I. (a) That which (without further change) is followed by a given event is its cause. II. (a) That which is not so followed is not the cause. I. (b) That which cannot be left out without impairing a phenomenon is a condition of it. II. (b) That which can be left out is not a condition of it. B. QUANTITATIVE DETERMINATION The Equality of Cause and Effect may be further explained by these rules: III. (a) When a cause (or effect) increases or decreases, so does its effect (or cause). III. (b) If two phenomena, having the other marks of cause and effect, seem unequal, the less contains an unexplored factor. III. (c) If an antecedent and consequent do not increase or decrease correspondingly, they are not cause and effect, so far as they vary. It will next be shown that these propositions are variously combined in Mill's five Canons of Induction: Agreement, the Joint Method, Difference, Variations, Residues. The first three are sometimes called Qualitative Methods, and the two last Quantitative; and although this grouping is not quite accurate, seeing that Difference is often used quantitatively, yet it draws attention to an important distinction between a mere description of conditions and determination by exact measurement. To avoid certain misunderstandings, some slight alterations have been made in the wording of the Canons. It may seem questionable whether the Canons add anything to the above propositions: I think they do. They are not discussed in the ensuing chapter merely out of reverence for Mill, or regard for a nascent tradition; but because, as describing the character of observations and experiments that justify us in drawing conclusions about causation, they are guides to the analysis of observations and to the preparation of experiments. To many eminent investigators the Canons (as such) have been unknown; but they prepared their work effectively so far only as they had definite ideas to the same purport. A definite conception of the conditions of proof is the necessary antecedent of whatever preparations may be made for proving anything. CHAPTER XVI THE CANONS OF DIRECT INDUCTION