238 
PHYSICS: F. C. BLAKE 
the different reflections for all the planes of atoms playing any part. In ac- 
cordance with this definition, if D is the depth of the 'effective plane' and if 
for the moment we limit ourselves to that portion of the reflected beam o- width 
s, viz., AI-BJ, it is clear, since for the separate rays we must add not ampli- 
tudes but intensities, that we must get D by integrating Di throughout the 
region s and taking mean values. Thus if we were concerned only with the 
reflected beam of width s we could get D from (1) by replacing the parenthesis 
But the reflected beam is not of width s only. Rather must we consider the 
effect of rays that penetrate the crystal to depths much greater than the plane 
through B. Consider for instance the ray AB penetrating to the plane through 
K say, where it is reflected along the direction KQ and emerges from the crys- 
tal at Q. At L, M, Nj 0 the ray KQ is reinforced by reflections in phase with 
one another, but at P and Q there are no reinforcements since the initial beam 
is determined by the slit width s. Accordingly the amplitude of the ray KQ 
upon emergence is 
where q is the number of the plane through 0. In other words the amplitude 
of the ray KQ upon emergence is 
where X\ is the distance (measured parallel to the slit s) between the incident 
ray through Q and that through O, and x 2 is the distance between the ray 
through Q and that through K. Necessarily x 2 — %i must equal s. Accord- 
ingly to get our mean penetration D for all the rays that penetrate into the 
crystal beyond the reflected ray BJ we must replace the parenthesis in (1) by 
Having found the mean penetration for all the rays between 0 and s and that 
for all the rays between s and °° it is a simple matter to get the mean of these 
means, which should be, finally, the depth of the 'effective plane.' 
Now in the above expressions the value of n is the amplitude coefficient of 
absorption while what is experimentally measured is the intensity coefficient 
of absorption. If we accordingly replace 2/jl in the above expression by p we 
have as our expressions for the depth of the effective plane the following: 
For the X-rays contained in the triangle ABJ, 
by 
g sin 0 cos 0 — g sin Q cos 0 
