2 PRINCIPLES OF STRUCTURE ZJ 



unknown for a long time, and there was a certain arbitrariness in the 

 use of valency lines as regards their direction and length (cf. Fig. 35 b, 

 p. 38). Today, however, the data needed for an exact morphological 

 representation are known, and, if written in a suitable way, at least the 

 simpler chemical formulae actually do represent molecular models, 

 which have been projected on to a plane. We 

 owe our knowledge of the exact distances and h x^ 



directions chiefly to X-ray analysis. X-rays ^ j. ^ ii' m 



enable us to measure dimensions of the order | hc^;;^^ joh 



of magnitude of their wavelength (e.g., copper ^ 



radiation: X = 1.54 A), if identical distances Fig. 24 



are often repeated and act as a lattice, causing 



interferences which can be photographed and thus made macroscopically 

 visible. It is, therefore, the principle oi repetition^hxch. has opened the 

 door to the morphology ofmolecular structure. The more regularly the 

 given distances are arranged, the more accurately can the absolute values 

 and directions be determined. From the considerations relating to ho- 

 mogeneity it follows, therefore, that in gases, liquids (Fig. 9-11, p. 14) 

 and solutions the morphology of the molecules cannot be determined 

 by means of X-rays, though an exception to this rule is provided by 

 solutions of very large molecules which in their own construction 

 show a certain periodicity (for example carbon chains). In such cases, 

 however, the measurements are often ambiguous, because the mole- 

 cules are not orientated in fixed directions. The most reliable values 

 of atomic distances, often attaining almost incredible precision (up to 

 i7oo of I '^)» have therefore been determined in crystal lattices. For a 

 quantitative determination of the arrangement of the atoms in a mol- 

 ecule one must necessarily make use of phases which possess a 

 structure. Amorphous phases without structure, such as liquids and 

 real solutions, are not suitable for the elucidation of such morpholo- 

 gical relations. 



In this respect, biological conditions are highly unfavourable. Al- 

 though the protoplasm must be presumed to have a structure, it is not 

 governed by the principle of repetition with sufficient consistency 

 to permit of X-ray analysis. Granted that periodicity plays an im- 

 portant part in all living matter as regards time and, to some extent, 

 also spatial arrangement; yet a strictly periodic order presupposes 

 an equilibrium of forces and this is opposed to life, which depends on 



