In Geographical Survey Institute (GSI) in Japan a few kinds of solutions [1] [2] [3] have been used in adjustment of any geodetic free networks by means of the method of least squares. The defect of rank in normal equation can be easily determined by con-sidering how many geodetic quantities we need at least in order to make it fix on the surface of the reference ellipsoid. When observations are only horizontal angles and directions in a geodetic network, that is pure triangulation, we can know its shape alone. Innumerable geodetic figures with the similar shape are able to exist for capable solutions in such a case, because we have no information of its size and azimuth. When longitudes and latitudes of any two stations in the network are given, it is fixed on the reference ellipsoid. Accordingly the defect in the normal equation in such a case is obviously four. If kind of observation is only length of side, that is pure trilateration, the defect will be three, because we can fix the network by giving a station its position (longitude, latitude) and the direction of a side its azimuth. The defect is reduced to three from four when some sides or azimuths are additionally observed in pure triangu-lation, because either size or rotation of the network is restrained from being free. As a matter of course the defect is two in such a network in which its shape, size and azimuth are known through observations, but its location is still unknown in spite of the most perfect observations. In other words, location of the adjusted network is essentially free, and there are infinite possibilities in the ways of putting it upon the original one which is made up of approximate coordinates given for every station at the beginning of the computation. If those approximate coordinates indicate old positions of the stations decided in the previous surveying, the difference between the approximate position and the corresponding adjusted one for each station will give its displacement-vector Vi. Out of infinite locations of adjusted network a desirable solution can be settled according to an appropriate condition that should exist among those displacement-vectors. Now in GSI in the Universal Program using ellipsoidal coordinates (longitude, lati-tude) for any geodetic network the both conditions ΣV=0 and ΣV2=min. are actually used. It is very important that we pay attention to the fact that the free network solution of ΣV2=min. is universally available for any geodetic networks, but on the contrary the utilization of V=0 is restricted in such a free network alone in which the defect in normal equation is two. The reasons are as follows. When the network can freely rotate on account of no observation of azimuth, if we assume an azimuth in it we will be able to find one location of the network satisfying ΣV=0 while we are making it move around keeping the azimuth. When the network can freely dilatate or contract on account of no observation of side-length, even though azimuths are observed, we can still find one location of the network satisfying ΣV=0 for every assumed size. As a matter of course infinite solutions satisfy ΣV=0 in both cases mentioned above. Therefore we cannot use the method of ΣV=0 except the cases in which the defect is two. The Universal Program has utterly taken the above into consideration.