138 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



Suppose, for simplicity, that we could determine accurately the 

 birefringence of any layer in the wall in both transverse and longi- 

 tudinal directions. Then the following considerations could be applied. 

 Let Fig. 52 represent the wall of a fibre seen in surface view and let 

 ABCD again be the trace of the index ellipsoid on the surface, OB 

 representing the major axis of an ellipse and equivalent to n^, the major 

 refractive index of the cellulose, and OC, «„, the minor refractive index. 

 Then, when viewed in transverse section along the direction marked 

 by the full arrow, the effective major refractive index is n^"- and in 

 longitudinal section, along the dotted arrow it is w^". These can clearly 

 be related to n^, «„, and d by the equations: 



(«^'-)^sin^0 ^ (/7,'-)^cos^6) _^ ^2) 



n ^ n ^ 



"Y "a 



(w/)^ cos^ d ^ {n^^f sin^ 6 _ ^ ^^^ 



n " n ^ 



"y "a 



If we can measure n^ and nj- then the only unknowns in these equations 

 are n^, «„ and d. Since «„ is never far from the value 1-530, then 

 effectively we have two simultaneous equations involving only n^ and 

 6 as unknowns and these can therefore be found. 



In practice the determinations are not quite so simple as this, for we 

 cannot observe one and the same cell in both directions. The procedure 

 is therefore as follows. The phase differences of the layers in thin, 

 transverse sections of measured thickness is measured for a large 

 number of cells and the average birefringence calculated. Identical 

 material is then macerated and the refractive indices of the fibres in 

 optical longitudinal section are measured by an immersion method as 

 described earlier (p. 54) (note that this gives a check on the value of 

 «J. It is found that the values of the major refractive index, w^", 

 depends on fibre length, so a graph is constructed connecting refractive 

 index with length (this will be discussed in detail later on). Finally, the 

 refractive indices corresponding to the average fibre length are read off 

 from the graph and these are used in the above equations. It must be 

 stressed that these latter refractive indices refer only to the outer layer 

 of the cells, since a Becke fine method is employed in determining them. 

 Hence the values of the refractive indices for the outer layer only in 

 transverse section are used, and the calculated values for n^ and 6 

 refer only to this outer layer. The results are presented in Table IX. 



It will immediately be obvious that the structure of the outer layer 

 in bamboo is closely similar to that in sisal and in conifer tracheids, so 



