The principles of science : a treatise on logic and scientific method / by W. Stanley Jevons.
- William Stanley Jevons
- Date:
- 1874
Licence: Public Domain Mark
Credit: The principles of science : a treatise on logic and scientific method / by W. Stanley Jevons. Source: Wellcome Collection.
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![weight in our mean conclusions, and should bear in mind the discrepancy as one demanding attention. To neglect a divergent result is to neglect the possible clue to a great discovery. Method of Least Squares. When two or more unknown quantities are so involved that they cannot be separately determined by the single Method of Means, we can yet obtain their most probable amounts by the Method of Least Squares, without more difficulty than arises from the length of the arithmetical computations. If the result of each observation gives an equation between two unknown quantities of the form ax + l>y = c then, if the observations were free from error, we should only need two observations giving two equations; but, for the attainment of greater accuracy, we may take a series of observations, and then reduce the equations so as to give only a pair with average coefficients. This re daction is effected by, firstly, multiplying the coefficients of each equation by the first coefficient, and adding to gether all the similar coefficients thus resulting for the coefficients of a new equation ; and secondly, by repeating this process, and multiplying the coefficients of each equa tion by the coefficient of the second term. Thus meaning by (sum of a2) the sum of all quantities of the same kind, and having the same place in the equations as a2, we may briefly describe the two resulting mean equations as follows :— (sum of a'} . x + (sum of «?>) . y = (sum of ac), (sum of ctb] . x + (sum of &2) . y — (sum of be]. When there are three or more unknown quantities the process is exactly the same in nature, and we only need additional mean equations to be obtained by multiply ing by the third, fourth, &c., coefficients. As the numbers](https://iiif.wellcomecollection.org/image/b21183326_0478.jp2/full/800%2C/0/default.jpg)
