MODE OF CONDUCTING AN ORIGINAL RESEARCH. 379 results,' and hypotheses raised upon these conclusions, at frequent and suitable intervals of time, while notes should also be continually made of the results, conclusions, remarks, and hypotheses. After having made every possible experiment, the utmost amount of new knowledge we are able to obtain should be extracted from the results. This is effected by classifying and combining them in every conceivable way, and stating all the observed uniformities of each class in the form of general conclusions. If, during the process of classification, we meet with exceptional instances, we must, in order to harmonise the general conclusion with them, infer a still more general conclusion which will include both the ordinary instances and the exceptional ones. It is in this way that the apparent truth is often shown to be different from the real, and the results of superficial examination to be opposite to those of deeper research; the apparent cause only of a phenomenon being disclosed by usual instances, and the real and deeper cause by exceptional ones. If we wish to extract more completely the truths implicitly contained in the results, we must subject the general conclusions themselves to every possible variety of combination and permutation; and to obtain a still further amount, we must add to the conclusions truths from other branches of science, and re-perform the same processes.2 The discovery of the general principle or law which pervades and regulates all the results usually completes the research. Sometimes, however, in addition to this, a perfect specimen of the apparatus is constructed for the purposes of illustration; also a practical form of it, for the 2 See Chap. XXXVI. p. 333. 1 See page 333. purpose of showing that it is probably capable of application to some immediately useful purpose. This latter act, however, is one not of scientific discovery, but of invention, and is a step towards an artistic, manufacturing, or commercial application of the discovery. In many cases, the last performance in an original research, viz., the drawing of general conclusions, and explaining the results, are much more complex and difficult than would be inferred from the foregoing remarks, because physical and chemical phenomena are often results of a combination of causes which cannot be separated, and are attended by a number of concomitant effects and circumstances which we cannot exclude, and which render it difficult to draw correct conclusions, and also to prove and explain the true relations of the phenomenon. Indeed, the complexity of nature far surpasses, in nearly all cases, man's usual ideas of it; the simplest phenomena of matter present almost infinitely more for us to explain than we can even imagine. The modes of discovering causes, coincidences, and other relations of phenomena, are described in Chapters XLVI., XLVII., and XLVIII. In an original research, we encounter difficulties at every step, and we must, if possible, overcome them. The fundamental rule for overcoming a difficulty in research is to attack it in detail, i.e., to divide it to the fullest extent, and analyse and treat each part separately. Thus when we wish to know the exact chemical composition of a complex substance, we dissolve one hundred parts of it, and then precipitate or otherwise separate its ingredients in several collections, known as the hydrochloric acid group, sulphuretted-hydrogen group, sulphide of ammonium and carbonate of ammonium groups, the alkaline earth and the alkaline groups; and we then subdivide each of these collections into several smaller ones, and so MODE OF CONDUCTING AN ORIGINAL RESEARCH. 381 on, until we have individually isolated each of the elementary bodies present in the original substance, and can subdivide them in that manner no further. We then ascertain if the sum of the weights of the elementary substances found exactly equals that of the original body. If it does, the analysis is complete; but if it does not, we have either omitted some substance present, introduced a foreign body, or committed an error of manipulation, observation, or calculation; and we proceed at once to correct the mistake. In the examination of a physical phenomenon, we proceed in a substantially similar manner, i.e., we divide the conditions of it in every possible way, and into the smallest distinct elements, and examine each portion, not only in a qualitative manner, but also quantitatively, as far as the circumstances of the case will admit. The quantitative analysis of a physical phenomenon, however, can often be only incompletely performed. In the analysis of such a phenomenon, instead of dividing its conditions first into groups, and then each group into its individual distinct elements, as in chemical analysis, we usually separate one only of its conditions at a time, leaving each time all the remaining ones together; and we then sometimes reduce the complexity of the phenomenon by an element at a time, or subdivide the phenomenon in other ways, according to the circumstances of the particular case. In every case, however, we reduce the phenomenon to its purest and simplest state, by separating from it all its unnecessary conditions, as soon as we can, in order to fit it for the actual analysis. CHAPTER XL. ADVANTAGES OF VARIETY OF EXPERIMENTS. A VARIETY of well-devised experiments is of the highest importance, and is much more likely to yield valuable discoveries than any mere number of similar ones, especially if the questions involved in the experiments are some of them intrinsically momentous. It also supplies us with results and data by means of which we can, by processes of comparison and inference, determine the causes, coincidences, and other abstruse relations of phenomena. Variety of experiments is also the chief means by which the indifferent and unessential circumstances, and those which interfere with a phenomenon we are investigating in a new research, are quickly disclosed and detected. If the conditions of an experiment are not sufficiently varied, we can hardly be sure that unsuspected influences have not affected the results; nor can we be certain that our interpretation of the results is correct. A uniform method of working may conceal a uniform error. In every experiment there are always many ways of failing, and usually only one way of succeeding; and no precise rule can be laid down, either for preventing errors in experiments or for excluding those errors which have been detected, because the methods of preventing or excluding them differ somewhat in every different case. Failure in experiments often arises from want of proper materials, or proper proportions of them, and in a great variety of other ways. Although the truth is not always arrived at by the first experiment, that is not the case because the first idea of the experiment is not very often 6 ADVANTAGES OF VARIETY OF EXPERIMENTS. 383 quite adequate to obtain the truth; but it may sometimes happen because the materials and means which are used to carry it out practically are not adapted to that purpose; and although these experiments cannot contaminate the purity of the theoretical speculations, they are nevertheless unfitted to second them, on account of the materials employed.'1 In an investigation, it is usual to exclude the largest errors first, because it is not of much use to exclude small ones if large ones remain; and it is highly important to reduce the mode of experimenting to its purest and simplest form as quickly as possible, because until that point is attained the results of the experiments are more or less untrustworthy, and, no matter what time or money they may have cost, have to be wholly or partially discarded. The mode of experimenting cannot, however, be reduced to its purest form until such a variety of experiments have been made as to disclose the existence of all the interfering circumstances. Some interfering circumstances are very treacherous sources of error, because they are unsuspected; such are usually disclosed by a want of uniformity in the results, even when the conditions are apparently similar; and this want of uniformity is produced by the previously unsuspected cause or causes operating according to a different law of variation to that of the cause of the pure phenomenon. As an example of this kind; I was investigating the 1 Magalotte. * I believe that Mr. Bailey, in his experiments made to ascertain the mean density of the earth (commonly known as 'weighing the earth'), after several years of labour and great expense, discovered an error which vitiated all the results; and he therefore discarded the whole of them, and repeated the entire series of experiments over again, with the source of error excluded from them. |