Weight of an observation

It is shown below that the weight of an observation is, in theory, inversely as its probable error in practice, it is usual to assign arbitrary weights to the observations. For instance, if one observation is made under favourable conditions, another under adverse conditions, it would be absurd to place the two on the same footing. Accordingly, the observer pretends that the best observations have been made more frequently. That is to say, if the observations av a2,. . ., an, have weights pv p2,. . ., pn, respectively, the observer has assumed that the measurement ax has been repeated p1 times with the result av and that an has been repeated pn times with the result an. 

III. The weight of an observation is inversely as the square of its probable error. Let a be a set of observations whose probable error is B and whose weight is unity. Let pl9 p2J..pn and rv r2,..., rw, be the respective weights and probable errors of a series of observations av aip..., any of the same quantity. By definition of weight, ax is equivalent to px observations of equal weight. From (17), page 530,... 

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