{{186}} CHAPTER V. ANALYSIS OF THE PROCESS OF INDUCTION. APHORISM XXXIV. _The Process of Induction may be resolved into three steps; the_ Selection of the Idea, _the_ Construction of the Conception, _and the_ Determination of the Magnitudes. APHORISM XXXV. _These three steps correspond to the determination of the_ Independent Variable, _the_ Formula, _and the_ Coefficients, _in mathematical investigations; or to the_ Argument, _the_ Law, _and the_ Numerical Data, _in a Table of an astronomical or other_ Inequality. APHORISM XXXVI. _The Selection of the Idea depends mainly upon inventive sagacity: which operates by suggesting and trying various hypotheses. Some inquirers try erroneous hypotheses; and thus, exhausting the forms of errour, form the Prelude to Discovery._ APHORISM XXXVII. _The following Rules may be given, in order to the selection of the Idea for purposes of Induction:--the Idea and the Facts must be_ homogeneous; _and the Rule must be_ tested by the Facts. SECT. I.--_The Three Steps of Induction._ 1. WHEN facts have been decomposed and phenomena measured, the philosopher endeavours to combine them into general laws, by the aid of {187} Ideas and Conceptions; these being illustrated and regulated by such means as we have spoken of in the last two chapters. In this task, of gathering laws of nature from observed facts, as we have already said[24\3], the natural sagacity of gifted minds is the power by which the greater part of the successful results have been obtained; and this power will probably always be more efficacious than any Method can be. Still there are certain methods of procedure which may, in such investigations, give us no inconsiderable aid, and these I shall endeavour to expound. [Note 24\3: B. ii. c. vi.]