In the first part of this paper the authors give the details of the synthetical production of numerous acids of the lactic family, which have been briefly described in a series of notes already published in these Proceedings during the years 1863, 1864, and 1865. In the concluding portion of the present paper, they discuss the theoretical considerations which arise out of these investigations. They call attention to the existence of a group of elements, to which they give the name oxalyl and the formula (COHo), and which exists not only in all acids of the lactic series, but also in nearly every known organic acid. The isolated molecule of this radical is oxalic acid, {C O Ho C O Ho, in proof of which they show that when oxalic ether is acted upon by nascent amyl, it is converted into caproic ether: { CO Eto + { C Bu H 2 = 2 { C B u H 2 CO Eto C Bu H 2 = C O Eto. Oxalic ether. Amyl. Caproic ether. Oxalyl is closely related to cyanogen, the two radicals passing into each other in a host of reactions; hence the production of cyanides from the ammonium-salts of the fatty acids on the one hand, and the synthesis of acids from certain cyanogen compounds on the other,—a reaction first pointed out by Kolbe and Frankland, and which has of late yielded such important results in the hands of Maxwell Simpson and of Kolbe and of Hugo Müller. { C N''' { C O Ho C N''' C O Ho. Cyanogen. Oxalyl. The researches of these chemists prove that the introduction of cyanogen into an organic compound, and its subsequent transformation into oxalyl, converts that compound into an acid, or, if already an acid, increases its basicity by unity (for each atom of oxalyl so developed), this result being apparently quite independent of the position of the oxalyl in the molecule. The atom of oxalyl (as the above molecular formula shows) may be regarded as methyl (CH 3 ), in which two atoms of hydrogen have been replaced by one of oxygen, and the third by hydroxyl (Ho).