  An analytical expression for the gravitational field of a homogeneous
cylinder is derived. The phase of the atom interferometer produced by the
gravity field of the set of cylinders has been calculated. The optimal values
of the initial positions and velocities of atomic clouds were obtained. It is
shown that at equal sizes of the atomic cloud in the vertical and transverse
directions, as well as at equal atomic vertical and transverse temperatures,
systematic errors due to the finite size and temperature of the cloud
disappear. To overcome the influence of the Earth gravitational field on the
accuracy of the phase double difference measurement, it is proposed to use the
technique of eliminating gravity-gradient terms. After eliminating, one can use
extreme values of the atomic positions and velocities. Nonlinear dependences of
the phase on the uncertainties of atomic positions and velocities near those
extreme values required us to modify the expression for the standard phase
deviation. Moreover, such dependences lead to a phase shift, which was also
calculated. The relative accuracy of measurements of Newtonian gravitational
constant 10^-4 and 2*10^-5 is predicted for sets of 24 and 630 cylinders,
respectively.
