MECHANICS. 



745 



And, by the remark under the rule, if the first make 

 14 revolutions in the minute, the speed of the last will 

 be 105 in the same time. The same rule will apply 

 to the case where the wheels act on each other by 

 ropes or straps, if the circumferences of the wheels 

 and pinions are used for the number of teeth. 



Inclined Plane. When a drayman lays a plank 

 from the street to the higher level of the floor of a 

 storehouse, that he may be able to roll in a heavy 

 cask, he employs the principle of the inclined plane ; 

 and the more gradual the inclination of the plank, 

 the more easily will he effect his purpose. That is, 

 the advantage gained by the inclined plane is greater, 

 the more the length of the plane exceeds its height. 

 A road which is not level, is an inclined plane. 

 When a road mounts over a hill, instead of winding 

 round its foot, a team of horses with a load of a ton 

 weight, must exert strength sufficient to lift the load 

 perpendicularly into the air, to a height equal to that 

 of the top of the hill, instead of that moderate exer- 

 tion which is necessary to overcome the friction of 

 the axis of the wagon, and the slight inequalities of 

 a level road. Hence the absurdity of constructing 

 roads in hilly countries to pass directly over the tops 

 of hills, instead of winding, by small circuits, along 

 their base. 



When a power acts on a body, 

 on an inclined plane, so as to 

 keep that body at rest ; then 

 the weight, the power, and the 

 pressure on the plane, will be 

 as the length, the height, and 

 the base of the plane, when the 



) AC 



power acts parallel to the plane ; that is, 

 The weight f 



The power < will be as BC 



The pressure on the plane (. 3 AB 



The force with which a body endeavours to de- 

 scend down an inclined plane, is as the heiglit of the 

 plane. When the power does 

 not act parallel to the plane, \ 

 then from the angle C of the 

 plane, draw a line perpendicular 

 to the direction of the power's 

 action ; then the weight, the 

 power, and the pressure on the plane, will be as AC, 

 CB, BA. When the line of direction of the power 

 is parallel to the plane, the power is least. 



If two bodies, on two inclined planes, sustain 

 each other, by means of a string over a pulley, their 

 weights will be inversely as the lengths of the planes. 



The space which a body describes upon an inclined 

 plane, when descending on the plane by the force of 

 gravity, is to the space which it would fall freely in 

 the same time, as the height is to the length of the 

 plane ; and the spaces being the same, the times will 

 be inversely in this proportion. If the elevation 

 were one sixteenth of the length, the body would 

 roll down one foot in the first second, and four in 

 two. It is on this principle that the equality in the 

 vibrations of a pendulum may be explained. A long 

 vibration takes no more time than a short one, be- 

 cause the body begins to fall, in this case down a 

 steep plane, and acquires gueat velocity. In a short 

 vibration, the beginning of its path is a very gradual 

 descent. A short pendulum vibrates more rapidly 

 than a long one, because it has a shorter distance to 

 move in a path of the same steepness. A body 

 moving down an inclined plane, moves four times as 

 far in two seconds as in one. A pendulum, to vibrate 

 once in two seconds, must be, therefore, four times as 

 long as one which beats seconds. The most remark- 

 able application of the inclined plane is in the con- 

 struction of the marine railway, on which, by the 

 power of a few horses, a ship of 600 tons is drawn. 



with all its cargo, out of the water, high enough tc 

 allow workmen to pass under its keel. 



The Screw. Imagine an inclined plane to pass 

 round an immense building, like the tower of Babel, 

 affording means of ascending to the top, and you 

 have the first idea of the screw. It is an inclined 

 plane, wrapped spirally round a solid cylinder. The 

 advantage gained by it depends on the slowness of 

 the ascent, that is, on the number of turns or threads, 

 as they are called, in a given distance. It is always 

 used in combination with a lever. It is a machine of 

 great power, commonly employed to produce com- 

 pression or to raise heavy weights. Hunter's screw 

 is a compound of two screws, with threads of different 

 degrees of fineness, one moving within the other, the 

 end advancing, at each revolution, through a distance 

 equal to the difference of the threads. 



The Wedge is a double inclined plane, used com- 

 monly to cleave wood cr stone, and sometimes to 

 elevate a large mass, as part of a building, or ship. 

 The effect of a wedge depends, apparently, upon fric- 

 tion, elasticity, and the slowness with which motion 

 is communicated to a mass of matter. When a wedge 

 is driven in, the particles immediately in contact with 

 it are, for a moment, displaced, the friction against it 

 prevents it from receding, and when the displaced 

 particles endeavour to resume their relative position, 

 the rift is lengthened. To the wedge may be referred 

 various cutting tools, such as axes, knives, swords, 

 chisels ; and nails and spikes to be driven into wood, 

 as well as pins, needles, awls, &c. The saw and the 

 file and rasp are modifications still more remote. 

 The colter of a plough, the blade of a spade, and other 

 instruments to penetrate the earth, are in the shape 

 of a wedge. 



The Rope is considered, in theory, as destitute of 

 weight, and perfectly smooth and flexible. In this 

 case, as in that of the other mechanical powers, the 

 allowances to be made in practice for weight, rigidity, 

 friction, &c. , are ascertained by experiment, and com- 

 bined with the results of theory. If a rope be 

 stretched horizontally between two fixed points, by 

 equal weights attached to the ends, any very small 

 weight applied to the rope between these points will 

 bend the rope, and thus raise the weights. If we 

 suppose the rope to have been perfectly horizontal, 

 the weight applied acts upon those at the ends with a 

 mechanical advantage which may be considered in- 

 finite, as it acts at right angles to the directions of the 

 opposite actions of those weights. This is a neces- 

 sary consequence of the principles of the resolution of 

 forces. The action of one or two forces can have no 

 effect in counteracting a third, unless they act in such 

 a direction, that their action can be resolved into two, 

 one of which is opposite to the direction of the third 

 force. While the rope is horizontal, the two weights 

 counterbalance each other, but produce no further 

 effect, until the rope is bent into an angle. A bend- 

 ing of the rope must, therefore, take place, in conse- 

 quence of the action of any force, however small. By 

 bending the rope, it must raise the weights, and sup- 

 port them at a point above their former position, thus 

 producing an equilibrium with them, however great 

 they may be. This arrangement is one form of what 

 is called the funicular machine. A necessary con- 

 sequence of the principle on which it depends is, that 

 when a rope or chain, of any material whatever, is 

 stretched horizontally, its weight alone will prevent 

 its being perfectly straight, and no force is sufficient 

 to straighten a rope unless it hangs perpendicularly. 

 Advantage is often taken of this power by seamen in 

 tightening ropes, which have previously been drawn 

 as closely as possible by the direct action of their 

 strength. 



The Pulley is a small wheel, moving on an axis of 



