Publisher's Synopsis
Excerpt from A Recalculation of the Atomic Weights
Suppose now that for every element we had a goodly number Of atomic weight ratios, connecting it with at least a dozen other elements, and all measured with reasonable accuracy. These hundreds Of ratios could then be treated as equations of Observation, reduced to linear form, and combined by the general method of least squares into normal equations. All errors would thus be distributed, never becoming cumulative; and the normal equations, solved once for all, would give the atomic weights Of all the elements simultaneously. The process would be laborious but the result would be the closest possible approach to accuracy. The data as yet are inadequate, although some small groups Of ratios may be handled in that way; but in time the method is sure to be applied, and indeed to be the only general method applicable. Even if every ratio was subject to some small constant error, this, balanced against the similar errors Of other ratios, would become accidental or unsystematic with reference to the entire mass Of material, and would practically vanish from the final means.
Concerning this subject Of constant and accidental errors, a word may be said here. My Own method Of discussion eliminates the latter, which are removable by ordinary averaging; but the constant errors, vicious and untractable, remain, at least partially. Still, where many ratios are considered, even the systematic errors may in part compensate each other, and do less harm than might be expected. They have, moreover, a peculiarity which deserves some attention.
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