( 328 ) 
smaller equilateral triangles, that in their turn could serve for deter- 
mining the measurement, so that we could do without the trihe- 
dral angle itself. 
Fig. 2 represents the equilateral triangle with omission of the 
trihedral angle. 
As soon as you eliminate one of the three measurements (Length, 
Breadth and Height), the stereometrical ordinate-system will of course 
alter into a diagram in a plane. 
Instead of the three ordinates: 
Fo (Sd), RAZ cd) and. Pyt ad), 
Le. the three perpendiculars, let down from the graphic point d to 
the sides of the trihedral angle, now come the perpendicular lines 
dj, dl and dk, let down from the same point to the sides of the 
equilateral triangle QRS. 
This will present no difficulty; for the sum of these perpendicu- 
lars is constant (or = the height of the triangle) and in future we 
will reckon this as 300, instead of the rib of the trihedral angle. 
This triangular diagram has this advantage over the rectangular, 
that all the three relative measurements are represented on it; by 
means of which the eye can compare them better, as all three come 
out equally right. 
HELMHOLTZ in his Physiologische Optik, just refers to the trian- 
gular diagram, in connection with LAMBERT’s Farbenpyramide : 
„Jeder Schnittpunkt einer dieser Liniën mit der Ebene des 
Dreiecks, würde den Ort der entsprechenden Farben in diesen 
anzeigen, und zwar wiirde die Vertheilung der einzelnen Farben 
darin genau der durch Schwerpunktsconstructionen herstellbaren 
Ordnung entsprechen. In jeder solche Ebene wiirden aber nur Farben 
gewisser Helligkeit angeordnet sein, welche durch die Summe der 
Werthe (« +y +2) gegeben ist.” 
Let the perpendicular dj, drawn on the basis QS, signify the 
relative height; the perpendicular dk the relative breadth, and di the 
relative length; then we shall be more conversant with the subject 
by the following : 
all points, drawn in a line parallel to the basis, have the same 
relative height; 
all points, in a line parallel to QR (resp. /S.) have equal relative 
breadth (resp. rel. length); 
