THEORY OF THE COMPINATION OF OBSERVATIONS
LEAST SUBJECT TO ERRORS

In a treatment of combinations of observations, which appeared in Vol. V of Commentationes Recentiores, it was assumed that certain quantities, whose values were given by imprecise observations, were functions of certain elements. The problem was to derive the elements from the observations as precisely as possible.

In very many cases the above assumption holds directly. In other cases, however, the problem is posed differently, and at first sight it is not obvious how to reduce it to the required form. In particular, it sometimes happens that the observed quantities are not represented as functions of given elements and do not seem to be reducible to such a form — at least not in a natural, straightforward way; yet at the same time the problem itself provides conditions which must be satisfied exactly by the true values of the observed quantities.