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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,
was able to explain the discrepancy. His theory of gravitation was then verified so far as the moon was concerned; but this was to him only the beginning of a long course of deductive calculations, each ending in a verification. If the earth and moon attract each other, and also the sun and the earth, similarly there is no reason why the sun and moon should not attract each other. Newton followed out the consequences of this inference, and showed that the moon would not move as if attracted by the earth only, but sometimes faster and sometimes slower. Comparisons with Flamsteed's observations of the moon showed that such was the case. Newton argued again, that as the waters of the ocean are not rigidly attached to the earth, they might attract the moon, and be attracted in return, independently of the rest of the earth. Certain daily motions would then be caused thereby exactly resembling the tides, and there were the tides to verify the fact. It was the almost superhuman power with which he traced out geometrically the consequences of his theory, and submitted them to repeated comparison with experience, which constitutes his preeminence over all philosophers.
What he began has been going on ever since. The places of the moon and planets are calculated for each day on the assumption of the absolute truth of Newton's law of gravitation. Every night their places are observed as far as possible at Greenwich or some other observatory; comparison of the observed with the predicted place is always in some degree erroneous, and if coincident would be so only by accident. The theory is never proved completely true, and never can be; but the more accurately the results of the theory are calculated, and the more perfect the instruments of the astronomer are rendered, the more close is the correspondence. Thus the rude observations of Kepler and the few slight facts which worked on New
ton's mind, were the foundation of a theory which yielded indefinite means of anticipating new facts, and by constant verification, as far as human accuracy can go, has been placed beyond all reasonable doubt.
Were space available it might be shown that all other great theories have followed nearly the same course. The undulatory theory of sound was in fact almost verified by Newton himself, though when he calculated from it the velocity of sound there was again a discrepancy, which only subsequent investigation could explain. This theory no doubt suggested the corresponding theory of light, which when followed out by Young, Fresnel, and others, always gave results which were ultimately in harmony with observation. It even enabled mathematicians to anticipate results which the most ardent imagination could hardly have guessed, and which mere haphazard experiment might never have revealed. Dalton's laws of equivalent proportions in chemistry, if not his atomic theory, were founded on experiments made with the simplest and rudest apparatus, but results deduced from them are daily verified in the nicest processes of modern chemical analysis. The still more modern theory of the Conservation of Energy, which had been vaguely anticipated by Bacon, Rumford, Montgolfier, Seguin, Mayer and possibly others, was by Mr Joule brought to the test of experimental verification in some of the most beautiful and decisive experiments which are on record. It will be long before scientific men shall have traced out all the consequences of this grand principle, but its correspondence with fact already places it far beyond doubt.
It will now be apparent, I think, that though observation and induction must ever be the ground of all certain knowledge of nature, their unaided employment could never have led to the results of modern science. He who merely collects and digests facts will seldom acquire a
comprehension of their laws. He who frames a theory and is content with his own deductions from it, like Descartes, will only surprise the world with his misused genius; but the best student of science is he who with a copious store of theories and fancies has the highest power of foreseeing their consequences, the greatest diligence in comparing them with undoubted facts, and the greatest candour in confessing the ninety-nine mistakes he has made in reaching the one true law of nature.
EXPLANATION, TENDENCY, HYPOTHESIS,
THEORY, AND FACT. In the preceding Lessons I have used several expressions of which the meaning has not been defined. It will now be convenient to exemplify the use of these terms, and to arrive as far as possible at a clear understanding of their proper meanings.
Explanation is literally the making plain or clear, so that there shall be nothing uneven or obscure to interrupt our view. Scientific explanation consists in harmonizing fact with fact, or fact with law, or law with law, so that we may see them both to be cases of one uniform law of causation. If we hear of a great earthquake in some part of the world and subsequently hear that a neighbouring volcano has broken out, we say that the earthquake is thus partially explained. The eruption shows that there were great forces operating beneath the earth's surface, and the earthquake is obviously an effect of such causes. The scratches which may be plainly seen upon the surface of rocks in certain parts of Wales and Cumberland, are explained by the former existence of glaciers in those mountains; the scratches exactly harmonize