Dr. Debus on the Oxidation of Glycol. 463 



By the help of my formula, I have succeeded in reducing the case 

 where the parameter is negative and greater than unity. The steps 

 are the mere counterpart of Legendre's work in the second supple- 

 ment of the treatise on Elliptic Functions. 



Both Legendre's case and mine are of the logarithmic form, and 

 can therefore be reduced to one another by algebraic transformation. 

 The cases where the parameter is positive, or negative and interme- 

 diate hetween unity and the square of the modulus, are still unre- 

 duced. The difficulty is exactly analogous to that between the two 

 cases of cuhic equations, and this analogy is even carried into the 

 very form of the solution. 



Dr. Booth's application of the trigonometry of the parabola to the 

 reducible case of the cubic equation, affords some hope that a corre- 

 lative calculus may exist, particular cases of which may solve the 

 cases now irreducible, just as the calculus of elliptic functions in- 

 cludes the trigonometry both of the parabola and the circle. My 

 own investigations on this subject are still without any useful result. 



Let 



cos ^, =cos 02 cos 03— sin 0., sin 03 V'l — sin" sin" 0, ; 



^ J (l-siu=0sin^0)i' 



E0=j* (1 -sin' Q sin'0)*^0, 



J C cos' M^ ^ 



J (1 — sin''9sin'0)*cos''0«/0' 



(1) F0,-F0, + F03=O 



(2) E0, — E02 + E03=sin^ sin 0^ sin 0^ sin 0, 



(3) Y0J — Y0,+ Y03= —cos- a tan 0i tan 0^ tan 



Euler. 



"On the Oxidation of Glycol, and on some Salts of Glyoxylic 

 Acid." By II. Debus, Ph.D. 



If glycol be oxidized with nitric acid, according to Wurtz*, it 

 is converted into gly colic and oxalic acids. 



CJI,0, + 0, = C, 11,03 + H.,0 



Glycolic acid. Water. 

 + 0, = C,H,0, + 2H,0t 



Glycol. Oxalic acid. Water. 



As the formation of these acids from glycol is analogous to the pro- 

 duction of acetic acid from cthylic alcohol, it may be assumed that 

 the bibasic oxalic acid stands to the biatomic glycol in the same rela- 

 tion as the fatty acids do to their corresponding alcohols. Alcohol 

 is not converted at once into acetic acid, an intermediate substance — 

 aldehyde — being formed. The formation of a similar body from gly- 

 col is highly probable. If two or four atoms of hydrogen be removed 

 * Comp. Keiid. xliv. 1306. f C = 12, 11 = 1, = 1G. 



