56 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



importance in fibres. This is the Wiener effect. If a number of iso- 

 tropic rods of refractive index n^ are immersed in a medium of different 

 refractive index «2 then, provided that the diameter of the rods is small 

 compared with the wavelength of light, the system has refractive indices 

 which are different for light vibrating parallel to the rods and perpendi- 

 cular to them. In other words the system is behaving like a crystal, 

 and, more particularly, the refractive indices of the whole body depend 

 both on that of the rod and that of the medium. They therefore change 

 as the medium is changed. Fortunately this effect seems to be of little 

 importance in cellulose, largely no doubt because the intermicellar 

 spaces are in fact filled with cellulose chains, and the refractive index 

 of a mixture of random cellulose chains and any of the media commonly 

 employed is never very different from that of dry cellulose itself. 



Nevertheless it is clear that the refractive indices of the fibre as a whole 

 may be considerably different from that of the micelles, particularly if 

 large amounts of incrusting material are present. It is well, therefore, 

 that the ordinary mixture formula, as used for liquids, holds to a 

 sufficiently close degree of approximation (in the sense of giving con- 

 sistent results). Thus if the refractive index of a dry fibre parallel to its 

 length is n^, that of the crystaUine portion n^cn of the non-crystalline 

 «ya and of other substances /7,-, then the following relation may be set up 



where /, a, i are the relative volumes of the crystalline cellulose, 

 non-crystalhne cellulose and amorphous substances respectively and 

 /+«+/== 1. Similarly, for the refractive index for light vibrating 

 perpendicular to fibre length, 



Hence, provided the assumption is made that the non-crystalline cellu- 

 lose is amorphous in the optical sense {i.e. that its refractive index is 

 invariate with vibration direction), then the difference between the two 

 refractive indices of a fibre is roughly a linear function of the amount of 

 crystalline cellulose present. It is clear from these considerations that 

 the refractive indices of a fibre will depend on its water content, so that 

 this must be standardized very carefully indeed in comparative estima- 

 tions. This is usually done by drying the fibre over phosphorus pent- 

 oxide (24, 25). 



The index ellipsoid 



Thus far reference has been made to only two refractive indices for a 

 fibre through which light is passed in a direction perpendicular to its 



