AbstractIn my former paper“Notes on the Adjustment of Trilateration”(S.R.Vol. xvii, No. 134 and Vol. xviii, No. 135), I showed that the conversion of equations for adjustment of co-ordinates into condition equations may often be facilitated by establishing corrections to the approximate co-ordinates as fictitious residuals. This is possible if these latter ones may be treated as independent, according to Thiele.If the corrections to the approximate co-ordinates cannot be rendered independent of one another for conversion into condition equations (as is the case with point 15 in Fig. 1, for example) it is suitable to establish in this point an auxiliary system of co-ordinates, the axisx′of which lies in the side whose initial point is given. In this case, at least one of the corrections to the co-ordinates will be directly residual.The computation of the numerical example given in Vol. xviii, p. 135, carried out with this method, shows the extent of further simplification attained.