Difference is the most common method of the experimental sciences. The characteristic features of difference are, the phenomenon does not always occur, one antecedent is variable, while the others are invariable. The methods of agreement and difference are complementary processes. Agreement attempts to eliminate all the antecedents but one, while difference aims to eliminate one only. Agreement is a method of observation, while difference is a method of experiment. The conclusion of the method of difference gives greater certainty than that of the method of agreement. (4) The joint method may be stated in this way: Among many instances if one circumstance is invariably present when the phenomenon occurs and invariably absent when the phenomenon does not occur, this circumstance is probably the cause or the effect of the phenomenon. The instances of the joint method are more numerous and more varied than those of either agreement or difference. The joint method has the distinguishing characteristics of both agreement and difference. Because it furnishes greater opportunities for multiplying and varying the instances involved, the joint method presents fewer objections than either of the two separate methods. The positive branch of the joint method suggests the hypothesis, while the negative branch proves it. This makes the method somewhat ideal. (5) The principle of concomitant variations may be stated as follows: If when one phenomenon varies alone, and another also varies alone, the one is either the cause or the effect of the other. This is the method of fluctuation, and is used when it is impossible to make the phenomenon disappear altogether, as in the case of difference. The chief function of concomitant variations is to establish exact quantitative relations between cause and effect. (6) The principle of residues is this: Subtract from any phenomenon those parts of it which are known to be the effect of certain antecedents, and what is left of the phenomenon is the effect of the remaining antecedent. The most valuable feature of residues is its suggestiveness; an attempt to explain the “residual phenomenon” has led to many important scientific discoveries. (7) The five methods are concerned with the establishment of causal connections between phenomena. Agreement _suggests_ the connection while difference _proves it_. The other methods are modified applications of difference, necessitated by some peculiar form which the phenomenon may take. A statement of the one principle involved is: “If the conjunction between two phenomena is _invariable_ then there is a causal connection.” All of the methods are forms of inductive thinking. =10. REVIEW QUESTIONS.= (1) Explain “the fundamental fact of causation.” (2) Show that the fact of causation is most conspicuous in induction by analysis. (3) Name the five special inductive methods of observation and experiment.