The Method of Gradations, the arranging of any phenomena to be studied in series, according to the degree in which some character is exhibited, is, perhaps, the most definite device in the Art of Discovery. (Bain: _Induction_, c. 6, and App. II.) If the causes are unknown it is likely to suggest hypotheses: and if the causes are partly known, variation in the character of the series is likely to indicate a corresponding variation of the conditions. § 5. THE CANON OF RESIDUES. _Subduct from any phenomenon such part as previous inductions have shown to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents_. The phenomenon is here assumed to be an effect: a similar Canon may be framed for residuary causes. This also is not a fresh method, but a special case of the method of Difference. For if we suppose the phenomenon to be _p q r_, and the antecedent to be A B C, and that we already know B and C to have (either severally or together) the consequents _q r_, in which their efficacy is exhausted; we may regard B C _q r_ as an instance of the absence of _p_ obtained deductively from the whole phenomenon A B C _p q r_ by our knowledge of the laws of B and C; so that A B C _p q r_ is an instance of the presence of _p_, differing otherwise from B C _q r_ in nothing except that A is also present. By the Canon of Difference, therefore A is the cause of _p_. Or, again, when phenomena thus treated are strictly quantitative, the method may be based on Prop. III. (b), ch. xv. § 7. Of course, if A can be obtained apart from B C and directly experimented with so as to produce _p_, so much the better; and this may often be done; but the special value of the method of Residues appears, when some complex phenomenon has been for the most part accounted for by known causes, whilst there remains some excess, or shortcoming, or deviation from the result which those causes alone would lead us to expect, and this residuary fact has to be explained in relation to the whole. Here the negative instance is constituted by deduction, showing what would happen but for the interference of some unknown cause which is to be investigated; and this prominence of the deductive process has led some writers to class the method as deductive. But we have seen that all the Canons involve deduction; and, considering how much in every experiment is assumed as already known (what circumstances are 'material,' and when conditions may be called 'the same'), the wonder is that no one has insisted upon regarding every method as concerned with residues. In fact, as scientific explanation progresses, the phenomena that may be considered as residuary become more numerous and the importance of this method increases.