508 REPORT—1904, 
dimensions of the elementary parallelepipeda of the crystal structure; by taking 
the planes of the elementary parallelepipedon as the basis for assigning symbols to 
the crystal faces, the so-called ‘elements’ of the crystal give immediately the 
angles, a, 8, and y, and the relative lengths a: 6 : ¢ of the sides of the elementary 
parallelepipedon, The elements of the two comparable substances being 
1, a: b,: ¢, and a,, B,, y; 
Zs, Ae 3 by > Cy aNd Gy) Boy Yos 
the comparison of the two sets of elements, if all the other necessary conditions 
are fulfilled, permits the determination of the alteration which ensues in the 
structure of the crystal 1, if it be converted by substitution into the substance of 
crystal form 2, This alteration may be regarded as a ‘ homogeneous deformation’ 
of the parallelepipedon, because a homogeneous edifice—the crystal structure of 
form 1 becomes thereby converted into another homogeneous edifice—the crystal 
structure of the crystal of modification 2. The character of this deformation 
cannot be recognised through the comparison of the axial ratios of the two sub- 
stances if these are stated in the ordinary way, but can only be ascertained if the 
axial ratios are expressed in terms of the same unit. For this purpose an exact 
determination of the specific gravity of the two substances is made and the 
‘equivalent volume’ calculated therefrom; the dimensions (parameters) of the 
elementary parallelepipeda can then be at once referred to the same unit, namely, 
to the side of a cubic elementary parallelepipedon of a substance of which the 
molecular weight is equal to the density (equivalent density —1). Such comparable 
parameters are termed the ‘ topical axial ratios,’ and are described as x, y, and o. 
The comparison of the following substances may be quoted as a simple example. 
Ammonium iodide erystallises in hexahedra and exhibits a perfect cleavage 
parallel to {100}, so that its crystal structure is undoubtedly hexahedral or cubic. 
Tetramethylammonium iodide crystallises in the tetragonal system and shows per- 
fect cleavages parallel to {100} and {001}; its most probable crystal structure 
therefore differs from that of ammonium iodide only in the ratio of the axes a 
and c, The direction in which the crystal structure has been altered by the sub- 
stitution of 4H by 4CH, is seen by a comparison of the topical axial rativs; as 
the following table shows, the principal axis c has undergone no noteworthy change, 
but the parameter of the two axes a and d is much greater in the methylated com- 
pound. Tetraethylammonium iodide is similarly tetragonal and exhibits a regular 
increase of the parameter of the two equal axes in the same direction ; the increase 
in the equivalent volume is also quite regular during the transition from 4H to 
40H, to 4C,H;. On further attempting to lengthen the dimension a and 6, by 
exchanging 4C,H, for 4C,H.,, a quite different deformation comes into play. Asa 
result of this » and increase, and y decreases. 
NH, N(CH;),I_ = N(C,H;),I  N(C,H,)4I 
05'9. 
Equivalent volume 57°51 108°70 162-91 255°95 
= 3:860 5°319 6:648 6-093 
v= 3 860 5-319 6648 7851 
w= 3-860 3 842 3°686 4:933 
The so-called morphotropic relationships between numerous organic substances 
which have been brought to light during many years past consist mainly in the 
observation that the substitution of H by CH,, NO,, OH, &c., gives rise in many 
cases to but partial changes in the crystalline form. In order, however, to deter- 
mine the direction of deformation, as has been done above for the alkylated 
ammonium iodides, all the substances must be studied in accordance with the 
principles laid down above, and their specific gravities determined; further, in 
cases in which no morphotropic relationships can be traced it must be ascertained 
whether the substances compared are not different—non-corresponding—modifica- 
tions. Regularities from which conclusions can be drawn concerning the position 
of the atoms or atomic groups in the crystal structure can only be traced as a 
result of this kind of complete investigation of long series of chemically related 
