Page:Elementary Text-book of Physics (Anthony, 1897).djvu/40

26 can impart to a gram of matter one unit of acceleration; that is to say, one unit of velocity in one second.

23. Impulse.— The product $$Ft$$ is called the impulse. If the force which acts upon the body vary during the time, the impulse is determined by dividing the time into intervals so small that the force which acts during any one of them may be considered constant, forming the product $$Ft$$ for each interval, and adding those products.

24. Momentum.— The product $$mv$$ is called the momentum of the body. It is sometimes defined as the quantity of motion of the body; in Newton's laws, which follow, the word "motion" is equivalent to momentum, when it designates a measurable quantity.

25. Laws of Motion.— The relation between force and acceleration, which is embodied in the formula $$F = ma$$, was first perceived by Galileo, and illustrated by him by the laws of falling bodies. This relation may be expressed otherwise by the statement that the effect of a force on a body is independent of the motion of the body. Newton, who first formulated the fundamental facts of motion in such a form that they can be made the basis of a science of Mechanics, extended Galileo's principle by recognizing that when several forces act on a body at once the effect of each is independent of the others. Newton's Laws of Motion, in which the fundamental facts of motion are stated, are as follows:

— Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by external forces to change that state.

— Change of motion is proportional to the external force applied, and takes place in the direction of the straight line in which the force acts.

— To every action there is always an equal and contrary reaction; or, the mutual actions of any two bodies are always equal and oppositely directed.

These laws cannot be applied, without some limitations or