Table 40 (continued) 93 



PROBABLE VALUES OF THE GENERAL PHYSICAL CONSTANTS 



The most recent accurate work, using method (b), is by Babcock. 1 A large 

 number of spectrum lines (116 in all) were employed. Nearly all showed a 

 complex Zeeman pattern. For determining e/m it was necessary to assume 

 the Runge denominator of each line. In cases where this is small, it was known 

 with certainty. In some cases it was large and rather uncertain. His work has 

 been criticized, and Gerlach, in his final table, 2 omits Babcock's result. It 

 appears to Doctor Birge that the criticism is unjustified; at his suggestion, 

 Babcock has recalculated his data, omitting all Zeeman patterns in any way 

 doubtful. The new result, 3 based on 48 lines for which the Zeeman pattern is 

 definitely established, is 1.7606 ±0.0012; the error is purely observational. 

 The difference between the two values is just that produced by the change in 

 the value of c. Doctor Birge therefore writes e/m = (1.761 ±0.002) x io 7 abs. 

 em units as the best result from Zeeman effect. 



The latest, most accurate work using method (c), is by Houston/ based on 

 the Bohr-Sommerfeld model consisting of a positive nucleus and one encircling 

 electron (moving in elliptic or circular orbits). Such atoms are H and He + . 

 In order to determine e/m, we must evaluate the so-called Rydberg constant 

 for hydrogen (Rh) and for ionized helium (R.He). Practically the entire error 

 in e/m is merely the error in the difference R H e — Rii- 



The pioneer work was performed by Paschen. 5 He obtained Rh= 109677.69 

 ±0.06 cm -1 , Rhc= 109722. 14 ±0.04 cm -1 . Those give e/m— 1.768 ±0.003, 

 using his values and assumed errors for R H and Rue, but the present accepted 

 values and errors for H, He, and F. The recent investigation by Houston, 4 is 

 so much more accurate than the work just mentioned that it alone will be 

 considered. Houston's new experimental results are 



R He = 109722.403 ±0.004 cm -1 , Rh= 109677.759 ±0.008 cm -1 . 



The stated errors are purely least squares probable errors. He believes the 

 relative values of R H c and Rh are correct to 0.02, although the absolute error 

 in each may be about 0.05. 



Houston used m=54X io~ 4 , #2 = 4.0001, H= 1.0077, ^ = 96470 abs. cou- 

 lombs, and obtained e/m— (1.7606 ±0.0010) xio 7 em units. Using his con- 

 stants and the corrected formula the result is 1.7603. The error in his formula 

 is therefore almost negligible. The entire probable error in e/m, due to errors 

 in all factors, aside from (Rhc — Rh), is less than 0.01 per cent and so is 

 entirely negligible compared to the error in (Rhc — Rh)- 



1 Astrophys. Journ., 58, 149, 1923. ; H.P., 22, 81. 3 Phys. Rev., 33, 268 A, 1929; Astro- 

 phys. Journ., 69, 43, 1929. 4 Phys. Rev., 30, 608, 1927. 6 Ann. Phys., 50, 901, 1916. 



Smithsonian Tables 



