684 Mr. C. G. Darwin on the 



which depends on a quadratic equation rather more compli- 

 cated than (2). The subsequent procedure follows the same 

 course as in § 3. The general problem, though straight- 

 forward, might be rather complicated, but by the following 

 argument is made unnecessary. The influence of a single 

 atom on another is always very minute, and the effect only 

 becomes important by its repeated recurrence. Consequently 

 no error will be introduced by regarding as the unit of 

 scattering, not the atom, but the group of atoms in a single 

 unit of the crystal lattice. Let f r be the scattering of an 

 atom of type ?% of which there are N r per c.c, and let this 

 atom occur at distance a r a from the first plane, a being the 

 distance in which the structure of the crystal repeats itself. 

 Then in the reflexion formula? the expression 



N|/k 

 must be replaced by 



■A(2»7T) 2 



7i'T , • . 

 I —VblTZCLr — i" r,(2W7r)2 



7. Comparison with Experiment. 



We now compare our result with experiment, and to do 



so shall take the same experiment as was discussed in the 



former paper f. The elimination of the higher orders of 



reflexion follows the same course as before, but the numbers 



7C 2 

 resulting measure now not E A — but E A \. We thus obtain 



revised values of E A . I do not give the details, because we 

 shall see that a further modification is necessary in the re- 

 flexion formula. The quadrature of E A now gives that 



E \o=l'3JE A ^, 



where E , \ refer to the wave-length 3*92 x 10" 9 cm. which 

 is reflected by rocksalt at 4°. We have seen that all the re- 

 flexion occurs in a region of about 8" and is practically 

 perfect in this region, so we estimate the efficiency for the 



reflexion in rocksalt at 4° as E o ^S0/JExtfA, where 80 = 8". 



Using the quadrature this becomes 1*3 cot 4° . S6 or 00004. 

 The observed efficiency is 0*0035, and this calculated value 

 is no better than the old one. 



* See the earlier paj er ; p. 325. 

 t Loc. cit. p. 830. 



