a history of science-2-第20章
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e； that a pendulum of a given length performs its oscillations with the same frequency though the arc described by the pendulum be varied greatly。＇1＇ He found； also； that the rate of oscillation for pendulums of different lengths varies according to a simple law。 In order that one pendulum shall oscillate one…half as fast as another； the length of the pendulums must be as four to one。 Similarly； by lengthening the pendulums nine times； the oscillation is reduced to one…third； In other words； the rate of oscillation of pendulums varies inversely as the square of their length。 Here； then； is a simple relation between the motions of swinging bodies which suggests the relation which Kepler bad discovered between the relative motions of the planets。 Every such discovery coming in this age of the rejuvenation of experimental science had a peculiar force in teaching men the all…important lesson that simple laws lie back of most of the diverse phenomena of nature； if only these laws can be discovered。 Galileo further observed that his pendulum might be constructed of any weight sufficiently heavy readily to overcome the atmospheric resistance； and that； with this qualification； neither the weight nor the material had any influence upon the time of oscillation； this being solely determined by the length of the cord。 Naturally； the practical utility of these discoveries was not overlooked by Galileo。 Since a pendulum of a given length oscillates with unvarying rapidity； here is an obvious means of measuring time。 Galileo； however； appears not to have met with any great measure of success in putting this idea into practice。 It remained for the mechanical ingenuity of Huyghens to construct a satisfactory pendulum clock。 As a theoretical result of the studies of rolling and oscillating bodies； there was developed what is usually spoken of as the third law of motionnamely； the law that a given force operates upon a moving body with an effect proportionate to its effect upon the same body when at rest。 Or； as Whewell states the law： 〃The dynamical effect of force is as the statical effect； that is； the velocity which any force generates in a given time； when it puts the body in motion； is proportional to the pressure which this same force produces in a body at rest。〃＇2＇ According to the second law of motion； each one of the different forces； operating at the same time upon a moving body； produces the same effect as if it operated upon the body while at rest。
STEVINUS AND THE LAW OF EQUILIBRIUM It appears； then； that the mechanical studies of Galileo； taken as a whole； were nothing less than revolutionary。 They constituted the first great advance upon the dynamic studies of Archimedes； and then led to the secure foundation for one of the most important of modern sciences。 We shall see that an important company of students entered the field immediately after the time of Galileo； and carried forward the work he had so well begun。 But before passing on to the consideration of their labors； we must consider work in allied fields of two men who were contemporaries of Galileo and whose original labors were in some respects scarcely less important than his own。 These men are the Dutchman Stevinus； who must always be remembered as a co…laborer with Galileo in the foundation of the science of dynamics； and the Englishman Gilbert； to whom is due the unqualified praise of first subjecting the phenomenon of magnetism to a strictly scientific investigation。 Stevinus was born in the year 1548； and died in 1620。 He was a man of a practical genius； and he attracted the attention of his non…scientific contemporaries； among other ways； by the construction of a curious land…craft； which； mounted on wheels； was to be propelled by sails like a boat。 Not only did he write a book on this curious horseless carriage； but he put his idea into practical application； producing a vehicle which actually traversed the distance between Scheveningen and Petton； with no fewer than twenty…seven passengers； one of them being Prince Maurice of Orange。 This demonstration was made about the year 1600。 It does not appear； however； that any important use was made of the strange vehicle； but the man who invented it put his mechanical ingenuity to other use with better effect。 It was he who solved the problem of oblique forces； and who discovered the important hydrostatic principle that the pressure of fluids is proportionate to their depth； without regard to the shape of the including vessel。 The study of oblique forces was made by Stevinus with the aid of inclined planes。 His most demonstrative experiment was a very simple one； in which a chain of balls of equal weight was hung from a triangle； the triangle being so constructed as to rest on a horizontal base； the oblique sides bearing the relation to each other of two to one。 Stevinus found that his chain of balls just balanced when four balls were on the longer side and two on the shorter and steeper side。 The balancing of force thus brought about constituted a stable equilibrium； Stevinus being the first to discriminate between such a condition and the unbalanced condition called unstable equilibrium。 By this simple experiment was laid the foundation of the science of statics。 Stevinus had a full grasp of the principle which his experiment involved； and he applied it to the solution of oblique forces in all directions。 Earlier investigations of Stevinus were published in 1608。 His collected works were published at Leyden in 1634。 This study of the equilibrium of pressure of bodies at rest led Stevinus； not unnaturally； to consider the allied subject of the pressure of liquids。 He is to be credited with the explanation of the so…called hydrostatic paradox。 The familiar modern experiment which illustrates this paradox is made by inserting a long perpendicular tube of small caliber into the top of a tight barrel。 On filling the barrel and tube with water； it is possible to produce a pressure which will burst the barrel； though it be a strong one； and though the actual weight of water in the tube is comparatively insignificant。 This illustrates the fact that the pressure at the bottom of a column of liquid is proportionate to the height of the column； and not to its bulk； this being the hydrostatic paradox in question。 The explanation is that an enclosed fluid under pressure exerts an equal force upon all parts of the circumscribing wall； the aggregate pressure may； therefore； be increased indefinitely by increasing the surface。 It is this principle； of course； which is utilized in the familiar hydrostatic press。 Theoretical explanations of the pressure of liquids were supplied a generation or two later by numerous investigators； including Newton； but the practical refoundation of the science of hydrostatics in modern times dates from the experiments of Stevinus。
GALILEO AND THE EQUILIBRIUM OF FLUIDS Experiments of an allied character； having to do with the equilibrium of fluids； exercised the ingenuity of Galileo。 Some of his most interesting experiments have to do with the subject of floating bodies。 It will be recalled that Archimedes； away back in the Alexandrian epoch； had solved the most important problems of hydrostatic equilibrium。 Now； however； his experiments were overlooked or forgotten； and Galileo was obliged to make experiments anew； and to combat fallacious views that ought long since to have been abandoned。 Perhaps the most illuminative view of the spirit of the times can be gained by quoting at length a paper of Galileo's； in which he details his own experiments with floating bodies and controverts the views of his opponents。 The paper has further value as illustrating Galileo's methods both as experimenter and as speculative reasoner。 The current view； which Galileo here undertakes to refute； asserts that water offers resistance to penetration； and that this resistance is instrumental in determining whether a body placed in water will float or sink。 Galileo contends that water is non…resistant； and that bodies float or sink in virtue of their respective weights。 This； of course； is merely a restatement of the law of Archimedes。 But it remains to explain the fact that bodies of a certain shape will float； while bodies
