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value. Any less scrupulous, any less philosophio mind, would have been content with this near approximation, and would have announced the discovery to the world. Not so with Newton. Nothing short of
. the most rigorous accuracy could satisfy his conscientious regard for truth. His manuscripts are laid aside, and the pursuit for the present abandoned.
Months roll by. Occasionally he returns to his computations, runs over the figures, hoping to detect some numerical error; but all is right, and he turns away. At length, while attending a meeting of the Royal Society in London, he learns that Picard had just closed a more accurate measurement of the diameter of the earth. This was one of the important quantities which entered into his investigation. He returns home,-and with impatient curiosity spreads before him his old computations—the new value of the earth's diameter is substituted-he dashes onward through the maze of figures—he sees them shaping their values towards the long sought result—the excitement was more than even his great mind could bear-he resigns to a friend—the work is completed, the results compared—they are exactly equal! The victory is won,-he had seized the golden key which unlocks the mysteries of the universe, and he held it with a giant's grasp !
There never can come another such moment as the one we have described, in the history of any mortal. There are no such conquests remaining to be made. Standing upon the giddy height he had gained, Newton's piercing gaze swept forward, through coming centuries, and saw the stream of discovery flowing from his newly discovered law, slowly increas
ing, spreading on the right hand and on the left, growing broader, and deeper, and stronger, encircling in its flow planet after planet, sun after sun, system after system, until the universe of matter was encompassed in its mighty movement. He could not live to accomplish but a small portion of this great work.Rapidly did he extend his theory of gravitation to the planets and their satellites. Each accorded perfectly with the law, and rising as the inquiry was pursued, he at length announced this grand prevailing law :
Every particle of matter in the universe attracts every other particle of matter with a force or power directly proportioned to the quantity of matter in each, and decreas ing as the squares of the distances which separate the particles increase.
Having reached this wonderful generalization, Newton now propounded this important inquiry. “ To determine the nature of the curve which a body would describe in its revolution about a fixed centre to which it was attracted by a force proportional tt the mass of the attracting body, and decreasing with the distance according to the law of gravitation."
His profound knowledge of the higher mathematics, which he had greatly improved, gave to him astonishing facilities for the resolution of this great problem. He hoped and believed that when the expression should be reached, which would reveal the nature of the curve sought, that it would be the mathematical language descriptive of the properties of the ellipse. This was the curve in which Kepler had demonstrated that the planets revolved, and a confirmation of the law of gravitation required that the ellipse
should be the curve described by the revolving body on the conditions announced in the problem.
There happens to be a remarkable class of curves, discovered by the Greek mathematicians, called the conic sections ; thus named, because they can all be formed by cutting a cone in certain directions. The figure of a cone with a circle for its base, and converge ing to a point, is familiar to all. Cut this cone perpendicular to its axis, remove the part cut, and the line on the surface round the cone will be found to be a circle. Cut it again, oblique to the axis, then the line of division of the two parts will be an ellipse. Cut again so that the knife may pass downward parallel to the slope of the cone, and in this case your section is a parabola. Make a last cut parallel to the axis of the cone, and the curve now obtained is the hyperbola.
When Newton reached the algebraic expression which, when interpreted, would reveal the properties of the curve sought and which he had hoped would prove to be the ellipse-he was surprised to find that it did not look familiar to his eye. He examined it closely-it was not the equation of the ellipse, and yet it resembled it in some particulars. What was his astonishment to find, on a complete examination, that the mathematical expression, which he had reached, expressing the nature of the curve described by the revolving body, was the general algebraic expression embracing all the conic sections. Here is a most wonderful revelation. Is it possible that under the law of gravitation, the heavenly bodies may revolve in any or either of these curves ? Observation responds to the inquiry. The planeta
were found to revolve in ellipses; the satellites of Jupiter in circles; and those strange, anomalous, outlawed bodies, the comets, whose motions hitherto had defied all investigation, take their place in the new and now perfect system, sweeping round the sun in parabolic and hyperbolic orbits.
Thus were these four beautiful curves, having a common origin, possessed of certain common properties, yet diverse in character, mingling in close proximity, and gliding imperceptibly into each other, suddenly transferred to the heavens, to become the orbits of countless worlds. For nearly twenty centuries, they had been the objects of curious speculation to the mathematician; henceforward they were to be given up to the hands of the astronomer, the powerful instrument of his future conquests among the planetary and cometary worlds.
The three great laws of Kepler, to which he had risen 'with such incredible toil and labor, were now found to flow as simple consequences of the law of gravitation. It is impossible to convey the slightest idea, in discussions so devoid of mathematics, of the incredible change which had thus suddenly been wrought in the mode of investigation. I never have closed Newton's investigation, by which he deduces the nature of the curve, described by a body revolving around a fixed centre, under the law of gravitation, bearing with it consequences so simple yet so wonderful, without feelings of the most intense admiration. I can convey no adequate idea of the difference of the methods employed by Kepler and Newton, in reaching the three laws of planetary motion. I see Kepler in the condition of one on whom the fates have fixed the task of rolling a huge stone up some rug ged mountain side, to its destined level, within a few feet of the summit. He toils on manfully, heav. ing and struggling, day and night, in storm and in darkness, never quitting his hold, lest he may lose what he has gained. If the ascent be too steep and rocky, he diverges to the right, then to the left, winding his heavy way zigzag up the mountain side. Years glide by–he grows gray in his toil, but he never falters—onward and upward he still heaves the heavy weight-his goal is in sight, he renews his efforts, the last struggle is over—he has finished his task-the goal is won.
Such was Kepler's method of reaching his laws. Now for Newton's. He stands, not at the base of the mountain, with its long, ascending rocky sides, but on the top. He starts his heavy stone, it rolls of itself over, slowly over, and once again, and falls quietly to its place. Let me not be misunderstood in this strange comparison, as detracting in the smallest degree from the just fame that is due to Kepler. But for his sublime discoveries, Newton could never have reached the mountain summit, on which he so proudly stood. Standing there, he never forgot by whose assistance he had reached the lofty point, and ever recognized, in the most public manner, his deep indebtedness to the immortal Kepler.
A few words with reference to the rigorous application of Kepler's laws in nature, will close this discussion. The first law, announcing the revolution of the planets in elliptic orbits, was now made general, and recognised the revolution of the heavenly bodies