(a) The methods of Agreement and Difference are complementary as may be discerned by comparing their characteristic features: In Agreement the phenomenon _always occurs_; in Difference the phenomenon _does not always occur_: In Agreement there is one _invariable_ antecedent; whereas in Difference there is one _variable_ antecedent: In Agreement the other antecedents are more or less _variable_; but in Difference the other antecedents are more or less _invariable_. (b) According to Mill the Method of Agreement insists that what _can be eliminated_ is _not_ connected; whereas the Method of Difference implies that what _cannot be eliminated is_ connected. (c) The Method of Agreement is more a method of observation, since it is chiefly concerned with the _discovery of causes_. The Method of Difference is distinctly a method of experiment, because its usual aim is to _discover effects_. (d) The Method of Agreement is so called because the object is to compare several instances to determine in what respect they _agree_; but in the case of Difference instances are compared to determine in what respects they _differ_. (e) The conclusions of the Method of Difference involve greater certainty than those of Agreement and, therefore, the former method should be adopted when there is a choice. =4. THE JOINT METHOD OF AGREEMENT AND DIFFERENCE.= (1) Principle stated. The uncertainty of the conclusions of Agreement and the impossibility at times of employing directly the Method of Difference, give rise to the use of the combination of Agreement and Difference known as the Joint Method. As stated by Mill, the principle conditioning the Joint Method is this: “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 an indispensable part of the cause, of the phenomenon.” More briefly the notion may be stated in this wise: _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._ This principle differs from the one underlying the Method of Difference in that the instances considered are more varied and more numerous. The principle of Difference requires but _two_ sets of instances, while the Joint Method demands at least three; _two_ when the phenomenon occurs and _one_ when it does not occur. A study of the symbolizations and illustrations will clarify this distinction. (2) Joint Method symbolized. If we use circumstances and phenomenon in place of antecedents and consequent, then one symbolization may be made to stand for ascertaining either the invariable antecedent, or the invariable consequent. _Circumstances_ _Phenomenon_