801 



MOTION, LAWS OF. 



MOTION OF THE EARTH. 



802 



The third law of motion was enunciated by Newton as follows : 

 "Action and reaction are equal and opposite." Thus, if a body A 

 exerts a force upon another body B by contact, tension, thrust, attrac- 

 tion, repulsion, or otherwise ; then B exerts the very same force on A 

 in the opposite direction. The principle thus laid down belongs as 

 much to statics as to dynamics, and is not therefore to be considered 

 a special law of motion. It seems indeed to establish a relation between 

 the statical and dynamical effects of a force the action being repre- 

 sented by the pressure employed, the reaction by the motion produced. 

 But how is this motion to be measured ? Newton had decided that 

 a body's motion should be measured by its momentum, and enunciated 

 the third law on this supposition. But taking as we now do the 

 velocity generated in a body to be the dynamical measure of the force, 

 that is, the reaction, the third law of motion asserts that " the velocity 

 generated in a body by the action of a force, whether impulsive or 

 otherwise, is proportional to the force." 



Where the force continues to act during a finite interval of time, 

 the body acquires an additional velocity in each succeeding instant 

 an evident consequence of the second law of motion. The velocity 

 thus generated in a unit of time (as one second) is termed by some 

 modern writers the " rate of acceleration." And this is all that is 

 meant by the expression " accelerating force," namely, a force that, 

 acting continually upon a body, produces in it a rate of acceleration. 

 Thus the force of gravity is called an accelerating force, because the 

 motion of a body, under its influence, becomes accelerated ; the rate of 

 acceleration being about 32'2 feet per second. [ACCELERATED MOTION.] 



Let / and / ' denote the rates of acceleration produced respectively 

 by the action of two forces r and F' ; then, by the third law of motion, 

 /:/'=F:F'. Also, if t be the time during which these forces act, 

 v and i j the respective velocities acquired at the end of time t. we have 

 v =ft and ' =/'(, hence v : v 1 = V : F'. If a body move under the action 

 of gravitation, the rate of acceleration is jr( = 32'2), hence if F act 

 upon a body whose weight is w, we have the following very useful 

 application of the third kw of motion : 



! : w =/ : -7 



or, F : w = v : yt 



when r= velocity acquired in time t by the action of F. 

 The three laws of motion, then, may be thus enunciated : 



1. A body, if acted upon by no external force, remains at rest ; or 

 if in motion, continues to move uniformly in the same direction. 



2. When any number of forces act upon a body in motion, each 

 force produces the same effect in altering the magnitude and direction 

 of the body's velocity, as if it acted singly on the body at rest. 



3. The velocity generated in a unit of time by a force continually 

 acting upon a body, is proportional to the force. 



The reader will meet with some very clear conceptions of the three 

 laws of motion in Dr. Young's ' Natural Philosophy,' edited by Pro- 

 fesgor Kelland ; also in O'Brien's ' Natural Philosophy,' published by 

 the Society for the Promotion of Christian Knowledge. He may 

 likewise refer to a paper by Dr. Whewell " On the Nature of the Truth 

 of the Laws of Motion." (' Camb. Phil. Trans.' vol. v. part ii.) 



The mistakes into which philosophers fell upon the laws of motion 

 are uninteresting except in the applications which were made of them ; 

 and in the article MOTION OF THE EARTH will be found enough of 

 these to give an idea of the difficulties which such fallacies placed in 

 the way of sound knowledge. For an account of Galileo's labours, see 

 OALILEI, in Bioo. Div. For an account of the notions of Descartes 

 on the same subject, see VOBTICES. The first distinct enunciation of 

 these laws appears in the Principia of Newton. 



Though all mechanical problems admit of solution upon the 

 assumption of these laws, in conjunction with those which may be 

 called the distinctive properties of the solid, fluid, and gaseous states, 

 yet the purposes of mechanical inquiry are better served by certain 

 general principles deduced from them, the proper conception of which 

 can only be made by mathematicians, and are therefore referred to a 

 purely mathematical article VIRTUAL VELOCITIES. [PRESSURE, FORCE, 

 INERTIA, CENTRIPETAL AND CENTRIFUGAL FORCES, ACCELERATED 

 MOTION, VELOCITY, Ac. ; MOVING FORCE. See particularly the article 

 INERTIA, for the reason of the non-introduction of that word.] 



Among the many absurdities which have arisen out of a misappre- 

 hension of the laws of motion, is the attempt to discover what is called 

 a pcr]>etual motion, or a machine which of itself would never stop. 

 The earth and planets are such machines in their rotations on their 

 axes ; and we have seen that any particle of matter, unacted on by 

 other matter, and once in motion, is a perpetual motion. If a wheel 

 attached to an axle could be deprived of friction at the pivots, and 

 enclosed in a permanently air-tight and perfectly exhausted receiver, 

 it would also, when once in motion, be a perpetual motion. But as 

 long as any friction or resistance, however small, is perpetually retard- 

 ing the motion, it is obvious that the velocity, if maintained, must be 

 indebted to some external supply of moving power. To take the case 

 of friction, which arises from the roughness of the supports, and which, 

 independently of adhesion, may be considered as a rapid succession of 

 very small jolts, by which the roughnesses of the one surface strike 

 upon those of the other, and communicate a portion of momentum to 

 the frame, and finally to the earth : to suppose that a wheel 86 above 



ARTS ADD SCI. DIV. VOL. V. 



described could go on for ever, with friction, would be to suppose that 

 there could be action without reaction. In fact, a perpetual motion, 

 such as is intended to be made by the speculators on the subject, ia 

 nothing less than a machine which wjll work for ever without new 

 moving power ; it being not one bit less absurd to suppose that it 

 would perpetually overcome friction and atmospheric resistance, than 

 that it would continue to supply the impetus necessary to carry on the 

 sawing of a plank or the weaving of lace. 



MOTION OF THE EARTH. The theory of gravitation has placed 

 this question on a footing entirely different from that on which it was 

 argued, whether by Ptolemaists or Copernicans. Both of the latter 

 parties supposed the existence of a fixed central body somewhere, 

 which the first of them would have to be the earth, and the second 

 the sun. This centrum mundi, or centre of the universe, is exploded, 

 and with it all the systems, whether Ptolemaic or Copernican, which 

 preceded the discoveries of Newton. But, as noticed in COPERNICUS, 

 in BIOG. Drv., the existing system preserves the name of that 'great 

 man ; the reason being, that its distinctive peculiarity is retained 

 relatively, if not absolutely, namely, that the planets all move round 

 the sun, or round a point near the sun. But it is added to the real 

 Copernican system, that sun, planets, and all, may be, and probably 

 are, in motion ; the translation, as it is called, of the whole system 

 being very nearly rectilinear, and the curvature, if any, arising from 

 the attraction of the fixed stars. Nothing but a long course of obser- 

 vation can settle this last part of the question, though much has been 

 done of late years to establish the affirmative. 



In approaching the old controversy on the motion of the earth, we 

 confine ourselves rather to the arguments by which it was opposed 

 than to those by which it was supported. For this we have two 

 reasons : first, that the latter are well known and extensively circu- 

 lated, while the former, unless preserved in historical articles, will find 

 the oblivion from which they have no intrinsic merit to rescue them ; 

 secondly, that the controversies of the present day may be usefully 

 illustrated by recurring to the long-decided struggle between the 

 Copernicans and their opponents. We have now among us those who 

 would fetter all new truths by their interpretation of the Scriptures, 

 though they quietly acquiesce in the defeat which their own principle 

 formerly received. The charges still brought against the cultivators 

 of the sciences, " to the distress and disgust of every well-constituted 

 mind," as Sir J. Herschel expresses it, should be looked at, not as the 

 honest manifestations of an alarm newly awakened by the circum- 

 stances of the present day, but as the effects of an abiding spirit, 

 which has always opposed investigation, and which, if it had prevailed, 

 would have smothered all the knowledge of nature which has been 

 acquired in the last two centuries. If some of those who have con- 

 stituted themselves successors to the cardinals who forced Galileo to 

 recant, have learnt from the past history of their own cause, and from 

 the temper of the present age, to show the real scope of their system 

 less openly than it appeared in the 17th century, the compliment 

 which they thus pay to the advancing intelligence of mankind, though 

 received with thanks and highly appreciated, should not be accepted 

 as an equivalent for the mischiefs which must result from a successful 

 attempt to place the great question of Revelation upon a false basis. 

 The case of those who now endeavour to impede the progress of 

 geology, or to limit speculation on the process of creation, is so similar 

 in its fundamental points with that of the labourers to the same effect 

 in the field of astronomy, that the circulation of some account of the 

 latter will perhaps enable our readers to help themselves in forming 

 their opinion of the former. 



When the work of Copernicus appeared in 1543, it seems to have 

 been considered as a mere attempt to demonstrate (see the old use of 

 this word in DEMONSTRATION) the motions of the heavenly bodies in a 

 more simple way. Guarded as it was by the expressions of the preface, 

 it was neglected as a purely speculative trial of a strange and impossible 

 hypothesis. In 1566 Ramus ('Scol. Math.') simply reproaches Coper- 

 nicus with the gigantic character of his hypothesis, and says it would 

 have been better to have taken one nearer to the truth, in a manner 

 which implies that he thought both were agreed as to what the truth 

 really was. Copernicus himself, as we have seen, treated his own 

 ideas as a reproduction of those of the ancients, and in truth the 

 existence of such a doctrine as the earth's motion was perfectly well 

 known to all men of learning. Aristotle (in his second book on the 

 Heavens) states that Pythagoras and his followers placed the sun in 

 the centre, on account of the superior excellence which they attributed 

 to the element of fire, of which they supposed the sun to be made. 

 Different authorities give the same opinion (whether with or without 

 the reason) to Philolaus, Anaximander, Nicetas, Seleucus, Cleanthes, 

 Leucippus, Ecphantus, Heraclides Ponticus, and Aristarchus. The 

 introduction of Pythagoras, as a predecessor of Copernicus, is as 

 rational as would be the connection of the modern atomic theory with 

 the doctrines of Epicurus ; and much of the same kind is an assertion 

 not unfrequently made, that Cardinal Cusa was a supporter of the 

 earth's motion. This writer (' Do Doctft Ignorantia," lib. ii., c. 11) 

 certainly denies that there can be any centre of the universe ; for, 

 says he, if there were a centre, there would be a circumference, that 

 is, a termination, to the universe; and his reasons relative to the 

 earth's motion are of the same degree of force. He is more rational in 

 the next chapter, where he explains that the apparent motion of other 



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