[29] Hist. Ind. Sc. b. ix. c. vi.
Though we cannot give rules which will be of much service when we have thus to divine the general form of the relation by which phenomena are connected, there are certain methods by which, in a narrower field, our investigations may be materially promoted;—certain special methods of obtaining laws from Observations. Of these we shall now proceed to treat.
CHAPTER VII.
Special Methods of Induction applicable to Quantity.
Aphorism XLIII.
There are special Methods of Induction applicable to Quantity; of which the principal are, the Method of Curves, the Method of Means, the Method of Least Squares, and the Method of Residues.
Aphorism XLIV.
The Method of Curves consists in drawing a curve of which the observed quantities are the Ordinates, the quantity on which the change of these quantities depends being the Abscissa. The efficacy of this Method depends upon the faculty which the eye possesses, of readily detecting regularity and irregularity in forms. The Method may be used to detect the Laws which the observed quantities follow: and also, when the Observations are inexact, it may be used to correct these Observations, so as to obtain data more true than the observed facts themselves.
Aphorism XLV.
The Method of Means gets rid of irregularities by taking the arithmetical mean of a great number of observed quantities. Its efficacy depends upon this; that in cases in which observed quantities are affected by other inequalities, besides that of which we wish to determine the law, the excesses above and defects below the quantities which the law in question would produce, will, in a collection of many observations, balance each other. 203