34 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



those defining the parallelogram ABEF, say the set IB, JC, KD, etc. 



(Fig. 11). Then this could be done by, for instance, stating the angle cf). 



An alternative way, and the way always adopted, seems at first sight 



more cumbersome. If we start from any point / as origin then, on 



passing along the lattice in the a 

 direction, two lines are crossed 

 before reaching the next iden- 

 tical point. The lines can 

 therefore be allocated the num- 

 ber 2 in the a direction. On 

 passing in the b direction only 

 one line is passed through and 

 the corresponding number is 1 



Fig. 11. For explanation see text. 



The sets of lines IB, JC, KD can therefore be defined as the 21* lines, 

 and their distance apart can be calculated. These numbers are referred 

 to as the indices of the lines, and a further example, the 11* lines, is given 

 in Fig. 11. Conversely, if the distance , • • ^ 



apart of a number of lines is known, 

 together with their indices, then the 

 dimensions a and b can obviously be 

 calculated. It should be noted that 

 the indices of a line can be found 

 alternatively by noting what fraction 

 of the parameter distance lies be- 

 tween each set of two neighbouring 

 lines. Thus for the lines IB, JC, etc., 

 the intercepts are «/2, Z)/l, corre- 

 sponding to the indices 21. Each 

 index represents therefore the recipro- 

 cal of the relative intercept of the 

 corresponding parameter cut off by 

 two neighbouring lines. In three 

 dimensions the same convention is 

 applicable, but now three indices 

 are required instead of two, and an example is presented in Fig. 12, 

 representing the planes 112. Planes parallel to one edge of the unit cell 

 will have index for the corresponding direction, so that the faces of 

 the unit cell can be represented by the indices 100, 010, 001. What is 

 needed, therefore, to define the spatial arrangement of the whole lattice 



* Formally, the last figure should be written I, implying that the index is— 1, since 

 the first line to the right of /cuts the b axis below, and therefore on the negative side 

 of/. 



Fig. 12. For explanation see text. 



