FARM IMPLEMENTS AND FARM MACHINERY, AND THE f Principles of their Construction and Use "WITH SIMPLE AND PRACTICAL EXPLANATIONS OF THE H.ATVS OF MOTION -AJSTD FORCE AS APPLIED ON THE FARM. ^Vith. 887 Illustrations. BY JOHN J. THOMAS. n NEW YORK: ORANGE JUDD AND COMPANY, 245 BROADWAY, Entered according to Act of Congress, in the year 1S69, by JOHN J. THOMAS, In the Clerk's Office of the District Court of the United States for the Southern District of New York. .^ ^iK^ PREFACE. A small treatise, — the basis of the present work, — was originally published in the Transactions of the New York State Agricultural Society for T850, under the title of "Agricultural Dynamics," or the Science of Farm Forces. A revised and greatly enlarged edition, adapted to general use, was afterwards issued in book form, with the name of " Farm Implements." Since the appearance of the earlier editions, great and rapid improvements have been made in farm machinery of nearly every kind ; and the aim of the work in its present form is to supply, so far as its limits will admit, the information eagerly sought by cultivators in relation to all that has proved of value. Another principal object has been to present in a simple and intelligible manner, the leading principles of Mechan- ical Science, applied directly in the farmer's daily routine, — that he may know the reasons of success and failure, and not be guided by random guessing. The first portion of the book is chiefly devoted to a practical explanation of these principles. Union Springs, N. Y., 1869. CONTENTS. PART L— MECHANICS. CHAPTER I. Introduction. — Value of Farm Machinery — Importance of a Knowledge of Mechanical Principles 7-10 CHAPTER II. General Principles of Mechanics. — Inertia, Experiments and Examples — Inertia of Moving Bodies, or Momentum — East Riding — The Tiger's Leap — Pile Engines— Fly-wheel— Esti- mating the Quantity of Momentum — Compound Motion — Various Examples — Centrifugal Force 10-22 CHAPTER III. Attraction. — Gravitation — Velocity of Falling Bodies — Resist- ance of the Air — Coin and Feather — Galileo's Famous Experi- ment — Cohesion — Soils — Strength of Materials — Capillary Attraction— The Earth a Desert without it— The Ascent of Sap — Centre of Gravity — Experiments — Upsetting Loads — Shouldering Bags— Rocking Bodies 22-42 CHAPTER IV. Simple Machines, or Mechanical Powers.— Law of Virtual Velocities — The Lever — Many Examples of Levers — Esti- mating the Power of Levers — Three-horse Wbiffle-tree — Compound Levers — Weighing Machines — Stump Pullers — A Wild Theory — Wheel and Axle— Examples — Band and Cog-work — The Pulley — Packer's Stone Lifter — The Inclin- ed Plane— Crooked Roads — Power of Locomotives — Good and Bad Roads — The Wedge — The Screw — Knee-joint Pow- er — Lever Washing Machine — Cheese Presses — Rolling Mills —Straw Cutters 42-74 CHAPTER V. Application of Mechanical Principles in the Structure of Implements and Machines — Various Examples — Calculating the Strength of Parts 75-81 CHAPTER VI. Friction. — How to ascertain its Amount — Friction on Roads — Resistance of Mud — The Results of the Dynamometer — Width of Wheels — Velocity — Size of Wheels on Roads — Friction Wheels — Lubricating Substances — Friction neces- sary to Existence 81-93 CHAPTER VII. Principles of Draught— Applied to Wagons— To Plows— Comr bined Draught of Animals — Whiffle-trees for Three Horses^ 4 CONTENTS. V Potter's do. — Wier's Single-tree— The Dynamometer— Self- registering do. — Waterman's do. — Dynamometer for Rotary Motion 93-108 CHAPTER VIII. Application of Labor. — Power of Horses — Of Men — Best Way to Apply Strength 108-113 CHAPTER IX. Models op Machines. — Common Blunders— Works of Creation Free from Mistakes 113-115 CHAPTER X. Construction and Use op Farm Implements and Machines — Implements of Tillage. — Importance of Simplicity — Plows — Rude Specimens — Cast-iron and Steel do. — Charac- ter of a Good Plow — The Cutting Edge— Mould- board- Easy Running Plows — Crested Furrow Slices— Lapping and Flat Furrows— How to Plow Well— Fast and Slow Plowing — The Double Michigan— The Subsoil Plow— The Paring Plow— Gang Plow— Ditching Plow— Mole Plow— Coulters — Weed Hook and Chain— Pulverizers— Harrows— Ged- des' Harrows — Scotch do. — Morgan Harrow — Norwegian do.— Shares' do.— Cultivators— Holbrook's— Alden's— Gar- rett's Horse-hoe— Two-horse Cultivators— Sulky do.— Coin- stock's Spader— Clod Crushers— Roller 115-152 CHAPTER XI. Sowing Machines— Wheat Drills— Bickford and Huffman's do. — Seymour's Broadcast Sower— Corn Plauters — True's Po- tato Planter— Hand Drills 152-157 CHAPTER XII. Machines for Haying and Harvesting. — Mowing and Reap- ing Machines — Cutter-bar — Combined Machines — Self Rakers— Johnson's do. — Marsh's and Kirby's do. — Dropper — Binders — Marsh's Harvester — Durability and Selection of Machines— Hay Tedders— Bullard's do. — American do. — Horse Rakes— Revolving do.— Sulky Revolvers— Warner's do. — Spring Tooth Rakes — Hollingsworth's do. — Hay Sweep— Horse Forks— Gladding's do.— Palmer's, Myers' Beardsley's, Raymond's — Harpoon Forks — Hay Carriers — Hicks' do.— Building Stacks— Palmer's Hay Stacker— Ray- mond's Hay Stacker— Dcderick's Hay Press— Beater do. — Hay Loaders 158-186 CHAPTER XIII. Thrashing, Grinding, and Preparing Products. — Value of Thrashing Machines — Endless Chain Power — How to Measure Power of— Churning by Tread Power— Pitt's Ele- VI CONTENTS. vator — Corn Shellers — Burralls', Richards' — Root Washer — Root Slicers — Farm Mills, Allen's, Forsman's — Emery Cotton Gin 186-197 PART II— MACHINERY IN CONNECTION WITH WATER. CHAPTER I. Hydrostatics. — Upward Pressure — Measuring Pressure — Cal- culating Strength of Tubes, etc. — Artesian Wells — Determ- ining Pressure in Vessels — A Puzzle Explained — Hydro- static Bellows— Press — Specific Gravities — Table of do. — Weigbt and Bulk of a Ton of Different Substances 198-210 CHAPTER II. Hydraulics. — Velocity of Water — Discharge of Water through Pipes — Velocity in Ditches — Leveling Ditches — Archime- dean Screw-pumps — For Cisterns — Non-freezing do. — For Deep Wells — Drive Pumps — Chain Pumps — Rotary do. — Suction and Forcing Pump — Turbine Water Wheels — The Water Ram — Water Engines for Gardens — Flash Wheel — Nature of Waves — Size of do. — Preventing Inroads by do. — Cisterns — To Determine Contents of 211-238 PART III.— MACHINERY IN CONNECTION WITH AIR. CHAPTER I. Pressure of Air. — Weigbt of the Atmosphere — Hand Fastened by Air — Barometer — Measuring Heights — Syphon 239-245 CHAPTER II. Motion of Air. — Wiuds — Wind-mills, how Used — Brown's do. — Causes of Wind — Chimney Currents — Construction of Chimneys — To Cure Smoky do. — Chimney Caps — Ventila- tion 245-259 PART IV.— HEAT. CHAPTER I. Conducting Power — Expansion, Great Force of— Experiments with — Steam Engine — do., for Farms — Steam Plows — Latent Heat— Green and Dry Wood 260-276 CHAPTER II. Radiation. — Several Examples in Domestic Economy — Dew and Frost— Frost in Valleys— Sites for Fruit Orchards 276-280 APPENDIX. Apparatus for Experiments 281-283 Discharge of Water through Pipes 284 Velocity of Water in Pipes 284 Rule for Discharge of Water 285-286 Velocity of Water in Tile Drains 286 Glossary 287-296 FARM IMPLEMENTS AND FARM MACHINERY. PART I. MECHANICS. CHAPTER I. INTRODUCTION. No farm can be well furnished without a large number of machines and implements. Scarcely any labor is per- formed without their assistance, from the simple opera- tions of hoeing and spading, to the more complex work of turning the sod and driving the thrashing-machine. The more perfect this machinery, and the better fitted to its work, the greater will be the gain derived by the farm- er from its use. It becomes, therefore, a matter of vital importance to be able to construct the best, or to select the best already constructed, and to apply the forces re- quired for the use of such machines to the greatest possi- ble advantage. 8 MECHANICS. Nothing shows the advancement of modern agriculture in a more striking light than the rapid improvement in farm implements. It has enabled the farmer within the last fifty years to effect several times the work with an equal force of horses and men. Plows turn up the soil deeper, more evenly and perfectly, and with greater ease of draught; hoes and spades have become lighter and more efficient ; grain, instead of being beaten out by the slow and laborious work of the flail, is now showered in torrents from the thrashing-machine ; horse-rakes accom- plish singly the work of many men using the old hand- rake ; horse-forks convey hay to the barn or stack with ease and rapidity ; twelve acres of ripe grain are neatly cut in one day with a two-horse reaper ; grain drills and planting machines, avoiding the tiresome drudgery of hand labor, distribute the seed for the future crop with even- ness and precision. The owner of a seventy-thousand-acre farm in Illinois carries on nearly all his work by labor-saving machinery. He drives posts by horse-power ; breaks his ground with Comstock's rotary spader ; mows, rakes, loads, unloads, and stacks his hay by horse-power ; cultivates his corn with two-horse, seated or sulky cultivators ; ditches low ground, sows and plants by machinery ; so that his labor- ers ride in the performance of their tasks without exhaust- ing their strength with needless walking over extended fields. The great value of improved farm machinery to the country at large has been lately proved by the introduc- tion of the reaper. Careful estimate determined that the number of reaping machines introduced throughout the country up to the beginning of the great rebellion, per- formed an amount of labor while working in harvest nearly equal to a million of men with hand implements. The reaper thus filled the void caused by the demand on workingmen for the army. An earlier occurrence of that VALUE OF FARM MACHINERY. 9 war must therefore have resulted in the general ruin of the grain interest, and prevented the annual shipment of the millions during that gigantic contest, which so greatly surprised the commercial savans of Europe. The implements and machines which every farmer must have who does his work well are numerous and often costly. A farm of one hundred acres requires the aid of nearly all the following; two or more good plows, a shovel-plow, a small plow, a subsoiler, a single and two- horse cultivator, a seed-planter, a grain-drill, a roller, a harrow, a fanning-mill, a straw-cutter, a root-slicer, a farm wagon with hay-rack, an ox-cart, a horse-cart, wheel-bar- row, sled, shovels, spades, hoes, hay-forks and manure- forks, hand-rakes and horse-rakes, scythes and grain- cradle, grain-shovel, maul and wedges, pick, axes, wood- saw, hay-knife, apple-ladders, and many other smaller con- veniences. The capital for furnishing the farms in the Union has been computed to amount to more than five hundred millions of dollars, and as much more is estimat- ed to be yearly paid for the labor of men and horses throughout the country at large. To increase the effect- ive force of labor only one-fifth would, therefore, add an- nually one hundred millions in the aggregate to the profits of farming. A knowledge of the science of mechanics is not so well understood among all classes of people as it should be. A loss often occurs from the want of a correct knowledge of mechanical principles. The strength of laborers is badly applied by the use of unsuitable tools, and that of teams is partly lost by being ill adjusted to the best line of draught. We may perhaps see but few instances of so great a blunder as the ignorant teamster committed who fastened his smaller horse to the shorter end of the whiffle-tree, to balance the large horse at the longer end ; yet instances are not uncommon where operations are per- formed to almost as great a disadvantage, and which, to 1* 10 ■ MECHANICS. a person well versed in the science of mechanics, would appear nearly as absurd. It is well worth while to look at the achievements made through a knowledge of mechanical principles. Compare the condition of barbarous and savage tribes with that of modern civilized nations. The former, scattered in com- fortless hovels, subsist by precarious hunting, or on scanty crops raised on patches of ground by means of the rudest tools. The latter are blessed with smooth, cultivated fields, green meadows, and golden harvests. Commerce with its hum of business, extending through populous cities, and along a hundred far-stretching lines of rail-ways, scat- ters comforts and luxuries to millions of homes ; while ships for foreign commerce thread every channel and whiten every sea. The contrast exhibits the difference between ignorance on the one hand, and the successful application of scientific principles on the other. It is our present object to point out to the farmer the advantages which would result from a wide extension, through all classes, of this knowledge, that the opportunities may be continually increased for general improvement. CHAPTER II. GENERAL PRINCIPLES OF MECHANICS. Having briefly pointed out some of the advantages to the farmer of understanding the principles of the ma- chines he constantly uses, we now proceed to an examina- tion of these principles. It will be most convenient to begin with the simpler truths of the science, proceeding, as we advance, to their application in the construction of machines. INERTIA. — EXPERIMENTS AND EXAMPLES. 11 rNERTIA. An important quality of all material bodies is inertia. This term expresses their passive state — that is, that no body (not having life), when at rest, can move itself, nor, when in motion, can stop itself. A stone has not power to commence rolling of its own accord ; a carriage can not travel on the road without being drawn ; a train of cars never commences gliding upon the rails without the power of the locomotive. On the contrary, a body, when once set in motion, will continue in motion perpetually, unless stopped by some- thing else. A cannon ball rolled upon the ground moves on until its force is gradually overcome by the resistance of the rough earth. If a polished metallic globe were driven swiftly on a level and polished metallic plane, it would Fig. i. continue in motion a long time and travel to a great distance ; but still the extremely minute roughness of the surfaces, with the resistance of the air, would continually diminish its speed until finally stopped. A wheel made to spin on its axis revolves un- til the friction at the axis and the impeding force of the air bring it to rest. But if the air is first removed, Fans revolving in a vacuum. Dv means of an air-pump, the mo- tion will continue much longer. Under a glass receiver, thus exhausted, a top has been made to spin for hours, and a pendulum to vibrate for a day. The resistance of the air may be easily perceived by first striking the edge and then the broad side of a large piece of pasteboard against the air of a room. It is further shown by means of an interesting experiment with the air-pump. Two fan-wheels, made of sheet tin, one, a, striking the air with its edges, and the other, b, with its broad faces (fig. 12 MECHANICS. 1), are set in motion alike; b is soon brought to rest, while a continues revolving a long time. If now they are placed under the receiver of an air-pump, the air exhaust- ed, and motion given to them alike by the rack-work c?, they will both continue in motion during the same period. There is no machinery made by man free from the checking influence of friction and the air; and for this reason, no artificial means have ever devised a perpetual motion by mechanical force. But we are not without a proof that motion will continue without ceasing when nothing operates against it. The revolutions of the planets in their orbits furnish a sublime instance ; where removed from all obstructions, these vast globes wheel around in their immense orbits, through successive centuries, and with unerring regularity, preserving undiminished the mighty force given them when first launched into the re- gions of space. To set any body in motion, a force is requisite, and the heavier the body, the greater must be the force. A small stone is more easily thrown by the hand than a cannon ball ; speed is more readily given to a skiff than to a large and heavy vessel ; but the same force which sets a body in motion is re- >C quired to stop it. Thus a wheel or a grindstone, made to revolve rapidly, would need as great an effort of the arm to stop it suddenly as to give it u ' sudden motion. An unusual exertion Inertia Apparatus. of the team is necessary in starting a loaded wagon; but when once on its way, it would require the same effort of the horses to stop it as to back it when at rest. The force of inertia is finely exhibited by means of a little instrument called the inertia apparatus (fig. 2). A marble or small ball is placed on a card, c, resting on a concave stand. A spring snap is then made to strike the INERTIA. — EXPERIMENTS AND EXAMPLES. 13 Fig. 3. card, throwing it to a distance, but leaving the ball upon the hollow end of the stand. The same experiment may- be easily performed by placing a very small apple or other solid on a card, the whole resting on a common sand-box, or even the hollow of the hand. A sud- den snap with the finger will throw the card away, while the apple will drop into^ the cavity. The following experiment is still more striking : Procure a thread just strong enough to bear three pounds, and hang upon it a weight of two pounds and a half. Another half pound would break it. Now tie another thread, strong enough to bear one pound, to the lower hook of the weight. If the lower thread be pulled gradually, the upper thread will of course break ; but if it be pulled with a jerk, the lower thread will break. If the jerk be very sudden, the lower string will break, even it be considerably stronger than the upper, the in- ertia of the weight requiring a great force to overcome it suddenly. The threads used in this experiment may be easily had. of any desired strength by taking the finest sewing cotton, and doubling to any desired extent. This experiment shows the reason why a horse, when he suddenly starts with a loaded wagon, is in danger of breaking the harness ; and why a heavier weight may be lifted with a windlass or pulley having a weak rope, if the strain is gradual and not sudden. For the same reason, glass vessels full of water are sometimes broken when hastily lifted by the handle. When a bullet is fired through a pane of glass, the inertia retains the surrounding glass in its place during the moment the ball is passing, and a round hole only is made; while a body moving more slowly, and pressing the glass for a longer space of time, fractures the whole pane. 14 MECHANICS. INERTIA OF MOVING BODIES, OR MOMENTUM. Momentum is the inertia of a moving body. When a force is applied to a heavy body, its motion is at first slow ; but the little momentum it thus acquires, added to the ap- plied force, increases the velocity. This increase of velocity is of course attended with increased momentum, which again, added to the acting force, still further quickens the speed. For this reason, when a steam-boat leaves the pier, and its paddle-wheels commence tearing through the wa- ter, the motion, at first slow, is constantly accelerated un- til the increasing resistance of the water becomes equal to the strength of the engine and the momentum.* Were it not for the momentum of moving bodies (inertia exist- ing), no speed ever could be given to any heavy body, as a carriage, boat, or train of cars. The chief danger in fast riding, or fast traveling of any kind, is from the momentum given to the traveler. If a rail-way passenger should step from a car when in full mo- tion, he would strike the earth with the same velocity as that of the train ; or if the train at thirty miles an hour should be instantly stopped, the passengers would be pitched forward with a swiftness equal to thirty miles an hour. When a horse suddenly stops, the momentum of the rider tends to throw him over the horse's head. When a wagon strikes an obstruction, the driver falls forward. A case in court was once decided against the plaintiff, who claimed that the defendant had driven against his wa^on with such force as to throw the plaintiff to a great distance; but the fact was shown that by such momentum he him- self must have been driving furiously, and not the defend- ant, and he lost his suit. * In ordinary practice, this is not strictly correct, as friction will make some difference. This influence will be more particularly considered on a subsequent page. Its omission here does not at all alter the principle under consideration. MOMENTUM. EXAMPLES. 15 An Eastern traveler once succeeded in saving his life by a ready knowledge of this principle. He was closely pur- sued by a tiger, and when near a precipice, watching his opportunity, he threw his coat and hat on a bush, and jumped one side, when the animal, leaping swift- ly on the concealed bush, was car- ried by momentum over the prec- ipice. As a large or heavy body pos- sesses greater momentum than a small or light one, so any body moving with great speed possesses more than one moving slowly ; for instance, the momentum of a rifle ball is so great as to carry it through a thick plank, while, if thrown slow- ly, it would scarcely indent it. This property of bodies is applied with great advantage to many practical purposes. The momentum of the hammer drives the nail into the wood; for the mere pressure of its weight would not do it, if it were a hundred times as heavy. Wedges are driven by employing the same kind of power. On a larger scale, the pile-engine operates in a similar manner. The ram or weight, h (fig. 4), is slowly lifted by means of a pulley and wheel-work, worked by the handles or cranks, b b, until the arms of the tongs which hold the ram are compressed in the cheeks, % i, when it suddenly falls with prodigious force on the pile or post to be driven. , In this Avay long posts of great size are forced into the mud of swamps and Pile Engine. 10 MECHANICS. Fie. 5. river bottoms, "where other means would fail. When a steam-engine is used for lifting the ram, the work is more rapidly performed. An interesting example of the use and efficiency of momentum is furnished by the water-ram, a machine for raising water, described on a subsequent page. The fly-wheel, a large and heavy wheel used to regulate the motion of machinery, derives its value from the power of inertia, or momentum, which prevents the machine from stopping suddenly when it meets with any unusual obstruction. In the common thrashing-machine, it has been found that a heavy cylinder, by acting as a fly-wheel, renders the motion steadier, and less liable to become im- peded by large sheaves of grain. An ignorance of this principle has sometimes proved a serious inconvenience. A farmer, having occasion to raise a large quantity of water, erected a horse-pump ; but at every stroke of the pump the animal was sud- denly thrown loosely for- ward, and again jerked back- ward, as the piston fell light- ly and rose heavily. A fly- wheel attached to the ma- chinery would have prevent- ed this unpleasant jerking, and have enabled the horse, straw-cutter with fly-xckcci. ^ conge quence, to accom- plish more work. In the pile-driving engine, where a great weight is suddenly thrown loose from a height, the horses would be pitched forward when suddenly relieved of this load but for the regulation of a fly-wheel, the motion of which is not quickly changed, neither from fast to slow nor from slow to fast. Where there is a rapid succession of forces required in practice, the fly-wheel is usually of great advantage. Hence its use in all revolving straw-cutters, where the INERTIA. THE FLY-WHEEL. 17 knives make quickly-repeated strokes (fig. 5). More re- cently it has been applied to the dasher-churn (fig. 6), where the rapid upright strokes are so well known to be very fatiguing for the amount of force applied. By thus regulating motion, the fly-wheel frequently enables an irregular force to accomplish work which other- wise it could not perform. Thus a man may exert a force equal to raising a hundred pounds, Fig. 6. yet, when he turns a crank, there is one part of the revolution where he works to great disadvantage, and where his utmost force will not balance forty pounds. Hence, if the work is heavy, he may not be able to turn the crank, nor to do any work at all. If, however, a fly-wheel be applied, by gather- ing force at the most favorable part of the turning, it carries the crank through the other part. An error is sometimes commit- ted by supposing the fly-wheel actually creates power, for as much force is required to give it momentum as it afterward imparts to the machine ; it consequently only accumulates and regulates power. On rough roads, the force of inertia causes a severe strain to a loaded wagon when it strikes a stone. The horses are chafed, the wagon and harness endangered, and the load jarred from its place. This inconvenience is avoided in part by placing the box upon springs, which, by yielding to the blow, gradually lessen the effects of the shock. For carts and slowly moving lumber-wagons springs are useful, but more so as the velocity and momentum increase. Even on so smooth a surface as a rail-road, it was found by experiments made some years ago, that when the machinery of a locomotive was placed Churn with a fly-wheel, for equal* izinff the motion. 18 MECHANICS. upon springs, it would endure the wear and tear of use four times as long as without them. For this reason, a ton of stone, brick, or of sand, is harder for a team than a ton of wool or hay, which possesses con- siderable elasticity. ESTIMATING THE QUANTITY OE MOMENTUM. The quantity of momentum is estimated by the velocity and weight of the body taken together. Thus a ball of two pounds weight moves with twice the force of a one- pound ball, the speed being equal ; a ten-pound ball with ten times the force, and so on. A body moving at the rate of two feet per second possesses twice the momentum of another of equal size with a velocity of only one foot per second. A musket ball, weighing one ounce, flying with fifty times the speed of a cannon ball, weighing fifty ounces, would strike any object with equal force ; or, if they should meet each other from opposite directions, the momentum of both would be mutually destroyed, and they would drop to the earth. Where the mass is very great, even if the motion is slow, the momentum is enormous. A large ship floating near a pier wall may approach it with so small a velocity as to be scarcely perceptible, and yet the force would be enough to crush a small boat. When great weight and speed are combined, as in a rail-way locomotive, the force is almost irresistible. This circumstance often insures the safety of the passengers ; for as nothing is capable of instantly overcoming so powerful a momentum, when accidents occur the speed is more gradually slackened, and the passengers are not pitched suddenly forward. A light wagon, rapidly driven, possessing but little compara- tive force, is more suddenly arrested, and the danger is greater. When two bodies meet from opposite directions, each COMPOUND MOTION. 19 sustains a shock equal to the united forces of both. Two men accidentally coming in contact, even if walking moderately, receive each a severe blow ; that is, if each were walking three miles an hour, the shock would be the same as if one at rest were struck by the other with a velocity of six miles an hour. This principle accounts for the destructive effects of two ships running foul of each other at sea, or of the collision of two opposite trains on a rail-road. The preceding principles show that a sledge, maul, or axe will always strike more effective blows when made heavier, if not rendered unwieldy. COMPOUND MOTION. It often happens that two or more forces act on the same body at the same time. If they all act in the same direction, the effect will be equal to the sum of the forces taken together ; but if they act in opposite directions, the forces will tend to destroy each other. If two equal forces act in contrary directions, they will be completely neutralized, and no motion will be produced. Thus, as an example of these forces — a bird flying at the rate of forty miles an hour, with a wind blowing forty miles an hour, will be driven onward by these two combined forces eighty miles an hour ; but if it undertake to fly against such a wind, it will not advance at all, but remain station- ary. A similar result will take place if a steam-boat, having a speed of ten miles an hour, should first run down a river with a current of equal volocity, and then upward against the current ; in the first case it would move twenty miles an hour, and in the latter it would not move at all. Where forces act neither in the same nor in opposite directions, but obliquely, the result is found in the follow- 20 MECHANICS. ing manner: If a ball, placed at the point a (fig. 7), be struck by two different forces at the same moment, in the Fi(r 7 direction shown by the two ar- rows, and if one force be just suf- ficient to carry it from a to c, and the other to carry it from a to b, then it will move inter- mediate between the two, in the direction of the diagonal of the parallelogram a d, and to a dis- tance just equal to the length of this diagonal or cross- diameter. "When the forces act very nearly together, the parallelo- gram of the forces will be very narrow aud quite long, with a long diagonal Fig. 8. (fig. 8) ; but if they act on nearly opposite sides of the ball, they will very nearly neutralize each other, and the diagonal or re- sult will be very short, showing that the motion given to the ball will be very small (fig. 9). These examples show the importance of having teams attached to a plow or to a wagon very nearly in a straight line with the draught, or else a part of the force will be Fig. 9. lost ; and also the impor- -^fi tance, when several animals are drawing together, of their working as nearly as possible in the same straight line. For, the more such forces deviate from a right line, the more they will tend to destroy or neutralize each other. A familiar example of the result of two oblique forces is furnished when a boat is rowed across a river. If the river has no current, the boat will pass directly from bank to bank perpendicularly ; but if there is a current, its track will form a diagonal, and it will strike the opposite bank CENTRIFUGAL FORCE. 21 lower down, according to the rapidity of the stream and the slowness of the boat. Another instance is afforded when a ferry-boat is anchored, by means of a long rope, to a point some dis- tance above (fig. 10) ; the boat, being turned obliquely, will pass from one bank to the other by the force of the current. Here the water tends to carry the boat down- Fig. 10. ward, while the force of the rope acts upward ; the boat passes be- tween the two from bank to bank. The ascent of a kite is precisely similar, the wind and the string being counteracting forces. When a vessel sails under a side wind, the resistance of the keel against the water, and the force of the wind against the sail, act in different directions, and produce a motion of the vessel between them. CENTRIFUGAL FORCE. All bodies, when in motion, have a tendency to move forward in a straight line. A stone thrown into the air is gradually bent from this straight course into a curve by the attraction of the earth. When a ball is shot from a gun, the force being greater, it flies in a longer and straighter curve. A familiar example also occurs, while driving a wagon rapidly, in attempting to turn suddenly to the right or left ; the tendency of the load to move straight on will sometimes cause its overthrow. An observance of this principle would prevent the error which some commit by making sharp turns or angles in ditches and water-courses ; the onward tendency of the water drives it against the bank, checks its course, and wears away the earth. By giving the ditch a curve, the water 22 MECHANICS. is but slightly impeded, and a much larger quantity will escape through a channel of any given size. When a grindstone is turned rapidly, the water upon its surface is thrown off by this tendency to move in straight lines. In the same way, a weight fastened to a cord, whirled by the hand, will keep the cord stretched during the revolution. A cup of water, attached to a cord, may be swung over the head without spilling, the water being held by centrifugal force. The same principle causes a stone, when it leaves a sling, to fly off in a line. This tendency to fly off from a revolving centre is called centrifugal force — the word centrifugal meaning flying from the centre. Large grindstones, driven with great velocity by machinery, are sometimes sj>lit asunder by centrifugal force. The most sublime examples of this force occur in the motion of the earth and planets, which will be more fully explained in a future page. CHAPTER in. ATTRACTION. GRAVITATION. The earth, as is well known, is a mass of matter in the form of a globe, the diameter being upward of 7900 miles. From its enormous size and the small portion seen from one point, the surface appears flat, except where broken into mountains and valleys. The tendency which all bodies possess of falling toward the earth is owing to the attractive force which this great mass of matter exerts upon them. This kind of attrac- GRAVITATION". VELOCITY OF FALLING BODIES. 23 tion is called gravitation. The force with which a body- is thus drawn is the iceight of that body. When a stone is dropped from the hand, its velocity is at first slow, but continues to increase till it strikes the earth ; hence, the further it falls the harder it will strike. This accelerated motion is precisely similar to that of a steam-boat when it first leaves the wharf; the force of gravity may be compared to the driving power of the engine, and the quickened velocity of the falling stone to the increased headway of the boat. All bodies, whether large or small, fall equally fast, un- less they are so light as to be borne up in part by the resistance of the air. In the first second of time they fall 16 feet; in the second, 3 times 16, or 48 feet ; in the third second, 5 times 16, or 80 feet, and so on. Or, if the whole distance fallen be taken together, they fall 16 feet in one second, 4 times 16 in two seconds, 9 times 16 in three seconds, and so forth. In other words, the whole distance is equal to the square of the time. This is plainly ex- hibited iu the following table : Seconds, from beginning to fall. 1 2 3 4 5 6 Whole height fallen in feet. 16 4X16 or64. 9X16 or 144. 16X16 or 256. 7X16 or 112. 25X16 or 400. 36X16 or 576. Space fallen in each sec- ond in feet. 16 3X16 or 48. 5X16 or 80. 9X16 or 144. 11X16 or 176. A stone or other body will fall 1 foot in a fourth of a second, 3 feet the next fourth, 5 feet the third fourth, and 7 feet the last fourth ; which is the same as 4 feet in half a second, 9 feet in three-fourths of a second, and 16 feet for the whole second. The depth of an empty well, or the height of a preci- pice, may be nearly ascertained by observing the time required for the fall of a stone to the bottom. The time may be measured by a stop-watch, or, in its absence, a pendulum may be made by fastening a pebble to a cord, which will swine: from the hand in regular vibrations of 24 MECHANICS. an exact second each if the cord be 39J inches long, or of half a second each if it be about 9f inches long. The velocity increases simply as the time, that is, the speed in falling is twice as great in two seconds as in one ; three times as great in three seconds ; four times as great in four seconds, and so forth. A stone will fall four times as far in two as in one second, while its velocity will be doubled ; nine times as far in three seconds, while its velocity will be tripled, etc. If a stone is thrown upward, its motion continues gradually to decrease, at the same rate as it increases in falling ; hence the same time is required to reach its highest point, as to fall from that point back to the earth. Therefore the velocity with which it is first projected up- ward is equal to the velocity which it attains at the moment of striking the ground. There is an exception, however, to this general rule. In a vacuum it would be perfectly correct, but in ordinary practice the resistance of the air tends to diminish the velocity while ascending, and still further to retard it while descending. For this reason, it will fall with less speed than it first arose. For heavy bodies and small distances, this exception would be imperceptible ; but with small bodies falling from great heights, the difference will be considerable. The velocity of a stone after falling one second, or six- teen feet, is at the rate of thirty-two feet per second; hence, if thrown upward at that rate, it will rise just six- teen feet high. After falling three seconds, the rate is ninety-six feet ; and hence, if projected upward at ninety- six feet per second, it will rise nine times sixteen feet, or one hundred and forty-four feet high. And so of other heights. Were it not for the resistance of the air, a feather would fall as swiftly as a leaden ball. This is conclusively shown by an interesting experiment. A tall glass jar (fig. 11), open at the bottom, is covered with a brass cap, fitting it TELOCITY OF FALLING BODIES. 25 Fig. 11. air-tight. Through this cap passes an air-tight wire, which, by turning, opens a small pair of pincers. Within these are placed a feather and a half dollar, and the air is then thoroughly drawn from the receiver by means of an air- pump. The wire is turned, and the feather and coin both drop at once, and strike the bottom at the same moment. There are many examples showing the accelerated motion and increased force of falling bodies. When a large stone rolls down a mountain, it first moves slowly, but afterwards bounds with rapidity, sweep- ing before it all smaller obstacles. Hail- stones, although small, acquire such veloc- ity as to break windows ; and but for the resistance of the air, they would be much more destructive. The blow of a sledge-hammer is more severe as it is lifted to a greater height. Newton was first led to the examination of the laws of gravity by observing, when sitting under an apple-tree, that the fruit struck his hand with greatest severity when it fell from the top of the tree. It is not an unusual error to suppose that a large body will fall more rapidly than a small one. Some can scarcely be- lieve that a fifty-Six pound Weight Will Feather and coin falling not drop with a greater velocity than a ^e m a vacuum. small nail, not remembering that a proportionately greater force is required to overcome the inertia and set the larger body in motion. This error existed for many centuries, from the time of Aristotle until Galileo first questioned its correctness. The celebrated ex- periment which established the truth on this subject, and led to the discovery of the laws of falling bodies just explained, and which formed an era in modern 26 MECHANICS. philosophy, was performed from the top of the leaning tower of Pisa. Galileo was a philosophical teacher, and, being a man who thought for himself, soon discovered, by reasoning, the errors that had been received without a doubt for more than twenty centuries. All the learning of the age and the wisdom of the universities were against him, and in favor of this time-honored error, the truth of which no one had ever thought of submitting to experi- ment. The hour of trial arrived, when he, an obscure young man, stood nearly alone on one side, while the multitude, with all the power and confessed knowledge of the age, were on the other. The balls to be employed were carefully weighed and scrutinized to detect deception, and the parties were satis- fied. The one ball was exactly twice the weight of the other. The followers of Aristotle maintained that when the balls were dropped from the top of the tower, the heavy one would reach the ground in exactly half the time employed by the lighter ball. Galileo asserted that the weights of the balls would not affect their velocities, and that the times of descent would be equal. The balls were conveyed to the summit of the lofty tower — the crowd assembled round the base — the signal was given — the balls were dropped at the same instant, and swiftly descending, at the same moment struck the earth. Again and again the experiment was repeated with uniform results. Galileo's triumph w r as complete — not a shadow of doubt remained; but, instead of receiving the con- gratulations of honest conviction, private interest, the loss of place, and the mortification of confessing false teach- ing, proved too strong for the candor of his adversaries. They clung to their former opinions with the tenacity of despair, and he was driven from Pisa.* * Mitchell's Lectures. COHESION. — EXAMPLES. 27 COHESION - . The attraction of gravitation, as we have just seen, takes place between bodies at a greater or less distance from each other. There is another kind of attraction, acting only when the parts of substances are in actual contact / this is called cohesion. It is this which holds the parts of a body together and prevents it from falling to pieces. It may be shown by taking two pieces of lead, and, after having made upon them two smoothly-shaven surfaces with a knife, pressing them firmly together with a twist- ing motion (fig. 14). The asperities of the surfaces are thus pushed down, and the Fig- 1*. particles are brought into close contact, so that cohc- W§ Sion immediately takes place Cohesive attracttoiiTn'two lead balls'. between them, and some force will be required to draw them asunder.* Two pieces of melted wax adhere to- gether in the same way. Melted pitch or other similar substance, smeared thinly over the polished surfaces of metal or glass, also causes cohesion to take place between them. Smooth iron plates, two inches in diameter, have been made to stick together so firmly with hot grease as to require, when cold, a weight of half a ton to draw them apart. Plates of brass of the same size, cemented by means of pitch, required 1400 pounds. On this prin- ciple depends the efficacy of those substances which are used for cementing broken vessels. The most perfect artificial polish which can be given to hard metals is still so rough as to prevent the faces from *.That this is not atmospheric pressure, like that which holds two panes of wet glass together, is shown by the fact that it requires nearly as great a force to separate them when the}' are placed under the exhaust- ed receiver of an air-pump. Besides this, atmospheric pressure is much weaker than this force, with so small a surface. 28 MECHANICS. coming into close contact; hence they must be either melted, or softened like iron when it is welded. The different degrees of cohesion which take place between the particles of various soils, to reunite them after they have been crumbled asunder, occasion the main difference between light and heavy soils. When a light soil becomes soaked with water \ the particles adhere in a very slight degree ; and hence, when it becomes dry again, it is easily worked mellow. But if it be of a clayey nature, too much moisture softens it like melted wax: the particles are thus brought into close contact, and strong adhesion takes place ; hence the hardness and diffi- culty of working such soils when again dried. This ad- hesion is lessened by applying sand, chip-dirt, straw, yard- manure, or by burning the earth, but more especially by thorough draining, which, preventing the clay from be- coming so moist and soft, lessens the adhesion of its parts. Different substances are hard, soft, brittle, or elastic, according to the different degrees or modes of action in the attraction of cohesion. STRENGTH OF MATERIALS. It is a matter of great utility in the construction of machinery to determine the different degrees of cohesion possessed by different substances ; or, in other words, to ascertain their strength. This is done by forming them into rods of equal size, and applying weights to their lower extremities sufficient to break them, by drawing them asunder. The amount of weight shows their rela- tive degrees of strength. The following table gives the weights required to break the different substances, each being formed into q rod one quarter of an inch square : STEENGTH OF MATEEIAES. 29 Woods. Ash, toughest 1000 lbs. Beech 718 « Box 1250 " Cedar .' 712 " Chestnut 656 " Elm 837 " Locust 1380 " Maple 056 " Oak, white 718 " Pine, white 550 « pitch 750 " Poplar 437 « Walnut 487 " Metals. Steel, best 0370 lbs. « soft 7500 « Iron, wire 0440 " best bar 4690 " " common bar. . ., 3750 " inferior bar 1880 " it cas t 1150 to 3100 " Copper, wire 3S00 - cast 2030 » Brass 2800 " Platina wire ooUU Silver, cast 2500 Gold, cast ' !250 " Tin 31° " Zinc, cast 10° " « sheet --1000 « Lead, cast 55 « milled 207 « From these tables we may ascertain the strength of chains, rods, etc., when made of different metals, and of timbers, bars, levers, swing-trees, and farm implements, when made of woods. Wood which will bear a very heavy weight for a minute or two, will break with two- thirds of the weight when left upon it for a long time. This explains the reason that store-house and barn timbers sometimes give way under heavy loads of grain, which have appeared at first to stand with firmness. 30 MECHANICS. Although the preceding table gives the strength of wood drawn lengthwise, yet the comparative results are not greatly different when the force is applied in a transverse or side direction, so as to break in the usual way. The following table shows the results of several experi- ments with pieces of wood one foot in length, one inch square, with the weight suspended from one end, breaking them sidewise. White oak, seasoned, broke with 240 lbs. Chestnut, " " 170 " White pine, " " 135 " Yellow pine, " " 150 " Ash, « " 175 " Hickory, « " 270 " A rod of good iron is about ten times as strong as the best hemp rope of the same size. The best iron wire is nearly twenty times as strong as a hemp cord. Hence the enormous strength of the wire cables, several inches in di- ameter, which are employed for the support of suspension bridges. A rope one inch in diameter will bear about 5000 lbs., but in practice should not be subjected to more than half this strain, or about one ton. The strength increases or diminishes according to the size of the cross-section of the rope ; thus a cord half an inch in diameter will support one quarter as much as an inch, and a quarter-inch cord a sixteenth as much. A knowledge of the strength of ropes, as used by farmers in windlasses, pulleys, drawing loads, etc., would sometimes prevent serious accidents. The following table may therefore be useful : Diameter of rope or Pounds borne Breaking cord in inches. with safety. weight. One-eighth 31 lbs. 78 lbs. One-fourth 125 " 314 " One-half 500 " 1250 " One 2000 " 5000 " One and a quarter 3000 " 7500 " One and a half 4500 " 12,500 " STRENGTH OF MATERIALS. 31 These results will vary about one-fourth with the qual- ity of common hemp. Manilla is about one-half as strong as the best hemp. The latter stretches one-fifth to one- seventh before breaking. Wood is about seven to twenty times stronger when taken lengthwise with the fibres than when a side force is exerted, so as to split it. The splitting of timber or wood for fuel is, however, accomplished with a comparatively small power by the use of wedges, the force of heavy blows, and the leverage of the two parts. The attraction of cohesion is very weak in liquids ; it is sufficient, however, to give a round or spherical shape to very small portions or single drops, and to furnish a beautiful illustration, on a minute scale, of the same prin- ciple which gives a rounded form to the surface of the sea. In one case, cohesion, by drawing toward a common centre, forms the minute globule of dew upon the blade of grass ; in the other, gravitation, acting in like manner, but at vast distances, gives the mighty rotundity to the rolling waters of the ocean. CAPILLARY ATTRACTION. Capillary attraction is a species of cohesion ; it takes place only between solids and liquids. It is this which holds the moisture on the surface of a wet body, and which prevents the water from running instantly out of a wet cloth or sponge. By touching the lower extremity of a lump of sugar to the surface of water in a vessel, capillary attraction will cause the water to rise among its granules and moisten the whole lump. It may be very distinctly shown by placing the end of a fine glass tube into water; the water will rise in it above the level of the surrounding surface. If the bore of the tube be the twelfth of an inch 32 MECHANICS. in diameter (a, fig. 15,) it will rise a quarter of an inch ; if but the twenty-fifth of an inch in bore, as b, it will rise half an inch ; but if only a fiftieth of an inch, the water will rise an inch. This ascent of the liquid is caused by the attraction of the inner surface of the tube, until the weight of the column becomes equal to the force of the attraction. Capillary attraction may be also exhibited by Fig. 16 Capillary attraction in tubes. Capillary attraction between two panes of glass. two small plates of glass, placed with their edges in wa- ter, in contact on one side, and a little open at the other side, as in fig. 16. As the faces of the plates ap- proach each other, the water rises higher, forming the curve, a. Capillary attraction performs many important offices in nature. The moisture of the soil depends greatly upon its action. If the soil is composed of coarse sand or grav- el, the interstices are large, and, like the larger glass tube, will not retain the rain which falls upon it. Such soils are, therefore, easily worked in wet weather, but become too dry in seasons of drought ; but when the texture is finer, and especially if a due proportion of clay be mixed with the sand, the interstices become exceedingly small, and retain a full sufficiency of moisture. If, however, there is too much clay, the soil is apt to become close and compact, and the water can not enter until it is broken up EARTH A DESERT WITHOUT CAPILLARY ATTRACTION. or pulverized. It is for this reason that subsoil plowing becomes so eminently beneficial, by deepening the mellow portion, and thus affording a larger reservoir, which acts like a sponge in holding the excess of falling rains, until wanted in the dry season. For the same reason, a well- cultivated soil is found to preserve its moisture much bet- ter during the heat of summer than a hardened and neg- lected surface. If capillary attraction should cease to exist, the earth would soon become a barren and uninhabitable waste. The moisture of rains could not be retained by the parti- cles of the soil, but would immediately sink far down into the earth, leaving the surface at all times as dry and unproductive as a desert ; vegetation would cease ; brooks and rivers would lose the gradual supplies which the earth affords them through this influence, and become dried up ; and all plants and all animals die for want of drink and nourish- ment. Thus the very existence of the whole human race evidently depends on a law, ap- parently insignificant to the unthinking, but pointing the observing mind to a striking proof of the creative design which planned all the works of nature, and fitted them with the utmost exactness for the life and comfort of man. Apparatus ex- plaining the rising of sap. ASCENT OF SAP. The following interesting experiments serve to explain the cause of the ascent of sap in plants and trees : Take a small bladder, or bag made of any similar sub- stance, and fasten it tightly on a tube open at both ends (fig. 17) ; then fill them with alcohol up to the point C, and immerse the bladder into a vessel of water. The al- cohol will immediately rise slowly in the tube, and if not o* 34 MECHAXICG. more than two or three feet high, will run over the top. This is owing to the capillary attraction in the minute pores of the bladder, drawing the water within it faster than the same attraction draws the alcohol outward. One liquid will thus intrude itself into another with great force. A bladder filled with alcohol, with its neck tightly tied, will soon burst if plunged under water. If a blad- der is filled with gum-water, and then immersed as before, the water will find its way within against a very heavy pressure. In this manner sap ascends through the minute tubes in the body of trees. The sap is thickened like gum-water when it reaches the leaves, and a fresh supply, therefore, enters through the pores in the spongelets of the roots by capillary attraction, and, rising through the stem, keeps up a constant supply for the wants of the growing tree. CENTRE OE GEAVITY. The centre of gravity is that point in every hard sub- stance or body, on every side of which the different parts exactly balance each other. If the body be a globe or Fig. 18. round ball, the centre of gravity will be exactly at the centre of the globe ; if it be a rod of equal size, it will be at the middle of the rod. If a stone or any other sub- stance rest on a point directly under the centre of gravity, it will remain balanced on this point ; but if the point be not under the centre of gravity, the stone will fall toward the heaviest side. Some curious experiments are performed by an ingenious management of the centre of gravity. A light cylinder of cork or pasteboard contains a concealed piece of lead, g (fig. 18). The lead, being heavier than the rest, will CENTRE OF GRAVITY. EXPERIMENTS. 35 cause the cylinder to roll up an inclined plane, when placed as shown by the lower figure on the preceding en- graving, until it makes half a revolu- tion and reaches the place of the up- per figure, when it will remain sta- tionary. If a curved body, as shown in fig. 19, be loaded heavily at its ends, it will rest on the stand, and present a singular appearance by not falling, the centre of gravity lying between the two heavy portions on the end of the stand. A light stick of some length may be made to stand on the end of the finger, by sticking in two penknives, so as to bring the centre of gravity as low as the Fig. 19. Body singularly balanced by lead knobs. finger-end (fig. 20). If any body, of whatever shape, be suspended by a hook or loop at its top, it will necessarily hang so that the centre of gravity shall be di- rectly under the hook. In this way the centre in any substance, no matter how irregular its shape may be, is ascertained. Sup- pose, for instance, we have the irregular plate or board shown in the annexed Fig. 21. figure (fig. 21) : first hang it by the hook a, andtf^ the centre of gravity will be in the dotted line a b. Then hang it by the hook c, and it will be somewhere in the line c d. Now the point e, where they cross each other, is the only point in both, conse- Centre of gravity maintained by two penknives. somewhere 36 MECHANICS. quently this is the centre sought. If the mass or body, instead of being flat like a board, be shapeless like a stone or lump of chalk, holes bored from different suspending points directly downward will all cross each other exactly at the centre of gravity. LINE OF DIRECTION. Fig. 22. Fig. 23. Centre of gravity on level and inclined roads. An imaginary line from the centre of gravity perpendic- ularly downward to where the body rests is called the line of direction. Now in any solid body whatever, whether it be a wall, a stack of grain, or a loaded wagon, the line of direction must fall within the base or part resting upon the ground, or it will immediately be thrown over by its own weight. A heavily and even- ly loaded wagon on a level road will be perfectly safe, be- cause the line of direction falls equally between the wheels, as shown in fig. 22, by the dotted line, c, being the centre. But if it pass a steep side- hill road, throwing this line outside the wheels, as in fig. 23, it must be instantly overturned. If, however, instead of the high load represented in the figure, it be some very heavy material, as brick or sand, so as not to be higher than the square box, the centre will be much lower down, or at 5, and thus, the line falling within the wheels, the load will be safe from upsetting, unless the upper wheel pass over a stone, or the lower wheel sink into a rut. The centre of gravity of a large load may be nearly ascer- tained by measuring with a rod ; and it may sometimes happen that by measuring the sideling slope of a road, all of which may be done in a few minutes, a teamster may save himself from a comfortless upsetting, and perhaps CENTEE OP GEAVITY. LOADING WAGONS. 37 Fig. 24 heavy loss. Again, a load may be temporarily placed so much toward one side, while passing a sideling road, as to throw the line of direction considerably more up hill than usual, and save the load, which may be adjusted again as soon as the dangerous point is passed. This principle also shows the reason why it is safer to place only light bundles of merchandise on the top of a stage-coach, while all heavier articles are to be down near the wheels ; and why a sleigh will be less likely to upset in a snow- drift, if all the passengers will sit or lie on the bottom. When it becomes necessary to build very large loads of hay, straw, wool, or other light substances, the "reach," or the long con- necting-bar of the wagon, must be made longer, so as tO increase the length of the Centre of gravity of an evenand one-sided load ; for, by doubling the length, two tons may be piled upon the wagon with as much security from upsetting as one ton only on a short wagon. Where, however, a high load can not be avoided, great care must be taken to have it evenly placed. If, for in- stance, the load of hay represented by fig. 24 be skillfully built, the line of direction will fall equally distant within each wheel ; but a slight misplacement, as in fig. 25, will so alter this line as to render it dangerous to drive except on a very even road. Thus every one who drives a wagon should understand the laws of nature sufficiently to know how to arrange the load he carries. It is true that experience and good judgment alone will be sufficient in many cases; but no person can fail to judge better, with the reasons clearly, accurately, distinctly before his eyes, than by loose con- jecture and random guessing. 38 MECHANICS. Zi. Every farmer who erects a wall or building, every team- ster who drives a heavy load, or even he who only carries a heavy weight upon his shoulder, may learn something use- ful by understanding the laws of gravity. It is familiar to every one, that a body resting upon a broad base is more difficult to upset than when the base is narrow. For instance, the square block (fig. 26) is less easily thrown over than the tall and narrow block of equal weight, because, in turning the square block over its lower edge, the centre of gravity must be lifted up considerably in the curve shown by the dotted line c y but with a tall, narrow block, this curve being almost on a level, very little lifting is re- quired. Hence the reason that a high load on a wagon is so much more easily overturned than a low one. Of all forms, a pyramid stands the most firmly on its base. The centre of gravity, c (fig. 26), being so near the broad bottom, it must be elevated in a very steep curve to throw the line of direction beyond the base. For this reason, a stone wall, or the dam for a stream, will stand better when broad at bottom and tapering to a narrow top than if of equal thickness throughout. When a globe or round ball is placed upon a smooth floor, it rests on a single point. If the Fig. 27. floor be level, the line of direction will fall exactly at this resting-point (fig. 27). To move the ball, the centre will move precisely on a level, without be- ing raised at all. This is the reason that a ball, a cylinder, or a wheel is rolled forward so much more easily than a flat-sided or irregular body. In all these cases, the line of direction, although constantly CENTRE OF GRAVITY. — EXAMPLES. 39 changing its place, still continues to fall on the very point on wnich the round body rests. But if the level floor is exchanged for a slope or inclin- ed plane (fig. 28), the line of direc- Fig 28. tion no longer falls at the touchinsr- poi-nt, but on the side from it down- ward ; the ball will therefore, by its mere weight, commence rolling, and continue to do so until it reaches the bottom of the slope. Wheel-carriages owe their comparative ease of draught to the fact that the centre of gravity in the load is moved forward by the rolling of the wheels, on a level, or paral- lel with the surface of the road, just in the same way that the round ball rolls so easily. Each wheel supporting its part of the load at the hub, the same rule applies to each as to a ball or cylinder alone. Hence, on a level road, the line of direction falls precisely where the wheels rest on the ground, but if the road ascend or descend, it falls else- where ; this explains the reason why it will run by its own weight down a slope. Whenever a stone or other obstruction occurs in a road, it becomes requisite to raise the centre by the force of the team and by means of oblique motion, so as to throw the wheel over it, as shown by fig. 29. One of the reasons thus. becomes very plain why a laro;e wheel will Fig. 29. run with more ease on a rough road than a smaller one ; the larger one mounting any stone or obstruction without lifting: the load so much out of a level or direct line, as shown by the dotted lines in the annexed figures, (figs. 29 40 MECHANICS. A firmly- set fruit-ladder A dangerous- ly-set fruit- ladder. and 30). Another reason is, the large wheel does not sink into the smaller cavities in the road. A self-supporting fruit-ladder (fig. 31) (the centre of gravity, when in use, being at or near the top) must have its legs more widely spread, to be secure from falling, than if the centre were lower down. Hence such a position, as in fig. 32, would be unsafe. The support of the human body, in standing and walking, exhibits some interesting exam- ples in relation to this subject. A child can not learn to walk until he acquires skill enough to keep his feet always in the line of direc- tion. When he fails to do this, he topples over toward the side where the line falls outside his feet. A man stand- ing with his heels touching the wash-board of a room can not possibly stoop over without falling, because, when he bends, the line of direction falls forward of his toes, the wall against which he stands preventing the movement of his body backward to preserve the balance. In walking, the centre rises and falls slightly at each step, as shown by the waved line in fig. 33. If it were not for the bending of the knee-joints, this exercise would be much more laborious, as it would then become needful to throw the centre into an upward curve at every step. For this reason, a wooden leg is more imperfect than the natural one (fig. 34). Hence the reason why walking on crutches is laborious and fatiguing, because at every on- Fig. 33. Fiff. 34. CENTRE OF GRAVITY. — EXAMPLES. 41 Fig. 35. Fie-. 36. ward step the body must be thrown upward in a curve, like a wagon mounting repeated obstructions. When a load is carried on the shoulder, it should be so placed that the line of direction may pass directly through the shoulder or back down to the feet, fig. 35. An unskillful person will sometimes place a bag of grain as shown in fio\ 36. The line falling: outside his feet, he is compelled to draw downward with great force on the other end of the bag. A man who carries a heavy pole on his shoulder should see that the centre is directly over his slioulder, otherwise he will be compelled to bear down upon the lighter end, and thus add in an equal degree to the weight upon his body. If an elliptical or oval body, fig. 37, rest upon its side a, rolling it in either direction elevates Fig. 37. the centre, c, because it is nearest the side on which the body rests. If, when raised, it be suffered to fall, its momentum carries it beyond the point of rest, and thus it continues rocking until the force is spent. The course of the centre during these mo- tions is shown by the curved dotted line, c. If it be placed upon end, as in fig. 38, then any motion toward either side brings the centre of gravity nearer the touching-point, that is, causes it to descend, and the body consequently falls over on its side. This may be easily illustrated with an egg, which will lie at rest upon its side, but falls when set on either end. The rockers of chairs, cradles, and cribs, are formed on the princi- If so made that the centre of gravity Fig. 38. pie just explained. 42 MECHANICS. of the chair or cradle is nearer the middle of the rocker than to the ends, the rocking motion will take place ; and when the distance from the centre of gravity to the ends _,. „ n w . ,„ of the rockers is but little greater Fi£. 39. Fig. 40. > # to than the distance to the middle, c, as in fig. 39, the motion will be slow and gentle ; but if this differ- ence be greater, as in fig. 40, it will be rapid. When the centre is high, the rockers must have less curvature than where it is low and near the floor. If the centre of gravity be nearer the ends than to the middle, the chair will immediately be overturned. This principle should be well understood in the construction of every thing which moves by rocking. CHAPTER IV. SIMPLE MACHINES, OR MECHANICAL POWERS. ADVANTAGES OE MACHINES. The moving forces which are applied to various useful purposes commonly require some change in velocity, direction, or mode of acting, before they accomplish the desired end. For example, a running stream of water has a motion in one direction only ; by the use of machinery, we change this to an alternating motion, as in the saw of the saw-mill, or to a rotatory or whirling motion, as in the stones of a grist-mill. The direct or straightforward power of a yoke of oxen is made, by the employment of the plow, to produce a side-motion to the sod, as well as to turn it through half a circle. The thrashing-machine . SIMPLE MACHINES, OR MECHANICAL POWERS. 43 converts the slowly-acting pace of horses to the swift hum of the spiked cylinder. Any instrument used for thus changing or modifying motion is called a machine, whether it be simple or com- plex in its structure. Thus even a crow-bar, used in lifting stones from the earth, by diminishing the motion given by the hand and increasing its power, may be strictly termed a machine; while a harrow, which neither alters the course nor changes the velocity of the force applied, may with more propriety be regarded as simply an implement or tool. In common language, however, these distinctions are not accurately observed, and a machine is usually con- sidered to be any instrument consisting of different mov- ing parts. All machines, however complex, may be resolved into two simple parts, or powers. These are, 1. The Lever ; 2. The Inclined Plane. The wheel and axle, and the pulley are modified ap- plications of the lever ; and the wedge and the screw of the inclined plane, as will be shown on the following pages. These six are usually termed the mechanical powers. As they really do not possess any power in themselves, but only regulate power, the term " simple machines " may be regarded as most correct. THE LAW OF VIRTUAL VELOCITIES. Before proceeding to the simple machines, it may be well to explain a very important truth, which should be considered as lying at the foundation of all mechanical philosophy, and which renders plain and simple many things which would otherwise seem strange or contradictory. This is, that the force required to lift any given body is always in proportion to the weight of that body, taken 44 MECHANICS. together with the height to be raised. For instance, it requires twice the force to raise two pounds as to raise one pound, three times the force to raise three pounds, and so forth. Also, twice as great a force is needed to elevate any weight two feet as one foot, or three times as great for three feet, and so on. Again, combining these together, four times as great a force is required to raise two pounds to a height of two feet as to raise one pound only one foot ; eight times as great for four feet, and so on. This holds true, no matter by what kind, of ma- chinery it is accomplished. Now this may all seem very simple, but it serves to explain many difficult questions in relation to the real power possessed by all machines. Take another example. Suppose that one wishes to raise a weight of 1000 pounds to a height of one foot. If his strength is equal to only 100 pounds, the weight would be ten times too heavy for him. He might, there- fore, divide it into ten equal parts of 100 pounds each. Raising each part separately the required height of one foot would be the same as raising one of them ten feet high. The weight is lessened ten times, but the distance is increased ten times. But there are some bodies, as, for example, blocks of stone or sticks of timber, which can not well be divided into parts in actual practice. He there- fore resorts to a machine or mechanical power, through which the same result is accomplished by raising the whole weight in one mass with his single strength ; but in this case as well as the other, the moving force which he applies must pass through ten times the space of the weight. We arrive, therefore, at the general rule, that the distance moved by the weight is as much less than that moved by the power as the power is less than the weight. This rule is termed by some writers the " rule of virtual velocities" virtual meaning not apparent or actual, but according to the real effect, because the increase in the velocity of the power makes up for increase in the size THE LEVEE. 45 of weight. This rule will be better understood after con- sidering its application to the different simple machines. The simplest of all machines is the lever. It consists of a rod or bar, one end resting upon a prop or fulcrum, F (fig. 41), near which is the weight, W, moved by the hand at P. The stone may weigh 1000 pounds; yet, if it is ten times as near the fulcrum as the man's hand is, a force of 100 pounds will lift it ; but it will be moved only a tenth part as high as the hand has been moved, as shown Fifr41. Lever of the second kind. by the dotted lines. By placing the stone still nearer the fulcrum, still less will be the power required to raise it, but then the distance elevated would be also still less. By sufficiently increasing the disproportion between the two parts of the lever, the strength of a child merely might be made to move more than many horses could draw. These performances of the lever often excite astonish- ment at what appears to be out of the common course of things ; yet, when examined by the principles of mechan- ics, instead of appearing matters of astonishment, they are found to be only the natural and necessary results of the laws of force. In the case of the lever just described, it is often incorrectly supposed that the power itself sustains the weight. But this is not the case ; nearly the whole of it rests upon the fulcrum. We often see proofs of this error in common practice, where fulcrums or props entirely insufficient to uphold the enormous weight to be raised are attempted to. be used. If the weight, for instance, be ten times as near the fulcrum as to the power, then nine- tenths of the weight rests upon the fulcrum, and the re- ierer of tlie first kind. 4Q MECHANICS. maining tenth only is sustained by the lifting power. The lever only allows the power to expend itself through a longer distance, and thus, by concentrating itself at the weight, to elevate the latter through the shorter distance, according to the rule of virtual velocities already ex- plained. The fulcrum may be placed between the weight and the Fig. 42. power, as in fig. 42, or the power may be placed between the fulcrum and the weight, as in fig. 43, the same principle of virtual velocities applying in all cases. Where the fulcrum is between the power and the weight, as in fig. 42, it is called a lever of the first hind. Where the weight is between the fulcrum and the power, as in fig. 41, it constitutes a lever of the second Icind. Where the power is between the fulcrum and the weight, as in fig. 43, it is termed a lever of the third kind. 1. Many examples occur in practice of levers of the first kind. A crow-bar, used to raise stones from the earth, is an instance of this sort ; so is a handspike of any kind used in the same way. A hammer n ■, ., Lexer of the third kind. tor drawing a nail operates as a lever of the first kind, the heel being the ful- crum, the nail the weight, and the hand the power; the distance through which the handle passes being several times greater than that of the claws, the force exerted on the nail is increased in like proportion. A pair of scissors consists of two levers, the rivet being the fulcrum ; and in using them, as every one has observed, a greater cutting force is exerted near the rivets than toward the points. THE LEVER. EXAMPLES. 47 This is owing to the power being expended through a greater distance near the points, according to the rule al- ready explained. Pincers, nippers, and other similar in- struments are also double levers of the first kind. A common steelyard is another example, the sliding weight becoming gradually more effective as it is moved further from the fulcrum or hook supporting the instru- ment. The brake or handle of a pump is a lever of this class, the pump-rod and piston being the weight. The common balance is still another, the two arms being exactly equal, so that one weight will always balance the Pig. 44. other, and on this its usefulness and accuracy entirely depend. The most sensitive balances have light beams with long arms, and the turning-point of hardened steel or agate, in the form of a faiiiiiiiiiiiiiniiiiiiiwii)iuiimiriiiiii;iimiiiiii:iii!iii.iiii;iiimiii,wi;iiiiuiiii ! iMA thin wedge, on which the balance turns almost without friction. Small balances have been so skillfully constructed as to turn with one-thousandth part of a grain. 2. Levers of the second kind are less numerous, but not uncommon. A handspike used for rolling a log is an ex- ample. A wheel-barrow is a lever of the second kind, the fulcrum being the point where the wheel rests on the ground, and the weight the centre of gravity of the load. Hence, less exertion of strength is required in the arm when the load is placed near the wheel, except where the ground is soft or muddy, when it is found advantageous to place the load so that the arm shall sustain a consider- able portion, to prevent the wheel sinking into the soil. A two-wheeled cart is a similar example ; and, for the same reason, when the ground is soft, the load should be placed forward toward the horse or oxen ; on the other hand, on a smooth and hard, or on a plank road, the load should be 48 MECHANICS. more nearly balanced. An observance of this rule would often save a great deal of needless waste of strength. A sack-barrow, used in barns and mills for conveying heavy bags of grain from one part of the floor to another, Fig. 45. and in warehouses for boxes, is a lever nearly intermediate between the first and second kind, the weight usually rest- ing very nearly over the fulcrum or wheels. When the bag of grain is thrown forward of the wheels, it be- comes a lever of the first kind ; when back of the wheels, it is a lever of the second kind. As it is used only on hard and smooth floors, and not, like the wheel-barrow, on soft earth, the more nearly the load is placed directly over the wheels, the more easily they will run. 3. In a lever of the third kind, the weight being further from the fulcrum than the power, it is only used where great power is of secondary importance when com- pared with rapidity and dispatch. A hand-hoe is of this class, the left hand acting as the fulcrum, the right hand as the power, and the resistance overcome by the blade of the hoe as the weight. A hand-rake is similar, as well as a fork used for pitching hay. Tongs are double levers of this kind, as also the shears used in shearing sheep. The limbs of animals, generally, are levers of the third Sack-bcwow. ESTIMATING THE POWEB OF LEVERS. 49 kind. The joint of the bone is the fulcrum; the strong muscle or tendon attached to the bone near the joint is the power; and the weight of the limb, with whatever re- sistance it overcomes, is the weight. A great advantage results from this contrivance, because a slight contraction of the muscle gives a swift motion to the limb, so import- ant in walking and running, and in the use of the arms. ESTIMATING THE POWER OF LEVERS. The power of any lever is easily calculated by measuring the length of its two arms, that is, the two parts into Fig. 46. which it is divided by ,.&h the weisrht, fulcrum, « v^ ; - ■ ■-■ - --- ■ •- ■ - . rg i TTi j-;^ -9^'— ~^ *f and power. In a w\ F lever of the first kind :--■:'''''' if the weight and Lever of the first kind. power be equally dis- tant from the fulcrum, they will move through equal dis- tances, and nothing will be gained ; that is, a power of 100 pounds will lift a weight of 100 pounds only. If the power be twice as far as the weight, its force will be doubled; if three times, it will be tripled; and so forth. In a lever of the second kind, if the weight be equidistant between the fulcrum Fig. 47. and power, the power c p-- : --r ; --__ will move through ! ; ~~~~~~~~ r -~-- rr -._ r\ twice the distance of ■ j ___j!L rgfe^^— , the weight, and the m^ n. . , , Lever of the second kind. power 01 the instru- ment will therefore be doubled ; if twice as far, it will be tripled, and so on, as shown in the annexed figures. The same mode of reasoning will explain precisely to what extent the force is diminished in levers of the third kind. These rules will show in what manner a load borne on a pole is to be placed between two persons carrying it, 3 50 MECHANICS. If equidistant between them, each will sustain a like por- tion. If the load be twice as near to one as to the other, the shorter end will receive double the weight of the longer. For the same reason, Fig. 48, when three horses are worked abreast, the two horses placed together should have only half the length of arm of the main w r hiffle-tree as the single horse, fig. 48. The farmer who has a team of two horses un- like in strength, may thus easily know how to adjust the arms of the whiffle-tree so as to correspond with the strength of each. If, for instance, one of the horses possesses a strength as much greater than the other as four is to three, then the weaker horse should be attached to the arm of the whiffle- tree made as much longer than the other arm as four is to three. In all the preceding estimates, the influence of the weight of the lever has not been taken into consideration. In a lever of the first kind, if the thickness of the two arms be so adjusted that it will remain balanced on the fulcrum, its weight will have no other efiect than to in- crease the pressure on the fulcrum ; but if it be of equal size throughout, its longer arm, being the heavier, w T ill add to its power. The amount thus added will be equal to the excess in the weight of this arm, applied so far along as the centre of gravity of this excess. If, for ex- ample, a piece of scantling twelve feet long, a b, fig. 49, mv COMBINATION OF LEVEES. 51 be used as a lever to lift the corner of a building, then the two portions, a c, e d, will mutually balance each other. If these be each a foot in length, the weight of ten feet will be left to bear down the lever. The centre of gravity of this portion will be at e, six feet from the fulcrum, and it will consequently exert a force under the building equal to six times its own weight, If the scant- ling weigh five pounds to the foot, or fifty pounds for the excess, this force will be equal to three hundred pounds. In the lever of the second kind, its weight operates 'against the moving power. If it be of equal size through- out, this will be equal to just one-half the weight of the lever, the other half being supported by the fulcrum. With the lever of the third kind, the rule applied to the first must be exactly reversed. COMBINATION OF LEVERS. A great power may be attained without the inconven- ience of resorting to a very long lever, by means of a com- bination of levers. In fig. 50, the small weight P, act- iA^ mg as a moving power, ex- erts a three-fold force on the next lever ; this, in its turn, acts in the same degree on the third, which again increases the power three times. Con- sequently, the moving power, P, acts upon the weight, W, in a twenty-seven-fold degree, the former passing through a space twenty-seven times as great as the latter. A combination of levers like this is employed in self- regulating stoves. It is in this case, however, used to multiply instead of to diminish motion. The expansion of a metallic rod by heat the hundredth part of an inch acts on a set of iron levers, and the motion is increased, by the time it reaches the draught-valve, to about one hundred times. 52 MECHANICS. Fig. 51. A more compact arrangement of compound levers is shown in fig. 51, where the power, P, acts on the lever A, exerting a force on the lever B five times as great as the power. B acts on the lever C with a force increased three times, and this, again, on the weight, W, with a four-fold force. Multiplying 5, 3, and 4 together, the prod- uct is 60 ; hence a force of one pound "at P will support 60 pounds at W. By gradu- ating (or marking into Itjwj ^ notches) the lever C, so that Compound levers. the distance is measured as the weight is moved along it, a compact and powerful steelyard for weighing is formed. WEIGHING MACHINE. A valuable combination of levers is made in the con- struction of the weighing machine, used for weighing cat- tle, wagons loaded with hay, and other heavy articles. Fisr. 52. Weighing Machine. The wagon rests on the platform A (fig. 52,) and this platform rests on two levers at W, W, which presses their other ends both on a central point, and this again bears on THE WEIGHING MACHINE. 53 the lever D, the other end of which is connected by means of an upright rod with the steelyard at F. There are two important points gained in this combina- Fig. 53. tion. In the first place, the levers multiply the power so much that a few pounds' weight will balance a heavy load of hay weighing a ton or more ; and, in the next, the load resting on both the levers, communicates the same force of weight to the central point, from whatever part of the platform it hap- pens to stand on : for if it presses hardest on one lever, Portable Platform Scale. it bears lighter, at a cor- responding rate, on the other. In practice, there are Fis. 54. Large Platform Scale. always two pairs, or four levers, which proceed from each 54 MECHANICS. Fig. 55. corner of the platform, and rest on one point at the centre. We have taken the two only, to simplify the explanation. A powerful stump-extracting machine, allowing a suc- cession of efforts in the use of the lever, is exhibited by- fig. 55. The lever, «, should be a strong stick of timber, furnished with three massive iron hooks, secured by bolts passing through, as represented in the figure. Small or truck wheels are placed at each end of the lever, merely for the purpose of moving it easily over the ground. The stump, b, used as a fulcrum, has the chain passing round near its base, while another chain passes over the top of the stump, c, to be torn out. A horse is at- tached to the lever Lever Stump Machine. at d, and, moving to e, draws the other end of the lever backward, and loosens the stump ; while in this position, another chain is made to connect g to A, and the horse is turned about, and draws the lever backward to i, which still further increases the loosening ; a few repetitions of this alternating process tear out the stump. Very strong chains are requisite for this purpose. Large stumps may require an additional horse or a yoke of oxen. Where the stumps are remote from each other, iron rods with hooks may be used to connect the chains. The power which may be given to this and to all other A WILD THE0EY. 55 Fi" 56. modes of using the lever, as we have already seen, depends on the difference between the lengths of its two arms. A yoke of oxen, drawing with a force of 500 pounds on the long arm of a lever 25 feet long, will exert a force on the short arm of six inches equal to 50 times 500 pounds, or 25,000 pounds, on the stumj). It was after an examination of the great power which may be given to the lever by increasing this difference that Archimedes exultingly exclaimed, " Give me but a fulcrum whereon to place my lever, and. I will move the earth !" Admitting the theoretical truth of this exclamation, and supposing there could be a lever which he might have used for this purpose, its practical impossibility may be quickly understood by computing the whole bulk of the globe ; for such is its enormous size and cu- bical contents, that Archimedes must have moved forward his lever with the strength of a hun- dred pounds and the swiftness of a cannon ball for eight hundred million years to have moved the earth the thousandth part of an inch ! WHEEL AND AXLE. In treating of the lever, it was shown to be capable of exerting a force through a small distance only. Hence, if a heavy body were required to be elevated to any con- siderable height, it would be necessary to accomplish it by a succession of efforts. This inconvenience is removed by a constant and unremitted action of the lever in the form of the wheel and axle. Let the weight, w (fig. 56,) be suspended by a cord 56 MECHANICS. from the end of the lever, a &, and a, wheel attached to the lever, so that this cord may wind upon it as the weight is elevated ; then let the power be applied at the other end by means of a cord, and a larger wheel be at- tached, so that this cord too may wind upon the larger wheel. These two wheels (fastened together so as to form one), as they are made to revolve on their axis, will now constitute, in a manner, a succession of levers, acting through an indefinite distance according to the length of the cords. The levers here successively acting are of the " first kind," and the axis of the wheel is the fulcrum. This arrangement constitutes in substance the wheel and axle ; and its power, like that of the simple lever, depends on the comparative velocity of the weight and the moving force. If, for example, the larger wheel is four times the circumference of the smaller, a force of one hundred applied to the outer cord will raise a weight of four hundred pounds. The annexed figure exhibits at one view the power ex- erted through the wheel and axle, where a small weight of C pounds wall wind up (or balance) other w r eights separately, weighing 8, 12, or 24 pounds, as the differ- ence increases between the size of the wheel and of the axle, ac- cording to the rule of virtual velocities already explained. The thickness of the rope has not been taken into con- sideration. This is very small when compared with the diameter of the outer wheel, but often considerable when compared with that of the inner. To be strictly accurate, Fig. 57. Wheel and axle, showing the heavier weight for less motion. WHEEL AND AXLE. EXAMPLES. 57 therefore, the force must be considered as acting at the centre of the rope ; hence the diameter of the rope must be added to the diameter of the wheel. There are various forms of the wheel and axle. In the common windlass, motion is given to the axle by means of a winch, which is a lever like the handle of a grindstone. The windlass used in digging wells has usually four pro- jecting levers or arms. The wheel used in steering a ves- sel is furnished with pins in the circumference, to which the hand is applied in turning it. In the capstan (for weighing anchor) the axis is vertical, and horizontal levers are applied around it, so that several men may work at once. The power of all these forms is easily calculated by the rule of virtual velocities — that is, that the velocity with which the power moves is as many times greater than the velocity of the weight, as the weight exceeds the power. A simple and convenient rule for computing in numbers the power of wheel-work is the following : Multi- ply all the numbers together which express either the cir- cumferences or diameters of the large wheels, and then multiply together all the numbers which express the diam- eters of the smaller wheels or pinions; divide the greater number by the less, and the quotient will be the power sought. BAND AND COG WHEELS Where great power is required, several wheels and axles may be combined in a man- Fig. 59. ner corresponding with that of the compound system of levers already explained. In this case the axis of one wheel acts on the circumference of the next, producing a continued slower motion, and increasing the power in a corresponding degree. Combined cog-wheels. The wheels are made thus to act by means of cogs or teeth, 3* 58 MECHANICS. Fig. 60. or of bands (fig. 59). In ordinary practice, however, com- bined wheels are made use of to multiply motion instead of to diminish it, familiar instances of which occur in the grist-mill and thrashing machine. In connecting a system of w T heels, the cord or strap may be used where great force is not required, the friction round the circumference being sufficient to prevent slip- ping. Bands are chiefly useful where motion is to be transmitted to a distance ; as, for example, from a horse- power without a barn to a thrashing-machine within it. Liability of sliding is some- times useful, by preventing the machinery from breaking when a sudden obstruction occurs. Where the force is great, the necessary tension or tightness of the cord produces too great a friction at the axle. In such cases, cogs or teeth must be resorted to. The term teeth is usually applied when they are formed of the same piece as the wheel, as in the case of cast- iron wheels. Cogs are teeth formed separately and inserted into the wheel, as with wooden wmeels. Pinions are the small wheels, or, more properly, teeth set on axles. Form of cogs— a, badly formed ; b, proper form. FORM OF TEETH OR COGS. The form of the teeth has a great influence on the amount of friction among wheel-work. Badly formed teeth are represented by the wheel-work at a, in the an- nexed figure, consisting of square projecting pins. When these teeth first come into contact with each other, they FORM OF TEETH OR COGS, 59 Fig. 61. act obliquely together, and thus a part of their force is lost, and they continue scraping together with a large amount of friction so long as they remain in contact. These effects are avoided by giving to them the curved form, represented by b. Here, instead of pressing each other obliquely, they act at right angles, that is, not obliquely, and instead of scraping, they roll over each other with ease. These curves are as- certained by mathemat- ical calculation, which can not be here given ; it may be enough to state that they should be so formed that the points in contact shall always work at right angles to each other. For ordi- nary practical purposes as shown in the annexed y-~- Mode of giving the best form to cogs. however, they may be made tne annexed figure (fig. 61), by striking circles whose diameters shall embrace just three teeth. The points of the teeth thus formed are removed, leaving a blunt extremity, according to the figure. There are a few other rules that should always be ob- served in constructing wheel-work, in order that the wheels may run easily together, without jerking o? rat- tling, the most important of which are the following : 1. The teeth must be of uniform size and distance from each other, through the whole circumference of the wheel. 2. Any tooth must begin to act at the same instant that the preceding tooth ceases to touch its corresponding tooth on the other wheel. 3. There must be sufficient space between the teeth not only to admit those of the other wheel, but to allow a cer- tain degree of play, which should be equal to at least one- tenth of the thickness of the teeth. 4. The pinions should not be very small, unless the 60 MECHANICS. wheels they act on are quite large. In a pinion that has only eight teeth, each tooth begins to act before it reaches the line of the centres, and it is not disengaged as soon as the next one begins to act. A pinion of ten teeth will not operate perfectly if working in a wheel of less than 72 teeth. Pinions of less than six teeth should never be used. 5. To give strength to the teeth of wheels, make the wheels themselves thicker, which increases the breadth of the teeth. 6. Wheel-work is often defective when not made of uniform material, in consequence of the relative number Fig. 62. of teeth working together not being such as to equalize the wear of all alike. If the number of teeth on a wheel is divided with- out a remainder by the number of the pinion, then the same teeth will repeatedly engage each other, and they will often wear uneven- ly. The number should be so arranged that every tooth of the pinion may work in succession into the teeth of the wheel. This is best effected by first taking a number for the wheel that will be evenly divided by the number on the pinion, and then adding one more tooth to the wheel. This will effect a continual change, so that no two shall be engaged with each other twice until all the rest have been gone through with. This odd tooth is called the hunting-cog. Cog-wheels are most usually made with the teeth on the outside or cir- cumference of the wheel ; these are termed spur-icheels. If the teeth are set on one side of the wheels, they are termed crown-wheels. When they are made so as to work together obliquely, they are called bev el-wheels, as in fig. 62. Where the obliquity is small, the motion may be com- Bevd-icheels. Fig. 03. Universal joint. THE PULLET. Gl municated by means of the universal joint, as shown in fig. 63. This is commonly used in the thrashing-machine, where there is a slight change in the direction of motion between the horse-power and the thrasher. THE PULLEY. Pulley doubling the force. fixed at one end pass round a movable grooved wheel, and be grasped by the hand at the other end : then, in lifting any weight attached to the wheel, by drawing up the cord, the hand will move with twice the velocity of the weight. It will, therefore, exert double the degree Fie. 65. of force. This operates precisely as a succession of levers of the second kind, the fixed cord being the fulcrum, and the cord drawn up by the hand, the power. It thus constitutes one of the simplest kinds of the pulley, fig. 64. The wheel is called a sheave; the term pulley is applied to the block and sheave ; and a combination of sheaves, blocks, and ropes is called a tackle. There are various combinations of single pulleys for increasing power, the most com- mon of which, and least liable to become deranged by the cord being thrown off the wheels, is shown in fig. 65. In this and in all similarly constructed pulleys, the weight is as many times greater than the power as the number of cords which support the low r er block. If there lie six cords, as in the figure, the weight will be six limes the power. Pulley of six-fold power. 62 MECHANICS. Pulley with no increase of power. Where a cord is passed over a single fixed wheel, as in fig. 66, or over two or more wheels, no power is gained, Fig. 66 . the moving force being the same in 17 velocity as the weight. Such pulleys are sometimes, however, of use by altering the direction of the force. The latter is applied with advantage to unloading or pitching hay by means of a horse-power, saving much time and labor, as explained on a future page. Among the many applications of the pulley, one is shown in the ac- companying figure (fig. 67) rep- resenting Packer's Stone Lifter, for raising large boulders from the soil, weighing from one to four and five tons, and afterwards placing them in Avails. It is also employed for tearing out small or partly decayed stumps. The usefulness of the pulley depends mainly upon its lightness and port- Fig. gt. able form, and the facility with which it may be made to operate in al- most any situation. Hence it is much used in building, and is extensively applied in the rig- ging of ships. In Packer's Stone Lifter. the computation of its power there is a large drawback, not taken into account in the preceding calculation, which materially lessens its advantage; this is the friction of the wheels and blocks and the stiffness of the cordage. THE INCLINED PLANE. 63 which are often so great that two-thirds of the power is lost. THE INCLINED PLANE. The inclined plane or slope possesses a power which is estimated by the proportion which its length bears to the height. If, for example, the plane be twice as long as the perpendicular height, then in rolling the body a up the inclined plane (fig. G8), it will move through twice the distance required to lift it directly from b to c. Therefore only one-half the strength else required need be exerted for this purpose. The same reasoning Fi g . es. will apply to any other proportion c between the height and length ; that is, the more gradual or less steep the slope becomes, the greater J) will be the advantage gained. A familiar example occurs in lifting a loaded barrel into a wagon : the longer the plank used in rolling it, the less is the exertion needed. A body, in rolling freely down an inclined plane, acquires the same velocity that it would attain if dropped perpen- dicularly from a height equal to the perpendicular height of the plane. Thus, if an inclined plane on a plank road be 100 yards long and 16 feet high, a freely running wagon, left to descend of its own accord, will move 32 feet per second by the time it reaches the bottom, that being the velocity of a stone falling 16 feet. Or, a rail- car on an inclined plane 145 feet high will attain a speed of 96 feet per second, or more than 65 miles an hour, at the foot of the plane, which is equal to the velocity of a stone falling three seconds, or 145 feet. ASCENT IN EOADS. - All roads not perfectly level may be regarded as inclined planes. By the application of the preceding rule, we 64 MECHANICS. may discover precisely how much strength is lost in draw- ing heavy wagons up hill. If the load and wagon weigh a ton, and the road rise one foot in height to every five feet of distance, then the increased strength required to draw the load will be one-fifth of its weight, or equal to 400 pounds. If it rise only one foot in twenty, then the increase in power needed to ascend this plane will be only 100 pounds. The great importance of preserving, as nearly as practicable, a perfect level is obvious. There are many roads made in this country, rising over and descending hills, which might be made nearly level by deviating a little to the right or to the left. Suppose, for example, that a road be required to connect the two points Ffe. 69. Smiles b a and b (fig. 69), three miles apart, but separated by a lofty hill midway between them, and one mile in diameter. Passing half a mile on either side would entirely avoid the hill, and the road thus curved would be only one hundred and forty-eight yards, or one-twelfth of a mile longer. The same steep hill is ascended perhaps fifty to five hundred times a year by a hundred different farmers, expending an amount of strength, in the aggregate, sufficient to elevate ten thousand tons annually to this height, as a calculation will at once show — more than enough for all the increased expense of making the road level. It is interesting and important to examine how much further it is expedient to carry a road through a circuitous level course than over a hill. To ascertain this point, we must take into view the resistance occasioned by the rough surface or soft material of the road. Roads vary greatly THE RESISTANCE OF ROADS. 65 in this particular, but the following may be considered as about a fair average. In drawing a ton weight (including wagon) on freely running wheels, on a perfect level, the strength exerted will be found about equal to the follow- ing On a hard, smooth plank road 40 pounds. On a good Macadam road 60 " On a common good Lard road 100 " On a soft road about 200 " Now let us compare this resistance to the resistance of drawing up hill. First, for the plank road — forty pounds is one-fiftieth of a ton ; therefore a rise of one foot in fifty of length will increase the draught equal to the resistance of the road. Hence the road might be increased fifty feet in length to avoid an ascent of one foot ; or, at the same rate, it might be increased a mile in length to avoid an ascent of one hundred and five feet. But in this estimate the increase in cost of making the longer road is not taken into account. If making and keeping in repair be equal to three hundred dollars yearly per mile, and one hundred teams pass over it daily, at a cost for traveling of four cents each per mile, being four dollars daily, or twelve hundred dollars per annum, then the cost of making and repair would be one quarter of the expense of traveling over it. Therefore the mile should be diminished one quarter in length to make these two sources of expense counterbalance each other. Hence a road with this amount of travel should, with a reference to public accommodation, be made three-fourths of a mile longer to avoid a hill of one hundred and five feet. This estimate applies to, loaded teams only. For light car- riages the advantages of the level road would not be so great. One-half to five-eighths of a mile would, there- fore, be a fair estimate for all kinds of traveling taken together. 66 MECHANICS. The following table shows the rise in a mile of road for different ascents : For a rise of 1 foot in 10, the road ascends 528 feet per mile, do. 1 do. 13, do. 406 do. do. 1 do. 15, do. 352 do. do. 1 do. 20, do. 204 do. do. 1 do. 25, do. 211 do. do. 1 do. 30, do. 176 do. do. 1 do. 35, do. 151 do. do. 1 do. 40, do. 132 do. do. 1 do. 45, do. 117 do. do. 1 do. 50, do. 106 do. do. 1 do. 100, do. 53 do. do. 1 do. 125, do. 42 do. The same kind of reasoning applied to a common good road will show that it will be profitable for the public to travel about half that distance to avoid a hill of one hundred and five feet. In this case the whole yearly- cost of the road, including interest on the land, and the cost of repairs, would not usually be more than a tenth part of the same cost for plank, or would not exceed thirty dollars. On rail-roads, where the resistance is only about one- fifth part of the resistance of plank roads, the dispropor- tion between the draught on a level and up an ascent be- comes many times greater. Thus, if a single engine move three hundred and fifty tons on a level, then two engines will be required for an ascent of only twenty feet per mile, four engines for fifty feet per mile, and six engines for eighty feet per mile. Such estimates as these merit the attention of the farmer in laying out his own private farm roads. It may be worthy of considerable effort to avoid a hill of ten or twenty feet, which must be passed over a hundred times yearly with loads of manure, grain, hay, and wood. The greatly increased resistance of soft materials, also, is too rarely taken into account. A few loads of gravel, well applied, would often prevent ten times the labor in plow- FORM AND MATERIALS FOR ROADS. 67 ing through deep ruts, to say nothing of the breaking of harness and wagons by the excessive exertions of the team. FORM AND MATERIALS FOR ROADS. The depth of the mud in common roads is often un- necessarily great, in consequence of heaping together with the plow and scraj>er the soft top-soil for the raised F\z. 70. Scclio7i of badly forined road. carriage-way. When heavy rains fall, this forms a deep bed of mud, into which the wheels work their way, and cause extreme labor to the team. A much better way is to scrape off and cart away into the fields adjoining all the soft, rich, upper surface, and then to form the harder subsoil into a slightly rounded carriage-way, with a ditch on each side. Such roads as this have a very hard and firm foundation, and they have been found not to cut up Fig. 71. Section of loett-formed road. into ruts, nor to form much mud, even in the wettest sea- sons. On this hard foundation six inches of gravel will endure longer and form a better surface than twelve inches on a raised " turnpike" of soft soil and mud. It frequently happens that the form of the surface in- creases the quantity of mud in a road, by not allowing the water to flow off freely. The earth is heaped up in a high ridge, but having little slope on the top (fig. 70), where the water lodges, and ruts are formed, the only dry portions being on the brink of the ditches, where the water can escape. Instead of this form, there should be a gradual inclination from the centre to the ditches, as shown in fi^. 71. This inclination should not exceed 1 68 MECHANICS. foot iii 20. On hill-sides the slope should all be toward the higher ground, as in fig. 72. Hard and durable roads are made on the plan of Telford. Their foundation is rounded stones, placed upright, with the smaller or sharper ends upward. The smaller stones Fig. 72. Section of road for hillsides. are placed near the sides, and the larger at the centre, thus giving to the road a convex form. The spaces are then filled in with small broken stone, and the whole covered with the same material or with gravel. The pressure of wagons crowds it compactly between the stones, and forms a very hard mass. IMPORTANCE OP GOOD ROADS. The principles of road-making should be better under- stood by the community at large. Farmers are deeply interested in good roads. Nearness to market, and facili- ties for all other kinds of communication, are worth a great deal, often materially affecting the price of land and its products. The difference between traveling ten miles through deep mud, at two miles per hour, with half a load, and traveling ten miles over a fine road, at five miles per hour, with a full load, should not be forgotten. " In the absence of such facilities," says Gillespie, " the richest productions of nature waste on the spot of their growth. The luxuriant crops of our western prairies are sometimes left to decay on the ground, because there are no rapid and easy means of conveying them to market. The rich mines in the northern part of the State of New GOOD AND BAD ROADS. G9 York are comparatively valueless, because the roads among the mountains are so few and so bad, that the expense of the transportation of the metal would exceed its value. So, too, in Spain it has been known, after a succession of abundant harvests, that the wheat has actually been allowed to rot, because it would not repay the cost of carriage." Again, " When the Spanish government re- quired a supply of grain to be transferred from Old Castile to Madrid, 30,000 horses and mules were necessary for the transportation of four hundred and eighty tons of wheat. Upon a broken-stone road of the best sort, one-hundredth of that number could easily have done the work." He further adds, in speaking of the improvements in roads made by Marshal Wade, in the Scottish Highlands, " His military road is said to have done more for the civilization of the Highlands than the preceding efforts of all the British monarchs. But the later roads, under the more scientific direction of Telford, produced a change in the state of the people which is probably unparalleled in the history of any country for the same space of time. Large crops of wheat now cover former wastes ; farmers' houses and herds of cattle are now seen where was previously a desert ; estates have increased seven-fold in value and annual returns ; and the country has been advanced at least one hundred years." THE WEDGE. The wedge is a double inclined plane, the power being- applied at the back to urge it forward. It becomes more and more powerful as it is made more acute ; but, on ac- count of the enormous amount of friction, its exact power can not be very accurately estimated. It is nearly always urged by successive blows of a heavy body, the momentum of which imparts to it great force. All cutting and piercing instruments, as knives, scissors, 70 MECHANICS. chisels, pins, needles, and awls, are wedges. The degree of acuteness must be varied according to circumstances ; knives, for instance, which act merely by pressure, may be made with a much sharper angle than axes, which strike a severe blow. For cutting very hard substances, as iron, the edge must be formed with a still more obtuse angle. The utility of the wedge depends on the friction of its surfaces. In driving an iron wedge into a frozen or icy stick of wood, as every chopper has observed, the want of sufficient friction causes it immediately to recoil, unless it be previously heated in the fire. The efficacy of nails depends entirely on the friction against their wedge-like faces. THE SCREW The screw may be regarded as nothing more than an Fig. 74 inclined plane winding round the surface of a j^t___jiifen cylinder (fig. 74). This may be easily under- stood by cutting a piece of paper in such a form that its edge, a b (fig. 75), may represent the inclined plane ; then, beginning at the wider end, and wrapping it about the cylindrical piece of wood, e, the upper edge of the paper will represent the thread of the screw. Although the friction attending the use of the screw is considerable, and without it it would not retain its place, yet the slope of its in- clined thread being so gradual, it possesses great power. This power is multijmed to a still greater degree by the lever which is usually employed to drive it, a (fig. 76). If, for example, a screw be ten inches in circumference, and its thread half an inch apart, it exerts a force twenty Fig. 75. THE SCREW. 71 Fig. 76. times as great as the moving power. If it be moved by a lever twenty times as long as the diameter of the screw, here is another increase of twenty times in force. Multiplying 20 by 20 gives 400, the whole amount gained by this combination, and by which a man applying one hundred pounds in force could exert a pressure equal to twenty tons. About one-third or one-fourth of this should, however, be deducted for friction. When the screw is combined with the wheel and axle (fig. 77), it is capable of exerting great power, which may be readily calculated by multiplying the power of the screw and its lever into the power of the wheel and axle. Screw and lever combined. THE KNEE-JOINT POWER. Fig. 77. The knee-joint or toggle-joint is usually regarded as a com- pound lever, and consists of two rods connected by a turn- ing joint, as represented in fig. 78. The outer end of one of the levers is fixed to a solid beam, and the other connected with a movable block. When the joint a is forced in the direc- tion indicated by the arrow, it produces a powerful pressure upon the movable block, which in- creases as the lever approaches a straight line. This is easily understood by the rule of virtual velocities, for the force moves with a velocity many times greater than the Screw, lever, and wheel cornbiiwcl. Knee-joint power. 72 MECHANICS. power given to the block, and this relative difference in- creases as the joint is made straighter. This power is made use of in the lever printing-press, where the greatest force is given just as the pressure is completed. Another example occurs in the Lever Wash- ing-machine (fig. 79), which is worked by the alternating motion of the handle, A, pressing a swinging board, per- Fiff. 79. Lever Washing-machine. forated with holes, with great force against the clothes next to one side of the water-box. Like the printing- press, this machine exerts the greatest power just as the motion of the lever is completed, and at the time it is most needed. The same principle is exhibited in Kendall's Cheese-press (fig. 80), where the lever and the wheel and axle are combined with the two knee-joints, one on each side of the press, drawing down a cross-beam upon the cheese with a greatly multiplied power. Dick's Cheese-press (fig. 83), operates on a similar principle. Figs. 81-2 show the structure of its working LEVER WASHING-MACHINE. Pig. 80. 73 Fig. 82. KendalVs Cheese-press. part, the dotted lines indicating the position of the lever, which is inserted into a roller or axle, and, by turning, drives the movable iron blocks asunder, and raises the cheese against the broad screw-head above, as shown in fig. 82. In fig. 81, the raised lever shows that the blocks Tip-. 81. are at ^ rs<} near together, but are crowded asunder as the lever is press- ed downward. This cheese-press is made of cast-iron, and has great power; to try it, weights were in- creased upon the lever, until the iron frame broke with a force equal to six- teen tons. The power exerted by a rolling- mill, where bars of iron are flattened in their passage between two strong rollers, is precisely like that of the knee-joint. The only 4 •74 MECHANICS. Fig. 83. Dick's cast-iron Cheese-press. difference is, that the rollers, which may be considered as a constant succession of levers coming into play as they re- volve, are both fixed, and consequently the bar has to yield between them (fig. 84). The Fig. 84. greatest power is exerted just as the bar receives the last pressure from the rollers. The most powerful and rapidly- working straw-cutters are those which draw the straw or hay between two rollers, one of which is furnished with knives set around it parallel with its axis, and cutting on the other, which is covered with un- tanned ox-hide (fig. 85). Principle of the knee-joint in the rolling-mill STRAW CUTTERS. Fig. 85. 75 Hide Boiler Straw Cutter. CHAPTER Y. APPLICATION OF MECHANICAL PRINCIPLES IN THE STRUCTUPvE OF SIMPLE IMPLEMENTS AND PARTS OF MACHINES. In contriving the more difficult and complex machines, the principles of mechanics must be closely studied, to give every part just that degree of strength required, and to render their operation as perfect as possible. But in making the more common and simple implements of the farmer, mere guess-work too often becomes the only guide. Yet it is highly useful to apply scientific knowledge even in the shaping of a hoe handle or a plow-beam. The simplest tool, if constantly used, should be formed with a view to the best application of strength. The laborer who makes with a common hoe two thousand 76 MECHANICS. strokes an hour, should not wield a needless ounce. If any part is heavier than necessary, even "to the amount of half an ounce only, he must repeatedly and continually lift this half ounce, so that the whole strength thus spent would be equal, in a day, to twelve hundred and fifty pounds, which ought to be exerted in stirring the soil and destroying weeds. Or, take another instance : A farm wagon usually weighs nearly half a ton ; many might be Fig. 86. W C Badly-formed fork handle. reduced fifty pounds in weight by proportioning every part exactly to the strength required. How much, then, should we gain here? Every farmer who drives a wagon with its needless fifty pounds, on an average of only five miles a day, draws an unnecessary weight every year equal to the conveyance of a heavy wagon-load to a dis- tance of forty miles. Now a knowledge of mechanical science will often ena- ble the farmer, when he selects and buys his implements, to judge correctly whether every part is properly adapted to the required strength. We shall suppose, for instance, that he intends to purchase a common pitchfork. He finds them differently formed, although all are made of the Fig. 87. Os Badly-formed fork handle. best materials. The handles of some are of equal size throughout. Some are smaller near the fork, as in fig. 86, and others are larger at the same place, as in fig. 87. Now, if he understands the principle of the lever, he knows that both of these are wrongly made, for the right hand placed at a is the fulcrum, where the greatest strength is needed, and therefore the one represented by fig. 88 is both stronger and lighter than the others. PRINCIPLES IN THE STRUCTURE OF IMPLEMENTS. 77 Again, hoe handles, not needing much strength, chiefly require lightness -and convenience for grasping. Hence, in selecting from two such as are represented in the annex- ed figures, the one should be chosen which is lightest near Fig. 88. Well-formed fork handle. the blade, nearly all the motion being in that direction, because the upper end is the centre of motion. The right hand, at «, acting partly as the fulcrum, the hoe handle should be slightly enlarged at that place. Fig. 89 rep- resents a well-formed handle ; fig. 90, a clumsy one. Rake handles should be made largest at the middle, or where the right hand presses. Rake-heads should be much larger at the centre, and tapering to the ends, where the stress is least, the two parts operating as two distinct lev- Fig. 89. a. Well-formed hoe handle. ers, acting from the middle. Wood horse-raJces might be made considerably lighter than they usually are by ob- serving the same principles. The greatest strength requir- ed for plow-beams is at the junction with the mould-board, and the least near the forward end, or furthest from the fulcrum or centre of motion. Now it may be that the farmer who has had much ex- perience may be able to judge of all these things without Fig. 90. c? Badly-formed hoe handle. a knowledge of the science. But this scientific knowledge would serve to strengthen his experience, and enable him to judge more accurately and understandingly by showing him the reasons ; and in many cases, where new imple- ments were introduced, he might be enabled to form a 78 MECHANICS. good judgment before he had incurred all the expense and losses of unsuccessful trials. Even so simple a form as that of an ox-yoke is often made unnecessarily heavy. Fig. 91 represents one that is faulty in this respect, by having been cut from a piece of Ficr. 91. timber as wide as the dotted lines a c / and being thus weakened, it requires to be correspondingly large. Fig. 92 is equally strong, much lighter, and is easily made from a stick of timber only as wide as a b in the former figure. In the heavier machines, it is necessary to know the de- gree of taper in the different parts with accuracy. A thorough knowledge of science is needed to calculate this Fig. 92. with precision, but a superficial idea may be given by cuts. If a bar of wood, formed as in a (fig. 93), be fixed in a wall of masonry, it will possess as much strength to sup- port a weight hung on the end as if it were the same size throughout, as b. The first is equally strong with the second, and much lighter.* The same form doubled must * The simple st} Y le of this work precludes an explanation of the mode of calculation for determining the exact form. Where the stick taper8 only on one side, it is a common parabola ; if on all sides, a cubic parabola, VARIOUS EXAMPLES. 79 be given if the bar is supported at the middle, with a weight at each end, or with the weight at the middle, supported at each end, as c. This form, therefore, is a proper one for many parts of implements, as the bars of whiffle-trees, the rounds of ladders, string-pieces of bridges, and any cross-beams for supporting weights. The proper form for rake-teeth and fence-posts, the pressure being nearly alike on all parts, is nearly that of a long wedge, or with a straight and uniform taper. Therefore a fence- post of equal size throughout contains nearly twice as much timber as is needed for strength only. The form of these parts must, however, be modified to suit circumstances ; as whiffle-trees must be large enough Fig. 93. at the ends to receive the iron hooks, wagon-tongues for ironing at the end, and spade handles for the easy grasp of the hand. The axle-trees of wagons must be made not only strong in the middle, or at centre of pressure, but also at the en- trance of the hub ; because the wheels, when thrown side- wise in a rut, or on a sideling road, operate as levers at that point, a and b (fig. 94), show the manner in which the axles of carts may be rendered lighter without lessen- ing the strength, a being the common form, and b the im- proved one. 80 MECHANICS. Sometimes several forces act at once on different parts. For example, the spokes of wagon- wheels require strength at the hub for stiffening the wheel ; they must be strong in the middle to prevent bending, and large enough at the outer ends, where they are soonest weakened by de- cay. Hence there should be nearly a uniform taper, slightly larger at the middle, and with an enlargement at the outer end, as c (fig. 94). A very useful rule in practice, in giving strength to structures, is this : The strength of every square beam or stick to support a weight increases exactly as the width increases, and also exactly as the square of the depth in- creases. For example, a stick of timber eight inches wide and four inches deep (that is, four inches thick), is exactly twice as strong as another onlv four inches wide, and with O J 7 the same depth. It is twice as wide, and consequently twice as strong ; that is, its strength increases just as the width increases, according to the rule given. But where one stick of timber is twice as deep, the width being the same, it is four thnes stronger ; if three times as deep, it is nine thnes stronger, and so on. Its strength increases as the square of the depth, as already stated. The same rule will show that a board an inch thick and twelve inch- es wide will be twelve times as stronsr when edgewise as when lying flat. Hence the increase in strength given to whiffle-trees, fence-posts, joists, rafters, and string-pieces to farm-bridges, by making them narrow and deep. CALCULATING THE STRENGTH OF PaF.TS. 51 Again, the strength of a round stick increases as the cube of the diameter increases ; that is. a round piece of wood three inches in diameter is eight tunes u strong as one an inch and a half in diameter, and twenty-seven time- strong as one an inch in diameter. This rule shows that a fork handle an inch and a halt' in diameter at the middle 9 much stronger than one an inch and a quarter in diameter, as seven is greater than four. Xcw this rule would enable the farmer to ascertain this without break- ing half a dozen fork handles in trying the experiment, and it would enable the manufacturer to know, without Kg. 95. the labor of trying many experiments, that if he makes a fork handle an inch and a half at the middle, tapering a quarter of an inch toward the ends, it will enable the workman to lilt with it nearly twice as much hay as with one an inch and a quarter only through its whole length. A mode of adding strength to light bars of wo J means of braces, is shown in fig. 95, representing light .me-trees. stiffened by iron rods in a simple manner. The same method is sometimes adopted to advantage in making light fruit ladders, and for other purposes, CHAPTER VI. FEICTIOX. The subject of friction lias been postponed, or merely alluded to, to prevent the confusion of considering too many t *sat once. As it has an important influence on the action of machines, it is worthy of careful investigation. 4* 82 MECHANICS. It is familiar to most persons, that when two surfaces slide over each other while pressing together, the minute unevenness or roughness of their surfaces causes some ob- struction, and more or less force is required. This resist- ance is known as friction. ROLLING FRICTION. The term is also applied to the resistance of one body rolling over another. This may be observed in various degrees by rolling an ivory ball successively over a carpet, a smooth floor, and a sheet of ice ; the same force which would impel it only a few feet on the carpet would cause it to move as many yards on a bare floor, and a still greater distance on the ice. The two extremes may be seen by the force required to draw a carriage on a deep sandy or loose-gravel road, and on a rail-road. NATURE OF FRICTION. If two stiff bristle brushes be pressed with their faces together, they become mutually interlocked, so that it will be quite difficult to give them a sliding motion. This may be considered as an extreme case of friction, and serves to show its nature. In two pieces of coarse, rough sandstone, or of roughly-sawed wood, asperities interlock in the same way, but less in degree ; a diminished force is consequently required in moving the two surfaces against each other. On smoothly planed wood the friction is still less ; and on polished glass, where the unevenness can not be detected without the aid of a powerful magnifying glass, it is reduced still further in degree. ESTIMATING THE AMOUNT OF FRICTION. In order to determine the exact amount of friction be- tween different substances, the following simple and in- TO ASCERTAIN THE AMOUNT OF FRICTION. 83 genious contrivance is adopted : An inclined plane, a b (fig. 96), is so formed that it may be raised to any desired height by means of the arc of a circle and a screw. Lay a flat surface of the substance we wish to examine upon this inclined plane, and another smaller piece or block of the same substance upon this surface ; then raise the plane until it becomes just steep enough for the block to slide down by its weight. Now, by measuring the degree of slope, we know at once the amount of friction. Suppose, for example, the two surfaces be smoothly-planed wood : it will be found that the plane must be elevated about half as high as its length ; therefore we know, by the Fig. 96. properties of the inclined plane, heretofore explained, that it requires a force equal to one-half the weight of the wooden block to slide it over a smooth wooden surface. Some kinds of wood have more friction than others, but this is about the average.* From the result of this experiment we may learn that to slide any object of wood across a floor requires an amount of strength equal to one-half the weight of the object. A heavy box, for instance, weighing two hundred pounds, can not be moved without a force equal to one hundred pounds. It also shows the impropriety of placing * These experiments may be made with tolerable accuracy, by hook- ing a spring-balance into any object of known weight, and then observ- ing the comparative force as measured by the balance, to draw it over a perfectly level surface. • - - : 84 MECHANICS. a heavy load upon a sled in winter for crossing a bare wooden bridge or a dry barn floor, the friction between cast-iron sleigh-shoes and rough sanded plank being nearly equal to one-third of the whole weight.* Hence a load of one ton (including the sled) would require a draught equal to more than six hundred pounds, which is too much for an ordinary single team. On bare unfrozen ground the friction would be still greater. On a plank bridge, with runners wholly of wood, it would be equal to half the load. All these facts may be readily proved by actually placing the sled on slopes of plank and of earth, and by observing the degree of steepness required for sliding down by its own weight. In a similar way, we are enabled easily to ascertain the force required to draw a wagon upon any kind of level surface. Suppose, for example, that we wish to determine the precise amount of force for a wagon weighing, with its load, one ton, on a plank road. Select some slight de- scent, where the wagon will barely run with its own weight. Ascertain by a level just what the degree of de- scent is ; then divide the weight of the wagon by the de- gree of the slope, and we shall have the force sought for. To make this rule plainer by an example : It will be found that a good, newly-laid plank track, if it possess a de- scent of only one foot in fifty feet distance, will be suffi- cient to give motion to an easy-running Avagon ; therefore we know that the strength required to draw it on a level will be only one-fiftieth part of a ton, or forty pounds. The resistance offered to the motion of a wagon by a Macadam road, by a common dry road, and by one with six inches of mud, may be readily determined in the same way by selecting proper slopes for the experiment. If by such trials as these the farmer ascertains the fact that a * On clean hard wood, with polished metallic shoes, the friction "would be much less, or a fourth or fifth. EESULTS WITH THE DYNAMOMETEE. 85 few inches of mud are sufficient to retard his wagon so much that it wiJl not run of its own weight down a slope of one foot in four (and few common roads are ever steeper), then he may know that a force equal to one-fourth the whole weight of his wagon and load will be required to draw it on a level over a similar road — that is, the enormous force of five hundred pounds will be needed for one ton, of which many wagons will constitute nearly one- half. Hence he can not fail to see the great importance, for the sake of economy, and humanity to his team, of providing roads, whether public or private, of the hardest and best materials. EESULTS WITH THE DYNAMOMETER. Another mode of determining the resistance of roads is by means of the Dynamometer* It resembles a spring- balance, and one end is fastened to the wagon and the other end connected with the horses. The force applied is measured on a graduated scale, in the same way that the weight of any substance is measured with the spring- balance. A more particular description of this instrument will be given hereafter. Careful experiments have been made with the dynamom- eter to ascertain accurately the resistance of various kinds of roads. The following are some of the results : On a new gravel road, a horse will draw eight times as much as the force applied ; that is, if he exerts a force equal to one hundred and twenty-five pounds, he will draw half a ton on such a road, including the weight of the wagon, the road being perfectly level. On a common road of sand and gravel, sixteen times as much, or one ton. On the best hard-earth road, twenty-five times as much, or one and a half tons. From two Greek words, dunamis, power, and metreo i to measure. 86 MECHANICS. On a common broken-stone road, twenty-five to thirty- six times as much, or one and a half to two and a quarter tons. On the hest broken-stone road, fifty to sixty-seven times as much, or three to four tons. On a common plank-road, clean, fifty times as much, or three tons. On a common plank-road, covered thinly with sand or earth, thirty to thirty-five times as much, or about two tons. On the smoothest oak plank-road, seventy to one hund- red times as much, or four and a half to six tons. On a highly-finished stone track-way, one hundred and seventy times as much, or ten and a half tons. On the best rail-road, two hundred and eighty times as much, or seventeen and a half tons. The firmness of surface given to a broken-stone road by a paved foundation was found to lessen the resistance about one-third. On a broken-stone road it was found that a horse could draw only about two-thirds as much w r hen it was moist or dusty as when it was dry and smooth; and when muddy, not one-half as much. When the mud was thick, only about one quarter as much. The character of the vehicle has an influence on the draught. Thus, a cart, a part of the load of which is sup- ported by the horse, usually requires only about two-thirds the force of horizontal draught needed for wagons and carriages. On rough roads the resistance is slightly diminished by springs. On soft roads, as earth, sand, or gravel, the number of pounds draught is but little affected by the speed ; that is, the resistance is no greater in driving on a trot than on a walk ; but on hard roads it becomes greater as the velocity increases. Thus a carriage on a dry pavement requires one-half greater force when the horses are on a trot than WIDTH 0? WHEELS. 87 on a walk ; but on a muddy road the difference between the two rates of speed is only about one-sixth. On a rail- road, where a draught of ten pounds will draw a ton ten miles an hour, the resistance increases so much at a hisfh degree of speed as to require a force of fifty pounds per ton at sixty miles an hour — that is, it would require five times as much actual power to draw a train one hundred miles at the latter rate as at the former ; but as the speed is six times as great, the actual force during a given time would be five times six, or thirty times as great. WIDTH OF WHEELS. Wheels with wide tire run more easily than narrow tire, on soft roads ; on hard, smooth roads, there is no sensible difference. Wide tire is most advantageous on gravel and new broken-stone roads, both by causing the vehicles to run more easily, and by improving the surface. For the latter reason, the New York turnpike law allows six-inch wheels to pass at half price, and twelve-inch wheels to pass free of toll. Wheels with broad tire on a farm would pass over clods, and not sink between them ; or would only press the surface of new meadows, without cutting the turf. But where the ground becomes muddy, the mud closes on both sides of the rim, and loads the wheels. On clayey soils, narrow tire unfits the roads for broad wheels. For these reasons, broad wheels are decidedly objection- able for clayey or soft soils, and they are chiefly to be recommended for broken-stone roads, and gravelly, or dry, sandy localities. They are also much better for the wheels of sowing or drilling machines, which only pass over mellowed surfaces. The larger the wheels are made, the more easily they run ; thus a wheel six feet in diameter meets with only half the resistance of a wheel three feet in diameter. A flat piece of wood, sliding on one of its broad sur- 88 MECHANICS. faces, is subject to the same amount of friction as when sliding upon its edge. Hence the friction is the same, provided the pressure be the same, whether the surface be small or large.* Or, in other words, if the surfaces are the same, a double pressure produces a double amount of friction ; a triple pressure, a triple amount, and so on. A narrow sleigh-shoe usually runs with least force, for two reasons : first, its forward part cuts with less resist- ance through the snow ; and, secondly, less force is re- quired to pack the narrow track of snow beneath it. The only instance in which a wide sleigh-shoe would be best, is where a crust exists that would bear it up, and through which a narrow one would cut and sink down. VELOCITY. Friction is entirety independent of velocity ; that is, if a force of ten pounds is required to turn a carriage wheel, this force will be ten pounds, whether the carriage is driven one or five miles per hour. Of course, it will re- quire five times as much force to draw five miles per hour, because five times the distance is gone over ; but, measured by a dynamometer or spring-balance, the pressure would be the same. In precisely the same way, the weight of a stone remains the same, whether lifted slowly or quickly. If the friction of the wheels of a wagon on their axles be equal to ten pounds, driving the horse fast or slowly will not increase or diminish it. But fast driving will require more strength, for the same reason that a man would need more strength to carry a bag of wheat up two flights of stairs than one, in one minute of time. FRICTION AT THE AXLE. A carriage wheel, or any other wheel revolving on an * Generally speaking, this is very nearly correct ; but when the pres- sure is intense, the friction is slightly less on the smaller surface. SIZE OF WHEELS ON EOADS. 89 Fig. 97. axle, will run more easily as the axle is made smaller. This is not owing to the rubbing surfaces being less in size, as some mistakenly suppose, for it has just been shown that this makes very little or no difference, pro- vided the pressure is the same; but it is owing to the leverage of the wheel on the friction at the axis ; and the smaller the axle, the greater is this leverage ; for, if the axle, a (fig. 97), be six inches in circumference, and the wheel, b c, be ten feet in circumference, then the outer part of the wheel will move twenty times further than the part next the axle. Therefore, accord- ing to the rule of virtual velocities (already ex- plained,) one ounce of force at the rim of the wheel will overcome tAventy ounces of friction at the axle ; or if the axle were twice as large, then, according to the same rule, it would require two ounces to over- come the same friction acting between larger surfaces. For this reason, large wheels in wheel-work for multi- plying motion, if not made too heavy, run with less force than smaller ones, the power acting upon a larger lever. Horse-powers for thrashing-machines, consisting chiefly of a large, light crown-wheel, well stiffened by brace-work, have been found to run with remarkable ease; a good example of which exists in what is known as Talpirts horse-power, when made in the best manner. .....^Srarf**' FRICTION-WHEELS. On the preceding principle, friction-wheels or friction- rollers are constructed, for lessening as much as possible 90 MECHANICS. Fisr. 9S. Friction-ivheels. Ficr. 99. the friction of axles in certain cases. By this contrivance, the axle, a (fig. 98), instead of revolving in a simple hole or cavity, rests on or between the edges of two other wheels. As the axle re- volves, the edges turn with it, and the rubbing of surfaces is only at the axles of these two wheels. If, therefore, these axles be twenty times smaller than the wheels, the friction will be only one-twentieth the amount without them. This contrivance has been strongly recom- mended and con- siderably used for the cranks of grind- stones (fig. 99), but it was not found to answer the intended purpose so well as was expected, for the very plain reason that, in using a grindstone, nearly all the friction is at the circumference, or between the stone and the tool, which friction-wheels could not, of course, remove. Grindstone on Friction-wheels. LUBRICATING SUBSTANCES. Lubricating substances, as oil, lard, and tallow, applied to rubbing surfaces, greatly lessen the amount of friction, partly by filling the minute cavities, and partly by sepa- rating the surfaces. In ordinary cases, or where the machinery is simple, those substances are best for this purpose which keep their places best. Finely-powdered black-lead, mixed with lard, is for this reason better for greasing carriage wheels than some other applications. Drying oils, as linseed, soon become stiff by drying, and LUBRICATING SUBSTANCES. 91 are of little service. Olive oil, on the contrary, and some animal oils, which scarcely dry at all, are generally pre- ferred. To obtain the full benefit of oil, the application must be frequent. According to the experiments made with great care by Morin, at Paris, the friction of wooden surfaces on wooden surfaces is from one quarter to one-half the force applied ; and the friction of metals on metals, one-fifth to one- seventh — varying in both cases with the kinds used. Wood on wood was diminished by lard to about one-fifth to one-seventh of what it was before ; and the friction of metal on metal was diminished to about half what it was before ; that is, the friction became about the same in both cases after the lard was applied. To lessen the friction of wooden surfaces, lard is better than tallow by about one-eighth or one-seventh; and tal- low is better than dry soap about as two is to one. For iron on wood, tallow is better than dry soap about as five is to two. For cast-iron on cast-iron, polished, the friction with the different lubricating substances is as follows : Water 31 Soap ^ Tallow Lard. 7 Olive oil 6 Laid and black-lead 5 When bronze rubs on wrought iron, the friction with lard and black-lead is rather more than with tallow, and about one-fifth more than with olive oil. With steel on bronze, the friction with tallow and with olive oil is about one-seventh less than with lard and black-lead. As a general rule, there is least friction with lard when hard wood rubs on hard wood ; with oil, when metal rubs on wood, or metal on metal— being about the same in each of all these instances. In simple cases, as with carts and wagons, where the 92 MECHANICS. friction at the axle is but a small portion of the resistance,* a slight variation in the effects in the lubricating sub- stance is of less importance than retaining its place. In more complex machinery, as horse-powers for thrashing- machines, friction becomes a large item, unless the parts are kept well lubricated with the best materials. Leather and hemp bands, when used on drums for wheel-work, should possess as much friction as possible, to prevent slipping, thus avoiding the necessity of tightening them so much as to increase the friction of the axles. Wood with a rough surface has one-half more friction than when worn smooth ; hence moistening and rasping small drums may be useful. Facing with buff leather or with coarse thick cloth also accomplishes a useful purpose. It often happens that wetting or oiling bands will prevent slipping, by keeping their surfaces soft, and causing them to fit more closely the rough surface of the drum. ADVANTAGES OF FRICTION. Although friction is often a serious inconvenience, or loss, in lessening the force of machines, there are many instances in which it performs important offices in nature and in works of art. " Were there no friction, all bodies on the surface of the earth would be clashing against each other; rivers would dash with an unbounded velocity, and we should see little besides collision and motion. At present, whenever a body acquires a great velocity, it soon loses it by friction against the surface of the earth. The friction of water against the surfaces it runs over soon reduces the rapid torrent to a gentle stream ; the fury of * If the friction at the axle be one-twelfth of the force, and the diam- eter of the wheels ten times as great as the diameter of the axle, the friction at the axles will be reduced to one-twelfth of a tenth, or one hundred and twentieth part of the force, according to the law of virtual velocities as applied to the wheel and axle. FRICTION NECESSARY TO EXISTENCE. 93 the tempest is lessened by the friction of the air on the face of the earth, and the violence of the ocean is subdued by the attrition of its own waters. " Its offices in the works of art are equally important. Our garments owe their strength to friction, and the strength of ropes depends on the same cause ; for they are made of short fibres pressed together by twisting, causing a sufficient degree of friction to prevent the sliding of the fibres. Without friction, the short fibres of cotton could never have been made into such an infinite variety of forms as they have received from the hands of ingenious workmen." * Deprived of this retaining force, the parts of stone walls, piles of wood and lumber, and the loads of carts and wagons, as well as the wheels themselves, would slide without restraint, as if their surfaces were of the most icy smoothness, and walking without support would be impossible. The tractive power of locomotives depends on the fric- tion between the wheels and iron rails, which is equal to about one-fifth of the weight of the engine ; that is, a locomotive weighing twenty-five tons will draw with a force of five tons, without producing slipping of the wheels. CHAPTER VII. PRINCIPLES OF DRAUGHT. An examination of the nature or laws of friction enables us to ascertain the best line of draught for teams when attached to wagons and carriages. If there were no fric- tion whatever upon the road, the best direction for the * Encyclopaedia Americana. 94 MECHANICS. traces would be parallel with its surface, that is, on a level ; but as there is always some friction, the line of draught should be a little rising, so as to tend to lessen the pressure of the wheels on the road. Now this upward direction of the draught should always be exactly of such a slope, that if the same slope were given to the road, the wagon would just descend by its weight. The more rough or muddy the road is, the steeper should be this line of draught or direction of the traces.* On a good common road it would be much less, and on a plank-road but slightly varied from a horizontal direction. On a rail-road the line should be about level. On good sleighing, some of the strength of the team is commonly lost by too steep a line of draught. The reason of this rule may be understood by the fol- lowing explanation : Let the obstruction, a, in the annexed Fi<>\ 100. figure (fig. 100) represent the friction the ^ wheel constantly meets with in rolling over a common road. To overcome this "friction, the wheel must rise in the di- rection of the dotted line. Therefore, if a the force is made to pull in this direction, ^fesSt^- fa w iu aC £ more advantageously than in any other, because this is the course in which the centre of the wheel must move. Now if a downward slope were given to the road at this obstruction, the wheel and the obstruction would both be brought on a level, and the wheel would move with the slightest degree of force. It will be understood from the preceding rule that a sled running on bare ground should be drawn by traces bearing upward in a large degree. The same remark will apply to the plow, which slides upon the ground in a similar way, with the pressure of the turning sod as a load. Hence * Provided the wheels are not made smaller for this purpose, increasing their resistance. PRINCIPLES OP DRAUGHT APPLIED TO PLOWS. 95 the reason that a great saving of strength results from the use of short traces in plowing. An experiment was tried for the purpose of testing this reasoning ; first, with traces of such length that the horses' shoulders were about ten feet from the point of the plow ; and secondly, with the distance increased to about fifteen feet. With the short traces a strength was required equal to 2^ cwt., but with the long traces it amounted to 3^- cwt. But the draught-traces may be made too short. When this is the case, the Fi - 101 - plow is necessarily ~A" thrown too much upon ^=*^. ,*-'' \ its point, to keep it "~""^jp ^~~fl "" j from flying out of the >» g^^ -- — ' — i ground, by which means it works badly in turning the fur- row. In addition to this evil, the plowman is compelled to bear down heavily, adding to the friction of the sole on the bottom of the furrow, and greatly increasing his labor. The line of draught should be so adjusted that the plow may press equally all along on its sole or bottom, which will cause it to run evenly and with a steady motion. Fig. 102. Line of draujht for the plmv. This end will be effected by giving the traces or draught- chain just such a length that the share of the plow (or centre of resistance), the clevis, and the point of draught at the horses' shoulders (or the ring of the ox-yoke) shall all form a straight line. This is shown in the annexed figure, where A is the place of the ox-ring or of the for- ward extremity of the traces (fig. 101). The centre of resistance will vary with the depth of 9G MECHANICS. plowing. When the furrow is shallow (as shown by the lines G H, fig. 102), the centre of resistance will be at A, requiring the team to be fastened to the lower side of the clevis, C ; but when the depth is greater (as shown by F H), the centre of resistance will be at B, requiring a higher attachment to the clevis ; the point of draught, E, remaining the same in both cases. So great is the difference between an awkward and skill- ful adjustment of the draught to the plow, that some workmen with a poor implement have succeeded better than others with the best; and plows of second quality have sometimes, for this reason, been preferred to those of the most perfect construction. COMBINED DRAUGHT OF ANIMALS. When several animals are combined together, it is of great importance that they should be exactly matched in gait. Much force is Fig. 103. often wasted when fc=qf= =$ 6= they draw unsteadily or unevenly. It is more difficult to di- vide the draught equally among several animals when placed one before the other, than when arrayed abreast, for some may hang back, and others do more than their share, unless a skillful driver is always on the watch. It also hap- pens, when thus arranged, that the forward horses draw hori- zontally, while the hindmost one draws in a sloping line, and the line of draught between them thus beincr crooked, more or less force is lost. This may be, however, remedied in part by placing the taller animals forward, and the smaller behind. For these reasons, when only three horses are used, they should always be placed abreast. The force required for each may be rendered exactly equal by the whiffle-trees COMBINED DRAUGHT OP ANIMALS. 97 usually employed for this purpose, and represented in fig. 103, where two horses are attached to the shorter end, and Fisr. 104 Whipplc-tree for three horses. the third to the longer end of the common bar. Another ingenious but more complex arrangement is shown by fig. 104, where also the ,.. «_ B ' Fig. 105. central horse has only half the two others, by being at- tached to the longer ends of the inter- mediate bars. An- other, and a more perfect contrivance, is Potters Three- horse Clevis, re- presented by fig. 105. It consists of two wheels to- gether, one twice the diameter of the other, and each having a groove in which a chain runs. The chains are fastened to the respective wheels, so that the single horse draws on the larger wheel, against the two horses on the smaller. With common whiflle-trees, the relative draught of each horse is maintained only when they draw evenly ; with Potter's there is no variation at any time. It is made by E. M. Potter, Kalamazoo, Mich. Fig. 108 represents the mode of attaching four horses in draught, their force being equalized by passing the chain round the wheel in the pulley-block, «, security being pro- vided that the hindmost pair shall not encroach on the 5 98 MECHANICS. Fig. 106. forward pair, by connecting the end of the chain at the same time to the plow. wiee's single-teee. This is used exclusively for plowing in orchards, and is worthy of notice here. The leather traces are hooked at Fig. 107. the rear of the wooden bar, and, passing around the ends, prevent the possibility of being caught in the bark of the trees. The teamster may therefore drive as closely as he chooses without danger of injury. For this reason he is able to turn over the whole surface without leaving an unplowed strip along the row. CONSTEUCTION AND USE OF THE DYNAMOMETEE. The dynamometer, or force-measurer, has been already briefly alluded to, but a more particular description will be useful. In the construction and selection of all ma- chines and implements that require much power in their use, the dynamometer is indispensable, although at present but little known. As an example of its utility, the farmer may wish to choose between two plows which, so far as he can perceive, may do their work equally well ; but this instrument, when applied, may show that the team THE DYNAMOMETER. 99 must draw with a force equal to 400 pounds in mov- ing one of them through the soil, while 300 pounds would be sufficient for the other. He would, therefore, select the one of easiest draught, and by doing so would save the labor of one day in four to his team, or twenty-five days in a hund- red, which would be worth many times the cost of the trial. The same advantage might be derived in the selec- tion of harrows, cultivators, horse-rakes, straw-cutters, and all other implements drawn by horses or worked by men. Again, the farmer may be in doubt in choosing between two thrashing-machines, which in other respects may work equally fast and well ; but the dynamometer may show that one requires a severer exertion from the team, and consequently is less valuable for use. The operation of this instrument may be readily under- Dynamometer, or Force-measurer. stood by fig. 108, where b represents the dynamometer, Fili H 1 1 3 520 115 U 3 8 243 9. 12 SMa 5 9 | 10 153 82 10 4 4^ 102 72 9 5 2*1x0 52 57 7.2 6 2 . 30 48 6 7 1M 2 19 41 5.1 8 l 1 Is 12.8 36 4.5 9 3 Ik 9 32 4 10 sj 4 6.6 28.8 3.6 From the preceding table it will be seen that a horse, at a moderate walk, will do more than four times as much work on a canal as on a rail-road ; but the resistance of the water increases as the square of the velocity, and therefore when the speed reaches five miles an hour, the rail-road has the advantage of the canal. On the rail- road and turnpike the resistance is about the same, whether the speed be great or little, the chief loss with fast driving resulting from the increased difficulty with which the horse carries forward his own body, which weighs from 800 to 1200 pounds. The table also shows that when it becomes necessary to drive rapidly with a load, it should be continued but for a very short space of time ; for a horse becomes as much fatigued in an hour, when drawing hard at ten miles an hour, as in twelve hours at two and a half miles an hour ; because when a boat is driven through the water, to double its velocity not only requires that twice the amount of water should be moved or displaced in a given time, but it must be moved with twice the velocity, thus requiring a four-fold force. The muscular formation of a horse is such that he will exert a considerably greater force when working horizon- POWER OP MEJf. Ill tally than up a steep, inclined plane. On a level, a horse is as strong as five men, but up a steep hill he is less strong than three; for three men, carrying each 100 pounds, will ascend faster than a horse with 300 pounds. Hence the obvious waste of power in placing horses on steeply inclined tread-wheels or aprons. The better mode is to allow them to exert their force more nearly horizontally, by being attached to a fixed portion of the machine. For the same reason, the common opinion is erroneous that a horse can draw with less fatigue on an undulating: than on a level road, by the alternations of ascent and descent calling different muscles into play, and relieving each in turn ; for the same muscles are alike exerted on a level and on an ascent, only in the latter case the fatigue is much greater than the counterbalancing relief. Any per- son may convince himself of the truth on* this subject by first using a loaded wheel-barrow or hand-cart for one day on a level, and for the next up and down a hill ; bearing in mind, at the same time, that the human body is better fitted for climbing and descending than that of a horse. A draught-horse can draw 1600 pounds 23 miles in a day, on a good common road, the weight of the carriage included. On the best plank-road he will draw more than twice as much. A man of ordinary strength exerts a force of 30 pounds for 10 hours a day, with a velocity of 2|- feet per second. He travels, without a load, on level ground, during 8^- hours a day, at the rate of 3.7 miles an hour, 31£ miles a day. He can carry 111 pounds 11 miles a day. He can carry in a wheel-barrow 150 pounds 10 miles a day. Well-constructed machines for saving human labor by means of horse-labor, when encumbered with little fric- tion, will be found to do about five times as much work for each horse as where the same work is performed by an equal number of men. For example : an active man will saw twice each stick of a cord of wood in a day. 112 MECHANICS. Six horses, with a circular saw, driven by means of a good horse-power, will saw five times six, or thirty cords, work- ing the same length of time. In this case the loss by friction is about equal to the additional force required for attendance on the machine. Again : a man will cut with a cradle two acres of wheat in a day. A two-horse reaper should therefore cut, at the same rate, ten times two, or twenty acres. This has not yet been accomplished. We may hence infer that the machinery for reaping has been less perfected than for sawing wood. It should, however, be remembered, that great force is exerted, and for many hours in a day, in cutting wheat with a cradle, and therefore less than twenty acres a day may be regarded as the medium attainment of good reaping-machines when they shall become perfected. Applying the same mode of estimate, a horse-cultivator will do the work of five men with hoes, and a two-horse plow the work of ten men with spades. A horse-rake accomplishes more than five men, because human force is not strongly exerted with the hand-rake. In using different tools, the degree of force or pressure applied to them varies greatly with the mode in which the muscles are exerted. The following table gives the results of experiments with human strength, variously applied, for a short period : Force of the hands Force of the tool on the tool. on the object. With a drawing-knife 100 lbs. 100 lbs. " a large auger, both hands 100 " about 800 " " a screw-driver, one hand 84 " 250 " " a bench-vice handle 73 " about 1000 " " a windlass, with one hand 60 " 180 to 700 " " a hand-saw , 36 " 36 " " a brace-bit, revolving 16 " 150 to 700 " Twisting with thumb and fingers, but- ton-screw, or small screw-driver 14 " 14 to 70 " The force given in the last column will, of course, vary BEST WAY TO APPLY STRENGTH. 113 with the degree of leverage applied ; for example, the arms of an auger, when of a given length, act with a greater increase of power with a small size than with a large one. This degree of power may be calculated for an auger of any size, by considering the arms as a lever, the centre screw the fulcrum, and the cutting-blade as the weight to be moved. The same mode of estimate will apply to the vice-handle, the windlass, and the brace-bit. Every one is aware that a heavy weight, as a pail of water, is easily lifted when the arm is extended downward, but with extreme difficulty when thrown out horizontally. In the latter case, the pail acts with a powerful leverage on the elbow and shoulder-joint. For this reason, all kinds of hand labor, with the arms pulling toward or pushing directly from the shoulders, are most easily per- formed, while a motion sidewise or at right angles to the arm is fat less effective. Hence great strength is applied in rowing a boat or in using a drawing-knife, and but little strength in turning a brace-bit or working a dasher-churn. Hence, too, the reason that, in turning a grindstone, the pulling and thrusting part of the motion is more powerful than that through the other parts of the revolution. This also explains why two men, working at right angles to each other on a windlass, can raise seventy pounds more easily than one man can raise thirty pounds alone. This principle should be well understood in the construction or selection of all kinds of machines for hand labor. CHAPTER IX. MODELS OF MACHINES. Serious errors might often be avoided, and sometimes gross impositions prevented, by understanding the differ- ence between the working of a mere model, on a miniature 114 MECHANICS. scale, and the working of the full-sized machine. It is a common and mistaken opinion that a well-constructed model presents a perfect representation of the strength and mode of operation of the machine itself. When we enlarge the size of any thing, the strength of each part is increased according to the square of the diameter of that part ; that is, if the diameter is twice as great, then the strength will be four times as great ; if the diameter is increased three times, then the strength will be nine times, and so on. But the weight increases at a still greater rate than the strength, or according to the cube of the diameter. Thus, if the diameter be doubled (the shape being similar), the weight will be eight times greater ; if it be tripled, the weight will be twenty-seven times greater. Hence, the larger any part or machine is made, the less able it becomes to support the still greater increasing weight. If a model is made one-tenth the real size intended, then its different parts, when enlarged to full size, become one hundred times stronger, but they are a thousand times heavier, and so are all the weights or parts it has to sustain. All its parts would move ten times faster, which, added to their thousand-fold weight, would increase their inertia and momentum ten thousand times. For this reason, a model will often work perfectly when made on a small scale ; but when enlarged, the parts become so much heavier, and their momentum so vastly greater, from the longer sweep of motion, as to fail entirely of success, or to become soon racked to pieces. This same principle is illustrated in every part of the works of creation. The large species of spiders spin thicker webs, in comparison with their own diameter. i comparison than those spun by the smaller ones. Enlarge a gnat until its whole weight be equal to that of the eagle, and, great as that enlargement would be, its wing will scarcely have attained the thickness of writing-paper, and, instead of supporting the weight of the animal, would bend down WORKS OP CREATION FREE FROM MISTAKES. 115 from its own weight. The larger spiders rarely have legs so slender in form as the smaller ones ; the form of the Shetland pony is quite different from that of the large cart-horse ; and the cart-horse has a slenderer form than the elephant. The common flea will leap two hundred times the length of its own body, and the remark has been sometimes made that a man equally agile, with his present size, Avould vault over the highest city-steeple, or across a river as wide as the Hudson at Albany. Now, if the flea were increased in size to that of a man, it would become a hundred thousand times stronger, but thirty million times heavier ; that is, its weight would become three hundred times greater than its corresponding strength. Hence we may infer that the enlarged flea would be no more agile than a man ; or that, if a man were proportionately reduced to the size of a flea, he could leap to as great a distance. All this serves to illustrate in a striking manner the great difference in the working of models and of machines. CHAPTER X. CONSTRUCTION AND USE OF FARM IMPLEMENTS AND MA- CHINES IMPLEMENTS FOR TILLAGE. The application of mechanical principles in the struc- ture of the simpler parts of implements and machines has been already treated of. It remains to examine more particularly those machines chiefly important to the farmer, and to show the application of these principles in their use and operation. 116 MECHANICS. Farm implements and machines for working the soil should be, as far as possible, simple and not complex, be- cause they mostly meet with an irregular resistance, con- sisting of hard and soft soil and stones variously mixed together. A locomotive is made up of many parts ; but having a smooth surface to traverse, the machinery works uniformly and uninjured; but if in its progress it met with formidable obstructions and uneven resistance, it would be soon racked and beaten to pieces. Hence the long-continued and uniform success of the simple plow ; as well as the failure of complex digging machines, unless worked exclusively in soils free from stone. A complex machine, that meets with an occasional severe obstruction, receives a blow like that of a sledge ; and when this is repeated frequently, the probability is that some part will be bent, twisted, knocked out of place, or broken. If the machine be light, the chances are in its favor ; but il heavy, its momentum is such that it can scarcely escape severe injury. If composed of many distinct; parts, the derangement or breakage of one of these is sufficient to retard or put a stop to its working, and men and teams must stand idle till the mischief is repaired. Hence, after the trial of the multitude of implements and machines, we fall back on those of the most simple form, other things being equal. The crow-bar has been employed from time immemorial, and it will not be likely to go out of use in our day. For simplicity nothing ex- ceeds it. Spades, hoes, forks, etc., are of a similar char- acter. The plow, although made up of parts, becomes a single thing when all are bolted and screwed together. For this reason, with its moderate weight, it moves through the soil with little difficulty — turning aside from obstructions, on account of its wedge form, when it can- not remove them. The harrow, although composed of many pieces, becomes a fixed solid frame, moving on through the soil as a single piece. So with the simpler IMPORTANCE OF SIMPLICITY IX MACHINES. 117 cultivators. Contrast these with the ditching machine (Pratt's) considerably used some years ago, but ending in entire failure. It was ingeniously constructed and well-made, and when new and every part uninjured, worked admirably in some soils. But it was made up of many parts, and weighed nearly half a ton. These two facts fixed its doom. A complex machine, weighing half a ton, moving three to five feet per second, could not strike a large stone without a formidable jar ; and con- tinued repetitions of such blows bent and deranged the working parts. After using a while, these bent portions retarded its working ; it must be frequently stopped, the horses become badly fatigued, and all the machines were finally thrown aside. This is a single example of what must always occur with the use of heavy complex machinery working in the soil. Mowing and reaping machines may seem to be exceptions. But mowers and reapers do not work in the soil or among stones ; but operate on a soft, uniform, slightly resisting substance, made of the small stems of plants. Every firmer knows what becomes of them when they are repeatedly driven against obstruc- ' tions by careless teamsters. There is another formidable objection to complex ma- chines — this is, their cost. Even with some of proved value, the expense is a serious item with moderate farm- ers. Mowers and reapers, $130; grain drills, $80 or $90; thrashing machines, $100 to $400 ; horse rakes, $45 ; hay tedders, $80 to $100 ; iron rollers, $50 to $100 ; and even some of the efficient new potato diggers are offered for not less than $100. Placing all these sums, and many others for necessary tools together, the whole will be found a large outlay — more economical by far, it is true, than doing without them; but greater simplicity and consequent cheapness, as well as durability, would facilitate progress in agricultural improvement. A single machine, Comstock's spader, is offered at $250 — twenty 118 MECHANICS. Fig. H6. times the price of the best cast-iron plow, and ten times that of the most finished steel plow. And yet it is ap- plicable only to land free from stone. The object of these remarks is to caution farmers against investing money in newly invented con- trivances of high promise at first, which are liable to the objection point- ed out ; and also in- Kool ° plow - ventors and manufacturers themselves against engaging in enterprises having at hand golden promises, but with failure in the distance. PLOWS. The simplest plow, used probably in the earlier ages of the world, and found at the present day only among de- graded nations, is the crooked limb of a tree, with a pro- jecting point for tearing the surface of the earth. The above figure represents an improvement on the first rude implement, and is found at the present day in Northern Fig. 117. Moorish Plow. India. Fig. 116 shows the Kooloo plow, consisting wholly of wood, except the iron point. Fig. 117 exhibits the implement now used in Morocco, which resembles the India plows, with the addition of a rude piece of tim- ber as a mould-board. Both these perform very imperfect PLOWS. 119 work, and have remained with little change for centuries, the owners not enjoying the benefit of agricultural read- rig. 118. ing and intelligence. Fig. 118 is a step in advance, and represents a plow still used in some parts of Europe. In the less improved portions of Germany, the Baden plow, Fig. na Pig. 120. Baden Plow. represented by Fig. 119, is employed, and does not differ greatly from the "bull plow" commonly used in this country at the beginning of the present century. Great im- provement has been made within the past fifty years, among others by the ingenuity and labors of Jethro Wood, and more recently by a great number of inventors and manufacturers in different parts of the country. Wood introduced the cast-iron plow . . , t n i Modern Improved Ploiv. into general and successiul use, by cheapening its construction and perfecting its form, 120 MECHANICS. and others have made important improvements, including the steel mould-board now largely employed at the West. Cast-iron plows have been generally used throughout the Eastern States ; but for the peculiar soil of the West, it has been found absolutely necessary to use steel plows exclusively ; and for the purpose of keeping them at all Fiff. 121. Moline Plow. times sharp for cutting the vegetable fibre and separating the parts of the soil readily, the practice is common to carry a large file or rasp for this purpose. These steel plows are made of plate previously rolled. They are be- coming partially introduced also at the East, although in hard and gravelly soils the cast-iron mould-board is pre- ferred by many, and Fig. 122. regarded as even more durable. The steel plate plow is lighter than the cast- iron, but is more expensive. The ac- companying figure Woodruff &, Allen's Steek-gkna. (Fig. 121,) represents the celebrated "Moline plow," made by Deere & Co., of Moline, 111., one of the best and most extensively introduced among the Western steel imple- ments ; and Fig. 122 shows an excellent one of Eastern manufacture, made by Woodruff, Allen & Co., of Auburn, CHARACTER OF A GOOD PLOW. 121 N". Y. Good steel plows cost about double those made of cast-iron. CHARACTER OF A GOOD PLOW. Every good plow should possess two important quali- ties. The first relates to its working. It should be easily drawn through the soil, and run with uniform depth and steadiness. The second refers to the character of the work when completed. The inversion of the sod, especially if encumbered with vegetable growth, should be complete and perfect ; and the mass of earth thus inverted should be left as thoroughly pulverized as practicable, instead of being laid over in a solid, unmoved mass. This is of the greatest importance on heavy soils, and is highly useful on those of a lighter character, except, it may be, clear sand or the lightest gravels. The harrow, at best, is an imper- fect loosener ; it pulverizes the surface, but its weight, and that of the team, press down the mass below. Whatever loosening, therefore, can be accomplished in plowing is a gain of vital importance. THE CUTTING EDGE. The point and cutting edge of the plow perform the first work in separating the furrow-slice from the land. It is important that this edge should not only do the work well, but with the greatest possible ease to the team. The force required to perform this cutting is greater than many sup- pose. The gardener who thrusts his sharp spade into the hard earth uses more force than afterwards in lifting and inverting the spit. We may hence infer that a large part of the power of the team is expended in severing the fur- row-slice. This inference has been proved correct by the use of the dynamometer, in connection with carefully con-? (lucted experiments, which have shown the force usually 122 MECHANICS. expended for cutting off the side and bottom of the furrow- slice, in firm soils, to exceed all the rest of the force re- quired to draw the plow. The point or share should therefore be kept sharp, and form as acute an angle as practicable, as shown in Fig. 123. Some plows which other- Fig. 123. Fig. 124. Fig. 125. Fig. 126. wise work well arc hard to draw because the edge, being made too thick or obtuse, raises the earth abruptly. Fig. 124. Where stones or other obstructions exist in the soil, it is important that the line of the cutting edge form an acute angle with the land-side, or, in other words, that it form a sharp wedge, (Fig. 125.) It will then crowd these obstruc- tions aside, and pass them with greater ease than when formed more obtuse, as shown in Fig. 12G, for the same reason that a sharp boat moves more freely through the water than one which is blunt or obtuse. The gardener or ditcher proves this advantage when he thrusts a sharj> pointed shovel, Fig. 127, more easily through stony or gravelly soil, than one with a square edge. (Fig. 128.) But when the soil is free from stones, or obstructions, or is filled with small roots which the plow should cut off, as in the Western prairies, the sharpness of the edge is more important than its form ; and hence the reason that the use of the rasp or file becomes neces- THE CUTTING EDGE. 123 saryin the field, to keep a sharp cutting edge at all times on the share. Note. — It has been shown in the Keport of the Trial of Plows at Utica, that so far as yet determined by experiment in England, about thirty-five per cent of the whole required draught is expended in overcoming the friction of the implement on its bottom and sides, about fifty-five for cutting the furrow-slice, and only about ten per cent for turning the sod. Hence the exclusive attention formerly given to forming the mould-board, as a means of reducing the draught, should have been directed more to lessening the force required for cutting the hard soil. These experiments, however, do not appear to have been entirely satisfactory, especially for the light plows of this country; and it may be interesting to test their accuracy by calculation. The average weight of hard earth is about 125 lbs. per cubic foot; and the average draught of plows at the trial near Albany in 1850 was about 400 lbs. for a furrow- slice a foot wide and six inches deep. If a team in turning such sod moves two miles an hour, it raises a slice three feet long, equal to a cubic foot and a half (weighing 187 lbs.,) six inches each second— which would be the same as raising 31 lbs. three feet per second, which is the velocity of the plow. The mere force required to turn the sod, not esti- mating friction, would therefore be only one-thirteenth of the 400 lbs. of draught force. But the friction of dry earth on smooth iron is never less than one-half its weight ; and if the earth is slightly plastic, its friction often is equal to, and sometimes exceeds, its weight. Taking the smallest amount, the friction on the mould-board would be equal to half the weight of the portion of sod resting on the mould-board, or about 31 lbs. This increased weight would also add equally to the fric- tion of the sole of the plow, or 31 lbs. more— making the whole friction 62 lbs. ; which added to the weight of the sod would amount to 93 lbs. —or more than one-fifth of the whole draught. To ascertain the amount of friction, suppose the plow weighs 100 lbs. Half its weight would be 50 lbs., the friction on the sole of the plow. The friction of the sides would vary greatly with plows, being very small with those having a perfect centre-draught, or with no tendency to press against the land on the left. The whole friction and force for lifting the sod would therefore be about 150 lbs. ; leaving 250 lbs. as the force for cutting the slice. A very easy running plow would leave a much smaller force— some as low as 200 lbs. This estimate is liable to great variation. A wet and clayey soil would double the friction ; a very hard piece of ground would add much to the force required for cutting the slice ; if loose, the force would be com- paratively small; or if quite moist, this force would be also much dim- ished ; while the great difference in the draught of plows would vary the results still farther. The estimate, however, for soil dry enough to be friable, and of medium tenacity, is probably not far from correct, for plowing in this country— showing that most of the force required is for 124 MECHANICS. the act of cutting', and indicating the importance of giving special at- tention to the cutting edge. THE MOULD-BOARD. A prominent difference between good and bad plows results from the form of the mould-board. To un- derstand the best form, it must be observed that the slice is first cut by the forward edge of the plow, and then one side is gradually raised until it is turned completely over, or bottom side up. To do this, the mould-board must combine the two properties of the wedge and the screw. The position of the furrow-slice, from the time it is first cut until completely inverted, may be represented by placing a leather strap flat upon a table, and then, while Fiff. 129. holding one end, turning over the other, so as to bring that also flat upon the table, as in Fig. 129. Now, if the sole object were merely to invert the sod, the mould-board might have just such a shape as to fit the furrow-slice while in the act Fig. 130. of turning over, or resemble pre- cisely the twist of this leather strap. All the parts of this screw will be found to fit a straight-edge, if measured across at right angles, as indicated by the dot- ted lines in Fig. 130. But there are two objections to this form in practice. The first is that the sod is laid over smoothly and un- broken, and without being at all pulverized. On heavy and hard soils this is a serious fault. The other objection is that the sod is elevated as rapidly at the first movement, when its weight is considerable, as just before falling, when its pressure on the mould-board is slight. These diffi- culties are in part removed by giving the mould-board a THE MOULD-BOARD. 125 shorter twist towards its rear. This form is distinctly shown in the figure of Holbrook's Stubble Plow, on a future page ; and it contributes largely to that crumbling movement of the sod, so important for effecting pulveriza- tion. The mould-board of a plow is capable of an almost infi- nite variety of forms, and the multitude of inventors have each adopted a different one. Some have made their selections by repeated random trials ; while others, among whom Thomas Jefferson was the first, devised a series of straight lines, mathematically arranged, by which uniform- ity was given to the shape. The limits of this work pre- clude a full explanation. Many modifications in com- bining lines have been adopted, the most successful of which is that of Ex-Governor Holbrook, of Vermont, whose plows made according to these rules have perform- ed admirably. It is less essential that farmers generally should understand these mathematical principles, provided they find a plow that will do good work ; because, as al- ready shown, the form of the mould-board has compara- tively little to do with the required draught of the team. Fi~ 1.31 ^ w *^ ^e rea dily understood, however, that more force will be needed for draw- ing a short or blunt ])low, like Fig. 131, than one in the form of a longer wedge, as in fig. 132, the latter, like a sharp boat in water, moving more easily. Care must be taken, however, that this slender wedge be not too long, else the friction of the sod on the extended sur- face may overbalance the advantage. Fi(r 133 The cutting part of the plow may be improperly formed like the square end of a chisel, and the sod may slide back- ward on a rise, with a very slight turn, until elevated to a considerable height before inversion ; this must require more force of the team, and make the plow hard 126 MECHANICS. Fig. 133. to hold, on account of the side pressure. The character of this kind of plow may be quickly perceived by simply ex- amining the mould-board after use ; the scratches, instead of passing around horizontally, as they should do, are seen to shoot upward across the face and disappear at the top. Instead of this form, the point should be long and acute, and the mould-board so shaped as to begin to raise the left side of the sod the moment it is cut, and before the right side is yet reached by the cutting edge. This turning: motion being continued, the Ilolbroolc' s Stubble Plow, or Deep Tiller. S0( J j g inverted bv be- ing scarcely lifted from its bed ; and the pressure which turns it being opposite to the pressure of the land-side, an equilibrium of these two pressures is maintained, and the plowman is not compelled to bear constantly to the right to keep the plow in its place. There is, however, an exception, in deep or trench plow- ing, where it becomes necessary to throw the earth from the bottom of a furrow to the top of the inverted sod. A plow of this kind is represented in Fig. 133, which shows Holbrook's deep tiller for stubble land, capable of plowing a furrow a foot deep, and elevating the earth, which passes lengthwise over the mould-board. A similar Crested Furrow-dicer. f orm mus t be adopted for the rear mould-board of the Double Michigan Plow, so that the lower earth of the furrow may be thrown on the sod inverted by the first or skim-plow. The share should also be so placed as to cut the slice at equal thicknesses on both sides. Some plows are made Fier hour, for each horse-power used in driving it. THE COTTON GIN. Since the invention of the Cotton Gin by Eli Whitney, great improvements have been made, by which the cotton is cleaned with great rapidity and in a perfect manner. Fig. 224. Emery's Cotton Gin— Section. The machine manufactured by H. L. Emery, of Albany," is one of the best for this purpose. It is represented in section in fig. 224. The hopper, at the right, is furnished with what is termed a Picker Moll Svpporter, which re- volves within the hopper, in the direction shown by the arrow, and prevents the cotton from becoming packed. It emeey's cotton gust. 197 is then taken by the teeth of the saw cylinder, which re- duce the cotton to a fine condition. These teeth are swept by the brush cylinder, which, running in the same direction with the teeth, and slightly faster, carries the cotton off from them. Fig. 225 represents the operation, the seed escaping from the bottom of the hopper and the Fiff. 225. Emery's Cotton Gin, with Condenser. cotton thrown to the rear into the condenser, which fin- ishes the cleaning process and packs or condenses the lint cotton within a limited space. The arrows shown in the section indicate the direction of the revolutions of the picker, saws, and brush cylinder, and also the course which the cotton takes in passing through the gin and condenser. PART II. MACHINERY IN CONNECTION WITH WATER. GENERAL PRINCIPLES. Htdeostatics * treats of the weight and pressure of liquids when not in motion ; Hydraulics^ of liquids in motion, as, conducting water through pipes, raising it by- pumps, etc.; and Hydrodynamics J includes both, by- treating of the forces of the liquids, whether at rest or in motion. CHAPTER I. HYDROSTATICS. UPWARD PRESSURE. A remarkable property of liquids is their pressure in all directions. If we place a solid body, as a stone, in a vessel, its weight will only press upon the bottom ; but if we pour in water, the water will not only press upon the bottom, but against the sides. For, bore a hole in the side, and the side pressure will drive out the water in a stream ; or bore small holes in the sides and bottom of a tight wooden box, stopping them with plugs ; then press this box, empty, bottom downward, into water, allowing none to run in at the top. Now draw one of the side plugs, and the water will be immediately driven into the * From two Greek words, hudor, water, and statos, standing, or at rest, t From two Greek words, hudor, water, and aulos, a pipe. t From two Greek words, hudor, water, dunamis, power. 198 UPWARD PRESSURE OF LIQUIDS. 199 box by the pressure outside. If a bottom plug be drawn, the water will immediately spout up into the box, show- ing the pressure upward against the bottom. Hence the pressure in all directions^ upward, sideways, and down- ward, is proved. The upward pressure of liquids may be shown by pour- ing into one end of a tube, bent in the shape of the letter U, enough water to partly fill it ; the upward pressure will drive the water up the other side until the two sides are level. On this principle depends the art of conveying water in pipes under ground, across valleys. The water will rise as high on the opposite side the valley as the spring which supplies it. The ancient Romans, who were unac- quainted with the manufacture of strong cast-iron pipes, conveyed water on lofty aqueducts of costly masonry, built level across the valleys. Even at the present day, it has been deemed safest to build level aqueducts for con- veying great bodies of water, as in very large pipes the pressure would be enormous, and might result in violent explosions. If the valleys are deep, the pipes must be correspond- ingly strong, because, the higher the head of water, the greater is the pressure. For the same reason, dams and large cisterns should be strongest at bottom. Reservoirs made in the form of large tubs require the lower hoops to be many times stronger or more numerous than the upper. MEASUREMENT OP PRESSURE AT DIFFERENT HEIGHTS. The amount of pressure which any given height of wa- ter exerts upon a surface below may be understood by the following simple calculation : If there be a tube one inch square (with a closed end), half a pound of water poured into it will fill it to a height 200 MACHINERY IN CONNECTION WITH WATER. of fourteen inches ;* one pound will fill it twenty-eight Fi£. 226. 2 lbs. 5Q5n. iy2.lbs.Alin, lib 28 in. inches; two pounds, fifty-six inches; ten pounds, twenty-three feet ; twenty pounds, forty-six feet, and so on. Now, as the side pressure is the same as the pressure downward for the same head of water, the same column will, of course, exert an equal pressure on a square inch of the side of the tube. Or, if the tube be bent, as shown in the annexed figure (fig. 226), the pressure upward on the end of the tube, at a, will be the same for the various heights. Now, as the pressure of a column fifty feet high is about twenty-two pounds on a square inch, the pressure on the four sides is equal to eighty- eight pounds for one inch in length. Hence the reason that considerable strength is required in tubes which have much head of water, to prevent their being torn open by its force. yfelb-ldin. DETERMINING THE STRENGTH OE PIPES. The question may now arise, and it is a very important one, How thick must be a lead tube of this size to prevent danger of bursting with a head of fifty feet, or of any other height ? To answer it, let us turn to the table of the Strength of Materials in a former part of this work, where we find that a bar of cast lead one-fourth of an inch square will bear a weight of fifty-five pounds. If the * This is nearly correct, for a cubic foot (or 1,728 cubic inches) of water weighs 62 lbs. Consequently, one pound will be 27.9 cubic inch- es, and will fill the tube nearly 28 inches high. CALCULATING TIIE STRENGTH OF TUBES. 201 tube be only one-sixteenth of an inch thick, one inch of one of its sides will possess an equal strength, that is, will bear fifty-five pounds only, and the tube would conse- quently burst with fifty feet head. If one-tenth of an inch thick, the tube would just bear the pressure, and, to be safe, should be about twice as thick, or one-fifth of an inch. Half this thickness would be sufficient for twenty- five feet of water, and would require to be doubled for one hundred feet. A round tube, one inch in diameter, having less surface to its sides, would be about one-third stronger. A tube twice the diameter would need twice the thickness ; or if less in diameter, a proportionate de- crease in thickness might take place. If, instead of cast lead, milled lead were used, the tube would be nearly four times as strong, according to the table of the strength of materials already referred to. SPRINGS AND ARTESIAN WELLS result from the upward pressure of water. Rocks are usually arranged in inclined layers (fig. 227), and when Fig. 22?. rain falls upon the surface, as at c d, it sinks down in the more porous parts between these layers, to c. If the lay- ers happen to be broken in any place below, the water finds its way up through the crevices by the pressure of the head above, and forms springs. If there are no open- ings through the rocks, deep borings are sometimes made 9* 202 MACHINERY IX CONNECTION WITH WATER. artificially, through which the water is driven up to the surface, as at , closes it. The stream being thus suddenly checked, its momentum opens the valve, J£, upward, and drives the water into the reser- voir, A, until the air within, being compressed into a smaller space by its elasticity, bears down upon the water, and again closes the valve, E. The water in the supply- pipe, _Z?, has, by this time, expended its mo- mentum, and stopped running ; therefore the valve, D, drops open again, and permits it to escape. It recommences running, until its force again closes the waste valve, D, and a second portion of water is driven into the reservoir as be- fore, and so it repeatedly continues. The great force of the compressed air in the reservoir drives the water up the discharge-pipe, C, to any required height or distance. The mere weight of the water will only cause it to rise as high as the fountain head ; but like the momentum of a hammer, w T hich drives a nail into a solid beam, which a hundred pounds would not do by pressure, the striking force of the stream exerts great power. The discharge pipe, (7, is usually half an inch in diame-" ter, and the supply-pipe should not be less than an inch and a fourth. A fall of three or four feet in the stream, with not less than half a gallon of water per minute, with a supply-pipe forty feet long, will elevate water to a height as great as the strength of common half-inch lead Water-ram. 228 MACHINERY IN CONNECTION WITH WATEE. pipe will bear.* The greater the height, in proportion to the fall of the stream, the less will be the quantity of wa- ter elevated, as compared with the quantity flowing in the stream, or escaping from the waste valve. H. L. Emery gives the following rule for determining the quantity of water elevated from a stream : — Divide the elevation to be overcome by the fall in the drive-pipe, and. the quotient will be the proportion of water, (passing through the drive-pipe), which will be raised, — deducting, also, for waste of power and friction, say one-fourth the amount. Thus, with 10 feet fall, and 100 feet elevation, one-tenth of the water would be raised if there were no friction or loss ; but, deducting, say one-fourth for these, seven and a half gallons in each hundred gallons would be raised, the rest escaping, or being required to accomplish this result. Or, if the fall of the water in the supply-pipe be 3 feet, and the elevation required in the discharge-pipe be 15 feet, about one-seventh part of all the water will be elevated to this height of 15 feet. But if the desired height be 30 feet, then only about one-four- teenth part of the water will be raised ; and so on in about the same ratio for different heights. A gallon per minute from the spring would elevate six barrels five times as high as the fall, in twenty-four hours, and at the same rate for larger streams. With a head of 8 or 10 feet, water may be driven up to a height of 100, or even 150 feet, provided the machine and pipes are strong enough. The best result is obtained when the length of the drive-pipe and the momentum it produces are just suf- ficient to overcome the reaction caused by the closing of * When water is raised to a considerable elevation by means of the water-ram, the reservoir must possess great strength. If the height be 100 feet, the pressure, as shown on a former page, is about forty-four pounds to the square inch. With an internal surface, therefore, of only 2 square feet, the force exerted by the column of water, tending to burst the reservoir, would be equal to more than twelve thousand pounds. THE WATER-RAM. 229 the waste valve at each pulsation, and prevent the current of water from being thrown backward or up the drive- pipe ; hence, the greater the disproportion between the foil and the required elevation, the longer or larger must be the drive-pipe, in order to obtain sufficient momentum. A descent of only a foot or two is sufficient to raise water to moderate elevations, but the drive-pipe should be of large bore. This pipe should always be very nearly straight, so that the water, by having a free course, may acquire sufficient momentum to compress the air in the ram, and push the water up the discharge-pipe. Water may be carried to a distance of a hundred rods or more, but as there is some friction in so long a discharge-pipe, a greater force is required than for short distances. The discharge-pipe should, therefore, be larger, as the length is increased. Half an inch diameter is a common size, but long pipes may be five-eighths or three-fourths ; and, when practicable, it is more economical to reach an eleva- tion with a short and strong pipe, and to use a lighter and weaker one for the upper part. A pit, lined with brick or smooth stone, for placing the ram, protects it from freezing ; and both pipes should be under ground for the same reason. The supply or drive-pipe is usually 40 to 50 feet long ; but where the fall is 8 or 10 feet, it should be sixty or seventy feet. Unlike a pump, there is no friction or rubbing of parts in the water-ram, and, with clean water, it will act for years without repairs, continuing through day and night its constant and regular pulsations, unaltered and unob- served. A small quantity of sand, or of dead grass or other fibre, in the water, will be liable to obstruct the valves, and render frequent attention necessary. WATER-ENGINES, including those for extinguishing fires and for irrigating gardens, are constructed on a principle quite similar to 230 MACHINERY IN CONNECTION WITH WATEK. Fiff. 25G. Fig. 257. Garden-engine that of the water-ram. In- stead, however, of compress- ing the air, as in the ram, by the successive strokes of a column of running water, it is accomplished by means of a forcing-pump, driving the water into the reservoir, from which it is again ex- pelled with great power, by means of the elasticity of the compressed air. Fig. 256 represents a garden-engine, movable on wheels, which may be used for watering gardens, washing windows, or as a small fire-engine. Fig. 257 is another, of smaller size, for the same purposes, and in a neat and compact cylindrical Garden-engbie. form, the working part being within the cylindrical case. THE FLASH-WHEEL, FOIi IIAISING WATER. 2S1 THE FLASH-WHEEL is employed with great advantage where the quantity of water is large, and is to be raised to a small height, as in draining marshes and swamps. It is like an undershot wheel with its motion reversed; in iig. 258 the ar- rows show the direction of the current when driven up- ward. It must, of course, be made to fit the channel closely, without touching and causing friction. In its best form, its paddles incline backward, so as to be nearly up- Fiff. 258. Flash or fen wheel for raising water rapidly short distances. right at the time the water is discharged from them into the upper channel. It has been much used in Holland, where it is driven by wind-mills, for draining the surface- water off from embanked meadows. In England, it has been driven by steam-engines ; and in one instance, an eighty-horse-power engine, with ten bushels of coal, raised 9,840 tons of water six feet and seven inches high, in an hour. This is equal to more than 29,000 lbs. raised one foot per minute by each horse-power, showing that very little force is lost by friction in the use of the flash-wheel. 232 MACHINERY IN CONNECTION WITH WATER. WAVES. NATURE OE WAVES. An inverted syphon, or bent tube, like that shown in fig. 259, may be used to exhibit the F >s- 259. principle on which depends the motion of the waves of the sea. The action of the waves on shores and banks, and the inroads which they make upon farms situated on the borders of lakes and large rivers, present an interesting sub- ject of inquiry. If the bent tube (fig. 259) be nearly filled with water, and the surface be driven down in one arm by blowing suddenly into it, the liquid will rise in the other arm. The increased weight or head of this raised column will cause it to fall again, its momentum carrying it down below a level, and driving the water up the other arm. The surfaces will, therefore, continue to vibrate until the force is spent. The rising and falling of waves depend on a similar action. The wind, by blowing strongly on a por- tion of the water of the lake or sea, causes a depression, and produces a corresponding rise on the adjacent surface. The raised portion then falls by its weight, with the add- ed force of the wind upon it, until the vibrations increase into large waves. THE WATER NOT PROGRESSIVE. The waves thus produced have a progressive motion (for reasons to be presently shown), as every one has ob- served. A curious optical deception attending this ad- vancing motion has induced many to believe that the water itself is rolling onward ; but this is not the fact. The boat which floats upon the waves is not carried for- ward with them 5 they pass underneath, now lifting it on WATER OF WAVES NOT PROGRESSIVE. 233 their summits, and now dropping it into the hollows between. The same effect may be observed with the wa- ter-fowl, which sits upon the surface. It often happens, indeed, that the waves on a river roll in an opposite di- rection to the current itself. If a cloth be laid over a number of parallel rollers, so far apart as to allow the cloth to fall between them, and a progressive motion be then given to them, the cloth remain- ing stationary, a good representation of waves will be afforded, and the cloth will appear to advance ; or if a strip of cloth be laid on a floor, repeated jerks at one end will produce a similar illusion. It is only the form of the wave, and not the water which composes it, which has the onward motion. Let the dark line in fig. 260 represent the surface of the water. Fig. 2G0. A B A is the crest of one of the waves, and being higher than the surface at i?, it has a tendency to fall, and B to rise. But the momentum thus acquired carries these points so far that they interchange levels. The same change takes place with the other waves, and the dotted line shows the newly formed surface as the water thus sinks in one place and rises in another. The same process is again repeat- ed, and each wave thus advances further on, and its pro- gressive motion is continually kept up. BREADTH AND VELOCITY OF WAVES. Each wave contains at any one moment particles in all possible stages of their oscillation ; some rising, and some falling ; some at the top, and some at the bottom ; and the distance from any row of particles to the next row that is in precisely the same stage of oscillation is called 234 MACHINERY IN CONNECTION WITH WATER. breadth of the wave, that is, the distance from crest to crest, or from hollow to hollow. There is a striking similarity between the rising and falling of waves and the vibrations of a pendulum, and it is a very interesting and remarkable fact, that a wave al- ways travels its own breadth in precisely the same time that a pendulum, whose length is equal to that breadth, performs one vibration. Thus, a pendulum 39|- inches long beats once in each second, and a wave whose breadth is 39J inches travels that breadth in one second. The length of a pendulum must be increased as the square of the time for its vibrations ; that is, to beat but once in two seconds, it must be four times as long as for one second ; to beat once in three seconds, it must be nine times as long, and so on. In the same way, waves which travel their breadth in two seconds are four times as wide as those traveling their breadth in one second ; and thus their breadth, and consequently their speed, increases as the square of the time. Large waves, therefore, roll on- ward with far greater velocity than small ones. If only thirty-nine inches wide, they move about two and a quar- ter miles an hour, and pass once each second ; if 13 feet wide, they move 4% miles an hour, passing once in 2 seconds. 52 do. do. 9 do. do. 4 do. 209 do. do. 18 do. do. 8 do. 830 do. do. 36 do. do. 16 do. Although the water itself does not advance where there is much depth, yet when it reaches a shore or beach, the hard and shallow bottom prevents it from falling or sub- siding, and it then rolls onward with a real progressive motion from the momentum it has acquired, breaks into foam, and lashes the earth and rocks. The sea billows are sometimes twenty-five feet in elevation,* and when these advance upon a stranded ship on a lee shore, with * No authentic measurement gives the perpendicular height of waves more than twenty-five feet. PREVENTING THE INROAD OF WAVES. 235 the speed of a locomotive, their effects are in the highest degree appalling; and iron bolts are snapped, and massive timbers crushed beneath their violence. PREVENTING THE INROAD OP WAVES. * To prevent the inroads of lake waves upon land, the remedies must vary with circumstances. The difficulty would be small if the water always stood at the same height. The greatest mischief is usually -done when they rise over the beach of sand and gravel which they have beaten for centuries. Wooden bulwarks soon decay. Where loose stones can be had in large quantities, form- ing sloping rip-rap walls, they may be cheapest ; but they are not unfrequently placed too near low-water mark to protect the banks. Substances which offer a gradual im- pediment to the waves are often quite effectual, though not formidable in themselves. It is curious to observe how so slender a plant as the bulrush, growing in water several feet deep, will destroy the force of waves. If it grew only near the shore, where the water has progressive mo- tion, it would soon be dashed in heaps on the beach. Parallel hedge-rows of the osier willow, protected by a wooden barrier until well grown and established would, in many cases, prove efficient. Stones and timber bulwarks are often made needlessly F .„ 261 liable to injury by being built nearly perpendicular, and the waves break suddenly, and w T ith full force, like the blows of a sledge against them. A better form is shown in fig. 261, where a slope is first presented, to weaken their force without imposing a full resistance, and their strength is gradually spent as they rise in a curve. A 236 MACHINERY IN CONNECTION WITH WATER. more gradual slope than the figure represents would be still better. It is on this principle that the stability of the world-renowned Eddystone light-house depends. The base spreads out in every direction, like the trunk of a tree at the roots ; and although the spray is sometimes dashed over its lofty summit by the violence of the storm, it has stood unshaken on its rocky base far out in the sea, against the billows and tempests, for nearly a century. An instance occurred many years ago in England, where the superiority of knowledge over power and capital without it was strongly exemplified. The sea was mak- ing enormous breaches on the Norfolk and Suffolk coast, and inundated thousands of acres. The government com- missioners endeavored to keep, it out by strong walls of masonry and breakwaters of timber, built at great ex- pense ; but they were swept away by the fury of the bil- lows as fast as they were erected. A skillful engineer visited the place, and, with much difficulty, persuaded them to adopt his simple plan. Observing the slope of the beach on a neighboring shore, he directed that suc- cessive rows of fagots or brush be deposited for retaining the sand, which was carted from the hills, forming an em- bankment with a slope similar to that of the natural beach. Up this slope the waves rolled, and became grad- ually spent as they ascended, till they entirely died away. The breach was effectually stopped, and this simple struc- ture has ever since resisted the most violent storms of the German Ocean. CONTENTS OF CISTERNS. Connected with the subject of hydraulics is the collec- tion and security of water falling upon roofs, in all cases where a deficiency is felt by farmers in the drought of summer. The amount which falls upon most farm-build- ings is sufficient to furnish a plentiful supply to all the CONTENTS OP CISTERNS. 237 domestic animals of the farm when other supplies fail, if cisterns large enough to hold it were only provided. Generally speaking, none at all are connected with barns and out-buildings, and even when they are furnished, they are usually so small as to allow four-fifths of the water to waste. If all the rain that descends in the Northern States of the Union should remain upon the surface, without sink- ing in or running off, it would form, each year, a depth of about three feet. Every inch that falls upon a roof yields two barrels for each space ten feet square; and seventy-two barrels a year are yielded by three feet of rain. A barn thirty by forty feet supplies annually from its roof eight hundred and sixty-four barrels, or enough for more than two barrels a day for every day in the year. Many farmers have in all five times this amount of roof, or enough for twelve barrels a day, year- ly. If, however, this water were collected, and kept for the dry season only, twenty or thirty barrels daily might be used. In order to prevent a waste of water on the one hand, and to avoid the unnecessary expense of too large cisterns, their contents should be determined beforehand by calcu- lation. RULE FOR DETERMINING THE CONTENTS. A simple rule to determine the contents of a cistern, circular in form, and of equal size at top and bottom, is the following :— Find the depth and diameter in inches; square the diameter, and multiply the square by the deci- mal .0034, which will give the quantity in gallons* for one inch in depth. Multiply this by the depth, and divide by * This is the standard gallon of 231 cubic inches. The gallon of the State of New York contains 221.18-i cubic inches, or 6 pounds at its maximum density. 238 MACHINERY IN CONNECTION WITH WATER. 31^-, and the result will be the number of barrels the cis- tern will hold. For each foot in depth, the number of barrels answer- ing to the different diameters are, For 5 feet diameter 4.66 barrels. 6 " 6.71 " 7 " 9.13 u 8 " 11.93 " 9 " 15.10 " 10 " 18.65 " By the rule above given, the contents of barn-yard cisterns and manure tanks may be easily calculated for any size whatever. The size of cisterns should vary according to their in- tended use. If they are to furnish a daily supply of water, they need not be so large as for keeping supplies for summer only. The average depth of rain which falls in this latitude, although varying considerably with season and locality, rarely exceeds seven inches for two months. The size of the cistern, therefore, in daily use, need never exceed that of a body of water on the whole roof of the building, seven inches deep. To ascertain the amount of this, multiply the length by the breadth of the building, reduce this to inches, divide the product by 231, and the quotient will be gallons for each inch of depth. Multiply- ing by 7 will give the full amount for two months' rain falling upon the roof. Divide by 31^-, and the quotient will be barrels. This will be about fourteen barrels for every surface of roof ten feet square when measured hori- zontally. Therefore, a cistern for a barn 30 by 40 feet should hold one hundred and sixty-eight barrels ; that is, as large as one ten feet in diameter, and nine feet deep. Such a cistern would supply, with only thirty inches of rain yearly, no less than six hundred and thirty barrels, or nearly two a day. Cisterns intended only for drawing from in times of drought, to hold all the water that may fall, should have about three times the preceding capacity. PART III. MACHINERY IN CONNECTION WITH AIR. CHAPTER I. PRESSURE OF AIR. Pneumatics treats of the me- chanical properties of the air. The actual weight of the air may be correctly found by weigh- ing a strong glass vessel furnished with a stop-cock, a (fig. 262), after the air has been withdrawn from it by means of an air-pump. Let it be accurately balanced by weights in the opposite scale; then turn the stop-cock and admit the air, and it will immediately descend, as shown in the figure. The weight of the admitted air may be ascertained by adding weights until it is again balanced. Fi. 289. A fflass tube with a small bulb is furnished with a solid, air- tight piston, capable of working up and 12 266 HEAT. down. The water in the bulb, «, is heated with a spirit-lamp or sand-bath ; the rising steam forces up the piston. Now, immerse the bulb in cold water or snow, and the steam is condensed again into water, the tube is left vacant, and the pressure of the atmosphere forces down the piston. By thus alternately applying heat and cold, it is driven up and down like the piston of a steam- engine. The only difference is, the steam-engine is fur- nished with apparatus so that this application of heat and cold is performed by the machine itself. The bulb repre- sents the boiler, and the tube the cylinder ; but in the steam-engine, the boiler is separate, and connected by a pipe with the cylinder ; and instead of applying the cold water directly to the cylinder, it is thrown into another vessel, called the condenser, connected with the cylinder. When IsTewcomen, who made the first rude regularly working engine, began to use it for pumping water, he employed a boy to turn a stop-cock connected with the condenser, every time the piston made a stroke. The boy, however, soon grew tired of this incessant labor, and endeavored to find some contrivance for relief. This he effected by attaching a rod from the piston or working- beam to the cock, which was turned by the machine itself at every stroke. This was the origin of the first self- acting engine. The different parts ot a common steam-engine may be understood from the following figures, one representing the boiler, and the other the working machinery. The boiler, JB (fig. 290), contains water in the lower part, and steam in the upper ; F JB is the fire ; v o is the feed-pipe y v, a valve, closed by the lever b c a, whenever the boiler is full enough, by means of the rising of the float, S, and opened whenever the float sinks from low water. _3f, barometer gauge, to show the pressure of the steam ; w, weight on the lever, e b, for holding down the safety-valve : this lever being graduated like a steelyard, THE STEAM ENGINE. 267 the force of the steam may be accurately weighed. £7" is a valve opening downward, to prevent the boiler being crushed by atmospheric pressure, by allowing the air to pass in whenever the steam happens to decline. Two Fig. 290. Boiler of Steam-engine. tubes, with stop-cocks, c and. d, one just below the water- level, and the other just above it, serve to show, by open- ing the cocks, whether the water is too high or too low. The working part of the engine is represented in the figure on the following page (fig. 291). The steam enters by the pipe, s, from the boiler on the other side of the brick wall, as shown in fig. 290. The steam passes through what is called a four-way-cock, a, first into the lower, then into the upper end of the cylinder, C, as the piston, P, moves up and down ; this is regulated by the levers, y y. The piston-rod, E, is attached to the working-beam, JB F, turning on the centre, A. The rod, F 7?, turns the fly- wheel, H H, and drives the mill, steam-boat, or machinery to be set in motion. 268 HEAT. The condenser,^', shown directly under the cylinder, re- mains to be described. It is immersed in a cistern of cold water, and is connected by pipes with the upper and lower end of the cylinder. Through these pipes the steam Through Fi.2\ 291. Low-pressure Steam-engine, passes out of the cylinder, first from one end and then from the other, and is condensed into water by a jet of cold water thrown into it by the injection-cock. When condensed, it is pumped out by the pump, 0, into the well or reservoir, W, and then again into the feed-pipe of the boiler. Warm water is thus constantly supplied to the boiler, and effects a great saving of fuel. The supply of steam and the motion of the engine are regulated by the governor, G. When the motion is too fast, the two suspended balls, which revolve on a vertical or upright axis, and which hang loosely like pendulums, are thrown out from the axis, producing the movement of a rod which shuts the steam-valve. When the motion QUALITIES OF THE STEAM-ENGINE. 269 is too slow, the balls approach the axis, and open the valve. In high-pressure engines, the steam is not condensed, but escapes into the open air at every stroke of the piston, which produces the loud, successive puffs of all engines of this kind. The steam-engine, in its most perfect form, is a striking example of human ingenuity, and its qualities are thus described by Dr. Arnott : "It regulates with perfect ac- curacy and uniformity the number of its strokes in a given time, arid records them as a clock does the beats of its pendulum. It regulates the quantity of steam ; the brisk- ness of the fire ; the supply of water to the boiler ; the supply of coals to the fire. It opens and shuts its valves with absolute precision as to time and manner ; it oils its joints; it takes out any air accidentally entering parts which should be vacuous; and when any thing goes wrong which it can not of itself rectify, it warns its at- tendants by ringing a bell ; yet, with all these qualities, and even when exerting a force of six hundred horses, it is obedient to the hand of a child. Its aliment is coal, wood, and other combustibles. It consumes none while idle. It never tires, and wants no sleep. It is not sub- ject to any malady when originally well made, and only refuses to work when worn out with age. It is equally active in all climates, and will do work of any kind ; it is a water-pumper, a miner, a sailor, a cotton-spinner, a weaver, a blacksmith, a miller, a printer, and is indeed of all occupations ; and a small engine in the character of a steam pony may be seen dragging after it, on an iron rail- way, a hundred tons of merchandise, or a thousand per- sons with the speed of the wind." Steam-engines have been much used on large farms in England for thrashing, grinding the feed of animals, cut- ting fodder, and for other purposes. A successful English farmer has used a six-horse steam-engine to drive a pair 270 HEAT. of mill-stones, for thrashing and cleaning grain, elevating and bagging it, pumping water for cattle, cutting straw, Fig. 292. turning a grindstone, and driving liquid ma- nure through pipes for irrigating his fields, employing the waste steam in cooking food for cattle and swine. In this country, where horse labor is cheaper, steam-engines have not come into so general use; but on large farms, where a Wood's Farm Engine. ten - horse - power or more is required, they have been employed to much advantage, consuming no food, and requiring no care Fie. 203. Wood's Engine on WJieels, with Pipe Folded Down. when idle. Excellent steam-engines for this purpose are manufactured by A. N. Wood & Co., of Eaton, wood's steam-engine. 271 Madison Co., N. Y., a representation of which is given in the accompanying figure (fig. 292.) When intended to move from place to place, these engines are furnished ready mounted on wheels (fig. 293). The twelve-horse-power engines cost about $1,000, and have thrashed over a hund- red bushels per hour, using half a cord of wood, or 300 or 400 lbs. of coal for ten hours. A Western farmer thrashed 14,250 bushels of wheat in five consecutive weeks, working five and a half days each, with one of these en- gines. The smoke-pipe is guarded, so that straw placed within a few inches cannot be set on fire. More difficulty obviously exists in adajDting the steam- engine to plowing than for stationary purposes. In order to possess sufficient power, when used as a locomotive, the engine must be made so heavy as to sink in common soft soil even with large and broad wheels ; and this tendency is increased by the jar of the machinery which these wheels support. For this reason, all locomotive plows have failed. Better success has attended the use of stationary engines, employed for drawing gangs of plows, by means of wire rope, across the fields. In Eng- land, wiiere much of the soil is tenacious, and where fuel and manual labor are cheap, and horse labor expensive, this mode of plowing has been found profitable when em- ployed on an extensive scale, and is now much used. EXCEPTION TO EXPANSION BY HEAT. A striking exception to the general law of expansion by heat occurs in the freezing of water.* During its change to a solid state, it increases in bulk about one-twelfth, and this expansion is accompanied with great force. The bottoms of barrels are burst out, and cast-iron kettles are split asunder, when water is suffered wholly to freeze in * There are a very few other substances which expand on passing from a liquid to a solid state. 272 HEAT. them. Lead pipes filled with ice expand ; but if it is often repeated, they are cracked into fissures. A strong brass globe, the cavity of which was only one inch in di- ameter, was used by the Florentine academicians for the purpose of trying the expansive force of freezing water, by which it was burst, although the force required was calculated to be equal to fourteen tons. Experiments were tried at Quebec, in one of which an iron plug, nearly three pounds in weight, was thrown from a bomb-shell to the distance of 415 feet ; and in another, the shell was burst by the freezing of the water which it contained. This expansion has a most important influence in the pulverization of soils. The water which exists through all their minute portions, by conversion to frost, crowds the particles asunder, and when thawing takes place, the whole mass is more completely mellowed than could pos- sibly be effected by the most perfect instrument. This mellowing is, however, of only short duration, if the ground has not been well drained to prevent its becoming again packed hard by soaking with water. But this is not the most important result from the ex- pansion of water. Much of the existing order of nature and of civilized life depends upon this property ; without it the great mass of our lakes and rivers would become converted into solid ice ; for, as soon as the surface became covered, it would sink to the bottom, beyond the reach of the summer's sun, and successive portions being thus add- ed, the great body of all large rivers and lakes would become permanently frozen. But instead of this disas- trous consequence, the ice, by resting upon the surface, forms an effectual screen from the cold winds to the wa- ter below. LATENT HEAT. If a vessel of snow, which has been cooled down to several degrees below freezing by exposure to the severe LATENT HEAT. 273 cold of winter, be placed over a steady fire with a ther- mometer in the snow, the mercury will rise by the increas- ing heat of the snow until it reaches the freezing point. At this moment it will stop rising, and the snow will be- gin to melt ; and although the heat is all the time passing rapidly into the snow, the thermometer will remain per- fectly stationary until it is all converted to water. The heat that goes to melt the snow does not make it any hot- ter ; in other words, it becomes latent (the Latin word for hidden), so as neither to affect the sensation of the hand nor to raise the thermometer. Now it has been found that the time required to melt the snow is sufficient to heat the same quantity of water, placed over the same fire, up to 172 degrees, or 140 degrees above freezing ; that is, 140 degrees have become latent, or hidden, in melting the snow. This same amount of heat may be given out again by placing the vessel of water out of doors to freeze. A thermometer will show that the water is growing colder by the escape of the heat, until freezing commences. Af- ter this it still continues to pass off, but the water becomes no colder until all is frozen, as it was only the latent heat of the water that was escaping. A simple and familiar experiment exhibits the same principle. Place a frozen apple, which thaw T s a little be- low freezing, in a vessel of ice-cold water. The latent heat of the water immediately passes into the apple and thaws it, and in an hour or two it will be found like a fresh apple and entirely free from frost ; but the latent heat having escaped from the water next the apple, a thick crust of ice is found to encase it. The amount of latent heat may be shown in still an- other way. Mix a pound of snow at 32 degrees, or at freezing, with a pound of water at 172 degrees. All will be melted, but the two pounds of water thus formed will 12* 274 HEAT. be as cold as the snow, showing that for melting it the 140 degrees in the hot water were all made latent. ADVANTAGES OF LATENT HEAT. If no heat became latent by the conversion of ice and snow to water, no time would, of course, be required for the process, and thawing would be instantaneous. On the approach of warm weather, or at the very moment that the temperature of the air rose above freezing, snow and ice would all dissolve to water, and terrific floods and inundations would be the immediate consequence. LATENT HEAT OF STEAM. A still larger amount of latent heat is required for the conversion of water into steam ; for, again place the ves- sel of water with its thermometer on the fire, it will rise, as the heat of the water increases, to 212 degrees, and then commence boiling. During all this time it will now remain stationary at 212, until the water is all boiled away. This is found to require nearly five times the period need- ed to heat from freezing to boiling ; that is, nearly one thousand degrees of heat are made latent by the conver- sion of water into steam. When the steam is condensed again to water, this heat is given out. Hence the use made of steam conveyed in pipes for heating buildings, and for boiling large vats or tubs of water, by setting free this large amount of latent heat which the fire has imparted to it. GREEN AND DRY WOOD FOR FUEL. A great loss is often sustained in burning green wood for fuel, from an ignorance of the vast amount of latent heat consumed to drive off the water the wood contains. When perfectly green, it loses about one-third of its weight GREEN AND DRY WOOD FOR FUEL. 275 by thorough seasoning, which is equal to about 25 cubic feet in every compact cord, or 156 imperial gallons. Now all this water must be evaporated before the wood is burn- ed. The heat thus made latent and lost, being five times as great as to heat the water to boiling, is equal to enough for boiling 780 imperial gallons in burning up every cord of green wood. The farmer, therefore, who burns 25 green cords in a winter, loses heat enough to boil more than fifteen thousand gallons of water, which would be saved if his wood had been previously well seasoned un- der shelter. The loss in using green fuel is, however, sometimes overrated. It has been found by experiment that one pound of the best seasoned wood is sufficient to heat 27 lbs. of water from the freezing to the boiling point.* This will be equal to heating and evaporating four pounds of water by every pound of wood. The 25 cubic feet of water, therefore, in every cord of green wood, weighing about 1,500 pounds, would require nearly 400 pounds of wood for its evaporation, or about one-seventh or one- eighth of a cord. Hence we may infer that seven cords of dry wood are about equal to eight cords of green. This imperfect estimate will apply only to the best hard wood, and will vary exceedingly with the different sorts of fuel ; the more porous the wood becomes, the greater will be the necessity for thorough seasoning. * The following results show the heating power of several combust- ibles : 1 lb. of wood (seasoned, but still holding 20 per cent of water) raised from 32° to 212° 27 lbs. water. lib. ofalcohol 68 " 1 lb. of charcoal 78 " 1 lb. of oil or wax 90 " 1 lb. of hydrogen 216 " It should be remembered that by ordinary modes of heating water, a very large proportion of the heat is wasted by passiDg up the chimney and into surrounding bodies, and the air. 276 HEAT. Superficial observation often leads to very erroneous conclusions. Seasoned wood will sometimes burn with great rapidity, and, producing an intense heat for a short time, will favor an overestimate of its superiority. Green wood, on the other hand, kindles with difficulty, and burns slowly and for a long time; hence, where the draught of the chimney can not be controlled, it may be the most economical, because a less proportion of heat may be swept upward than by the more violent draught pro- duced from dry materials. Where the draught can be perfectly regulated, however, seasoned wood should be always used, for convenience and comfort, and for economy. Where wood is to be drawn to a distance, the preceding estimate shows that the conveyance of more than half a ton of water is avoided in every cord by seasoning. CHAPTER II. RADIATION OF HEAT. The passage of heat through conducting bodies has been already explained. There is another way in which it is transmitted, termed radiation, in which it is thrown off instantaneously in straight lines from hot bodies, in the same way that light is thrown off from a candle. A familiar instance is furnished by the common or open fire- place, before which the face may be roasted with the radiated heat, while the back is chilled with cold. A screen held in the hand will intercept this radiated heat, showing that it flies in right lines like the rays of light. Radiated heat is reflected by a polished metallic surface, RADIATION OF HEAT. 277 in the same way that light is reflected by a looking-glass. A plate of bright tin held near the fire will not for a long time become hot, the heat being reflected from it without entering and heating it. But if it be blackened with smoke, it will no longer reflect, but absorb the heat, and consequently will speedily become hot. This experiment may be easily tried by placing a new tin cup containing water over a charcoal fire, which yields no smoke. The heat will be reflected into the fire by the tin, and the wa- ter will scarcely become warm. But if a few pine shav- ings be thrown on this fire, to smoke the surface of the tin, it will then absorb the heat rapidly, and soon begin to boil. This explains the reason that bread bakes more slowly in a new tin dish, and that a polished andiron be- fore a fire is long in becoming hot. A concave burning-mirror, which throws the rays of heat to a focus or point, may be made of sheet-tin, by Fi£. 294. beating it out concave so as to fit a regularly curved gauge. If a foot in diameter, and carefully made, it will condense the rays of heat so powerfully at the focus, when held several feet from the fire, as to set fire to a pine stick or to flash gunpowder (fig. 294). The reflection of radiated heat may be beautifully ex- hibited by using two such concave tin mirrors. Place them on a long table several feet apart, and ascertain the focus of each by means of the light of a candle. Then place in the focus of one a red-hot iron ball, or a small chafing-dish of burning charcoal. In the focus of the 278 HEAT. other place the wick of a candle with a small shaving of phosphorus in it. The heat will be reflected, as shown by Fig. 295. the dotted lines (fig. 295), and, setting fire to the phos- phorus, will light the candle. If a thermometer be placed in the focus of one mirror while the hot iron ball is in the other focus, it will rise rapidly ; but if a lump of ice be substituted for the ball, the thermometer will immediately sink, and will continue to do so until several degrees lower than the surrounding air ; because the thermometer radiates more heat to the mirrors , and then to the ice, than the ice returns. DEW AND FROST. All bodies are constantly radiating some heat, and if an equal amount is not returned by others, they grow colder, like the thermometer before the lump of ice. Hence the reason that on clear, frosty nights, objects at the surface of the earth become colder than the air that surrounds them. The heat is radiated into the clear space above without being returned ; plants, stones, and the soil thus become cooled down below freezing, and, coming in con- tact with the moisture of the air, it condenses on them and forms dew, or freezes into white frost. Clouds return or prevent the passage of the heat that is radiated, which is the reason there are no night-frosts in cloudy weather. A very thin covering, by intercepting the radiated heat, will often prevent serious injury to tender plants. Even FEOST IN VALLEYS. 279 a sheet of thin muslin, stretched on pegs over garden vegetables, has afforded sufficient protection, when those around were destroyed. FROST IN VALLEYS. On hills, where the wind blows freely, it tends to re- store to plants the heat lost by radiation, which is the reason that hills are not so liable to sharp frosts as still valleys. When the air is cooled it becomes heavier, and, rolling down the sides of valleys, forms a lake of cold air at the bottom ; this adds to the liability of frosts in low places. The coldness is frequently still fuither increased by the dark and porous nature of the soil in low places radiating heat faster to the clear sky than the more com- pact upland soil. A knowledge of these properties teaches us the import- ance of selecting elevated places for fruit-trees, and all crops liable to be cut off by frost ; and it also explains the reason that the muck or peat of drained swamps is more subject to frosts than other land on the same level. Therefore, corn and other tender crops upon such porous soils must be of the earliest ripening kinds, so as to escape the frosts of spring by late planting, and those of autumn by early maturity. REMARKABLE EFFECTS OF HEAT ON WATER. The effects of heat and cold on water are of a very in- teresting character. "Without its expansion in freezing, the soil would not be pulverized by the frost of winter, but would be found hard, compact, and difficult to culti- vate in spring ; without its expansion into steam, the cities which are now springing up, and the continents that are becoming peopled, through the influence of rail-ways, steam-ships, and steam manufactures, would mostly re- 280 HEAT. main unbroken forests ; without the crystallization of wa- ter, the beautiful protection of plants by a mantle of snow, in northern regions, would give place to frozen sterility ; without the conversion of heat to a latent state in melt- ing, the deepest snows would disappear in a moment from the earth, and cause disastrous floods ; without its con- version to a latent state in steam, the largest vessel of boiling water would instantly flash into vapor. All these facts show that an extraordinary wisdom and forethought planned these laws at the creation ; and even what appears at first glance as an almost accidental exception in the contraction of bodies by cold, and which causes ice to float upon water, preventing the entire masses of rivers and lakes from becoming permanently frozen, furnishes one out of an innumerable array of proofs of creative de- sign in fitting the earth for the comfort and sustenance of its inhabitants. APPENDIX. SIMPLE APPARATUS FOR ILLUSTRATING MECHANICAL ' PRINCIPLES. For the assistance of lecturers, teachers, and home students, the fol- lowing list is given of cheap and simple apparatus and materials for performing most of the experiments described in the first part of this work. These experiments, although simple, exhibit principles of much practical importance. 1. Inertia apparatus, p. 12. The concave post or stand is sufficient, the snapping being done by the finger, although a spring-snap performs the experiment more perfectly. 2. "Weight with two hooks and fine thread, p. 13. 3. The inertia of falling hodies may be simply shown, and the pile- engine illustrated, by placing a large wooden peg or rod upright in a box of sand, and then dropping a weight upon its head at different heights, which will drive the rod into the sand more or less, according to the distance passed through by the falling weight. 4. A straw-cutter, so made that the fly-wheel can be easily taken off, will show in a very striking manner the efficacy of this regulator of force. 5. Two lead musket balls will exhibit the experiment in cohesion, p. 27. Balls or lead weights with hooks may be separated by sus- pending weights, to show the amount of force required to draAv them asunder. Metallic buttons or plates an inch in diameter, with hooks, will show the great strength needed to separate them when coated with grease, p. 27. 6. Capillary tubes of different sizes, two straight small panes of glass, and a vessel of water, highly colored with cochineal or other dye, to ex- hibit capillary attraction. 7. Glass tube, piece of bladder, and alcohol, for experiment described on p. 33. 8. The cylinder for rolling up the inclined plane, represented by fig. 18, p. 34, may be very easily made by using a round pasteboard box a few inches in diameter, and securing a piece of lead inside by loops made with a needle and thread. The object shown by fig. 19 may be cut in one piece out of a pine shingle, the centre rod being lengthwise with the grain ; the two extremities are shaved small, and wound with thick sheet-lead, and the whole then colored or painted a 281 282 APPENDIX. dark hue, to render the lead inconspicuous. The experiment with the penknives, p. 35, is very simple, care being taken to insert them low enough in the stick. 9. Irregular pieces of board, variously perforated with holes, and fur- nished with loops to hang on a pin, may be used to determine the centre of gravity, according to the principle explained by fig. 21, p. 35. 10. Portions of plank and blocks of wood, with the centre of gravity determined as in the last experiment, may have a plumb-line (which may be a thread and small perforated coin) attached to this centre, and then be placed on differently inclined surfaces, to show their upsetting just as this line of direction falls without the base. Toy-wagons, bought at the toyshops, may be variously loaded and used in experiments of this sort. 11. Experiments with the lever of the first kind may be easily per- formed by the use of a flat wooden bar, two or three feet in length, marked into inches, and placed on a small three-cornered block as a fulcrum. Weights, such as are used for scales, may be variously placed upon the lever. Levers of the second and third kind, which are lifted instead of borne down, may have a cord attached to the point where the power is to be applied, running up over a pulley or wheel, with a weight suspended to the other end. 12. An axle, furnished with wooden wheels with grooved edges, of different sizes, may be used to exhibit the principle of the wheel and axle, in connection with scale-weights that are furnished with hooks. The power of combined cog-wheels may be shown by a combination like that represented on p. 57, using weights for both cords. 13. Interesting experiments with the inclined plane, at different de- grees of slope, by a contrivance similar to that represented by fig. 96, p. 83, with the addition of a small wheel at the upper side for a cord to pass over. This cord is fastened at one end to a light toy-wagon, run- ning up and down the plane, and at the other to a weight suspended perpendicularly just beyond the upper edge of the plaue. The wagon is variously loaded with weights, to counterpoise the suspended weight at different degrees of inclination. 14. A lecturer may quickly demonstrate before a class the small in- crease in the length of a road, in consequence of a considerable curve to one side of a straight line (as shown by fig. 69), by using a cord for measuring, the diagram being marked on a board or the wall. 15. A round stick of wood, and a long, wedge-shaped slip of paper, easily show the principle of fig. 75, p. 70. 16. A cog-wheel with endless screw and winch (fig. 77, p. 71), exhibits distinctly the great power of the screw in this combination. 17. Pine sticks, two feet long, and one-fourth to one-half inch through, of different shapes and sizes, supported at each end, and with weights hung at the middle till they break, may be made to illustrate the princi- ples described on pp. 80, 81. 18. Some of the manciples of draught may be shown, and especially APPARATUS FOR EXPERIMENTS. 283 those in relation to the different angles of inclination for hard and soft roads, by using a common spring-balance as a dynamometer, attached to a hand-wagon, and also to a sliding block of wood. 19. Bent glass tubes, with arms of different sizes, to indicate the up- ward pressure of liquids, may be procured cheaply at glass-works. The experiment described by fig. 231, p. 204, may be rendered easy and inter- esting by purchasing a large and perfectly-working syringe, and attach- ing to its nose, by means of sealing wax, a slender glass tube two or three feet long. Fill the syringe with water, leaving the tube empty ; then, with the tube upright, drive the water up through it with the pis- ton of the syringe, and the increased weight felt on the piston as the column of water rises will be very evident. 20. A hydrostatic bellows a foot in diameter, made by any good mechanic, will answer the purpose well, and exhibit an important prin- ciple! 21. Specific gravities may be shown before a class by a common balance and a fine cotton or silk thread. 22. A tin pail, with a hole half an inch or an inch in diameter at the bottom, will show the contracted stream which pours from it, p. 212. A short tin tube, with a slight flange at the upper end (quickly made by any tin-worker), fitted into this hole, will increase the discharge, as shown by figs. 236, 237, and the difference in time for emptying the ves- sel may be measured by a stop-watch. 23. Archimedes' screw is readily made by winding a lead pipe rouud a wooden cylinder. 24. A glass syphon, filled with cochineal water, shows distinctly the theory of waves, by blowing with the mouth into one end. 25. Any vessel, filled with saud which has been heated over a fire, with rods of different substances, nearly of an equal size and length, and thrust with one end into the hot sand, in an inclined or nearly hori- zontal position, will exhibit the various conducting powers of these rods b) r melting pieces of wax or tallow placed on the ends most remote from the sand. 26. The expansion by heat may be demonstrated by fitting an iron rod to a hole in sheet-iron ; on heating the bar it can not be made to enter. Or, if a hot iron ring be slipped on a tapering cold iron rod, it will contract on cooling so that the force of a man can not withdraw the rod. 27. The rising and descending currents in a vessel of heating water are easily rendered visible by throwing into a glass vessel, or flask, over a lamp, particles of sawdust from any hard, greeu wood, whose specific gravity is about the same as that of water. 28. Instrument figured on p. 265, for showing the principle of the steam-engine. 29. Experiments in latent heat may be easily exhibited with the as- sistance of a common thermometer. 30. Tin mirrors for showing radiation, p. 278. 284 APPENDIX. DISCHARGE OF WATER THROUGH PIPES. Table showing the amount of water discharged per minute through an orifice one inch in diameter ; also through a tube one inch in diame- ter "and two inches long, according to experiment. To ascertain the amount in gallons, divide the cubic inches by 231. Height of head Amount discharged Amount discharged of water. through Orifice. through Tube. 1 Paris foot* 2,722 cub. in. 3,539 cub. in. 2 " 3,846 " 5,002 " 3 " 4,710 " 6, 6 " 4 " 5,436 " 7,070 " 5 " 6,075 " 7,900 6 " 6,654 " 8,654 7 " 7,183 " 9,340 " 8 " 7,672 " 9,975 " 9 " 8,135 " 10,579 " 10 " 8,574 " 11,151 " 11 " 8,990 " 11,693 " 12 " 9,384 " 12,o 5 " 13 " 9,764 " 12,699 " 14 " 10,130 " 13,177 " 15 " 10,472 " 13,620 " VELOCITY OF WATER IN PIPES. The following table shows the height of a head of water required to overcome the friction in horizontal pipes 100 feet long, and to produce a certain velocity, according to Smeaton : Bore of Pipes. 6 Inches. lfOOt. IVzfeet. 2/eet. Zfeet. 4feet 5 feet. in. in. in. in. ft. in. ft. in. ft. in. ft. in. K 4.5 16.7 35.1 4 9.7 10 1.0 17 10.0 28 0.2 % 3.0 11.1 23.3 3 2.5 6 8.6 11 10.6 18 8.1 l 2.2 8.4 17.5 2 4.9 5 0.5 8 11.0 14 0.0 IK 1.8 6.7 14.0 1 11.1 4 0.4 7 1.6 11 2.5 IK 1.5 5.6 11.7 1 7.2 3 4.3 5 11.3 9 4.1 1% 1.3 4.8 10.0 1 4.5 2 10.6 5 1.1 8 0.1 2 1.1 4.2 8.7 1 2.4 2 6.2 4 5.5 7 0.0 2U 1.0 3.7 7.8 1 0.8 2 9.9 3 11.6 6 2.7 2K 0.9 3.3 7.0 11.5 2 0.2 3 6.8 5 7.2 3 0.7 2.8 5.0 9.6 1 8.2 2 11.7 4 8.0 3K 0.6 2.4 5.0 8.2 1 5.3 2 6.6 4 0.0 4 0.6 2.1 4.4 7.2 1 3.1 2 2.7 3 6.0 * A Paris foot is about 12 4-5 U. S. inches, and 15 Paris feet are about 16 U. S. feet. RULE FOR THE DISCHARGE OF WATER. 285 Look for the velocity of the water per second in the pipe, in the up- per line ; and in the column beneath it, and opposite the given diameter of the pipe, is the height of the columu or head required to obtain the required velocity. To find the quantity of water discharged each minute, multiply the velocity by 12, which will give the inches per second ; then multiply this product by 60, which will give the inches per minute ; then, to change these cylindrical inches into cubic inches, multiply by 4 and divide by 5.* Divide the cubic inches by 231, and the result will be gallons. Bj T comparing this table with the next preceding, we shall perceive that the water flows from three to four times as fast through the tube two inches long, as through a tube one hundred feet long, the diameter of the tube and the head of water being the same. RULE FOR THE DISCHARGE OF WATER. The following general formula or rule, applicable to different cases, has been furnished by a practical engineer. It may be useful in ascer- taining the quantity required to fill the driving pipe of a water-ram, and for various other purposes occasionally occurring in practice. Let A represent the fountain or reservoir from which water is to be conveyed to the trough B through the pipe L. Let // be the height of the surface of the water in the reservoir, above the place of discharge, L the length of the tube in feet, and let D be the diameter of the tube in the smallest part. It is required to find the quantity, §, which will be discharged in a second of time. The length and height being given in feet, and the diameter of the tube in inches, the formula, when the quantity is required in gallons, is as follows : Q = 0.608 V^ D l) • This gives the cubic inches very nearly ; but, to be more accurate, multiply the decimal .7854, which represents the difference between the area of a square and of a circle. 286 APPENDIX. In order to make the above formula more intelligible : Let L = SO rods or 1320 feet. " H = 50 feet, " D = 2 inches. " Q = gallons. Then Q =0.60S i / (32x-,f|o) = 0.67; or, the same maybe thus ex- pressed in words : Divide the height (50) by the length (1320) ; multiply the quotient by the fifth power of the diameter (fifth power of 2 = 32) ; extract the square root of the product, which, being multiplied by 0.608, will give (0.67) the number of gallons the tube will discharge in one second ; which, in this case, is 40 gallons in one minute. VELOCITY OF WATER IN TILE DRAINS. An acre of laud in a wet time contains about one thousand spare hogsheads of water. An underdrain will carry oft' from a strip of land about two rods wide, and one eighty rods long will drain an acre. The following table will show the size of the tile required to drain an acre in two days' time, (the longest admissible), at different rates of descent, or the size for any larger area : Rate of Descent. 1 foot in 100 1 foot in 50 1 foot in 20 1 foot in 10 1 foot in 100 1 foot in 50 1 foot in 20 1 foot in 10 1 foot in 100 1 foot in 50 1 foot in 20 1 foot in 10 A deduction of one-third to one-half must be made for the roughness of the tile or imperfection in laying. The drains must be of some length, to give the water velocity, and these numbers do not, therefore, apply to very short drains. iameter of Bore 2 iuches. 2 inches. 2 inches. 2 inches. 3 inches. 3 inches. 3 inches. 3 inches. 4 inches. 4 inches. 4 inches. 4 inches. Velocity of Hogsheads Current per discharged second. in 24 hours. 22 inches. 400 32 inches. 560 51 inches. 900 73 inches. 1290 27 inches. 1170 38 inches. 1640 67 inches. 3100 84 inches. 3600 32 inches. 2500 45 inches. 3500 72 inches. 5600 100 inches. 7800 GLOSSARY OF TERMS USED IN MECHANICS AND FARM MACHINERY. Axis, a real or imaginary line, passing through a body, on which it is supposed to revolve. Axle or axle-tree, the bar of metal or timber, on the ends of which the wheels of a carriage or wagon or other wheels revolve. Babbett metal, an alloy, usually of tin and copper, for casing the supports of journals, either for repair, or for easier running. Back furrow, to throw the earth from two plow -furrows together. Ball-cock, a self-regulating stop-cock, closed or opened by the rising or falling of a floating hollow ball. Ball-valve, a valve consisting of a loose ball, fitting closely, pre- vented from moving beyond a certain limit. Band-wheel, a wheel in machinery on which a band or belt runs. Beam, the main lever of a steam-engine, turning on the centre, with the piston rod at one end, and the working-rod at the other. Also, the main timber or bar of a plow. Bearing, the part of a shaft or spindle which is in contact with the supports. Bed, the foundation on which a fixed machine rests, as "the bed of an engine." Bell-crank, a crank resembling that by which the direction of a bell- wire is changed. Bevel-gear, the gearing of cog-wheels placed obliquely together, or with the two axes forming an angle. Bolster, the cross-bar of a wagon, resting on the axle, holding the box, and through which the king-bolt passes. Brake, a lever or other contrivance used for retarding the motion of a wheel by friction against it. Breast-wheel, a water wheel where the current is delivered upon it about one-half or two-thirds its height, which distinguishes it from un- dershot and overshot wheels. Bridle, the forward iron on the beam of a plow, to which the team is attached. Brush-weeel, a wheel in light machinery, turned by friction merely, instead of cogs ; bristles or brushes being often fixed to them to increase the friction of their pressing surfaces. Bush, the hollow box fitted into the centre of a wheel to take the bearing of an axle or journal. 287 288 GLOSSAET. Cam, the projecting part of an eccentric or wavy wheel, to produce alternate or reciprocating motion. Cant-hook, a wooden lever with an iron hook near one end, used for moving heavy articles, particularly saw-logs, etc. The end of the lever is usually placed on the fulcrum, and the hook is fixed into the weight, making it a lever of the second kind. Capillary attraction, the attraction which causes liquids to rise in very small tubes, or which retains water among sand and the particle? of soil. Centre of gravity, that point in a body or mass of matter, arouno which all parts exactly balance each other. Centrifugal force, tending to fly from the centre, as the stone from a sling. Centripetal force, drawing towards the centre, like the cord of a sling. Chamfer, a slope, channel, or groove, cut in wood or metal. Chase, a wide groove. Chilled, applied to cast-iron rendered harder by casting the melted metal against cold metal in the mould, for rendering certain parts harder which are most liable to become worn. Chine, the ends of the staves of a barrel, outside the heads. Clamp, a cross-bar used to give additional strength, or to prevent warping. Also, a piece of metal or wood, generally resembling in shape the letter U, furnished with a screw, to fasten objects to a table or other fixed bodies, or to each other. Cleat, a piece of wood nailed across, to give strength or security. Clevis, a draught iron, usually somewhat in the form of a bow or let- ter U, placed on the forward end of a plow-beam for draught, or for similar purposes. Click, a pawl, a latch, or the ratchet of a wheel. Cog, the tooth or projection of a cog-wheel. Collar, a metal ring around the end of a cylinder of wood to prevent splitting, or a ring around a piston or a journal, for securing tightness or steadiness. Colter or Coulter, the upright cutting iron of a plow. Compass, an instrument for describing circles, measuring distances^ etc. Counter-sink, a cavity made to receive the head of a screw. Coupling-box, a contrivance for connecting shafts, or throwing wheels in and out of gear. Crab, a small portable crane. Cradle, a scythe with fingers, for cutting grain by hand. Crane, a machine for raising weights and then swinging them side- wise ; generally made by attaching a pulley to a swinging bar or frame. Crank, an axle with a crooked portion for changing a rotary to an alternate motion, or the reverse. A three-throw crank has three bends, for driving three pumps, each stroke separated from the others by the GLOSSARY. 289 third of a revolution, thus making a regular and uniform application of the force. Cross-cut Saw, a large saw worked by a man at each end, for cutting logs. Cutter-bar, the cutting apparatus of a mowing or reaping machine. Cycloid, a curve made by any point in a circle rolling on a straight line, and marking the curve on a plane surface at the side of the circle. A rail driven in the rim of a wagon-wheel, driven through a snow bank, will mark a cycloid on the snow. An epicycloid is made by a similar revolution of a circle, rolling on the circumference of another circle, externally or internally. Dead centre, a centre which does not revolve. Dead furrow, the furrow where the plow throws the earth in oppo- site directions, or where the furrows meet in plowing a strip of land. Derrick, a pole or upright timber for supporting a crane, used in lift- ing heavy materials in building and for other purposes. Dog, an iron catch or clutch, driven into the end of a saw-log, to hold it in a fixed position while sawing. Double-tree, the central wbiffle-tree of a two-horse set. Dowel, a short iron or wooden pin to join two pieces of timber, pro- tecting from one timber into a hole in the corresponding one. A familiar example occurs in the manner in which a cooper secures two or more boards in forming the head of a cask. Draught, Angle of, the angle made by a line of draught with a line drawn on ,he surface over which the body is drawn. Dredge, or Dredging Machine, a machine for scooping up mud or earth from under water; for clearing the channels of canals, rivers, and harbors. Drill, a furrow for the reception of seed, or a row of growing plants ; also a machine for sowing seed in continuous rows. Driving-wheel, the wheel of a mowing or reaping machine, which runs on the ground, and propels the gearing. Drum, a revolving cylinder, around which belts or endless straps are passed, to communicate motion. Dynamics, the science of motion and forces. Dynamometer, an instrument for measuring forces, applied to plows, mowing machines, thrashing machines, etc., to show the amount of force required to work them. Eccentric, out of centre; applied to wheels, discs, or circles, with the axle out of centre, to create reciprocating motion. Eccentric rod is the rod that transmits the motion of the eccentric wheel. Elevator, an endless revolving leather strap, set with sheet-iron boxes or cups, for raising grain. The term is also applied to buildings into which grain is thus elevated and stored. Emery wheel, a wheel set with emery at the circumference, for grinding or polishing metals. Endless chain, a chain with the ends connected together, running on in ' 290 GLOSSARY. two drums or cylinders ; as in the endless chain or tread-powers to thrashing machines. Endless screw, a screw working in a toothed wheel or cog-wheel, and imparting a motion to the wheel equal to the advance of one tooth to each revolution of the screw. Epicycloid, see Cycloid. Epicycloidal wheel, a wheel with cogs on its interior rim, fitting into another cog-wheel precisely one-half its diameter, for converting circular into alternate motion ; any point in the circumference of the smaller wheel, while in motion, describing a straight line. Evener, the central or larger whiffle-tree of a set of whiffie-trees for two horses, called also a double-tree. Fan, the vane of a wind-mill, to keep the sails facing the wind. Feather, the thin cutting part of a plowshare, on the right-hand side. Felloe, or Felly, the circumference or rim of a wheel, or a segment of it, into which the spokes are inserted. Ferrule, a ring or hand on the end of a wooden rod or bar, to pre- vent splitting. Female screw, a hole cut with the threads of a screw, into which a screw fits. Finger-bar, that portion of the cutting-bar of a mowing or reaping machine, in which the knife-bar works. Flange, a projection from the end of a pipe or from any piece of mechanism, so as to screw to another part ; a term also applied to the projection of a car-wheel to keep it from running off the rail. Flash- wheel, a water-wheel used for elevating water, resembling a breast-wheel with a reversed motion. Float-board, one of the boards forming the exterior of a water- wheel, against which the stream of water dashes. Flume, the water passage of a mill, usually a box of plank. Fly-wheel, a wheel with a heavy rim, for retaining inertia and equal- izing the motion of machinery. Foot-valve, a valve in a steam-engine, opening from the condenser towards the air-pump. Force-pump, or Forcing-pump, a pump with a solid piston, which drives instead of sucking water. Friction-wheel, made by two wheels overlapping each other, and bearing between them the axle or journal of another wheel, thus dimin- ishing the friction of the latter. Fulcrum, a support ; applied to the support used for the lever, in raising weights. Furrow slice, the strip of earth thrown out by the plow at a passing. Furrows, plat and lapping; when the slice is laid flat or level, and when the edge of one overlaps the preceding, respectively. Gang-plow, a compound plow made of a series of plows running side by side. Gavel, a sheaf of grain reaped but not bound. GLOSSARY. 291 Gearing, a series of cog-wheels working together. Governor, a self-regulator of a steam-engine, so constructed that centrifugal force throws up weights When the engine runs too fast, and partly closes the admission pipe of steam ; and, dropping again when it runs too slow, opens the steam pipe. Gravitation, the attraction between bodies in mass, as distinguished from cohesion between the particles; the force which causes bodies to fall by the attraction of the earth. Guard, one of the fingers in the cutting apparatus of a mowing or reaping machine, for protecting the knives from injury from external ob- jects. Open Guard has an opening above the knives, to prevent clog- ging. Hat-tedder, a niachiue for spreading and turning hay. • Header, a reaping machine which cuts the heads of the grain and leaves most of the straw standing. Head-land, the strip or border of unplowed land left at the ends of the furrows. Hound, the forward portion of a wagon, to which the tongue is at- tached. Hydraulic Ram, see Ram. Hydraulics, the science of water in motion, or the laws of motion and force as applied to running water, and to machinery driven by it. Hydrodynamics, the laws of motion and force, as applied to liquids, both in motion and at rest, and embracing Hydraulics and Hydrostatics. Inclined plane, a plane or surface deviating more or less from a level. if Inertia, the property or force of matter by which it retains its state of motion or rest, — requiring force to start a body at rest or to stop one in motion. Jack, an engine or machine for raising heavy weights. Jack-screw, a strong iron screw for raising timbers, buildings, etc. Journal, the portion of a shaft or axle which revolves on a support. Kerf, the opeuing or slit made by the passage of a saw. Key, a wedge of wood or metal driven iuto a mortise or opening, to secure two parts together. Knee-joint, or Toggle-joint, a contrivance for exerting power or pressure, by straightening a double bar with a joint like that of the knee. Land, a term applied to the oblong portion of a field around which the team passes in plowing, the field being usually divided into several lands for this purpose. The term is also applied to the side of a plow opposite the mould board, and a plow is said to run to land when it takes too wide a furrow-slice. Land-side, the side of that portion of a plow which runs in the soil, opposite the mould-board, and next the unplowed portion of ground. Lantern-wheel, a pinion made of two small wheels connected by parallel rods which form the teeth. 292 GLOSSARY. Lever, a bar or rod for raising weights, resting on a point called a fulcrum. Lever-power, see Sweep-power. Male screw, a screw with a spiral thread, fitting into a hole with cor- responding threads called a female screw. Mechanical powers, the simple machines or elements of machinery, consisting essentially of the Lever and Inclined Plane ; the lever com- prising the Wheel and Axle and the Pulley, and the inclined plane com- prising the Wedge and the Screw. Mash, or Mesh, to interlock, as the teeth of cog-wheels. Mechanics, the science that treats of forces and powers, and their action on bodies, and particularly as applied to the construction of ma- chines. Mitre, to cut to an angle of 45 degrees, so that two pieces joined shall make a right angle. Momentum, impetus ; the force of a moving body. Monkey, an apparatus for disengaging and securing again the ram of a pile-engine. Mortise, a hole cut to receive the end or tenon of another piece. Nut, a piece of iron furnished with a screw-hole, used on the end of a screw for securing the parts of machinery. Overshot wheel, a water-wheel, the circumference of which is fur- nished with cavities or buckets, into which the stream of water is deliv- ered at the top, turning the wheel by its weight. Pall, or Pawl, the catch of a ratchet-wheel ; a click. Pent-stock, an upright flume. Perambulator, a measurer of distances, consisting of a wheel, and index to show by wheelwork the number of its turns. Percussion, Centre op, that point of a moving body at which its im- petus is supposed to be concentrated. Pile-driver, or Pile-engine, an engine for driving piles into the ground, effected by repeatedly dropping a heavy weight on the heads of the piles ; used mostly in swamp or water when the bottom is mud. Pinion, a small-toothed wheel, working in the teeth of a larger one. Pitch, the distance between the centres of two contiguous cog-wheels. Pitch line, the circle, parallel with the circumference, which passes through the centres of the teeth of a wheel. Pitman, a rod connected with a wheel or crank, to change rotary to reciprocating motion, or the reverse. Planet-wheels, two elliptical wheels connected by teeth running into each other, and revolving on their foci. Plow-beam, the main timber of a plow, by which it is drawn. Plow-share, the front part beneath the soil, which performs the cut- ting — sometimes called plow-s7we, or plow-point. Plunger, the piston of a forcing pump. Pneumatics, the science treating of the mechanical properties of air. Pole, the tongue of a reaping or other machine. GLOSSARY. 293 Power, the moving force of a machine, as opposed to the weight, load, or resistance of the substance wrought upon ; also called prime mover. Projectile, a body thrown through the air. Pulley, one of the mechanical powers, consisting of a grooved wheel called the sheave, over which a rope passes ; the box in which the wheel is set is called the block. The term is also applied to a fixed wheel over which a band or rope passes. Pump, a hydraulic machine for raising water; or one for withdrawing air. The handle is called the brake. Quantity of motion, the velocity of a moving body multiplied by its mass. Rabbet, to pare down the edge of a board or timber. Rack, a straight bar cut with teeth or cogs, wprking into a correspond- ing cog-wheel or pinion which drives or follows it. Rag-wheel, a wheel with teeth or notches, on which nn endless or re- volving chain usually runs. Also applied to a ratchet wheel. Rake-head, the cross-bar of a rake, which holds the teeth. Ram, Hydraulic ram, or Water-ram, a hydraulic machine or engine for raising water to a height several times greater than that of the head of water, by employing the momentum of the descending current in successive beats or strokes. Ratchet-wheel, a wheel cut with teeth like those of a saw, against which a click or ratchet presses, admitting free motion to the wheel in one direction, but insuring it against reverse motion. Reach, the bar which connects the forward and rear axles of a wagon or carriage. Rea.m, to bevel out a hole. Reciprocating motion, alternate motion, or a movement backwards and forwards in the same path. Reel, the revolving frame of a reaping machine, to throw the stand- ing grain towards the knives. Resolution of forces, dividing a force iuto two or more forces act- ing in different directions ; rendering a compound force into its several simple forces. Resultant, a force produced by the combination of two or more forces. Safety valve, a valve opening outwards from a steam boiler, and kept down by a weight, permitting the escape of steam when the press- ure reaches a certain point, regulated by the degree of weight. The term also applies to a valve opening inwards, and similarly regulated, to prevent the pressure of the atmosphere from crushing in the boiler when the steam cools and leaves a vacuum. Scoop- wheel, a water-wheel with scoops or buckets around it, against which the current dashes. Screw-bolt, a bolt secured by a screw, or with a screw cut upon it. Screw-propeller, an instrument for driving a vessel, by means of 294 GLOSSAEY. blades twisted like a screw, revolving beneath the water, the axis being parallel with the keel. Section, one of the knives or blades on the cutter-bar of a mowing machine. Self-raker, a contrivance attached to a reaping machine, to throw off the cut grain in gavels, to obviate raking off by hand. Shears, or Sheers, two poles lashed together like the letter X, for placing under heavy poles, etc., in raisiug them; also to single vertical poles supporting pulleys, for a similar purpose. Sheave, the wheel of a pulley set in a block. Shoot, or Shute, a passage-way down which grain, hay, or straw, is slid or thrown. Side-draught, the side pressure of a machine on the team which draws it, as distinguished.from centre draught. Single-tree, a single whiffle-tree, the cross-bar to which the traces of a horse are attached, as distinguished from a double-tree, or two-horse whiffle-tree. Siphon, or Syphon, a bent tube for drawing off liquids ; the column of liquid in the outer or longer leg overbalancing the inner column, and producing a current. Skein, the iron casing of a wagon-axle on which the wheel runs. Skim-coulter, a coulter of a plow so constructed as to pare the sur- face before the mould-board. Skim-plow, the small forward mould-board of a double Michigan or Sod-and-subsoil plow. Slide-rest, the rest or support of the chisel in a turning lathe, made to slide along the frame for cutting successively the different parts of the work. Slot, a slit or oblong aperture in any part of a machine, to admit an- other part. Snath, the handle or bar to which the blade of a scythe is attached. Sod, the slice of earth cut by the passing of a plow. Sole, the bottom plate under a horse-shoe tile, in draining. Spindle, a small axle in machinery, as distinguished from a shaft or large axle. Spirit-level, a glass tube containing alcohol with an air-bubble, her- metically sealed at both ends, the position of the bubble at the middle showing the tube to be level. Spur-wheel, or pinion, a cog-wheel with teeth parallel to the axle. Standard, an upright supporting timber ; the front upright bar in a plow to which the mould-board is fastened. Steam chest, a box attached to the c} 7 linder of a steam-engine, in which the sliding valves work. Stirrup, an iron band encasing a wooden bar, for attaching to some other part. Stud, a short, stout support. GLOSSARY. 295 Subsoil-plow, a plow running below the furrow of a common plow, for breaking up or loosening the subsoil or lower soil of a field. Swage, to give shape to a substance by stamping with a die. Sweep-power, a horse-power for driving thrashing and other ma- chines, where the horses arc attached to a pole and walk in a circle. Swingle-tree, also called" swing-tree, single-tree, whipple-tree, and whiffle-tree ; the cross-bar to which traces are attached. Swing-plow, a plow with no wheel under the beam. Swivel, a ring and axis in a chain, to admit of its turning. Swivel bridge, a bridge which turns round sideways on its centre. Swivel plow, a side-hill plow, or a plow with a reversible mould-board. Tackle, a pulley, or machine with ropes and blocks for raising heavy weights. Tail-race, the channel which carries off the water below a water wheel. Tedder, a machine for turning and spreading hay. Thill, one of the shafts of a wagon between which the horse is put — often corrupted to Fill. Throttle- valve, a valve which turns at its centre on an axis — gener- ally used to regulate the supply of steam to the cylinder of a steam-en- gine. Thumb-screw, a screw with its head flattened in the direction of its length, so as to be turned with the thumb and finger. Tide- wheel, a wheel adapted to currents flowing both ways — the float- boards pointing from the centre. Tine, the tooth or prong of a fork. Tire, the iron band which binds together the fellies of a wheel. Toggle-joint, or knee-joint, a mechanical power exerted by straight- ening a double bar with a hinge at the middle or connection. Torsion, the act of twisting by the application of lateral force. The force of torsion is the elasticity of a twisted body, Track-cleaner, an attachment to a mowing machine, to throw the cut grass away from that which is uncut. Traction, Angle of, the angle between the line of draught and any given plane, as that of the earth's surface. Trammel, an instrument used by carpenters for drawing an ellipse. Tread-power, a machine on which the horse or other animal working it walks. It may be either a horizontal or slightly inclined wheel ; or an endless-chain power, the term being more frequently applied to the latter. Trench-plow, a plow cutting deep furrows and bringing the subsoil up to the surface; as distinguished from a subsoil plow, which only loosens the subsoil and leaves it below the surface. Trundle-head, a wheel turning a mill-stone. Tub-wheel, a horizontal water-wheel, driven by the percussion of the stream against its floats, and not submerged in water. 296 GLOSSARY. 3 the Tumbler, a latch in a lock, which, by means of a spring, detains bolt in its place until lifted by the key. Tumbling rod, the rod which connects the motion of a horse-power with that of a thrashing or other machine. Turbine wheel, a horizontal water-wheel, so constructed that the current strikes all the floats or buckets around the circumference at the same time, thus imparting to it great power for its size. It is sub- merged, the water escaping towards the centre and below, or above and below together. Undershot wheel, a water-wheel moved by the current striking against the lower portion of its circumference. Universal joint, a connecting joint between two rods, consisting of a sort of double hinge, admitting motion in any direction. Valve, a lid for closing an aperture or passage, so as to open only in one direction. Velocity, speed or swiftness; which may be uniform, or equal throughout ; accelerated, or increasing ; or retarded, or rendered slower. Virtual velocities, Principle of, that by which certain powers are equal to each other, where the force and space moved over, whatever these may be, are the same when multiplied together. Washer, a circular piece of metal, pasteboard, or leather, placed be- low a screw-head, or nut, or within a linch-pin, for protection. Water-ram, see Ram. Whiffle-tree, or Whipple-tree, the cross-bar to which the traces of a horse are attached ; see Single-tree. Whip-saw, a large saw, worked by a man at one end, with a wooden spring at the other ; a cross-cut saw. Winch, a bent handle or right-angled lever, for turning a wheel or grindstone, or producing rotary motion for other purposes. Windlass, a machine for raising heavy weights, by the winding of a rope or chain on a horizontal axle, and turned by a winch or by levers. Winrow, or Windrow, the ridge of hay raked up on a meadow. Wrest, a partition which determines the form of the bucket in an overshot wheel. INDEX Air, Pressure of 239 u Mode of weighing 239 " Pump 240 " Hand fastened, by 241 " Motion of. 245 " Resistance of. 247 Alden's Cultivator 14G Allen's Farm Mill 195 Altitudes measured by the Barome- ter 243 American Hay-tedding Machine 165 Appai-atus for Experiments 281 Aqueducts of the Romans 199 Archimedean Root Washer 193 " Screw 217 Archimedes, would move the earth with a lever 55 Artesian Springs and wells 201 Atmosphere, Height and Weight of 239, 241 B Bags, How to carry 41 Balance, a lever 47 Balls, Why they roll easily 38 Barometer 241 Bars of wood, Strength of. 79 Beardsley's Hay Elevator 177 Bellows, Hydrostatic 204 Bevel Wheels or Bevel Gear GO Billings' Corn Planter 155 Binders for Reaping Machines 163 Boat, Compound motion of. 20 Broadcast Sower, Seymour's . .154 Brown's Wind-mill 251 Brush Harrow 142 Buckeye Mower 159 Bullard's Hay-tedding Machine 165 Bulk of a ton of different substances. 210 Burrairs Corn-sheller 191 C Capillary attraction 31 " " its great import- ance 32 Cayuga Chief Mower 160 " " Dropper 162 Cements, Effects of. 28 Centre of Gravity 34 " " curious examples of ) 35 " how determined 35 Centrifugal Force 21 Chain Pump 221 Cheese Press 72 ." " Dick's 74 11 " Kendall's 73 Chimney Currents 253 " Caps 254 Chimneys, Construction of 254 " To prevent smoking 256 Churn with fly-wheel 17 " worked by dog-power 191 Cistern Pumps 219 Cisterns, To calculate contents of. .237 " Proper sizes for 238 Clod Crusher .149 " " Croskill's and Ameri- can 150,151 Cog, Hunting 60 Cogs, Form of 58 " and Cog-wheels 58 Cohesion, Attraction of 27 " between lead balls 27 " weak in liquids 31 Complex Machines, objectionable.. 116 Compound motion 19 " " How to calculate. 20 Comstock's Rotary Spader. . . .148, 117 Conducting power of bodies 260 " " liquids 261 Corn Planter, Billings' 155 " Shelter, 'Burrairs 191 297 Q* 298 INDEX. Corn Sheller, Horse-power 192 Richards' 192 Corn Planters 155 Cost of Implements and Machines. 117 Cotton Gin, Emery's 196 Coulter for Plows 127 Crested Furrow-slice 126 Crosskill's Clod-crusher 150 Crow-bar, a simple power 43 Crown Wheels 60 Cubic foot of different substances, Weight of 210 Cultivator, or Horse-hoe 145 Claw-toothed 146 Alden's Thill 146 " Duck-foot 146 " Two-horse 148 " Harrington's 157 Cutter for the Plow 127 " Bar in Mowers and Reapers. 158 B Dederick's Hay-press 185 " Capstan 185 Deep-tiller Plow, Holbrook's 126 Deep Wells, Pump for 220 Dew and Frost 278 Discharge of water through pipes.. 284 " " Rule for 2S5 Ditches, Velocity of water in. .214, 286 " Leveling instruments for.. 115 Dog-power Churn 191 Draught, Combined 96 Draught of wheels, explained 37 " Line of 95 " Principles of 93 " How to measure 94 " of Plows 95 Drilling wheat 153 Drills, Hand 157 Drive-pump 220 Dropper, attachment to reapers 162 Dynamometer, applied to roads S5 " Construction and use of 98 " Self-recording 101 " Waterman's 102 ■ " for rotary motion... 106 E Elevators for Hay 173 Emerson's Chimney Cap 255 Emery's Horse-powers 1S8 Cotton Gin 196 Empire Wind-mill 251 Endless-chain power 1S8, 189 Engine, Garden. . : 230 Experiments, apparatus for 281 F Falling Bodies, Velocity of 23 " " Resistance of air on 25 " " in vacuo 25 Farm, Seventy-thousand-acre 8 " implements, Construction and use of. 115 " implements, Cost of 117 " mills 195 Finger-bar in mowers and reapers.. 15S Flail, Old sort 187 " Estimate of comparative work with 187 Flash-wheel 231 Flea, power of leaping 115 Fly-wheel 16 " used on horse-pump 16 Forcing-pump 223 Fork Handles, Proper form of 76 Forsman's Farm Mill .195 Friction '. 81 " Nature of 82 " How to Measure 83 " not influenced by velocity. 88 " of axles 89 " of wheels . 90 " Lubricating substances for. 91 " Advantages of 92 Frost and Dew 278 " in valleys 279 Fuel, Green wood for 275 Furrow-slice, Crested 126 Furrows, Lapping and flat 127 G Galileo's experiment on falling bod- ies 26 Garden Engine 230 Garrett's Horse-hoe 147 Geddes' Harrow 143 Gladding's Hay -fork 175 Glossary of terms 287 Gravitation 23 Gravity, Centre of. 34 INDEX. 299 Gravity, Specific, how measured.. .208 " "of different sub- stances 200 Green wood for fuel , 274 H Hand-drills 157 " rakes, sulky 160 Harrington' s Seed sower 157 " Cultivator 157 Harrow, Norwegian 144 " Morgan 144 " Scotch, or square 143 Harvester, Marsh's 163 Hay-forks, Horse. 173 " carriers 180 " loaders 186 " rake, Revolving 168 " " Warner's 169 " rakes 166 " Simple 167 " stacking machine 184 " tedder, Bullard's 165 " " American.. 166 " presses 184 " sweep 171 Headers 163 Heat, Properties of. 260 " Expansion by 263, 271 " Latent 273 " Radiation of 276 Hicks' Hay -carrier 180 High pressure steam-engines 269 Hoe-handle, Proper form of 77 Holbrook's Plow 125 " Swivel or side-hill Plow.133 Horse, day's work at different de- grees of speed 110 " hoe, Garrett's 147 " power, Estimating 109 " Hay-forks, Operation of 174 fork, Gladding's 175 " " Palmer's 176 " " Myers' 177 " " Beardsley's 177 " " Raymond's 178 " " Harpoon 179 " Walker's 179 " Sprout's 179 Hydraulic Ram 226 " " Regulating 227 Hydrostatic Paradox 203 Hydrostatic Bellows 204 " Press 203 Hydrostatics , 198 I Implements required for the farm. . 7 9,117 " Construction and use of 115 Improvements in Farm Machinery. 8 Inclined Plane 63 Inertia 11 " apparatus 12 M Effects of, on wagons 13, 17 J Joint, Universal 60 K Kirby Mower and Reaper 159 " Reaper, Hand-rake for 160 " " Self-raking 161 Knee-joint, or Toggle-joint 71 Knives in mowers and reapers, Form of 158 Kooloo Plow 118 I< Labor, Application of 108 " of men and horses 110 Ladders, Self-supporting 40 Lapping and flat furrows 127, 128 Latent heat 273 " " Advantages of. 275 Law of virtual velocities 43 Leveling Instruments 215 Levers 45 " of the second kind 45 " " first kind 46 • « " third kind 46 " Calculating power of. — 49,50 " Examples of. 46 " Combination of 50 Line of direction 36 Liquids, Velocity of, in falling 211 " Discharge through pipes. .212 Loads on sideling roads 37 Lubricating substances 90 300 INDEX. M Machinery iu connection with water.198 Machines, Advantages of 42 11 Models of 113 " Complex, objectionable. .116 " Construction and use of. .115 " Required for the Farm. 7, 9,117 Marsh's Harvester 163 Materials, Measuring strength of. .. 29 Mechanical powers 42 " principles, Advantages of 10 Mechanical principles, Application of 75 Models of machines 113 Moline Plow 120 Momentum 14 " Calculating quantity of.. 18 " of railway trains 18 Moorish Plow 118 Morgan's Harrow 144 Motion, Compound 19 Mouldboard of the Plow, Form of. .124 Mountains, Height of, measured by barometer 243 Mowing Machine, Wood's 158 " " Kirby's 159 " " Buckeye 159 " " Cayuga Chief.... 160 Mowing Machines, Construction of.158 " " How to select... 164 Myers' Horse-fork 177 N Norwegian Harrow 144 O Ogle, inventor of the Finger-bar.... 159 Ox-yokes 78 P Packer's Stone Lifter 62 Palmer's Horse-fork 176 ' ' Hay-stacking Machine 183 Paradox, Hydrostatic 203 Pile Engine or Driver 15 Pinions, Operation of 60 Pipes, To determine strength of 200 " Discharge of water through, 213, 2S4 Pitts 1 Straw-carrier and Thrasher. . . 190 Plank roads, Amount of resistance on 84,86 Planting Machines 152 Plaster Sower, Seymour's 155 Platform Scales 52, 53 Plow, Kooloo 118 " Moorish , 118 " German 119 " Modern improved 119 " Moline Steel ...120 " Woodruff & Allen's 120 " Double Michigan 131 " Mole 139 " Ditching 138 " Side-hill or Swivel 132 " Subsoil 133, 135 ' l Trench 134 " Paring 137 " Gang 137 " Defects in 122 " Character of a good one 121 " Cutting edge of. 121 " Resistance of different parts. .122 " Form of the mouldboard 124 " Appendages to 140 " Wheel coulter and Weed-hook on 140 Plowing, Operation of. 128 " Fast and slow 130 " Requisites for success in.. 129 Potato Planter, True's 156 " Digger 144 Power of a horse, Estimating 110 Press, Hydraulic 205 Presses for hay 184 Pressure of liquids, Determining. . . 202 " Upward, Measuring 199 " " in liquids 198 Pulley 61 Pulverizers 140 Pump, Cistern : 219 " Non-freezing 219 " Drive 220 " for deep wells 220 " Chain 221 11 Rotary 222 " Suction and Forcing 223 Pumping water by wind 248 Pumps, Construction of 218 Pyramids, Firmness of 38 Pyrometer, how made 26« 9 INDEX. 301 R Rake, Simple form of. 167 " Revolving 108 " " Warner's 10!) " Spring-tooth 170 " " " Hollingsworth's.171 Ram, Hydraulic 226 Raymond's Hay Elevator 17S Reaping Machines during the war. . 8 Self-rakers for.. 161 11 " Headers 163 " " How to select... 161 Revolving Hay Rake 168 Roads, importance of good ones.... 6S " How to form the bed of 67 ** Measuring the friction on. . . 81 " Amount of resistance on 86 " Goodandbad 69 " Ascent in 63, 66 " Cost of going up and down hill 65 Rocks, Machines for removing 62 Rockers, How to make 41 Rogers 152 Rolling Mill, Principle of 74 Root Washer 193 " Slicers 194 Rotary Spader, Comstock's 148, 117 " Pump 222 S Sack-barrow, a lever 48 Sap, Ascent of. 33 Scotch or Square Harrow 143 Screw 70 " Archimedean 217 " Estimating power of.. 71 Seed Sower 153 " " Harrington's 157 Self-raking Reapers 161 Seymour's Broadcast Sower 154 Shares' Harrow 145 Side-hill or Swivel Plow 132 Single-tree, Wier's 98 Sowing Machines 152 Specific gravities, how determined. 208 " " Table of. 209 Springs of water 201 Stacks, Building by machinery 182 Steam engine, Construction of. 265, 267 " " for farm purposes..,. 270 Steel Plows... 120 Steelyard 47 Stone-lifter 62 Straw-cutters 16, 75 " carrier, Pitts' 190 Strength of materials 29 " " wood, iron, and ropes. 30 " " rods and bars 79,80 " " pipes, To determine... 200 Stubble Plow, Holbrook's 126 Stump-puller 54 Subsoil plowing 133 " Plows 135 Swivel Plow 132 Syphon 244 " used for draining 243 T Teeth of wheels 58 Thill-cultivator, Alden's 146 Thrashing by machinery 187 " machine, Comparative cheapness of. 188 Thrashing machine, Endless-chain power for 188 Thrashing machine, Pitts' 190 Toggle-joint power 71 Tread horse-powers 1S8 " " " To determine work of 188 Turbine Water-wheel 223 " " " Reynolds' 224 " " " Van de Wa- ter's 224 U Universal joint 60 Upward pressure of liquids 198 V Vacuum, Machine running in 11 Velocity affects friction but slightly. 88 " of falling water 211 " of water in ditches .... 214, 286 " " through pipes 284 Ventilation 257 " through walls and gar- rets 258 Ventilator, Griffith's 258 " Emerson's 255 Virtual velocities, Law or rule of. . . 43 302 INDEX. W Wagon springs, Advantages of 17 " wheels, Proper width for. . .-. 87 Warner's Revolving Rake 169 Washing Machine 72 Water, Remarkable effects of heat on 279 Water, Velocity of 211, 213 " Discharge of, through pipes. 212 " in ditches .„ 214 " wheels, Turbine. 223 " ram 226 " engines 230 Waves, Nature of. 232 " Velocity of 234 " Breadth and height of 233 4 ' To prevent inroads of . . 235, 236 Weather glass 243 Wedge 69 Weed hook on plows 140 Weighing machine, or platform scales. 52, 53 Wheat drill 152 " " Bickford & Huffman's, Construction of 153 Wheel and axle. . 55 " " " Modifications of ... . 57 Wheelbarrow, Operation of 47 Wheel-cutter to plows 140 Wheels, large ones run best 39 " for wagons Proper width for 87 Whiffle-tree? for three horses 50, 97 Wind, Causes of 252 " Velocity of. . . . 246 " mill 247 " " Pumping water by 248 " "Brown's 251 Wooden legs, why hard to walk on. 40 Wood's Plow 119 Work of men and horses, Estima- ting 110 3477