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.

Then

Antecedents	Consequent
X no. of cal. of heat in room	= 68° F. temp. of room
X no. of cal. of heat + burning candle	= 68° + 2° = 70°
X (no. of cal. of heat + burning candle) − burning candle	= (68° + 2°) − 2° = 68°

As large “A” is increased and decreased by little “a” so large “P” appears to be increased and decreased by little “p.” This strongly suggests a causal connection between little “a” and little “p.”

(3) Other concrete illustrations.

Problem: To ascertain nature of sound.

Antecedent	Consequent
Bell rung when within a glass jar filled with air,	Loud sound.
Some of the air pumped out of the jar,	Sound not so loud.
More air pumped into jar again,	Sound louder again.

The conclusion must be that air has something to do with the production of sound.

Problem: To find best feed for egg production.

100 lbs. beef scraps,		30 doz. eggs.
100 lbs. wheat,
100 lbs. oats,
100 lbs. corn,
50 lbs. beef scraps,		27 doz. eggs.
100 lbs. wheat,
100 lbs. oats,
100 lbs. corn,
90 lbs. beef scraps,		28 doz. eggs.
100 lbs. wheat,
100 lbs. oats,
100 lbs. corn,

Since the variation in the amount of beef scraps is accompanied by a like variation in the number of eggs produced, it may be assumed that beef scraps are essential to large egg production.

(4) Distinguishing features.

The phenomenon always occurs but in varying degrees;

One antecedent varies in degree;

The other antecedents are invariable.

(5) Advantages and disadvantages.

Concomitant Variations is applicable in cases when it is impossible to use Difference. Recourse is made to the latter when the phenomenon can be made to appear or disappear at will, but there are times when it is impossible to cause the phenomenon to disappear altogether. For example, in the case of the varying degrees of heat in the room it would be scientifically impossible to take all of the heat out of the room; or in experimenting with gravitation, to do away with its influence entirely, is beyond the power of man.It is thus evident that Concomitant Variations may be used in cases where the conditions forbid doing away entirely with the phenomenon.

The special function of Concomitant Variations seems to be to establish the exact quantitative relation between the varying cause and the varying effect. To illustrate: As a general law it is known that bodies attract each other in varying degrees according to their distances apart and according to their relative sizes; by Concomitant Variations this law has been given definite quantitative value and reads like this: “Bodies attract each other directly as the product of their masses, and inversely as the square of the distance between them.” This illustration suggests that the variation between antecedent and consequent may be direct or inverse.

The error most common in this method is the assumption that the quantitative relation between two varyingphenomena will always be according to a constant ratio. For example, when being reduced from a high temperature to 39¹⁄₅° F., water steadily contracts; but at 39¹⁄₅° F. it commences to expand until it becomes ice. Thus the ratio of contraction of water is constant only within certain limits. In any event the established ratio of variation can with absolute safety be applied only to the instances investigated. Another disadvantage incident to this method, is the situation of two elements varying together constantly, and yet having no causal connection whatever.