Adjustment of a spatial network according to conditional observations when various kinds of corrections are introduced

Summary In the present paper the adjustment of the Hradilek's spatial network[3] was carried out in space using the least-squares method according to conditional observations. Triangle, side and base equations of condition are given (see also[1]). In the first method of adjustment (Alternative A) the corrections are assigned to oblique (position) angles and the lengths of sides. In the second method of adjustment (Alternative B) the corrections are assigned to horizontal directions, zenith distances and lengths of sides. The refraction coefficients in both alternatives are introduced as unknown parameters. Neither method of adjustment depends on the directions of the verticals. Theoretically, Alternative B is more correct. However, for practical purposes the results yielded by Alternative A are little better than those yielded by Alternative B. As regards the economical aspect Alternative A is considerably more convenient. Both methods seem suitable for computing the rectangular spatial co-ordinates, less so for determining the refraction coefficients.