Note 419 — Part I.—Experience

("A combination of these methods is sometimes employed, and is termed the Indirect Method of Difference, or the Joint Method of Agreement and Difference. It is, in fact, a double employment of the Method of Agreement, first applying that method to instances in which the phenomenon in question occurs, and then to instances in which it does not occur. The following is its canon:—

"'III. If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common, save the absence of that circumstance; the circumstance in which alone the two sets of instances differ, is the effect, or the cause, or a necessary part of the cause, of the phenomenon.'")—Mill's "Logic," I. 429.

"If we take two groups—one of antecedents and one of consequents—and can succeed in connecting by previous investigations all the antecedents but one to their respective consequents, and all the consequents but one to their respective antecedents, we conclude that the remaining antecedent is connected to the remaining consequent. For example, scientific men had calculated what ought to be the velocity of sound according to the laws of the propagation of sonorous waves, but found that a sound actually travelled quicker than their calculations had indicated. This surplus, or residue of speed, was a consequent for which an antecedent had to be found. Laplace discovered the antecedent in the heat developed by the condensation of each sonorous wave, and this new element, when introduced into the calculation, rendered it perfectly accurate. This is an example of the Method of Residues, the canon of which is as follows:—

"'IV. Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.'"—Mill's "Logic," I. 431.