a history of science-2-第46章
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vault at once to the full expression of this law； though he had formulated it fully before he gave the results of his investigations to the world。 We have now to follow the steps by which he reached this culminating achievement。 At the very beginning we must understand that the idea of universal gravitation was not absolutely original with Newton。 Away back in the old Greek days； as we have seen； Anaxagoras conceived and clearly expressed the idea that the force which holds the heavenly bodies in their orbits may be the same that operates upon substances at the surface of the earth。 With Anaxagoras this was scarcely more than a guess。 After his day the idea seems not to have been expressed by any one until the seventeenth century's awakening of science。 Then the consideration of Kepler's Third Law of planetary motion suggested to many minds perhaps independently the probability that the force hitherto mentioned merely as centripetal； through the operation of which the planets are held in their orbits is a force varying inversely as the square of the distance from the sun。 This idea had come to Robert Hooke； to Wren； and perhaps to Halley； as well as to Newton； but as yet no one had conceived a method by which the validity of the suggestion might be tested。 It was claimed later on by Hooke that he had discovered a method demonstrating the truth of the theory of inverse squares； and after the full announcement of Newton's discovery a heated controversy was precipitated in which Hooke put forward his claims with accustomed acrimony。 Hooke； however； never produced his demonstration； and it may well be doubted whether he had found a method which did more than vaguely suggest the law which the observations of Kepler had partially revealed。 Newton's great merit lay not so much in conceiving the law of inverse squares as in the demonstration of the law。 He was led to this demonstration through considering the orbital motion of the moon。 According to the familiar story； which has become one of the classic myths of science； Newton was led to take up the problem through observing the fall of an apple。 Voltaire is responsible for the story； which serves as well as another； its truth or falsity need not in the least concern us。 Suffice it that through pondering on the familiar fact of terrestrial gravitation； Newton was led to question whether this force which operates so tangibly here at the earth's surface may not extend its influence out into the depths of space； so as to include； for example； the moon。 Obviously some force pulls the moon constantly towards the earth； otherwise that body would fly off at a tangent and never return。 May not this so…called centripetal force be identical with terrestrial gravitation？ Such was Newton's query。 Probably many another man since Anaxagoras had asked the same question； but assuredly Newton was the first man to find an answer。 The thought that suggested itself to Newton's mind was this： If we make a diagram illustrating the orbital course of the moon for any given period； say one minute； we shall find that the course of the moon departs from a straight line during that period by a measurable distancethat： is to say； the moon has been virtually pulled towards the earth by an amount that is represented by the difference between its actual position at the end of the minute under observation and the position it would occupy had its course been tangential； as； according to the first law of motion； it must have been had not some force deflected it towards the earth。 Measuring the deflection in questionwhich is equivalent to the so…called versed sine of the arc traversedwe have a basis for determining the strength of the deflecting force。 Newton constructed such a diagram； and； measuring the amount of the moon's departure from a tangential rectilinear course in one minute； determined this to be； by his calculation； thirteen feet。 Obviously； then； the force acting upon the moon is one that would cause that body to fall towards the earth to the distance of thirteen feet in the first minute of its fall。 Would such be the force of gravitation acting at the distance of the moon if the power of gravitation varies inversely as the square of the distance？ That was the tangible form in which the problem presented itself to Newton。 The mathematical solution of the problem was simple enough。 It is based on a comparison of the moon's distance with the length of the earth's radius。 On making this calculation； Newton found that the pull of gravitationif that were really the force that controls the moongives that body a fall of slightly over fifteen feet in the first minute； instead of thirteen feet。 Here was surely a suggestive approximation； yet； on the other band； the discrepancy seemed to be too great to warrant him in the supposition that he had found the true solution。 He therefore dismissed the matter from his mind for the time being； nor did he return to it definitely for some years。 ｛illustration caption = DIAGRAM TO ILLUSTRATE NEWTON'S LAW OF GRAVITATION （E represents the earth and A the moon。 Were the earth's pull on the moon to cease； the moon's inertia would cause it to take the tangential course； AB。 On the other hand； were the moon's motion to be stopped for an instant； the moon would fall directly towards the earth； along the line AD。 The moon's actual orbit； resulting from these component forces； is AC。 Let AC represent the actual flight of the moon in one minute。 Then BC； which is obviously equal to AD； represents the distance which the moon virtually falls towards the earth in one minute。 Actual computation； based on measurements of the moon's orbit； showed this distance to be about fifteen feet。 Another computation showed that this is the distance that the moon would fall towards the earth under the influence of gravity； on the supposition that the force of gravity decreases inversely with the square of the distance； the basis of comparison being furnished by falling bodies at the surface of the earth。 Theory and observations thus coinciding； Newton was justified in declaring that the force that pulls the moon towards the earth and keeps it in its orbit； is the familiar force of gravity； and that this varies inversely as the square of the distance。）｝ It was to appear in due time that Newton's hypothesis was perfectly valid and that his method of attempted demonstration was equally so。 The difficulty was that the earth's proper dimensions were not at that time known。 A wrong estimate of the earth's size vitiated all the other calculations involved； since the measurement of the moon's distance depends upon the observation of the parallax； which cannot lead to a correct computation unless the length of the earth's radius is accurately known。 Newton's first calculation was made as early as 1666； and it was not until 1682 that his attention was called to a new and apparently accurate measurement of a degree of the earth's meridian made by the French astronomer Picard。 The new measurement made a degree of the earth's surface 69。10 miles； instead of sixty miles。 Learning of this materially altered calculation as to the earth's size； Newton was led to take up again his problem of the falling moon。 As he proceeded with his computation； it became more and more certain that this time the result was to harmonize with the observed facts。 As the story goes； he was so completely overwhelmed with emotion that he was forced to ask a friend to complete the simple calculation。 That story may well be true； for； simple though the computation was； its result was perhaps the most wonderful demonstration hitherto achieved in the entire field of science。 Now at last it was known that the force of gravitation operates at the distance of the moon； and holds that body in its elliptical orbit； and it required but a slight effort of the imagination to assume that the force which operates through such a reach of space extends its influence yet more widely。 That such is really the case was demonstrated presently through calculations as to the moons of Jupiter and by similar computations regarding the orbital motions of the various planets。 All results harmonizing； Newton was justified in reaching the conclusion that gravitation is a univ
