[418]"A bird in the air breathes; plunged into carbonic acid gas, it ceases to breathe. In other words, in the second case, suffocation ensues. In other respects the two cases are as similar as possible, since we have the same bird in both, and they take place in immediate succession. They differ only in the circumstance of immersion in carbonic acid gas being substituted for immersion in the atmosphere, and we conclude that this circumstance is invariably followed by suffocation. The Method of Difference is here employed. Its canon is:—
"'II. If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or the cause, or a necessary part of the cause, of the phenomenon.'"—Ibid. I. 423.
[419]("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.
[420]"Let us take two facts—as the presence of the earth and the oscillation of the pendulum; or, again, the presence of the moon and the flow of the tide. To connect these phenomena directly, we should have to suppress the first of them, and see if this suppression would occasion the stoppage of the second. Now, in both instances, such suppression is impossible. So we employ an indirect means of connecting the phenomena. We observe that all the variations of the one correspond to certain variations of the other; that all the oscillations of the pendulum correspond to certain different positions of the earth; that all states of the tide correspond to positions of the moon. From this we conclude that the second fact is the antecedent of the first. These are examples of the Method of Concomitant Variations. Its canon is:—
"'V. Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation.'"—Mill's "Logic," I. 435.
[421]"The Method of Agreement," says Mill ("Logic," I. 4-14), "stands on the ground that whatever can be eliminated, is not connected with the phenomenon by any law. The Method of Difference has for its foundation, that whatever cannot be eliminated, is connected with the phenomenon by a law." The Method of Residues is a case of the Method of Differences. The Method of Concomitant Variations is another case of the same method; with this distinction, that it is applied, not to the phenomena, but to their variations.
[422]This quotation, and all the others in this paragraph, are taken from Mill's "Logic," I. 451-9. Mr. Mill quotes from Sir John Herschel's "Discourse on the Study of Natural Philosophy."