fications, to all bodies. They are to be understood as applying to very small masses, for which we can neglect the velocity of rotation in comparison with the velocity of translation. Such a mass is called a particle. A particle may also be defined as a mass concentrated at a point. Another definition will be given in § 37.
These laws of motion are not immediately susceptible of proof; they are abstractions, which can be illustrated but not proved by experiment. They cannot be referred to any more ultimate principles deduced from our observation of Nature, and are therefore to be considered as postulates upon which the science of Mechanics is erected. The question of their validity as expressions of the mode of motion of matter is one which lies outside the range of the purely physical study of the subject.
26. Discussion of the Laws of Motion.—(1) The first law is a statement of the important truths, that motion, as well as rest, is a natural state of matter; that moving bodies, when entirely free to move, proceed in straight lines, and describe equal spaces in equal times; and that any deviation from this uniform rectilinear motion is caused by a force.
That a body at rest should continue indefinitely in that state seems perfectly obvious as soon as the proposition is entertained; but that a body in motion should continue to move in a straight line is not so obvious, since motions with which we are familiar are frequently arrested or altered by causes not at once apparent. This important truth, which is forced upon us by observation and experience, may, however, be presented so as to appear almost self-evident. If we conceive of a body moving in empty space, we can think of no reason why it should alter its path or its rate of motion in any way whatever.
(2) The second law presents, first, the proposition on which the measurement of force depends; and, secondly, states the identity of the direction of the change of motion with the direction of the force. Motion is here synonymous with momentum as before defined. The first proposition we have already employed in deriving the formula representing force. The second, with the
