Table 40 (continued) 89 



PROBABLE VALUES OF THE GENERAL PHYSICAL CONSTANTS 



linear graph, its intercept on the y axis giving e' 2/3 , and leading to the desired 

 quantity. 



Millikan found that for values of i/pa less than about 700 (p in cm Hg, a, 

 radius of drop, in cm), the resulting graph was linear. Only that part of the 

 curve corresponding to i/pa less than 700 was used in precise determinations 

 of e. The 1917 value of e was deduced from 25 oil drops, each giving one point 

 on the graph. The 25 observations form a beautifully consistent set of data. 

 The least squares solution, as calculated by Doctor Birge, gives for the inter- 

 cept (61.111 ±0.032) x io~ 8 ; but plotted data are based on the 1913 value 

 (0.0001824) for the viscosity of air. The value of a (=e 2/3 ) is proportional 

 to the viscosity. With the improved 1917 value of the viscosity (0.00018227), 

 e = a 3/2 = (4.7721 ±0.0038) x io" 10 es units. 



Millikan stars 18 of the points, with conditions of observation as perfect as 

 possible. These 18 drops give a = 6i. 121 ±0.038 (e = 4.7733 ±0.0045, I 9 I 7 

 viscosity). These 18 drops deviate from the best straight line more than do 

 the other 7. The standard deviation of the 25 drops is 0.121 x io -8 , while for 

 the 18 drops it is o. 123X io -8 . The drops of smaller radius fall more slowly, 

 and can be more accurately timed. Actually they are less reliable. Thus 13 

 smaller drops have a standard deviation of 0.134, considered as part of the 

 25 drops, definitely larger than the 0.121 average of the 25. A least squares 

 solution of these 13 drops gives a = 6i.i43±o.O5O, standard deviation of 0.132. 

 This is so close to 0.134 that we can conclude that the 13 drops fit the graph of 

 the entire 25 as well as a graph designed to fit them alone. On the other hand, 

 the 12 larger drops give for the least square solution, 0^ = 61.078 ±0.045, stand- 

 ard deviation 0.117, thus definitely more reliable than the smaller drops. The 

 resulting value of e, reduced to the 191 7 viscosity, is 4.7759 ±0.0058 for the 

 13 smaller drops, and 4.7683 ±0.0053 for the larger drops. The weighted 

 mean is 4.7718, in essential agreement with the value (4.7721) obtained from 

 all 25 drops. This, of course, is what we should expect. 



The average deviation from the average for small and large drops is 0.0038, 

 much less than the probable error of either. This is an analytic proof that 

 the true value of e is not a function of the radius of the drop. This also indi- 

 cates that the larger drops are, if anything, more reliable than the smaller. 

 If the larger are given a higher weight, the resulting value of e would lie 

 between 4.772 and 4.768. The final conclusion is that there is no particular 

 reason for giving different weights to the different drops, and that any such 

 weighting, if made, would slightly lower e. We therefore take 4-77 2 X icr 10 es 

 units as the best result of the 191 7 work. 



Smithsonian Tables 



