797 



MOTION, APPAKENT. 



MOTION, LAWS OF. 



796 



from A to B, or from A to c, would have been performed. This is pre- 

 cisely the course the body would have taken in space, if, while it moved 

 from A to B on the paper, the paper itself had taken the motion A c ; 

 but the establishment of the latter assertion must not be confounded 

 with the proof of the composition of velocities impressed on matter ; 

 the latter requires those considerations which lead to the second law of 

 motion. 



There are a great many uses of the word " motion," which are con- 

 venient, but require the introduction of arbitrary suppositions. Thus 

 the moon never cuts the ecliptic twice running in the same place, and 

 the intersection of her orbit with the ecliptic being called a node, it is 

 said that the node moves, thus giving this node a sort of imaginary 

 existence in the interval. 



MOTION, APPARENT. [Monos.] 



MOTION, DIRECTION OF. We have inserted this article, not for 

 the sake of rectilinear, but of circular motion, the consideration of 

 which is apt to cause some embarrassment to the beginner. In motion 

 along a given right line there can be but two directions, in one or 

 other of which the course must be ; and these two directions are oppo- 

 site to one another. But in circular or other rotatory motion, all 

 imaginable directions are taken in the course of a revolution, and 

 whatever linear direction the moving body takes at any one point, it 

 has the opposite direction at the opposite point. Still, however, there 

 are two ways of moving on a circle : the motion may either be from 

 c to A through B, or from A to c through B. These are called, some- 

 what improperly, different directions of motion. 



If two bodies be moving over two circles, they are said to move in 

 the same direction when, two radii being taken in the same direction, 

 the linear directions of motion are the same, as B D and Q R. Thus 

 care must be token not to compare two circular motions by positions 

 which belong to radii in opposite directions. If, for instance, the 

 directions of motion be A B c and q v s (which are the same), and if at 

 the same time the two bodies be at B and s, their linear directions of 

 motion are opposite, though according to the definition their circular 

 motions are in the same direction. Thus, in the case of the moon, and 

 her revolution round her own axis [Moon], the middle point of the 

 visible moon is moving round the moon's axis in a direction opposite 

 to the orbital motion of the moon ; but the radius of that middle 

 point is opposite in direction to the line joining the centres of the 

 earth and moon ; so that the direction of revolution of the moon's 

 rotation is the same as that of the orbital rotation. 



MOTION, LAWS OF. The laws of motion mean those universal 

 methods of receiving and losing motion which close attention to 

 mechanical phenomena, coupled with strict inductive reasoning, has 

 shown to be inherent in the constitution of matter. 



If an intelligent observer, not used to inductive reasoning, nor 

 instructed in the results of mechanics, were required to state the views 

 which experience had taught him of the constitution of matter, as an 

 agent or patient in the production or reception of motion, he would 

 perhaps reply as follows : Matter seems to have no power of moving 

 itself, though if we judge from the fall of bodies towards the earth, 

 the phenomena of magnetism, &c., it would appear as if matter might 

 be the cause of motion in other matter. And it seems moreover that 

 motion i an accident of matter which diminishes and dies out of itself, 

 if some sustaining cause be not perpetually in action ; for in all cases 

 in which the experiment can be tried, we find that moving bodies are 

 reduced to rest by being left to themselves. The motions of the 

 heavenly bodies, it is true, appear to be permanent ; but we have no 

 certain assurance that there is not a constant sustaining physical 

 cause of this permanency. 



There would be something of truth, and a good deal of falsehood, in 

 the preceding conclusions, and it is not an easy thing to give that 

 exhibition of the real constitution of matter which is placed beyond all 

 doubt by the coincidence of its results with all the more complicated 

 phenomena of nature. There is no question that those principles, to 

 take two cases out of thousands, on which a ball can be projected 

 almost unerringly to its mark from the mouth of a cannon, and the 

 motions of the moon can be predicted within a small fraction of a 

 second, are founded in truth ; but it does not therefore follow that an 

 it priori demonstration of them, mathematical or experimental, can be 

 given ; and in fact the method of presenting the laws of motion to a 

 beginner is encumbered with serious difficulties. 



We shall begin by the assumption that those laws of motion which 



are to be found in all works on mechanics are true ; the reason for such 

 assumption being, that if we take them for granted, and use them as 

 the basis of a mathematical system of mechanics, all results of that 

 "ystem, however many the links in the chain of deduction, are found 

 to agree with observed phenomena in species, and as nearly in magni- 

 tude as the various resistances and disturbances will allow. In 

 astronomy and optics, phenomena have been predicted with all but 

 geometrical accuracy, by deduction from principles which would 

 certainly be false if the received laws of motion were false. In 

 terrestrial mechanics, the number of instances is unlimited in which 

 these laws lead to that near approximation to prediction which is fully 

 as much as can be expected with our imperfect knowledge of data. 

 Many hundreds of phenomena admit, upon these laws, of an explana- 

 tion which, compared with that which they could receive from any 

 others, is as easy as the hypothesis of the motion of the earth compared 

 with that of its stability. 



So simple are the laws of motion themselves, that many have 

 supposed them to be necessary, in the same sense as when we say it is 

 a necessary consequence of our conception of straightness that two 

 straight lines cannot inclose a space. We shall mention this notion 

 again presently : in the meanwhile we are in this situation, that while 

 it is difficult, as a matter of reasoning, to disentangle the fundamental 

 laws from the variety and complication of the phenomena in which 

 their effects are exhibited, yet these laws themselves, when disengaged, 

 are of that startling simplicity which disinclines the mind to receive 

 them as the results of a train of deduction, and disposes it rather to 

 think that it could have dictated them from its own previous con- 

 ceptions. 



It will make some difference in our method of seeking for these 

 laws, whether we suppose the earth to be at rest or in motion. Now 

 the decisive proofs of the motion of the earth, as it happens, are them- 

 selves derived from certain consequences of the laws of motion. 

 [MoTion OF THE EARTH.] We seem then to be reasoning in a vicious 

 circle ; nor do we see any mode of escape except by establishing the 

 truth of these laws, whether the earth be at rest or in motion. And 

 the process will be, first to detect laws for which there is a high and 

 almost overpowering degree of probability in their favour ; next to 

 appeal to the above-mentioned uniform truth of the results deduced 

 from the assumption of such laws for the conversion of this high state 

 of probability into one of absolute demonstration. 



We will first assume the motion of the earth : every point of its 

 surface then is in a state of revolution round the axis, while at the 

 same time the whole is carried forward round the sun ; to which we 

 must add, the slight motion arising from the precession of the 

 equinoxes, and the possible translation of the whole system. But this 

 motion is very different in different parts ; at the pole, for example, 

 there is no diurnal motion, near it only a small one, and at the equator 

 a considerable one. The points near the pole, all the motions con- 

 sidered, are describing a trochoidal orbit, the undulations of which are 

 small, and the rotatory velocity small ; those near the equator make 

 larger undulations, with greater velocity of rotation. Our first idea 

 might be, then, that at the different parts of the earth some modifica- 

 tion of general laws would be observed, arising from the difference of 

 the motions of the several places. It woxild not surprise a person 

 wholly unacquainted with mechanics, to whom the preceding facts 

 were stated for the first time, if lie were told that some mistakes were 

 made in the pointing of guns in our Indian battles, arising from the 

 artillerymen having been trained by officers who had learnt their ait 

 in the latitude of Addiscombe, near Croydon, in Surrey, and had 

 forgotten to allow for the difference in the diurnal motion of the two 

 countries. Now the considerations which tend to establish the Second 

 Law of Motion depend upon the fact that it never has been found 

 necessary to take any notice of the difference of place on the earth in 

 estimating effects of motion. It is not found necessary to write 

 different treatises on gunnery for different latitudes, nor to alter the 

 disposition of parts in any machine moved from one latitude to another 

 to produce a more advantageous effect. There is, it is true, a small 

 diminution in the weight of bodies, as they are carried toward the 

 equator, and [CENTBJFUGAL FOHCE ; PENDULUM] the results of this are 

 apparent in experiments in which the acquisition of motion depends 

 upon weight, or rather, upon its proportion to the quantity of matter. 

 But this very problem of the pendulum is one in which the question 

 of the truth of the laws of motion is established by a test which would 

 detect the smallest quantities, and furnishes an answer to those who 

 might say that the possible effects of the difference of diurnal motions, 

 though not distinguishable in such cases as that of a cannon-ball, might 

 be perceptible in delicate instruments. 



If to the motion of the earth we guperadd another, such as the 

 motion of a carriage, the same sort of result is found. Those who 

 move on a railroad at the rate of 30 miles an hour, or 44 feet in a 

 second, do not find the relation in which they stand to the objects in 

 the carriage in any degree changed by the motion. At the instant of 

 taking the motion, or on any sudden jolt or change of motion, effects 

 may be produced to which we shall frequently refer : but when the 

 speed is once obtained, it is well known that a person might occupy 

 himself in reading a work on mechanics written on terra Jirma (so 

 called), and might verify all the experimental conclusions, without 

 coming to any result which would remind him of the difference of 



