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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 (65o 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 metals 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 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:Direct Induction.

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I.

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 should remain yellow whatever 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

ter to the top of a mountain. If the weight of the atmosphere were really the cause of the suspension of the mercury, it ought to stand lower on the mountain than below, because only the higher parts of the atmosphere pressed upon the mountain. The success of the experiment completely verified the original hypothesis. The progress of the experimental sciences mainly depends upon the mode in which one experiment thus leads to others, and discloses new facts, which would in all probability have never come under our notice had we confined ourselves to the purely Baconian method of collecting the facts first and performing induction afterwards.

The greatest result of the deductive method is no less than the theory of gravitation, which makes a perfect instance of its procedure. In this case the preliminary induction consisted, we may suppose, in the celebrated fall of the apple, which occurred while Newton was sitting in an orchard during his retirement from London, on account of the Great Plague. The fall of the apple, we are told, led Newton to reflect that there must be a power tending to draw bodies towards the earth, and he asked himself the question why the moon did not on that account fall upon the earth. The Lancashire astronomer Horrocks suggested to his mind another fact, namely, that when a stone is whirled round attached to a string, it exerts a force upon the string, often called centrifugal force. Horrocks remarked that the planets in revolving round the sun must tend in a similar way to fly off from the centre. Newton was acquainted with Horrocks' views, and was thus possibly led to suppose that the earth's attractive force might exactly neutralise the moon's centrifugal tendency, so as to maintain that satellite in constant rotation.

But it happened that the world was in possession of certain empirical laws concerning the motions of the pla

nets, without which Newton could scarcely have proceeded further. Kepler had passed a lifetime in observing the heavenly bodies, and forming hypotheses to explain their motions. In general his ideas were wild and unfounded, but the labours of a lifetime were rewarded in the establishment of the three laws which bear his name, and describe the nature of the orbits traversed by the planets, and the relation between the size of such orbit and the time required by the planet to traverse it. Newton was able to show by geometrical reasoning that if one body revolved round another attracted towards it by a force decreasing as the square of the distance increases, it would necessarily describe an orbit of which Kepler's laws would be true, and which would therefore exactly resemble the orbits of the planets. Here was a partial verification of his theory by appeal to the results of experience. But several other philosophers had gone so far in the investigation of the subject. It is Newton's chief claim to honour, that he carried on his deductions and verifications until he attained complete demonstration. To do this it was necessary first of all to show that the moon actually does fall towards the earth just as rapidly as a stone would if it were in the same circumstances. Using the best information then attainable as to the distance of the moon, Newton calculated that the moon falls through the space of 13 feet in one minute, but that a stone, if elevated so high, would fall through 15 feet. Most men would have considered this approach to coincidence as a proof of his theory, but Newton's love of certain truth rendered him different even from most philosophers, and the discrepancy caused him to lay “aside at that time any further thoughts of this matter."

It was not till many years afterwards (probably 15 or 16) that Newton, hearing of some more exact data from which he could calculate the distance of the moon,

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