226 Prof. Millikan : New Modification of the Cloud Method 



observers appear to involve larger elements of uncertainty 

 than are found in any of the foregoing methods. 



Ehrenhaft's mean value *, obtained by a method similar to 

 the one here presented save that it involves the measurement 

 of the velocities produced first by the action of gravity, and 

 second by the action of an electrical field upon the charged 

 particles thrown off by a metallic arc, is 4* 6 x 10~ 10 . Although 

 this number is in very good agreement with the preceding 

 values the method itself appears to involve the following un- 

 certainties : first, an uncertainty as to the correctness of the 

 assumption that Stokes'' law is applicable to the motion of 

 particles whose diameters are not negligible in comparison 

 with the mean free path of gas molecules, and which are 

 perhaps also of doubtful sphericity ; second, an uncertainty 

 which arises from the fact that instead of making the two 

 observations of velocity upon one and the same particle, as is 

 done in the method herein described, Ehrenhaft is compelled 

 to take the mean of the velocities of different particles al- 

 though these velocities vary among themselves by 60 per cent. ; 

 third, an experimental uncertainty involved in the determina- 

 tion of the mean radius of the particles. The value of tl»is 

 radius, computed by applying Stokes' law both to the velocity 

 under gravity and the velocity in the electrical field, is checked 

 to within about 7 per cent, by direct microscopic measure- 

 ment, and it is this observed rather than the computed radius 

 which is substituted in the Stokes' law equation as applied to 

 the motion in the electrical field to obtain the final value 

 e = 4*6 x 10 -10 . The observed radii of the different particles 

 are found, however, to vary by more than 50 per c nt., and 

 since the mean value is but about '00003 cm., it is obvious that 

 even a moderate degree of precision in this measurement 

 must be very difficult to obtain. Finally there may be some 

 question as to whether multiples of the elementary charge 

 may not be carried by some of the particles. 



Perrin's work f, while ot the utmost importance from 

 other points of view, involves so many assumptions of ques- 

 tionable rigour that it can scarcely be regarded as furnishing 

 a determination of e with a certainty which is at all compar- 

 able with that found in any of the five methods first consi lered. 

 Thus, it assumes that Stokes' law holds for particles showing 

 Brownian movements in liquid emulsions. Second, it assumes 

 that these same particles follow the Maxwell- Boltzmann law 

 of distribution of velocities in gas mixtures. Third, it assumes 



* Ehrenhaft, Phys. Zeit. 1 Mai, 1909. 



+ Perrin, C. JR. vol. cxlvii. p. 594 and p. 530 ; also C. JR. vol. cxlvi. 

 p. 967. 



