(2) Of the second group of instances: (1) The phenomenon must never occur, (2) One antecedent must be variable, (3) The other antecedents must be more or less invariable. Briefly, the one principle concerned is this: There must be an invariable conjunction between the phenomenon involved and the antecedent suspected of being the cause. (5) Advantages and Disadvantages of the Joint Method. Since the Joint Method permits a consideration of the negative aspect of the question as well as the affirmative, the opportunities for testing the many instances concerned are doubled. In consequence, the conclusions of the Joint Method are more positive than those of the other methods. It follows that this same opportunity to multiply the instances would tend to lessen the other objections raised against the Method of Agreement; viz., plurality of causes, immaterial antecedents, complexity of phenomenon. The student must regard the given illustrative symbolizations and concrete examples as being of the simplest form; in life such are the exceptions rather than the rule. When investigating questions, like the cause of the high cost of living, the effect of high tariff, the reason for the typhoid epidemic, etc., there is often a confusion of circumstances which makes the Joint Method unsatisfactory, even though it furnishes a larger opportunity for the multiplication of instances. The strongest case which the Joint Method is able to present is when the negative instances repeat the positive in every detail, with the one exception of the variable antecedent. To wit: _Strong Argument_: _Circumstances_ _Phenomenon_ A B C P₁ A L M P₂ ‒ L M ― ‒ B C ― _Weak Argument_: A B C P₁ A L M P₂ ‒ R S ― ‒ T K ― Despite the disadvantages, the conditions of the Joint Method are more or less ideal; since the positive branch of the argument _suggests_ the hypothesis, while the negative branch _proves_ the accuracy or inaccuracy of such. =5. METHOD OF CONCOMITANT VARIATIONS.= (1) Principle stated. Mill’s statement is this: “Whatever phenomenon varies in any manner whenever another phenomenon varies in a particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation.” To put it differently: _If when one phenomenon varies alone, another also varies alone, the one is either the cause or the effect of the other._ (2) Concomitant Variations symbolized. Circumstances Phenomenon A P A + a P + p (A + a) − a (P + p) − p It is evident from this that little “a” is the cause or the effect of little “p.” To put it in concrete form: Let A = X number of calories of heat, And P = 68° F., the original temperature of room, And a = candle burning in room for ½ hour, And p = 2° F.