i 
The equation 
ant = ¢ ay? 9 
F=a,,0 + 2a,,¢y + re y* + 2a,,¢ + 2a,,y — 0 
11 
or 
(a,,%+4,,4)* + 2a,,(4,,2 + 4,,y) = 0 
passes by the substitution 
i} i (GY 
dt TT Uy = 2a,,8 
5 (91) 
Ast + Ag = — 2d 
into 
n—=s, 
a solution of which (see 2"d comm. p. 590) is 
Eze V2 ’ der melde eve et 
Out of (91) and (92) we deduce 
2 es On 
ee ane “V2+a,,¢ hie 
At, 
(93) 
2a = ite page 
y= ve (os Vir la, € ie ) 
12 
These formulae are always applicable, as the supposition A,, = 0 
would imply the degeneration of the parabola. 
Chemistry. — “On some internal unsaturated ethers’. By J. W. 
LE Hux. (communicated by Prof. van ROMBURGH). 
(Preliminary communication). 
(Communicated in the meeting of April 26, 1912). 
By the action of formic acid on mannitol Fauconnier obtained a 
mixture of formic esters of this hexavalent alcohol, which submitted 
to dry distillation, yielded among other products a liquid of the 
composition C,H,O, boiling at 107°—109°. 
Van MAANEN (Dissertation, Utrecht 1909) who investigated this 
substance and mentions it as a liquid boiling at 107° proposed as 
the most probable structural formula : 
CH,—CH—CH—CH=CH—CH, 
cae ee 
As the mode of formation of this substance does not give a com- 
plete insight into its structural formula, Prof. van ROMBURGH proposed to 
me to prepare the various possible oxides of hexadiene by other 
2* 
