TABLE 40 (continued) QI 



PROBABLE VALUES OF THE GENERAL PHYSICAL CONSTANTS 



Compton, Beets and DeFoe, 1 that, to obtain the true X-ray wave length A, it 

 is necessary to use an effective grating space d, automatically correcting for 

 the refraction of the X rays at the crystal surface. For first order spectra and 

 the high frequencies of ordinary X rays, the true grating space d' is connected 

 with the effective space d by the relation 



d = d'{ i— 0.000135). (2) 



Siegbahn uses for calcite d = 3.02904 x io~ 8 cm, at i8°C. This is a more or less 

 arbitrary value, assuming that d for rock-salt, at i8°C, is 2.81400 X io -8 cm. 

 We shall denote by d" 18 this 3.02904 value, and by A" the resulting wave- 

 length. Hence .„ ,„ 



A =2d 18 sin# (2) 



and \/\" = d 18 /d" 18 (3) 



where A is the true wave length from a ruled grating, d ls the effective grating 

 space of calcite at 18 C, A" the supposed true wave length from measures with 

 a calcite crystal with d" 18 as an assumed grating space at i8°C. d 18 follows 

 knowing d" 18 and A. From (2) we obtain d\ 8 , the true grating space of calcite. 

 The temperature coefficient 2 is 1.04 x io" 5 ; d' 20 is accordingly 2.08 Xio -5 

 larger. This 20 value is given theoretically by the formula 



d' 20 =lnM/ fi No4>(fi))- 1/a (4) 



where n is ■£, M, the molecular weight of calcite (CaCo 3 ), p, its density at 

 20 C, </>(/?), a geometrical constant depending on the crystal structure, and 

 N , F/e; knowing d' 20 we can obtain N and then e. 



We have M= 100.078 ±0.005 > the best value of p is 2.7i02±o.ooo4 g • cm -3 

 (DeFoe, Compton 3 ), of <£(/?), 1.09630 ±0.00007 at 20°C (Beets 4 ) whence 



e=( 1. 7i76± 0.0003) X io 13 (rf' 20 ) 3 . (5) 



The two published determinations of d 18 , based on absolute X-ray wave 

 lengths, are by Backlin, 5 and Wadlund. 6 Using (3), Wadlund obtains 1.5373 

 ±o.ooo8A for the Ka x line of Cu, combined with Siegbahn's values of d" 18 and 

 A", giving d 18 = (3.0290 ±0.0016) X io -8 cm. The corresponding value of d 20 is 

 3.02906 ; the true grating space d' 20 , (3.0295 ±0.0016) X io~ 8 cm. This value is 

 to be substituted in (5). It gives e= (4.7757 ±0.0076) X io~ 10 abs. es units. 

 This is not as accurate as the oil-drop value. • 



It is difficult to appraise the work of Backlin, as regards its accuracy. He 

 gets 8.333 ±o.oo8A f° r the absolute wave length of the Al Ka line. Compar- 

 ing this with an unpublished result by A. Larsson (8.3229±o.ooo8A), ob- 

 tained with a crystal, Backlin obtains d 18 = 3.033 ±0.003A. This gives d' 20 

 — 3-°334/A, and e— (4.794±o.oi5) X io" 10 abs. es units. This value is 0.55 

 per cent higher than the oil-drop result. 



1 Phys. Rev., 25, 625, 1925. ~ Siegbahn, Spectroscopy of X-rays, p. 85. 3 Phys. Rev., 

 25,618,1925. * Phys. Rev., 25, 621, 1925. G Upsala Dissertation, 1928. e Proc. Nat. Acad. 

 Sci., 14, 588, 1928; Phys. Rev., 32, 841, 1928. 



Smithsonian Tables 



