uniform motion in a right line unless it is compelled to change that state by forces impressed thereon.

(2.) The alteration of motion is ever proportional to the motive force impressed, and is made in the direction of the right line in which that force is impressed.

(3.) To every action there is always opposed an equal reaction, or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

Up to this time it was the general idea that motion can only be maintained by a perpetual application, impression, or expenditure of force. Galileo himself for many years entertained that error, but in 1638 he plainly states in his "Dialogues on Mechanics" the true law of the uniformity and perpetuity of motion. Such a view necessarily implies a correct and clear appreciation of the nature of resistances. No experimental motion that man can establish is unrestrained. But a perception of the uniformity and perpetuity of motion lies at the very basis of physical astronomy. With difficulty the true idea was attained. The same may be said as respects rectilinear direction, for many supposed that uniform motion can only take place in a circle.

The establishment of the first law of motion was essen

Establishment of the first law of motion,

tial to the discovery of the laws of falling bodies, in which the descent is made under the influence of a continually acting force, the velocity increasing in consequence thereof. Galileo saw clearly that, whether a body is moving slowly or swiftly, it will be equally affected by gravity. This principle was with difficulty admitted by some, who were disposed to believe that a swiftly moving body would not be as much affected by a constant force like gravity as one the motion of which is slower. With difficulty, also, was the old Aristotelian error eradicated that a heavy body falls more swiftly than a light one.

second,

The second law of motion was also established and illusand of the trated by Galileo. In his "Dialogues" he shows that a body projected horizontally must have, from what has been said, a uniform horizontal motion, but that it will also have compounded therewith an accelerated motion downward. Here again we perceive it is necessary

to retain a steady conception of this intermingling of forces without deterioration, and, though it may seem simple enough to us, there were some eminent men of those times who did not receive it as true. The special case offered by Galileo is theoretically connected with the paths of military projectiles, though in practice, since they move in a resisting medium, the air, their path is essentially different from the parabola. Curvilinear motions, which necessarily arise from the constant action of a central force, making a body depart from the rectilinear path it must otherwise take, are chiefly of interest, as we shall presently find, in the movements of the celestial bodies.

A thorough exposition of the third law of motion was left by Galileo to his successors, who had di- and of the rected their attention especially to the deter- third. mination of the laws of impact. Indeed, the whole subject was illustrated and the truth of the three laws verified in many different cases by an examination of the phenomena of freely falling bodies, pendulums, projectiles, and the like. Among those who occupied themselves with such labours may be mentioned Torricelli, Castelli, Viviani, Borelli, Gassendi. Through the investigations of these, and other Italian, French, and English natural philosophers, the principles of Mechanics were solidly established, and a necessary preparation made for their application in astronomy. By this time every one had become ready to admit that the motion of the planetary bodies would find an explanation on these principles.

tial motions.

The steps thus far taken for an explanation of the movements of the planets in curvilinear paths therefore consisted in the removal of the old miscon- of Mechanics Application ception that for a body to continue its motion to the celesforward in a straight line a continued application of force is necessary, the first law of motion disposing of that error. In the next place, it was necessary that clear and distinct ideas should be held of the combination or composition of forces, each continuing to exercise its influence without deterioration or diminution by the other. The time had now come for it to be shown that the perpetual movement of the planets is a consequence of the first law of

motion; their elliptic paths, such as had been determined by Kepler, a consequence of the second. Several persons almost simultaneously had been brought nearly to this conclusion without being able to solve the problem completely. Thus Borelli, A.D. 1666, in treating of the motions of Jupiter's satellites, distinctly shows how a circular motion may arise under the influence of a central force; he even uses the illustration so frequently introduced of a stone whirled round in a sling. In the same year a paper was presented to the Royal Society by Mr. Hooke, "explicating the inflection of a direct motion into a circular by a supervening attractive principle." Huygens also, in his " Horologium Oscillatorium," had published some theorems on circular motions, but no one as yet had been able to show how elliptical orbits could, upon these principles, be accounted for, though very many had become satisfied that the solution of this problem would before long be given.

Newton; pub

In April, 186, the "Principia" of Newton was presented to the Royal Society. This immortal work not lication of the only laid the foundation of Physical Astronomy, “Principia." it also carried the structure thereof very far toward its completion. It unfolded the mechanical theory of universal gravitation upon the principle that all bodies tend to approach each other with forces directly as their masses, and inversely as the squares of their distances.

To the force producing this tendency of bodies to approach each other the designation of attraction of gravitation, or gravity, is given. All heavy bodies fall to the earth in such a way that the direction of their movement is toward its centre. Newton proved that the the ry of this is the direction in which they must necessarily move under the influence of an attraction of every one of the particles of which the earth is composed, the attraction of a sphere taking effect as if all its particles were concentrated in its centre.

Propounds

universal gravitation.

Galileo had already examined the manner in which Preparation gravity acts upon bodies as an accelerating force, for Newton. and had determined the connexion between the spaces of descent and the times. He illustrated such facts experimentally by the use of inclined planes, by the aid of

which the velocity may be conveniently diminished without otherwise changing the nature of the result. He had also demonstrated that the earth's attraction acts equally on all bodies. This he proved by inclosing various substances in hollow spheres, and showing that, when they were suspended by strings of equal length and made to vibrate, the time of oscillation was the same for all. On the invention of the air-pump, a more popular demonstration of the same fact was given by the experiment proving that a gold coin and a feather fall equally swiftly in an exhausted receiver. Galileo had also proved, by experiments on the leaning tower of Pisa, that the velocity of falling bodies is independent of their weight. It was for these experiments that he was expelled from that city.

Up to the time of Newton there were only very vague ideas that the earth s attraction extended to any considerable distance. Newton was led to his discovery Extension of by reflecting that at all altitudes accessible to attraction or man, gravity appears to be undiminished, and gravity. that, therefore, it may possibly extend as far as the moon, and actually be the force which deflects her from a rectilinear path, and makes her revolve in an orbit round the earth. Admitting the truth of the law of the inverse squares, it is easy to compute whether the moon falls from the tangent she would describe if the earth ceased to act upon her by a quantity proportional to that observed in the case of bodies falling near the surface. In the first calculations made by Newton, he found that the moon is deflected from the tangent thirteen feet every minute; but, if the hypothesis of gravitation were true, her deflection should be fifteen feet. It is no trifling evidence of the scrupulous science of this great philosopher that hereupon he put aside the subject for several years, without, however, abandoning it. At length, in 1682, learning the result of the measures of a degree which Picard had executed in France, and which affected the estimate of the magnitude of the earth he had used, and therefore the distance of the moon, he repeated the calculations with these improved data. It is related that " he went home, took out his old papers, and resumed his calculations. As they drew to a close, he became so much agitated that he was obliged to

desire a friend to finish them." The expected coincidence was verified. And thus it appeared that the moon is retained in her orbit and made to revolve round the earth by the force of terrestrial gravity.

These calculations were founded upon the hypothesis that the moon moves in a circular orbit with a uniform velocity. But in the " Principia" it was demonstrated that when a body moves under the influence of an attractive force, varying as the inverse square of the distances, it must describe a conic section, with a focus at the centre of force, and under the circumstances designated by Kepler's The cause of laws. Newton, therefore, did far more than Kepler's laws. furnish the expected solution of the problem of elliptical motion, and it was now apparent that the existence of those laws might have been foreseen, since they arise in the very necessities of the case.

Resistless

This point gained, it is obvious that the evidence was becoming unquestionable, that as the moon is spread of the made to revolve round the earth through the beliocentric influence of an attractive force exercised by the theory. earth, so likewise each of the planets is compelled to move in an elliptical orbit round the sun by his attractive force. The heliocentric theory, at this stage, was presenting physical evidence of its truth. It was also becoming plain that the force we call gravitation must be imputed to the sun, and to all the planetary bodies as well as to the earth. Accordingly, this was what Newton asserted in respect to all material substance.

But it is a necessary consequence of this theory that Perturbations many apparent irregularities and perturbations accounted for. of the bodies of the solar system must take place by reason of the attraction of each upon all the others. If there were but one planet revolving round the sun, its orbit might be a mathematically perfect ellipse; but the moment a second is introduced, perturbation takes place in a variable manner as the bodies change their positions or distances. An excessive complication must therefore be the consequence when the number of bodies is great. Indeed, so insurmountable would these difficulties be, that the mathematical solution of the general problem of the solor system would be hopeless were it not for the fact that