THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 281 



(2) mX = 2(Z sin 6, where m = 1, 2, 3 . . . (the spectral order), and A = the 

 wavelength of the X-rays. 



The imposition of simultaneity upon these equations means that, for a 

 given orientation of the crystal, only a few sets of planes indeed will serve 

 to create constructive interference in the scattered X-rays. In order to 

 obtain spots from many sets of planes of different {h h I) values it is neces- 

 sary, in one way or another, to rotate the crystal about different axes during 

 the recording of the spots. 



Certain geometrical characteristics of a crystalline lattice may be calculated 

 from relatively simple measurements of the intensities and positions of the 

 diffracted X-ray spots. First of these is the size of the unit cell. Since a crystal 

 is composed of repeating units it is convenient to thinli of it as being com- 

 posed of a number of identical elementary volume elements. A unit cell is 

 the smallest parallelepiped that can be constructed within the crystal such 

 that the entire crystal can be built up by means of unit displacements of 

 the cell. If the density of the crystal, and its chemical composition (mole- 

 cular weight of its molecules) are known, a knowledge of the size of the imit 

 cell allows a computation to be made of the number of molecules (or atoms) 

 within it.* It is also possible to determine fairly readily the symmetry of the 

 crystalline array. While the general subject of crystal symmetry is too 

 extensive to discuss here, certain clarifying points can be made. A crystal 

 can be thought of as a regular array of points. A given point, then, will be 

 related to other points by certain operations of symmetry. If a crystal 

 lattice is distinguished by a certain group of symmetry elements, and if a 

 point is placed anywhere (to start with), the operation of the symmetry 

 elements will effectively multiply this point into a collection of points. 

 Translations of this collection will build up an ordered pattern in space. 

 Depending upon the exact location of the original point there will be dif- 

 ferent patterns built up, but all will have the same symmetry elements. 

 If the initial "point" is an asymmetric collection of N atoms disposed as 

 would be the case in, say, a protein molecule, the operations of symmetry 

 will build up, for each atom, a space pattern. Each space pattern is identical 

 in its synunetry vfith those made of the other atoms. The entire set of space 

 patterns would be the actual protein crystal, if it were infinitely extended. 

 The scaffolding of symmetry elements upon which an infinite crystal may 

 be built is known as its space-group; there are 230 such space-groups possible. 

 For a detailed analysis of an actual crystal structure it is first necessary to 

 determine the number of molecules per unit cell, and the space-group to 

 which the crystal belongs (see Robertson, 1953). 



b. The Compound Lattice. As we have seen, a crystal structure with N 



* Alternatively, if the number of molecules in a unit cell is known, the same kind of 

 calculation provides an accurate value of the molecular weight. 



