INTRODUCTION TO MECHANICS. xi 



it be thrown with a force which will make it rise only sixteen feet, in 

 that case it will fall in one second of time. Now it is proved by expe- 

 riment, that an impulse requisite to project a body sixteen feet upwards, 

 will make it ascend that height in one second ; here then the times of 

 the ascent and descent are equal. But supposing it be required to throw 

 a stone twice that height, the force must be greater. Thus the impulse 

 of projection in throwing a body upwards, is equal to the accumulated 

 effect produced by gravity during its descent ; and it is the greater or 

 less distance to which the body rises, that makes these balance each 

 other, for it gives more time for the force of gravitation to act. 



We must now explain to you what is meant by the momentum of bodies. 

 It is I he force, or power, with which a body in motion would strike against 

 another body, so as to set the latter in motion. The momentum of a 

 body is composed of its weight, multiplied by its velocity. The quicker 

 a body moves, the greater will be the force with which it will strike 

 against another body j so that a small light body may have a greater 

 momentum than a large heavy one, provided its velocity be sufficiently 

 great. For instance, the momentum of an arrow shot from a bow is 

 greater than that of a stone thrown by the hand. We know also by 

 experience, that the heavier a body is, the greater is its force, if it acts 

 in other respects under the same circumstances, therefore the whole 

 power or momentum of a body is composed of these two properties. 

 But why should not these be added together, instead of being multiplied 

 by one another ? It is found by experiment, that if the weight of 

 a body be represented by the number 3, and its velocity also by 

 3, its momentum will be as 9; not 6, as would be the case were 

 these figures added, instead of being multiplied together. The same 

 conclusion may very easily be deduced by reasoning. If two bodies, 

 one of one pound weight, the other of two, have the same velocity, 

 the moving force of the second, or its momentum, is double that of the 

 first. If a third body, also of two pounds, move with three times the 

 velocity of the second, its momentum, the weights being in this case 

 equal, is three times that of the second. But the momentum of the 

 second is twice that of the first; therefore the momentum of the third is 

 three times this quantity, or six times that of the first. By thus dividing 

 the process, and looking first to the effect of a change of the velocity, 

 and afterwards to that of the change of the weight, it becomes evident that 

 these effects are to be multiplied together. 



The re-action of bodies is the next law of motion to be explained. 

 When a body in motion strikes against another body it meets with resist- 

 ance ; the resistance of the body at rest will be equal to the blow struck 

 by the body in motion ; or, in philosophical language, action and re-action 

 will be equal, and in opposite directions. 



The most strikingexperiments on these subjects are made with elastic bo- 

 dies. Elasticity is a property, by means of which bodies that are compressed 

 return to their former state. If you bend a cane, as soon as it is at liberty 

 it recovers its former position ; if you press your finger upon your arm, 

 as soon as you remove it, the flesh, by virtue of its elasticity, rises and 

 destroys the impression. Of all bodies, those in the form of air or gas 

 are the most eminent for this property. Hard bodies are in the next 

 degree elastic: if two ivory or metallic balls be struck together, the 

 parts at which they touch will be flattened, but no mark is perceptible, 

 their elasticity instantly destroying all trace of it. If, however, a very 

 small spot of ink be placed on one of the balls at the point of contact, 



