THE SPACE RELATIONS OF ATOMS. 449 



obtained, at least for bodies of similar constitution. And the 

 attempt to apply these results to the determination of the 

 degree of molecular dissymmetry has been made by Guye. 



Assuming for the body CR 4 the form of a regular tetra- 

 hedron, it will have six planes of symmetry, at the intersec- 

 tion of which will be the centre of gravity of the molecule. 

 In a body CR'R'R "R iv the C.G. of the molecule is re- 

 moved from all the six planes by distances d\ d\ d\ d\ d 5 , 

 d 6 . The product of these distances is the measure of the 

 dissymmetry (i.e., of the activity of the molecule). 



This theory fulfils the condition that when two groups 

 become identical the activity must vanish, for in this case 

 one ol the distances, d\ d\ etc., becomes nil, and their pro- 

 duct is likewise nil. 



The distances d will be determined in the first place by 

 the relative weights and distances of the groups R, and as 

 it is the relative weights alone which can at present be de- 

 termined, the first step was to see how far the distances d 

 depend on the difference of the weights R : in short, 

 whether for the equation 



P = d l x d 2 x d 3 x d A x d 5 x d 6 



we may substitute 



P = (R' - R") (R' - R'") (R' - R iv ) (R" - R"')(R" - R iv )(R'" - R iv ), 



where P is the " asymmetry-product ' or the measure of 

 the dissymmetry of the tetrahedron. 



Assuming this formula we get the following results : — 



(1) If two of the groups R change places the activity 

 remains the same, but the sign changes, as the existence of 

 isomers of equal and opposite activity demands. 



(2) If the group-weights change, but their order remains 

 the same, the magnitude of the rotation will change but not 

 the sign. 



(3) If the heaviest group, say R ,v , be replaced by groups 

 of constantly decreasing weight the rotation (say positive) 

 will decrease, and will reach nil when R ,v becomes equal to 

 the next heaviest group R ". Beyond this point the rotation 

 (now negative) will increase, declining again to nil when 

 R IV = R", and changing sign again when this point is passed, 



