Thinking has been defined as the deliberative process of affirming and denying connections. It is obvious that these five methods are a matter of affirming and denying connections between antecedents and consequents. As soon as the looked for connections are established, the antecedents and consequents are known to be related to each other as causes and effects. In this attempt to find and prove connections the Method of Agreement is chiefly valuable in suggesting workable hypotheses, and the method of difference in verifying, through experiment, the correctness or incorrectness of these hypotheses. In substance the principle conditioning both methods is this: “_If a single antecedent is invariably present when the phenomenon is present and invariably absent when the phenomenon is absent then this antecedent is the cause of the phenomenon._” To put it still more briefly: _Between two phenomena there is a causal connection, if the conjunction between the two is invariable._ It is the business of Agreement to _single out the one antecedent_ and of Difference to show, by presenting the negative as well as the affirmative side of the case, that the _conjunction of the one antecedent and the particular phenomenon is invariable_. The Joint Method is merely a combination of Agreement and Difference carried into more varied and complex situations. The methods of Concomitant Variations and Residues are merely modifications of Difference; the former being used when the _chief feature is the fluctuation_ of the phenomenon, and the latter when it is desired to find _what is left over_. _Agreement suggests the hypothesis, “difference” proves it; the joint method is “difference” more or less complicated, concomitant variations is “difference” applied to fluctuating phenomena, residues is “difference” used to find what and how much is left over._ Agreement is the method of observation and belongs to the physician and nature student. Difference and the Joint Method are experimental devices which are used by the physicist and chemist. Concomitant Variations is the method of unstable phenomena and naturally attaches itself to the economist and statistician. Residues is the method of “lurking exceptions” and is favored by the astronomer and mathematician. Residues, being the method of “what is left over,” is the most common in daily affairs.[14] _All the five methods are forms of inductive thinking which lead to the establishment of causal connections by means of the principle of the invariable conjunction of phenomena._ =8. OUTLINE.= THE FIVE SPECIAL METHODS OF OBSERVATION AND EXPERIMENT. (1) Aim of Five Methods. Fundamental fact of causation. Aim of analysis. { agreement { difference Methods of { joint { concomitant variations { residues