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.