On the Determination of the Convergent Point of a Moving Cluster from Proper Motions.

The paper discusses several methods which have been used to determine the convergent point of a moving cluster from the proper motion of the stars which are members of the cluster. These methods rep- resent, in the main, different ways of utilizing the position angle, 0, as observed for each star, and it is desirable to see if they would be affected by the form of the frequency distribution expected for 0. With reasonable assumptions as to the distribution of the errors of the observed quantities, namely, the components of proper motion, it is possible to derive the frequency distribution of 0, and4his suggests an alternative method of solution which would appear to have some advantages over the existing methods. As an illustration of the method, its application to the nucleus stars of the Ursa Major cluster is considered. Because of a geometrical peculiarity of this particular case,the directions of the proper motions are insufficient in themselves to define the convergent point accurately; they define a curve on which the convergent point should lie, but additional information is required to fix the position of the convergent point on this curve with any precision. Using the amount of the proper motion in right ascension for each star helps to locate the position of the convergent point on the curve and leads to a solution which gives good agreement with the radial-velocity observations. However, it is emphasixed that there is still an appreciable uncertainty associated with the determination.