INTRODUCTION TO MECHANICS. ix 



SECTION II. On the Laws of Motion, and the Centre of Gravity. 



THE science of mechanics is founded on the laws of motion ; it will 

 therefore be necessary to explain these laws before we examine the me- 

 chanical powers. Motion consists in a change of place. A body is in 

 motion whenever it is changing 1 its situation with regard to a fixed point. 

 Now having observed that one of the general properties of bodies is 

 inertia, that is, an entire passiveness either with regard to motion or rest, 

 it follows that a body cannot move without being put into motion : the 

 power which puts a body into motion is called force ; thus the stroke of 

 the hammer is the force which drives the nail ; the pulling of the horse, 

 that which draws the carriage. Gravitation is the force which occasions 

 the fall of bodies, cohesion that which binds the particles of bodies 

 together, and heat a force which drives them asunder. The motion of 

 a body acted upon by a single force is always in a straight line, in the 

 direction in which it received the impulse. 



The rate at which a body moves, or the length of time which it takes 

 to move from one place to another, is called its velocity ; and it is one 

 of the laws of motion that the velocity of the moving body is proportional 

 to the force by which it is put in motion. The velocity of a body is called 

 absolute, if we consider the motion of the body in space, without any 

 reference to that of other bodies. When, for instance, a horse goes fifty 

 miles in ten hours, his velocity is five miles an hour. It is termed 

 relative, when compared with that of another body which is itself in 

 motion. Thus a man sailing in a ship may remain at rest relatively to 

 the vessel, though he partakes of its absolute motion ; but if he walk the 

 deck in the same direction as that in which the ship is sailing, his 

 absolute motion will be increased by the rate at which he moves along it, 

 and his relative motion will be the difference between his own absolute 

 motion and that of the ship. So if two carriages go along the same road 

 in the same direction, their relative velocity will be the difference of their 

 absolute velocities ; if in opposite directions, the same. If they start 

 from the same point along two roads, making an angle with each other, 

 their relative motion will be measured by their distance, in a straight 

 line, from each other after a given time, and the direction of this relative 

 motion will be the direction of that line. The absolute velocity of a body 

 is measured by the space over which it moves, in some particular time, 

 selected as the standard ; the velocity per hour, for instance, would be 

 shewn by dividing the number of miles travelled over by the number of 

 hours occupied in the journey. Thus, if you travel one hundred miles 

 in twenty hours, and wish to know what is your velocity, you divide 100 

 by 20, and the answer will be 5 miles an hour. We say, also, that space 

 is equal to the velocity multiplied by the time ; if your velocity be three 

 miles an hour, and you travel six hours, you will have gone, in all, a 

 space of eighteen miles. 



Uniform motion is that of a body which passes over equal spaces in 

 equal times. It is produced by a force having acted on a body once, 

 and having ceased to act, such as the stroke of a bat on a cricket-ball. 

 But it may be said, that the motion of a cricket-ball is not uniform, its 

 velocity gradually diminishing till it falls to the ground. In answer to 

 this objection, you must observe that the ball is inert, having no more 

 power to stop than to put itself in motion ; if it fall, therefore, it must be 

 stopped by some force superior to that by which it was projected ; and 



