The equations of a normal are therefore: 
» (X-*) = t {Y-y) = (Z-z ); 
this normal must pass through the centre of gravity of the parallelopi- 
don so that the condition of equilibrium becomes: 
u(a-x) = v(b-y) = w(l-z) = o J .(2) 
where a becomes known after the position of equilibrium being 
calculated. 
To judge the stability it is necessary to know the position of the 
principal centres of curvature. On each normal are two of such 
points. They form together a two-sheeted surface which we shall 
call for the future surface (M). Let §, tj and £ be the coordinates of 
the point of (M) corresponding to an arbitrary point x, y, z of(6r), 
= = = 5.(3) 
where .S’ is introduced for convenience. As now also the normal 
in one of the points x + dx, y dy, z + dz of the surface (G) must 
pass through §, r\, and £ on account of two adjacent normals inter¬ 
secting each other in this point, this furnishes after substitution in (3): 
— u — dv — u — dw — dS — 0, 
„ d » 
a* 
du+(r,-y-v)fdv -v^dw-dS= 0, 
uu Ov OW 
dz dz f dz\ 
- w a» d “ — S* + C 6 "'— 
Now the point x -f- dx, y -(- dy, z-\-dz lay on the surface (G), therefore 
ftp ajp a* 7 
dw=i 0. 
dn, dv, dw, and dS, 
fe dU + ^ d ' 
Eliminating out of the last foi 
after having introduced g — x = 
find: 
. dx 
dF 
die 
