QO TABLE 40 {continued) 



PROBABLE VALUES OF THE GENERAL PHYSICAL CONSTANTS 



In 1 91 3 data on 58 drops were obtained. Millikan used, in evaluating e, 

 the 23 drops (out of 58) of smallest i/pa. These are more consistent, having a 

 standard deviation of only 0.092. They lead to £ = 4.7665 ±0.0058 (1917 

 viscosity), while the entire 58 give 4.7703 ±0.0022. This last figure might 

 appear more reliable than that of 191 7 ; such a conclusion ignores other errors. 

 In 1913 Millikan estimated four factors, each with a maximum uncertainty 

 of 0.1 per cent. In 1917 he estimated two such factors, each with a maximum 

 uncertainty of 0.05 per cent. His final 191 7 estimate for the maximum uncer- 

 tainty in e is 0.1 per cent, based mainly on these two factors. The above calcula- 

 tions show, however, a probable error of 0.08 per cent ( ±0.0038) in the 1917 

 value, due to accidental errors. The final uncertainty is therefore several times 

 as large. Doctor Birge estimates that the final probable error is about 0.1 per 

 cent, and writes e— (4.772 ±0.005) x 10 ' 10 es units. 



This value is now subject to two further corrections. In reducing the result 

 to es units per cm, Millikan used c = 2.999 x iq10 cm * sec. -1 , and made no dis- 

 tinction between international and absolute electrical units. It has been shown 

 definitely that the int. volt differs from the abs. volt by an appreciable amount. 

 We have also now the new value, c — 2.99796. The change in c is obvious, it 

 lowers e from 4.772 to 4.770. The other change seems to have been overlooked 

 by everyone. Because the electrical potential forces the charged drops against 

 the viscosity of air, instead of against electrical resistance, one has only electric 

 voltage coming into the calculations. One int. volt = 1.00046 ±0.00005 aDS - 

 volts. The true value of F, in abs. volts, is larger and the true value of e, in 

 abs. es units is smaller by just this ratio. Hence, the value of e is reduced 1 

 from 4.770 to 4.768. Since the error in each of these corrections is negligible, 

 the final result is e= (4.768 ±0.005) x I0_1 ° aDS - es units. This should be the 

 most reliable value from Millikan's oil-drop work. 



Recently an entirely different method has been devised for e. The two 

 results which have already been published are apparently less reliable than the 

 oil-drop value. This new method measures directly the Avogadro number N , 

 and from this and the value of the faraday, e immediately follows. It utilizes 

 the absolute wave lengths of X-ray lines, determined with an ordinary ruled 

 grating at grazing incidence, as compared with the wave lengths determined 

 with a crystal grating. 



\ = 2d'S\n$ (1) 



where d is the grating space. It has been pointed out by Siegbahn, 2 and by 



1 Professor Millikan agreed, 1928. 2 Siegbahn, Spectroscopy of X-rays, p. 26. 

 Smithsonian Tables 



