one may be distinguished by its introduction (all other conditions remaining the same) being attended by a total cessation of the effect. In the discovery of static conditions, as well as in that of dynamic causes, we often meet with circumstances. which cannot be altered or removed at all, and others which can only be altered by changing several at the same time; in each of these cases we proceed as in the discovery of causes. CHAPTER XLVIII. DISCOVERY OF COINCIDENCES. BEFORE we can completely explain a phenomenon we require not only to find its true cause, its chief relations to other causes, and all the conditions which determine how the cause operates, and what its effect and amount of effect are, but also all the coincidences. Before we can determine the cause of an effect, we usually require to know what are the coincidences. By a coincidence is meant any circumstance which, although occurring with or immediately before a phenomenon, is not at all necessary to its production or existence; for example, gold is heavy and yellow, but its yellowness is not a cause or an essential condition of its heaviness, although usually occurring with it. Darkness also invariably precedes, and a somewhat higher temperature usually accompanies, daylight; but neither is a cause or a necessary condition of it, for we know that the relative position of the sun to a particular part of the earth is the cause of each. A coincidence is an independent circumstance. All the immediate conditions of an effect are concomi DISCOVERY OF COINCIDENCES. -445 tant circumstances of that effect; and any condition, except a preventive one, may be a concomitant circumstance. All the properties of a body, and many of the effects of those properties, must always co-exist with the body, and be present in all static and dynamic phenomena in which the body itself is present or takes a part, and therefore form either necessary or mere coincident circumstances in all such phenomena. Also in any case where one force produces two or more effects in a single substance, or where two or more forces are inseparable and act together, coincidences are likely to occur. For instance, as the influence of gravity is always acting throughout all space, and cannot be excluded, its effects must be coincident with those of all other forces in every instance. The effects of magnetism and of an electric current are also frequently coincident, because the latter force cannot exist without the former accompanying it. In consequence of the number of forms of energy continually operating; and of the action of a single force only upon a single substance producing simultaneously many effects; and in consequence also of the almost infinite number of phenomena continually occurring throughout all space, many phenomena must exist at the same moment in the same space, or in close conjunction and contiguity; and coincident circumstances must be extremely abundant, and single isolated ones excessively rare. Remarkable events must also sometimes happen together, independent of all real connection. Coincident circumstances may be divided into separable and inseparable. The former are usually called fortuitous or accidental circumstances, and are often the result of independent chains of causes; for instance, the collision or non-collision of two ships at sea during dark I See Chapter IV., pp. 32, 33.. ness is largely a fortuitous result of independent trains of conditions. As causes and their effects are indissolubly connected together, separable effects are usually produced by separable causes, and inseparable ones by the same cause; for instance, the various effects of heat produced simultaneously in a piece of metal are mostly inseparable. Two coincident circumstances may be inseparable because they are produced by the same force or agent; such phenomena, if they follow different rates of variation, must be separately investigated. By allowing only one cause to operate in a given case, we know that any two phenomena or effects which then occur must be related to each other, either as an intermediate cause and its effects, or as a necessary condition and effect, or as coincident effects of the original cause. Separable coincidences, after having been proved to be such by being excluded by experiment, need not be further considered; we must not, however, assume either separable or inseparable circumstances to be mere coincidences without proving them to be such. Inseparable circumstances can only be proved to be coincidences by indirect means, i.e. by showing that they cannot be anything else; and this is usually done by fully accounting for the effect by the other causes and conditions present, and thus showing them to be unnecessary; the determination of inseparable coincidences, therefore, is one of the last steps in an experimental research. We find causes and necessary conditions before we find inseparable coincident circumstances. An inseparable coincidence may be distinguished both from a cause and from a necessary static condition by its not being indispensable to the effect nor contributing to it.' That which appears to 1 Respecting fortuitous circumstances, see Jevons's Principles of Science, vol. i. p. 302. DISCOVERY OF INSEPARABLE COINCIDENCES. 447 be the cause of a phenomenon is sometimes shown to be only a mere coincidence by the discovery of exceptional cases; a properly-stated cause has no real exceptions. The sum total of a dynamic phenomenon, reduced to its simplest form, may be viewed as consisting of the effect, its cause, static conditions, and inseparable coincidences. CHAPTER XLIX. EXPLANATION OF RESULTS. A SCIENTIFIC investigator should possess the power of correctly interpreting effects; of detecting fallacy when in the guise of truth, and of recognising truth when intermixed with error. The power of quickly perceiving the true explanations of new physical and chemical phenomena is a most comprehensive one, and very difficult to attain, and that which characterises chiefly a great discoverer; it also requires a greater combination of mental powers, and a larger degree of exercise of the reasoning faculty, than any other part of original research. Comparison must precede inference. We cannot draw inferences respecting phenomena unless we can perceive likeness or difference; we cannot recognise real likeness or difference unless we possess an accurate knowledge of and are familiar with the facts to be compared; and we cannot possess that knowledge and be familiar with those facts unless we have had extensive mental contact with them; and as the truths of science are almost infinite in number, accurate and familiar knowledge of even a small portion of them requires great reading and experience. There are also many ways of observing, and many aspects of comparing things which require to be practised before we can extensively reason respecting them. In order to explain the entire collection of the results of a research, we usually require to devise a theory or an idea sufficiently great to include and agree with the whole of the circumstances and results. The explanation of results is essentially a logical process, and especially requires a capacity for accurate inference. The power of inference is based upon the universal principle that we may substitute like for like in material phenomena without altering the effects, and like for like in our thoughts without weakening the argument; two things also which are similar or equivalent to a third one are like or equivalent to each other, and may be substituted in a similar manner. In proportion as two things are alike in the essential points which influence the effect or conclusion, so far may we substitute the one for the other in our experiments, and the conception of one for that of the other in our classifications and reasoning. But frequently the two things are not exactly alike in close essential points, and it usually requires extensive knowledge and experience to be able to judge how far and to what extent they are really similar, and therefore how far the effect or conclusion derived from the one may be inferred from the other. In order to explain phenomena correctly, we must draw correct conclusions. That great mistakes are frequently made in inferring explanations, is proved by the very different and frequently incompatible causes assigned for the same phenomenon by different scientific men. We frequently explain (or rather seem to explain) one mystery by stating another. One of the commonest errors is that of generalising too widely, or drawing conclusions from an insufficient variety or too small a number of instances. The inferences we draw from each observation or example |