( 260 ) 
As further 
yy =—A4Anfie, and yw»= — An fd 03 
or 
YW, = — 240) and wy = — 2a 03 
we may also write: 
Dee pan A ge ee 
=d) Gt NEN 
a 
If we neglect @9 with respect to @j, we get the well-known 
expresssion of LAPLACE: 
K =a @;? 
LAPLACE, however, proved this relation only in the supposition 
that the density in the liquid (also in the surface layer) is constant 
everywhere. 
For the tension normal to the lines of force, so in our case in 
the direction parallel to the separating surface, we found: 
Er (+5) 
This expression holds for a unit of surface. For an elementary- 
rectangle of transverse section of the capillary layer, (i. e. normal 
to the potential surfaces), two sides of which are parallel to the 
potential surfaces and have the length of a unit, whereas the other 
two sides have the direction of the tangents of the surface and 
a differential length dh, we get: 
575 (ee + La 
The total tension in the capillary layer will be equal to the sum 
of these differential-expressions, i. e.: 
2 2 
1 1 
Sj EE Bee Ae ML pe 
) enk UP IK a a: 
1 1 
’) This quantity S is zot the quantity H of Lapuace. - 
