LEAST SQUARES ADJUSTMENT OF DISSIMILAR QUANTITIES

In the least squares adjustment of observations on quantities of different physical dimensions (such as angles and lengths) it is proposed that the concept “sum of the squares of the residuals” be replaced by the concept “sum of the squares of the reduced residuals”, where “reduced residual” is defined as the ratio of the residual to the probable error. This is equivalent to using weighted squares of residuals, and regarding weights as dimenflional quantities instead of pure numbers. The treatment is applied to a few simple cases, with satisfactory results.