combinations and registering all relations between conditions and results which are found capable of existence. It would thus resemble the exclusion of contradictory combinations carried out in the Indirect Method of Inference, except that the exclusion of combinations is grounded not on prior logical premises, but on à posteriori results of actual trial.
The reader will perceive, however, that such exhaustive investigation is practically impossible, because the number of requisite experiments would be immensely great. Four antecedents only would require sixteen experiments; twelve antecedents would require 4096, and the number increases as the powers of two. The result is that the experimenter has to fall back upon his own tact and experience in selecting those experiments which are most likely to yield him significant facts. It is at this point that logical rules and forms begin to fail in giving aid. The logical rule is—Try all possible combinations; but this being impracticable, the experimentalist necessarily abandons strict logical method, and trusts to his own insight. Analogy, as we shall see, gives some assistance, and attention should be concentrated on those kinds of conditions which have been found important in like cases. But we are now entirely in the region of probability, and the experimenter, while he is confidently pursuing what he thinks the right clue, may be overlooking the one condition of importance. It is an impressive lesson, for instance, that Newton pursued all his exquisite researches on the spectrum unsuspicious of the fact that if he reduced the hole in the shutter to a narrow slit, all the mysteries of the bright and dark lines were within his grasp, provided of course that his prisms were sufficiently good to define the rays. In like manner we know not what slight alteration in the most familiar experiments may not open the way to realms of new discovery.
Practical difficulties, also, encumber the progress of the physicist. It is often impossible to alter one condition without altering others at the same time; and thus we may not get the pure effect of the condition in question. Some conditions may be absolutely incapable of alteration; others may be with great difficulty, or only in a certain degree, removable. A very treacherous source of error is the existence of unknown conditions, which of course we cannot remove except by accident. These difficulties we will shortly consider in succession.
It is beautiful to observe how the alteration of a single circumstance sometimes conclusively explains a phenomenon. An instance is found in Faraday’s investigation of the behaviour of Lycopodium spores scattered on a vibrating plate. It was observed that these minute spores collected together at the points of greatest motion, whereas sand and all heavy particles collected at the nodes, where the motion was least. It happily occurred to Faraday to try the experiment in the exhausted receiver of an air-pump, and it was then found that the light powder behaved exactly like heavy powder. A conclusive proof was thus obtained that the presence of air was the condition of importance, doubtless because it was thrown into eddies by the motion of the plate, and carried the Lycopodium to the points of greatest agitation. Sand was too heavy to be carried by the air.
Exclusion of Indifferent Circumstances.
From what has been already said it will be apparent that the detection and exclusion of indifferent circumstances is a work of importance, because it allows the concentration of attention upon circumstances which contain the principal condition. Many beautiful instances may be given where all the most obvious antecedents have been shown to have no part in the production of a phenomenon. A person might suppose that the peculiar colours of mother-of-pearl were due to the chemical qualities of the substance. Much