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.
6. THE METHOD OF RESIDUES.
(1) Principle stated.
As stated by Mill the principle of residue is this: “Subtract from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.”
In simpler form the notion 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 antecedents.
(2) Principle symbolized.
| Antecedent | Consequent |
| A | x |
| B | y |
| C | z |
The total cause of the phenomenon xyz is ABC.But it is known that the cause of x is the antecedent A; whereas the cause of y is the antecedent B; hence it is concluded that the cause of z is the antecedent C.