236 
PHYSICS: F. C. BLAKE 
THE DEPTH OF THE EFFECTIVE PLANE IN X-RAY CRYSTAL 
PENETRATION 
By F. C. Blake, 
Department of Physics, Ohio State University 
Communicated by E. H. Hall, May 25, 1918 
In determining the value of ( h' by means of X-rays Blake and Duane 1 (p. 
636) found out by experiment that the 'depth of the effective plane' was 0.203 
mm. for the case of calcite, using X-rays of a wave-length 0.454 A. An 
attempt is made in this note to explain this theoretically. 
Call n the coefficient of true absorption and r the reflection coefficient. 
Suppose a parallel beam of X-rays strikes the crystal face at glancing angle 6. 
Then if A 0 is the amplitude of the primary beam the total effect at the ioniza- 
tion chamber is the sum of the various reflections from all those planes of 
atoms that are able for any reason to play a part at the ionization chamber. 
Call the last plane of atoms that is thus effective the rath plane. Figure 1 will 
render the situation clear. Let AB-IJ represent the parallel beam of X-rays 
as determined by the slit-width s. The reflected beam bdf, for instance, is the 
sum of the various reflections at b, d, and f. Ray AB suffers partial reflection 
at A and arrives at a with amplitude A 0 l ~ Mc/ csc 6 where it again suffers reflection. 
The reflected part has the amplitude rA 0 l csc(? at a and by the time it gets to 
c its amplitude has been reduced to rAol~ 2tJdcscd . Thus the total amplitude 
along any reflected ray bdf situated a distance x away from the first reflected 
ray A I is 
rA 0 (l + e- 2fldcsc9 +e-^ icscd + .... + £T 2w ^ csc *), m which = 
2d cos 9 
This gives for the amplitude of the ray bf, 
I — e ~ 2 (*+« /xdcscfl \—e sin 0 cos 0 
rA 0 t— 5 — 2 — reducing to rA 0 > 
1 _ e -2 t *dcsc8 > * 2 fid CSC d 
very approximately. 
( Call D\ the mean depth of the ray bdf. Then 
1 p SUl $ COS Q on n 
rA 0 — = nr A 0 e- 2txDlC5Cd . 
2(id csc 6 
Solving for D x we have 
^ sin 0 , \x% ( v 
