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pointed to the existence of some cause of attraction not
then known, but which was in consequence soon dis-
covered in the shape of the planet Neptune. The motions
of several comets have in this way been calculated, but it
is observed that they return each time a little later than
they ought. This retardation points to the existence of
some obstructive power in the space passed through, the
nature of which is not yet understood.
Mill's System of Logic, Book III. Chap. 10, Of the

Plurality of Causes; and of the Intermixture of
Effects.

LESSON XXX.

EMPIRICAL AND DEDUCTIVE METHODS.

WE have hitherto treated of Deduction and Induction as if they were entirely separate and independent methods. In reality they are frequently blended or employed alternately in the pursuit of truth; and it may be said that all the more important and extensive investigations of science rely upon one as much as upon the other. It is probably the greatest merit in Mr Mill's logical writings that he points out the entire insufficiency of what is called the Baconian Method to detect the more obscure and difficult laws of nature. Bacon advised that we should always begin by collecting facts, classifying them according to their agreement and difference, and gradually gathering from them laws of greater and greater generality. He protested altogether against "anticipating nature," that is, forming our own hypotheses and theories as to what the laws of nature probably are, and he seemed to think that systematic arrangement of facts would take the place of

all other methods. The reader will soon see that the progress of Science has not confirmed his opinions.

When a law of nature is ascertained purely by induction from certain observations or experiments, and has no other guarantee for its truth, it is said to be an empirical law. As Mr Mill says, “Scientific inquirers give the name of Empirical Laws to uniformities which observation or experiment has shown to exist, but on which they hesitate to rely in cases yarying much from those which have been actually observed, for want of seeing any reason why such a law should exist." The name is derived from the Greek word eumreipia, meaning experience or trial. Instances of such laws are abundant. We learn empirically that a certain strong yellow colour at sunset, or an unusual clearness in the air, portends rain; that a quick pulse indicates fever; that horned animals are always rụminants; that quinine affects beneficially the nervous system and the health of the body generally; that strychnine has a terrible effect of the opposite nature: all these are known to be true by repeated observation, but we can give no other reason for their being true, that is, we cannot bring them into harmony with any other scientific facts; nor could we at all have deduced them or anticipated them on the ground of previous knowledge. The connection between the sun's spots, magnetic storms, auroras, and the motions of the planets mentioned in the last Lesson, is perhaps the most remarkable known instance of an empirical induction; for no hint has yet been given of the way in which these magnetic influences are exerted throughout the vast dimensions of the planetary system. The qualities of the several alloys of metals are also good instances of empirical knowledge. No one can tell before mixing two or three metals for the first time in any given proportions what the qualities of the mixture will be—that brass should be both harder

and more ductile than either of its constituents, copper and zinc; that copper alloyed with the very soft metal tin should make hard and sonorous bell-metal; that a certain mixture of lead, bismuth, tin and cadmium, should melt with a temperature (65° cent.) far below that of boiling water*.

However useful may be empirical knowledge, it is yet of slight importance compared with the well-connected and perfectly explained body of knowledge which constitutes an advanced and deductive science. It is in fact in proportion as a science becomes deductive, and enables us to grasp more and more apparently unconnected facts under the same law, that it becomes perfect. He who knows exactly why a thing happens, will also know exactly in what cases it will happen, and what difference in the circumstances will prevent the event from happening. Take for instance the simple effect of hot water in cracking glass. This is usually learnt empirically. Most people have a confused idea that hot water has a natural and inevitable tendency to break glass, and that thin glass, being more fragile than other glass, will be more easily broken by hot water. Physical science, however, gives a very clear reason for the effect, by showing that it is only one case of the general tendency of heat to expand substances. The crack is caused by the successful effort of the heated glass to expand in spite of the colder glass with which it is connected. But then we shall see at once that the same will not be true of thin glass vessels; the heat will pass so quickly through that the glass will be nearly equally heated; and accordingly chemists habitually use thin uniform glass vessels to hold or boil hot liquids without fear of the fractures which would be sure to take place in thick glass vessels or bottles.

The history of science would show conclusively that * Roscoe's Lessons in Elementary Chemistry, p. 175.

deduction was the clue to all the greatest discoveries. Newton, after Galileo the chief founder of experimental philosophy, possessed beyond all question the greatest power of deductive thought which has ever been enjoyed by man. It is striking indeed to compare his results in optics with those in chemistry or alchemy. It is not generally known that Newton was really an alchemist, and spent days and nights in constant experiments in his laboratory, trying to discover the secret by which inetals could be transmuted into gold. But in these researches all was purely empirical, and he had no clue to guide him to successful experiments. A few happy guesses given in his celebrated Queries are all the result of this labour. But in the science of Optics it was quite otherwise ; here he grasped general laws, and every experiment only led him to devise and anticipate the results of several others, each more beautiful than the last. Thus he was enabled to establish beyond all doubt the foundations of the science of the Spectrum, now bearing such wonderful results. Some persons may suppose that Newton, living shortly after Bacon, adopted the Baconian method, but I believe that there is no reference to Bacon in Newton's works; and it is certain that he did not employ the method of Bacon. The Principia, though containing constant appeals to experiment and observation, is nevertheless the result of a constant and sustained effort of deductive mathematical reasoning.

What Mr Mill has called the Deductive Method, but which I think might be more appropriately called the Combined or Complete Method, consists in the alternate use of induction and deduction. It may be said to have three steps, as follows:

1. Direct Induction. 2. Deduction, or, as Mr Mill calls it, Ratiocination. 3. Verification,

The first process consists in such a rough and simple appeal to experience as may give us a glimpse of the laws which operate, without being sufficient to establish their truth. Assuming them as provisionally true, we then proceed to argue to their effects in other cases, and a further appeal to experience either verifies or negatives the truth of the laws assumed. There are, in short, two appeals to experience connected by the intermediate use of reasoning. Newton, for instance, having passed a ray of sun-light through a glass prism found that it was spread out into a series of colours resembling those of the rainbow, He adopted the theory that white light was actually composed of a mixture of different coloured lights, which became separated in passing through the prism. He saw that if this were true, and he were to pass an isolated ray of the spectrum, for instance, the yellow ray, through a second prism, it ought not to be again broken up into different colours, but hould remain yellow hatever was afterwards done with it. - On trial he found this to be the case, and afterwards devised a succession of similar confirmatory experiments which verified his theory beyond all possible doubt.

It was no mere accident that led Pascal to have a barometer carried up to the top of the mountain Puy de Dôme in France. Galileo, indeed, became acquainted by accident with the fact that water will not rise in an ordinary pump more than 33 feet, and was thus led to assert that the limited weight of the atmosphere caused it to rise. Torricelli, reasoning from this theory, saw that mercury, which is fourteen times as heavy as water, should not rise more than one-fourteenth part of the distance, or about 29 or 30 inches. The experiment being tried verified the theory. It was the genius of Pascal, however, which saw that the experiment required to be varied in another way by carrying the mercurial barome.

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