Fig. 11. 



898 Intensity of Reflexion of X Rays by Crystals. 



side and turning the crystal through 180°. The glancing 



angle is the mean of the two values observed. It is probably 



easier to measure with accuracy the difference between the 



glancing angles of the first and third 



orders, as the angular movements are 



simpler and smaller. But there is an 



entirely different reason for preferring 



the latter measure to the former. Where 



the rays fall on the diamond they penetrate 



some distance into it, as shown in the 



figure, and the actual point of reflexion is 



indeterminate. The reflected pencil is 



broader than the incident. The angle at 



which the ionization chamber is set to catch 



the reflected pencil is a little smaller than 



if the reflexion took place at the surface, 



the defect being greater at the smaller 



angles *. In the original paper the series of the glancing 



angles of the first, third, fourth, spectra were found to be 



0*1456, 3x0-1475, 4 x 0'1485, and 5x0-1490. The true 



value of the glancing angle was assumed to be 0*1495. 



When, however, we turn the crystal round to look for the 

 angle of reflexion, the observed values require no such 

 qualification. The angle at which reflexion takes place is 

 determined by the setting of the crystal table, and the place 

 at which the reflexion occurs is of no consequence. By 

 taking the difference of the settings of the crystal table at 

 the reflexions of the first and third order, we eliminate any 

 error in the placing of the crystal. 



Let 6 be the glancing angle of tbe first order. We take 

 18° 00' 5' as the mean of the two angles given above. 



We then have 



whence 



sin ((9 + 18° 00-5') = 3. sin 6; 

 0=8° 35-2', and sin (9 = 0-1494. 



The density of diamond is 3*520. Let fit denote the mass 

 of the hydrogen atom. It has been shown f that there are 

 eight carbon atoms in the elementary cube of side 2 a 

 (loc. cit.). 



Hence (2a) 3 x 3*520 = 8 X 12 x m. 



.\ 2a = 3*01 x mh 



* Proc. Eoy. Soc. lxxxix. p. 279. 

 t Proc. Roy. Soc. lxxxix. p. 282. 



