742 



MECHANICS. 



tlio impulse of the wind, when the sails are set. ; ils 

 motion increases as new portions are successively 

 imparted. A horse does not start at once will) a 

 carriage into his utmost speed ; his force is at first 

 >l>nit in giving motion to the inert mass. After- 

 wards, with far less exertion, he keeps up the 

 motion, being required to supply that portion only 

 which is destroyed by the obstacles of the road. 

 The motion communicated to a body, if not destroyed 

 by some force, is accumulated. Thus a nail is 

 driven in by all the force of the hand, accumulated 

 through the whole time of the descent of the ham- 

 mer. The knowledge of this fact gives the means 

 of increasing the effective force of a moving power 

 in a very great degree. A force of fifty pounds 

 communicated every second to a loaded wheel, will, 

 if not diminished by friction, or other cause of waste, 

 enable it to overcome a resistance of 500 pounds 

 once in every ten seconds. Such a wheel is called 

 &fly wheel, (q. v.) 



II. " The alteration of motion is ever propor- 

 tioned to the motive force impressed, and is made 

 in the direction of the right line hi which that force 

 is impressed." This is only a statement, that a 

 double force generates a double motion ; that 

 motion cannot increase or diminish itself, nor turn 

 to the right or left, without cause. In consequence 

 of this, two or more forces acting at once on a body 

 in different directions, cause it to take a direction 

 different from that of either force, and, if one of 

 them is a variable or constantly acting force, to 

 move in a curve line. This is called the composition 

 of forces ; the single motion impressed upon the 

 body being considered as composed of the several 

 motions which the forces acting separately would 

 have produced. A boat rowed, at the rate of three 

 miles an hour, directly from the bank of a river 

 which runs at the rate of two miles an hour, is acted 

 on at once by the force of the rowers and that of the 

 current, and will be found, at the end of an hour, 

 three miles from the bank, and two miles below the 

 point from which it started, having moved in a dia- 

 gonal line between the directions of the two forces. 

 (See Forces.) The resolution of forces is the reverse 

 of tin's. A single force is considered as resolved 

 into two or more others. A ship, sailing on a side 

 wind, is sent forward by a part only of its force. 

 The other part has no effect, or that only of driving 

 her out of her course. 



III. " To every action there is always opposed an 

 equal reaction ; or the mutual actions of two bodies 

 on each other are equal and in opposite directions." 

 If you press a stone with your finger, the finger is 

 equally pressed upon by the stone. A horse 

 drawing a load, is drawn backward by its whole 

 weight, and if he succeed in moving it, it can only 

 be with a velocity proportioned to the excess of his 

 strength over the reaction of the load. A magnet 

 and piece of iron attract each other equally ; and if, 

 when in the sphere of mutual attraction, one is fixed 

 and the other free, whichever is free will be drawn 

 to the other. Two equal boats, drawn towards each 

 other by a rope, act in the same manner ; if both 

 are free, they meet in the middle. When a gun is 

 discharged, it recoils with a force equal to that with 

 which the ball is propelled, but with a velocity as 

 much less as its weight is greater. If, in the side 

 of a vessel of water, hanging perpendicularly by a 

 cord, a hole be opened, the vessel will be pushed 

 back from the perpendicular by the reaction of the 

 jet of water, and will remain so while it flows. A 

 consequence of this law is, that the earth is attracted 

 by each body on its surface as much as it attracts, 

 and that when a stone falls towards the earth, the 

 earth rises to meet it. 



The force with which a body acts is estimated by 

 its velocity and mass conjointly, and is called its 

 momentum. Thus, if two balls, of one and two 

 pounds weight, respectively, be moving with the 

 same velocity, the larger has twice the momentum 

 of the smaller, since each pound of the larger has 

 the same velocity as the ball of a single pound. A 

 body of small weight may therefore be made to pro 

 duce tile same mechanical effect as a large one, by 

 sufficiently increasing its velocity. The cannon ball 

 of modern times is not less effectual in battering down 

 walls than the massy battering ram of the ancients. 



The forces which may be employed to give 

 motion to machines are called mechanical agents, or 

 first movers. They are water, wind, steam, gun 

 powder, and the strength of man and other animals 

 They may be indirectly referred to three indepen 

 dent sources gravity, heat, and animal strength 

 See these several articles. 



Gravity. A body falling from a state of rest, 

 descends sixteen feet, nearly (16*095), in one second ; 

 but, as all the motion which is communicated by gra- 

 vitation remains in it, and it receives an accession 

 of motion every indefinitely small portion of the first 

 second, it is moving more rapidly at the end of the 

 second than at any previous time, and, with that 

 motion alone, if it continued uniform, would descend 

 through twice 16, or 32 feet, in the next second ; but, 

 during this next second, as much motion is communi- 

 cated as during the first, and consequently the botly 

 descends through three times 16, or 48 feet, in this 

 next second. The whole of this accumulated motion 

 would, alone, carry it through four times 16, or 64 feet, 

 in the third second, and the continued action of gra- 

 vitation carries it once 1 6 ; so that it actually descends 

 five times 16, or 80 feet, during the third second. In 

 the fourth second, it would, in the same manner, de- 

 scend seven times 1 6 feet ; in the fifth, nine times 16, 

 &c., the series of odd numbers expressing the distances 

 passed through in the successive seconds. By adding 

 these numbers, we find that, at the end of two seconds, 

 the body will have descended four times 16 feet ; at 

 the end of the third, nine times 16 ; at the end of the 

 fourth, 16 times 16, &c.; the whole distance fallen 

 through at the end of any number of seconds being 

 found by multiplying the square of that number by 

 16 feet. Such is the simple and remarkable law of 

 the descent of bodies by the uniformly accelerated 

 velocity produced by gravitation. The velocity 

 acquired in one second is sufficient, of itself, to carry 

 a body through twice 16 feet ; that acquired in two 

 seconds would carry it four times 16 feet; that 

 acquired in three seconds, through six times 16 feet, 

 &c.; the velocities possessed at the end of any num- 

 ber of seconds being represented by twice that num- 

 ber multiplied by 16 feet. The following table 

 exhibits, 1. the space fallen through in the succes- 

 sive seconds ; 2. the whole space fallen through at 

 the end of a number of seconds ; and, 3. the final 

 velocity : 



Time. 183456789 10 seconds. 



1. .Successive Spaces, 1357 9 11 13 15 17 19 times 16 feet, 



a. Total Spaces, 1 4 9 16 25 36 49 64 61 100 " " 



3. Final Velocity, 2 4 6 8101*141618 20 " 



By means of this table, a traveller standing on the 

 summit of a cliff, might ascertain its height above the 

 plain or torrent below, with considerable accuracy, 

 by letting fall a stone, and observing the time of its 

 fall. It would only be necessary to make allowance 

 for the resistance of the air, which, for small velocities, 

 is not very great. (See Projectiles.) The same 

 cause which communicates motion to a falling body, 

 would gradually destroy that of a body ascendingr. 

 A ball projected upwards with the velocity of 10CO 

 feet per second, would, therefore, rise with a uni- 

 formly retarded motion to the height from which a 



