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LAWS

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Originally appearing in Volume V18, Page 909 of the 1911 Encyclopedia Britannica.
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LAWS OF base uniformly in a circle; that is to say, with constant acceleration directed towards the earth's axis. What is done is to divide the resultant force due to gravitation into two components, one of which corresponds to this acceleration, while the other one is what is called the " weight " of the body. Weight is in fact not purely a combination of forces, in the sense in which that term is defined in connexion with the laws of motion, but corresponds to the Galileo acceleration with which the body would begin to move relatively to the earth if the string were cut. Another way of stating the same thing is to say that we introduce, as a correction for the earth's rotation, a force called " centrifugal force," which combined with gravitation gives the weight of the body. It is not, however, a true force in the sense of corresponding to any mutual relation between two portions of matter. The effect of centrifugal force at the equator is to make the weight of a body there about '35% less than the value it would have if due to gravitation alone. This represents about two-thirds of the total variation of Galileo's acceleration between the equator and the poles, the balance being due to the ellipticity of the figure of the earth. In the case of a body moving relatively to the earth, the introduction of centrifugal force only partially corrects the effect of the earth's rotation. Newton called attention to the fact that a falling body moves in a curve, diverging slightly from the plumb-line vertical. The divergence in a fall of roo ft. in the latitude of Greenwich is about TIT in. Foucault's pendulum is another example of motion relative to the earth which exhibits the fact that the earth is not a Newtonian base. For the study of the relative motions of the solar system, a provisional base established for that system by itself, bodies outside it being disregarded, is a very good one. No correction for any defect in it has been found necessary; moreover, no rotation of the base relative to the directions of the stars without proper motion has been detected. This is not inconsistent with the law of gravitation, for such estimates as have been made of planetary perturbations due to stars give results which are insignificant in comparison with quantities at present measurable. For the measurement of motion it must be presumed that we have a method of measuring time. The question of the standard to be employed for the scientific measurement of time accordingly demands attention. A definition of the measurement' dependent on dynamical theory has been a characteristic of the subject as presented by some writers, and may possibly be justifiable; but it is neither necessary nor in accordance with the historical development of science. Galileo measured time for the purpose of his experiments by the flow of water through a small hole under approximately constant conditions, which was of course a very old method. He had, however, some years before, when he was a medical student, noticed the apparent regularity of successive swings of a pendulum, and devised an instrument for measuring, by means of a pendulum, such short periods of time as sufficed for testing the pulse of a patient. The use of the pendulum clock in its present form appears to date from the construction of such a clock by Huygens in 1657. Newton dealt with the question at the beginning of the Principia, distinguishing what he called " absolute time " from such measures of time as would be afforded by any particular examples of motion; but he did not give any clear definition. The selection of a standard may be regarded as a matter of arbitrary choice; that is to say, it would be possible to use any continuous time-measurer, and to adapt all scientific results to it. It is of the utmost importance, however, to make, if possible, such a choice of a standard as shall render it unnecessary to date all results which have any relation to time. Such a choice is practically made. It can be put into the form of a definition by saying that two periods of time are equal in which two physical operations, of whatever character, take place, which are identical in all respects except as regards lapse of time. The validity of this definition depends on the assumption that operations of different kinds all agree in giving the same measure of time, such allowances as experience dictates being made for changing conditions. This assumption has successfully stood all Gravitation. Measure-meat of Time. tests to which it has been subjected. All clocks are constructed on the basis of this method of measurement; that is to say, on the plan of counting the repetitions of some operation, adopted solely on the ground of its being capable of continual repetition with a certain degree of accuracy, and possibly also of automatic compensation for changing conditions. Practically clocks are regulated by reference to the diurnal rotation of the earth relatively to the stars, which affords a measurement on the repetition principle agreeing with other methods, but more accurate than that given by any existing clock. We have, however, good reasons for regarding it as not absolutely perfect, and there are some astronomical data the tendency of which is to confirm this view. The most important extension of the principles of the subject since Newton's time is to be found in the development of the Theory of theory of energy, the chief value of which lies in the Energy. fact that it has supplied a measurable link connecting the motions of systems, the structure of which can be directly observed, with physical and chemical phenomena having to do with motions which cannot be similarly traced in detail. The importance of a study of the changes of the vis viva depending on squares of velocities, or what is now called the " kinetic energy " of a system, was recognized in Newton's time, especially by Leibnitz; and it was perceived (at any rate for special cases) that an increase in this quantity in the course of any motion of the system was otherwise expressible by what we now call the " work " done by the forces. The mathematical treatment of the subject from this point of view by Lagrange (1736–1813) and others has afforded the most important forms of statement of the theory of the motion of a system that are available for practical use. But it is to the physicists of the 19th century, and especially to Joule, whose experimental results were published in 1843–1849, that we practically owe the most notable advance that has been made in the development of the subject—namely, the establishment of the principle of the conservation of energy (see ENERGETICS and ENERGY). The energy of a system is the measure of its capacity for doing work, on the assumption of suitable connexions with other systems. When the motion of a body is checked by a spring, its kinetic energy being destroyed, the spring, if perfectly elastic, is capable of restoring the motion; but if it is checked by friction no such restoration can be immediately effected. It has, however, been shown that, just as the compressed spring has a capacity for doing work by virtue of its configuration, so in the case of the friction there is a physical effect produced—namely, the raising of the temperature of the bodies in contact, which is the mark of a capacity for doing the same amount of work. Electrical and chemical effects afford similar examples. Here we get the link with physics and chemistry alluded to above, which is obtained by the recognition of new forms of energy, interchangeable with what may be called mechanical energy, or that associated with sensible motions and changes of configuration. Such general statements of the theory of motion as that of Lagrange, while releasing us from the rather narrow and strained view of the subject presented by detailed analysis of motion in terms of force, have also suggested a search for other forms which a statement of elementary principles might equally take as the foundation of a logical scheme. In this connexion the interesting scheme formulated by Hertz (1894) deserves notice. It is important as an addition to the logic of the subject rather than on account of any practical advantages which it affords for purposes of calculation. r1882) ; H. Streintz, Die physikalischen Grundlagen der Mechanik 1883) ; E. Mach, Die Mechanik in ihrer Entwickelung historischkritssch dargestellt (1883; 2nd edition (1889 translation) by T. J. McCormack, 1893) ; K. Pearson, The Grammar of Science (1892) ; A. E. H. Love, Theoretical Mechanics (1897). H. Hertz, Die Prinzipien der Mechanik (1894, translation by Jones and Walley 1899). (W. H. M.)
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