Space Group of a Cubic Crystal. 179 



ing all reflecting planes into three classes having indices 

 that are (1) two even and one odd, (2) two odd and one 

 even and (3) all odd, the A and B terms of expression [1] 

 are found to be as follows for the first order region of 

 the spectrum (which can be distinguished in Laue photo- 

 graphic data from cubic crystals without any uncer- 

 tainty) : 



(1) "When the indices are two even and one odd, and 

 p, c[, and r are any integers : B = 0, and 



A=2cos 27r[2px+2qy+(2r+\)z] + 2cos 27r[-2px+2qy-(2r+l)z + $] 



+ 2 " I2pz+2qx+(2r+l)y] +2 



+ 2 " [2py+2qz+(2r+l)x] +2 



+ 2 " [2px-2qy-(2r+\)z\ +2 



+ 2. " [2pz-2qx-(2r+l)y] +2 



+ 2 " [2py-2qz-(2r+X)x : ] +2 



[-2pz + 2qx-(2r+l)y+1 i ] 

 [-2py+2qz-(2r+l)x+l] 

 [_2px-2qy+(2r+l)z+h] 

 l_2pz-2qx+(2r+l)y+h] 

 [-2py-2qz+{2r+l)x+i] 



(2) When the indices are two odd and one even: B = 

 Oand 



A=2cos 27r[223x+(2q+l)y+(2r+l)z] +2cos 27r\2px-(2q+l)y-(2r+l)z + l] 

 + 2 " I2pz+(2q+'i)x + (2r + \)ii] +2 " \2pz-{2q+\)x-{2r+\)y+\] 

 + 2 " [2py+(2q+l)z+(2r + l)x] +2 " [2py-{2q+l)z-(2r+l)x + \] 

 -1-2 " [-2px+(2q+l)y-(2r+l)z] +2 " [-2px-(2q+l)y+(2r+i)z + $] 

 [-2pz+(2q+l)x-(2r+l)y] +2" [-2pz-(2q + \)x+(2r+l)y-±] 

 [-2py + (2q+l)z-(2r+l)x] +2 " [-2py-(2q+l)z+(2r+l)x + i] 



.9 



(3) When the indices "are all odd : B = 0, and 



A = 2cos 2-[(2p + l)x+(2q + l)y+(2r+l)z) +2cos 2n[-(2p+l)x+(2q+l)y-(2r+l)z] 



+ 2 " $(2p+l)z+(2q+l)x+(2r+l)y] +2 

 \(2p + l)y+(2q+l)z+(2r+\)x] +2 



2 " f(9,-n-L--\Yy>—<0 r ,i-\\,.(O- i ,_ L .-\\~-\ iO 



.9 



l(2p + l)x-(2q+l)y-(2r+l)z-] 



.9 



[(2p+l)z-(2q+l)x-(2r+l)y] +2 

 + 2 " [(2p+l)y-{2q+l)z-(2r+l)x] +2 



[-(2p+l)z+(2q+l)x-(2r+l)y] 

 [-(2p+iyy+(2q+l)z^{2r+l)x) 

 [-(2p + l)x-(2q+l)y+@r+l)z] 



[-(2p+\)z-(2q+l)x+(2r+l)y] 

 [-(2p+l)y-(2q+l)z+(2r+l)x] 



It is thus seen that in general all three groups will 

 appear in the first order region of the spectrum. The 

 following procedure will, however, serve to determine 

 whether there may not be classes of planes within these 

 groups which will show a different behavior. 

 cos27r(a)= — cos2tt( / 8), when a=(±/3±^) 



Consequently any and all values of p, q, and r which 

 will make A = for the region n = 1 can be found by 

 equating the revolutions of the first term of A, [Zpx+Zqy 

 + (2r+l)s], to the revolutions of each of the other terms 

 of A plus i (and any integer s) and solving the resultant 



