|
< = 1 from z = 0 to z = a, \
[phi](z) = 0 from z = a to z = [oo]; / (42)
and corresponding therewith,
[Pi](z) = a - z from z = 0 to z = a, \
[Pi](z) = 0 from z = a to z = [oo], / (43)
[psi](z) = 1/2a(a^2 - z^2) = 1/3(a^3 - z^3) from z = 0 to z = a, \
[psi](z) = 0 from z = a to z = [oo], / (44)
Equations (37) now give
_
2[pi] / [oo] [pi]a^4
K0 = ----- | z^3dz = -------, (45)
3 _/0 6
_
[pi] / a [pi]a^5
T0 = ---- | z^4 dz = -------. (46)
8 _/0 40
The numerical results differ from those of Young, who finds that "_the
contractile force is one-third of the whole cohesive force of a
stratum of particles, equal in thickness to the interval to which the
primitive equable cohesion extends_," viz. T = (1/3)aK; whereas
according to the above calculation T = (3/20)aK. The discrepancy seems
to depend upon Young having treated the attractive force as operative
in one direction only. For further calculations on Laplace's
principles, see Rayleigh, _Phil. Mag._, Oct. Dec. 1890, or _Scientific
Papers_, vol. iii. p. 397.]
ON SURFACE-TENSION
Definition.--_The tension of a liquid surface across any line drawn on
the surface is normal to the line, and is the same for all directions of
the line, and is measured by the force across an element of the line
divided by the length of that element._
_Experimental Laws of Surface-Tension._--1. For any given liquid
surface, as the surface which separates water from air, or oil from
water, the surface-tension is the same at every point of the surface and
in every direction. It is also practically independent of the curvature
of the surface, alt]]>
|