86 Dr. L. Vegard on 



N l5 N 2 , N 3 are the atomic numbers of Zr, Si, and 

 respectively, or atoms which may substitute them in the 

 lattice. 



The angles a. x and a 2 are connected to the two parameters 

 €1 and e 2 (Table IV.) in the following way : 

 « 1 = 47T€ 1 , a 2 = 47re 2 . 



§ 8. Zircon. 



To get the intensities of: zircon we have in equations (9) 

 to put 



Ni = 40, N 2 = 14, N 3 = 8 ; 

 and putting 



*i = *— A 

 we get 



f/ 1 (n) = 40 + (-l) n 14 + 86cosn^-f-(-l) n 16 (cos nfi 



(HI) N 



7r + COS na 2 ). 



(110) 



(101) 



(100) 



.y 2 (n) = 26 sin 



|'/i(n) = 70 + 8 (cos 2nfi + cos 2na 2 ). 

 /i(n) = 0. 



/i(w) = 54 + 16 (( — 1) TC cos n/3-f cos na 2 ). 

 /,(n)=0. 



C/ 1 (n) = 54 + 16 (cos 2«/3 + cos 2na 2 ). 

 V/ 2 («) = 0. 



In determining the intensities we shall have to remember 

 that the spectra from the faces (101) and (100) were deter- 

 mined by reflexion from an edge of the crystal. Especially 

 in the case of the (100) face the reflexion to be observed 

 was very weak ; and under these conditions we must expect 

 too low a value for the first order spectrum, because a 

 smaller portion of the primary beam will be reflected into 

 the chamber when the glancing angle is small. 



The reflexion from the (101) face was better ; but in this 

 case also the first order spectrum is found too weak in 

 comparison with those of higher order. 



The spectra for the faces (111) and (110), however, are 

 very accurately determined ; but we see from the expression 

 for f\(n) that the spectrum of the face (110) will be very 

 nearly normal, and the position of the oxygen atoms will 

 affect the intensities very little. Still, we notice from fig. 2 

 that the intensity of the third order spectrum is too large as 

 compared with that of the second order. 



(13) 



