Regression Lines and the Functional Relation. II. Charlier's Formulae for a Moving Cluster.
Abstract
Whenever two or more coefficients of an observation equation (counting the absolute term as a c~ efficient) depend on measured quantities, the coefficients of the normal equations used to determine ti unknown quantities wifi include the squares of the errors of observation. If the squares of the pe centage errors of measurement are not negligible, the solution for the unknowns wifi be systematical] affected by regression error. This error can be eliminated only by sufficiently increasing the precision measurement or by correcting the coefficients of the normal equations. In practice, correction of ti coefficients is often necessary. The formulae for the functional coefficient of a linear relation derived in Mt. W. Conir. No. 698 a extended in the present article to the solution of Charlier's equations for the convergent of the motions a moving star cluster. Application of the formulae to the Taurus cluster shows that neglect of the r gression error leads to a distance for the cluster that is too small by about 7 per cent (different for oth clusters). Solutions by Merriman and by Hertzsprung for a linear equation involving constant weights th~ have recently come to light are shown to be a special case of the general solution given in Mt. W. Con~  No. 698. Equations (45) of the present article correct an error in the weights given in the original di cussion
 Publication:

The Astrophysical Journal
 Pub Date:
 November 1945
 DOI:
 10.1086/144766
 Bibcode:
 1945ApJ...102..366S