Z2§ Mr. 0. Gr. Darwin on the Reflexion of 



10. The Poicder Method. 



From the preceding sections it appears that the pheno- 

 menon of primary extinction is likely to make serious 

 difficulty in determining Q by the method of: reflexion, 

 whether from a face or through a plate. The only way to 

 ensure its absence is to use crystals so small that it is bound 

 to be negligible. For example, from the numerical data 

 of § 6, primary extinction would be absent, if the crystals 

 were so small as to be just about invisible under a high- 

 power microscope. The only practicable way of using such 

 is by the powder method of Debye and ^BLull, which has 

 recently been used quantitatively by Sir W. H. Bragg *. 

 For the sake of completeness we shall apply our processes 

 to this, adopting an arrangement which is probably not the 

 most convenient, but which could easily be modified. 



We shall suppose a speck of powder is illuminated by rays 

 and shall find the total power thrown off into a cone (of half- 

 angle 20), corresponding to one particular set of planes. 

 Let the volume be V and let it be composed of small blocks, 

 the typical block being of volume W with normal in the 

 direction of colatitude and longitude t», <p. Let the distri- 

 bution of the blocks be given by 



YF(W)dW sin a> da d<j> (10-1) 



F is nearly the same as in § 5, but is now independent 

 of «,(/>, as they are pointed equally in all directions. We 

 have then 



47rjWF(W)iW = l, 



co is the inclination of the normal to the incident beam, and 



IT 



so co = -r •—.$ — u. Multiplying (4*5) by the appropriate 



factors we have for the whole reflected power arising from 

 this set of planes 



J (3) r(2) f(6) 



F (W) dW da dcj> I dv difr \ dV dV 



exp ik {(x—x f )(u — v) sin 6 -f (y-y')'fy cos 6 



r (z-z')(u + v)cos0}. . (10-3) 



Here J is the incident intensity and of the factor cos 2 6 one 

 term is due to the sin a>, the other to the r 2 cos 6 dv dty 

 integration. The integrations follow the same course as 



* W. H. Bragg, Proc. Lond. Phys. Soc. vol. xxxiii. p. 222 (1921). 



