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 would not surprise a person wholly unacquainted with mechanics, to whom the preceding facts were stated for the first time, if he 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 art 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 [CENTRIFUGAL FORCE ; 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 eases as that of a cannon-ball, might be perceptible in delicate instruments.
If to the motion of the earth we superadd 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 firma (so called), and might verify all the experimental conclusions, without coming to any result which would remind him of the difference of state between the writer and himself, as to motion. Hence we are led to the conclusion that all the relations of matter to matter remain unaltered. if the whole system be made to move, provided that the same motion be communicated to all its parts. And though we do not, absolutely speaking, know what rest is, since no point of the earth, nor of any heavenly body, can be shown to be at rest, yet since we see that the relations remain unaltered when the velocity of • whole system is changed, we are led to conclude that the same laws which prevail when all the parts of a system have the same motion, would also prevail if the whole system were at rest; the ground of our pre sumption being, that the laws remain unaltered under any alteration of the common motion which it is in our power to make.
Let us now suppose that the carriage, instead of moving in a right line, is carried on a curved road, say a simple circle. It is no longer observed that loose objects in the carriage have a tendency to repose relatively to the carriage itself. If the motion become sufficiently rapid, or the friction of the substances on which they stand be suffi ciently small, they will endeavour to move outwards, or from the' centre of the circle of motion. This phenomenon can be made a con sequence of the laws of motion, when the latter have obtained their simplest form; we do not at present enter into this subject further than to point out that it is only of rectilinear motions we can predicate any law as descriptive of what is inherent in matter. We have, it is true, already spoken of circular motions in taking into account those of the earth; but it must be remembered, firstly, that the circles in question are so large, that a small arc of any one is nearly a straight line ; secondly, that we hare been obliged to advert to this tendency outwards, which is the reason of the diminution of weight (or of much the greater part of it) detected from the oscillations of a pendulum which is carried towards the equator.
This second law of motion (for such it is called, though it must be deduced first when the earth's motion is considered) may be thus stated :—If them be two or more causes of motion, taking place in two different right lines, whether inherent in the body or external to it, their effects do not interfere, nor does either diminish or augment the effect of the other. If, for instance, the body A be subject to two actions, one of which, being entirely in the direction A n, would bring the body to B in a given time, and the other, entirely in the direction • c, would bring it to C in the same given time ; then the body will move from A to D, precisely as it would have done if, moving along A B in the manner first specified, the lino A B had been translated with its extremity A moving in the second manner specified, the, said lino A B not changing its direction.
The most simple and general method of stating this law is as fellows :—The distance of a point from a straight lino or plane, measured in any given direction, and as it will be at the end of a given time, is not affected by the action, during that time, of any causes of motion, provided they act in the direction of, or parallel to, that straight line or plane; or no force, in a given direction, can produce motion to or from a line in that direction. Thus if a ball were thrown up iu still air, in such a manner that it would mount 50 feet in one second, no imaginable ho frontal current or whirlwind, however touch it might alter the actual course of the ball, would prevent its rising 50 feet in the second. The statement of the law by Newton, namely, that when • force acts upon a body in motion, the change of motion which it produces is in the direction and proportional to the magnitude of the force which acts, is perhaps rather too vague to give a distinct notion to learners.