must neither contain too much information nor too little. If they contain too much, the excess is uncertain, and may be entirely false; and if they include too little, they do not render manifest the whole amount of truth warranted by the evidence.

Quickness in explaining phenomena correctly depends also upon a capacity for estimating the relative degrees of generality and frequency of occurrence of different phenomena. There are common causes and unfrequent ones; usual impurities in substances, and rare ones; and other circumstances being alike, the more frequent the existence of a substance or action, the more likely is it to be the cause of a newly-observed phenomenon. Success in explaining phenomena manifestly also depends, to a large extent, upon the intensity and amount of thought bestowed upon each particular question.

The explanation of results and of scientific facts in general is a complex process, and often extremely difficult. It consists in showing the various similarities of the fact or phenomenon to other ones, also its cause, and the various true relations of it to all the different circumstances or phenomena which precede, accompany, or follow it. To ascertain all these usually requires a scientific research. An isolated fact or phenomenon of a novel kind, cannot be fully explained without a proper and sufficient investigation, because the explanation requires much more information than the fact or phenomenon manifestly implies, and we cannot evolve that information by means of study of the fact alone, however intense that study may be. The correct explanation of a fact and of the results of experiments bearing upon it, can be given with safety only when a research is completed, and its causes, conditions, and coincidences ascertained; at the same time the whole course of an investigation is a

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gradual but irregular unfolding of the true explanation, some parts of the progress being very slow and others very rapid.

In actual research we do not wait until an investigation is completed before we seek to explain the results; but we draw conclusions at intervals as we proceed, usually after each experiment, each class of experiments, and after all the experiments have been made. We also note down remarks, comparisons, and suggestions of every kind bearing upon the subject, which occur to us as we proceed. The most comprehensive inferences, or those which include the greatest number of cases, are generally formed the last, because they require to be drawn from the greatest variety and number of results. The various conclusions, certain or probable, inferred from the results as we proceed, continually enable us to clear away false hypotheses, and suggest to us additional new questions to be decided. It is very rare indeed that a collection of scientific truths lying ready to hand, are sufficiently complete or systematic in themselves, to contain all the information necessary for their true and complete explanation, or for entirely proving a new theory. The true explanation is that one which completely agrees with all the facts, and not only with all the ordinary instances, but also with all the exceptional ones.

The method of obtaining an explanation of the results of a research (and of scientific facts in general) consists of two processes, viz. the comparing and classifying them, and thereby evolving analogies, similarities, and differences; and 2nd, drawing conclusions or inferences in the form of general truths, laws, principles, causes, coincidences, &c., from such similarities and differences. In each of these two processes we only alter the form of the original truths, and thereby make apparent more of the

information they implicitly contain, but we do not actually create new knowledge. An unlimited amount of information cannot be extracted from a limited number of truths, nor can we by either of these generalising processes attain from them more than their equivalent, because a true conclusion never exceeds the limits of its premises, and a general statement respecting any number of facts or instances contains only as much information on the specified point as all the instances put together.

In some cases the correct interpretation of results is an easy matter, the causes or other relations of them being simple and obvious; in other cases it is a difficult problem, requiring intense study and much sagacity; and in others again it is not possible to ascertain the exact explanation, either because other scientific questions bearing upon this one have not yet been settled, or because the secret lies beyond our powers. One great difficulty in the way of obtaining a correct explanation in some cases arises from the fact that there are various causes, and many combinations of them, and each cause may act in many degrees, and be modified by various circumstances, and the phenomenon may arise from a combination or permutation of causes. Many cases occur where an effect depends upon several causes, each of which increases its magnitude; many others happen in which the effect does not take place unless all the causes are present, and it is common for persons to be misled by this circumstance to consider that because the effect does not take place when some of the conditions are present, that those conditions form no part of the cause of the phenomena. It follows also, from these and other considerations, that whilst there can be only one true interpretation, there may be many erroneous ones, each of which may mislead us. An erroneous interpretation may appear to agree with the facts, but that

is not sufficient, it must be thoroughly tested. So long also as our knowledge of nature is incomplete, there will always remain phenomena which we cannot fully explain. In order to obtain the true and complete explanation, we ought to ascertain the effect of each condition, both in the presence and absence of every other condition; but as the trouble is often too great, we frequently pursue the more direct plan of trusting to insight; this, however, often causes us to miss some new truth or important point, and especially to miss exceptional cases. Newton missed the discovery of Fraunhofer's lines in this way. Moreover, if we were willing to take the trouble, we could not succeed, because multitudes of conditions are probably unknown to us respecting the simplest physical phenomena, and, in consequence of this, our most perfect explanations of such phenomena are always very far from complete.

With regard to the publication of the explanation, whilst a scientific enquirer may give an almost unlimited freedom to his imagination in his study and private hypotheses, he must limit his statements to the strictest truth in his conclusions and published researches, lest he may propagate error; he must combine boldness in thinking and experimenting with cautiousness in concluding and asserting.

Nothing, perhaps, conduces so much to damp the ardour of an investigator as premature disclosure of results; but when the results are disclosed by proper publication, sufficient detail, both of circumstances and quantities, should be explicitly stated, in order that other persons may readily obtain similar effects.

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PART V.

SPECIAL METHODS OF DISCOVERY.

CHAPTER L.

SPECIAL EMPIRICAL METHODS OF SCIENTIFIC RESEARCH.

As but few investigators have left behind them a record of the exact circumstance or conditions which immediately led to their discoveries, I have been obliged in many cases to infer from such few particulars as have been handed down, and from my own experience as an investigator, what must have been, or probably was, one or more of the conditions which led to those discoveries, and have classified the discoveries accordingly.

The methods and processes of discovery, although essentially and chiefly mental, are partly physical, and are determined by the laws of nature; obedience to nature is the prime condition of discovering new truths. No two investigators work exactly alike, but all are practically guided by the same general rules, because the fundamental laws of science and rules of thought are the same for all men. As scientific investigation is not a supernatural process, but is subject to laws, there must exist a system of general rules of qualitative re