cussing collisions in which two bodies collide and stick together, or come together nd bounce apart, we shall first consider two bodies that are held together by a ring or something else, and are then suddenly released and pushed by the spring or perhaps by a little explosion. Further, we shall consider motion in only one direction. First, let us suppose that the two objects are exactly the same, are nice symmetrical objects, and then we have a little explosion between them. After the explosion, one of the bodies will be moving, let us say toward the right, with a velocity v. Then it appears reasonable that the other body is moving toward the left with a velocity v, because if the objects are alike there is no reason for right or left to be preferred and so the bodies would do something that is symmetrical. This is an illustration of a kind of thinking that is very useful in many problems but would not be brought out if we just started with the formulas. The first result from our experiment is that equal objects will have erials speed, but now suppose that we have two objects made of different mater say copper and aluminum, and we make the two masses equal. We shall now suppose that if we do the experiment with two masses that are equal, even though the objects are not identical, the velocities will be equal. Someone might object But you know, you could do it backwards, you did not have to suppose that You could define equal masses to mean two masses that acquire equal velocities in this experiment, We follow that suggestion and make a little explosion between the copper and a very large piece of aluminum, so heavy that the copper flies out and the aluminum hardly budges. That is too much aluminum, so we reduce the amount until there is Just a very tiny piece, then when we make the explosion the aluminum goes flying away, and the copper hardly budges. That is not enough alu minum. Evidently there is some right amount in between; so we keep adJusting he amount until the velocities come out equal. Very well then-let us turn it around, and say that when the velocities are equal, the masses are equal. This appears to be Just a definition, and it seems remarkable that we can transform physical laws into mere definitions. Nevertheless, there are some physical laws involved, and if we accept this definition of equal masses, we immediately find one of the laws as foll Suppose we know from the foregoing experiment that two pieces of matter, A and B(of copper and aluminum), have equal masses, and we compare a third body, say a piece of gold, with the copper in the same manner as above, making sure that its mass is equal to the mass of the copper. If we now make the experiment between the aluminum and the gold there is nothing in logic that says these masses must be equal; however, the experiment shows that they actually are. So now, by experiment, we have found a new law. A statement of this law might be: If two masses are each equal to a third mass(as determined by equal velocities in this experiment), then they are equal to each other. (This statement does not follow at all from a similar statement used as a postulate regarding mathematical quanti From this example how quickly we start to infer things if we ar careless. It is not just a definition to say the masses are equal when the velocities are equal, because to say the masses are equal is to imply the mathematical laws hich in turn makes a prediction abo As a second example, suppose that A and B are found to be equal by doing the experiment with one strength of explosion, which gives a certain velocity; if we then use a stronger explosion, will it be true or not true that the velocities now obtained are equal? Again, in logic there is nothing that can decide this question but experiment shows that it is true. So, here is another law, which might be stated If two bodies have equal masses, as measured by equal velocities at one velocity, they will have equal masses when red at another velocity. From these examples we see that what appeared to be only a definition really involved physic In the development that follows we shall assume it is true that equal mass have equal and opposite velocities when an explosion occurs between them. We shall make another assumption in the inverse case: If two identical objects, moving in opposite directions with equal velocities, collide and stick together by some kind of glue, then which way will they be moving after the collision? This is again a 104