A correct algorithm for the proper motion of cluster members

In this paper we give, for the case where the proper motions of stars are unknown, a method of calculating the correct relative proper motion, the linear model being assumed always. We also show that the proper motion usually found on assuming Σxμ_x = Σyμ_x = 0, Σxμ_y = Σy_y = 0, Σμ_x = 0, Σμ_y = 0, is not the relative proper motion, and that the difference between the two depends on the positions of the reference stars on the plate.