238 



of an irregular tetrahedron, which shall represent in outlines the 

 configuration of the four substitutes round the central asymmetric 

 carbon-atom, then the gravitation-centre of the whole complex will 

 seem to be shifted towards the heaviest substitute, its position being 

 determined with relation to the planes which pass respectively 

 through every edge of the tetrahedron and the middle of the opposite 

 edge. If the distances of this gravitation-centre from the six planes 

 thus obtained be known, its position in space will be absolutely 

 determined. Guye concludes from these reasonings that a substi- 

 tution in an active molecule always produces a change of algebraic 

 sign of the rotatory power, whenever the gravitation-centre of the new 

 product, in comparison with that of the original molecule, is dis- 

 placed by the substitution in such a way that it arrives at the 

 opposite side of one of the six planes mentioned above; if after 

 substitution the centre of gravitation remains at the same side of 

 the six planes as it was before, the algebraic sign of the rotation 

 will remain unchanged. If d t , d z , d s ,....d 6 be the distances of the 

 gravitation-centre from each of the six planes mentioned above, 

 the product: P = djd^d^ifd^ will be, according to Guye's views, 

 a measure for the dissymmetry of the chemical molecule 1 ). The algebraic 

 sign -of the product will change from positive to negative, and 

 conversely, and with it that of the rotatory power of the molecule, 

 when the number of factors out of this group of six which are changed 

 from positive to negative and conversely, happens to be an odd one. 

 Indeed, if one of the four substitutes obtain the same mass as one 

 of the others, one of the factors d becomes zero, and therefore so 

 does P also: i.e. the activity disappears, and experience often 

 confirms this. If instead of the one antipode, the enantiomorphous 

 one be considered, the number of factors d which change their signs, 

 is always odd; thus the activity too changes 'its sign from positive 

 to negative and conversely 2 ). 



If m lf m z> m 3 and m^ be the masses of the four substitutes, Guye's 

 formula may be reduced also to the form: 

 P --= (m Wg) (*! m 3 ) (m l w 4 ) (m z w 3 ) (w 2 w 4 ) (m s w 4 ). 



The same considerations can be used here : thus, if two of the 

 masses become equal, P becomes zero, etc. 



1) About an application of these views to compounds which contain a pentava- 

 lent asymmetric nitrogen-atom, see: M. B. Thomas and H. O. Jones, Journ. 

 Chem. Soc. London, 89. 280. (1906). 



2 ) Force more general form of argumentation, cf . : W. Nernst, Theoretische 

 Chemie, (1898). p. 325. 



