308 BELL SYSTEM TECHNICAL JOURNAL 



It should be noted that b should not exceed 6. If 5 exceeds 6, it is neces- 

 sary for the X-ray beam to pass through a great thickness of quartz which 

 would so weaken the beam that the reflected rays could not be detected. 

 Further, even when 5 does not exceed d there is still a variation of the 

 reflected ray intensity with the angle between the entering ray and the 

 plate-face, which may be expressed as follows:^ 



r _ J sm g( 



sin gf -\- sin ge 

 where 

 Tr = The intensity of the reflected ray 

 ge = The "entering angle" — The angle between the entering ray 



and the plate face 

 gf = The "leaving, angle" (In Fig. 3.11 g, ^ 6 - d; gf ^ 6 + 3 ^ 



26 - ge) 

 In = The maximum obtainable reflected intensity (i.e., when ge = 

 and gf — 26). 



or 



sin {26 - ge) 



Ir — Ir 



sin {26 — ge) + sin ge 



The curves in Fig. 3.12 show the variation of It/Ir with ge/26 for various 

 values of 26. It is seen that for plates as described above and figured in 

 3.11 a stronger reflection is obtained when ge = 6 — 8 than when ge = 

 6 -\- 8 (i.e., after 180° rotation in the plane of the plate-face). In other 

 words the smaller ge angle gives the larger intensity of reflection. It 

 might be added, however, that in practice it may not be possible to obtain 

 the maximum values of reflection intensity due to the fact that, as ge ap- 

 proaches zero, the width of the reflected beam may exceed the width of the 

 ionization chamber. (See inset, Fig. 3.12.) 



Quartz plates containing an .Y axis are checked as described above 

 (case b) for rotation around the A' axis. For this check they are oriented 

 as shown in Fig. 3.13, case b with the X axis parallel to the axis of the instru- 

 ment. The stippled face in Fig. 3.13 represents the so-called "reference 

 bevel", the remnant of the surface of the Z section, and is therefore normal 

 to the Z axis. 



(c) Atomic plane intersecting plate-face in a line parallel to the plane 

 of the instrument. 



The case described above and illustrated in Fig. 3.11 was the case of 

 single rotation plates (AT, BT and others shown in Fig. 3.8) being corrected 

 about the X axis by the use of atomic planes parallel to the .Y axis. When 



^ Debye, P. and Menke, H., "Untersuchung der Molekularen Ordnung in Fliissigkeiten 

 mit Rontgenstrahlung," Ergeb d. Techn. Rontgenkunde, B.2, P. 16; Leipzig (1931). 



