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 isimpossible 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.