_Caroline._ We know also by experience, that the heavier a body is, the greater is its force; it is not therefore difficult to understand, that the whole power, or momentum of a body, must be composed of these two properties, its weight and its velocity: but I do not understand why they should be _multiplied_, the one by the other; I should have supposed that the quantity of matter, should have been _added_ to the quantity of motion? _Mrs. B._ It is found by experiment, that if the weight of a body is represented by the number 3, and its velocity also by 3, its momentum will be represented by 9, not by 6, as would be the case, were these figures added, instead of being multiplied together. _Emily._ I think that I now understand the reason of this; if the quantity of matter is increased three-fold, it must require three times the force to move it with the same velocity; and then if we wish to give it three times the velocity, it will again require three times the force to produce that effect, which is three times three, or nine; which number therefore, would represent the momentum. _Caroline._ I am not quite sure that I fully comprehend what is intended, when weight, and velocity, are represented by numbers alone; I am so used to measure space by yards and miles, and weight by pounds and ounces, that I still want to associate them together in my mind. _Mrs. B._ This difficulty will be of very short duration: you have only to be careful, that when you represent weights and velocities by numbers, the denominations or values of the weights and spaces, must not be changed. Thus, if we estimate the weight of one body in ounces, the weight of others with which it is compared, must be estimated in ounces, and not in pounds; and in like manner, in comparing velocities, we must throughout, preserve the same standards both of space and of time; as for instance, the number of feet in one second, or of miles in one hour. _Caroline._ I now understand it perfectly, and think that I shall never forget a thing which you have rendered so clear. _Mrs. B._ I recommend it to you to be very careful to remember the definition of the momentum of bodies, as it is one of the most important points in mechanics: you will find that it is from opposing velocity, to quantity of matter, that machines derive their powers. The _reaction_ of bodies, is the next law of motion which I must explain to you. When a body in motion strikes against another body, it meets with resistance from it; the resistance of the body at rest will be equal to the blow struck by the body in motion; or to express myself in philosophical language, _action_ and _reaction_ will be equal, and in opposite directions. _Caroline._ Do you mean to say, that the action of the body which strikes, is returned with equal force by the body which receives the blow? _Mrs. B._ Exactly.