330 Mr. C. G. Darwin on the 



N 2 a 2 1 + cos 2 20-1 / ei \ 2 / , vv 2nir , A - ^V*** '(E>\*\ . 



—2 o S- 1 -7^1 (v + 2 XX cos — (p s -p t ))e ° a { ■ ■ -I 



.... (10) 



14. Comparison with Experiment. 

 We will now compare this result with experiment, and 

 shall find that our formula gives more reflexion than is 

 possible. The comparison is with the experiments on rocksalt 

 in Moseley and Darwin*. The Braggs' workf has shown 

 that Na and 01 both contribute to the reflexion, and for a 

 rough comparison it will be good enough to take them as 

 identical and deduce the average character of the two. 

 They are then arranged on a simple cubic lattice. Using 

 Mil Khan's J most recent values, we find that the side of the 

 lattice a is 2*81 x 10~ 8 cm. and N is 4* 50 x 10 22 . The work 

 of Moseley §, combined with that of Barkla||, shows that 

 over a considerable range of the softer rays p is exactly 

 proportional to X 5/2 . For very much harder rays this is 

 confirmed by a single experiment in Moseley and Darwin If. 

 We shall assume this relation to hold. Of the other quan- 

 tities in (10) a can be found from the infra-red absorption 

 band of rocksalt. If M be the average mass of an atom 

 M£+ erf = expresses the vibration of an atom. The wave- 

 length of the absorption band is 54 p**. From this <r can be 

 found. The temperature factor is found to be 0*96 for the 

 first order, 0*86 for the second. For the sixth it is 0*27. 

 The smallness of the effect accounts for its not having been 

 hitherto observed. The excess radiation factor is much in 

 doubt until the structure of the atom is better known. The 

 simplest process is to take the ratio of first to second order 

 from the heights of the " peaks " in Bragg* s experiments. 

 Using this, it is a simple matter to disentangle the separate 

 orders, and the work shows that a considerable error in esti- 

 mating the strength of the second order will not change the 

 result very much. No allowance can be made for the pola- 

 rization of the rays coming from the tube, as it is not known 

 which are the components polarized. Taking as standard 

 wave-length X , that reflected in rocksalt (1, 0, 0) plane 



* Lga. cit. p. 219. 



t W. L. Bragg, Proc. Roy. Soc. A. vol. lxxxix. p. 248 (1913). 



% R, Millikan, Pliys. Rev. vol. ii. p. 109 (1913). 



§ H. G. J. Moseley, loc. cit. 



|| C. G. Barkla, Phil. Mag. vol. xxii. p. 396 (1911). 



f Loc. cit. p. 220. 



** Rubens and v. Baeyer, Berl Ber. 1913, p. 802. 



