LETTERS TO THE EDITOR 509
plot of Co(S) versus s, and must therefore be independent of time t. This
was confirmed experimentally.
If the cell is sector-shaped, a similar reasoning leads to the following
result, which replaces Eq. [3]:
(Oc/Ox)x2tx3/xo 2 = c0(q); q = (1/z2t)ln(x/xo), [41
which is true irrespective of whether x is approximately the same through-
out the cell or not.
From the distribution co(s) we can derive the size distribution when the
relation between s and size is known. When Stokes' law applies, a plot of
SiCo(S) against s~ is equivalent with a plot of g(R) versus R, where R is the
particle radius and g ( R ) d R the volume (or the weight) of the particles
the radius of which lies between R and R + dR. The application to Ludox
gave a curve the width of which was in good agreement with the results
reported b y Alexander and Iler.
I:~EFER]~NCE
1. ALEXANDER,G. B., AND ILER, R. K., J. Phys. Chem. 57,932 (1953).
Cellulose Research Institute J . J . HERMANS
State University College of Forestry, A.M. R ~ E
Syracuse, New York
Received August 18, 1958
A NOTE ON YOUNG'S EQUATION
A. J. G. Allen recently published (1) a mathematical proof of the equation
W = 21~ cos 0, [1]
in which W is the weight of the meniscus at a vertical wall, 21 the perimeter
of the wall, ~ the surface tension of the liquid, and 0 the contact angle. An
equivalent proof has also been given b y J. F. P a d d a y (2). It seems worth
mentioning t h a t Eq. [1] was first derived b y Laplace in 1806 (3) and can
be found in several textbooks, for example, reference 4.
Both Dr. P a d d a y and Dr. Allen refer to Eq. [1] in connection with m y
criticism (5) of Young's equation. In reality, there is no connection. The
fact that one of Laplace's formulas, as usual, is correct has no bearing on
the correctness or otherwise of a relation proposed by Young.
]:~EFERENCES
1. ALLEN A. J. G., J. Colloid Sci. 1S, 273 (1958).
2. PADDAYJ. F., Proc. 2nd Intern. Congr. Surface Activity S, 187 (1958).
3. LAPLACE "Oeuvres completes," Vol. 4, p. 432. Gauthier-Villars, Paris, 1880.
4. NEUMANN, FRANZ, "Vorlesungen ueber die Theorie der Capillarit~t," p. 97.
Teubner, Leipzig, 1894.
5. BIKERMAN, J. J., Proc. 2nd Intern. Cong. Surface Activity S, 125 (1958).
Massachusetts Institute of Technology, J . J . BIKERMAN
Cambridge, Massachusetts
Received August 20, 1958
