(555 ) 
ean be brought under the form: 
ay Pp ey 
de? dedv dy dv 
Ow ow AW AW 
: 8 Ro Sy) Pe ieee eee 
dv" ss dedv de? dowdy 4 (4) 
eae age 
dy dv dedy dy? 
And we know from the theory of the quadric surfaces that if 
a relation exists between the coefficients as is indicated by the 
equation (4), such a surface is an ellipsoid. Coexisting phases being 
stable phases, the surface is a real ellipsoid, if C is positive. 
If we bring through the line connecting the coexisting phases 
a plane cutting the tangent plane at the v,,y-surface along a 
straight line and the surface of stability along an ellipse, then the 
directions of the nodal line and the before- hentai straight line 
are conjugate directions for those elliptic sections. In the same way 
conjugate directions are the projection of these two lines on an 
arbitrary plane for the elliptie projection on that plane. If we give 
to the plane such a position that: 
dw dw dw 
dv? de Li de dv dv a oy dy dv 
dy == 
or what is the same p = constant, then the factor of vy—v, is equal 
to zero, and we get after having eliminated dv: 
3° 3° 
eeens ze NT | + (y2—y1) Pe ade Th ay zj =0 (9) 
The projection on the «xy-plane of the line connecting the coexisting 
phases, is therefore conjugate to the projection on that plane of 
the section of the tangent plane, indicated by p= constant, with 
respect to the elliptic projection of the section of the surface of 
stability. This is the theorem which has been proved under another 
form Arch. Néerl. p. 76. 
By giving such a position to the plane that 
dw dw 
eee Al 
rere do + ded y 
