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, Montgoifier, 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.

LESSON XXXI.

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

with the effects of glaciers now existing in Switzerland, Greenland, and elsewhere. These may be considered explanations of fact by fact.

A fact may also be explained by a general law of nature, that is the cause and mode of its production may be pointed out and shown to be the same as operates in many apparently different cases. Thus the cracking of glass by heat was explained (p. 257) as one result of the universal law that heat increases the dimensions of solid bodies. The trade-winds are explained as one case of the general tendency of warm air to rise and be displaced by cold and dense air. The very same simple laws of heat and mechanics which cause a draught to flow up a chimney when there is a fire below, cause winds to blow from each hemisphere towards the equator. At the same time the easterly direction from which the winds come is explained by the simplest laws of motion; for as the earth rotates from west to east, and moves much more rapidly at the equator than nearer the poles, the air tends to preserve its slower rate of motion, and the earth near the equator moving under it occasions an apparent motion of the wind from east to west.

There are, according to Mr Mill, three distinct ways in which one law may be explained by other laws, or brought into harmony with them.

The first is the case where there are really two or more separate causes in action, the results of which are combined or added together, homogeneously. As was before explained, homogeneous intermixture of effects (p. 252) means that the joint effect is simply the sum of the separate effects, and is of the same kind with them. Our last example of the trade-winds really comes under this case, for we find that there is one law or tendency which causes winds to blow from the arctic regions towards the equator, and a second tendency which causes then to blow

from east to west. These tendencies are combined together, and cause the trade-winds to blow from the NorthEast in the northern hemisphere, and from the South-East in the southern hemisphere. The law according to which the temperature of the air is governed in any part of the earth is a very complicated one, depending partly on the law by which the sun's heating power is governed, partly on the power of the earth to radiate the heat away into space, but even more perhaps on the effect of currents of air or water in bringing warmth or carrying it away. The path of a cannon-ball or other projectile is determined by the joint action of several laws; firstly, the simple law of motion, by which any moving body tends to move onward at an uniform rate in a straight line; secondly, the law of gravity, which continually deflects the body towards the earth's surface; thirdly, the resistance of the air, which tends to diminish its velocity.

The reader will perhaps have noticed the frequent use of the word tendency, and I have repeatedly spoken of a cause as tending to produce its effect. If the joint and homogeneous action of causes has been clearly explained, it will now be clear that a tendency means a cause which will produce an effect unless there be opposite causes, which, in combination with it, counteract and disguise that effect. Thus when we throw a stone into the air the attractive power of the earth tends to make it fall, but the upward motion we have impressed upon it disguises the result for a certain time. The interminable revolving motion of the moon round the earth is the result of two balanced tendencies, that towards the earth, and that to proceed onward in a straight line. The laws of motion and gravity are such that this balance must always be preserved; if the moon by any cause were brought nearer to the earth its tendency to fly off would be increased, and would exceed the effect of gravity until it had regained