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FUTURE QUANTITATIVE RESULTS.

395

are limited to the ordinary range of atmospheric pressure and temperature, but we require additional ones for all pressures and all temperatures, and for all combinations of these. A probable result of the formation of such tables will be a profound alteration of our views of nature, because every single substance has more or less different properties at every different pressure and temperature.1

'Now with respect to accurate measurement, theory was left far behind by practice, and I need not to be reminded how very much more accurate were the measurements of resistance in the practical telegraphy of Dr. Werner Siemens and his brother than in any laboratory of theoretical science. When in the laboratory of theoretical science, it had not been discovered that the conductivity of different specimens of copper differed at all, in practical telegraphy workshops they were found to differ by from thirty to forty per cent. When differences amounting to so much were overlooked, when their very existence was not known to scientific electricians, the great founders of accurate measurements in telegraphy were establishing the standards of resistance accurate to onetenth per cent. Dr. Werner Siemens and his brother were among the first to give accurate standards of resistance, and the very first to give an accurate system of units founded upon those standards.'2

Accuracy of measurement is often obtained by means of repetition, as in the pendulum; also by means of coincidence, as in the vernier. Descriptions of the numerous ways in which measurements have led to discoveries, and

1 See Chapter IV. p. 34.

2 Address by Sir W. Thomson. On Electrical Measurement. Conferences, Special Loan Collection, London, 1876, p. 247.

396

ACTUAL WORKING IN ORIGINAL RESEARCH.

of the various methods of measuring substances, forces, conditions, and actions; of weighing, and taking the specific gravities of solids, liquids, and gases; of determining the coefficients of elasticity and of numerous other properties, the positions of spectral lines, the degrees of conduction-resistance to heat and electricity, also of paramagnetic and diamagnetic capacity, and a multitude of other phenomena, at all temperatures and pressures, form a portion of the subject of quantitative research, and may be found in the various text-books of the different sciences.1

CHAPTER XLIII.

COMPLETION OF RESEARCHES.

Ir is desirable that researches which have been commenced should be completed. Not unfrequently they are abandoned when only partly made. The difficulty of completing them arises partly from the immensity and complexity of nature. The most trifling fact, when exhaustively investigated, gives rise to many varied questions, each of which requires a separate research, and these separate researches in their turn give rise to others, so that it appears impossible to exhaust the subject, or make the first research complete, and thus the results of valuable investigations are in consequence often withheld from publication: this is a common case. Researches are also

1 For illustrations of the great value of mathematics in scientific discovery, see Whewell's Philosophy of the Inductive Sciences, vol. i. pp. 150–156; Whewell's History of Scientific Ideas, vol. i. 3rd edition, chap. xiv. pp. 153–167; also G. C. Foster's Address to Physics Section of the British Association, 1877,

sometimes put aside in an incomplete state by the investigator for the purpose of pursuing new ones, which appear more important or more attractive.

A complete research should be exhaustive, because it often happens that if a research is not thorough, instances of an important or exceptional kind remain undiscovered, essential similarities or differences continue unnoticed, and the true explanations may remain unattained and a wrong one be assumed. Some scientific men, having made an experiment and observed its result, or observed some singular natural phenomenon, stop short, and fail to examine it further. Others make a partial investigation only, either making an insufficient variety of experiments, and thereby failing to exclude interferences; or an insufficient number, and thus missing extreme and exceptional instances.

Every part of an investigation, and even each single experiment, may however be viewed as a smaller research, complete as far as it goes, because we can compare and classify results, and draw analogies and inferences from them as we proceed, and also infer from each result and class of results the full amount of conclusion warranted by the evidence. Viewed from the opposite aspect, the most extensive research is never complete, and never can be until it extends to the utmost bounds of knowledge.

THIS is an important process in scientific research; it is closely related to the act of comparison, and is the next step towards the interpretation of results. We first observe two or more things, one at a time, then compare them together, and perceive either a similarity or difference, and classify them accordingly. For instance, we immerse a large number of different substances in a liquefied gas, and observe them one by one, and find that many of them are dissolved and the remainder are not, and we then form them into two classes, viz., those which are soluble and those which are insoluble in that liquid. We also arrange things of a similar kind together in classes, and then observe for some relation between them; for instance, we class together all the acid substances which we immersed in the liquid, also all the magnetic ones, &c., and then observe whether either of those classes agrees with the soluble or insoluble In the first of these cases we class together a number of different things, and look for similarities and differences, and thus divide the results into two classes, which we may again treat in a similar way; and in the second, we class together each group of similar things, and observe for other similarities and differences, and subdivide them also and repeat the process if necessary.

ones.

During a research we classify at every convenient stage of progress, because every classification affords an opportunity of generalising; we also classify in every possible way, not only according to the more manifest similarities and differences of the phenomena or facts, but

also according to the more abstruse or hidden ones, because the great object of classifying is to render evident the general truths contained in the results, and thus to enable us to extract from those results, by means of the subsequent processes of generalisation and inference, the largest possible amount of knowledge. Even the exceptional cases, if a sufficient number of them can be obtained, should be classified in a similar manner. A few of the leading heads of classification of properties, actions, and substances, in physics and chemistry, have already been enumerated in Chapter XXXV., pp. 330, 331.

Although for the purpose of scientific discovery, it is necessary to classify ideas in every possible way in order to extract the maximum amount of truth from them, yet it is equally necessary in a systematic representation of knowledge, and in all cases where we wish to determine the relative degrees of intrinsic value or importance of things, to classify them upon the most fundamental basis we can find.

As the number of similarities and differences which we are able to perceive between the results of a given number of experiments or observations is limited, and as the number of properties, actions, and substances with which we are at present acquainted is not infinite, the number of ways in which we can classify the results of a single research is also limited. Still, we never exhaust the possible modes of classifying them, because many of their similarities and differences are latent and unperceived, and the phenomena really present before us are far more numerous than they appear to be, and every instance contains far more information than we can even imagine.