We have examined the action of a body under the accelerating or speed-quickening force due to gravity, the attractive force of which on any body is always proportional to the mass of that body. Let us now consider another form of acceleration. [Illustration: FIG. 30.] Take the case of a strip of indiarubber. If pulled it resists and tends to spring back. The more I pull it out the harder is the pull I have to exert. This is true of all springs. It is true of spiral springs, whether they are pulled out or pushed in, and in each case the amount by which the spring is pulled out or pushed in is proportional to the pressure. This law is called Hooke’s law. It was expressed by him in Latin, “Ut tensio, sic vis”: “As the extension, so the force.” It is true of all elastic bodies, and it is true whether they are pulled out or pushed in or bent aside. The common spring balance is devised on this principle. The body to be weighed is hung on a hook suspended from a spring. The amount by which the spring is pulled out is a measure of the weight of the body. If you take a fishing rod and put the butt end of it on a table and secure it by putting something heavy on the end, then the tip will bend down on account of its own weight. Mark the point to which it goes. Now, if you hang a weight on the tip, the tip will bend down a little further. If you put double the weight the tip will go down double the distance, and so on until the fishing rod is considerably bent, so that its form is altered and a new law of flexure comes into play. Suppose I use a spring as an accelerating force. For example, suppose I suspend a heavy ball by a string and then attach a spiral spring to it and pull the spring aside. The ball will be drawn after the spring. If then I let the ball go, it will begin to move. The force of the spring will act upon it as an accelerating force, and the ball will go on moving quicker and quicker. But the acceleration will not be like that of gravity. There will be two differences. The pull of the spring will in no way depend on the mass of the ball, and the pull of the spring, instead of being constant, like the pull of gravity, will become weaker and weaker as the ball yields to it. Consequently the equations above given which determine the relations between this space passed through, the velocity, and the time which were determined in the case of gravity are no longer true, and a different set of relations has to be determined. This can be easily done by mathematics. But I do not propose to go into it. I prefer to offer a rough and ready explanation, which, though it does not amount to a proof, yet enables us to accept the truth that can be established both by experiment and by calculation. [Illustration: FIG. 31.]