310 THE REALITIES OF MODERN SCIENCE 



viscous fluid, where the velocity is proportional to the 

 force. In the case of the fall, the velocity, v\, was 

 therefore directly proportional to mg, the force of 

 gravitation. 



The time of rise would be found to be the same for 

 several trips and then suddenly it would change, in- 

 dicating a change in the charge carried by the droplet. 

 The velocity v 2 of the motion upward is also propor- 

 tional to the force. This force is Fnemg, where F 

 is the force due to the field maintained by the battery 

 upon one electrostatic unit of quantity, e is the charge 

 in e.s. units of an electron, and n is the number of elec- 

 trons carried by the droplet. If the number of electrons 

 is altered to n f , then the velocity v 2 will be altered, say 

 to the value v 2 '. Thus 



(1) 



mg (2) 



but 



Vt'&Fn'e mg (3) 



Hence 



(ri -n)e = (v 2 '- v 2 }mg/Fv l (4) 



That is, the change in the number of electrons carried 

 by the droplet should be proportional to the change 

 in the velocity which is thereby occasioned, provided 

 that the value of F is maintained constant. 



The changes in velocity which Millikan observed 

 always bore simple ratios to each other. He found, 

 in other words, that there was one minimum value for 

 (v 2 v 2 ) and that all the other values were simple multi- 

 ples. That could only mean that the change in charge 

 was due to the additions or subtractions of a definite 



