68 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



mention of them. Further details can be obtained from any of the 

 standard text-books (e.g. Arabronn and Frey, Hartshorne and Stuart, 

 Johannsen(12)), but the method can be illustrated by considering a 

 quartz wedge. Since the birefringence of quartz is known, then the 

 path difference at any point in a wedge made of quartz can be calcu- 

 lated. If the wedge is inserted in the microscope, again at 45° to the 

 vibration directions but with the m.e.p. at right angles to that of the 

 object under investigation, then by sliding the wedge into the micro- 

 scope a point can be reached at which the path difference of the object 

 equals the path difference of that part of the wedge lying over it. The 

 object plus the overlying wedge has then zero path difference and is 

 black. The point is noted therefore at which the object appears black 

 and a previous calibration gives the path difference. With care, the 

 object can then be turned on its side so that its thickness, d, can be 

 measured and the birefringence, ri^—n^ can be calculated. 



Normally, however, methods based on this principle are too in- 

 sensitive to be used with cell walls, since the path differences to be 

 measured fall rather low in the first order. For cell walls a much more 

 delicate method is necessary and fortunately this is available in a com- 

 pensator devised by de Senarmont and called after him. The method 

 has been described by Ambronn and Frey (12) but as far as the writer 

 is aware the theory has not been given in any formal way. This will be 

 presented elsewhere* and at the moment attention can only be given 

 to the method itself. In point of fact the compensator measures not the 



path difference but what is called the phase 

 difference. This can best be understood by 

 ^^\ reference back to Fig. 13 (p. 36). If two 



I \ vibrations differ in path length by A then one 

 \ has completed one whole vibration in advance 

 I of the other. Consider for a moment the 

 / vibration at any one point M (Fig. 32). The 

 y point M is vibrating along MM' with simple 

 ^"-^ harmonic motion and this motion can be 



■^ derived by describing a circle with MM' as 



Fig. 32. For explanation, diameter. Suppose a point P is then chosen on 

 sec text 



this circle and the perpendicular from it to the 



line MM', Pm, be constructed. Then if P is allowed to move round the 



circle with constant velocity the point m moves along MM' in the 



manner required. If the point moves from M to M' and back again, 



* In Problems and Methods in Plant Biophysics to be published by Elsevier, 

 Amsterdam. 



