MECHANICS. 



MECHANICS. XX. 



PRIME MOVERS: WIND AND STEAM-DYNAMICS. 

 TUB next of tho prime movora ia tho foroo of the wind. Heat 

 expand* all substances; hence, when any place is greatly heated 

 by the sun* a rayn, tho air over it expands and risoa, and cold 

 air from around ruHhoa in to fill ita place. Thin air in motion 

 in railed wind, and iiroduooa tho effects with which all aro 

 familiar. It acquires momentum aa it travels, and when any 

 ..l.MnicN it, presses against tho obstacle with a force pro- 

 portional t<> ita speed. This pressure produces tho greatest 

 effect when it ads in thti direction in which motion is required, 

 instance, when :i ship i* propelled by a stern wind. The 

 sails an .-preod as nearly as possible across the ship, and tho 

 full force of tho wind drives it onward. 



If the vanes of a windmill are arranged like tho float of a 

 paddle-wheel, so that tlio wind acts sideways on tho wheel, no 

 Heel will bo produced unless one-half of it is protected from 

 tho wind ; for its action on those floats which are uppermost 

 tends to turn the wheel one way with exactly the same force that 

 its action on tho lower ones does the other way. Even if the 

 lower half bo thus shielded the wind acts on those at tho side 

 very obliquely, and these keep it off from tho vertical ones. 

 Hence little effect can bo gained in this way, and tho vanes are 

 always arranged so as to make a small angle with the plane in 

 which they revolve, and it is found that most effect is produced 

 when different parts of the vane have a different inclination, 

 those nearest tho centre being inclined at a greater angle than 

 those more remote. 



Tho fourth, and in some respects the most important of the 

 prime movers, is the expansive force of gases and vapours. 

 Tho great advantage of this class is, that an almost unlimited 

 amount of power may always bo obtained, and that the cost is 

 much less. Wind and water power often fail, but a steam- 

 engine, which is tho most common example of this class of prime 

 movers, can work as well at one time as another. 



We cannot stop now to explain the details of tho construction 

 of an engine, but tho principle on which it acts is simply this : 

 When water is heated to 212, a portion of it is converted into 

 an invisible vapour called steam ; this occupies a space nearly 

 1 ,800 times as large as the water, and we have thus an expansive 

 force which is utilised and converted into any kind of motion 

 we may require. The usual plan of employing it is to procure a 

 large cylinder, with a piston capable of moving up and down in it; 

 tho pressure of tho steam is first caused to act below this piston, 

 which it drives to tho top of the cylinder ; by an arrangement 

 of tho valves the steam is then caused to act above instead of 

 below, and thus an alternating motion is produced from the pres- 

 sure, and this is, by means of a crank, changed into one of rotation. 



If wo have a piston with a surface of one square inch, the 

 evaporation of a cubic inch of water will raise it 1,800 inches, 

 or 150 feet. Now the pressure of the air on the piston is 15 

 pounds, and as this is overcome, tho work done is 15 pounds 

 raised 150 feet. This is 2,250 foot-pounds ; or, to put it in a 

 way more easy to remember, tho evaporation of a cubic inch of 

 water will produce force enough to raise a ton te a height of 1 foot. 



Now this force is not created ; something must be consumed 

 in order to produce it, and this something is the fuel employed. 

 A very important question, therefore, is to ascertain how much 

 work ought to be accomplished by a given quantity of fuel. Of 

 course this varies much with the construction of the furnace and 

 boiler, but it is reckoned that a pound of good coal will, when 

 employed in tho best way, evaporate about 240 cubic inches of 

 water, and therefore produce a force of about 540,000 foot-pounds. 



The explosive force of gunpowder and similar explosive com- 

 pounds come under this class of prime movers, though they are 

 sometimes set down to chemical agency. When they aro ignited 

 they set free a large amount of different gases, which occupy a 

 space many hundred times greater than that of tho substances 

 themselves, and this sudden liberation give* rise to the violent 

 effects we are accustomed to see produced by their employment. 

 EXAMPLES. 



1. How many units of work are required to raise CO gallons of water 

 to a height of 70 feet? 



2. What power moat an engine have to raise 20 tons of cool per 

 hour from a mine 400 feet deep ? 



3. From what depth will an engine of 6 horse-power raise 8 tons 

 per hour >. 



85 N.E. 



4. How much ooal will to consumed ia raising 5,000 cubic fort of 

 water from a depth of 90 feet, a cubic foot of water weighing 2| 

 pounds? 



5. How long will it take a man to raise 50 tons of material to > 

 height of 60 feet bjr a windlass ; sad how long by Mf^pg a ladder 

 and letting his own weight raise it ? 



DYNAMICS THE THBKB LAWS OF MOTIOK. 



We have now to paaa on to the second and more difficult part 

 of Mechanics. Hitherto we hare had to deal with forces which 

 acted on a body and produced equilibrium. If any of these fo 

 bo now altered or modified in any way, BO that one or 

 remain unbalanced, aome motion will take place, and the nature 

 of this motion will, of coarse, depend upon the force*. It u the 

 object of dynamics to inquire what these motions will be, Mid 

 what are tho laws that govern them ; and though at first they 

 may appear comparatively unimportant, we shall find aa we 

 advance that an acquaintance with them ia of groat practical 

 use for many purposes. 



The investigation of the action of the earth's attraction, of the 

 motion of bodies projected with any given velocity, and of many 

 other common things, depends on the principles of dynamics, and 

 the laws wo discover by examining these are found to apply on 

 an infinitely more grand and glorious scale in nature, for by 

 their action all the stars and planets are kept in their orbits 

 and made to perform their varied revolutions. By these laws 

 astronomers can not only explain and account for their varying 

 distances and motions, but can foretell with the utmost accuracy 

 eclipses and other phenomena of the heavenly bodies. 



There is one important difference between statics and 

 dynamics, and that is, that the latter is one of the inductive 

 sciences, though perhaps the simplest of them. Some sciences, 

 like arithmetic and geometry, are called deductive, their 

 principles being deducible from abstract truths without re- 

 ference to experiment, thongh that is sometimes resorted to 

 as a corroborative evidence or a simpler mode of proving their 

 truth. To this class statics belongs, for all its fundamental 

 truths can bo mathematically proved. Not so with dynamics, 

 many of the truths of which can only be ascertained by experi- 

 ment, and in order to ensure accuracy in these experiments they 

 must be repeated again and again, for slight errors are likely 

 to creep in, and it is only by taking the average of many 

 different experiments that we can arrive at accurate results. 

 Many, however, of its principles can be ascertained by deduc- 

 tion, and it thus approaches much more nearly to the deductive 

 sciences than the other branches of natural philosophy, 



As previously stated, we have in dynamics to introduce a 

 fresh idea, that of time. In statics force was considered only 

 as producing pressure, and therefore this element did not enter 

 into our calculations ; but it is clear that, in treating of motion, 

 the time occupied is an important thing to consider. 



It is needful at starting that we should have some mode of 

 measuring tho degree and intensity of motion, that is, the 

 velocity of any body, and, as we saw, two quantities are needed 

 to determine this the space passed over, and tho time occupied 

 in passing over it. Wo may know that a force applied to a 

 body causes it to move over a certain space, but to form a 

 correct idea of the force, we must also know how long it takes 

 to travel this distance. When we speak of a speed of 12 miles 

 an hour, we mean that if the motion continued uniform through 

 that space of time the body would have travelled 12 miles. It 

 does not, however, imply that the body actually passes over 

 12 miles, but merely that it moves with that degree of speed. 

 Great inconvenience often results from thus requiring two 

 numbers to represent a velocity, and hence it is usual to ex- 

 press it by the number of feet passed over in one second. If 

 a body moves a mile in 8 minutes, it passes over a furlong, or 

 660 feet, in one minute, and therefore over 1 1 feet in one second, 

 and it is said to have a velocity of 11. When, therefore, we 

 represent a velocity by a number, it is always to be understood 

 as tho number of feet passed over by the body in one second. 



The motion of any body may be either uniform or variable. 

 It is uniform when equal spaces are always passed over in equal 

 times, and its velocity is then measured by the number of feet 

 actually passed over in a second. When this number is not 

 constant, the motion is variable, and the velocity at any point 

 of time is measured by the space it would pass over in one 

 second if it continued during the whole second to move at tho 

 same rate as at the given moment. A variable motion may bo 



