When a particle is falling freely, it is acted upon by the gravitational force minus the force of buoyancy:
These forces balance the force of viscosity giving:
Defining r' to be:
yields a droplet radius:
Equations 3 and 4 show that knowing the velocity of free fall and the parameters associated with the small size of the droplets, the radius of the droplet can be calculated directly.
When the electric field is turned on, an equilibrium between electric and other forces is soon reached, which makes the droplets move with a constant velocity. If the direction and magnitude of the electric field is appropriate, the droplets will move slowly upwards. In that case, the following equation is obtained:
where V is the potential of the capacitors, s the separation, ne the charge of the oil droplets and the rise velocity of the droplets.
By combining 3 and 5 the following equation is found:
Defining e' as:
gives that :
By making repeated measurements of as a function of 1/r' a graph is obtained from which the value of as can be extrapolated. Since as the extrapolation will therefore yield the elementary charge.
Two problems arise when completing this procedure. First n has to be determined correctly when e' is determined. Secondly, it is necessary to extrapolate the graph of as a function of 1/r' with a high level of accuracy. Both these problems require that a large number of observations be made. The first requires a large number so that a clustering around certain values is found, and the second so that we have observations for a broad band of 1/r'.