THE SPACE RELATIONS OF ATOMS. 451 



moment of the chain CH 3 CH 2 CH 2 — about the central car- 



CH \ 

 bon atom being greater than that of the chain p„ 3 \CH ; 



3 

 unfortunately for this explanation it is found that iso-propyl- 



tartaric acid is more active than propyl-tartaric acid ; and 



Freundler {Bull. Soc. Chem. [3], ii., 305 and 366) finds that 



in general the calculation of the moments of the carbon 



chains gives no satisfactory results. 



It remains to mention the theory of Crum Brown, who 

 proposes to determine, for each of the radicals linked with 

 carbon, a function K, the " rotation-equivalent," a function 

 which perhaps varies with the temperature, etc. ; the dif- 

 ference between these functions would determine the rota- 

 tion of the molecule. The rotation-equivalent is considered 

 by Crum Brown as a function of the composition and con- 

 stitution of the radical, not necessarily proportional to the 

 mass and the distance of the centre of gravity from the 

 centre of the carbon atom. This hypothesis, as its author 

 observes, takes no account of the mutual action of the 

 radicals, and it is unlikely that a radical will in every com- 

 pound have the same rotation-equivalent, its distance from 

 the central carb n atom not being always the same. In 

 closely allied compounds, however, it seemed possible that 

 the effect of such differences would be inappreciable, that in 

 them the rotation-equivalent of each radical might be con- 

 stant. Acting on this supposition, J. Wallace Walker 1 has 

 recently found that in the ethereal lactates there is a con- 

 stant increase of 5*5° in the rotation of the molecule for 

 each addition of CH 2 to the carboxyl group. In the brom- 

 propionates the same addition causes a much greater in- 

 crease of rotation. Thus ethyl brom-propionate has a 

 rotatory power I4'3° greater than the methyl compound, 

 and propyl brom-propionate 14*2° greater than the ethyl 

 compound. Further, almost all bromine derivatives are 

 found to have a greater rotation than the corresponding 

 chlorine derivatives, showing that the rotation-equivalent of 

 bromine is greater than that of chlorine. 



So far our review of stereochemistry has occupied itself 



1 Jo urn. Chem. Soc, p. 914, 1895. 

 32 



