a ver- 
tical plane through the axis to be a parabola, as a first ap- 
proximation, with a small correction of the result as a second 
approximation. . 
Success with these cases led the author of the paper to in- 
vestigate the form of the capillary surface for a liquid of indefinite 
extent in contact with a single plane vertical surface of a solid 
of which the lower edge was immersed in the liquid. ‘This is 
the first case treated in the paper as the fundamental one of 
capillary attraction. By taking an elementary vertical prism in 
the liquid held above the original level, and finding the condi- 
tions for equilibrium amongst the forces acting at its upper sur- 
face, a differential equation for the tension was obtained, and from 
the consideration that the tension must be the minimum pos- 
sible at each point when the liquid is at rest, the calculus of 
variations gives the form of the section of the surface by a ver- 
tical plane perpendicular to the plane of the body as an ex- 
ponential curve with the equation z=/. an where # and & are 
constants, z the vertical and y the horizontal ordinate of any 
point in the surface, with the origin the point where the ver- 
tical solid meets the level of the liquil at a great distance. 
An addendum to the paper contained investigations for the 
forms of the capillary surfaces between vertical parallel plates 
at any distances and for tubes of any diameter without approxi- 
“mation For parallel plates at any distances the equation of the 
section of the surface by a plane perpendicular to them was 
found to be expressed in finite terms as follows: 
hi 2 Es us, # 
Liais fe"te “I, 
where h’ and m are constants, z and y the vertical and hori- 
3—2 
