CORRECTIONS FOR STOKES FORMULA
Stokes formula described very well the homogeneous
balls moving in a viscid, continuous medium. But Milikan came to the conclusion that,
although the droplets of oil could be assumed as homogenous, still
the medium in which the move can't be told continuous. The main
path between collisions of droplets and atoms of the air was equal
10-5 centimeter. That distance called 1 is much shorter
than the radius a of the drop (a is equal 10-4). In that
case the velocity of the drop in the gravity field is equal the
product of the velocity given by the
Stokes' formula and some factor of correction that is the
function 1/a. Milikan assumed
that the factor of correction could be expanded into the infinite
power series:
(1)
where v is the velocity from the
Stokes' formula, and the coefficients A,B etc. could be
determined experimentally. Milikan noticed that it is enough to
leave in the formula only the A coefficient because the rest of
them didn't influence v0 much:
(2)
The uncorrected radius of the drop is from Stokes formula:
(3)
So after the v0and the v evaluation there is:
(4)
and after the transformation:
(5)
