The simplest invariant is S = (abc) (abd) (acd) (bcd) cf degree 4, which for the canonical form of Hesse is m(1 -m 3); its vanishing indicates that the form is expressible as a sum of three cubes.
Its symbolic expression, to a numerical factor pres, is (Hbc) (Hbd) (Hcd) (bcd), and it is clearly of degree 6.
The summit C of the branch BCD occurs at a percentage exactly corresponding to the formula Hg 2 T1.
Then ABF = angle of elevation; EFB =quadrant angle; BCD=angle of sight; EBF=ABF - ABE; and since ABE = BCD, it also equals ABF - BCD.
Also, let angle ABC =7r - 0, angle BCD =ir - 4, angle between BC and AD = G.
BCD c is the solubility curve of phenol in water.