By this article, the author deduces several properties of the above mentioned movements, chiefly the following theorems: a) If an orientation movement produces at three points of space the same (suffieiently small) y-parallax dpy this movement produces also the same parallax dp~ at all points of a spatial cubic curv.e which contains the three given points as well as two points on the base-line and the two cyclic points on the infinite line of all planes which are perpendicular to the base-line.
b) We say n points of space are ,,situated generally" (n > 4) if there exists no orthogonal surface of second degree which contains these n points as well as the above mentioned cyclic points and the base-line. Thus, there exists no orientation movement which will produce the same small y-parallax dpy at more than four ,,generally situated" points. Especially, we cannot find any orientation movement which leaves the y-parallaxes (e.g. dpy = 0) unchanged at more than at four points of this kind.
By means of these theorems, we may once more recognize the real reason of the curious but well known fact that the orientation methods, being in use hitherto, do not converge with sufficient accuracy towards the perfect solution of the main problem of photogrammetry.