We may now consider the great advantages which we enjoy in examining the combinations of phenomena when things are within our reach and capable of being experimented on. We are said to experiment when we bring substances together under various conditions of temperature, pressure, electric disturbance, chemical action, &c., and then record the changes observed. Our object in inductive investigation is to ascertain exactly the group of circumstances or conditions which being present, a certain other group of phenomena will follow. If we denote by A the antecedent group, and by X subsequent phenomena, our object will usually be to discover a law of the form A = AX, the meaning of which is that where A is X will happen.
The circumstances which might be enumerated as present in the simplest experiment are very numerous, in fact almost infinite. Rub two sticks together and consider what would be an exhaustive statement of the conditions. There are the form, hardness, organic structure, and all the chemical qualities of the wood; the pressure and velocity of the rubbing; the temperature, pressure, and all the chemical qualities of the surrounding air; the proximity of the earth with its attractive and electric powers; the temperature and other properties of the persons producing motion; the radiation from the sun, and to and from the sky; the electric excitement possibly existing in any overhanging cloud; even the positions of the heavenly bodies must be mentioned. On à priori grounds it is unsafe to assume that any one of these circumstances is without effect, and it is only by experience that we can single out those precise conditions from which the observed heat of friction proceeds.
The great method of experiment consists in removing, one at a time, each of those conditions which may be imagined to have an influence on the result. Our object in the experiment of rubbing sticks is to discover the exact circumstances under which heat appears. Now the presence of air may be requisite; therefore prepare a vacuum, and rub the sticks in every respect as before, except that it is done in vacuo. If heat still appears we may say that air is not, in the presence of the other circumstances, a requisite condition. The conduction of heat from neighbouring bodies may be a condition. Prevent this by making all the surrounding bodies ice cold, which is what Davy aimed at in rubbing two pieces of ice together. If heat still appears we have eliminated another condition, and so we may go on until it becomes apparent that the expenditure of energy in the friction of two bodies is the sole condition of the production of heat.
The great difficulty of experiment arises from the fact that we must not assume the conditions to be independent. Previous to experiment we have no right to say that the rubbing of two sticks will produce heat in the same way when air is absent as before. We may have heat produced in one way when air is present, and in another when air is absent. The inquiry branches out into two lines, and we ought to try in both cases whether cutting off a supply of heat by conduction prevents its evolution in friction. The same branching out of the inquiry occurs with regard to every circumstance which enters into the experiment.
Regarding only four circumstances, say A, B, C, D, we ought to test not only the combinations ABCD, ABC d , AB c D, A b CD, a BCD, but we ought really to go through the whole of the combinations given in the fifth column of the Logical Alphabet. The effect of the absence of each condition should be tried both in the presence and absence of every other condition, and every selection of those conditions. Perfect and exhaustive experimentation would, in short, consist in examining natural phenomena in all their possible