These four are not all the scientific methods, but they lead up to the
rest. They are all linked together, and no one has shown their
connection better than Mill. In many cases these processes of isolation
are powerless; namely, in those in which the effect, being produced by a
concourse of causes, cannot be reduced into its elements. Methods of
isolation are then impracticable. We cannot eliminate, and consequently
we cannot perform induction. This serious difficulty presents itself in
almost all cases of motion, for almost every movement is the effect of a
concurrence of forces; and the respective effects of the various forces
are found so mixed up in it that we cannot separate them without
destroying it, so that it seems impossible to tell what part each force
has in the production of the movement. Take a body acted upon by two
forces whose directions form an angle: it moves along the diagonal; each
part, each moment, each position, each element of its movement, is the
combined effect of the two impelling forces. The two effects are so
commingled that we cannot isolate either of them, and refer it to its
source. In order to perceive each effect separately, we should have to
consider the movements apart, that is, to suppress the actual movement,
and to replace it by others. Neither the Method of Agreement, nor of
Difference, nor of Residues, nor of Concomitant Variations, which are
all decomposing and eliminative, can avail against a phenomenon which by
its nature excludes all elimination and decomposition. We must,
therefore, evade the obstacle; and it is here that the last key of
nature appears, the Method of Deduction. We quit the study of the actual
phenomenon to observe other and simpler cases; we establish their laws,
and we connect each with its cause by the ordinary methods of induction.
Then, assuming the concurrence of two or of several of these causes, we
conclude from their known laws what will be their total effect. We next
satisfy ourselves as to whether the actual movement exactly coincides
with the movement foretold; and if this is so, we attribute it to the
causes from which we have deduced it. Thus, in order to discover the
causes of the planetary motions, we seek by simple induction the laws of
two causes: first, the force of primitive impulsion in the direction of
the tangent; next, an accelerative attracting force. From these
inductive laws we deduce by calculation the motion of a body submitted
to their combined influence; and satisfying ourselves that the planetary
motions observed coincide exactly with the predicted movements, we
conclude that the two forces in question are actually the causes of the
planetary motions. "To the Deductive Method," says Mill, "the human mind
is indebted for its most conspicuous triumphs in the investigation of
nature. To it we owe all the theories by which vast and complicated
phenomena are embraced under a few simple laws." Our deviations have
led us further than the direct path; we have derived efficiency from
imperfection.