  Using the results found previously for the cooling rates of the emittances,
due to collisions between the electrons and the ions, a result is found for the
friction force acting on the ions. It is shown that the friction force found
here when used to track the ion bunch will give the same emittance cooling
rates as those found using the intrabeam scattering theory for electron cooling
>.For the case of the uniform in space electron bunch distribution, the
friction force found here agrees with the friction force result found with the
usual theory of electron cooling.
