The main problems which arise in the application of this method are connected with the accuracy of terms o higher order in the development of the disturbing function: 1) Because of the presence of small divisor, now it is rather difficult to set up rules to search for the complete set of terms for a pre-established accuracy. 2) The fact that in Leverrier's developments the coefficients of the Aᵢʲ's are unbounded when the index increases in absolute value puts the problems of accuracy under severe conditions. The calculations show that the Aᵢʲ's tend to zero for those values of i. For these reasons the resulting coefficients in the expansions, in the case of terms of higher order, are extremely inaccurate, unless a special criterium is devised to build up a set of "absolute" values for the initial values of the orbital constants. 3) The calculations have also shown that Poincaré's variables are quite suitable for the present purposes. The above mentioned issues are closely connected with the problem of finding out an adequate program for high speed calculators.