exceptional and residuary instances requires, again, a different process.

And 4. With respect to its dependence upon the state of knowledge at the time, and upon the chronological order of the sciences, it is evident that as our mental faculties have only a finite degree of power, we can only use a method of discovery successfully, provided the subject is ripe, or has arrived at that stage at which discovery is possible, i.e. at which the intellectual and other labour necessary to effect it has come within the limit of our

means.

In the practical discovery of new truths, and in the investigation of those already known, every known variety, combination, and permutation of mental and physical method is employed, those methods being selected which are best suited to the particular case; for instance, the senses, with instrumental aids, for discovering sensible things; comparison in detecting similarities and differences; analysis in finding the constituent parts, either simple or compound, of phenomena and substances; division and exclusion in discovering causes, coincidences, and their relations; induction and inference in disclosing abstract qualities, and general laws and principles; and synthesis and deduction in discovering new compounds and effects.

In most cases of discovery we imagine new hypotheses, and test them by experiment and observation, or by the latter alone, as in astronomy; but we do not always imagine an hypothesis before we make an original research. Many discoveries are evolved by means of study and reasoning, i.e. by classifying and comparing known truths, or by drawing conclusions from facts already observed; some are effected by the invention of new experiments, and especially by new methods of examining a force or phenomenon; others, by the employment of more powerful

EMPIRICAL STARTING-POINTS OF A RESEARCH. 465

means, and thus obtaining more conspicuous effects; many are effected by the use of more refined, sensitive, or accurate apparatus and tests; some, by investigating neglected parts of science; others, by seeking to completely account for the total quantity of a substance or force in a given instance, and by endeavouring to explain residuary or exceptional phenomena; some, again, by continuing incompleted researches. Many, by making experiments which occur to the mind at the moment; or in a number of other ways, depending upon the nature of the science, the circumstances of the case, &c.

There are several empirical ways by which to commence a research: 1. We wish to extend our knowledge of a certain undeveloped part of some known scientific subject. 2. We have invented a new instrument, and wish to ascertain its effects. 3. We desire to know the cause, effect, and explanation of some known fact or phenomenon which has not yet been elucidated. 4. We have asked a question or raised an hypothesis, and wish to ascertain whether it is true or not. 5. We have devised a new experiment, i.e. a new combination of matter and its forces, and wish to ascertain, by trial and observation, what its effects will be. 6. We make new observations, or devise new or improved means of observation. Or 7. We classify and study known truths, in order to evolve others from them. Each of these methods includes the succeeding ones, and the series constitutes the successive steps usually taken in making any scientific research.

As this is a treatise chiefly on the general method of research in physics and chemistry, I shall say much less respecting the special methods which are employed, and shall not attempt anything further than a mere empirical classification of them, somewhat of the kind just given. But although a truly scientific classification of the special

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methods of discovery is not here attempted, I may safely assert, for the purpose of encouraging beginners in original scientific research, that by judiciously adopting and carrying out one or other of the following empirical methods, they are certain to discover new truths of nature. And as to write an account of all the most special methods of scientific discovery, and to completely illustrate them, would be to write a history of all discoveries, I shall merely speak of the less special methods, and illustrate them by a few only of the numerous instances which might be mentioned.

CHAPTER LI.

DISCOVERY BY EXTENDING UNDEVELOPED OR NEGLECTED PARTS OF SCIENCE.

THIS is the least special of the methods to be described, and is therefore the widest in extent, because all discovery must consist in developing those departments of science which are incomplete. Where there is room for new scientific research, there is there room for discovery.

The rate of progress of discovery is not uniform, neither in science in general nor in its branches. It is influenced by all that affects civilisation, either to advance or retard it. The recent war between France and Germany, for example, stimulated the branches of science relating to the arts of attack and defence, but diminished or retarded research for the time in other directions. The different sciences, and branches of science, are always more or less unequally developed; there exist at all times sciences, and parts of sciences, which have been left comparatively behind, by the advance

DISCOVERY IN UNDEVELOPED PARTS OF SCIENCE. 467

of others. One part of knowledge cannot make progress until certain others have acquired a particular state of development. Some, therefore, must take the lead; and when the latter have advanced until they can proceed no farther, the others must advance in their turn. Combinations of circumstances occasionally occur which cause one science to be more attractive and studied for the time being than any other; at one time it is astronomy, at another light, heat, electricity, magnetism, chemistry, or biology. Similarly, with particular branches of science and with particular arts, at one period electro-magnetism, at another electro-metallurgy, and at another spectrum analysis, has been the engrossing subject. If a great discovery happens to be made, or a startling effect produced, in one particular branch of science, soon, by its novelty and popularity, it causes that subject to attract many inquirers, and to be investigated until no more truths are readily discovered in it. Any branch of science, therefore, which has not been much investigated for a long time is, so far, a promising one for research.

We may extend undeveloped departments of science by several methods, viz. by inventing new apparatus for research; by investigating likely circumstances; by raising hypotheses and testing them; by inventing new experiments and making them; by making new observations; by employing improved means of observation, and by classifying and studying known truths; each of which will be subdivided and treated of in separate chapters.

Many discoveries have been made by investigating, with the aid of more advanced branches of knowledge, those sections of science which have been left comparatively behind by the progress of other sections; because, as a man cannot, if his senses are active, traverse an unknown country without seeing new places and perceiving new

things, so in examining an unexplored scientific subject, we are certain to discover new truths, if we properly investigate.

All geographical discoveries have been made by this method. For instance, Columbus in 1492 crossed the Atlantic and discovered America; Vasco de Gama sailed round the Cape of Good Hope, and discovered a new route to India; Cabral discovered Brazil; Magellan discovered Patagonia, the Straits which bear his name, the South Pacific Ocean, and that our earth is a globe; and in a similar way others discovered Australia, New Zealand, and many other parts of our world. The discoveries also made by Carpenter, Wyville Thompson, and others, in the subject of deep sea dredging; and by the numerous investigators who have sounded the depths of the oceans, ascertained their temperature, composition, currents, &c., in different parts, may all be included under this heading.

The discovery by Professor Boole, that the same laws which govern algebra govern thought; the invention of Jevons's 'logical machine,' and the consequent discovery of the possibility of drawing inferences by purely mechanical means, arose from the study of a neglected department of science. Other discoveries might probably be made in the same direction.

A difficulty in employing this method lies at the very outset, and that is, to determine not so much what are undeveloped parts of science-for these lie in nearly all directions-but what undeveloped ones are likely to yield important results, and what are sufficiently ripe. But as the subjects of the relative importance and frequency of different kinds of discoveries, and the selection of a suitable subject of research, have already been treated of in Chapters XIX., XX., and XXXVIII., I need not again consider them here. Amongst the undeveloped or neg