758 



SCIENCE 



[Vol. LVI, No. 1461 



getting their absolute magnitudes is not 

 feasible. 



An independent method of getting d is to 

 employ the quantum relation 'between ■wave- 

 length of X-rays and volts required to give 

 electrons equivalent energy. In using this 

 method we must take care to leave out of ac- 

 count those values of h which themselves de- 

 pend upon X-ray wave-lengths. 



Using the first method we select the foUoiwing 

 data : 



Number of molecules per 



mol, N = 6.0594 X 10^3 (i, 5) 



Density of ealeite 2.7116 gm/em3 (2, 5) 



Interaxial angle for ealeite 101°-55' (3.5) 



Molecular weight CaCOs 100.07 (4) 



The volume of the unit rhombohedron is 

 1.09'626 d^ and it contains one half of a mole- 

 eule^ so that the grating constant d — 3.02855 

 X 10"® cm. The ratio of the grating constant 

 of ealeite, d 



basis we must multiply those based on 3.028 X 

 10-s for d. 



by ^^^^^ = 1.00018, and 



CaCOs 



to 'that of rocksalt, 



cZj^j^^j, has been determined by Uhler and 



Cooksey'^ and by Siegbahn®, their respective 



, , . 3.0307 , „^^„, ^ ^ 3.02904 

 values bemg -^^ = 1.07701, and ^^^^^ = 



1.076417 (log-i 0.0319806), the latter of which 

 is the more accurately determined and wiR be 

 taken as the true ratio. This requires that 

 ^Naci ^^ ^tanged to 2.81355 X lO-s cm. The 

 values given by Duane'' for these two con- 

 stants are 3.028 X lO-s and 2.814 X lO-s, the 

 ratio of which, 1.07605, is probably a little low. 

 To correct Duatne's wave-lengths to the new 



IR. T. Birge, Fhys. Bev., (2), 14, 365 (1919). 



2 A. H. Comipton, Fhys. Bev. (2), 7, 646-685 

 (1916). 



3 P. Groth, Chcmische Krlstallographie, 2, 204 

 (1908). 



4 " Imteruational Atomic Weights," (1921). 

 5H. S. Uhler, Fhys. Bev. (2), 12, 39-46 (1918). 

 C This is not a true unit -of structure, which, 



however, is of no importance for these calcula- 

 tions; cf. E. W. G. "Wyekoff, Amer. Jour. Sci., 50, 

 317-360 (November, 1920). 



7H. S. Uhler, C. D. Cooksey, Fhys. Bev., (2), 

 10, 645-652 (1917). 



8M. Siegbaim, Phil. Mag., (6), 37, 601-612, 

 (1919). 



OW. Duane, Nat. Bes. Counc. Bull, 1, 383-408 

 (November, 1920). 



3.02800 



those based on 2.814 X lO"® for d^^^^^ by 

 2.81355 

 2:81400= "•9^^«*- 



It should be noted further that Siegbahn^" 



has more recently obtained a value for - = 



d 



sin 9 for the Kaj^ line of copper which does 

 not agree with that which he obtained at the 

 time 'the above-mentioned ratio was oibtained. 

 His new value for X is 1537.302 X 10"" for 

 ^CaC03 — 3.02904 X lO-s as compared with the 

 previous value 1537.36 X 10-" for d^ ^„ = 

 3.028 X 10-8. Referred to the same basis (the 

 new value of d^^^^^ = 3.02855 X lO-s) this 

 means a change from 1537.64 X lO-ii to 

 1537.056 X 10-11, a decrease of 0.038 per cent. 

 Since this eoiTection amounts to 'more than the 

 difference involved in changing 3.028 X 10"* 

 to 3.02855 X 10-8 and 2.814 X 10-^ to 2.81355 

 X 10-8, and since Compton's value for the 

 density of rock-salt has been critiedzed as prob- 

 ably too low" it seems premature on the basis 

 of the above evidence to decide in favor of 

 either of the two eonstants used by Duane. i-. 



A recent note by Daveyi* bases a similar 

 analysis upon a value, of iV = 6.0642 X 10^* 

 and upon 2.173 gm/cm.^ as the density of rock- 

 salt, thus getting 'a spacing for the (100) 

 planes in this crystal of only 2.810 X 10"® cm. 

 Adoption of tJiis value would require extensive 

 correction of all reported wave-lengths without 

 any considerable advantage, and observers 

 agree that rock-salt is a less suitable standard 

 than ealeite, on account of the greater prob- 

 ability of inclusions leading to abnormally 

 high densities. The density con-esponding to 

 the value here chosen for d , 2.8135 X 10-*, 



10 M. Siegbahn, Comptes Bendus, 173, 1350- 

 1352 (Dec&m;ber 19, 1921). 



11 E. Xjedoux-Lebard, A. Dauvillier, Comptes 

 Bendus, 169, 965-967 (November 24, 1919) ; H. S. 

 Uhler, loc. cit.^. 



1^ Loc. cit.O; ef. M. Siegbahn, Jahrh. d. Bad. u. 

 meUr., 18, 240-292 (1921). 



13 W. P. Davey, Science, 54, 497-498 (Novem- 

 ber 18, 1921). 



