247 



eating the existence of a "plane of indirect symmetry"; however 

 the symmetry-operation corresponding to it is nothing but an 

 inversion, as has already been indicated. The /raws-form of 1-4.- 

 diketo- 2 -5 -dimethyl-piper azine (trans-alanyl-anhydride) has an in- 

 version-centre, and has thus the symmetry of the group /. The 

 ci's-form (B) however evidently has a single polar binary axis A t ., 

 perpendicular to the plane of the ring ; it possesses therefore only 

 axial symmetry (C^\ A 2 



A. B. 



and accordingly its arrangement must differ from its mirror-image t 

 Indeed, Fischer and Raske x ) have shown that these compounds 

 exist in four isomeric forms: a laevo- and a dextrogyrate isomeride, 

 and a racemic compound, all three corresponding to the as-form, 

 and one inactive toms-isomeride which can not be resolved into 

 optically active antipodes. 



Pope and Read 2 ) tried to demonstrate the same with 2-5- 

 dimethyl-piperazine itself, without result however. Afterwards they 

 made it probable 3 ) that here not the 2-5-, but the 2-6-cis-denva.- 

 tive was treated, which cannot be split up, because it has a single 

 plane of symmetry perpendicular to the plane of the ring, and 

 passing through both NH-groups: 



1) E. Fischer and K. Raske, Ber. d. d. Chem. Ges. 89. 467, 3981. (1906). 

 2 W. J. Pope and J. Read, Journ. Chem. Soc. 101. 2325. (1912); C. Stoehr 

 and collaborators, Journ. f. prakt. Chemie (2). 55. 4977. (1897). 

 3) W. J. Pope and J. Read, Journ. Chem. Soc. London 105. 219. (1914). 



