In 1896 Joseph John Thomson discovered the electron. However he didn't manage to define its mass neither its charge. He only calculated the proportion of the charge to the mass of the electron (q/m). He believed that the newly discovered particle was a part of an atom. But he didn't give enough evidence for that hypothesis. Defining the charge and the mass could be the final proof.

Many scientists tried to solve this problem. The first who managed to measure what was the elementary charge was one of Thomson's students- J.S. Townsend. Unfortunately the final result he got had a big measurement error. The first scientist who quite precisely defined that charge was Robert Andrews Millikana. It must be said that he didn't measure the charge of the electron. He only showed that there is some indivisible amount of charge in nature- the elementary charge. All other charges are exact multiples of that elementary one. Later it emerged that the elementary charge was the the charge of the electron.

How did Millikan manage to define the elementary charge?

He conducted an experiment, in which small oil droplets given some electrical charge were falling in gravitational field between two parallel plates. He measured velocities of the droplets and so he came to know their mass. After that he put some electric potential difference on the plates generating electric field between them. Hence he watched droplets moving in both gravitational and electric fields. Measuring velocities of the droplets he could then define the charge of each one. He conducted the experiment many times. However each time the charge was different on different droplets, it always was some exact multiple of some constant charge. He never noticed a difference of a fraction of that charge. Millikan came to the conclusion that there was a basic, indivisible, elementary charge occurring in nature. The charge should have been equal to about 1,6*10^-19 coulombs. Further experiments confirmed that Millikan was right. There is an elementary charge and nowadays we accept it is equal to about 1,602*10^-19 coulombs. It also appeared that electrons discovered by Thomson were of the elementary charge defined by Millikan.

Knowing the charge e of an electron and the proportion q/m for an electron one can define its mass m. It is equal to about 9,11*10^-31 kilograms. The mass is many times smaller than the one of the lightest atom (hydrogen). That is the final proof of the subsistence of something smaller than atoms.