« 
ON THE STUDY OF ISOMORPHOUS DERIVATIVES OF BENZENE. 143 
spheres and the insertion of the substituting groups in the spaces thus 
provided. 
It is possible to test the correctness of the conclusions briefly referred 
to above by aid of crystallographic data for benzene derivatives. Com- 
pounds may be compared by means of their ‘equivalence parameters,’ 
which are the linear dimensions of parallelepipeds having volumes repre- 
sented by the sums (W) of the valencies of the atoms composing the 
respective molecules, those linear dimensions being proportional to the 
crystallographic axial ratios. In the case of benzene, which crystallises in 
the orthorhombic system a:b:c: = 0°891:1:0°799, the value of W 
is 30; the equivalence parameters calculated from these data are 
g:y:% = 3101 : 3°480 : 2-780. 
The last of these values, z = 2-780, represents the height of two 
links in the columns of carbon spheres in the crystalline hydrocarbon ; 
if, as has been suggested, these columns remain intact in the crystalline 
derivatives of benzene, the value 2°780 should recur amongst the 
equivalence parameters of the derivatives. This has beenalready shown 
to be the case in a long series of crystalline derivatives of picric and 
styphnic acids; the data now contributed enable the conclusion to be 
extended to the sulphonic derivatives of benzene described above. 
The following table gives the equivalence parameters, «, y and z 
and the valency volumes, W, for the substances numbered in the above 
table of axial ratios :— 
if W =36. @ iyi 2=5 787 : 2337 : 2-674, B=95° 26’. 
2. 36. 5°796 : 2-338 : 2°676, B=96° 49’. 
3. 36. 5761 : 2°333 ; 2°692, B=95° 50’. 
4, 36. 3°409 : 3°986 : 2°661, B=95° 22’. 
5. 36. 3095 ; 4:247 : 2°779, B=99° 42’. 
The third equivalence parameter, z, calculated from the axial ratios 
and the valency volumes, in each case approximates to the corresponding 
value, z = 2-780, of benzene. The corresponding value in the case of the 
series of picric and styphnic acid derivatives examined by Jerusalem ! 
varies between 2°660 and 2°788. 
The axial ratios of the more complex benzene derivatives represented 
by the labile form of 1 : 4-dibromobenzene-2-sulphanilide and the ethylic 
1; 4-dibromobenzene-2-sulphonate do not, in the form stated above, 
immediately yield values approximating to 2°780 amongst their equiva- 
lence parameters. On dividing unit length along the axis b by two in 
the former case and multiplying it by two in the latter, the following 
equivalence parameters are, however, obtained in which the value 2°780 
recurs : — 
6. W =68. @:Yy 5 %2=5'327 : 2-782 : 4:°653, B=99° 30’. 
7 = 49. =2°859 : 6410 : 2:679, B=90° 0’. 
The confirmation of Barlow and Pope’s conclusion as to the existence 
of the columns of carbon spheres in crystalline benzene derivatives which 
Jerusalem obtained by the study of the picrates and styphnates may 
consequently be extended to the quite different class of derivatives dealt 
with in this report. 
The Committee are indebted to Messrs. Colgate, Rodd and Runeckles, 
students in the Chemical Department of the Central Technical College, 
South Kensington, for assistance they have rendered in preparing and 
measuring compounds described in this report. 
! Trans. Chem. Soc., Jaly 1909, }». 1276. 
