MECHANICS. 



I 



who is turning it, hi* force produce* the greatest effect; the 

 next greatest effect i* produced when it boa passed the highest 

 ind is being pressed downwards, but evidently the pressure 

 is now limited to his own weight. When the handle is being 

 poshed or pulled horizontally, still less is accomplished. If we 

 raise any weight by a winch, we shall easily feel those differences 

 in the strain. 



In some modes of applying force nearly all the muscles of the 

 body are set to work, and the strain is distributed, while in 

 only a few act, and hence fatigue soon follows. When a 

 boat if propelled by oars, the force exerted is applied very 

 advantageously ; nearly all the body helps, and the strain is in 

 the most favourable direction. When the foot is firmly planted 

 against the foot-board, the strong muscles of the back and 

 thi^h.s exert their force ; the hands, too, pull in a direction 

 at right angles with the oars. Hence we find that the 

 amount of work a man can accomplish this way is half as great 

 again as he can by turning a winch. 



The mode of employing human power by which the greatest 

 advantage is gained is by ascending a ladder, and then allowing 

 the weight of the body to act, and, by descending, raise a weight 

 nearly equal to itself. An interval of rest is gained in this way 

 while descending, and experience shows that more work can be 

 accomplished if frequent short intervals of rest are thus taken 

 between short periods of work. The body being specially 

 framed for walking, nearly all the force expended is effective. 



When a largo amount of heavy matter, such as building 

 material, or earth for an embankment, has to be raised to a 

 height, human power is sometimes thus applied : A bucket in 

 which a man can sit, or the material to be raised can be placed, 

 is fixed at each end of a rope, which passes over a pulley fixed a 

 little above the level to which the material has to be raised. The 

 length of the rope is so adjusted, that when one bucket is on the 

 ground, the other shall be at the required height. The lower 

 bucket is then loaded, and one or more men ascend a ladder or 

 incline and enter the upper one ; their weight causes it to 

 descend, and thus the material is raised. Nearly all the labour 

 is thus expended in raising themselves to the top of the ladder, 

 and while they are descending, and the material is being removed 

 from the upper bucket, they have an interval of rest. In the 

 treadmill the power is applied in a very similar way. This 

 consists essentially of a large and very broad wheel, with steps 

 fixed all round it ; the men hold on to a fixed bar, and attempt 

 to ascend the steps. The wheel, however, turns with their weight 

 aa fast as they ascend, and thus they do not raise themselves at 

 all ; but still the principle is the same, and nearly as much effect 

 is gained from the power in this way as in the former, the slight 

 difference arising mainly from the fact that the intervals of rest 

 are less frequent. 



In some quarries the mineral is raised in a similar way, by 

 men climbing on cross-pieces fixed through the rim of a very 

 largo wheel, round the axle of which the rope winds. This is 

 an example of the employment of the wheel and axle ; the 

 power, however, does not act at the circumference of the large 

 wheel, for the men are not on a level with the axle, but at a 

 radius which varies with the weight to be raised. 



To calculate the gain, we must imagine a vertical line to pass 

 through the centre of gravity of the men ; this line will meet the 

 spoke which is horizontal in some point, and the distance of this 



point from the centre is the radius at which the power really j have"a"movin'g force of 1,000 x 10 x 6, which is 60,000 foot- 

 acts. Hence, when the weight to bo raised is greater, the men poundg. But even in the best modes of employing this, there is 



a very great loss. 



Working a pile engine by hand . . 1,000,000 

 Throwing earth with a spade 



We now pass to the power of animal*, which i* much more 

 frequently applied than that of man it being found better to 

 employ man where skill and thought, and not mere mechanical 

 labour, are required ; hence skilled labour is alway* more highly 

 paid than unskilled. The animal most commonly employed in 

 this country is the horse, and Watt estimated the amount of 

 work it was capable of performing at 33,000 foot-pound* per 

 minute. This amount was accordingly adopted a* a unit of 

 measurement, and i* called a hone-power. Thus, when we speak 

 of a steam-engine of 12 hone-power, we mean one capable of 

 raising 12 times 33,000, which is 396,000 pound*, 1 foot high in 

 1 minute, or 1,000 pound* 396 feet, for each require* the same 

 amount of power. Though this unit of measurement i* still 

 retained, it is more than a horse can accomplish continuously, 

 and in practice its power is not found to be more than 22,000 

 units, or ] of the nominal amount. The power of a mule is about 

 | that of a horse, while that of an ass is only }. 



The most common way of employing animal power is in 

 drawing or carrying a load, and it i* clear that if this load be 

 increased, the speed with which it is carried must be diminished. 

 HI i c it is an important question to decide at what rate of 

 motion the greatest effect can be obtained, and the best way of 

 determining this is by experiment. There are two extreme 

 cases: the animal may sustain so heavy a load that it can 

 scarcely move ; or, on the other hand, it may travel very rapidly, 

 but without being able to carry any load at all. The greatest 

 effect is at some intermediate speed, and the weight that can be 

 carried varies inversely as the speed. The useful effect is the 

 product of the numbers which represent the speed and the load. 

 Thus, if a horse can carry 12 hundred- weight 6 miles an hour, 

 or 15 hundred- weight 5 miles an hour, the greatest advantage 

 is obtained by letting him take the heavier load, the useful 

 effect then being 15 x 5, or 75, while in the other case it is 

 12 x 6, or 72 only. 



Now, it is found by practical experience that the largest 

 amount of work is done by giving such a load that the animal 

 can travel about three miles an hour ; if the speed be increased 

 much beyond this, the weight must be diminished in a more 

 than equal proportion. 



The second prime mover is the force of water. Of this, how- 

 ever, we shall treat more fully when we pass on to Hydrostatics, 

 and need, therefore, say little now. We may have the force of a 

 running stream, or that of the ebb and flow of the tide. The 

 latter of these is a source of power very little used, but which 

 might often be well employed. Water has always a tendency to 

 obey the law of gravity and sink to the lowest point ; in doing 

 this it presses against or moves any obstacle that opposes its 

 motion, and this pressure may in many different ways be em- 

 ployed to drive machinery. The simplest mode of applying it 

 is seen in the common water-mill, where the stream presses 

 against the floats of the wheel, and thus turns it. 



We can calculate the force of a stream or waterfall by 

 measuring the distance through which the water falls, and 

 multiplying the weight of the water by this, we thus obtain the 

 number of units of work it is capable of effecting. If, for 

 instance, 1,000 gallons of water pass every minute, and the fall 



is 6 feet, then, since a gallon of water weighs 10 pound*, we 



are higher up on the wheel, and thus their weight acts at a I 



greater leverage. Animal power is sometimes applied in a 

 similar way, the animal being made to walk round the inside 

 of a large cylinder, and thus to turn it. 



The following table, which is the result of many experiments 

 and calculations by different scientific men, shows approxi- 

 mately the effect produced by human power when employed 

 in different ways, and gives us a good idea of their comparative 

 efficacy. The average duration of the labour may be reckoned 

 at eight hours per day. 



UNITS OP WORK DONE BY A MAN IN A DAT. 



Raising his own body .... 2,000,000 



Rowing a boat 1,900,000 



Working at a treadmill . . . 1,870,000 



Pushing or drawing a carriage . . 1 ,500,000 



Turning a winch , . . . . 1,250,000 



The remaining prime movers, the force of the wind, and the 

 expansive force of gases and vapours, must be considered in 



another lesson. 



ANSWERS TO EXAMPLES IN LESSON XVIII. 



1. The resultant is 15 pounds. 



2. The second force ia 8 pounds. 



3. Let B be the point at which the ropes A B and 

 B c act on the barge. Take B o and B B each to 

 represent 100. Complete the parallelogram and 

 join D B. Since D B B is 60, and D B and B x are 

 equal, the triangle ia equilateral, and therefore 

 D B is equal to 100, and o B to 50. Now B r is the 

 resultant of B o and B x, and B o ia eTidently 

 J B r. But B o 3 + o x 2 = B E*. that is = 10,000| 

 I or B = 100, and a x 3 = 2,500 ; B o 3 must, then, 



