The transformation of matter and energy, then, is the essence of causation:  because it is continuous, causation is immediate; and because in the same circumstances the transformation always follows the same course, a cause has invariably the same effect.  If a fire be lit morning after morning in the same grate, with coal, wood, and paper of the same quality and similarly arranged, there will be each day the same flaming of paper, crackling of wood and glowing of coal, followed in about the same time by the same reduction of the whole mass partly to ashes and partly to gases and smoke that have gone up the chimney.  The flaming, crackling and glowing are, physically, modes of energy; and the change of materials into gas and ashes is a chemical and physical redistribution:  and, if some one be present, he will be aware of all this; and then, besides the physical changes, there will be sensations of light, sound and heat; and these again will be always the same in the same circumstances.

The Cause of any event, then, when exactly ascertainable, has five marks:  it is (quantitatively) equal to the effect, and (qualitatively) the immediate, unconditional, invariable antecedent of the effect.

Sec. 3.  This scientific conception of causation has been developed and rendered definite by the investigations of those physical sciences that can avail themselves of exact experiments and mathematical calculation; and it is there, in Chemistry and Physics, that it is most at home.  The conception can indeed be carried into the Biological and Social Sciences, even in its quantitative form, by making the proper allowances.  For the limbs of animals are levers, and act upon mechanical principles; and digestion and the aeration of the blood by breathing are partly chemical processes.  There is a quantitative relation between the food a man eats and the amount of work he can do.  The numbers of any species of plant or animal depend upon the food supply.  The value of a country’s imports is equal to the value of its exports and of the services it renders to foreigners.  But, generally, the less experiment and exact calculation are practicable in any branch of inquiry, the less rigorously can the conception of causation be applied there, the more will its application depend upon the qualitative marks, and the more need there will be to use it judiciously.  In every inquiry the greatest possible precision must be aimed at; but it is unreasonable to expect in any case more precise proof than the subject admits of in the existing state of culture.

Wherever mental action is involved, there is a special difficulty in applying the physical notion of causation.  For if a Cause be conceived of as matter in motion, a thought, or feeling, or volition can be neither cause nor effect.  And since mental action is involved in all social affairs, and in the life of all men and animals, it may seem impossible to interpret social or vital changes according to laws of causation.