210 Prof. Millikan : New Modification of the Cloud Method 



have thus far been used, the error in the final mean value 

 being not more than 2 per cent. Furthermore, with the 

 use of a chronograph in place of a stop watch for taking 

 time intervals, the method is perhaps capable of a slightly 

 greater accuracy than has as yet been given to it. 



As is well-known, H. A. Wilson's modification * of" 

 Thomson's cloud method t of determining e consists in 

 observing first, the rate of fall under gravity of a cloud 

 produced in an ionized fog-chamber by a sudden expansion, 

 and second, the rate of fall of a like cloud when a vertical 

 electrical field is superposed upon gravity. 



If i\ is the velocity under gravity alone, v. 2 the velocity 

 when the field is on, e the charge on an ion, m the mass of a 

 drop, a the radius of a drop, X the field strength in electro- 

 static units, d the density of the falling drop, and 77 the 

 coefficient of viscosity of the medium through which the 

 cloud falls, then the equations from which e is determined 

 are : — 



v. 2 mg + Xe' 



(i) 



Cl = I ^(Stokes),. . . . (2) 



m = r> TTOT (3) 



o 



The solution of these equations is 



-{HD'Kt- • • • » 



Substituting in this equation the value of 77 which he 

 considered appropriate, and placing the density of fc water 

 drops equal to unity, Wilson obtained 



e = 3-1 X 10~ 9 x -| {v, - v ± ) !>!* .... (5) 



As the mean of 11 determinations which varied from 

 2-0 x 10- 10 to 4-4 x 10- 10 , Wilson obtained e = 3'l x 10" 10 . 



In view of the importance of the constant and the wide 

 variations in Wilson's individual determinations, which were 

 perhaps due to the variability of the X-ray bulb which 

 produced the ionization, Mr. Begeman and the writer 



* H. A. Wilson, Phil. Mag. ser. 6, vol. v. p. 429 (1903). 

 t J. J. Thomson, Phil. Mag. ser. 5, vol. xlvi. p. 528 (1898) : vol. xlviii. 

 p. 547 (1899) ; ser. 6, vol. v. p. 346 (1903). 



