166 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



It is interesting next, therefore, to turn again to the outer layers in the 

 secondary wall of these fibres to examine any length relationships there. 

 Thanks to the painstaking attention to this problem paid by Dr. Kartar 

 Singh in my laboratory we are able to be much more certain about the 

 condition here than was possible with the tracheids. We saw in the last 

 chapter that the refractive index of bamboo fibres for light vibrating 



L(mm.) 

 Fig. 58. For explanation, see text. 



parallel to their lengths is a function of length. The function can be 

 expressed by saying that this refractive index, w^", increases linearly as 

 length increases, while the refractive index, n^, for light vibrating per- 

 pendicular to the length, decreases linearly as length increases. We 

 saw in the last chapter (p. 138) that by combining optical determinations 

 on whole cells with those made on transverse sections it is possible to 

 calculate, for the outermost layers of these fibres, the specific refractive 

 indices n^ and n^ of the cellulose and the angle d between the molecular 

 chains of cellulose and cell length, for fibres of average length. Now 

 taking the calculated value of n^ as 1-60 we can then estimate, from the 

 value of «y" for any fibre of length /, the value 0/ for the spiral angle 

 in the outer layer. The relation which can then be derived between / 

 and 0/ takes the form 



/=5980 (cot di -0-95), 



so that in these outer layers the variation of 0/ with / is less than with 

 inner layers. It is further interesting to note that, provided the linear 

 regression line can be extrapolated to zero length, then no fibre should 

 have an outer spiral flatter than about 0=45°. 



