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Containing the latest Improvements. 8vo, Sheep, $1 50. A SCHOOL AND COLLEGE ALGEBRA. Containing the latest Improvements. &v Muslin, $1 00. AN ELEMENTARY COURSE OF GEOMETRY. 12mo, Sheep, 75 cents. Professor Parker's f the Atmosphere 186 Vlll CONTENTS. IV. Temperature of the Atmosphere Page 187 V. Phenomena of Winds 188 VI. Moisture of the Atmosphere 193 VII. Meteorolites 198 VIII. Relations of the Atmosphere to Animals and Vegetables 199 IX. Ventilation 199 CHAPTER V. OF UNDULATIONS. I. Origin of Undulations 207 II. Laws of Undulations 208 HI. Undulations of Liquids Water-waves 213 IV. Undulations of Gases Air-waves 219 CHAPTER VI. ACOUSTICS. SECTION I. OF SOUND 225 I. Sound-waves 226 II. Varieties of Sound 227 III. Varieties of Tone 228 IV. Conduction of Sound 228 V. Velocity of Sound 230 VI. Distance to which Sound may be propagated 232 VII. Reflection of Sound 233 SECTION II. MUSICAL TONES 236 I. Relation between a vibrating String and musical Notes 237 II. Musical Tones in Pipes 240 III. Transmission of Tones 244 IV. Organs of Voice 245 V. Organs of Hearing 246 CHAPTER VII. OF CALORIC OR HEAT. I. Property of sensible Calorie 248 II. Effect of sensible Caloric 248 III. Insensible Caloric . . .249 CONTENTS. lx IV. Steam Page 249 V. Steam-engine , 252 CHAPTER VIII. ELECTRICITY. SECTION I. STATICAL, OR COMMON ELECTRICITY 259 I. Modes of producing Electricity 260 II. Modes of detecting Electricity 262 III. Electrical States produced by Friction of different Substances. 263 IV. Property of the Electric Fluid 266 V. Distribution of Electricity on Conductors 271 VI. The Leyden Jar 272 VII. Effects of Electricity 277 VIII. Electricity of the Atmosphere 286 IX. Velocity of Electricity 290 X. Nature of Electricity 291 SECTION II. VOLTAIC ELECTRICITY, OR GALVANISM 293 I. Electricity produced by Contact 293 II. Electricity generated by Chemical Action 295 III. Quantity of Electricity in simple and compound Circles 299 IV. Effects of Voltaic Electricity 299 SECTION III. MAGNETIC EFFECTS OF ELECTRICITY, MAGNETISM, ELECTRO-MAGNET- ISM, AND MAGNETO-ELECTRICITY 303 I. Magnetism 304 II. Electro-magnetism 307 III. Influence of Voltaic Currents on soft Iron and Steel 310 IV. Volta-electric Induction 313 V. Magneto-electric Induction 316 VI. Theories of Magnetism, Electro-magnetism, and Magneto- electricity 317 VII. Application of Electro-magnetism to useful Purposes 320 1. Magnetic Telegraphs 320 2. Electro-chronograph 322 VIII. Vital Effects of Electricity 323 IX. Animal Electricity 323 X CONTENTS. CHAPTER IX. LIGHT, OR OPTICS. SECTION I. ORIGIN OF LIGHT, AND THE LAWS WHICH GOVERN ITS TRANSMIS- SION Page 325 I. Origin of Light 326 II. Luminous and non-luminous Bodies 327 III. Laws of the Transmission of Light 328 IV. Intensity of Light 330 V. Velocity of Light 333 SECTION II. REFLECTION OF LIGHT, OR CATOPTRICS 334 I. Laws of the Reflection of Light from Plane Surfaces 335 Images formed by Plane Mirrors 336 II. Laws of the Reflection of Light from Curved Surfaces 339 Images formed by Concave Mirrors 341 Images formed by Convex Mirrors 343 SECTION in. DIOPTRICS, OR REFRACTION OF LIGHT 344 I. Laws of Refraction 345 II. Refraction of Light by Prisms 349 III. Refraction of Light by Lenses 350 IV. Decomposition of Light 357 V. Application of the Laws of Refraction and Reflection to the Explanation of Natural Phenomena ^. 365 SECTION IV. OF THE EYE AND OPTICAL INSTRUMENTS 371 I. Compound Eyes 372 II. Simple Eyes with Convex Lenses 372 III. Distance of Distinct Vision 373 IV. Optical Instruments 376 SECTION V. THEORIES OF THE NATURE OF LIGHT, WITH THEIR ILLUSTRATION AND APPLICATION 384 I. Theory of Emission 384 II. Theory of Undulations 384 CONTENTS. Xi III. Interference of Light Page 386 IV. Polarization of Light 392 1. By Reflection 392 2. By Refraction 394 V. Double Refraction 395 SECTION VI. CHEMICAL AGENCY OF LIGHT, AND THE CONNECTION OF LIGHT, HlAT, AND ELECTRICITY 39f* I. Chemical Agency of Light 40( II. Photography 40( III. Connection of Light, Heat, and Electricity 401 NOTE TO TEACHERS. THE author would recommend to those teachers who may use this work to adopt a method which he has employed and found successful, in refer- ence to the analysis at the head of each section. H has been accustom- ed to require his pupils, especially in the junior classes, to o*nrart thorough- ly to memory the analysis before studying the section. UNI7EESITY [ N r R D U C 1 ION. THE term Philosophy means the love of wisdom. Its object is to ascertain the causes of events, or of changes in matter and in mind. When the facts or phenomena which result from some common cause are arranged and classified in accordance with cer- tain fixed principles, they constitute a Science. Mental science consists of an orderly arrangement of the laws and phenomena of mind ; physical or material science, of a similar arrangement of facts and principles which relate to matter. Natural Philosophy is that science which relates to the forces and laws which govern matter in masses. Its object, therefore, is to attain a knowledge of forces and motions. The science of Chemistry, on the other hand, has reference to the composition of bodies. Its object is to ascertain what kinds of matter exist, to determine the forces which produce the compo- sition and decomposition of masses, and the laws by which such forces are regulated. If there were but one kind of matter, as water or iron, there would still be a wide field open for the natural philosopher, for he does not regard the nature of matter, but simply its mechan- ical properties, the phenomena of perceptible distance. If there were not more than one kind of matter, the chemist would have no subjects for investigation, as his object is to study those changes of imperceptible distance, which can occur only when two or more kinds of matter are in apparent contact. In Natural Philosophy we are to regard masses of matter as a collection of very small particles called atoms, all similar in con- stitution, and held together, in solids and liquids, by a force of Meaning of Philosophy, of Science, of Natural Philosophy, of Chemistry. Of what does a mass of matter consist ? 14 INTRODUCTION. attraction called Cohesion, and in gases by the force called At- traction of Gravitation. In Chemistry, too, we view masses of matter as composed of atoms, but they are, for the most part, different from the preceding, in the fact that we view them as consisting of different kinds of matter, and capable of being combined together by a force called Chemical Affinity, and by such a combination of producing com- pounds entirely different in property from either of the elements which enter into the combination. Thus, when oxygen and hy- drogen gases unite, they form ^vater, a liquid, different in every respect from either oxygen or hydrogen. It has been said that "matter was the object of Chemistry," " motion of Natural Philosophy ;" but this is true only in a gen- eral sense. Matter, as well as motion, is the subject of investi- gation in the latter science ; not its composition, but its consti- tution, form, and mass. The science of Chemistry may be included in a few fundament- al ideas connected with changes produced by the force of affinity among the atoms of different kinds of matter. The science of Natural Philosophy may also be embraced in a few simple ideas, connected, not with atoms simply, but with changes which collections, or masses of matter, undergo under the influence of certain forces yet to be mentioned. These ideas may be expressed by a few terms, by means of which, when thoroughly comprehended, nearly all the facts in natural philosophy may be explained. Most of these facts may be referred to four funda- mental ideas. 1. The Idea of Matter, which arises from a perception of ex- tension, that is, the property of being extended in space, having length, breadth, and thickness. As every portion of matter, how- ever small, has these three dimensions, we may view a mass of matter as a collection of atoms, which are incapable of being di- vided, each one of which fills a separate space, and of necessity excludes for the time every other atom from the space which it What is the distinction between cohesion, gravitation, and affinity? How many fundamental ideas include most of the facts in Natural Philos ophy ? From what does the idea of matter arise ? INTRODUCTION. 15 occupies. The idea of matter, then, may be expressed by the term atom. A collection of atoms is called a mass or body. 2. The Idea of Force, which arises from change of place or form. This force either exists in matter or is exerted upon it, and produces, or has a tendency to produce, motion or a change of motion. When force exists among atoms, and tends to draw them to- gether, it is expressed by the term attraction, of which there are several kinds. When the force existing among atoms, or applied to them, tends to separate them from each other, it may be described by the term repulsion, a force supposed to be due to caloric. When the force arises from the resistance which an atom or a mass opposes to a change of state, either of motion or of rest, it is called the force of inertia. 3. The Idea of Law. A clear conception of forces leads di- rectly to the idea of the laws by which their action is governed. By the laws of nature are meant the uniform modes in which the forces of nature exert their powers. A law, then, is a uniform mode of action. The fact that under the same circumstances the same effects ensue, is denominated a law of nature. Thus we speak of gravity as the force which retains the planets in their orbits, but the laws of gravitation are the uniform modes by which this force is exerted. One of these laws is, that the in- tensity of the force decreases as the square of the distance in- creases ; that is, at twice the distance, two bodies will attract each other with but one fourth the power. A law, then, is nothing more than a general truth in nature, including many that are minor and subordinate. Thus, for example, the law of gravity extends to matter under every form and throughout all space ; to bodies in the heavens and to masses near the earth. It is therefore a general truth. 4. The Idea of Design or Utility. Our investigations of mat- From what does the idea of force arise ? What names are given to the several forces of nature ? What is the third idea, and from what do we derive it? Meaning of law, law of nature, &c. What is meant by de- sign or utility ? 16 INTRODUCTION. ter, its forces and laws, do not attain their highest importance and significance until we reach their grand purpose and design until we are able, not only to understand the uses to which they may be applied, which opens to us the whole field of the useful and ornamental arts, but also clearly to perceive the great plan and purpose of God in the material universe, thus enabling us to rise above these material forms to their great Author, in whom resides all power, and from whom all forces and laws proceed. If, therefore, the student will fully comprehend what is meant by the terms atom, attraction, repulsion, inertia, force, law, and purpose or utility, he will be able to explain most of the phe- nomena of nature, and to understand those processes of art which belong to, or are connected with, the science of Natural Philos- ophy. In addition to Chemistry and Physics, or Natural Philosophy, there is another branch of natural science, called Natural History, which includes a classification and history of all natural objects, mineral, vegetable, and animal. The nat- ural history of simple minerals constitutes the science called Min- eralogy ; of rocks, or the crust of the earth, Geology ; and of ani- mals and vegetables, Biology (or science of life), including Bota- ny, the natural history of plants, and Zoology, a similar history of animals. It is the province of Natural History to describe particular bodies, and arrange them in groups or classes. It is restricted, however, to the phenomena of perceptible distance. DIVISION OP THE SUBJECT. The term Physics is sometimes used instead of Natural Phi- losophy. The expression Mechanical Philosophy, too, some- times designates the same science. That part of Physics which relates to the mechanical proper- ties of solids is called Mechanics. That which relates to the What terms must be clearly understood in order to gain a correct knowl- edge of Natural Philosophy? Meaning of Physics. Define the different branches of Natural Philosophy. Mention the different branches of Nat- ural History; INTRODUCTION. 17 equilibrium and motion of liquids is called Hydrodynamics* a term including Hydrostatics and Hydraulics. That which treats of the mechanical properties of air and other gases has received the name of Pneumatics. It is thus that the three forms of matter furnish the foundation for this threefold division. But there are other branches of the subject, viz., Undulations, which relate to water-waves, waves of sound, music, &c., and Electricity, Magnetism, Light, and Heat. The four last-men- tioned terms designate powers or forces of nature, and are called imponderable agents. The subject of heat or caloric is generally assigned to the science of Chemistry, but the others, in consequence of their giving rise to the phenomena of perceptible motion, come properly into the province of Natural Philosophy. Astronomy is also another branch, though frequently regarded as a separate science ; but as it is in the motions of the heaven- ly bodies alone that the great doctrines of Physics find their highest and truest exemplifications, Astronomy, for this reason, is a most important branch of Natural Philosophy. * By some writers Mechanics is divided into, 1. Statics, which treats of the equilibrium of solids; 2. Dynamics, which treats of the effects offerees on solids when motion is produced; 3. Hydrostatics, which treats of the equilibrium of fluids ; and, 4. Hydrodynamics, which treats of the motion of fluids. NATURAL PHILOSOPHY, CHAPTER I. MATTER AND ITS GOVERNING FORCES. SECTION I. OF MATTER. The material universe is made up of very minute atoms, each one of which Jills a certain portion of space, and though fre- quently changing its position in reference to other atoms, is in- capable of being annihilated, unless it be by that Power which first brought it into being. THE idea of matter includes at least the perception of two properties, Extension and Impenetrability. By extension is meant, that every particle of matter, however small it may be conceived to be, has still an upper and an under surface, or the dimensions, length, breadth, and thickness. The capability which a mass of matter has of being divided, is called the prop- erty of 1. Divisibility. The extent to which matter is susceptible of division is not known. In theory it is indefinitely divisible. Thus, for example, if a silver wire, an inch in length, be cut in the middle, and then one half taken and divided into two parts, and the process of halving each division continued, it is evident that there would always be an undivided half, at whatever point in the series the process should be arrested. We should have a series which may be represented by the fractions {., i, }, T \, -^, ^ T , &c. Now, you might multiply the denominators of the frac- tions by 2, or halve them to an indefinite extent. Such a series would never terminate The idea of matter includes the perception of what properties ? Divis- ibility of matter, how illustrated ? 20 NATURAL PHILOSOPHY. Or, suppose you should attempt to walk out of your house by walking one half the way, and then one half the remaining space, and so on, it is evident that you would never reach the threshold. In practice, we should soon arrive at a limit, for the want of mechanical instruments sufficiently refined to carry on the divis- ions ; but in theory, the divisions might be infinitely extended. It is believed, however, that there is a limit in nature to this division, and that we should finally come to the ultimate atoms* or molecules, which are incapable of further division, being abso- lutely hard and impenetrable. The ultimate atoms of matter are exceedingly minute. This is shown in numerous cases in which division has been carried to such an extent that many millions of them in a mass could not be seen by the naked eye. Thus, gold leaf .may be hammered to the g-g-o^o'o^th ^ an * ncn m "thickness ; and if silver wire be coated with gold, it may be drawn out to such an extent that the thickness of the gold shall be a thousand times less than the gold leaf itself. A grain of musk will send off particles sufficient- ly numerous to fill a space of two hundred cubic feet every day for twenty years, without losing any perceptible weight. The number of atoms thus diffused exceeds computation or expression ; yet, if they were collected and placed in the scale of a delicate balance, their weight could not be appreciated. The thread of the spider's web is so attenuated that one half pound of it would reach around the globe (25,000 miles), and five pounds would reach to the moon, a distance of 240,000 miles. Some of the best illustrations of the extreme minuteness of the atoms of matter are furnished by changes in liquids and gases. Experiment. Take one gallon of water colored with an infusion of pur- ple cabbage, and put into it a single drop of sulphuric acid. The acid will be diffused through the whole quantity of the water, as is proved by the change in color. A drop of any alkali will change it green. The atoms of the acid and of the alkali must be diffused through the whole mass of the liquid in order to produce the effect. The * The term atom means that which is incapable of being cut or divided. Is matter indefinitely divisible ? What supposition is made in reference to the ultimate atoms ? Can we ascertain by experiment the exact size of atoms ? What facts show their extreme minuteness ? DIVISIBILITY IMPENETRABILITY. 2 1 evaporation of any liquid, by which it takes the state of gas or vapor, also illustrates the great extent to which this division must proceed. But perhaps the most striking example is in the animal kingdom, in the case of those infusorial animals which are found to exist in all solid and liquid bodies, and throughout the regions of the atmosphere. Many millions of these animals would not exceed a grain of sand in bulk, and yet they have a very compli- cated organization ; a stomach, organs of respiration, circulation, &c. The blood vessels of these animals are very minute tubes, but the globules of blood would seem to be well-nigh elementary atoms, and yet blood is a complex body, the smallest globule of which contains seventy-five elementary atoms. To such minute- ness must the division of matter be carried in the several exam- ples above referred to, that the thought has often been suggested that the ultimate atoms are nothing but the forces of nature, act- ing in determinate directions, and producing what we call matter. This idea, however, can not be received, for it is evident that each of these atoms, however minute they may be, must have the other property of a mass. 2. Impenetrability. Not that we are ever able to arrive at the ultimate atom and try the experiment upon it, but we are able, by various experiments and from facts in nature, to prove that every atom must occupy a portion of space, and exclude for the time any other atom from it ; for it is obvious that a col- lection, of atoms can not occupy a large space, if one single atom does not occupy a small portion of it. The impenetrability of matter may be proved by experiment, and illustrated by many familiar phe- nomena of nature and art. Exp. Place a lighted taper, attached to a piece of cork, a, Fig. 1, on water contained in a deep glass vessel. Place over it a tubulated receiver, b, and press it down. The taper will be carried down apparently into the water, showing that the air which is in the receiver will not permit the water to take its place. If now the stop-cock, c, be turned, the air will escape, the water will rush in to fill its place, and the taper will apparently rise out of the water. This is the prin- What examples of the minuteness of atoms are most remarkable ? What is meant by impenetrability ? What experiments prove the impenetrabili- ty of matter ? 22 NATURAL PHILOSOPHY. ciple of the diving bell, the taper representing the man and the receiver the bell. A funnel or a glass tube, a, Fig. 2, will also show the same fact. Exp. Place your finger upon the open end of the funnel, and attempt to force it into the water; the air will exclude the water, but, on removing your finger, the air will rush out and the water will rise to the same level within as without the vessel^ By these and other experiments it is demonstrated that gases and liquids can not be made to penetrate each other. Therefore, the presence of the one neces- sarily excludes the other from the space it occupies. Numerous illustrations of the same fact are constantly occur- ring in nature and in art. Two solid bodies can not be forced into each other by any known mechanical power. A nail is driven into wood, but it only displaces the particles of the wood. The same is true in all other cases. We can not force a solid piston into the barrel of a pump if there is water below it. When a solid is thrown into water, it separates, but does not penetrate the water. The same is true of solids pressing through air ; the particles of air are separated, but not penetrated ; for if air be contained in a cylinder, and a solid piston introduced, no power is sufficient to force it to the bottom. This is illustrated by the fire-syringe. Hence it is manifest that every atom of matter has the property of excluding every other from the space it occupies, and has, therefore, a veritable existence. Is it possible to destroy an atom of matter ? If the ultimate particles can not be further separated by me- chanical means, we should infer that their annihilation was im- possible. Hence a third property of matter is 3. Indestructibility. A mass of atoms may be separated and changed from one form to another by chemical and mechanical forces, but not one of them can ever be lost ; for in all cases where a body is apparently destroyed, it can be shown experi- mentally that the parts are only separated, and can be collected again. Thus, when wood is burned in the fire, it appears to be Difference between penetrating and separating the atoms of matter. Can matter be destroyed ? What becomes of wood when it is burned in the fire? INDESTRUCTIBILITY OP MATTER. 23 annihilated ; but if we collect the products the smoke and ash- es, we shall find the same quantity in weight that existed in the wood. In fact, we shall find a larger amount of matter than was originally contained in the wood, owing to the oxygen of the air which has combined with the wood in the process of com- bustion. When gunpowder is exploded, the products may all be collect- ed again. The same is found true in every case where matter changes its form or composition. We know that the material atoms of our own bodies are constantly changing, but not one of them is ever annihilated. That atom of matter which was struck from its kindred particles ages since, may have passed through many forms, solid, liquid, and gaseous, perhaps through animal and vegetable bodies, before it entered the kernel of grain, and became a portion of our own system ; and there are many changes which it will undergo there before it shall be cast out into the air as pure as at first, to enter other forms and nourish other systems. Matter is thus ever changing, but never destroyed. In saying that matter is indestructible, it is simply meant that, as far as our observation goes, and by means of the powers we are able to exercise upon it, it is so. It is not pretended to decide whether He who formed matter may not also destroy it. We are to conceive of the material universe as made up of atoms, and our idea of matter is an idea of one of these atoms exceedingly minute, incapable of further division, absolutely hard, excluding every other atom from the space itself occupies, and, though constantly changing its position in reference to other at- oms, incapable of annihilation exceprt by the hand of God. What changes are taking place in the human system? How much is implied in saying that matter is indestructible ? 24 NATURAL PHILOSOPHY. SECTION II. OF THE FORCES WHICH GOVERN MATTER AND THE PROP ERTIES RESULTING THEREFROM. Material atoms are subjected to certain forces, called Attrac- tion, Repulsion, and Inertia, which give rise to the most import- ant properties of matter in masses. I. Attraction is of various kinds, such as I. Cohesion, which holds the atoms of solids and liquids to- gether, and which, being opposed by the Repulsion of heat or caloric, gives rise to the three forms of matter, solid, liquid, and gaseous, and to that crystalline struc- ture which matter is universally disposed to assume ; also to the properties of hardness, density, elasticity, porosity, tenacity, and the like. 2. Capillary Attraction, which takes place between solids and liquids. 3. Electrical and Magnetic Attraction. 4. Chemical Affinity ; and, 5. Attraction of Gravitation. II. Matter also possesses the force of Inertia, which is a re- sistance to motion, or to a change of motion in bodies. THERE are three generic forces which govern matter, Attrac- ti&n, Repulsion, and Inertia. The form which matter assumes and some of its properties depend upon their action. I. Attraction and Repulsion. If there were but one atom in the universe, it would remain in the state in which it might chance to be placed. But if another atom were introduced, there would spring up between them a mutual attraction, and, unless otherwise prevented, they would move toward each other. This property is called attraction, of which there are several kinds. Their actual contact, however, would be prevented by a force of repulsion which surrounds each atom of matter, so that no force is sufficient to cause the atoms in a solid block to touch each other. 1 . As the atoms which compose a block adhere to each other and require force to separate them, it is evident there must be some force residing in the atoms themselves to cause this adhe- sion, and which must be overcome when the particles are separ- ated. This force is called the attraction of What are the forces which govern matter ? Define attraction. ATTRACTION OF COHESION. 25 Cohesion or Aggregation. It is exerted only when the atoms are so exceedingly near each other as to be brought into ap- parent contact ; and the only reason why this force is not al- ways exhibited whenever two solid bodies are brought near each other is, that the roughness of the surface prevents the particles from coming sufficiently near to be brought under its influence. If two solids be made very smooth by polishing their sur- faces, and then be pressed together, they will cohere with great force. , ?. Take two bars or balls of lead, Fig. 3, and scrape their surfaces smooth with a sharp knife, and then press them together; it will require a force of several pounds to separate them. If the surfaces could be made r/' perfectly smooth, the bars would sepa- rate in any other place as readily as at the point where they are joined. Exp. Take a piece of India rubber, and cut it in two pieces with a sharp knife. On applying the surfaces of the severed parts they will cohere with nearly the same force that they did before they were separated. The cohesion between a solid and a liquid may be shown by taking pieces of glass or wood, and suspending them from the end of a balance, Fig. 4, so that the flat sur- face of the glass may touch the sur- face of the water, b. By applying weights in the other scale, the exact force of cohesion may be determined. This is sometimes called the force of adhesion, and is found to be con- siderable, depending upon the extent of surface. When the glass is removed a film of water adheres to its sur- face, showing that the separation does not take place between the water and glass, but that the particles of water are separated. This experiment also proves that the particles of water attract each other. If the force of adhesion is greater than that exist- ing between the particles of the liquid, the liquid will adhere to Cohesion. Why do not all bodies cohere when they meet each other? Experiment of lead balls India rubber. How may the attraction be- tween solids and liquids be shown 1 Which is greater, the attraction be- tween the liquid and solid, or between the particles of the liquid 1 B Fig. 4. 26 NATURAL PHILOSOPHY. the body and wet it. If it be less, the liquid will not adhere to it. The power of cohesion among the particles of liquids, how- ever, is very small compare^ with that between the particles of solids. The fact that a small quantity of any liquid assumes a globular form, as in drops of water or mercury, is further proof that cohesion exists to a certain extent, though their particles are so far removed from each other that the force is slight. Gaseous bodies seem to be destitute of this power, because their particles are removed beyond the reach of each other's attraction. There is, however, a strong attraction between some solids and gases, and also between liquids and gases. Charcoal and many porous bodies will absorb many times their volume of several gases, as ammonia, watery vapor, &c. Water always contains air and other gases, which it absorbs in greater or less quanti- ties, according to the nature of the gas, the time of exposure, and degree of pressure. Hence the force of cohesion is strongest in solids ; in liquids it is slight, and in gases it is wholly inoperative. The explanation of the different degrees of cohesion among the atoms of matter is found in the action of an antagonistical force called Repulsion, or the Force of Caloric. When heat is applied to any solid body, it expands it, and the higher the temperature is raised, the greater will the increase of volume become for equal additions of heat, until at a certain temperature the solid becomes liquid, or melts. In such cases the cohesion is mostly overcome by the repulsive tendency of heat ; the particles become removed beyond the reach of their mutual attraction, and thus separate. If the heat be continued, most liquid bodies may have their cohesion entirely overcome, and be made to assume the state of gas or vapor. Now the moment that the change takes place from a solid to a liquid, or from a liquid to a gas, a large quantity of heat is absorbed by the body, or passes into an insensible state. This heat is given out again when the body is condensed, and re- turns to the liquid or solid form. Hence it is inferred that the three forms of matter, solid, liq- Cohesiou of solids, liquids, and gases compared. What constitutes the difference ? What force opposes cohesion ? CRYSTALLINE FORMS. 27 uid, and gaseous, are due to the different quantities of caloric existing among their atoms. This heat, however, does not affect the thermometer. It is the caloric of fluidity and of gases. Thus, for example, water at a certain temperature is in a state of gas, in which state it contains a thousand degrees of heat, which is insensible to the thermometer, and which must be abstracted before it can assume the liquid form. Water in its liquid form contains a quantity of heat (140), which, at the moment it freezes, must be given out, or it will not- become solid. The different forms of matter, therefore, depend upon the rel- ative intensity of cohesion, and of heat, or repulsion. In solids, cohesion preponderates ; in liquids there seems to be a balance of powers, but in gases caloric has entirely overcome the cohesive force, by removing the atoms beyond the influence of their mu- tual attractions. When gases or liquids pass to the solid state, they are disposed to assume definite forms, called Crystalline Forms. This seems due to a peculiar action of cohesion. If we suppose that the atoms are like magnets, that is, that they have two points which have the power of attraction, so that they will form themselves into rows in definite directions, all other points being destitute of attractive power, we may ac- count for the forms which matter is thus universally inclined to assume. The crystalline forms which different bodies assume are quite uniform for the same kind of matter, and from the shape of the crystal we may perhaps infer the shape of the atoms which com- pose it. SJiape of Atoms. The shape of atoms, however, must be a matter of conjecture. They are generally considered to be either spheres or spheroids. If we suppose the atoms of cubes and all rectangular solids to be spheres, it is easy to account for these forms ; thus, The different forms of matter are due to what circumstance ? What forces appear to act in opposition to each other? What forms are gases and liquids disposed to assume when they pass to the solid state ? From what may we infer the shape of atoms ? 28 NATURAL PHILOSOPHY. Let A, Fig. 5, represent a number of atoms of a liquid. Now, when this liquid crystallizes in the form of a cube, each of the atoms is supposed to assume a polarity, and ^-Q-VV ^HEES^oJGh Ji- tney arrange themselves as in B, there being two axes of attraction at right angles to each other, as e d, i n, &c. A great many forms may be made out by changing the direction which the two axes bear to each other. B, however, represents only one face of the cube. If the atoms are spheroids, that is, egg-shaped, then it will be evident, by inspecting the figure, that a great variety of crystalline forms may result from a change in the direction of the polarizing axes. Thus the axes might be varied indefinitely. Fig. 6, A, B, C, D, exhibits four forms. Fig. 6. These different di- A B rections of the axes, and there are gener- ally three or more axes, would give rise to almost any conceivable form of crystal. It is true the molecule or atom may have the same form as the crystal itself, but the sphere and spheroid are the most simple, and enable us to account for all the fo^ms which matter assumes.* When a body crystallizes, as when water freezes, it generally expands, in consequence of the different arrangement of its atoms requiring more space than formerly. This is seen in Fig. 5, A, B. It is owing to this fact, and to the repulsive tendency of heat, together with what may be called the natural repulsion of atoms, that a mass of atoms always has the property called (1.) Porosity. If the atoms of which a mass is composed were round or spheroidal, there would naturally be spaces between them, even if there were no repulsive power to separate them from each other, and this property of porosity would result directly from the shape of the atoms ; but when we add the repulsion of heat and the polarity of the atoms, we can easily see how all * See J. D. Dana on Cohesive Attractiop, Silliman's Journal, Nov., 1847 How may the different forms of crystals be accounted for ? What is tha most probable shape of atoms ? What does porosity result from ? POROSITY ELASTICITY. 29 matter, however dense it may be to appearance, is yet filled with pares. This property may easily be seen by aid of the microscope, or by very simple experiments in relation to most organic bodies, but in the more dense bodies, as gold and platinum, the existence of pores is not so easily demonstrated. In the famous Florentine experiment, water was forced by great pressure through the substance of a hollow gold ball in such quan- tities that it oozed in drops from the outer surface. Many solid bodies, such as crystalline stones, sugar, &c., will absorb c'onsid- erable quantities of water, which proves them to be porous. But the best examples are found in the animal and vegetable world. The pores in bone and wood are easily seen by the na- ked eye. With the aid of the microscope, they appear like large tubes running lengthwise through the bone or wood. The po- rosity of wood is beautifully exhibited in what is called the Air Shower. Exp. A solid piece of wood, a, Fig. 7, is fitted to the receiver, c, of an air pump, with one end inserted in a vessel of water, b. On exhausting the air from the receiver, the external air will press through the pores of the wood, from a to b, and rise up in bubbles through the water. It is more difficult to show the pores in liquids and gases, but they must exist in much greater mag- nitude than even in solids, as is evident from the fact that some liquids and all gases and vapors occu- py more space than when in the solid state. In consequence of the repulsion existing among the particles of bodies, and also because of the shape and position of the atoms, there arises another property called , (2.) Elasticity. In some solid bodies the particles are so sit- uated as to yield to any force to a certain extent, and then return to their former position. This is exemplified in the case of steel springs, glass, marble balls, ivory, India rubber, and many other substances. The degree of elasticity varies in different bodies. How is this property shown ? What are the best examples of porosity ? Illustrate. From what is elasticity derived ? Define what the property is. How does it vary in different bodies ? 30 NATURAL PHILOSOPHY. The particles of some "bodies may be removed very far from each other without being thrown out of the sphere of their mutual at- traction. The celebrated blade of Damascus can be bent double without breaking, while some bodies break with the least jar. Hard bodies are generally elastic, and in most cases regain their form when subjected to a momentary pressure ; but if any solid body be subjected to a pressure for a long time, it gradually loses its power to spring back to its original form. It is probable, in this case, that some change may take place in, the direction of the cohesive force as respects the molecules of which the body is composed. Thus, a spring or marble slab, when bent for a long time, at length retains the impression, and becomes perma- nently crooked. Liquids are much more elastic than solids ; when subjected to pressure, they yield with difficulty, but return to their former volume when the pressure is removed. Gases, such as air, are perfectly elastic ; that is, when a given portion is compressed, it returns to its former bulk in all cases, unless condensation takes place, and the gas changes its form and becomes a liquid. This is exemplified in pressing a gas bag or bladder filled with air. Gases are distinguished from solids and liquids by the greater extent of their elasticity, and this is due to the absence of cohesion ; the particles, being left to move with the greatest freedom upon each other, are held together by grav- itation, or their weight alone. Elasticity implies another prop- erty of matter, (3.) Compressibility, by which is meant that the particles in bodies are capable of being compressed into smaller spaces than they ordinarily occupy. Thus, for example, the atoms of solids, both elastic and non-elastic, may be made to approach each other by pressure or hammering, in various degrees of contiguity. Liquids are less compressible than solids, but gases possess this property in the highest degree. Air, for instance, is perfectly Do bodies ever lose their elasticity ? What bodies are most elastic ? How do liquids compare with solids ? How do gases compare with liquids and solids ? What is meant by compressibility, and what bodies possess it in the highest degree ? DENSITY HARDNESS. 31 compressible ; twice the force halves the volume it occupies. It is on this account that the same substance may be made to occu- py less space ; hence arises another property, (4.) Density, which has reference to the number of atoms or quantities of matter which occupy a given space. If we suppose the weight and proximity of atoms in any two bodies to vary, it is easy to see that the one may be more dense than the other. When the different weights of equal volumes are compared with some standard, as water or air, density becomes specific gravity. Of course, bodies most dense have the greatest specific gravity. Hydrogen is the lightest body, and Platinum the heav- iest. We do not know how dense a body might become, were its atoms made to touch each other. It has frequently been assert- ed, as a supposition of Newton, that " if the matter of the earth were compressed so much that the particles should touch each other, the whole might not exceed a cubic inch in diameter," which, if not an absurd, is at least rather an extravagant idea. There are several other properties resulting from modifications of the cohesive force, as (5.) Hardness, which might be supposed to result from dens- ity, but this is not always the case. This property appears to de- pend upon the direction of the axis of force in the atoms of which different bodies are composed, so that the particles maintain their position with great fixedness in certain directions. The diamond is the hardest body in nature, and the degrees of hardness in dif- ferent bodies are generally determined by their power in cutting and scratching other bodies. Some bodies become hard by heat- ing, and then suddenly cooling them. Such is the fact in the operation of making steel, from which all our edged tools, and a great variety of machines useful in the arts, are produced. (6.) Brittleness is still another property of matter. A brittle body, such as glass or flint, may be very hard, but the cohesion of the particles is such that a slight concussion is sufficient to sep- arate them. (7.) Ductility is that property of matter by which it is capa- Describe density, specific gravity, and hardness. Describe brittleness and ductility. 32 NATURAL PHILOSOPHY. ble of being drawn out into wire. Iron, gold, silver, and platinum are very ductile substances. (8.) Malleability is the property of being beaten or rolled out into thin leaves. Gold is the most malleable of all bodies. (9.) Pliability is the name given to the ready yielding of the particles, as in elastic bodies ; but the atoms do not change their places, as in the case of ductility. (1,0.) Tenacity. The force of cohesion varies greatly in dif- ferent bodies, and is the cause of their form and strength. This cohesive force produces the property of tenacity, by which is meant the force by which the parts cohere or resist a steady strain in one direction. This force is measured by the power required to part a given weight or volume of any substance in the form of wire or cord. Thus, by suspending different weights to several wires of the same size, that which will sustain the greatest weight is said to be the most tenacious. It is found that iron and steel are most tenacious. If iron, copper, gold, and oak were thus compared, their absolute strength, or that in the direction of their length, would be as the respective numbers 70, 19, 9, 12. Portions of the animal body have very great tenacity, as silk, wool, hair, animal tendons, and portions of the intestines, which constitute the material for stringed instruments, as the harp and violin. Ships are now made of iron, and bridges are suspended by iron wires. It is one of the most important objects of the engineer and architect to become acquainted with the relative strength of the materials which he wishes to use in the construc- tion of various works of art. 2. Capillary Attraction takes place between liquids and solids. When a solid body is immersed in a liquid, Fig. 8. if the liquid wets the body, it is drawn up- ward ; if it does not wet it, a depression takes place. Thus: Exp. By immersing small glass tubes, a, Fig. x\~ 8. in any liquid, as water, the liquid will rise \\ higher on the inside of the tubes than on the out- side. The effect is rendered more perceptible by coloring the liquid. Describe malleability, pliability, tenacity. What bodies possess these 'properties in the highest degree? How is the tenacity of different bodies ascertained ? Capillary attraction. Describe and illustrate it. CAPILLARY ATTRACTION. Fig. 10. If the tubes are of different diameters, the smaller the aper- ture of the tube^ the higher will the liquid rise. v Fig. 9. Exp. This law is beautifully illustrated by means of two pieces of glass, Fig. 9, joined by their edg- es, b c, at a small angle, and immersed in a col- ored liquid. The different heights to which the liquid will rise forms a curve, a b, the heights de- pending upon the different distances the two plates are from each other ; hence, when water is contain- ed in a glass vessel, the surface is not level, but curves upward where it touches the glass, while the sur- face of a similar vessel of mercury curves downward.. . This is seen in A B, Fig. 10. It is due to this figure of the surface that float- -n ing solids sometimes move toward and sometimes from each other, a phenomenon often ascribed to attraction and repulsion. Thus, for example : Let A B, Fig. 11, be two balls of cork, or some light substance. If they are oiled, so that the water will not wet them, there will be a depression around them, and when they approach each other, the water at C will be repelled, and they will fall together ; ^^^^^ or, if both are wet, they will also approach each other, because the elevation between them will be less than that around them. If one, D, is wet, and the other, E, oiled, the water will be elevated around D and depressed around E ; hence they will seem to repel each other. If the tubes are immersed in mercury, there will be a depres- sion of the metal around the inner surface. When the liquid rises the bounding surface is concave, and when it sinks it is convex. It is due, also, to capillary attraction that the fluids of animals Fig. 12. and vegetables are carried through many portions of their substance. All vegetable and animal tissues consist of bundles of tubes, which continually absorb and circulate their liquids with an astonishing force. This fact may be mechanically illustrated by means of a bladder tied over one end of a glass tube or cup- ping-glass. If the tube with the bladder be immersed in a vessel of water, B, as represented m Fig-. 12, Is the surface of water or of mercury in a vessel le-l? Why are they not ? Why do floating bodies sometimes approacl and at others recede from each other ? B2 34 NATURAL PHILOSOPHY. and then filled with alcohol to the same height of the water, , in a vftry short time the liquid will rise in the tube to d, and even to the height of thirty inches or more. The bladder is full of small tubes, and the water is forced in while a small quantity of the alcohol flows out. The internal flow was called by Du- trochet endosmose, and the outward flow exosmose. The upward flow of sap in vegetables is due to a similar force , the ends of the roots, or spongioles, are capillary tubes, and they have the power of forcing up the sap to the leaves. The force of these capillary tubes is not confined to liquids, but it is also exerted upon gases. If a piece of India Fig. is. rubber be tied over a jar of carbonic acid, A, Fig. 13, the acid will force its way out so much faster than the air rushes in, that a deep concavity will 33 be made in the surface of the rubber ; but if air be placed in the jar, and it be surrounded by an atmosphere of carbonic acid, the rubber will be forced out in the form of a ball, B. Gases have been known to flow through membranes which required a force to be exerted of fifty atmos- pheres, or seven hundred and fifty pounds to the square inch. 3. Chemical Affinity. Another kind of attraction which gov- erns matter has been called the force of affinity, or chemical af- finity. This force differs from cohesion in being exerted between atoms of different kinds of matter, and in being attended by the formation of a new body possessing different properties from either element of the compound. Cohesion does not alter the properties of the atoms which it causes to cohere in the formation of a mass. Those changes which are produced by chemical force or affin- ity belong to the subject of Chemistry, and are not the specific objects of investigation in Natural Philosophy. They pertain to the composition of bodies, the atoms being so arranged that when they are separated they are resolved into their original forms. Cohesion may act between atoms of the same kind in either body before they are combined to form the compound, and between the What is endosmose and what exosmose ? How does the capillary force act upon gases ? Difference between chemical affinity and cohesion. To what science do those changes belong which are produced by chemical af- finity? ATTRACTION OF GRAVITATION. 35 atoms of the compound after it is formed, but has nothing to do with the force which unites them.* 4. Electrical and Magnetical Attraction. The polarity spoken of in relation to the atoms of matter, in the formation of crystals, seems to pervade masses so that an attractive and re- pulsive force is given to bodies under certain conditions. This state of polarity is sometimes permanent, as in the case of mag- netism, and at others it only exists while certain conditions are maintained, as in the case of electrified bodies that arising from common and Voltaic electricity. This kind of attraction will be specially considered in the chapters on Electricity and Magnetism. 5. Attraction of Gravitation, or Gravity, is generally described as that property by which bodies tend toward the center of the earth. This, however, is a limited view of the case, the one which is confined to mechanical philosophy. This property exists among masses at all distances, and tends to bring them together. It differs from cohesion in the fact that it not only exerts its force upon atoms which are near each other, but also upon those which are far separated. Its force, too, does not depend upon any other property, but is universally as tJie quantity of matter, and must, therefore, be connected with the atoms themselves. It is the most important force in Natural Philosophy, giving rise, in common with inertia, to all the motions of the heavenly bodies, and to many of the changes which take place on the surface of the earth. It is important to examine it, therefore, somewhat in detail. Attraction of Gravitation is witnessed in the fact that two bodies in space have a tendency to approach each other, and, if one body be much greater than the other, the lighter body will have a perceptible motion ; as, when a stone is let fall, it moves toward the center of the earth ; but the plumb-line at the base of a mountain will not obey the force of gravity in the specific sense, and fall toward the center of the earth, but will incline * See Gray's Chemistry, Chemical Affinity, for a full view of this force. Describe the other kinds of attraction. Gravitation, &c. How does gravity differ from cohesion ? With what is this force connected ? How does this force manifest its existence ? 36 NATURAL PHILOSOPHY. toward the mountain, as was proved by Dr. Maskelyne, in his celebrated experiments near the Schehallien Mountain, in Scot- land. It has been supposed that logs of wood in a pond are drawn together by this force, but the phenomenon may be at- tributed to capillary attraction (p. 33). It is due to the general attraction of one body for another, and of each part for every other part, that the earth and all the heav- enly bodies are round. The same force that makes a dew-drop is concerned in the rounding of the spheres, in the rising of the tides, and the revolution of the heavenly bodies. Although the attraction of gravitation exists between all bodies, however small or distant, yet its force varies according to the three following laws, which are generally stated thus : (1.) The force of gravity is proportioned to the quantity of matter. If we consider this force to be exerted in the matter of our globe, it will be seen that all. the atoms will mutually at- tract each other, and that the combination of all the attractions will result in causing small bodies to tend toward its center. Hence we gain the idea of iveight, which is the measure of the force of gravity near the earth's surface ; and as that force is as the quantity of matter, the weight of bodies is taken as equiva- lent to their quantity of matter.^ It follows, from this law, that all bodies, whatever their quan- tity of matter, must fall with the same velocity to the earth; for, if one body contain twice the quantity of matter which another does, it will be attracted with twice the force, and, of course, will move with the same velocity. A lead ball and a feather will * In this case, however, it is essential to have some standard, or some- thing to compare different weights with. A given quantity of water is taken by measure, as a cubic foot, and counterpoised in a balance by a solid, and called 1000. This solid 1000 ounces may then be divided into parts, and constitute a series of weights by which to determine the relative quantity of matter in different bodies, or their weights. If it is divided into 1000 parts, of course each part will be an ounce; into one fourth as many, they will make a four ounce weight ; into one sixteenth as many, a pound weight. See page 105. Why are the heavenly bodies round ? How does the force of gravity operate? Illustrate the first law of gravitation. What is weight, and how is a standard of weight formed ? Will large bodies fall with greater or less velocity than small ones ? UKIVElfeSIT LAWS OF GRAVITATION. fall to the earth in the same time from the is not the fact in nature, because of the resistance mosphere offers. But, Fig. 14. Exp. If a guinea and a feather, a, b, Fig. 14, be placed in a /fT\ long glass tube, and the. air exhausted from the tube, both will fall from one end to the other in the same time. ) (2.) The second law is, The force of gravity varies in* versely as the square of the distance from the center of the earth ; or generally, " The attraction of gravitation is inversely as the square of the distance." " Inversely" means " that as the distance increases, the force dimin- ishes." " As the square of the distance" means that, if we take distances represented by 1, 2, 3, 4, or once, twice, or three times any given distance, the square of these numbers will make the series 1, 4, 9, 16. The radius of the earth, 4000 miles, is taken as unity. A body weigh- ing one pound at the earth's surface, or 4000 miles from the earth's center, will weigh but one fourth as much at twice the distance, or 8000 miles from the center ; one ninth as much at three times the distance, or 12,000 miles ; and one sixteenth as much at four times the distance, or 16,000 miles from the center of the earth. This law may be illustrated by a diagram, as it applies to all forces acting from a center, and geometrically de- monstrated. Let C, Fig. 15, be the center of the earth. The force of Fig. 15. gravity contained in the earth may be conceiv- ed to proceed from this center. Now, any in- c fluence proceeding in right lines, and in ev- ery direction, from the center of the earth, as light, heat, and gravity, will diminish inversely as the square of the dis- r tance. For, let the dis- What is the second law of gravity ? What is meant by inversely, square of the distance 1 How may this law be proved ? 38 NATURAL PHILOSOPHY. tance CA be 4000 miles, and CF 8000 miles from the center, C, the surface FGHI will be four times the surface ABDE ; and, of course, as the force is spread over four times the space, it will be but one fourth as great over the same space at the former as at the latter distance. That is, the space ABDE : FGHI : : AB* : FG 2 , or CA 2 : CF 2 ;* or the force of gravity at twice the distance from its source is spread over four times the space, and, of course, is but one fourth as strong. As we descend from the surface of the earth to its center, a different law prevails ; for, if we suppose a body carried from the surface to the center of the earth, the force toward the center would be constantly diminished by the attraction of the quantity of matter which the body left behind it. Thus, suppose A B, Fig. 16, represents the earth, C the cen- ter, and d a body 2000 miles from the center. It can be proved that the body, d, would remain at rest in any part of a hol- low sphere of uniform density. The force, therefore, which attracts it toward the cen- , ter will be exerted only by the matter in x d e, the exterior portions having no tend- ency to attract it toward the center. As the force of attraction is proportioned to the quantities of matter, the matter in A B is to that in d x e as A C 3 to d C 3 ; but the force varies inversely, as A C 2 and d C 2 ; .-. the force at A : d : : A C 3 -^ A C 2 : d C 3 +d C 2 , or : : A C : d C. The third law is, that the force of gravity from the center to the surface of the earth is directly as the distance ; the greater the distance, the greater the force, and the less the distance, the less the force. A body, then, falling through a hole made through the earth's center, if the air were removed, would fall to the cen- ter, where it would weigh nothing ; but another force would be generated, which would carry it to the opposite side. One pound at the surface would weigh half a pound 2000 * Two similar triangles, CFG, CAB, are to each other as the squares of their homologous sides CA and CF, or AB, FG ; but CF is double CA, and FG double AB ; but the square on half a line is one fourth the square upon the whole line. Does the force of gravity increase or diminish as we descend toward the center of the earth? Illustrate this law. What would a body weigh at the center of the earth ? PROBLEMS. 39 miles from the center, three quarters of a pound 3000 miles from the center, a quarter of a pound at 1000 miles, and in the same ratio for all other distances. PROBLEMS. In order to render the above laws familiar, the following prob- lems are added : 1. What would be the weight of a sixty-four pound cannon ball at the distance of the moon, 240,000 miles ? Ans., f j libs. 2. A meteoric stone was observed 4000 miles from the earth, to which it fell, and was found to weigh 2000 Ibs. What would it have weighed at the point where it was first observed ? Ans., 500 Ibs. 3. What would a ton of iron weigh 500 miles from the sur- face of the earth ?* Ans., 158011- Ibs. 4. What would a ton of iron weigh 500 miles below the sur- face of the earth ?. What 500 miles from its center ? Ans., 1750 Ibs., and 250 Ibs. If the formula in the note below be applied to the third ex- ample in numbers, the loss of weight will be equal to 2000(2X4000X500+250,000) __8,500,000,000_ 6J 16,000,000-j-2 X 4000 X 500-j-25,000~~ 20,250,000 ~ If the height is not more than half a mile, x* may be neglect- ed, and then the formula will be W W 7 = * Let A, Pig. 17, be the earth, C its center, x the height from the surface, then will the weight at s be to the weight at x as the squares of the distances Cx and Cs. Now, to find the loss of weight, we must sub- tract the weight at x from the weight at s, and then, if we represent the weight at s by W, and at x by W ; also, Cs by r, and sx by x, we shall have the proportion W : W W : : (r+x? : 2rx+x*, or W : W W : : r*+2rx+x* : 2r*-f-a; 2 , The loss of weight, then, will be = W w/ = What is meant by inertia ? 40 NATURAL PHILOSOPHY. II. Inertia, as well as gravity, or attraction in general, and re- pulsion, is sometimes called a property of matter, but it is one of the principal forces which govern matter. Inertia is a peculiar force ; it is the force of resistance to a change of state. Thus, when a body is at rest, it requires some force to put it in motion. This resistance, or inertia of a body, is proportioned to the quantity of matter. So, also, when any body is in motion, as a carriage or rail-road car, it acquires a force which must be overcome before its motion can be stopped. But the force in this case will vary with the velocity of the mov- ing body, and is not a measure of the quantity of matter. This force of inertia is exemplified in the most common phe- nomena in life, in walking, riding, and in all cases where mo- tion is generated or destroyed. It is used to regulate the motion of machinery, as in the fly-ivheel. This force is so important that it will be more fully illustrated in connection with Motion and its laws. There are other forces, such as the muscular force, the force of gunpowder, &c., but we have given a general view of such as belong to matter as such. Matter in the mass, then, consists of minute atoms, which are endowed with extension and impenetrability. It is governed by the forces cohesion and repulsion, which give rise to the forms solid, liquid, and gas, and to properties, as density, hardness, elas- ticity, tenacity, &c. It is also governed by capillary attraction, chemical affinity, electrical attraction, magnetic attraction, the attraction of gravitation, and the force of inertia. We now proceed to note the effects of these forces and the laws of their action, or the doctrine of Motions and Forces. How is inertia estimated when bodies are at rest? How when they are in motion ? What other forces exist ? Repeat those which have been named, and the properties which result from them. MOTION AND ITS LAWS. 41 CHAPTER II. MOTION AND ITS LAWS. INERTIA. SECTION I. OF MOTION. Motion is a change of place. It is of several kinds : 1st. Absolute; that is, motion in reference to a fixed point. 2d. Relative ; that is, the motion of one body in respect to another in motion. 3d. Apparent ; tliat is, ivhen bodies appear to move in cons&> quence of the motions of other bodies. 4th. Real; that is, ivhen a body is in actual motion : a con- dition which, taking the whole universe into view, pertains to all matter. MOTION is the change of place among bodies. It is divided into absolute and relative, apparent and real. 1 . Absolute Motion refers to a change of place in reference to some point that is fixed. Thus, when a man walks from his house to the church, he has an absolute motion as regards both his house and the church. 2. Relative Motion has reference to a change of place between two or more bodies which are in motion. Thus, a man walking on the deck of a sailing ship has a motion with the ship and in respect to the ship. If he walk toward the stern as fast as the ship sails, he has a relative motion in respect to the ship, and ab- solute rest in respect to the earth. So two men traveling with different velocities- have a motion relative with regard to them- selves, but absolute in reference to the point from which they started or to which they tend, but not in respect to the earth it- self; for the earth has two motions, one from west to east, and one in its orbit around the sun, and all bodies on its surface par- take of these two motions. Hence every body on the earth's Define motion. What is absolute and what relative motion 2 42 NATURAL PHILOSOPHY. surface is either in relative motion or relative rest as it respects the earth itself. Now the earth revolves in its orbit about 100,000 feet per second. The velocity of a cannon ball is not greater than 2000 feet per second. If, then, it be fired in the direction in which the earth moves, its motion will only be increased to 102,000 feet per second ; if fired in the opposite direction, its motion will be decreased to 98,000 feet per second. But the earth moves from west to east about 1500 feet per second. A ball fired at that rate toward the west would be relatively at rest in respect to a fixed star, its motion toward the west being just counteracted by the earth's motion. In fact, the cannon would move away from the ball ; it would be in a state of absolute motion and rel- ative rest. Now it has been shown that all the heavenly bodies are in motion, so that absolute rest, when we look at the universe as a whole, is not a condition of matter. It appears highly probable, for several reasons, that the atoms of matter are in a constant state of vibration ; due, perhaps, to the relative intensity of attraction and repulsion which exist among them, and which are constantly varying as the tempera- ture of bodies varies. 3. Apparent Motion.- When the seeming motion of a body actually at rest arises from the real motion of a body apparently at rest, it is called apparent. This apparent motion generally arises from the apparent rest of the observer. Thus, in riding in a rail-road car, by not becoming conscious of our own motion, all the external, visible world, houses, trees, fences, &c., appear to be hurrying past with great velocity. The revolution of the heavenly bodies apparently from east to west is due to the actual motion of the earth on its axis in an opposite direction. 4. Real Motion. As all the heavenly bodies are in motion, it is difficult to determine what bodies are in actual or real mo- tion, and what in apparent. If we know any cause which should How rapidly does the earth move in its orbit? How fast from west to east 1 Velocity of a cannon ball ? Are there any bodies in a state of abso- lute rest? Apparent and real motion defined. How can we determine real, and how apparent motion ? LAWS OF MOTION. 43 give motion to one body and not to another, or if the tendency of their motion is in one uniform direction, we may regard it as real, and not apparent. . SECTION II. LAWS OF MOTION IN THEIR RELATION TO FORCES, ESPE- CIALLY TO THE FORCE OF INERTIA. In consequence of the inertia of matter, force is necessary to produce, to destroy, or to cfiange the motion of a body. Motion is as natural to bodies as rest ; hence the first laiv of Motion is, that a body will continue in tlue state in which it is, either of rest or of uniform, rectilinear motion, unless acted on by some force to change its condition : a law which is also proved by experiment and observation. A state of motion is therefore as permanent as a state of rest ; though, in consequence of the resistance of the air and the attrac- tion of gravitation, bodies in motion near the earth are soon brought to a state of rest ; but the heavenly bodies are in a state of perpetual motion. Motion is naturally uniform ; that is, bodies move over equal spaces in equal times. In consequence, also, of the inertia of matter, motion is al- ways in proportion to, and in the direction of the force impress- ed, ivhich is the Second law of Motion ; and, for a similar reason*; Action and reaction are equal, and in opposite directions, ^vhich is the Third law of Motion. Force is that which moves, tends to move, or to counteract the motion of a body. All forces we have already noticed may be reduced to four, attraction, repulsion, inertia, and muscular force. Every motion is the result of some active force, and yet a state of rest is no more natural to bodies than a state of motion. A body at rest requires force to put it in motion by overcoming its inertia. A body in motion requires force to stop it, or to over- come its inertia. Hence Define force. What is the natural state of bodies ? 44 NATURAL PHILOSOPHY. Tlie First Law of motion is, that a . body continues in the state in which it is, either of rest or uniform rectilinear motion, unless acted on by some force to change its condition. 1. That a body at rest requires force to put it in motion, results directly, as we have seen, from its inertia, which must be over- come in order that the motion may take place. The attraction of the earth, for example, is just sufficient to cause a body to fall toward it sixteen and one twelfth feet in a second ; but if there were no inertia to be overcome, it would fall with the speed of lightning, in which case it would exert no force as it fell. This law is proved by universal experience, but it may be il- lustrated by numerous experiments and examples, and by refer- ence to the most familiar natural phenomena. Thus we know, that, in order to impart motion to any body at rest, we must al- ways employ force of some kind, and a force proportioned to the weight of the body. The inertia of a body at rest, however, is not overcome at once, but time is required for the force to be impressed upon it. We have observed, for instance, that when a large load is to be moved, as a loaded train of cars by a single locomotive, all of them could not be set in motion at the same instant. Greater effort is required to set a carriage in motion than to keep it in motion, because its inertia mustjirst be overcome. This fact is beautifully illustrated by an apparatus called the Inertia Apparatus,. Exp. In Fig. 18 a marble ball, a, is placed upon a card, c, and a spring, d, is forced against the card. The card is thrown j^.. is. out from under the ball, leaving it upon the stand. Exp. The same may be shown by laying a dollar on a card, balanced upon the tip of the fin- ger. By snapping the finger suddenly against the edge of the card, the card will be forced out, leaving the dollar balanced on the finger in place of the card. So, by a sudden blow, a piece may be broken off from any First law of motion. How is this law proved ? How much time is re- quired to overcoma the inertia of matter? Illustration. Inertia appara- tus. Desci'ibe the experiments to illustrate the inertia of matter. Why will a sudden blow break off a piece from a solid ? FIRST LAW^OF MOTION. 45 solid "body without injury to the adjoining parts. A "ball may be fired through a pane of glass, making only an aperture where it strikes it ; or a soft body, as a tallow candle, may be fired through a board, because in each case there is not time for the force to be distributed over the parts, and, being concentered upon the points struck, the cohesion in those parts suddenly gives way. Glass vessels are often broken by taking them up hastily by the handle. When a horse suddenly starts with a load, there is danger of his breaking some part of his harness. If one stands in a wagon when it is suddenly pulled forward, there is danger of having his feet pulled out from under him, and his body thrown in an oppo- site direction. If we wish to raise a heavy weight with a slen- der rope, the strain should be gradual, lest a sudden pull should break it. In these and numberless other instances, which the student may easily supply, there are both proof and illustration of the resistance of inertia, and of the necessity of overcoming it to produce mo- tion ; and, in general, force should be applied gradually, some time being required to impart motion to the whole mass. 2. Force, on the other hand, is equally requisite to stop a body in motion ; or, a body in motimi has a tendency to continue in motion. This also results directly from inertia, for there is no power in the body to change its state, and hence some external force must be applied. Illustrations of this property of motion are equally numerous with the preceding. It is proved by observation that if the propelling force of one or more bodies in motion is removed, they will continue to move forward by the force of their inertia. Thus, when the engine is detached from a train of cars, they move forward with great velocity by the force of their inertia ; so, when a horse suddenly stops, he throws his rider over his head. When a wagon in motion strikes against any solid body, the driver is thrown for- ward. A case in court was once decided by the testimony of What illustrations of the resistance of matter to motion ? What is neces- sary to stop the motion of any body ? Why will a train of cars continue to move after the engine is detached 1 46 NATURAL PHILOSOPHY. the plaintiff's witness, that the shock was so great that he was thrown to a great distance. This fact showed that his own vehicle was in rapid motion, not that of the defendant. Were the motion of the earth suddenly stopped, we should be launch- ed into space with the velocity with which the earth is moving, about 100,000 feet per second ; a velocity more than fifty times greater than a cannon ball. Arnott gives an account of an African traveler who saw him- self pursued by a tiger, from which he could not escape by run- ning, but perceiving that the animal was watching an opportu- nity to seize him by its usual spring or leap, he artfully led it to where the plain was terminated by a precipice hidden by brush- wood, and he had but just time to transfer his hat and coat to a bush, and to retreat a few paces, when the tiget sprang upon the bush, and, by the motal inertia of his body, was carried over the precipice and destroyed. The destructive effect of bomb shells is due to the same prin- ciple. When they burst, the various materials, balls, &c., with- in them partake of the same velocity as the whole shell, and scat- ter death and destruction around. The good effects of riding, as an exercise, are due to the inertia of the blood in the veins. When the body moves up and down, the blood, by its inertia, is also set in motion in an opposite direction. Motion, in consequence of the force of inertia which it gen- erates, is as permanent a state of matter as rest, and yet there' is a general opinion that any body in motion will naturally come to a state of rest. We often observe bodies in motion* and also notice that they all, on the surface of the earth, gradually be- come quiescent. But this is due to friction, gravity, and the re- sistance of the air. If these forces were removed, a body once set in motion would never stop. (1.) Influence of Friction. Thus we may easily show the in- fluence of friction upon a body. If a ball be rolled over a rough surface, it is soon brought to a quiescent state by friction. If it What would be the effect of stopping the earth in its orbit 1 What oth- er illustrations of inertia 1 Why does the motion of bodies near the earth cease ? What is the influence of friction, gravity, and the resistance of the air ? UNIFORM MOTION. 47 be rolled on a smooth plane, it will continue in motion much longer. (2.) Gravity. If there were no friction of the surface, the force of gravity drawing it continually toward the center of the earth would finally bring it to a state of rest, unless its velocity were sufficient to overcome gravity, which would require a rate nine- teen times more rapid than at present. In this case it would continue to revolve about the earth, and its motion would be per- petual. (3.) Resistance of the Air. The resistance of the air is also considerable, which aids in bringing all bodies projected through it to a state of rest ; but if this resistance is removed, the motion will be much longer continued. Thus a top in an exhausted re- ceiver will revolve for hours. A pendulum in the same condi- tion has been known to vibrate for a day. Exp. But a beautiful illustration of the resistance of the air as influ Fi ig encing motion is shown in two fan-wheels, Fig 19. When set in motion in the air, one of them, b, is soon brought to rest because of the greater re- sistance it meets with. But if they are both re- volved in the exhausted receiver of an air pump, they will both continue in motion for the same length of time. Now, as we remove opposing forces, we observe that the motions of bodies are long- er continued, and hence, if all such forces were removed, motion would become as per- manent as rest. In fact, when we observe the motions of the heavenly bodies, we find their course is perpetual. The revolution of the planets around the sun is accomplished by two forces. One is the force of in- ertia, by which they always tend to move in a straight line, and the other the attraction of gravitation, which causes them all to move toward the sun. A planet once set in motion with a force sufficient to carry it around the sun, will never lose that motion, but continue to move on forever. t 3. Motion is naturally uniform. If force is required alike Where shall we find the best illustrations of this law 1 What is meant by uniform motion ? 48 NATURAL PHILOSOPHY. Fig. 20. to move or to stop a body in motion, it follows that the body will move over Equal spaces in equal times,; that is, undisturbed motion is uniform. This is proved by the revolutions of all the heavenly bodies, the great standard of uniform motion being the diurnal and annual revolutions of the earth. With such uniform cer- tainty do all the heavenly bodies revolve, that any phenomenon, as an eclipse^ may be v calculated thousands of -years before its oc- currence. We rarely ee, to be sure, uniform motion upon the surface of the earth, owing to the presence of the same causes which bring all bodies to a state of rest, but we see a constant tendency to uniform as well as to perpetual motion. Thus, in falling bodies, there is the resistance of the air, which may be re- garded as of equal effect upon the body for the space of a few hundred feet, but the force of gravity is exerted at successive instants, and a body falls with a velocity which is said to bq uniformly accelerated. Now if 'the force of gravity could be counteracted after the body had received the first impulse, it would fall over equal spaces in equal success- ive portions of time. 'Atwoods Machine. The force of gravity is just balanced in an apparatus for falling bodies, called Atwoods Machine. Fig. 20 contains all^the parts essential to its opera- tion. By counterpoising two weights, m n, attached by a string and passing over a fric- tion wheel, the force of gravity is overcome, and by adding a slight force to impart motion to one of the weights, n, it is found by experi- ment that it will move over equal spaces in equal times, or with a uniform 'motion. 4. Motion is naturally rectilinear.- If force is required to move a body or to stop its ^notion, it will require force to bend it from Examples ef uniform motion. Describe Atwood's Machine. How does it prove that motion is naturally uniform ? How is the tendency to rec- tilinear motion proved 1 SECOND LAW OF MOTION. 49 a rectilinear direction. Under the influence of its inertia, mat- ter has a tendency, as we have seen, to move uniformly ; it has also a tendency to move in right lines, though this disposition is rarely carried out in nature, nearly every motion being either circular or curvilinear. All the heavenly bodies move in curves ; bodies on the surface of the earth have a curvilinear motion, but the tendency to move in right lines is always manifest. It is proved by the fact that any body moving around a center will fly off in the direction of a tangent to the curve in which it is mov- ing, as water from a grindstone or a stone from a sling, if the force which binds it to the center is destroyed. This tendency to break away from the central power is called the centrifugal force, and is another name for inertia, while the force which confines it to the center is termed the centripetal force. The tendency of bodies to move in straight lines is beautifully illustrated by the following apparatus, Q mni ,., 7 Fig. 21 : two balls are placed on a bar, a b, which may be made to revolve rap- idly on an axis ; through the center of 3 this axis a cord passes, one end attach- ed to the spring c, and the other to the balls. When the axis and balls are turn- ed, the balls tend to pass to a or b, and M- ^ i consequently bend the spring, which in- 7 H VI dicates the amount of centrifugal force. 3 1 ' 1 If the balls are placed near the axis and J u are free to move, they will pass to a and b as soon as the revolution has generated sufficient centrifugal force to overcome their inertia. Second Law. Motion is proportioned to the force impressed, and is in the direction in which the force acts. 1 . That motion is in proportion to the force impressed upon a body is proved by experiments with Atwood's Machine. Thus, by means of different weights, c, applied to n, Fig. 20, at e, and taken off by the brass ring, a, different velocities may be given to the ball, n. It is found that the velocity of n in a given time Describe the figure. What is the second law of motion ? How is it proved ? C 50 NATURAL PHILOSOPHY. will increase with the increase of force, and diminish with the diminution of force. Twice the force will double three times the force with treble the velocity. A body which falls two seconds has twice the velocity it would have by falling one, and the impelling force is just twice as great. This constant relation between the force and the velocity of motion is a matter of common observation. If a powerful force be used upon a small quantity of matter, the velocity becomes very great. If a slight force be used upon a large quantity of matter, the velocity will be proportionably less. Hence any force, however small, will cause motion in any mass, however great. The fall of an apple or of a meteoric stone lifts the earth. This may seem an extravagant assertion, but the velocity of any two bodies toward each other will be proportioned inversely to their quantities of matter ; for it is the matter which originates the force, and hence the larger body will move as much slower than the smaller as its quantity of matter exceeds it. The quantity of motion, then, which any body may have, is measured by the velocity and quantity of matter. Hence the quantity of motion in any body is an exact measure of the force which gave rise to it ; for if the mass is great, with a small force its motion will be slow, and if the mass is small, the motion will be more rapid, but in each case the quantity of motion just equals the quantity of matter multiplied into the velocity. The quan- tity of motion is also called momentum. In consequence of the inertia of a body, it receives a given force which it can not ose except by imparting it to other bodies, and hence the quantit / of motion or momentum of any body is the force which it can reproduce. The momentum of a cannon ball may only be sufficient to destroy a single man, and it may be able to pierce through the walls of a fort ; it may set a body in rapid motion, and it may be entirely stopped by it. In each case, the force it generates is a measure of the force by which it was What relation has force to velocity ? What effect has the fall of an ap- ple upon the earth ? What is meaut by the quantity qf motion 1 What is momentum? THIRD LAW OF MOTION. 51 originally impelled. For these and other reasons, it is clearly proved that force and motion are always proportioned to each other. 2. Motion is always in the direction ofthefo^ce. This would also seem to be a direct inference from the doctrine of inertia. If the inertia of a body is overcome by any force, it must move in the direction in which the force acts, because there can be no reason for it to move in any other direction. This view is con firmed by experience. We should be astonished to find a ball which was acted upon by a force toward the east taking a con- trary direction, or at all deviating from the course we designed it to take. Third Law. When one body acts upon another, action and reaction are equal and in opposite directions. By this law it is meant, that when two bodies meet, each gives and receives exactly the same shock. 1. This law may be easily established by the action of two Fig. 22. balls, a b, of lead or clay, suspended, as in Fig. 22, by small cords, so as to move freely through the arc x y. The balls are of exactly equal weight. (1.) If, therefore, the ball a fall upon b with a velocity represented by 6 0, both balls will move on with one half the velocity of the first. The ball a acts on b, and b reacts with the same force on a, so that action and reaction are equal. (2.) If b is larger than a, then the momentum of the two after impact will be just equal to that of a before ; and, generally, whatever be the relation of a to b, one will lose just as much motion as the other acquires. (3 ) If they fall with equal velocities, but in opposite directions, they will be brought to rest, which shows that action and reac- tion are not only equal, but in opposite directions. This same law applies to bodies at rest. If one body press upon another, and is sustained by it, the second body must react with What is the third law of motion, and how is it illustrated and proved ? How does this third law apply to bodies at rest ? 52 NATURAL PHILOSOPHY. an equal force, or there will be motion of both bodies ; and when- ever motion takes place, it is due to the same cause as the im- pact of one body upon another. 2. Numerous illustrations of this law might be mentioned. The following are a few of them : (1.) Birds fly by striking the air with their wings. If the ac- tion of their wings against the air was not met by an equal re- action, it would be impossible for them to commence their flight, for they could riot raise their bodies. By striking the air with a force sufficient to overcome the resistance of the weight of their bodies, they are borne aloft. If the wing is small, it must move with greater velocity. (2.) A boat is forced along by the oar, which strikes against the water, and receives from the water an equal reaction. (3.) When two men meet, the shock they sustain is precisely equal, and it makes no difference whether one or both are in motion. The one standing still receives and imparts the same shock as the one who is in motion ; but if both are in motion at the same rate, the shock is twice as great. (4.) Two ships, whether both are in motion or only one, strike each other with equal force, and when both are in motion with great velocity, the shock becomes very great. (5.) A man pulling a boat by a rope, or two bodies attracted by any force, exemplify the same law. Two magnets attract each other mutually ; the influence exerted upon one is given back upon the other ; so that, if several forces act upon each other, they have not the power of changing their motion in the slightest degree. Thus, if twenty men in a boat attempt to push it in the same or in opposite directions, they may exert great force, but they can not alter the direction of the boat, because, if they all push it in the same direction, that very force, by reaction, tends to drive it equally in the opposite direction. Hence, the forces being equal and in opposite directions, no motion is produced. How do birds fly? How is a boat propelled by the oar? When two bodies meet, which receives the greater shock? What other illustrations of action and reaction ? Why can not several men standing in a boat move it through the water by pushing against the side ? THIRD LAW OF MOTION. 53 According to this law, all attempts to produce perpetual motion must necessarily fail, because, by whatever force a body is set in motion, there is always an equal tendency to an opposite motion. If a man should step into a basket, and attempt to lift himself by taking hold of the handle, he would find that if he lifted up two hundred pounds, he would be obliged, in order to do it, to press down upon the bottom of the basket just two hundred pounds, and hence he would remain stationary. In observing the motion of bodies, we have noticed three par- ticulars : time, space, and velocity, that is, the time any body is moving, the space it passes over, and the rapidity of its motion, or its velocity. If the body pass over equal spaces in equal times, it is said to move with uniform velocity. Thus, if a man travel thirty miles at the rate of five miles an hour, he travels with uniform velocity. If the spaces over which a body passes are constantly increas- ing, it is said to move with an accelerated velocity. Thus, when a stone rolls down the side of a mountain, its velocity constantly increases until it reaches the base. If its velocity increases equally at each successive instant of time, it is said to move with uniformly accelerated velocity. This is nearly, though not strictly, the condition of bodies falling toward the earth under the influence of gravity. But if the spaces over which a body moves in equal times con- tinually diminish, it is said to move with a retarded velocity ; and if its velocity diminishes equally at each instant of time, the body has a uniformly retarded velocity. This is illustrated in throwing any body into the air : its velocity continually decreases until it finally stops, and returns to the earth with a velocity which may be regarded as uniformly accelerated. On comparing time, space, and velocity, we shall be ena- bled to derive several highly important truths. Thus, for ex- Why is perpetual motion near the earth impossible ? Where is it pos- sible ? What three things are to be particularly noticed in observing the motions of bodies ? Describe accelerated and retarded velocities. Uni- formly accelerated and retarded velocities. 54 NATURAL PHILOSOPHY. ample, it is evident that if the time during which any body is moving over a given space be diminished, the velocity must be increased ; and if the time is increased, or the body has a longer time to move, it must move slower, or its velocity must be di- minished. In other words, if the space is given, the time will be inversely as the velocity. 1. The space over which any body moves will always be equal to the time multiplied into the velocity ; or, if S = the space, T = the time, and V = the velocity, then S = T x V. For it is evident that the space to be passed over will be measured by the time the body moves, multiplied by the rate at which it moves. Thus, for example, at the rate of five miles per hour, how far will a man travel in six hours ? Ans., 30 miles. Six hours is the time ; multiply this by five, the velocity, and it equals thirty miles, the space. 2. The time will equal the space divided by the velocity, or c T= . For example, how long will it take a man to travel thirty miles at five miles per hour ? Ans., six hours. This is obtained by dividing the space, thirty miles, by five, the velocity, and it equals six, the time. 3. The velocity equals the space divided by the time, or, S V =: For example, a man travels thirty miles in six hours, at what rate must he travel ? Ans., five miles per hour. This is obtained by dividing the space, thirty miles, by six, the time, and it is equal to five, the velocity. It will be noticed that when different times, spaces, and ve- locities are compared, instead of "equals," in the above cases, we may read " varies as." Thus the velocity varies as the space divided by the time. We have also seen that the quantity of motion or momentum of a body was measured by the quantity of matter multiplied Mention the three equations of time, space, and velocity. THIRD LAW OF MOTION. 55 into the velocity ; or, in other words, if M represent the momen- M turn, and Q the quantity of matter, M = QxV, and Q= , V V = ??. That is, Q 1 . The momentum is equal to the quantity of matter multi- plied by the velocity ; or, when different momenta are compared, varies as Q X V. 2. The quantity of matter is equal to the momentum divided by M the velocity, or Q = 3. The velocity is equal to the momentum divided by the quan- TVT tity of matter, or V = . Q 4. With a given quantity of matter, as a pound or a ton, the momentum will vary as the velocity ; or, the faster the body moves, the greater its momentum. 5. With a given velocity, the momentum will vary as the quantity of matter ; for, the larger the body is, the greater the ob- stacle it will overcome. 6. In two bodies, whose velocities are inversely as their quan- tities of matter, the momenta will be equal. Thus, if a ten pound ball move ten feet per second, its momentum will just equal a one pound ball moving one hundred feet per second ; hence the smallest body may be made to stop or to put in motion the largest body, provided its velocity be as much greater as its matter is less. It is necessary in all these calculations to fix upon a unit of time and of measure ; one second is taken for the unit of time, and one foot is generally taken as a unit of measure. PROBLEMS. 1 . A sixty-four pound cannon ball was fired against a fort with a velocity of 2000 feet per second. What was the force with which it struck ? Ans., 128,000 Ibs. 2. A square block of stone, weighing 500 pounds, was just hQ NATURAL PHILOSOPHY. equal to resist the action of a cannon ball moving at the rate of 1500 feet per second. What was the weight of the ball ? Am., i Ib. 3. A battering ram, weighing 200 pounds, was forced againsl the walls of a fortified town, and overcame a resistance of twenty tons. What was the velocity with which it moved ? Ans., 200 feet per second. SECTION EI. COMPOSITION AND RESOLUTION OF MOTION AND FORCES. When a body is acted upon by two forces, it will move in a direction which is called the resultant of the tivo forces. 1. If the forces are equal, and at right angles to each other , the body will describe the diagonal of a square ; but 2. If the forces are unequal, it will describe the diagonal of a rectangle. 3. If the forces act either at acute or obtuse angles, the body will describe the diagonal of a parallelogram. 4. If a body be acted upon by three or more forces, its direc- tion may be represented by a single force, which is the resultant of them all. 5. If any body is acted upon at the same time by a constant and a variable force, it will describe a curve. A single force may also be resolved into several other forces, acting in different directions. HITHERTO we have considered the motions which were pro- duced by a single force. But most of the motions with which we are familiar are the result of two or more forces, and the prob- lem to determine the direction any body will take, moving under the influence of several forces, which act in different directions, is called the problem of the Composition of Forces. When two forces act upon any body, as the forces e/upon the ball A, Fig. 23, at right angles to each other, and with equal power, the body will move between them thus : What is meant by the composition of forces? What figures represent tije action of two forces ? COMPOSITION OF FORCES. 57 - 23- 1 . If the force e would cause the ball to move to B in one minute of time, and the force /would make it move in the same time to C, the body will obey both forces, and move between them in the direction A D. It will describe the diagonal of a square, and will be found at the end of one minute at D ; and a force, acting in the D direction AD, which would cause the body to move to D in the same time that both forces would produce the same effect, is called the resultant. 2. If the forces act as before, but one of them is greater than the other, the body will describe the diagonal of a rectangle ; thus, let the force e, Fig. 24, be twice that off; then the ball will de- Fig. 24. scribe the diagonal A D ; and the greater the difference between the two forces, the nearer will the lines A B, C D approach each oth- er, or the longer will be the rect- angle in proportion to its width. 3. If the forces act at oblique or at acute angles to each other, as e b, upon the ball A, Fig. 25, then the ball will describe the diagonal of a parallelogram, A D, and will be found at D in the same time that would be required to carry it to B or C by either force acting singly. 4. If a body is acted upon by three or more forces, it is easy to reduce them to one force, and hence to determ- ine the direction which the body will take. Thus, sup- pose the ball A, Fig. 26, to be acted upon by four forces, abed. If the ball move under the influence of a and b, it will be found at C, or the resultant of the two forces would act in the di- rection of A C. If the ball Fig. 25. Illustrate by the diagrams the action of several forces. C2 58 NATURAL PHILOSOPHY. is moved by this resultant and the force c, it will be found at E, or the force will act in the direction of A C. Finally, if the ball move under the influence of this latter resultant and d, it will be found at F ; or if it be acted upon by all the four forces at the same time, it will describe the line A F in the same time that either force singly would have carried it to either of the sides of the three parallelograms. By inspecting the diagrams above, the following truths become obvious : 1. When two forces, acting separately, would cause a body to describe the two sides of a triangle, when acting together they will cause it to describe the third side. This is evident from Fig. 26. Any two of those forces, as a b, acting together, since the side B C is equal to A D, would cause a body to describe the third side, A C, of the triangle ABC. 2. If a. body be acted upon by several forces, represented by all the sides of a polygon but one, the resultant will describe the last side. Thus, abed, Fig. 26, represents the four forces acting upon A. The sides A B, B C, C E, and E F, also rep- resent these forces. By their joint action, the body will describe the remaining side, A F. 3. Any number offerees, acting in an indefinite number of di- rections, may all be represented by one force, the resultant of them all, acting in a single direction. Hence, if any body is acted upon by three forces, represented by three sides of a triangle,* as A B, B C, and C A, it will remain at rest ; and if it be acted upon by a number of forces, represented by the sides of a polygon, it will also remain at rest ; and, finally, if a body be acted upon by opposite and equal forces, it will remain at rest. This may be called the equilibrium offerees. In all these cases it is assumed that the motion is of uniform velocity. But, suppose a body be acted upon by two or more forces, one of which is variable, then the body will not describe a straight line, but a curve. This curve will be examined under Central Forces. * Taken in order. Mention the several truths derived from the composition of forces. What direction will a body take acted upon by two forces, one of which is variable T RESOLUTION OF FORCES. Resolution of Forces. The resolution offerees is just the op- posite process to their composition. By the former several forces are reduced to one, and by the latter one force is resolved into two or more, acting in different directions. Fig. 27. Thus, suppose that a ball be propelled by a force, Fig. 27, so that in a given time it shall reach D the point B. This force may be resolved into two, acting in the di- rection A E and A D, or into four, acting in the directions abed. Many illustrations are found in nature and art of the composition and resolution of forces, hi which bodies are acted upon by sev- eral forces, and the results are always conformable to the princi- ples above laid down. Thus, a ship sails under the influence of two forces, which may be reduced to one. In Fig. 28, let the direction of the ship be a b, the sail c e, and the direction of the wind f e. Now the force of the wind, represented by the line g e, may be re- solved into p g and e p. The part e p acting par- allel to the direction of the sail, e c, does not pro- pel the vessel at all, but the force g p is the only force which causes it to move. The force g p acts obliquely, and must be resolved into g i and i p. The force g i is equal to the action of the water on the keel of the vessel, and the force i p represents the force of the wind in the direction which the ship sails. It is evident that two ships may sail in exactly opposite directions with the same wind. A kite ascends under the influence of three forces : the wind, the string by which it is held, and the kite itself, and it always moves, in accordance with the laws above stated, in a direction which is the resultant of these forces. Fig. 28. b What is meant by the resolution of forces? Explain the diagram, illustrations of the composition and resolution of forces ? What 60 NATURAL PHILOSOPHY. PROBLEMS. A carrier pigeon flew directly west twenty miles per hour for five hours, and a wind from the north carried her toward the south at the same rate. What figure would represent the space she passed over, and what distance would she be from the place of starting at the end of five hours ? Ans., 141.42 miles. A vessel sailed from New York, steering directly south for ten days, at the rate of one hundred miles each day, while the west- erly winds drove her directly east at the rate of fifty miles a day. What kind of figure will represent the space, and at what dis- tance will the ship be from New York ? Ans., 1118-f- miles. What would be her latitude and longitude, New York being in latitude 41 ? SECTION IV. GRAVITATION. VARIABLE FORCES AND MOTIONS. All bodies near the earth's surface are under the influence of gravity, a force which is constantly repeated, and hence gives rise to variable motions. Bodies falling toward the earth con- stantly increase in velocity, and the laivs which govern their de- scent or ascent are called the I. Laws of Falling Bodies. The space which a falling body describes may be represented by a triangle, as that of uniform motion is by a rectangle. I . The great law of falling bodies is, tJiat the spaces they de- scribe are as the squares of the times during which they are falling. II. Every body has a certain point called the center of grav- ity : if this point is supported, the whole body will be at rest ; if it is moved, the whole body ivill move ; and if it is not support- ed, the body will fall. III. Bodies moving around an immovable center, tend to move in a tangent to the curve, and the force generated by their revolution is called tangential or centrifugal. This force is great or small, according to the size of the body, its distance from the axis of revolution, and the velocity with which it moves. GRAVITATION. 61 IV. Wlien ladies impinge upon each other, they give and re- ceive the same amount of motion. 1 . Inelastic bodies, after im- pact, move ivith such a velocity that the sum of their united mo- menta just equals the sum of their separate momenta previous to impact. 2. Elastic bodies, when they impinge upon each other, give znd receive double the shock that they would if inelastic. IN the motion of bodies hitherto considered, we have regarded them, with a single exception, as moving over equal spaces in equal times, under the influence of a force which is imparted for once only, and the motion thus generated necessarily becomes uniform. But there are variable forces, and, of course, variable motions. When a body is acted upon by a force which is repeated at every instant of time, the motion of it is constantly increasing, and its velocity is uniformly accelerated. The attraction of gravita- tion, in respect to bodies near the earth, may be considered, with- gut material error, as repeated at each instant of time, and hence a body drawn toward the center of the earth constantly increases in velocity. The laws which govern the ascent and descent of bodies from and to the earth are called I. The Laws of Falling Bodies. These laws may be demon- strated and illustrated by means of diagrams, and proved by ex- periments. 1. Illustration. In uniform motion we have seen that the space equals the time mul tiplied into the velocity. If, therefore, one side of a rectangle, A B, Fig. 29, represent the ve locity with which a body moves, and A 1 2 3 C the several instants of time it is moving the figure A C D B will represent the space il will pass over, and hence a rectangle is a prop- er representation of uniform motion. But when the force acts so as to produce a uniformly accel- erated motion, we must find a different figure. Suppose a force How are variable motions produced ? How does the force of gravitation act ? What figure represents uniform motion ? 62 NATURAL PHILOSOPHY. be repeated upon a body three times during its motion, what kind of a figure would represent the space it would describe ? Let the space in the first impulse be represented by a rectan- gle, Fig. 30, as before, A B C 1, A I F&.ao. the time, and A B the velocity. At 1 let A -R the force be repeated, and as it is under the influence of twice the force, its veloc- ity will be doubled, and the next instant ^ it will describe the figure 1 2 E D. On repeating the force at 2, its velocity will 2 be tripled, and the figure 2 3 G- F will be described. Now, if we consider the force as repeated constantly from A to 3, the space described will be represented by the triangle A 3 G. Gravity is such a force, and hence we may represent the time a body is falling by one side of a right-angled triangle, and the last acquired velocity by the other, while the triangle itself will represent the space which a body passes over. If we compare the spaces described by any body during sev- eral seconds of time, we shall jind them to be as the squares of the times. Thus, let A B C and ADE, Fig. 31, represent the spaces de- scribed in two seconds of time, A B and A D. _ 31 The two triangles are similar, and we obtain the proportion ABC : ADE : : AB 2 : AD 2 ; or as BC 2 : DE 2 .* Since the spaces are to each other as the squares of the times, if the times or number of seconds during which a body is falling from a state of rest under the influence of gravity be as the numbers 1, 2, 3, 4, 5, &c., then the r spaces may at once be determined by simply squaring the times, 1,4, 9, 16, 25, &c. If, therefore, we can ascertain how far a * This is on the principle that similar triangles are to each other as the squares of their homologous sides. By another principle we have AB X BC to AD X DE, as the triangles themselves. What figure may represent bodies moving to or from the earth under the influence of gravity? What relation do the spaces and times bear to each other when bodies fall freely under the influence of gravity ? If the times are 1, 2, 3, 4, what numbers will represent the spaces ? LAWS OF FALLING BODIES. 63 body will fall during the first second, it will be easy to determ- ine that of all the rest. It has been found by experiment that near the earth's surface a body falls 16^ feet in a second, and hence it would fall in two seconds four times as far, or 64 feet ; in three seconds, nine times as far, or 144f feet ; in four seconds, sixteen times as far, or 2571 feet. This may be shown in a different manner. Thus, at the end of one second, the velocity generated, if gravity were to cease its action, would be sufficient to carry it during the next second feet; but as gravity acts constantly, it will cause it to fall feet further, which being added, makes 48 T 3 2- feet for the second instant ; and now it has acquired a velocity which will carry it 64 T 4 ^ feet during the third second, while gravity will carry it 16y~ further^: 80 feet ; and the fourth second, by the same law, it will fall 1 12 T 7 2 feet. If we examine the numbers, we find them to be 16 T ^, 48 T 8 , 80-&, 112 T \, which represent the spaces for each successive second of time, and we shall observe that they are as the numbers 1, 3, 5, 7, 9, &c. If we add to each the space previously passed over, we shall find uiey are as the squares of the times. Thus the first and second second make 64 T 4 , or the square of 2 z= 4 X 16^ ; add the third second, and it will equal 9X 16 T ^ = 144 T 9 ^ ; and adding the fourth second, it will equal 257 T 4 T . Hence, if the times are as 1, 2, 3, 4, &c., then the spaces are as 1,4, 9, 16, &c., and the spaces for each second as 1, 3, 5, 7, 9, 11, &c. 2. This law, so readily demonstrated by figures and numbers, may be proved experimentally by means of Atwood's Machine. The arrangement is such in this appa- ratus that the body descends much slower than if it were wholly under the influence of gravity, and yet the relation between the times and spaces is perfectly preserved. Thus, Fig. 32, the weights m n are exactly balanced, and weigh 31^ ounces each, so that both of these weigh 63 ounces. If, now, a weight of one ounce be placed on one of these weights, it will carry down How far does a body fall under the influence of gravity in one second ? What velocity does it acquire the first second, and what the second second ? What series of numbers represent the spaces passed over by a body in each successive second of timel Describe the principle of Atwood's Machine. NATURAL PHILOSOPHY. one 31|- ounces, and cause the other 31^ ounces to rise, so that the whole amount of matter in motion is 64 ounces. If the one ounce fell freely, it would fall IGy^ feet in a second ; but as it has 64 ounces to move, it will fall but one sixty-fourth as fast : 16^3- feet reduced to inches equals 192 inches,* a sixty-fourth part of which is three inches. The first second the weight would fall 3 inches ; in two seconds it would fall freely 768 inches, one sixty-fourth of which is 12 inches ; a third second 27 inches, a fourth 48 inches, a fifth 75, a sixth 108 = 9 feet. Hence, by this machine, a body which, by falling freely, would descend 576 feet in six seconds of time, would only fall nine feet. Fig. 32. Seconds . . 1 2 3 4 5 Gravity, feet . 16 rV 64^ 144f 2571 402 T V Atwood's Ma- ) i /* in* chine . . J 3 12 27 48 75 There is some friction to be overcome, yet when this theory is subjected to the test of experiment, the weights are found to fall in exact obedience to it. There is a pendulum, and clock-work attached, which beats seconds, and some other parts not fully represented. In proving the above laws experimentally, two small weights, i c, are applied to n, one of which will pass through the ring, and the other will be taken off by it. (1 .) To prove that the spaces passed over are as the squares of the times, . Place n at c, and lay the one ounce weight, i, upon it. If now the slide b is placed three inches from c, and the weight allowed to fall, it will reach the slide in one second. Then place the slide one foot from c. and the weight will reach it in just two seconds; in three seconds it will fall 27 inches, and in four seconds 48 inches. The spaces are as the squares of the times, ?' ^' ?' , 4 r . The time is measured by the pendulum, which 1 7 *1 ? i/j 10 beats seconds. * Omitting the fraction T \j. LAWS OF FALLING BODIES. 65 (2.) To determine the velocity acquired at the end of each sec- ond, and the distance passed over in each successive instant of time. Exp. Place the weight e on n, and place the brass ring a three inches from c ; on letting the weight fall, it will arrive at the ring in one second ; the weight, e, is now taken off by the ring, and the velocity ac- quired will carry it six inches the next second ; its velocity, therefore, at the end of the first second, is sufficient to carry it twice the distance in the same time, and the apace passed over during the next second will be nine inches, if the load remain attached. If the slide be placed twelve inches from c, and the weight fall two seconds before the load is taken off, its ac- quired velocity will carry it down twelve inches the third second; hence, if the load had not been taken off, the space passed over would have been fifteen inches. It is evident that the spaces 3, 9, 15 are obtained by mul tiplying the numbers 1, 3, 5 into the distance which the weight fell tho first second, or by three. The weights m n may be varied at pleasure, and also the loads i e; the smaller the load in respect to the weight, the slower the motion, but the laws are the same. In nature we have numerous illustrations of bodies falling with a constantly accelerated motion, as when any mass slides down an inclined plane, or a stone rolls down the side of a mountain, but the law is the same. Few bodies fall perpendicularly. Rain-drops* and hail sometimes acquire considerable velocity ; the latter frequently breaks panes of glass and destroys vegetation. Meteoric stones, falling from great heights, acquire such velocity as to bury themselves in the earth. The blow of a sledge or hammer is greatly increased by the distance through which it falls. The logs which slide down the wooden troughs from the Alpine heights acquire a velocity which seems almost incredible. 3. When a body is thrown perpendicularly upward, its motion is constantly retarded, under the influence of gravity, until it stops and returns again to the earth, and in this case the law is reversed ; that is, if it be projected with a velocity which it would gain by falling six seconds, it will rise to the height from which it must fall to gain that velocity ; but the spaces for each instant will be reversed, and we should have, instead of the se- ries 1, 3, 5, 7, 99, 7, 5, 3, 1. What illustrations in nature of the laws of falling bodies ? What is the law when bodies are thrown perpendicularly upward ? What kind of mo- tion does such a body describe ? 66 NATURAL PHILOSOPHY. In consequence of the relation of a rectangle to a right-angled triangle, the latter being half of the former, the one representing uniform motion, and the other accelerated motion, it is easy to Bee that a body moving uniformly with a velocity equal to that which a falling body acquires in a given time, would describe twice the space in the same time, and also that a body moving directly upward uniformly with the velocity it may acquire in falling from a given height, will describe double the space it would under the retarding influence of gravity. It is also evident, that a body projected downward from a given point, will describe a space equal to that described by a body falling during the same time, and one moving uniformly with the velocity of projection. If it be thrown upward, the space will be the difference between a body moving uniformly with the veloc- ity of projection for the time, and a body falling freely during the same time. For those acquainted with algebra and geometry, the following repre- sentations of the relations of time, space, and velocity are highly important. Let g-=:the space which a body falls during one second of time =16^- feet. 2^:=the velocity acquired at the end of one second. S=the space described by the body in any given time, as T, and V -the velocity acquired in the time, T. Then, since the spaces are as the squares of the times, &'.g:: T a : I 2 , or. . . . Sr=g-T 2 ; also, S:#::V':(^) 2 ,or. . . S=, and V 2 =%S, or ...... V but 1 : Zg : : T : V . . . . . V=2gT. As V=2^T.- ....... T~; and as S=*T . ...... These formula? may be employed in the solution of the following PROBLEMS. 1. What space will a body fall through in ten seconds, and what velocity will it acquire ? The space, S = g-T a , g = 16^ feet. The square ofT = 10XlO=100 X16 T V=1608 feet, Ans. Velocity, V = 2 g >xT = 2Xl6 T 1 I X 10=321 feet, Ans. 2. How long would a stone be in falling from the top of the great pyra- What relations do the spaces described by uniform motion bear to those described by falling bodies ? CENTER OF GRAVITY. 67 raid in Egypt to the base, a distance of 500 feet, and vfrhat velocity would it acquire ? Ans., T = 5.5756, arid velocity = 179.3485 feet per second. 3. To what height would a ball ascend, shot directly upward with a ve- locity of 2000 feet per second ? Ans., 62176+ feet. 4. If it was twenty seconds before the ball returned, to what height did it reach, and with what velocity was it projected ? Ans., Height, 1608^ feet; velocity, 321^ feet a second. 5. A cannon ball let fall from the top of a tower was four seconds in reaching its base. What was the height of the tower ? Ans., 257 feet. 6. If a ball is projected downward with a velocity of twenty feet a sec- ond, how far will it fall in ten seconds? The velocity given to the ball will be uniform, and will be equal to T X V, or 10x20 = 200, and the space which the ball will describe under the in- fluence of gravity will be = g-T 2 , or 16 T ^X 100 = I608j feet. Ans., 1608 1- + 200 = 1 808 feet. To determine the spaces described by any body in one or more seconds during its fall, we have only to refer to the law, where the spaces described in equal successive times are as the odd numbers 1, 3, 5, 7, 9, &c. The space for the first second is g feet, the second second 3g feet, third second 5g feet, &c. 7. A body fell eight seconds. How far did it fall the third second ? how far the fifth second ? and how far the last ? Ans., Third = 80 T 5 2 feet; fifth = 144; eighth =2411 8. An aeronaut, after ascending 23 16 feet, found it necessary to throw out a bag of sand. What space would it describe during the last second of its fall? Ans., 369}| feet - II. Center of Gravity. The force of gravitation, acting on a mass of atoms, tends to draw them all toward the center of the earth in lines, which for small distances may be regarded as par- allel. The atoms of a mass one foot square all tend toward the center of the earth in lines so nearly parallel that it would be difficult to detect any convergence. But if we take a mass sev- eral miles in extent, then the lines will be perceptibly diverg- ent. If now we could substitute one force for all these parallel forces acting on one mass, a line passing through that force to the center would be the resultant of all the lines of force. If, there- fore, a body were supported on a point any where on that line, its tendency to fall would be exactly counteracted, and it would remain at rest, or would be in equilibrium, because it would be acted on by equal and parallel forces in exactly opposite directions. How does the force of gravity act upon the atoms of a mass ? When will a body remain at rest? 68 NATURAL PHILOSOPHY. To render this evident, let the line d b, Fig. 33, be the resultant of all the forces in the mass. If any portion of this line were supported, the body could not fall, but the stability of its support would depend upon a very important circumstance. 1. If d b were a rod, and the point b were supported, it is evident that, as all the mass is above b, a very slight motion of the body would cause some other line to be the resultant, as a c, and the body would fall. This is called unstable equilibrium. 2. But if the body were supported by the point d, the matter all being below the point of suspension, it is evident that it could not fall without an entire revolution of the body. This is called stable equilibrium. 3. If the body were sustained by a point which is at the cen ter of its mass of atoms, as at c, it could remain at rest in what- ever position it was placed, and such a state is called Indifferent equilibrium; and the point which thus sustains all the parts in equilibrio is called the Center of gravity, and also the center of inertia, which may be denned to be that point in any body which, if supported, the whole body will remain at rest, whatever position it may occupy. Every solid body must have such a center, and, if that is sup- ported, the whole mass will be, and if that moves, the whole mass will move. For example, if two atoms, a b, Fig. Fig. 34. 34, on the end of an inflexible rod, have their center of gravity at c, and that point be supported, they will remain at rest. If any force is applied to the point c, the a two atoms will move in the same manner that they would if the force were applied directly to each. If the support is placed in any other part of the line out of this center, the equilibrium will be destroyed, and one or both will fall. Describe unstable, stable, and indifferent equilibrium. What is meant by the center of gravity ? If the center of gravity is supported, in what condition will a body be ? CENTER OF GRAVITY. 69 If there are four atoms, a b and a f b', Fig. 35, and the center of gravity, c, be supported, they will all be in equilibrium ; hence any number of atoms have their cen- ter of gravity, which being supported, the whole mass will be at rest, or if moved, the whole will move. It becomes now an important problem to determine where this center is in any body we may have to examine. 1 . If the body is a sphere, a regular prism, or a cylinder, and of uniform density, the center of gravity will evidently be at the center of its magnitude, or geometrical center. 2. If the body be a disc of uniform density, the centers of mag mtude, of motion, and of gravity will exactly coincide ; but if one Fig. 36. side of the disc is thicker, or loaded with lead, then its center of gravity will not coincide with either the center of magnitude or of motion. The apparatus, Fig. 36, is well fitted to illustrate these facts. The disc is loaded with a piece of lead, d, and pierced through the center of magnitude and of gravity, a c, so that it can be revolved upon an axis. It may be used, also, to illustrate stable and indifferent equilibrium. 3. If the body is in the form of a triangle, the center of gravity is found by bisecting two sides by lines drawn from the op- posite angles. Thus, let a.b c, Fig. 37, be a triangle. Bisect the side a c by b n, and b c by a m; the center of grav- ity will be at g, which is found to be one third of m a. For, join n m ; then c n m and cab are sim- ilar ; therefore c n : c a : : n m : a b ; but c n is half of a c, therefore m n is half of a b. Again, the triangles n g m and gab are sim- How is the center of gravity determined in a sphere, prism, and cylin- der? How in a disc ? How is the center of gravity in a triangle determ- ined ? 70 NATURAL PHILOSOPHY. ilar, and g m: g a'.'.m n: a b. m n is half of a b, and hence m g is half of g a. The point g is therefore one third the distance from m to a. Now, as the center of gravity must be in the line m a, since every line drawn parallel to b c would be bisected, and the center of gravity of aline is the center of the line, and as it must also be in the line b n, for a similar reason it must be at their point of intersection, g. Practically, the center of gravity may be determined by sus- pending the triangle from the two corners b and , and letting fall a plumb line from each, as a m, b n. Where the lines cross at g will be the center of gravity. 4. The center of gravity in a regular polygon may be found by dividing it into triangles, arid then finding the centers of the several triangles. 5. In a regular pyramid or cone, the center of gravity is at a point one fourth of the distance from the center of their bases to the apex 6. If bodies have irregular shapes, their center of gravity may be found by suspending them from two corners, as in Fig. 33. Thus, suspend Fig. 33 from the point d, with a plumb lin* passing in the direction d b, and then from the point e. The in- tersection of the two lines at c will be the center of gravity, foi this center must be in the line b d, and also in ef; it must be, therefore, at the point where these lines cross each other at c. Stability of Bodies. We have seen that when the center of gravity is supported, the body will be at rest. But its stability will depend upon thtj fact whether it is in a state of stable, un- stable, or indifferent equilibrium. 1 . A solid body is supported ivhenever a plumb line from the center of gravity falls within its base. Thus, Let A B, Fig. 38, represent the leaning tower of Pisa. When the top, B, is taken off, the cen- ter of gravity is at C, and the line from C fall- ing within the base, the tower will be sustained ; but by inserting the top, B, the center of gravity is raised to E ; and as the line falls without the base, the tower will fall. Where is the center of gravity in a pyramid and cone ? How can the center of gravity be determined in an irregular figure ? What rule for de- termining when any body will be supported ? STABILITY OF BODIES. 71 d A sphere, d, Fig. 39, on an inclined B plane, A B, will roll down simply be- cause the center of gravity is not sup- ported, while the square body, g, will remain at rest, or only slide down the plane, because the line of the center of C gravity falls within the base. 2. The broader the base is, and the lower the center of grav tty, the firmer will the body stand ; and, on the contrary, as the base is made more narrow, and the center of gravity raised, the body becomes more and more unstable. Thus broad, low bodies, as houses, are upset with much greater difficulty than those that are high, with narrow bases. Quad- rupeds stand much more firmly than birds and other bipeds. A person carrying a weight on his back must lean forward in order to bring the line of the center of gravity within his base. If he carry the weight in one hand, he must lean in the opposite direction for the same reason. He will, therefore, carry a greater burden if it be suspended on both sides of his body. The wonderful feats of rope-dancers, tumblers, &c., depend mainly on their power of keeping their bodies in such positions as to cause the line of the common center of gravity always to pass through the point on which they support themselves. Carriages and loaded teams, Fig. 40, are sometimes upset, be- cause the direction of the center of gravity falls without the base. The danger of upsetting is in- creased if the vehicle is in rapid motion and the road curved, for 61 p in this case inertia will aid in throwing the center beyond the base. In such cases the danger may be avoided by lying down in the carriage, so as to lower the center of gravity. A beautiful illustration of stable equilibrium is found in a little What influence has the size of the base upon the stability of bodies ? Why are carriages upset ? What can be done to prevent a carriage from upsetting 1 What illustration of stable equilibrium ? Fig. 40. 72 NATURAL PHILOSOPHY. toy, in which a trooper is made to stand without any apparent support. In case a tody is suspended, as a pendulum, or the beam of a pair of scales, it is necessary that the point of suspension should be a very little above the center of gravity, in order to make a stable equilibrium. If it be suspended at the center of gravity, the equilibrium will be indifferent, and if it is below, the equi- librium will be unstable. III. Central Forces. Under the action of gravity and any projectile force which is not in the direction of the center of the earth, the motion described by any body is curvilinear. 1 . Thus, suppose a body to move under the influence of a pro- jectile force, A, Fig. 41, which in four Fig 41 seconds, moving with uniform velocity, would describe the line A B. Now if, under the influence of gravity, it would fall from B to C in the same time, then in four seconds it would describe the curve Afhk C, or the force of gravity acting constantly will cause it to move through spaces which will be as the squares of the times. That is, if the times A e, e g, g i, i B, are equal, the lines ef, g h, i k, B C will be as the squares of these distances. The body, therefore, under the influence of both forces, will describe the curve of a parabola,* if the force of gravity is assumed to act parallel to it- self ; but as it, in fact, never does, the curve is an ellipse. These figures, however, are not described unless the body move in a vacuum ; for the resistance of the air is such that the tend- ency is to uniform motion, and the curve actually described is what is called the Balistic Curve. That is, in all cases where bodies, as cannon balls, are fired through the atmosphere, the air becomes com- pressed before them, so as to alter their course to the right or left; and if their velocity be above 1280 feet per second, the * A parabola is one of the sections of a cone. It is a curve, any point of which is equally distant from a fixed point and a given straight line. How should a balance be suspended? How is curvilinear motion pro- duced? Illustrate by the diagram. What kind of a curve does a body describe under the influence of a projectile force and gravity 7 PROJECTILES GUNNERY. 73 rate at which air flows into a vacuum, it is soon reduced below that rate. 2. Projectiles, Gunnery. Bodies thrown into the air by any force are called projectiles. Such bodies are under the influence of three forces, the force of projection, the resistance of the air, and gravity. A knowledge of the laws of projectiles is applied to the Art of Gunnery. The force (which is gunpowder) is measured by the motion which a b511 of a given weight will give to a block of wood, sus- . 42. perided as A, Fig. 42, and called the Holistic Pendulum. When the ball is fired into the center of per- cussion, the ball and block move over the graduated arc with a velocity as much less than the ball, as the ball and pendulum together is greater. By ascertaining the weight of the ball and of the block, and then the velocity of both over the graduated arc, it is easy to determine the velocity of the ball ; for the weight of the ball will be to that of the block, as the velocity of the block is to that of the ball. By this instrument the strength of powder, and the influence of a large or small charge, may be determined. Gunpowder expands 5000 feet per second, which will commu- nicate a velocity of 2000 feet per second ; but, owing to the re- sistance of the air, it is soon reduced below 1200 feet per second ; hence there is little advantage in using a large charge of powder. The random of a projectile is the distance it reaches in a hori- zontal line before it strikes the earth. An angle of 45 gives the greatest random, and for the same number of degrees above or below 45 the random is the same. 3. If a body be projected in the direction of a tangent to the earth's surface, the direction of the force of gravity being toward What is a projectile ? To what art are the laws of projectiles applied ? How is the velocity of a cannon ball measured ? What is its expansive force ? Greatest velocity of a cannon ball ? What figure will a body de- scribe if it be projected in the direction of a tangent to the earth's surface ? 74 NATURAL PHILOSOPHY. its center, we can easily determine the course of the moving body. Thus, Let C, Fig. 43, be the center of the earth, and a body, as at a, acting under the influ- ence of the projectile force a ft, which in one second of time, moving with uniform velocity, would describe the line a b. If, under the in- fluence of gravity, it would fall from a to d, then in one second it will describe the diago- nal a f. Then, if the centrifugal force at f would carry it to g during the second instant, and the force of gravity to h, it will describe the line/&; and so the third second it will be found at n. But as gravity is a constant force, it will actually describe the curve afk n. If the projectile and central forces are equal, the body will describe a circle ; but if the force of projection, which becomes the centrifugal force, diminishes at different points of its orbit as the square of its distance from the center of attraction increases, then it will be an ellipse. All the planetary bodies revolve in ellipses, moving under the influence of the centripetal force, which is gravity, and the cen- trifugal force, which is the force by which they were first sent forth into space. As the planets are at different distances from the sun, and revolve with different degrees of velocity, their mo- tions are found to conform to the laws of bodies revolving under the influence of two such forces as gravity and the force of pro- jection. These laws may be illustrated and proved with the apparatus, Fig. 44, which has attached to it several bodies of different shapes, as a double cone, a chain, spheroid, &c. It is found that all bodies, when rapidly revolved, will assume that axis which represents their shorter diameter ; the shorter diameter, there- fore, becomes the permanent axis. It is found by experiment, 1. That the centrifugal force is proportioned to the quantity By what circumstance is the nature of the curve determined ? What curves do the heavenly bodies desciibe ? Which is the permanent axis of a revolving body ? What is the centrifugal force proportioned to ? CENTRAL FORCES. 75 of matter. That is, as the quantity of matter increases, the force increases. 2. This force is proportioned to the distance of the body from the center of motion. At twice the distance, the body must be forced toward the center twice as far at every revolution. 3. If the velocity is doubled, then the centrifugal force is four times as great ; for double the velocity gives double the power to fly off, and also requires the body to be moved toward the cen- ter with twice the velocity, which makes its force four times as great. Hence the reason why large mill-stones are sometimes separated by a very rapid revolution, and why a carriage in rapid motion, when turning the corner of a street, is upset ; why, in the circus, the rider inclines his body within the ring, to coun- teract the constant tendency to be thrown off in a tangent to the circle in which he is moving. Hence, in consequence of the fact that the centrifugal forces of bodies revolving in the same circles are as the squares of the velocities, when the velocity is very great this force may become so great as to cause the body to break away from the central force. Thus, the velocity of the earth might be so increased as to change the form of its orbit from an ellipse to a parabola, in which case it would never return again to the central power, the sun. 4. But when bodies revolve in dif ferent circles in the same time, the centrifugal forces generated will be as their distances from the centers of motion, or as the radii of the circles. At twice the distance from the cen- ter, the body must be forced inward twice as far at each revolution, and, of course, its force must be twice as great. This principle may be illus- trated by an apparatus, Fig. 44, in which several bodies, capable of altering their figure, are rapidly whirled about. The matter What effect has it to double the velocity of the revolving body ? What other illustrations of centrifugal force? What would be the effect of in- creasing the velocity of the earth in its orbit? What is the law when bodies are placed at different distances from the center of revolution ? Fig. 44. 76 NATURAL PHILOSOPHY. tends to move as far as possible from the axis of revolution. If our earth were at first in a plastic state, it would tend to bulge out at the equator, and become compressed at the poles ; for the velocity at the equator would cause the matter to accumulate there. This is the shape which it actually has. The same principle is illustrated in the case of the rings of Saturn, and in the shape of all the bodies of the solar system. The clay in a potter's wheel also bulges out to form bottles and other vessels as the wheel rapidly revolves. It will be seen that the effect of centrifugal force is to destroy either wholly or in part the weight of bodies. Thus any body at the equator will weigh less, on account of its greater velocity, than at the poles, being diminished | th of its weight. If, therefore, the velocity at the equator were seven- teen times as great as at present, all loose bodies would be thrown off, and revolve about the earth.* IV. Collision of Bodies. We have noticed that certain mod- ifications of the cohesive force gave rise to the property of elas- ticity, a power which some bodies have, when compressed, of re- storing themselves to their former position ; but this property is possessed in different degrees, and in some bodies it is wholly wanting. Thus ivory, glass, India rubber, wool, &c., are very elastic; lead, clay, and wax are non-elastic bodies. These properties give rise to different effects in the two classes when they impinge or strike against each other. 1 . When inelastic bodies impinge upon each other, there is no rebound ; but if both bodies are moving in the same direction, they will move on together after impact with a velocity corre- sponding to their quantities of matter and the sum of their veloc- ities before impact, or their velocities will equal their momenta divided by their quantity of matter. * The weight of a body is diminished as we go from the pole to the equator in the ratio of the square of the cosine of latitude. What shape wouttl the earth assume if it were first created in a plastic state? What other illustrations in nature? What is the effect of centrifu gal force upon the weight of bodies ? When inelastic bodies impinge upon each other, what is the law of motion ? COLLISION OF BODIES. 77 If two bodies are moving in opposite directions, their velocity after impact will equal the difference of their momenta divided by their quantity of matter. For it has already been shown, that the velocity of any moving body may be found by dividing the momentum by the quantity of matter ; and hence the velocity of any number of moving bodies after impact may be found by dividing the sum or difference of their momenta by their quantity of matter, whether they are moving in the same or in opposite directions before they come into collision. These facts may be illustrated by two lead or clay balls, Fig. 22, p. 51, which are of exactly equal size. Exp. By raising a to 6 and allowing it to fall upon b, the two balls will move to 3 in the same time that a moved from 6 to 0. PROBLEMS. 1 . If a lead ball weighing two pounds, and moving with a ve- locity of 1200 feet per second, strike another ball of the same weight at rest, what will be their velocity after impact ? Ans., 600 feet per second. 2. If, in the above problem, the second ball were moving 200 feet per second in the same direction, what would be their ve- locity after impact ? Ans., 700 feet. 3. If the second ball were moving 200 feet in an opposite di- rection, all other conditions being the same as in the first prob- lem, what would be their velocity after impact ? Ans., 500 feet. 4. If the two balls were moving with equal velocities in op- posite directions, what would be their velocity after impact ? 2. When elastic bodies come into collision, a very remarkable law is developed, which appears at first view to be paradoxi- cal ; viz., The velocity lost by one and imparted to the other is exactly double that which it would have were the bodies inelastic. This How may the velocity of any number of moving bodies impinging upon each other be determined ? What is the law of impact when elastic bodies impinge upon each other ? 78 NATURAL PHILOSOPHY. law is due to the power the parts compressed have of restoring themselves. Thus, if one ivory ball impinge upon another, Fig. 45, and strike it with a force equal to three, both m 45 balls will be compressed at the point of impact, and the parts, in being restored, react upon each other, and double the effect, or make the blow equal to six. If the balls are equal, the momentum of one is wholly communicated to the oth- A er, and it moves after impact with the same velocity as the first ball, which will r- be stopped. If they move with equal ^ ! " i|in ' |i!i " 11 "" 1 'H"'i"'i'i'iniiii"ii."iiMiinii velocities in opposite directions, they will rebound, each with the same velocity with which they met. This fact is easily shown by these balls. This is the reason that a hard body, when struck, causes a rebound to take place. Exp. If the ball a be let fall from A upon b, its own motion will be stopped, but it will impart an equal motion to c, and thence through d to e. As there are no bodies beyond e, it will receive the motion, and move to 3. If a b be let fall from 3 upon the remaining balls, d e will move to 3, and all the rest will be stationary. If two balls are met at from 3 3, they will rebound with equal velocities. In cases where elastic bodies strike on a hard surface, in the rebound, the angle of incidence is always equal to the angle of reflection. Thus, let d, Fig. 46, strike on the surface c, the angle d c b is equal to b c a. The same law holds in respect to light and heat. If the ball fall per- pendicularly, it will return by the same path. _ It appears from the preceding experiments with the marble balls, that When two equal elastic bodies impinge on each other, each ynoves after impact with the velocity which the other body had before impact. Thus, when b and a meet with equal velocities, they rebound with equal velocities ; when d falls upon c at rest, c moves with the velocity of d, and d with that of c ; that is, d re- mains at rest. If the balls are not all of the same weight, then the velocity Explain this law. Illustrate the laws of impact with the ivory balls. What is the angle of incidence and of reflection ? How do they compare with each other ? COLLISION OF BODIES. 79 of the larger ball, if at rest when struck, will be as much less than that of the smaller as its quantity of matter is greater, while the velocity of the smaller ball, under the same conditions, will be as much greater than that of the larger as its quantity of matter is less. If there are a succession of balls of equal weights, and one of the balls, as e, Fig. 45, be let fall against the others, they will all remain at rest except a, and that will move with the velocity of e. If two balls, a b, be let fall upon the remaining three, they will impart their velocity to the two on the other side of c. These laws may be rendered familiar by a few problems : 1 . If a marble ball weighing two pounds, and moving ten feet per second, strike another ball of the same weight at rest, what will be the velocity of each ball after impact ? 2. If the two balls in the above problem are each moving ten feet per second, but in exactly opposite directions, what will be their velocity then after impact ? Ans., 10 feet per second. 3 . If the two balls, A B, as above, are each moving in the same direction, the first 20, and the second 200 feet per second, what will be the velocity of each after impact ? Ans., A 200 feet, B = 20 feet. 4. The ball A, weighing ten pounds, and moving with a ve- locity of twenty feet per second, impinges on the ball B, which weighs five pounds, and is at rest. What are the velocities of A and B after impact ? Ans., Velocity of A = 10 feet, B = 20 feet per second. 5. If both balls are in motion in the same direction, A twenty feet, and B ten feet per second, what velocity will each have after impact ? Ans., A=10 feet, B=30 feet. 6. If both balls move in opposite directions, the velocity and weight being as in problem 5, what would be their velocities after impact ? 80 NATURAL PHILOSOPHY. CHAPTER III. OF THE MECHANICAL POWERS. FOR the purpose of transmitting force and motion, certain ma- chines have been invented, called The Mechanical Powers, the object of which is to change the direction of motion, to increase force at the expense of ve- locity, or velocity at the sacrifice of force. All machines, what- ever their form, may be reduced to six : 1. The Lever. 2. The Wheel and Axle. 3. The Pulley. 4. The Inclined Plane 5. The Screw. 6. The Wedge. These may be further reduced to two elementary principles, for the wheel and axle, and the pulley, act on the same principle as the lever, while the wedge and screw are inclined planes. By the term weight is meant any resistance to be overcome, and by power, the force which overcomes it. They are repre- sented by P and W. There is one law which applies to all machines, whatever their form or structure. It is called the law of Virtual Velocities. This law is, that the power and weight will be in equilibrium when The product of the weight into the vertical space which it passes through is equal to the prod- uct of the power into the vertical space it passes through ; and if this relation is disturbed, motion will ensue. Thus, in Fig. 47, let P W re- volve on/; then P : W : : c d : a b. = Wxcd. When motion What is the object of machines? Mention the several mechanical powers. To how many simple principles may they be reduced ? Meaning of weight and power. What law applies to all machines 1 MECHANICAL POWERS. 81 takes place, the velocity of the weight into the weight equals the velocity of the power into the power. In estimating the force of any of the mechanical powers, we must first determine in each one the Law of Equilibrium, that is, the conditions which must be observed that the power and weight may exactly balance each other ; and in ascertaining what these laws are, no notice is taken of any impediments to motion arising from friction or any other cause. The laws are first determined theoretically, and allowance made afterward, as there always must be in practical mechanics, for any disturb- ing causes. SECTION L OF THE LEVER, THE WHEEL AND AXLE, AND THE PULLEY. As it is the object in all the mechanical powers first to ascer- tain the laws of equilibrium between the power and the weight, it is found I. In the lever that equilibi'ium will be maintained when the pi'oduct of the poiver into its distance from the fulcrum is equal to the product of the weight into its distance from the same point. II. In the wheel and axle, the poiver and weight will balance each other when the power multiplied into the radius of the wheel is equal to the weight multiplied into the radius of the axle ; and in itie wheel and pinion, the product of the power into the number of teeth in the wheel is equal to the product of the weight into the number of notches or leaves in the pinion. III. In the pulley, equilibrium will be maintained when the power multiplied into twice the number of movable pulleys is equal to the weight; and in case each movable pulley has a sep- arate string, we may ascertain the weight by raising 2 to a power equal to the number of movable pulleys, and multiply- ing it by the power. In all the above cases, if a slight force be added to the power, the weight will be raised. But there is no advantage gained, for wlutt is gained in power is lost in time^ or the poiver must move as much faster tfian the weight as its quantity of matter is less. What is the first object in investigating the action, of the mechanical powers ? D 2 82 I. Lever. A lever is an inflexible rod, of uniform magnitude, capable of moving freely around some point as a center of mo- tion, called ihefidcrum. Law of Equilibrium in the Lever. In the lever, the weight and power will be in equilibrium, when they are to each other inversely as their distances from the fulcrum; or when the prod- uct of the weight into its distance from the fulcrum is equal to the product of the power into its distance from the same point. Thus, let A B, Fig. 48, be a lever, and F the fulcrum, the power and weight will be in Fig. 48. equilibrium when P : W : : B 4 r ^ 2 1 A i 3 3 F : A F ; for if the power p ^ I? and weight are at equal dis- ^0 10 tances from F, the power will equal the weight, and they will remain at rest ; for W(10) into B F(4) is just equal to P(10) into A F(4) = 40. But if the fulcrum were placed at 2 toward W, then, as the long arm would be three times the length of the short arm, one pound at P would sustain three at W, or ten pounds would sus- tain thirty ; if the long arm be four times the short arm, then the power will sustain four times its weight. On the other hand, if the fulcrum be placed near P, the power must be proportion- ably increased to sustain the weight. Levers are of three kinds. In the first, the fulcrum is between the power and the weight. In the second, the weight is between the fulcrum and the power ; and In the third, the power is be- tween the fulcrum and the weight. 1 . In the first kind of lever, the fulcrum is between the power and the weight. Thus, as in the common crow- Fig. ^9. bar, let A B, Fig. 49, be a lever, and F the fulcrum ; then I **** i The power and weight will be in p A equilibrium when the product ofPll f w multiplied into A F equals the prod- * d! uct of W multiplied into FB, orPxAF = What is the law of equilibrium in the lever 1 Illustrate this law. How many kinds of levers are there 1 How are they distinguished? What is *,he law of equilibrium in a lever of the first kind ? THE LEVER. 83 Prob. 1. If the weight is 200 pounds, the short arm 2 feet, and the long arm 10 feet, what is the power ? To determine this, we have only to apply the rule : Multiply the short arm into the weight, and divide the product by 10, the 2 X 200 long arm, and it will equal the power. =40 Ibs. 2. If the power is 40 pounds, the long arm 10, and the short arm 2, what is the weight ? Multiply 40 by 10, and divide by 2. Ans., 40 x 10-^2=200 Ibs. If the product of the long arm of the lever into the power is greater than that of the short arm into the weight, motion will take place, and the weight will be lifted. But an important circumstance should be noticed here, one which pertains to most machines for raising weights. The power must move as much further than the weight as its distance from the fulcrum is greater, and its velocity must be increased in the same ratio. Thus, if 40 pounds set in motion 200 pounds, it must be placed five times as far from the fulcrum ; and, in order to move it one foot, the power must travel five feet, and, of course, its velocity must be five times as great ; hence what is gained in power is lost in time. One man may lift a weight which requires the strength of five, but then he must pass over five times the space, and, of course, will be five times as long in doing it. PROBLEMS. 1. What would be the length of the long arm of a lever, placed undei the earth, supposing it to weigh 800 trillions of tons, the fulcrum being 4000 miles from the center, and the power being a man weighing 200 pounds ? Ans., 32 quintillioos of miles. 2. How far must he move to raise the earth one foot? Ans., 8 quadrillions of feet. 3. How long would he be in accomplishing the feat, if, in his motion, he followed the law of falling bodies? (See page 66, T= /-.) 4. What would be his velocity the last second of his fall ? Arts., V=2g-T. 2. In the second kind of lever, the weight is between the Is there any advantage gained by the lever ? 84 NATURAL PHILOSOPHY. power and the fulcrum ; thus, A F, F &- 50 - Fig. 50, is the lever, F the fulcrum, W the weight, and P the power. The same rule applies in this case as in the F B preceding. /\ I e 3 4 i The product of the weight into its w distance from the fulcrum is equal to the product of the power into its distance from the fulcrum ; for example, let W = 200, P = 40, FB:=2, and FA = 10; then 200 x 2 = 40 X 10 = 400. Prob. 1. What power would be sufficient to upset a building weighing 20 tons, applied to the end of a lever 100 feet long, the fulcrum being 1 feet from the weight ? Ans., 2 tons. 2. A man, by exerting a force of 250 pounds, uprooted a tree with a lever 30 feet long, the fulcrum being 5 feet from the base of the tree. What resistance did he overcome ? Ans., 1500 Ibs. 3. Two men carried a weight of 200 pounds between them on a lever 8 feet in length ; the weight was placed 3 feet from the end of the lever ; what portion of it did each sustain ? Ans., 75 Ibs. and 125 Ibs. ^^vl*} p ' 3. In a lever of the third kind, the Fig. 5L power is between the weight and ful- crum ; thus, B F, Fig. 51, is the lever, F the fulcrum, P the power, and W the weight. The same rule may be ap- plied here : PxAP = WxFB. But it will be observed, in this case, that the power must be greater than the weight, and there is said to be a mechanical dis- advantage ; and yet what is lost in power is gained in time. For example, if A F is but half of F B, the power must be double that of the weight ; but when motion takes place, the power moves but one foot to raise the weight two feet. In the limbs of animals we have examples of levers ; they are Describe the third kind of lever. What relation does the power bear to the weight ? COMPOUND LEVER. 85 mostly of the third kind, and the loss in power has a full com- pensation in the greater extent and freedom of motion. Prdb. A man sustained on the ends of his fingers, in a hori- zontal position, a weight of 200 pounds ; on the supposition that his arm, from the elbow, was 1 8 inches in length, and the power applied 2 inches from the fulcrum, how much force did he exert ? Ans., 1800 Ibs. 4. Weight of the Lever. In determining the laws of equilib- rium in all the above cases, the weight of the lever has not been taken into the calculation ; but in practice, this weight must be considered. (1.) In a lever of the first kind, if the prop is in the middle, the lever will be sustained on its center of gravity, and no allow- ance is required ; but in any other position, the weight of the lever must be determined. As the whole weight of a lever is at its center of gravity, the part for which allowance must be made will be equal to its iveight multiplied into the distance of its center of gravity from the fulcrum. If we represent the weight of the lever by w, then, in a lever of the Fig. 53. first kind, Fig. 52, c being its center of gravity, A W F B ^ e distance of this point from F is equal to half I - -J - TT - 1 of AB BF ; hence half of w, multiplied into <* JH AB BF, must be added as a portion of the JL power, and then the formula for the equilibrium Op -WO will bePxAF + jw (AB BF)=WxBF. (2.) In the second kind of lever, the fulcrum being at the end, the dis- tance of the center of gravity will be half of A B. Hence the lever be- comes a portion of the weight, and we shall have the expression P xAB = (3.) In the third kind of lever, the weight of the lever is a portion of the weight to be raised, and we have the same formula as in the lever of the second kind. 5. Compound Lever. The compound lever consists of sev- eral simple levers united together. a be, Fig. 53, represents three levers, so arranged that the long arms are all on the side of the fulcrum with the power, and the short arms on the side with the weight ; hence What effect has the weight of the lever in modifying the laws of equilib- rium ? What is the rule for determining the allowance to be made for the weight of the lever ? Describe the compound lever. 86 NATURAL PHILOSOPHY. Fig. 53. 24 CF 1 2 3 4 5 \6 7i f 8Q* m a .dl ! L i t (7 A~ 16 6 J 32 /\ ^X 1 T%e power and weight will be in equilibrium when the prod- uct of all the long arms into the power equals that of all the short arms into the weight. By means of this apparatus the laws of equilibrium may be proved experimentally. Thus, Exp. Suspend a 32 ounce weight, W, from the end of a; the long arm of a is twice the short arm ; 16 ounces at d will just sustain the weight The long arm of the lever b is also double its short arm, and hence 8 ounces at f will sustain the 16 ounces at d. The long arm of c is also twice that of the short arm, and hence 4 ounces at P will sustain 8 ounces atf. To sustain 32 ounces at W, then, will require a force of only 4 ounces at P. If the rule is applied in this case, it will be found that 2X2X2X32 = 4x 4X4X4 256. 6. Weighing Machine. Large machines for weighing coal, hay, and other heavy articles, are constructed on the principle of the compound lever. Thus, let A B, Fig. 54, be a platform, resting on H I, on to Fig. 54. which the load may be drawn. The platform, when used, presses On what principle does it act ? On what principle are weighing chines constructed ? Describe the cut. * LEVERS BALANCE. 87 on two levers of the second kind, C P 77 , having their fulcrums at C C', at the points W W. DP 7 is also a lever of the second kind, receiving the weight at W. To this lever there is attached a wire, P 7 W, connected with a lever of the first kind, which acts on the principle of the steel-yard, W 7 P. It is easy to estimate the power of this machine ; for, suppose the long arms of the two levers, C P' 7 , are each five times their short arms, then only two tenths of the load will press at P 77 upon W. If the long arm of the lever D P 7 is also five times the short arm, then a force equal to }th of /^ths, or -^jth at P' or W 7 , will sustain the load. If, finally, the long arm of the lever W 7 P is five times its short arm, then the force at ? S need be but ,-^3-th of the weight. Prob. 1. On the above supposition, if the load weigh 5 tons, what power will balance it at S ? Ans., 80 Ibs. 2. If a 25 pound weight is applied at S, what is the weight of the load ? Ans., 3125 Ibs. 7. Illustrations of different Levers. (1.) The common steel- yard is a lever of the first kind, in which one arm is much longer than the other. The power is applied to the long arm, and is made to counterbalance different weights attached to the short arm, by moving it to a greater or less distance from the fulcrum. Handspikes, crowbars, &c., are levers of the first kind. (2.) Balance. The common balance is also a lever of the first F . K kind, in which the two arms are ex- actly equal, Fig. 55. The fulcrum is placed at a very small distance below the center of gravity, and weights are applied in one scale, and the substance weighed in the other. The longer the beam of the balance, the more sensitive it becomes. In delicate balances, the fulcrum is made of hardened steel, or agate, in the form of a thin edge, so as to avoid friction, and prevent it from wearing as the beam turns. The beam should be as light as possible, and all the parts con- nected with it should be made in the most accurate manner. Describe the common balance. On what principle does it act ? 88 NATURAL PHILOSOPHY. Balances are now constructed so accurately as to weigh of a grain. (3.) The Bent-lever Balance, Fig. 56, Fig. 56. differs from the preceding in the fact that the weight is counterbalanced by a loaded index, C, which moves over a graduated arc, G F. In this scale an equilibrium will be produced when B K is to B D as C to E, or when the 'product of the short arm, B K, multiplied into the iveight, equals the product of the long arm, B D, multiplied into the poiver. If weights are placed in the ^cale E, the index will move toward G until the equilibrium is restored, and the number on the graduated arc will indicate the number of pounds which have been added. (4.) The Crane is a lever of the second kind, and is much used in unloading vessels, where heavy merchandise is to be moved a short distance. Shears are double levers ; so are the jaws of animals. The bones of animals are striking illustrations of levers of the third kind. The joints are the fulcrums, the muscles the powers, and the limbs or weights held upon the ends of the bones are the weights. In this case the mechanical disadvantage has a full compensation, for it is only necessary for the muscle to con- tract slightly in order to move the limb through a large space ; and this is what is especially needed by man in order to give him quickness of motion. By the aid of his superior intelligence, he is enabled to employ the various agents of nature to supply him with physical power. II. Wheel and Axle. 1. The wheel and axle is a combina- tion of a series of levers of the first kind. The radii of the wheel are the long arms, and the radii of the axle the short arms, while the axis is the fulcrum. If, therefore, we can ascertain the diameter of the wheel and Describe the bent-lever balance. Describe the crane. What kind of levers are the limbs of animals ? What advantage have they ? Describe tne wheel and axle. WHEEL AND AXLE. 89 of the axle, the law of equilibrium is easily determined : it is the same as that of the lever. Fig. 57. Thus, let a t>, Fig. 57, be a wheel and axle, or a series of them ; let the ra- dius of the axle be one inch, and the radii of the wheels two, three, and four inches . E ach of the small- er wheels may be used as an axle in reference to the larger one. By the law of inverse proportion, the power is to the weight as the radius of the axle to the radius of the wheel, or The power and weight will be in equilibrium when the power multiplied into the radius of the wheel equals the weight midti- plied into the radius of the axle. This rule may be proved experimentally thus : Exp. Suspend 24 ounces, W, from the axle b. As the wheel c has twice the radius of b, it will require but 12 ounces to balance the weight. The wheel d is three times b, and hence 8 ounces will sustain the weight ; a is four times b, and hence 6 ounces at a will keep the 24 ounces at b exactly balanced. Prob. 1. A weight of 72 pounds was suspended on the axle at b. What power will balance it on the large wheel a ? what one? 2. One hundred pounds applied to the wheel a will sustain how many pounds at b ? how many at c and d ? 3. If 100 pounds applied to a keep in equilibrium 2000 pounds at b, what is the relation of the wheel to the axle ? Fig, 58. 2. The Capstan, Fig. 58, acts on the same prin- ciple as the wheel and axle. Instead of the wheel, levers are used to turn the axle. If it is placed in a horizontal position, it is called a Windlass. In practical mechanics, something must be allowed for friction and for the rigidity of the cordage. A slight force must also be What is the law of equilibrium ? Describe the capstan windlass. Why must a slight force be added to the power in using the wheel and axle ? 90 NATURAL PHILOSOPHY. added to the power to cause motion \o take place, and the mo- tion will be rapid or slow according to the intensity of this addi- tional force. 3. The wheel and axle is a very useful machine, and, as the power depends upon the relation of the radius of the wheel to that of the axle, if the latter is diminished and the former in- creased, the greater, in both cases, will the power become. But there is a limit to this increase of power ; the axle can not be diminished beyond a certain size without breaking, nor can the wheel be enlarged to a very great extent without becoming un- wieldy. To obviate this and to secure the requisite power, the axle is made of unequal size. Thus, in Fig, 59, the rope is coiled around the smaller part of the axle, b, and, passing around a pulley, is coiled also around the larger diameter a. When the wheel is turned, the rope un- winds at b, and winds up at a. The weight W is sustained, one half by the rope d and the other by c; but as the rope d is on the same side of the fulcrum with the power P, the length of the short arm of the lever is equal to the difference between the ra- dii of the axle at a, and b. This difference may be made very small. Hence almost unlimited power, coupled with great strength of axle, may be given to the .machine. In this case a very heavy weight may be raised, but its ve- locity, compared with that of the power, is very small, so that what is gained in power is lost in time. It is on this principle that a power which is variable may be made to exert a constant force. This is exemplified in the shape given to the fusee of a watch, Fig. 60. The force of the main spring, as it uncoils, diminishes ; but by passing the chain around the smaller axle, B What limit is there to the power of the wheel and axle? By what What shape is given to the fusee of a watch, and for what reason ? WHEEL-WORK. 91 when the force is most intense, arid increasing the size of the axle as it diminishes, a uniform motion is given to the hands and all the other parts of the watch. 4. Communication of Motion by Wheel-work. By the action of two or more wheels upon each other, a very rapid or a very slow movement may be given to machinery. If two wheels of equal size touch each other by their circumferences, the motion of the one, if there is considerable friction, will cause the motion of the other ; or, if a band is made to pass around two wheels, motion may be communicated from one to the other, and their relative velocities will depend upon their size. The smaller wheel will move as much faster as its diameter is less. But the most common mode of communicating motion from one wheel to another is by means of teeth cut into the circum- ference of one wheel, and corresponding notches, called leaves, into the axle of the other. This arrangement is called Fig. 6i. The Wheel and Pinion, Fig. 6 1 . The number of teeth in the wheel and of leaves in the axle will be in proportion to their circumferences or to their radii, and hence The product of the power into the num- ber of teeth in the wheel will be equal to the product of the weight into the number of leaves in the axle. The velocity of each wheel and of its pinion will be inversely as the number of teeth ; that is, the greater the number of teeth, the less the velocity, and the reverse. By means of several wheels of different diameters, motion may be increased or dimin- ished to an indefinite extent. In the pendulum of the common clock it is necessary to add a slight force to overcome the resistance of the air and the friction at the point of suspension. For this piirpose, a weight, W, is applied to an axle connected with a wheel with teeth, and its motion is modified by the pal- lets, a b, Fig. 62, of the pendulum. When the pendulum vi- How can motion be communicated from one wheel to another? De- scribe the wheel and pinion. What is the law of equilibrium ? 92 NATURAL PHILOSOPHY. brates to the right, the pallet a strikes against a tooth, and, as it swings to the left, the pallet b also presses against a tooth ; but, in performing a double vibration, one tooth passes the pallet, - receiving a^ slight force from it sufficient to con- tinue the vibrations. In order to communicate a slow motion to the weight, several wheels with cogs are placed between it and the wheel containing the teeth ; by this means the weight will not run down for a day, a week, and, in some cases, for a year. The motions of the hour and minute hands are also regulated by wheels. Watches and chronometers are regulated by wheels connected with springs instead of weights. 5. Wheel Carriages. The advantages of wheel carriages over drags are twofold : the friction is less, and the power of the lever is used to overcome obstacles. (1.) It is evident that pressure perpendicularly downward on an even surface will not prevent motion in a horizontal direction if there is no friction, but there is friction in proportion to the weight and surface. Now the friction in a wheel is not on the ground, but at the axle, where it is much less, and, to overcome it, the spokes act as levers. (2.) When any obstacle presents itself, as a block of wood, the load must be lifted over it ; the block becomes a fulcrum ; the power is applied at the axle, on which the load rests, and the spokes act on the principle of the bent lever. The advantage, therefore, gained over all other modes of surmounting obstacles is due to the diminution of friction, and the difference between the diameter of the wheel and that of the axle. Hence high wheels overcome obstacles more easily than those that are low ; but they may be too high for easy draught ; for, besides the in- creased danger of upsetting, the line of draught should always ascend from the axle, so as to be at right angles to the collar of the animal. How are the motions of clock-work rendered uniform? What are the advantages of wheel carriages over drags ? To what are these advantages due? THE PULLEY. 93 Springs facilitate the motion of wheel carriages, because they prevent the inertia of the load from acting suddenly upon the power. When the wheel strikes any obstacle, the shock is felt gradually. The center of gravity, at the same time, is lowered by the elasticity of the spring, the load is not raised so high, and hence less force is required to move it. III. Pulley. The pulley is a wheel with a groove in its cir- cumference, freely movable about either a fixed or movable pivot ; hence the pulley is either fixed or movable : the latter is termed a runner. The principle on which the pulley acts is the same as that of the lever, but the mode of estimating its power is different. Fig. 66. Fig. 65. Fig. 64. Fig. 63. 1. Thus, in a single fixed pulley, Fig. 63, the weight and pow- er must be equal, because the arms of the lever, a b, are equal. There is, therefore, no advantage in such a pulley. Its use is, in connection with the rope, to change the direction of motion. 2. But if one pulley, Fig. 64, is fixed and the other movable, then it is evident that the weight will be divided between the two strings, and in this arrangement the power and weight will be in equilibrium, when the poiver multiplied into the number of strings is equal to the weight ; or, if a number of fixed and mov- How do springs facilitate the motion of wheel carnages ? Describe the pulley. What is the advantage of one fixed pulley ? What is the law when a number of fixed and movable pulleys are combined ? 94 NATURAL PHILOSOPHY. able pulleys are arranged in a block, as in Fig. 65, the poiver will equal the weight divided by twice tlie number of movable pulleys. 3. When each, movable pulley has a string of its own, Fig, 66, a different rule must be found. Thus the string e sustains half the weight, i also half, f one quarter, g one eighth. Each movable pulley divides the weight, or the power is to the weight in the first pulley as 1 to 2, in the second as 1 to 2, and in the third as 1 to 2. Therefore the power is to the weight as 1 to 2x2x2 8, or as 1 to 8. It will be seen that 2 is raised to a power represented by the number of movable pulleys, in this case the third power of 2. If there are four movable pulleys, 2 must be raised to the fourth power. Hence, in this system of pulleys, there will be an equi- librium of the power and weight When the weight equals the product of 2, raised to a power represented by the number of movable pulleys, multiplied into the power. Prob. 1. A weight of ten tons was sustained by a system of four movable pulleys. What was the power ? Ans., 1250 Ibs. 2. What weight could a man weighing 200 Ibs. raise by means of a system of five movable pulleys ? Ans., 6400 Ibs. 4. In all the above cases the strings are F - 67 parallel to each other, but, in case their action is oblique, then the force which sus- " tains the weight must be resolved into two others. Thus, let the strings A/, B/act obliquely on the weight around the pulley, e, Fig. 67. Let e f represent the force acting in the direction eB. This force may be resolved into c e and cf. cf will represent the force which the string B e sustains, equal to half the weight; hence %cf will represent the force which sustains the whole weight. We then have the pro- portion P : W : : ef : %cf; or, as radius to twice the cosine of the angle cfe, or twice I*\~W the cosine of the angle made by the lines which represent the direction of the power and the weight. 5. Uses of the Pulley. The pulley is one of the most useful of the mechanical powers. In loading and unloading ships, rais- What is the law \vhen each movable pulley has a string of its own ? THE INCLINED PLANE. ing weights, moving of buildings, and, g resistance is to be overcome, the pulley is either in connection with the other mechanical powers. It has a great advantage over the lever, by furnishing a ready means of changing the direction of motion. But its mechanical advantage is the same as that of all machines : what is gained in power is lost in time. If one man, by means of a system of pulleys, can raise a weight through a given space which would require ten to lift, it will take him ten times as long to do it ; in other words, the power must move as much faster than the weight as its quantity of matter is less. In the use of the pulley, as in that of the wheel and axle, allowance must be made for the ri- gidity of the cordage, and for the diameter of the rope, half of which must be added to the radius of the wheel, and also to the radius of the axle ; and, in order to produce motion of the weight, a slight force must be added to the power. SECTION II. OF THE INCLINED PLANE, THE SCREW, AND THE WEDGE. I. In the inclined plane, the power may act parallel to the plane, or parallel to the base of the plane, or at any angle with the weight. 1 . In the first case, the power multiplied into the length of the plane equals the weight multiplied into its height. 2. In the second case, the power is equal to the weight multi- plied into the height of the plane, and divided by the length of the base. II. The screw acts on the same principle with the inclined plane, and there will be an equilibrium of the power and the weight when the poiver, multiplied into the circumference of the base, is equal to the weight midtiplied into the distance between two contiguous threads. III. The wedge is two inclined planes combined, and the pow- er multiplied into the length of the wedge will equal the weight multiplied into one half the height of the back. In practical mechanics, a slight force must be added in all the above cases to the power, to overcome friction and to give mo- tion to the weight. 96 NATURAL PHILOSOPHY. Fig. 68. I. Inclined Plane. In the inclined plane the power and the weight are in equilibrium, or balance each other, on the general principle which applies to all machines. Notwithstanding the plane may be at any angle from to 90, and the power ma$r act at any angle or parallel to the plane, the problem of the equi- librium of the power and weight admits of a general solution. But it is more practical to obtain a rule for each of the modes in which the power acts upon the weight ; for the power may act parallel to the plane, or parallel to the base of the plane, or at any angle with the weight. 1 . When the poiver acts parallel to the plane, it is easy to as- certain the conditions of equilibrium. Let ABC, Fig. 68, be an inclined plane, so constructed that A C may be raised to any an- gle that maybe required, W the weight, and P the power, acting by means of a pulley parallel to the plane. Let e h, per- pendicular to the base A B, represent the direc- tion and force of gravity which causes the body to descend. This force may be resolved into two others : e i, acting perpendicular- ly to the plane A C, and h i, acting parallel to it. h i will equal the force which impels the load down the plane, e i the pressure upon the plane represented by p, and e h the weight W. (1) Now the triangles e h i and ABC are similar, and we have the proportions hi : eh : : CB : AC, or P : W : : CB : AC. That is, The power is to the weight as the height of the plane to its length. If, therefore, the length be twenty feet and the height ten, the power will be one half of the weight. (2) From the same triangles we have the proportion hi : ei : : BC : AB, or P \p : : BC : AB. Hence the power is to the press- ure as the height of the plane to its base. By multiplying the extremes and means in the above proportions, we de- rive the following formulae : What are the laws of equilibrium when the power acts parallel to the plane ? THE INCLINED PLANE. 97 P xlength=W X height. P X base=p X height. It will be seen that if any three parts are known, the other may be found. Thus, if the height, length of the plane, and the weight are given, the pow- i A - A t t> WXheight er can be easily determined ; tor r = - = . length If the height, length, and power are known, the weight may be found: height (3) If we represent the angle B A C by x, we may derive a general expres- sion for every angle which the plane makes with the base ; for hi : BO : : eh : AC, or P : sin. a? : : W : R or 1, P X R=sin. of xX W ; that is, The force which urges the weight down the plane is equal to the weight into the sine of the angle of elevation. We have also the proportion ei : eh : : AB : AC, or p : W : : cos. x : R or 1 ; .-. >xR or l=cos. ,#xW. That is, The pressure of the weight on the plane equals the weight multiplied into the cosine of the angle of elevation. By using the little carriage represented in the figure, and placing weights in it, these laws may be illustrated by experiment. Exp. Place a weight in the little carnage, which, with the carriage, weighs fifty ounces, and elevate the plane to an angle of 30 ; then the sine of this angle will be equal to half of radius, or half A C, and hence hibeh. That is, the force which urges the carriage down the plane is equal to half of the weight, and therefore the power required to balance fifty ounces is only twenty -five ounces. For any other angle the computations are easily made, though these computations require some knowledge of trigonometry. (4) When the power acts at any angle with the weight, we have only to sub- stitute the sine of this angle for radius in the above proportions to determ- ine the relation of the power and weight, and then we shall have an equi- librium When the power is to the weight as the sine of the angle of elevation to the sine of the angle made by the direction of the power with a perpendicular to the plane at the point where the weight rests. If we represent this last angle by y, then P : W : : sin. x : sin. y ; .: W X sin. x=P X sin. y, W E>XS1 "' y , and P=r . - - , and the pressure on the plane will equal = XCQS. x sin. y sin. y PROBLEMS. 1. A train of loaded cars, weighing 300 tons, were drawn up an inclined plane whose angle of elevation was 40 ; what was the power exerted by the engine ? Ans., 192-803-J- tons 2. To what was the pressure of the cars in the above example equal? Ans., 229-9-}- tons. 3. In raising a vessel on an inclined plane at an angle of 3, it was nec- essary to exert a power of 2QOO Ibs. How much did the vessel weigh ? Ans., 38210-f-lbs. What was its pressure on the plane ? Ans., 38160+ Ibs. How much power would have been required if the vessel had been rais- ed by a block of five movable pulleys? Ans.. 62 A Ibs, E - NATURAL PHILOSOPHY. 4. On a plane inclined at an angle of 10, two men exerted a force of 300 Ibs. by means of a rope passed over a fixed pulley, the rope making an angle with the plane of 8. What was the value of the weight ? Ana. 17 01+ Ibs. 5. What was the pressure of the weight on the plane in the above ex- ample ? 2. When the power acts parallel to the base of the plane. When the power is applied in a direction parallel to the base of the plane, the relation of the power to the weight may be de- termined in the same manner with the preceding ; for, producing e i to g, and drawing h g perpendicular to B c. Fig. 69, we shall have the sim- ilar triangles ABC and e h g. h g will equal the power and e h the weight. We shall then have the proportion hg : eh : : BC : AB ; or, The power is to the A weight as the height of the plane to its base. From the same triangles we shall also have the proportion kg: eg:: BC : AC ; or, as eg is equal to the pressure on the plane, The power is to the pressure as the height of the plane to its length. Finally, eh : eg \ : AB : AC ; or, as eh is equal to the weight, The weight is to the pressure as the base of the plane to its length. From these proportions, by multiplying the extremes and means, we derive the following formulae : P X base = W X height. P X length pressure X height. W X length = pressure X base. The mathematical deductions which are derived from the inclined plane are easily illustrated by experiment. It may also be proved that the power to sustain a given weight is least when What are the laws of equilibrium when the power acts parallel to the base of the plane ? PROBLEMS. 99 its action is parallel to the plane, and greatest when the line of force is parallel to the base of the plane. PROBLEMS. 1. If an inclined plane is 50 feet long and 10 feet high, what power acting parallel to the plane will balance a weight of 20 tons ? Am. 4 tons. 2. What would the pressure be equal to in the above example ? 3. A train of baggage cars, passing down on an inclined plane 300 feet long and 30 feet high, was held back by an engine which exerted a force of 10 tons ; what was the weight of the train ? Ans. 100 tons. 4. If the length of a plane is 500 feet, the weight of a train of cars 400 tons, and the force 10 tons, what is the height of the plane ? Ans. 121 feet. 5. If the height of a plane is 20 feet, the weight 500 tons, and the power 20 tons, what is the length of the plane ? Ans. 500 feet. 6. If the pressure on a plane is 200 tons, the height 40 feet, and tfye power 5 tons, what is the length of the base ? Ans. 1600 feet. 7. An inclined plane is 10 feet long and 6 feet high ; what power acting parallel to the base would sustain 30 tons ? Ans. 22 tons. 8. What would the pressure in the above example be equal to ? Ans. 37^ tons. 9. In an inclined plane 25 feet long and 7 feet high, what weight would a force of 200 Ibs. sustain acting parallel to the Ans. 685f Ibs. 3. Uses of the Inclined Plane. The inclined plane is much used in the arts. Roads leading up the sides of hills are inclined planes, and the force necessary to draw heavy wagons up these planes must be sufficient not only to overcome the friction, but to sustain that portion of the force of gravity which acts parallel to Mention the uses of the inclined plane. 100 NATURAL PHILOSOPHY. the plane, and which, of course, increases with the steepness of the ascent. Where the hill is very steep, the road is made to wind around it, by which its steepness is greatly diminished. It is supposed that the ancient Pyramids of Egypt were built by means of inclined planes, up which those ponderous masses of rock were raised to their present position. Railways consist of a series of inclined planes, generally vary- ing but little from a horizontal plane, but in some cases so in- clined as to require stationary engines to draw up and let down trains of cars. By means of steam power, hundreds of tons are transported by a single engine. The speed, also, has been great- ly increased, amounting to 20, 30, and, in some cases, 60 miles an hour. 4. Motion down Inclined Planes. Having investigated the laws of the equilibrium of the power and weight on inclined planes, let us now ascertain the laws which govern the motions of bodies descending planes of different elevations. Let ABC, Fig. 70, be an inclin- ed plane, and a weight, W, just bal- anced by the power, P. We have found, p. 96, that P : W : : CB : AC. Now the force with which the weight W tends to fall down A C will be to its weight as CB : to AC ; hence The force which urges any body down an inclined plane is to the force of gravity as the height of the plane to its length. Let H = the height and L = the length of the plane, F = the force which urges the body down the plane, and 1 = to gravity ; TT then F : 1 : : H : L, or F = . Hence we may always ascer- L tain the force which urges a body down an inclined plane, what- ever the inclination may be, by dividing the height of the plane by its length (gravity being 1). As the velocity of any body depends upon the intensity of the forces acting upon it, and the time they have acted, What law governs the motion of bodies down inclined planes ? What does the velocity of a body depend upon? THE INCLINED PLANE. 101 The velocity generated by a body falling down an inclined plane, as A C, is equal to that acquired by falling freely through the height of the plane C B ; for the times are found to be as the length to the height, and the forces are also as the length to the height, and hence the velocities must be equal. It may also be shown that the spaces described by bodies fall- ing down inclined planes vary as the squares of the times the same law which applies to bodies falling freely by the force of TT gravity that is, S = -f gT 2 ; but HLg are known, and hence Ju S varies as T 2 , page 66. Hence the spaces described in equal successive portions of time are as the numbers 1, 3, 5, 7, 9, &c. It is found, also, that the time varies as the length of the plane, and inversely as the square root of its height, and that the velocity varies as the square root of its height. The motion of bodies down several planes differently inclined depends upon similar laws. Thus, let Ae^C, Fig. 71, be a series of inclined planes : it is evident, from what has been previously stated, that the velocity acquired by falling down C d, d e, e A, would be a equal to that acquired by fall- " ing through the several heights of those planes, Cf,fg, gift, B or the velocity in falling from C to A would equal that acquired in falling from C to B. If, now, the number of planes be indefinitely increased, they will form a curve, A C, Fig. 72, and hence The velocity acquired by any body in falling through a curve is equal to that acquired in fall- ing through the perpendicular height of the curve. From this point we may examine the proper- ties and uses of 5. The Pendulum. The pendulum is a heavy ball, suspended by a flexible thread from a point Fig.TL Fig. 72. What velocity does a body acquire in falling down an inclined plane? What law is observed by bodies falling down different systems of inclined ' Describe the pendulum. 102 NATURAL PHILOSOPHY. about which it has a free motion, as A B, Fig. 73. If B be raised to D, and allowed to fall, the force of gravity will cause it to descend through the arc DEC, acquir- ing at the point C a velocity which will carry it to G, equal to the height from which 'it fell. This motion through the arc D C G is called a vibration or oscil- lation. From G the pendulum will de- scend again through the arc to D, and thus it would continue to vibrate forever were there no friction at A, and no resistance of the air ; but, in consequence of these obstacles, the lengths of its oscillations grow less and less, until it is brought to a state of rest at C. To keep up the vibrations in our common clocks, a slight force is applied by means of a wheel, which acts upon the pallets of the pendulum (page 92). Center of Oscillation. If we suppose the rod A C to be destitute of weight and a single atom to be suspended from its point, it would constitute a simple pendulum; but the rod consists of a series of such atoms, and hence the pendulum A C is compound. The parts near A tend to vibrate more rapidly than those near C, and hence tend to increase their motion, while the parts near C tend to diminish the motion of the parts near A. There must be some point between A and C which vibrates exactly as fast as a simple pendulum whose length is equal to its distance from A, and this point is called the center of oscillation. This point describes the arc G C D. It is a difficult problem practically to determine this point. In most pend- ulums the center of oscillation lies a little below the center of gravity. In the pendulum the laws of oscillation are generally derived from the properties of the cycloid. This is a curve described by a fixed point, as P, Fig. 74, in the cir- cumference of a circle as it rolls on a plane, as from D to B. It is the jurve of swiftest descent , and the vi- brations of a pendulum, whether longer or shorter, in such an arc are all exactly equal. In a circular arc there is a slight va- riation. It is found by experiment, however, that when the vi- brations are through a small part of the arc of a circle, there is but a slight error, which may easily be corrected, for the arc of the cycloid and the laws of vibration accurately deduced. What and where is the center of oscillation ? Why do the vibrations cease ? How is a cycloid arc produced ? In what arc are the vibrations of a pendulum equal ? Fig. 74. THE PENDULUM. 103 (1.) The duration of the oscillations of a pendulum is not in- fluenced by its iveight or by the nature of its substance. This law is easily proved by experiment ; for if we take several pendu- lums of equal lengths, but of different weight and substance, their vibrations will be exactly equal. This shows that the force of gravity is the same for all kinds of matter. (2.) The oscillations of a pendulum, are all equal in duration, whether they are performed through the less or the greater arc. Thus the vibrations in the arc D G, Fig. 73, will be performed in the same time with those in the arc F E. This law is proved by noticing a great number of vibrations, and observing accu- rately the time of each. The 'reason of this law is simply this, that in the longer vibrations the velocity is so much greater than in the* shorter, that they are performed in the same time. (3.) The duration of the vibrations of a pendulum depends upon its length. The longer the pendulum, the slower are its oscillations. This law is also proved by experiment. (4.) The oscillations of two pendulums of unequal lengths are to each other inversely as the square roots of their lengths. That is, if we compare any two pendulums, Fig. 75, one and four, or one and nine feet in length, their oscillations will be inversely as the square roots of their lengths. Thus, while the pendulum which is four feet makes one, that which is one foot will make "two oscillations, and while that which is nine feet makes one, that which is one will make three oscillations. A pendulum, there- fore, which beats seconds, must be four times * ^ as long as one that beats half seconds, arid V' one which beats once in two seconds must be four times as long as one which beats seconds. 6. Uses and Applications of the Pendulum. The p'endulum is used for three most important purposes : 1. As a measure of time. 2. To determine the 'form of *the earth. 3. To fix a stand- ard of weights and measures. Upon what does the duration of the vibrations of a pendulum depend ? What relation do the vibrations of pendulums of different lengths bear to each other ? How much faster will a pendulum one foot in length vibrate than one four feet in length ? than one nine feet in length ? What are the uses of the pendulum? 104 NATURAL PHILOSOPHY. (1.) As a Measure of Time. Galileo made the rirst observa- tions on this subject by noticing that the oscillations of a lamp in a church were nearly equal. He applied this knowledge to the measure of time, but Huygens first made use of clock-work in or- der to render the vibrations constant and to register their number. Pendulums which beat seconds, that is, which occupy y^ o^th part of a mean solar day in one vibration, are 39-11 inches in length, though their length varies a little in going from the equa- tor to the pole. As heat expands the metal out of which they are constructed, thus making it longer, and as cold contracts it, thus making it shorter, there arise slight inaccuracies, which are remedied by means of compensation pendulums, the principal of which are the Mercurial Pendulum and the Gridiron Pendulum* The compensation is effected by combining two or more metals, which are expanded differently by the same degree of heat, in such a manner that their expan- sions shall mutually counteract each other, and keep the center of oscillation at the same distance from the point of suspension. Steel and brass are the metals usually combined. If the ex- pansion for brass be represented by 100, that of steel will be about 6 1 . Then, by making the pendulum rods 100 parts of steel and 61 of brass, and so arranging them that one shall expand up- ward and the other downward, their ex- pansions will exactly compensate for each other. Thus, the steel bars s s, Fig. 76, ex- pand only downward, and the brass, b b, only upward ; and as the expansions up- ward are just equal to the expansions downward, the length of the pendulum remains constant under all the variations of temperature. By this contrivance the pendulum becomes the most accurate measurer of time. * So named because it resembles the gridiron. How long must it be to beat seconds ? What are the causes of inaccu- racy in the pendulum 1 Describe the gridiron pendulum. USES OF THE INCLINED PLANE. 105 (2.) The pendulum is used to determine the figure of the earth, and this is one of its most interesting applications. The length being the same, the frequency of the vibrations at any place on the earth's surface will depend upon the intensity of the force of gravity at that place. As this force is inversely as the square of the distance from the center of the earth, if one portion of the earth's surface is nearer than another portion (conceiving the whole force of attraction to be situated at the center of the earth), the vibrations of the pendulum will be more rapid at that point. Now it is found by observation, that as we go from the equa- tor to the pole, the vibrations are gradually increased in frequen- cy, which shows that the poles are nearer the center of the earth 4han the equator by about 17 miles. By measurement of arcs of the meridian, the difference is a little less, being only 13 miles. (3.) The last and a very important use of the pendulum is to fix a standard of measure and of weight. The only standard which is not liable to vary is derived from the revolutions of the earth. The pendulum which beats seconds, or which measures ^g-i^ths of a mean solar day, is, as we have seen, 39'11 inches in length. The linear yard is a little less, having the ratio of 1 to 1-086158, or 36 inches. When such a measure is accurately made at the temperature of melting ice, it may be used for a long time as a standard ; but, as it may vary, it is easy to verify or correct it by a standard pendulum. There is one kept in Co- lumbia College, New York city, which beats seconds, the .oscil- lations being performed in a cycloidal arc, and also in a vacuum. Having fixed upon the length of the yard, it may be subdivid- ed into feet, inches, &c. From linear measure, square measure, or the measure of surfaces, is directly derived, and also solid measure. But how shall we derive a standard of weights from the length of a yard or the revolution of the earth ? This is done by taking a box containing just one cubic foot, or twelve linear inches in length, breadth, and height, filling it with distilled wa- ter, and counterpoising it by a bar of lead or some other metal. Describe the process by which the shape of the earth is determined. How is the standard of weight and measure determined ? E 2 106 NATURAL PHILOSOPHY. This bar is then divided into 1000 equal parts, and these are called ounces. Sixteen of these make a pound avoirdupois, and from these all other measures and weights are derived. A gallon of dry measure holds 10 Ibs. of distilled water ; a bushel, 80 pounds. A gallon of liquid measure contains 8 Ibs. of distilled water. In all these cases the water is taken at its max- imum density, which is about 40 F. The standards adopted by the United States are as follows : 1 . Of Length. The yard of 3 feet, taken from Troughton's brass scale, which is 82 inches in length. This is the same as the imperial standard. 2. Of Weight. The Troy pound, or 5762-38 grs., is used for a standard at the Mint of the United States. 3. Of Dry Measure. The Winchester bushel, which contains 2150-4 cubic inches. 4. Of Liquid Measure. The English wine gallon, containing 231 cubic inches. All merchandise, however, is bought and sold by avoirdupois weight, a pound being 7680 grs. Iir The Screw. The screw is an inclined plane wound around a cylinder. It generally consists of a spiral groove cut either into the convex or concave surface of a cylinder ; in fact, the action of a screw requires both to be united. That on the concave surface is called the nut. The thread of a screw may be triangular or flat. The law of equilibrium in the screw is the same as that of the inclined plane, where the power acts parallel to the base. Thus, Let the inclined plane, A Fi.rt. B C, Fig. 77, be wound around the cylinder D, which has a base equal in circumfer- ence to the base of the plane A B. The line A C will rep- resent the threads of the screw, and B C the distance between them, 1, 2, 3. Now, by ap- Mentiou the different standards of weight and of measure. Describe the screw. On what principle does it act ? What is the law of equilibrium ? THE SCREW. 107 Fig. is. plying the principle, The power is to the weight as the height of the plane to its base, we shall find that an equilibrium will be produced when 1. The power is to the weight as tlie distance between two con- tiguous threads to the circumference of the base. The screw, when used as a mechanical power, is elevated and depressed by being turned within a concave nut, b, Fig. 78, and for turning it a lever, a, is usually employed, so that the screw combines the advantages of the lever and inclined plane. Hence the power which a screw is capable of exerting will be increased over that of the in- clined plane in the ratio of the length of the lever to the radius of the cylinder. In this case it is found that equilibrium is maintained when 2. The power is to the weight as the distance between two con- tiguous threads to the circumference of a circle made by one rev- olution of the power. PROBLEMS. 1. In pressing a bale of cotton by a screw, the distance of whose threads was 1 inch, a power of 300 Ibs. was applied on the end of a lever 10 feet long ; what was the amount of press- ure exerted ? Ans. 113-0976 tons. 2. What power must be applied in the above example to exert a pressure of 20 tons ? FY^.79. Ans. 53-05+ Ibs. f! .vivSL Jl The screw is generally used for the pur- Upose of compression ; but it matters not how the power is applied, for a force that will lift a weight of ten tons will impart the same amount of pressure. The endless screw, Fig. 79, combined with the wheel and axle, is employed for certain purposes, and is capable of exert- ing great pressure. What two mechanical powers are combined in the screw? For what is the screw employed ? 108 NATURAL PHILOSOPHY. It will be noticed that the power of the screw depends upon the distance between the threads and the length of the lever. If the threads are very near each other, one revolution of the power will raise the weight but a short distance, and hence but little power will be required ; or, if the lever is very long, the power required to turn the screw will be proportionably diminished. Now, by diminishing the distance between the threads, their size will at length become too small to sustain any great resistance, and a very long lever is inconvenient, because the power must travel over too great a space. What we need is compactness and strength connected with great power, and this has been achieved by Hunter's Screw, Fig. 80, which acts on the principle of the wheel and axle, page 89. This screw is composed of two parts, consisting of larger and smaller threads, A B, the one within the other. One turns upward, while the other turns downward with a little greater velocity, so that the whole screw advances in pro- portion to the difference between the larg- er and smaller threads. This difference may be very small, and hence the power may be very great ; but in this, as in all cases where great power is generated with a sfight force, the screw moves very slowly, so that the force must be applied for a long time to exert very great pressure. The Micrometer Screw acts on the above principle, and is much used to measure very small distances, particularly where very accurate measurements are required. In order to understand this, suppose the lever, Fig. 80, moves over a graduated arc three inches in circumference, divided into 100 equal parts, and that the larger screw, A, is one inch in length, with 100 threads; the smaller, B, of the same length, and 101 threads. Now one revolution of the index will advance the screw the difference be- tween T o-th and - TT tn f an mcn > or Too T^T To-^oT f an inch. While the index, therefore, is passing one division T foth Upon what does its power depend, and how is it limited ? Describe the principle of Hunter's screw the micrometer screw, THE WEDGE. 109 of a revolution, the screw will lengthen only T o-th of TO-TO^^ T-OTF-O^O- inches, or one million ten thousandth of an inch ! spaces so small as to require a powerful microscope to distin- guish them. F! g . i. Ill- Wedge. The wedge, Fig. 81, is another form of using the inclined plane, for the purpose of cleaving rocks and wood, for raising vessels, &c. All instruments used for cutting or separating bodies into parts, such as axes, knives, chisels, awls, &c., are wedges. We may estimate the power of the wedge by considering one half of the back as the height of the plane, and the sides its length. If, now, the wedge be driven under a beam, it will raise it, and the power requisite to do this will be to the weight of the beam as the height of the plane, or half the back of the wedge to its length : P : W : : c e : c d; .-. Pxlength=Wx^ back ; or, the power equals the weight multiplied into half of the back and divided by the length. Unlike all the other mechanical powers, the practical use of the wedge depends upon friction. Were the friction destroyed, it could be of no service. This is illustrated in attempting to split a frozen log. The wedge, when driven in by a stroke of the beetle, as there is little friction, is forced out again by the elasticity of the parts which are separated. The wedge is an instrument of great power, and is much used in all the mechanical arts. SECTION III. REGULATION OF, MACHINERY AND MODIFICATION OF MO- TION. FRICTION. I. In order to give uniformity to the 'motion of machinery under the influence of varying forces, certain contrivances are resorted to, in which the' force of inertia is employed to accumu- late power, and to apply it when it is needed. The most im- portant of these are the fly- wheel and the governor. II. To change the direction of motion, certain other contri- vances, are employed, as cog-wheels and joints. Describe the wedge. How does its action differ from other mechanical powers ? 110 NATUilAL PHILOSOPHY. III. In consequence of the rubbing of the parts of machinery there arises a certain amount of friction, to overcome wliich a force must be applied, the intensity of which will depend upon the nature of the surfaces and the degree of p)-essure. I. IN consequence of the inertia of matter, and of the fact that this inertia is overcome by any force gradually, there is in ma- chinery a tendency to uniformity of motion ; hence, If the amount of matter set in motion is very large, as is the case in large mill-stones or a steam vessel, any sudden increase or diminution of force will but slightly affect the rate of motion ; but when machinery is not so ponderous, variations of power will produce variations of motion sudden jerks or impulses, which not only diminish the utility of the machine, but tend to injure or destroy it. In such cases, certain contrivances are re- sorted to for the purpose of rendering the motion uniform, under the influence of varying degrees of force. The most important regulators of machinery are the fly-wheel and the governor. 1 . Fly-wheel. The fly-wheel is simply a heavy wheel of cast iron, attached to the revolving parts of machinery in such a way as to be put in motion, and thereby to accumulate power. If the force is deficient at any one moment, this power will supply it ; if the force is suddenly increased, the fly will oppose its inertia to any sudden impulse, and by these means the motion is rendered uniform. This accumulation of power by means of the fly-wheel is of great importance in the printing press and some other machines where force is required to be applied by successive strokes. For coining metals and for stamping patterns, where great power is required, a different kind of fly is used, or, rather, the fly is made to act upon a screw, so as to force the end of the screw, which is connected with the die t against the object which is to receive the stamp. A great variety of useful and ornamental work, such as fire- What causes operate to produce uniformity of motion ? What contrivan- ces are resorted to to render motion uniform ? Describe the action of the fly-wheel. How is the fly employed in coining and stamping metals ? MODIFICATION OF MOTION. Ill fenders, grates, silver, copper, and bronze ware, are stamped in this way. 2. Governor. The governor is another instrument to regulate motion, especially that connected with steam power. Fig. 82. It consists of two heavy balls, Fig. 82, which are so attached to an axis that, when revolution takes place, they separate more or less, according to their velocity. When the motion becomes too rapid, the balls separate so far as to close a valve which lets the steam into the piston, and this checks the motion. As the motion is slower, the balls fall together, open the valve, and let the steam in again to increase the motion. As the valve is opened and closed gradually, there is a gradual increase or diminution of power, and the motion of the machinery is thereby rendered uniform. II. Modification of Motion. It is often desirable to change the direction of motion from horizontal to vertical, or from circu- lar to reciprocating, and the reverse. For this purpose, cog- wheels and joints are employed, called Gearing. Cog-wheels have been noticed on page 91, where the object was to increase or diminish velocity. They are also used to change the direction of motion, in which case they oc- cupy different positions in reference to each other, or else the di- rection in which the teeth are cut is varied. 1 . If the teeth lie in the same plane with the wheels, it is call- ed spur gearing, in which case the direction of the motion is not changed. 2. If the teeth are cut obliquely to the axis, it is called spiral gearing. 3. If the wheels are situated in different planes, and are shaped like the frustra of cones, Fig. 83, the teeth also being cut obliquely, so as to give different directions to motion, varying according to the angle which the axes of the wheels make .with each other, it is called bevel gearing. Describe the governor. How does it regulate the motion of the steam- engine 1 What are the contrivances for changing the direction of motion 1 Describe the different kinds of gearing. .83. 112 NATURAL PHILOSOPHY. Fig. 84. If the teeth are so cut as to prevent motion in one direction by means of a catch, while it allows it in the opposite direction, it is called a ratchet wheel. If the axis of motion is one side of the center of a wheel, so that the velocity of the circumference varies at different points, it is called an eccentric wheel. Such wheels are used in orreries, to exhibit the varying motions of the planets in their orbits. Reciprocating Motion is generally produced by means of a crank attached to a wheel with a shaft, which rises up and down as the wheel turns. This is exemplified in the saw-mill, steam-engine, and some other rna- chines. The arch head is also used for reciprocating motion. It consists of an arc on the end of a lever, Fig. 84, moving upon a pivot, C. Some- times a chain, P B, is laid upon the arc B D, so that, as the lever w r orks back and forth, a vertical motion is given to a rod attached to P. This is often the arrangement in the lifting- pump. Sometimes teeth are cut in the arc B D, so as to act on rack-ivork. The knee joint is a mechanical power used in the printing-press. It consists of two levers, Fig. 85, united by a joint, a, with the end of one firmly secured, and that of the other con- nected with a movable block. The joint, a, on being forced in, causes the levers to press down upon the block with a force which increases rapidly as they approach a straight line. By this means a very great pressure may be exerted with but slight additions of power. The universal joint, Fig. 86, consists of two semicircular arcs connected by cross pieces, upon which the arcs may turn in every direction. Sometimes a ball is made to turn in a socket, so as to give a free motion. In surveyor's compass- es and some other instruments this kind of joint is employed. How does the ratchet wheel operate ? How is the eccentric wheel con- structed ? How is reciprocating motion produced 1 Describe the arch head. Describe the knee joint the universal joint. Fig. 85. Fig. ROLLING AND SLIDING FRICTION. 113 III. Friction. In treating of the mechanical powers, we have regarded them as destitute of friction, simply alluding to the al- lowance which must be made for it. There is a certain force re- quired to overcome friction produced by the rubbing of the parts upon each other, and upon surfaces in contact with the machine. Friction arises from the elevations of one surface falling into the depressions of another. The following diagram will illus- trate the manner in which such resistance to motion takes place. The body a, Fig. 87, in order to be Fig.&t. dragged across c b, must be lifted over the proj ecting points. All surfaces, how- ever smooth they may appear to be, have elevations and depressions, and to over- come the friction thus produced, a cer- tain force, varying for different surfaces and substances, must be expended. This force can only be determined by experiment. Thus it is found by experiment that it requires 27 '7 Ibs. to overcome the friction of 100 Ibs. of iron, moving on a horizontal layer of iron : hence its coefficient of friction is 0- 27 -7, or 27*7 per cent. The mode of determining the amount of friction is to place a block, as of oak, of a given weight, upon a horizontal surface of oak, and ascertaining the force necessary to move it over the surface. The ratio which this bears to the weight of the block is called the coefficient of friction. It is thus found that the coefficient of iron upon iron is 0-277 " " iron upon brass is 0-263 " " iron upon copper is 0-170 " " oak upon oak is 0-418 " " oak upon pine is 0-667 " pine upon pine is 4-562. MU'LLKR. Where the experiment is tried with wood, the coefficient of friction will be greater when the motion is across the grain than when it is in the same direction with the fiber. How does the friction of machinery arise ? How is the. force of friction determined ? What is the coefficient of friction ? 114 NATURAL PHILOSOPHY. In all these cases the friction is directly proportioned to the weight of the block, and not to the extent of sur/ace. If a block have two square feet on one side and one on the other, it will make no difference which side is applied to the horizontal sur- face, the friction will be the same. This is called sliding friction, and may be diminished by oil- ing the surfaces. Oil is the best for metals, but tallow for wood. Sliding friction occurs at the point where axles revolve in their supports, as in the case of common wheels. The amount is de- termined by experiment, and obviated, in part, by keeping the axles well oiled. Rolling friction is the resistance which a round body meets with in rolhng along a level surface. This kind of friction is much less than sliding friction. The amount may be determined in the same way. In the wheels of carriages, there is sliding friction at the axles and rolling friction at the circumferences, both of which are di- minished as the wheels increase in size. The driving wheels of a locomotive, as they are turned by the force of steam, propel the whole carriage, with twenty or thirty heavy cars in connection, because the rolling friction of all the wheels, together with the sliding friction of all the axles, is less than the sliding friction between the wheel and the rail. When the rolling friction of all the attached cars becomes equal to the sliding friction between the propelling wheels and the iron rail, the propelling wheels will revolve without moving the load. This often takes place when the track is wet, covered with ice, or frozen. We may then notice rapid revolutions of the propelling wheels, especially when the train attempts to start. Hence it appears, that the weight of the locomotive, which increases the sliding friction, is as much concerned in moving heavy loads as the power of its engine. Strength of Materials. It is an important problem in all mechanical structures to determine the strength of the materials To what is friction proportioned? Describe sliding friction. What is rolling friction? What kind of friction in wheel carriages? Why do the propelling wheels of the locomotive sometimes revolve without moving the train? STRENGTH OF MATERIALS. 115 employed, and then so to arrange them as to give to the struc- ture the greatest strength of which the materials are capable. The strength of materials is estimated in different directions. 1. The resistance which a bar or wire of any substance op- poses to a force which tends to part it in the direction of the length, is called the ABSOLUTE strength. This is determined by fastening one end, and applying weights to the other till it is parted or drawn asunder. If several metallic wires of the same diameter are fastened by their ends, and weights applied, iron, in the form of steel, will be found to have the greatest tenacity. A steel bar of one inch square will sustain 135,000 Ibs., a gold bar of the same size will sustain but 22,000 Ibs., while a similar lead bar will part with a weight of only 800 Ibs. The strength of wire is increased by drawing it out, as there is given to the atoms of the surface greater tenacity than to the atoms within the wire, so that if the surface of a wire be removed by a piece of sand paper, its strength will be much diminished ; hence, by twisting many wires to- gether and increasing the surface, the strength of the metal is much greater than when it is in one solid wire. Some of the heaviest bridges are sustained by iron cables made of small wire. The same is true of hemp and silk cords ; the latter possesses twice the strength of the former ; and their tenacity is still fur- ther increased by gluing the threads together. By wetting the cord it is also rendered stronger. 2. The resistance which a body opposes to a force applied di- rectly across it, when one or both ends are supported, is called the LATERAL strength. This is generally much less than the absolute strength. The strength of a beam, supported at the two ends, and weights applied at the center, will depend, 1st, upon its length ; the shorter it is, the greater its power of resistance ; 2d, upon its breadth and depth, the strength being as the breadth multiplied into the square of the depth ; hence a board will be strongest when placed How is the strength of materials estimated ? What is absolute strength, and how is it determined ? Of the metals which is the most tenacious ? What influence has the twisting of the fiber upon the strength? What is the lateral strength of material ? 116 NATURAL PHILOSOPHY. on its edge. If the beam is supported at one end, its strength is but about one fourth as great. 3. The resistance to compression increases with the thickness of the body until it has reached a certain diameter, and then di- minishes. In this case the pressure may be made directly across the body, as is the case with a wedge, or lengthwise, as is illus- trated by pillars that sustain heavy structures. 4. The resistance which a body opposes to being twisted is called the strength of torsion. This power varies very much, arid depends upon elasticity. Some bodies may be twisted to a great extent and return again to their former position, while others are easily broken by twisting them, or become permanent- ly bent. These points are the limits of the force of torsion. In the arrangement of materials to form any structure, as a bridge, the form of the arch gives the greatest strength, because \he weight is more equally distributed through all the materials which compose the structure. In the case of beams they should be much deeper than broad, and if inclined at an angle will bear a greater strain than when laid horizontally. The strength of a beam may be increased by making it of several pieces, one laid upon the other, or side by side, and fastened together. Circular beams may be made stronger with the same weight, and even with a less weight, by making them hollow. In estimating the strength of materials and in their arrange- ment, allowance must be made for their own weight as well as the weight they are intended to sustain. It sometimes happens that a structure will be very strong when a small model only is tried, but when it is applied on a larger scale it will be crushed by its own weight. The structure and size of animals and of plants bear a constant relation to the strength of the material of which they are composed. The bones of birds are hollow. The limbs of animals, from the smaller to the larger, increase in breadth more than in length or height. Practical Utility of the Medianical Powers. In treating of the mechanical powers, we have frequently repeated the fact, that What the resistance to compression ? How is the strength of torsion esti- mated ? What arrangement of material offers the greatest resistance ? ..xILITY OF THE MECHANICAL POWERS. 117 there is no mechanical advantage in their use, on the broad prin- ciple tlwt ivliat is gained in power is lost in time. This is the- oretically, but not always practically true. 1 . For, even when muscular power alone is applied, there is practically a very great advantage in their use. Take, for ex- ample, the pulley. In theory, if one man, by means of the pul- ley, is able to raise a block 200 feet which would require the strength of five men to raise it through the same space, it will take him five times as long to do it. But when we come to ap- ply this theory in practice, we often find that one man, by means of the pulley, will actually raise a weight 200 feet which five men without mechanical aid would be unable to raise at all ; for, al- though they may be able to exert five times the force, yet they may not be able to expend that force upon the block in such a way as to raise it to the required position. The same is true in the use of the lever. Where a heavy weight is to be raised a small distance, one man may exert the force of five men, and actually raise the weight in less time than it could be done by the direct muscular effort of the five. The same may be true in the use of all the mechanical pow- ers. It is emphatically true in relation to the screw and wedge, in cases where the strength of numbers can not be applied. We know that a single individual, by means of the wedge, is able to split open rocks and blocks of wood which the strength of 5000 men could not accomplish by the mere exertion of muscular power. It should be observed further, that even if |he force of num- bers could be as readily applied as that of one, there is a special advantage in the use of the lever and pulley, in consequence of the direction in which the force is generally applied; for we make use of the gravity or iveight of the body, in connection with its muscular power, to raise weights in opposition to gravity. 2. But the utility of the mechanical powers is more strikingly illustrated in cases where natural forces, as those of water, air, and steam, are applied to impart motion to machinery. In such Mention the practical uses of the mechanical powers. Upon what do the useful results of water and steam power depend? 118 NATURAL PHILOSOPHY. cases, the doctrine -that "what is gained in power by the mech- anism is lost in time" has no practical application, for it is at once obvious that the running of water, the motion of air, and the expansive force of steam, depend wholly, for any useful result, upon the machinery by which their power is directed and applied. By the application of steam and water to various combina- tions of the mechanical powers, we are enabled to accomplish that which no unaided human effort is able to achieve ; and not only so, But there is in the use of mechanism greater perfection, great- er economy, and saving of time and expense in respect to those products of art in the production of which both muscular and mechanical forces are employed. The whole circle of the me- chanical arts, from the steam-ship to the pin factory, is filled with illustrations of their great utility to civilized man. "Practical Mechanics," says Herschel, "is, in the most pre- eminent sense, a scientific art, and it may be truly asserted that almost all the great combinations of modern mechanism, and many of its refinements and nicer improvements, are creations of pure intellect, grounding its exertion upon a moderate number of very elementary propositions in Theoretical MecJianics and Ge- ometry. On this head we might dwell long, and find ample matter both for reflection and wonder ; but it would require, not volumes merely, but libraries, to enumerate and describe the prodigies of ingenuity which have been lavished on every thing connected with machinery and engineering. By these it is that we are enabled to diffuse over the whole earth the productions of any part of it ; to fill every corner of it with miracles of art and labor in exchange for its peculiar commodities, and to con- centrate around us, in our dwellings, apparel, and utensils, the skill and workmanship, not of a few expert individuals, but of all who in the present and past generations have contributed their improvements to the processes of our manufactures." 3. The utility of the mechanical powers may indeed be viewed from a higher position. They have furnished the human intel- What special advantage in the use of machinery ? From what higher point may we view the mechanical powers ? HYDRODYNAMICS. 119 lect with an opportunity for achieving some of its highest tri- umphs. They have enabled it to penetrate into the mysteries of the universe, and to gain a more enlarged and clearer view of the plans and purposes of the Creator. CHAPTER IV. HYDRODYNAMICS. HYDRODYNAMICS* is that branch of science which treats of the Mechanical Properties of Liquids. It is divided into Hydrostat- ics and Hydraulics. Hydrostatics is a term derived from two Greek words, and means Water-statics. As a branch of Natural Philosophy, it treats of the equilibrium and pressure of liquids. Hydraulics treats of the motion of liquids, and the effects of their motion. Liquids differ from solids in the circumstance that their par- ticles move freely upon each other. They differ from gases and vapors in the fact that it requires much greater force to compress them, and hence they have been called non-elastic fluids, while gases and vapors have been termed elastic fluids. There are slight grounds, however, for this distinction. Li- quids are elastic fluids. According to the experiments of Mr. Perkins, a pressure of 30,000 Ibs. to the square inch causes a mass of water to contract one twelfth of its volume, and the vol- ume is restored when the pressure is removed. SECTION I. HYDROSTATICS. Liquids differ from solids in the fact that their atoms are less under the influence of cohesion, and hence Imve a freer motion * The term hydrodynamics is sometimes used in the same sense as hy- draulics. It jaeans water-dynamics, but may appropriately be used in a more generic sense ; for water at rest, as well as in motion, exerts a con- stant force, which is due to its gravity. What is the meaning of: hydrostatics and of hydraulics 1 Of what do they treat T 120 NATURAL PHILOSOPHY. among themselves, in conseque^e of which the force of gravity draws each atom separately toward the center of the earth; hence I. The pressure of any liquid contained in a vessel is equal in all directions, downward, upward, and laterally. II. The amount of pressure of any liquid contained in a ves- sel is equal to a column whose base is the area of the lottoin, and whose height is equal to the depth of the liquid, whatever be the form or size of the vessel. III. It results from the laws of pressure that liquids will rise to the same height in tubes connected with a common reservoir, whatever their form or capacity; and also that the surface of a liquid at rest is always level. IV. A body immersed in any liquid loses a portion of its weight equal to the weight of the liquid displaced, and hence by weighing bodies in air and then in water, their relative weights or specific gravities may be determined. V. Bodies lighter than liquids will float upon tJieir surfaces, and displace a quantity of liquid equal to their own weight. LIQUIDS as well as solids are under the influence of gravity, but, in consequence of the freedom of motion among their atoms, each atom of a mass is separately attracted toward the center of the earth. T^Q fundamental difference between a liquid and a solid in this respect depends upon the relative force of cohesion and gravity* This distinction may be il- lustrated by the opposite dia- gram : Let a b, Fig. 88, be two atoms of a solid, e d two sim- ilar atoms of any liquid, a e b /the 'direction of the force * Liquids have an attraction for solids, which is manifested in the case of capillary tubes, called capillary attraction (see page 32). There are many phenomena of liquids which are explained by reference to this force. All porous bodies .will absorb water. The wick of a lamp consists of a series of capillary tubes, which draw up the oil to supply the flame. A cloth with one end dipped into a basin of water will empty the vessel, &c. How do liquids differ from solids ? Illustrate the distinction. Fig. 88. B PRESSURE OF LICIUID3. 121 of gravity, a b of cohesion. Now, as the cohesive force in a b is greater than that of gravity, the two atoms will have a common center of gravity at n, and if that point is sustained the two atoms will be ; but as the force of cohesion in the two atoms of the liquid, e d, is less than gravity, if their common center, c, is sus- tained, they will separate and fall. If now a third atom be added to each, , g, the three atoms of the solid will still have a common cen- ter of gravity ; but, on adding the third atom to the liquid, it will press between the other two, force them apart, and the three atoms will arrange themselves at the same distance from the center of the earth, as in e g d, Fig. 89. It will be seen, that while the solid presses downward only, the liquid presses in a lateral direction ; and if there are a series of atoms, those below must sustain those above, and hence an up- ward pressure. From this peculiar property of the atoms of a liquid, each being free to move in all directions, influenced by its own proper gravity in a manner independent of all the rest, we derive the fundamental proposition of hydrostatics : I. The pressure of a liquid contained in any vessel is equal in all directions, downward, upivard, and laterally. 1. Doivnivard Presswe. That liquids have a downward pressure is too evident to need illustration. It results directly from gravity. It is also evident that each stratum, from the top to the bottom of the vessel, must add its own weight to the next below it, until the whole downward pressure rests on the bottom of the vessel. 2. Lateral Pressure of Liquids. Liquids press later ally with the same force that they press downward. Fig. 90. This fact is not so obvious as the preceding, and yet it results directly from it, and from the absence of cohesion among the atoms. Thus, suppose a c, Fig. 90, represent two atoms of any liquid, so plac- ed in a vessel that they shall touch the sides and bottom. If a third atom, b, is placed between them, it will tend to press them asunder, and must cause a lateral force to be exerted upon the sides of the vessel. What is the fundamental proposition in hydrostatics? What evidence of downward pressure ? How is the lateral pressure of liquids proved ? 122 NATURAL PHILOSOPHY. That the lateral pressure is equal to the doivmvard pressure may be proved by experiment. Thus : Exp. If an aperture be opened in the side of a vessel con- taining water, Fig. 91, on a level with the bottom, and one of the same size in the bottom, the two streams will issue with the same velocity, and discharge the same quantity of water during any given time. 3. Upward Pressure. Liquids press upward with the same force that they press downward and laterally. The upward pressure of a liquid is due directly to its down- ward pressure, on the principle that action and reaction are equal, and in opposite directions. If one stratum of a mass, 1 {Fig. 91), press downward with a force of one pound upon a second stratum, 2, then this second stratum must press upward with an equal force, or it could not sustain it. The same must be true of each stratum, 3,4, &c., to the bottom of the vessel. This may be shown more clearly by the following . Exp. Take a piece of glass, a, Fig. 9U, with a string, d, at- tached to its center, and place it over the end of a glass tube, b, open at both ends. Immerse the tube in a vessel of water, an not the ocean be sounded to its bottom ? Describe the hydrostatic ellows f HYDROSTATIC PARADOX. 125 pressure will be increased, the height remaining the same. If, therefore, the surface of the bottom be made very large and the tube very high, the pressure will be increased in a compound ra- tio. This is called the Hydrostatic paradox, because a very small quantity of liquid may be so applied as to raise a very large weight. A single pound of water may be made to exert a pressure of 10, 50, or a 1000 Ibs. This force is limited only by that of capillary attraction. The precise manner in which this is effected may be illustrated by the following diagram : Let the box a b, Fig. 96, be three feet square and one foot high. It will contain nine cubic feet. Let the tube 1 2 3 be one foot square and three feet high. If the box is filled with water, it will press upon its bottom with a force of 62^ Ibs. upon each square foot. Pour into the tube 62 Ibs. of water, and it will fill the tube to 1, which will double the pressure upon the base of the column im- mediately below the tube ; but the lateral pressure upon d, and the upward pressure upon a, must each be equal to the down- ward pressure, and the same must be true at e and b, and upon every square foot of the inner surface of the box. Hence the weight of 62^ Ibs. of water will increase the pressure nine times 62^ Ibs. upon the bottom, nine times 62| Ibs. upon the top, and twelve times 621 Ibs. upon the four sides ; or the whole pressure upon the inner surfaces of the box will be 1875 Ibs. If the tube be filled, or twice 62 Ibs. of water be added, the pressure will be twice as great. If now the tube be but one half the capac- ity, then it will require but half as much water to fill it, and yet it will exert the same pressure. The tube might be dimin- ished in size until the force of capillary attraction (see p. 32) be- gan to overcome the pressure, and three feet of height would ex- ert the same force upon the interior of the box. There is a limit, therefore, to the increase of pressure ; for the tube may become so small that, whatever its height, the liquid will be wholly sus- tained by the capillary force. It should be noticed here that a pound of water in a tube of What is the principle of the hydrostatic paradox? Describe the mauuer in which increase of pressure takes place. 126 NATURAL PHILOSOPHY. Fig. 97. one square inch will fill the tube as much higher than it will the box as its surface is less, and hence the law of the equilibrium is the same as in the mechanical powers, what is gained in pmcer is lost in time or space. A cubic foot of water, if put into a tube the section of which is one square inch, will fill it to the height of 1728 inches. If such a tube were inserted in a box contain- ing one cubic foot filled with water, it would exert 62^ Ibs. upon every square inch of its surface, or 144 times 62|- Ibs. upon each of the six surfaces of the cube. It is evident that a piston may be fitted to the tube, and a pressure exerted by mechanical power instead of a column of water. On this principle The Hydrostatic Press is con- structed. It consists of a large and a small cylinder, a, b, connected by a tube, Fig. 97, with a piston, c, to press upon the water in a, and a larger piston, e, capable of sliding up in the cylinder b, to which a rod is attached connected with a sliding block, which is forced against the object to be pressed, d. is a fixed frame. The spaces below the pis- tons a and e contain water. By means of the lever, a pressure of a few pounds on the water in a will communicate a very great force to the piston e, the degree of force depending upon the rel- ative number of square inches in a section of each cylinder. The larger b is in proportion to a, the greater will be the power of the press. It is obvious that there is no limit to the force which such a press may be made to exert but that which arises from the strength of the material of which it is constructed. This press may be used for pressing paper, books, cotton, hay, and many other substances where great force is required. By means of a lever applied to the cylinder, the weight of one man is sufficient to tear up the largest tree by its roots ; in fact, to exert a pressure of more than two millions of pounds. Compressibility/ of Water. By means of this instrument the Describe the hydrostatic press. What limit is there to its power? RESULTS OF PRESSURE. 127 compressibility of water may be determined, though the best instrument for this purpose is one in which the power is exerted by means of a screw. Fig. 98, upon a column of water contained in a strong vessel, a a, called (Ersted's Machine. By this instrument, slightly mod- ified, the exact compressibility of water and some other liquids has been determined. Water is found to di- minish -220 oo^o- f i* 8 volume for each atmosphere, or 15 Ibs. to the square inch. Alcohol diminishes of its volume for each atmosphere of pressure. PROBLEMS. 1. A submarine telescope was sunk in the East River, Ne\v York, to the depth of 30 feet, when a glass plate, 6 inches square, in the side of the box, near the bottom, was forced in. What Was the pressure exerted upon the plate ? Ans. 468f Ibs. 2. A whale was harpooned, and drew the boat under water to such a depth that, after having been taken and the boat drawn up, it was found to be permanently compressed so as to sink in water. On the supposition that it required a force of 540 Ibs. to the square inch to compress it, what was the depth to which it was sunk ? Ans. 1244-16 feet. 3. If a section of the cylinder a. Fig. 97, is one square inch in surface, and that of b 4 square feet, or 576 square inches, what pressure on b will be exerted by 100 Ibs. on a? Ans. 57600 Ibs. 4. The water in the distributing reservoir of the New York city water- works is 80 feet above the jet at the Park. What is the pressure exerted upon a square foot of pipe at the point where the jet issues ? Ans. 5000 Ibs. III. Results derived from the Laws of Pressure. 1. It re- sults directly from the laws of pressure above considered that 1 . Liquids will rise to the same level in tubes connected with a 128 NATURAL PHILOSOPHY. Fig. 99. common reservoir, ivhatever be their size or form. This is illus- trated in the common tea-pot. It may be shown experimentally by means of tubes which are curved, perpendicular, or inclined. Thus, if the tubes a b c d e, Fig. 99, are connected with a reservoir, r, and water poured into one of them, it will rise to the same height in all, though their form and capacity may vary indefinitely. It is on this principle that water conveyed in tubes will rise as high as the source, whatever the inequality of the surface between the fountain and the outlet. This fact appears not to have been well understood by the an- cient Romans, who, in the construction of their aqueducts, filled up the valleys and cut through the mountains, in order to form a passage for the water with which their cities were supplied. Springs and Artesian Wells result from hydrostatic pressure. As the water falls upon the surface of the land, as b' b c d, Fig. 100, it sinks down among the rocks, which are arranged in lay- Fig. 100. a ers, as b' b, c' c, d' d, and often inclined to the horizon more 01 less. Some of the s 1 rata, as c' c, are porous, while others are impervious to the water. If the strata are broken, the water is forced out through the crevices, and constitutes a spring. If the water-bearing strata are reached by means of boring, as at a, then the pressure will force the water through the aperture. These are termed Artesian Wells. The water which supplies these wells may fall 20, 30, or 40 miles from the place where it is forced up, and hence the pressure will depend upon the height of the country afyove the outlet. Some of these wells are 1200 or 1500 feet in depth. Ou what principle is it that water may be conveyed over mountains? SPECIFIC GRAVITY. 129 Artesian wells are very common in the salt regions of Western Virginia. By boring down from 800 to 1200 feet through the coal strata, they reach a stratum which contains salt water, and, in many cases, the water flows out upon the surface, being forced up, not only by hydrostatic pressure, but by the elastic force of the compressed gases of the coal beds. These gases are combus- tible, and are employed to evaporate the water in order to obtain the salt. 2. Another result derived from the properties of a liquid and the laws of pressure already stated is, that The surface of a liquid at rest is always level or horizontal. This fact is also established by observation and experiment. Ev- ery particle of the surface is attracted toward the center of the earth. If, therefore, we take a large surface, as the ocean, it is not a plane, but spherical ; the convexity, however, is very slight for a few feet. It deviates only 8 inches from a plane for a mile, 2| feet for 2 miles, and 6 feet for 3 miles.* For all practical purposes, the surface of a vessel of water is a plane, and we may therefore employ a liquid to determine wheth- er any surface is horizontal. Hence the use of Fig. 101. The Spirit Level. This consists -=n of a glass tube, a, Fig. 101, filled ' with alcohol, excepting a small por- tion, which contains a bubble of air. When the tube is placed horizontally, the bubble of air will be in its center ; but if it is inclined to the horizon in any direction, the bubble will move to- ward the elevated end. Instruments for engineering, surveying, astronomical observa- tions, and for leveling generally in the art of building, are fur- nished with spirit levels. IV. Specific Gravity. When any solid is immersed in a liquid, it displaces a quantity of it just equal to the bulk of the * The following formula will enable us to estimate the variation for any distance. Let L = number of miles, and D = depression in feet; then What position does the surface of a liquid at rest assume ? Describe the spirit level. What is its use ? F 2 130 NATURAL PHILOSOPHY. Fig. 102. body immersed. That is, if the body be one cubic foot, and im- mersed in water, it will displace one cubic foot of that liquid, and hence it must be sustained by an upward pressure just equal to the weight of a cubic foot of water, or 62^ Ibs. If the solid is heavier than water, it will weigh $2% Ibs. less in water than in the air. It is on this principle, first discovered by Archimedes,* that the relative weights or specific gravities of different substances are determined. Specific gravity may be defined to be the weight of any body compared with the weight of an equal bulk or volume of some other body which is taken as a standard. Distilled water is taken as the standard with which all solids and liquids are compared, and atmospheric air is taken as the standard for gases and vapors. 1. Specific Gravity of Solids. In or- der to determine the specific gravity of a solid body, a common balance, Fig. 102, is employed. The body, suppose it to be gold, is first weighed in air and then in water,, and the loss of weight noted. Whatever it loses in water will be the weight of a quantity of water equal in bulk to the gold. As many times, there- 1 fore, as this loss is contained in its weight in air, so many times heavier will the gold be than the water. In this case the gold will lose in water T V"th of its weight in * Hiero, the king of Syracuse, suspecting that his workmen had adulter- ated a golden crown which they had made for him, employed Archimedes to detect the imposture. One day, while in the bath, he noticed that his body caused the water to rise, and the thought occurred to him that any other body of equal bulk would raise the water to the same height. He immediately procured two pieces, one of gold and the other of silver, equal in weight to the crown, and noticed the quantity of water each displaced. Then, on placing the crown in the water, the quantity displaced was great- er than that by the gold, and less than that by the silver ; and hence he con- cluded that it was not pure gold, but an alloy of these two metals. Define specific gravity. How is the specific gravity of solids determined ? SPECIFIC GRAVITY. 131 air, arid hence its specific gravity is 19, or it is nineteen times heavier than water. If copper is treated in the same manner, it will lose th of its weight, and hence the specific gravity of copper is 9. To de- termine the specific gravities of solid bodies we may apply the following rule : Divide the weight of the body in air by its loss of weight in water. The reason of this rule has already been given. The loss of weight is exactly the weight of a mass of water equal to the mass of the solid immersed. If the solid is lighter than water, it must be attached to a heav- ier body whose specific gravity is known, so that it may be whol- ly immersed in the water. 2. Specific Gravity of Liquids. The specific gravities of liquids are determined in three ways . (1.) By means of a small bottle, Fig. 103, which contains exactly 1000 grains of distilled water. When the bottle is filled with any other liquid, it will contain more or less than 1000 grains, according as the liquid is lighter or heav- ier than water. If filled with sulphuric acid, for example, it will weigh 1900 grains ; if with alcohol, but 800 grains. And hence the specific gravity of sul- Fi g 104. phuric acid is T9, and of alcohol 0'8. (2.) By means of a bulb of glass, which loses 1000 grains when weighed in water. If this glass is weighed in any other liquid, it will lose more or less, according to the density of the liquid. If it lose more than 1000 grains, then the liquid is lighter than water ; if it lose less than 1000 grains, it is heavier than water. (3.) By the Aerometer. This instrument consists of two bulbs of glass, A B, Fig. 104, with a slender stem, a few shot being put in the lower bulb to cause it to sink. The stem is graduated, to determine the depth to which it sinks in different liquids. If it sink in distilled water to What is the rule for ascertaining the specific gravities of solids? H>w are the specific gravities of liquids determined ? Describe the several modes. 132 NATURAL PHILOSOPHY. zero, then in any liquid heavier than water it will not sink so far. In any liquid lighter than water it will sink below zero. The numbers marked on the scale enable us to ascertain the specific gravity of any liquid under examination. This instrument is much used in ascertaining the strength of alcoholic spirits. The lighter they are, the greater is the quan- tity of alcohol which they contain. Nicholson's Gravimeter, Fig. 105, is similar in its construction, but weights are applied to the top of the tube. It will evident- ly require different weights to cause it to sink to the same depth in different liquids. It may also be used to determine the specific gravities of sol- ids as well as liquids. The instrument is placed in distilled wa- ter, and weights added until it sinks to a. The weights are then taken off, and the solid placed in the cup c, with weights sufficient to sink the instrument to a as before. The weight of the solid will be equal to the difference of the weights applied in the two cases. We have, therefore, the weight of the body in air. By placing the same solid in the cup b, we may ascer- tain its weight in water, for it will be the difference between the weight which must now be added to sink the instrument to a, and that which was previously added to the solid to sink the instrument to the same point; then, by dividing the weight in air by its loss of weight in water, its specific gravity is found. The pressure exerted by liquids will depend upon Fig.iw. their specific gravities. Hence, if two liquids press upon each other in a curved tube, Fig. 106, their heights will be inversely as their specific gravities. That is, if mercury be poured into one arm, a, and wa- ter into the other, c, the water will rise 13.5 times as high as the mercury. 3. Specific Gravity of Gases. The specific grav- ity of aeriform bodies is determined by accurately"?! weighing a given quantity of air, and calling it 1 . Then, by weighing the same quantity of any other gas, its spe- cific gravity will be directly ascertained. Thus, if the air weigh 1 grain and the other gas 2 grains, its specific gravity is twice that of air, or 2. The following table contains the specific gravities of several substances : 1-5 Describe Nicholson's gravimeter. What is the law when liquids of dif- rent specific gravities ity of gases determined ferent specific gravities press upon each other ? How is the specific grav- " termmed? FLOATING BODIES. 133 Sp. Gr. Platinum 21-250 Gold 19-257 Silver 10-510 Mercury 13-568 Lead 11-352 Copper 8-895 Iron 7-780 Tin 7-200 Sp. Gr. Zinc 7-00 Ivory 1-917 Amber 1-226 Ebony 1-226 Cork 0-240 Alcohol 0-793 Sulphuric ether 0-715 Air > m i me(L Pressure ^ As substances weigh less in water than in air, it is obvious that, if any body is but a little heavier than water, it may be moved about in it with a comparatively slight force. It is due to this fact that very large rocks are moved great distances by water and ice. The specific gravity of ice is about T Vth less than that of water, and where the ice envelops the stones at the bot- tom of ponds and rivers during the winter, the spring floods, which raise the ice, lift up the rocks also, and float them to a greater or less distance. The ice thus formed on the shores of the ocean, especially in high northern and southern latitudes, takes up large masses of rock and soil, and floats them toward the equator, until the ice- berg or island entirely melts away by coming into warmer climes. By ascertaining the specific gravity of an irregular body, we may determine its size or solid contents ; for, by noting the quan- tity of water which it will displace, and allowing a cubic foot for every 62 Ibs., the size is readily obtained. V. Floating Bodies. Bodies lighter than liquids float on their surfaces, and the parts immersed will displace a quantity of the liquid equal in weight to the iveight of the floating body. This fact is a direct result of the upward pressure of liquids ; for, in order to sustain the body, there must be an upward pressure just Fig. 107. equal to its weight. It is also proved by experiment. Thus : Exp. Fill a vessel, A, Fig. 107, with water, and place in it a ball of wood. The water which will flow out at a, when weighed, will exactly equal the weight of the wood. Bodies thus floating on the surface of liquids By what means are rocks transported ? How can the size of an irregu- lar solid be determined ? What quantity of a liquid does a floating body displace f 134 NATURAL PHILOSOPHY. must have their centers of gravity supported ; and hence, in ordei that they may be supported, these centers must be in a line with the center of gravity of the displaced liquid ; so that a body on the water will have its center of gravity either directly above or below that of the displaced liquid ; but if this center be situated above a certain point, which must be determined for each sub- stance, called the metacenter, the body will be upset. " A great inventor (in his own estimation) published to the world that he had solved the problem of walking safely upon the water, and he invited a crowd to witness his first essay. He stepped boldly upon the waves, equipped in bulky cork boots, which he had previously tried in a butt of water at home ; but it soon appeared that he had not pondered sufficiently on the cen- ter of gravity and of flotation, for, on the next instant, all that was to be seen of him was a pair of legs sticking out of the wa- ter, the movements of which showed that he was by no means at his ease. He was picked up by help at hand, and, with his genius cooled, and schooled by the event, was conducted home." Arnott. The human body, when the lungs are filled with air, is light- er than water, and will float upon it ; but if one attempt to walk on the water, the center of gravity will sink so low as to im- merse all but the top of his head. If one could lay upon his back with only his face out of water, he would float upon its surface in safety. The art of swimming depends upon the power of striking the water with the limbs, which, by its reaction, supplies the addi- tional force requisite to keep the head above the water. When persons fall into the sea from the mast of a vessel, they often sink so far that the pressure compresses the air in their lungs, and they never rise to the surface. When ships float upon water they observe the law above con- sidered ; but as they roll in different directions, and as their load- ing is thereby liable to alter its position, their center of gravity What position will any body assume when thrown on water ? In what way may persons float upon water? Why do persons never rise when they fall into the sea from the mast of a vessel ? FLOATING BODIES. 135 may be thrown above the metacenter. Hence the importance of so stowing their cargo as to sink the center of gravity, as low as possible ; for the lower it is, the less is its disturbance, and, of course, the less is the danger to the vessel of being capsized. A ship in a close dock or a canal boat in a lock are supported by displacing a quantity of water equal to their immersed por- tions, though a very small quantity of water, on the principle of the hydrostatic paradox, may be made to float the largest ships. A boat in the lock of a canal is sustained by a small quantity of water on the same principle, and it is only necessary to ascer- tain, in such cases, the height of the column of water and the di- mensions of the vessel, to determine its weight. In this way canal boats are sometimes weighed. Sea water is rather more dense than fresh water, and hence a ship draws rather less wa- ter in the ocean (about Jj th less) than in a river or lake. Liquids of different specific gravities float upon each other, as oil and ether upon water, water upon mercury, cream upon milk. Fish are of the same specific gravity as water, and they are enabled to rise and fall by means of an air bladder within them, which may be contracted or enlarged at pleasure ; so that a fish in his native element is said to be destitute of weight. The question was once proposed why a pail of water would weigh the same with a fish in it that it would when the fish was taken out, and several learned explanations were given ; but when the question was proposed to Franklin by some of the French savans, he suggested that they should try the experiment, and ascertain, in the first place, whether it were a fact. Life Preservers and Life Boats. It is evident that bodies heavier than water may be made to float upon its surface by at- taching to them bodies lighter than water. On this principle life preservers and life boats are constructed. A bag of air placed around the body just under the arms will cause it to float, and to sustain a pressure proportioned to its size. How should the cargo in a vessel be stowed ? Does a ship in a close dock displace a quantity of water equal to its immersed portions? How does the specific gravities of fresh and salt water compare with each other ? On what principle are life preservers and life boats constructed ? 136 NATURAL PHILOSOPHY. Sunken vessels are sometimes raised by means of air-bags placed under them and filled with air. Life boats are made partly of cork, and some have also air- bags fitted to their sides, so that they will not sink, though filled with water. People in China, who live in boats upon the rivers, attach hol- low balls of some light substance to the heads of their children, to prevent them from sinking when they chance to fall into the water. PROBLEMS. 1. It is required to determine the quantity of gold and copper in a chain composed of an alloy of these metals, which weighs 2 ounces in the air, and 1 ounce 17 pennyweights in water ? Ans. Gold, 171 pennyweights; copper, 22| pennyweights. 2. If a cannon ball, whose specific gravity is seven times that of water, were dropped into the ocean, at what depth would it float ?* * This problem requires considerable knowledge of algebra. Those not acquainted with algebra may omit it. The following is one mode of solving it. It proceeds on the supposition that one column of 34 feet at the surface pi'oduces a compression of TTO^OT f itself. Suppose the whole depth to be divided into columns of 34 feet each. Let the amount of com- pression TT2iTo7 be represented by R, and the height of one column by = h. Let d represent the density of the first column. d,, " " at the depth of n such columns. As the density of each column increases an R part of the preceding col- umn, We shall have the density of the first column =d, " " second " " " " third " =d(l-f-R) 2 , " " " fourth " =d(l-j-R) 3 , " " " nth " =d(l-fR) n , But as the first column is not compressed, the density of the column at the point where the ball will float, or and at this point the water is seven times the density of the surface, or 7d y hence Log. (1+R)' and the depth from the surface would be Log. 7 \ 34 / -8450980 .. . ^ miles nearly - HYDRAULICS. 137 3. A loaded ship was found to draw 20 feet of water ; on the supposition that the part immersed was equal to a block 100 feet long, 10 high, and 20 wide, what is the weight of the ship ? Ans. 625 tons. 4. An iceberg, of a conical shape, was found to rise 250 feet above the water. The part which appeared was estimated to contain 5000 cubic feet. What was the size of the berg ? Ans. 50,000 cubic feet. To what depth did it sink below the water, on the supposition that its center of gravity and center of magnitude coincided ? Ans. 2250 feet. 5. Two gold chains were placed in a vessel full of water, and the weight of water which overflowed was found to be 6 ounces. What were the solid contents of the chains ? Ans. 10 4 cubic inches. SECTION II. HYDRAULICS. The motion of liquids is generally due to gravity, though it often results from other forces; but, oiuing to the peculiar proper- ties of liquids, the laws of motion, derived from theory, are some- what modified in practice. I. The velocity of a liquid spouting from an orifice in the Bide of a vessel is just equal to that which a falling body would acquire in descending through the perpendicular height of the column above the orifice. II. The quantity of liquid discharged from any vessel is mod- ified by friction and the crossing of currents at the orifice. III. The quantity is also modified by conducting tubes, which, if short, increase, and if long, diminish the quantity of efflux. IV. A jet ofivater issuing from the side of a vessel describes the curve of a parabola ; and the random from a jet at the cen- ter of the column is greatest, ivhile those at equal distances from the center above and below have the same random. V. When liquids flow in rivers, pipes, and canals, the velocity of the stream, at any part of its course, is inversely as the area of the section of that part. VI. Liquids resist the motion of bodies passing through them in the ratio of the square of the velocity. 138 NATURAL PHILOSOPHY. VII. Liquids are practically applied to move machinery by means ofivheels which are placed either vertically or horizontal- ly, and are moved by the force of the stream. HYDRAULICS* treats of the motion of liquids, and of the ma- chines which are put in motion by them. The motion of liquids, whether they flow in pipes, rivers, 01 canals, results from the attraction of gravitation ; but, owing to the peculiar properties of a liquid, and the action of this force al- ready noticed, page 1 20, their motions are subject to special laws, different somewhat from those of solids, so that the laws of their motion derived from theory must be modified in actual ex- perience, in order to be fully relied upon. That is, when we de- termine how a liquid should move by the laws of motion, we find, by experiment, a considerable deviation from the theoretical law. We must therefore combine experiment with theory in order to arrive at the exact truth. I. Laivs of the Efflux of Liquids flouring from the Bottom or Sides of Vessels. As the motion of any liquid is due to the force of gravitation, if we make an aperture in the bottom or the side of a cylindrical or prismatic vessel filled with water, 1. The velocity ivith ivhich it will flow out will be equal to that which a falling, body ivould acquire in falling from the surface of the liquid to the opening whence the liquid escapes. The truth of this proposition, which is called the Torricellian Theorem, will be evident when we Fif 108 consider that the stratum, Fig. 108, next to the ori- fice, is forced out not only by its own gravity, but by the pressure of every other stratum above it to the surface ; so that the top stratum, instead of falling freely to the orifice, imparts its own motion to the $&& second, and then to the third, and so on until it reach- es the stratum at the orifice, which receives this motion, and * iidup, water, and aJMof, a torrent. What is the meaning of hydraulics? What gives rise to the motion of Mqu-l3? Of what value is the theory of the motion of liquids? What is H "w of the efflux of a liqtaid ? LAWS OF SPOUTING LIQUIDS. 139 flows out with the same velocity which the first would have ac- quired if free to fall through the same distance. If, therefore, we know the height of the column, we may apply to it the laws of falling bodies to determine the velocity of efflux ; for it is evident that the velocity will depend upon the height of the column or depth of the orifice below the surface of the liquid, and not upon the quantity of liquid or size of the vessel. Now the velocities of a falling body are as the square roots of the spaces through which it falls, page 62, and hence the veloci- ties of jets of water issuing from the side or bottom of a vessel are also as the square roots of the depth of the orifices below the surface. That is, the velocity at 16 inches below the surface is twice as great as at 4 inches, the square roots of 1 6 and 4 being 4 and 2. By observing this law we may determine 2. The quantity discharged from the same orifice at different depths. For as the quantity discharged will be as the velocity, an aperture at 16 inches below the surface will discharge twice the quantity in the same time as one at 4 inches ; at 64 inches, four times the quantity will be discharged. This principle is of great practical importance in determining the quantity of water which will issue from a given orifice at the bottom of dams and reservoirs where the depth is known. 3. If we apply the law of falling bodies to a liquid issuing from an orifice of one square foot of surface, the velocity at the depth of 16* feet will be 32 feet per second, and therefore the quantity of liquid discharged will be 32 cubic feet per second. The same orifice at the depth of 4 feet will discharge but half as much in the same time. This law, however, is deviated from in actual practice, as we shall presently show ; yet, if we" assume it to be strictly true, it may be applied to the solution of the fol- 1 owing * The fraction y^h is omitted for the sake of rendering the expression more simple. How is the velocity of a liquid issuing from the side of a vessel determ- ined ? What law controls the quantity discharged at different depths be- low the surface ? 140 NATURAL PHILOSOPHY. PROBLEMS. 1. There is a certain dam, 16 feet in height, kept constantly full of water. It is required to determine the quantity of water discharged per hour by a tube at the bottom, a section of which contains 4 square feet of surface ? Ans. 460,800 cubic feet. 2. Three men, A, B, and C, own a dam which is 16 feet high, out of which each wishes to draw water. A inserts a tube, the section of which is one square foot in surface at the bottom ; B inserts a tube of 2 square feet, 9 feet from the top ; and C inserts a tube of 3 square feet, 4 feet from the top. It is required to determine the quantity of water which each would draw from the dam in the space of 24 hours. Ans. A=2,764,800; B=4,147,200; 0=4,147,200 cub. feet. 3 In the side of a dam an aperture of 4 square feet was made, which was found to discharge 1.00 cubic feet of water per second. At what depth below the surface of the water was the aperture made ? Ans. 9|f feet. 4. A certain pipe at the depth of 16 feet was found to dis- charge 384 cubic feet of water per second. What was the size of the pipe ? Ans. 12 square feet. 4. If a tube bent upward be inserted in the ori- fice, the jet ought to rise to a height equal to that of the surface of the liquid in the vessel ; for a body projected upward, page 65, with the velocity ac- quired in falling through a given space, will rise to the same height as that space ; but in the case of liquids the law is deviated from more or less. For we find by experiment that the jet, Fig. 109, falls far below the surface of the liquid. This is due to the greater resistance of the air. The jet is somewhat divided in its ascent, and presents a larg- er surface to the air. The law is strictly true only when a solid or liquid body moves in a space void B of air 109. To what height will a liquid spout from a bent tube inserted in the sidt of a vessel filled with water 1 LAWS OF SPOUTING LiaUIDS. 141 For the same reason, water falling through the air upon a wheel, from a given height, will be retarded in its descent, and the force of its fall will be less than when it is conducted through a tube, though in theory the effects ought to be exactly equal. In all the above cases the vessel is supposed to be kept con- stantly full of liquid, and, of consequence, the velocity of the jet always uniform,. 5. But if a vessel be emptied from an orifice in the side, then the velocity of the jet and of the descending surface will be uni- formly retarded ; for as the pressure will constantly diminish, the velocity of the jet, and, consequently, the quantity of liquid discharged, must also diminish, and the surface, as it descends, must be in the same condition as that of a body projected direct- ly upward, and subjected to the retarding influence of gravity ; that is, the velocity of the surface must constantly diminish; and as the spaces through which a body will fall in several success- ive seconds of time are as the odd numbers 1, 3, 5, 7, 9, the spaces described by the descending surface in equal successive portions of time will be as these numbers inverted, or 9, 7, 5, 3, 1. If, therefore, a vessel be divided into portions having the same ratio as these numbers, and then filled with water, it may be made to measure time. Such a tube, in principle, constitutes the Clep- sydra, or water-clock, which was formerly used as a time-piece. From these two laws it follows that the quantity of liquid dis- charged in a given time from a vessel kept constantly full, is double that discharged if the vessel, after being filled, is simply allowed to empty itself to the level of the same orifice ; just as a body projected downward with uniform velocity will describe double the space it would if projected upward with the same ve- locity, under the retarding influence of gravity. Prod. 1. A certain dam, 16 feet deep, was drained by an ori- fice of 4 square feet in the bottom in 24 hours. Required the quantity of water which it contained. Ans. 5,529,600 cubic feet. What resistance does a jet meet with in rising or falling ? When a ves- sel empties itself from an orifice, according to what law does the surface descend ? What is the Clepsydra ? 142 NATURAL PHILOSOPHY. 2. There is a pipe 64 feet high, and 1 foot in diameter, filled with water. How long will it take to empty it from an orifice in the bottom of 1 square inch in surface ? Ans. 3m. 4Gs.+ . II. Influence of the Orifice upon the Quantity of Liquid disclutrged. I . When an aperture is made in the side of a vessel, and the actual velocity and quantity discharged in a given time are accu- rately noted, it is found that the velocity and the quantity are each less than what is demanded by the laws above considered. This is due to the crossing of currents near the orifice, and also to the fact that those portions immediately above the open- ing have a greater velocity at first than those on the opposite sides; the consequence of this is, that the center of the jet, which flows with a velocity in proportion to the pressure, will be " sur- rounded by lines of water whose velocity diminishes in propor- tion as they approach the edge of the aperture," and this causes a contraction of the stream as it issues from the ori- fice, as s s', Fig. 110, called "the contracted vein," so that the area of a section of the jet, s s', just after it reaches the orifice, is only two thirds that of the aperture, and, consequently, only two thirds of the quantity is discharged which theory requires. The greater velocity of the water through the center of the orifice, and the influence of the cur- rents flowing from the sides toward the center of the jet, may be illustrated by making an orifice in the center of the bottom of any vessel, Fig. Ill, and putting into the water powdered amber. It will be found that the particles of amber will de- scend in right lines until they arrive within three or four inches of the aperture, and then they will flow toward it. This meeting of the currents at the cen- ter retards the motion of the water near the sides of the vessel, and produces a whirl in the form of a conical cavity, a, upon the surface. This cavity increases in depth, so that an aperture is made quite through the center of the jet before all the What influence has the orifice upon the quantity of liquid discharged ? and to what is this influence due ? What is the cause of the funnel-shaped cavity when liquids flow through a hole in the bottom of any vessel ? Fig. 110. INFLUENCE OF CONDUCTING TUBES. 143 water is discharged ; or, as the central portions have a greater velocity, the pressure of the atmosphere aids in opening a pas- sage directly through the jet. According to the experiments of Bossut, the actual discharge per minute compared with the computed discharge is as follows : Height of Liquid. Computed. Actual. 1 foot above the orifice, 4,427 cubic inches. 2,812 inches. 5 feet " " 10,123 " " 6,277 " 10 " " " 14,317 " " 8,860 " 15 " " " 17,533 " " 10,821 " It will be perceived that only about 64 per cent., or two thirds the quantity is discharged which the theory requires ; and on this account, therefore, an allowance must always be made when- ever it is required practically to determine the quantity discharg- ed from any dam or reservoir. The answers to the problems on page 140 must be reduced one third in order to correspond to the quantity actually discharged. III. Influence of Conducting Tubes upon the Quantity of Liquid discharged. When tubes are inserted in the orifice of a vessel, a still further modification of the quantity of efflux takes place. 1 . If a short tube be inserted in the orifice, having the exact form and length of the jet from the orifice to the point where it contracts when the orifice is a thin wall, no effect will be pro- duced upon the quantity discharged ; but if the pipe is cylindrical, and not more than four times the length of its diameter, the quantity discharged will be much greater, in a given time, than when the efflux is made through the same aperture in the side of the vessel. This increase is sufficient to raise the quantity discharged from 64 to 84 per cent, of the amount which theory requires. The increased quantity discharged by the tube is due in part to the adhesion of the liquid to the sides of the tube, which pre- vents the contraction, and in part to the pressure of the air, which accelerates the flow of the liquid into the tube, but retards its efflux from it. The result of this is, that the tube is kept con- stantly full. What is the effect of conducting tubes on the quantity of liquid dis- charged ? How is the effect explained? 144 NATURAL PHILOSOPHY. That the pressure of the air has this effect is proved by the fact that the quantity of efflux is not increased by conducting tubes if the liquid flow into a vacuum. The velocity of the efflux is diminished by the tube, but, owing to the tw T o causes above stated, the quantity discharged in a given time is greater than it would be through a thin wall, because the tube is kept constant- ly full. 2. Lateral Pressure of Liquids in Conducting Tubes. If long tubes are inserted jri the sides of a vessel, the quantity of liquid discharged will be diminished, because of the lateral pressure, and consequent friction against the sides of the tube. The smaller the tube is in proportion to its length, the greater will the resistance become. If a tube project within the vessel, it will also diminish the quantity of efflux. 3. Now the lateral pressure is equal on the whole interior sur- face of a tube ; if, therefore, the end of the tube be stopped, and an aperture made in the side, this pressure will be removed from that side while it remains upon the opposite side. This pressure will tend to force the tube in a direction opposite to that from which the liquid flows. This is called The reaction produced by efflux. It is on this principle that Barker's Mill or Seigner's Water Wlieel is constructed. It consists of a hollow cylinder, c, Fig. 112, revolving on an axis, with horizontal tubes inserted near the lower end, b e, and perforated by apertures in the sides, a d, near the ends. When the cyl- inder is filled with water from a pipe, p, and the pressure is removed on opposite sides of the arms a and d, the reaction produced by pressure upon the sides b and e turns the wheel with great velocity in the direction indicated by the arrows. As the pressure de- pends upon the height, a small quantity of water may be made to exert very great force. 4. When water is flowing in a pipe, if it is suddenly stopped a very considerable force is exerted by its reaction, sufficient, in What effect has the lateral pressure of liquids in long tubes? Describe Barker's mill. Fig. 112. RANDOM OF SPOUTING LIQUIDS, 145 Fig. 113. some cases, to burst the tube. This is due to its inertia. The stream, as it is confined in a tube, acts like a solid bar. A high- ly practical use is made of this force, in. connection with the elas- ticity of the air, to raise water to various elevations, -and to pro- duce a constant flow. This is effected by an instrument called The Hydraulic Ram. Thus, a tube, p, Fig. 113, is made to conduct water from a spring, which must be elevated a few feet, so as to give considerable velocity to the stream. At the end of the tube there is an upright pipe, c, in which a valve, a, plays, and per- mits a portion of the water to pass by it un- til it is raised to the top, when it suddenly stops the flow. In the side of the tube there is a valve, i, opening into a strong air-cham- ber, 6. When the stream is stopped at c, its reaction opens the valve at i, and forces into b a portion of water. This relieves the pressure upon the valve a, and it falls to the bottom of the tube, and is again raised up by the force of the stream, c? is a tube to conduct the water to any required height. As the air becomes compressed in b, it presses upon the surface of the water, and renders the stream from d constant. IV. Form of the Jet flowing from the Sides of a Vessel, and its Random, or Horizontal Distance from the Base of the Vessel. Fig. 114. 1. A jet of water, or of any other liquid, which flows from the sides of a vessel, de- scribes in its descent the curve of a parab- ola. Thus, let a cylindrical vessel, Fig 114, be filled with water, and a b c three orifices in its side : c at the center, and a and b at equal distances from c. The three jets will describe a parabola ; for it is evi- dent, setting aside the resistance of the at- mosphere, that the water will be in the ^1\ condition of a projectile which moves un- der two forces, the force of projection and that of gravity (see page 72). If now a semicircle be described upon the side, and lines drawn from a, 5, and c perpendicular to the side and meeting the circle, it is found that What is the principle of the hydraulic ram 1 What is its use 1 Describe the hydraulic ram. What is the form of the jet flowing from the sides of a vessel ? 146 NATURAL PHILOSOPHY. 2. The random of each jet, a, b, c> ivill be just double the length of these lines, which are called the ordinates to the curve. This law results directly from the laws of falling bodies, the force of projection being the pressure of the liquid, The jets from a and b will reach the point d, which is twice the distance a e, b i. The jet c will reach a point which is equal to twice cf. Hence the jet which spouts 4rom the center of the vessel will have tho greatest random, and the two jets equally distant from c will havo the same random, or spout to exactly the same distance from the base of the column. It should be observed, however, that when liquids spout against the air, they meet with a resistance which gives the jet the same form that is given to projectiles, and they actually describe the Balistic curve instead of the curve of a parabola. It is only in a vacuum that the curve of a parabola is actually described either by a solid or a liquid (see page 72). The degree of resistance will of course depend upon the velocity of the jet. If the ve- locity is doubled, the resistance will be four times as great. V. Motion of Liquids in Pipes, Rivers, and Canals. The motion of liquids in rivers and canals is modified by their depth and width, or by the size of the channel. If the channel or pipe is constantly full, the velocity will be greatest where the channel is smallest, and least where the channel is largest ; in other words, The velocity of the stream in any part of its course is inverse- ly as the area of its section at that point. The central portions of the stream move with greater velocity than the sides, and the top moves faster than the bottom. This is due to friction. Hence, in order to determine the quantity of water which flows in a river during any given time, it is necessary to determine the area of a section of the stream and the average velocity. 1. The area is obtained by measuring its depth in different places so as to obtain a mean depth, and then multiplying this into the width of the stream. 2. The mean velocity is determined by ascertaining the veloci- From what point is the random greatest ? Where is the random equal ? When liquids spout through the air, what kind of a curve do they actually describe ? -What is the velocity of a stream, in any part of its course, pro- portioned to ? How is the area of a section of a stream determined ? How is the velocity ascertained ? VELOCITY OF RIVERS. 147 ty at the surface, sides, and bottom of the stream. If these ve- locities are 3, 4, and 5 miles per hour, by adding them together, and dividing by 3, we obtain the mean velocity in this case, 4 miles per hour Fig. 115. These different velocities may be ascertained by noticing the velocity of light bodies on the surface arid edges of the stream, but more ac- curately by means of a bent tube, Fig. 115. When this tube is placed so that the current flows into the larger end, the velocity of the stream will cause the water to rise up in the tube, and the height to which it rises will indi- cate the velocity at the point where it is insert- ed. The velocity is determined from the height to which the liquid rises, on the principle that a body projected upward with the velocity it has acquired in falling through a given space, will rise to the point from which it fell ; and, if we know the height to which it rises under the influence of gravity, we may determine its velocity. Thus, if the water rise in the tube 16 feet, then the velocity of the stream is 32 feet per second ; for a body projected upward with a velocity of 32 feet per second would rise to the height of 16 feet. Having obtained the mean velocity in feet, this quantity mul- tiplied into the area of the section will give the number of cubic feet of water which flows in the river during the given time. Thus, if the area of a section of a stream is 200 square feet, and the velocity 4 miles, or 21,120 feet per hour, the quantity dis- charged in one hour will be 200 times 21,120, or 4,224,000 cu- bic feet. 3. The velocity of rivers is greatly retarded* not only by the friction on their sides and bottoms, but also by their irregular and ivinding course. If the water in its descent observed the laws of solid bodies falling down inclined planes, its velocity, con- stantly increasing from the source to the outlet, would become so great as to sweep along every thing in its course ; but a fall of 3 inches per mile is said to give a velocity of only 3 miles in an How is the quantity of water flowing in any river determined f 148 NATURAL PHILOSOPHY. hour. A fall of 3 feet per mile gives the velocity of a torrent. Many rivers, as the Ganges and Magdalena, fall not more than 500 feet in a thousand miles, and hence their progress is very slow. A descent of y 1 ^ th of an inch per mile is the least inclina- tion which will give motion to water. PROBLEMS. 1. The Mississippi River, at a certain point, is 500 feet wide, and the depth, taken at six different parts of the stream, 10, 15, 20, 30, 25, and 8 feet. What is the area of the section ? Ans. 9000 square feet. 2. The velocity at the bottom and sides was 3 miles per hour, at the top 4, and at the center 5 miles per hour. What was its mean velocity ? Ans. 4 miles per hour. 3. What quantity of water would the river, on the above sup- position, discharge in one year, or 365 days ? Ans. 1,666,241,280,000 cubic feet. 4. On the supposition that j^-^th part of the water in the above example was mud, how many tons of mud would the river dis- charge if its specific "gravity was 2 times that of water ? Ans. 260,350,200 tons. VI. Resistance of Liquids to the Motion of Bodies immersed in them. Liquids, as well as solids, have the property of iner- tia, and bodies moving through them must overcome this force, and give motion to their particles. In other words, a liquid, as water, must resist the motion of any solid in it with a force equal to the inertia of the particles, and the velocity with which they are moved. Thus, a boat passing through water at the rate of one mile per hour, meets with a certain resistance from the water which it displaces. If it move two miles an hour, the resistance will be not twice, but four times as. great, and of course will re- quire four times as much power ; for, in the latter case, the quan- tity of water displaced by the boat in the same time will be doubled, which will double the resistance, and .the velocity with which it is moved will also be twice as great. Hence the re- Illustrate tue law of resistance when bodies move through water. RESISTANCE OF LIQUIDS. 149 sistance will be four times as great for two miles per hour as for one. If the velocity be increased to three miles per hour, then, the resistance will be nine times as great, since both the quantity displaced and the velocity are trebled. And so, if the velocity be four miles per hour, the resistance is increased sixteen times. This law of resistance may be thus ex- hibited : if we take the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, to represent the velocities with which any body moves through wa- ter, we shall find the resistance to be as the numbers 1,4, 9, 16, 25, 36, 49, 64, 81, 100. 1 . That is, the force of resistance increases as the square of the velocity. Hence, if it required the force of one engine to drive a vessel one mile per hour, it will require a hundred such engines to pro- pel it ten miles per hour. In fact, it requires rather more force than is indicated by the above law, especially when the motion becomes very rapid, owing to the diminution of the pressure upon, the vessel's stern. This pressure is equal to that on the prow when the vessel is at rest ; but as soon as it begins to move, the water is parted and thrown each way from the vessel's sides, so that the pressure is removed from the stern ; and hence this pressure must be supplied by the force of the steam or the wind. The observance of this is very important in steam navigation. It is evident that the law of resistance must be the same if the solid is at rest and the liquid in motion. Thus, a vessel at anchor, when the tide or currents are running past her, must bear a strain upon her cable in proportion to the square of the velocity. Hence it will require four times the strength of cable to fyold a vessel against a tide moving two miles per hour that it would if moving one mile per hour, for the reason that^ twice as many particles strike the vessel in the same time ; and, as they are moving twice as fast, they strike it with double the force. 2. Limit of Velocity. It is obvious from the above laws that there must be a limit to the velocity with which a solid may be forced through a liquid; 20, or, at most, 25 miles per hour, is the highest velocity which can possibly be given to a steam ves- What limit is there to the velocity of a body moving tiu-auqrh a liquid? 150 NATURAL PHILOSOPHY. sel ; beyond these rates the resistance becomes so great that no mechanical powers can be constructed to overcome it, or increase the speed. A force requisite 4o propel a vessel 15 miles per hour would have to be doubled to give a velocity of 20 miles per hour, and to be increased eight times to move the vessel 40 miles per hour. In this case no material would be sufficient to sustain the shock of the resistance, even if the force could be applied. 3. Influence of the Form upon the Degree of Resistance. It would seem, from a slight examination of the subject, that if a solid removed a given number of particles of water to a and then of the atmosphere, or that gaseous fluid which sur- rounds the earth, and extends to the distance of forty or fifty miles above it. SECTION I. PROPERTIES OF ATMOSPHERIC AIR. It is a common impression that the air does not possess the essential properties of matter. I. But the materiality of air is proved by its extension, im- penetrability, weight, inertia, and pressure. These and other properties of air may be best exhibited by means of the air pump. II. The air is a perfectly elastic fluid ; that is, when com- pressed, it always returns to its original volume when the press- ure is removed. The law of compressibility and expansibility is, that the volume of a confined portion of air is inversely as the compressing force. III. The air presses equally in all directions, downward, up- ward, and laterally. The amount of pressure is determined by means of a barometer, and is about 15 Ibs. to a square inch of surface, though ilie pressure varies at different times and places on the earth's surface. IV. It is due to the pressure of the air that water may be rais- ed from wells and pits by means of the lifting pump, syphon, fyc. V. When air is compressed, it exerts a greater or less force, which is due to its elasticity, and in this state may be employed as a mechanical power. VI. In consequence of the pressure of the air and its attrac- tion for other matter, it diffuses itself among the particles of sol- ids, liquids, and gases. VII. Air, like water, sustains a portion or the ivhole of the weight of bodies which are immersed in it. VIII. It also opposes a resistance to bodies passing through it, which is in the ratio of the square of their velocity. IT is a very common impression that air does not possess the essential properties of matter, extension and impenetrability; but What is the common opinion respecting atmospheric air? MATERIALITY OP AIR. 157 Fig. 121. it is easy to show, by experiment and reference to various phe- nomena, that it is not only extensible and impenetrable, but that it possesses also the other properties of matter, such as attraction, weight, and the like. I. That the Air is Material may be proved by the following properties, which can be fully illustrated by experiment : 1 . The Air is Impenetrable. This may be shown by placing a lighted taper, Fig. 121, upon a cork float- ing on the surface of a jar of water, and inverting over it a receiver of common air. By pressing the receiver down, the taper will descend apparently be- neath the water, the same effect being produced as would be if the column of air in the receiver were solid ; that is, the air excludes the water from the space it occupies. If a solid piston be fitted to a cylinder closed at the bottom, no force can press it to the bottom, as is exemplified in the fire syringe. 2. The Air is extended in Space. It is evident, from the above experiments, that the particles of air are extended ; for, if they were not, it would be impossible for any number of them to fill a por- tion of space, and the cork, in the first experiment, would not be forced down apparently below the water. Hence the air must possess the other essential property of matter, extension. 3. The Air has Weight. That air has weight, or that its atoms are at- tracted toward the center of the earth, is shown by weighing a portion of air confined in a glass flask. Exp. Take a glass flask, Fig. 122, with a stop-cock attached, and with an air pump exhaust the air, and then weigh it. After the readmission of the air, the flask will as- sume the position shown in the figure. By Fig. 122. How is the material! air is extended ? teriality of air proved ? What experi that it has weight and inertia ? experiments to prove that 158 NATURAL PHILOSOPHY. adding weights to the opposite scale, the weight of the air may be determ ined; and it will be found that every 100 cubic inches will weigh a little more than 31 grains. Other gases may be shown to have weight in a sim- ilar manner. 100 cubic inches of hydrogen weigh only 2'1 grains, while the same quantity of carbonic acid weighs 47*2 grains. 4. The Air has Inertia. The materiality of air is further shown by its inertia. It requires force to put it in motion, or stop it when in motion. This property of air may be made evi- dent by reference to the most familiar phenomena. Ships sail by the force of moving air. Birds fly by the resist- ance which the air offers to the stroke of their wings. Light bodies, as straw and feathers, and even, in some cases, trees and dwellings, are swept along or overturned by currents of air. Solid and liquid bodies, moving through air, meet with resistance, and the resistance follows the same law as when solid bodies move through water, which is as the square of the velocity ; that is, a double velocity meets with a quadruple resistance ; for one body moving with twice the velocity of another, meets with twice as many atoms in the same time, and must move these with twice the velocity ; hence the resistance is four times as great. Air is about eight hundred times lighter than water, and its inertia and momentum are always found to be in proportion to its weight. 5. The Air is a Fluid. The fluidity of the air is proved by the same kind of facts as that of water : " it presses and is pressed equally in all directions ;" and if confined, a pressure or blow on one part presses equally on every other part. From these and many other facts, it is evident that air is ma- terial ; that it occupies space, is impenetrable, has weight, iner- tia, momentum, and pressure. For the purpose of illustrating the properties of air, several art- icles of apparatus are necessary, among which the air pump is most essential. The Air Pump. The air pump was invented by Otto de Gue- ricke, of Magdeburg, Germany, in the year 1654. It was a sin- gle barrel, with a piston and two valves, and by means of it he exhausted two hollow brass hemispheres, 12 inches in diameter, having the edges ground so that when placed together they were What other proofs of the materiality of air? What apparatus most im portant for experiments upon air? Describe the air pump. THE AIR PUMP. 159 Fig. 123. air-tight. Air pumps are constructed with double or with single barrels. The latter are the most simple, and worked with the least power. The single barrel air pump consists of a barrel, b, Fig. 123, with a valve opening upward, and a piston connect- ed with a hollow tube, c, which passes up through the pump plate, a. The piston has a valve which opens up- ward, and the barrel is worked up and down by means of the handle, h. The j valves work precisely like those of the common lifting pump ; but as, in this form, the barrel is worked up and down instead of the piston, the valve is in the top of the barrel, and there- fore the greatest force is required to press the barrel down, which lifts the piston from the bottom to the top of the cylinder, and forces out the air which flows into it from the receiver when the barrel is raised up. To indicate the degree of exhaustion, a mercurial gauge is at- tached. It consists of a tube, g, open at both ends ; the upper end opens into the receiver, and the lower extends through the pump frame and dips into a cup of mercury. When a receiver is placed upon the pump plate, a, and the air exhausted, the tube is also exhausted, and the pressure of the air on the surface of the mercury in the cup forces it up the tube, and the height to which it rises will indicate the degree of ex- haustion. The law of exhaustion with each stroke of the piston is readily deduced from a knowledge of the capacity of the barrel and of the receiver. Thus, if the capacity of the receiver is equal to that of the barrel, then, when the barrel is raised, the air will expand and fill it, so that the quantity in the barrel will be half of the whole. When the barrel is forced down, this half will be forced out, leav- ing half of the original quantity in the receiver. When the bar- rel is raised again, the air in the receiver will expand and fill the What is the law of exhaustion in the air pump when the capacity of the receiver is equal to that of the barrel ? 160 NATURAL PHILOSOPHY. barrel, which will then contain \ of \ = \ of the original quan- tity. This will be expelled by the second stroke, leaving one quarter in the receiver. The third stroke will halve this quan- tity* expelling one eighth, and leaving one eighth of the original quantity in the receiver. That is, each stroke will expel half of the quantity of air which remains, and hence the whole can never be exhausted from the receiver. It will be seen by examining the portions expelled by several successive strokes, that they form the series , |, , T L. These numbers constitute a geometrical series whose ratio is . Such a series will never terminate. Hence the rate of exJiaustion proceeds in a geometrical ratio. If the receiver is five or ten times the capacity of the barrel, the same law may be deduced ; only the series will be different, and the greater the capacity of the receiver in proportion to that of the barrel, the slower will the exhaustion proceed. Thus, in the above case, five strokes of the piston will expel |i, or nearly the whole of the original quantity in the receiver ; but if the re- ceiver were nine times the capacity of the barrel, then the series would be T L, T 2-o-, T o-, &c., and five strokes of the piston would expel only i-Y^W* or I GSS than half of the original quantity ; hence the most perfect exhaustion is produced when the receiver is small, and the barrel of the pump large ; hence, also, the ad- vantage of pumps with large barrels. Prob. 1 . The barrel of an air pump contains 9 cubic inches of air, and a receiver placed on the plate contains 81 cubic inches. What quantity of the air would be expelled by 1 strokes of the piston ? 2. A receiver, containing 12 cubic inches of air, contained a quantity equal to 3 cubic inches after 2 strokes of the piston. What was the size of the barrel ? Ans. 12 cubic inches. By means of the air pump and other apparatus to be described, we proceed to illustrate and prove the principal properties of air. II. Elasticity of the Air. 1 . The air is a permanently and 'perfectly elastic fluid. By the elasticity of the air is meant that What is said of the elasticity of the air ? ELASTICITY OF THE AIR. 161 Fig. 124. Fig. 125. power which a compressed portion of it has to spring back to its original dimensions, or to expand when the pressure is removed. It is perfectly and permanently elastic ; for if a portion of air be compressed for any length of time whatsoever, upon the removal of the pressure it will regain its original volume. The elasticity of the air may be illustrated by many ex- periments. Exp. Thus, if we take a tube with a bulb at the end, and invert it in some coloi-ed liquid, Fig. 124, on cooling the bulb the air will contract, and the heat of the hand will expand it. These contrac- tions and expansions are indicated by the rise and fall of the liquid in the stem of the tube. This instrument is therefore used as a ther- mometer, under the name of the Air Thermometer. Exp. Fill a bladder with air, and compress it ; when the press- ure is removed, it will return to its original volume. Exp. Place a portion of air confined in an India rubber bag in a receiver, Fig. 125. Upon exhausting the air around the bag, that is, removing the pressure from the exterior surface of the bag, the air within will expand and fill the bag full. Upon the read mission of the surrounding air, the bag will collapse and re turn to its original dimensions. Exp. If some soap bubbles be placed under the receiver and the air exhausted, they will increase rapidly, owing to the expansion of the air which they contain. 2. Force exerted by the Elasticity of Air. It will be noticed that the elasticity of the air, when the pressure is femoved, is capable of exerting consider- able force. This fact may be illustrated by many beautiful experiments. Exp. Fill a small bolt-head with water, leaving a small bubble of air, Fig. 126, and invert it in a vessel of water. If this be placed under the air pump receiver and the air ex- hausted, the bubble will expand and drive the water en- tirely out of the ball. On admitting the air, the water will be forced back again. In this case, however, the force of gravity aids the elasticity of the air. Exp. There is a small portion of air in the large end of an egg, and by breaking the small end and placing the egg under the exhausted receiver, the air will expand and drive the egg out of its shell, Fig. 127. On admit- ting the air, it will be forced back again. The force of expansion, when the pressure is removed, is sufficient to break thin glass ves- Fiff. 126. Fig.VZJ. What experiments to prove the elasticity of air ? Illustrate the force of the elasticity of the air when the pressure is removed. 162 NATURAL PHILOSOPHY. Exp.-Pla.ee a square glass jar, c, Fig. 128, tightly closed, *V- 128- under the receiver of an air pump, a. On exhausting, the elasticity of the confined air will be sufficient to burst the ves- sel. A gauze wire should be placed over the jar b, to pre- vent the glass from injuring the pump plate. Exp. Take a jar of water, in which place a ball of glass ; fill it with water except a small bubble of air in the top, suf- ficient to render it a very little lighter than water, and tie over the jar a piece of India rubber cloth. If pressure is ap- plied to the top by the finger, it will condense the air in the glass ball, and cause it to sink. On removing the pressure, it will rise. This is a beautiful toy, Fig. 129, called the Hydrostatic Balloon. If the ball is made a little heavier than the water, so as to remain at the bottom of the jar, and the cloth removed, on placing the whole under the receiver and exhausting the air, the bubble in the ball will expand, drive the water out, and the ball will rise to the surface. On admitting the air, the balloon will sink, because the air within is condensed, and the water, being forced in, renders the balloon spe- cifically heavier than water. The elasticity of the air may be employed to pro- duce a beautiful jet of water, by using an instrument called The Transferrer, Fig. 130, which consists of p^. i 30 . two glass globes, a b, permanently connected to- gether. The upper ball, b, is open at the top, and a flask, c, is inverted over a jet pipe, d e, which extends to the bottom of a. The lower bulb, a, is partially filled with water, having a small quan- tity of air confined in its upper portion. Now, by placing a receiver over the whole and exhausting, the air expands in a, and forces the water up through the tube into the second vessel, b, and when the air is admitted, the water is forced by the pressure of the air into the flask c. By this process the liquid is transferred from the lower to the upper vessel. 3. Law of Expansibility and Compressibility of Air. The general law of the compressibility and expansibility of the air may be thus stated : Describe the experiment with square bottle. Describe the hydrostatic balloon. How does this experiment illustrate the force of elasticity ? De- scribe the transferred What is the law of the compressibility and expansi- bility of air? PRESSURE OF THE AIR. 163 The volume of a confined portion or given iveight of air is inversely as the compressing force, or the greater the force the less the volume, and the less the force the greater the volume. F^. i3i. This law may be illustrated by means of a bent glass tube, Fig. 131, closed at b. By pouring a little mercury into the tube, a, sufficient to insulate the air in d, the press- ure upon it will be equal to that of the atmosphere, which is 15 Ibs. to the square inch. If now the tube be filled to the height of 30 inches with mercury, which is also equal to a pressure of 15 Ibs. to the square inch, the vol- ume of air in d will be reduced just one half, or it will oc- Hc cupy but one half the space, and the mercury will rise to c. m Hence double the pressure will halve the volume. Four times the pressure will diminish the volume to one quarter its former bulk. On the other hand, if the pressure be removed, one half the pressure will double the volume, or one quarter the pressure will render the volume four times as large. The air becomes denser as the pressure is increased, or both the density and elasticity of the air are always as the pressure. We may account for this property of air by the fact that the atoms of which it is composed are surrounded by a resisting and expand- ing power, and hence, when the pressure is removed, they tend to separate further and further from each other. For the purpose of condensing the air, a machine called 132 T^ Condensing Pump is employed, Fig. 132. This instrument is similar to the exhausting pump, with this exception, the piston f contains no valve. The valve in the barrel at d opens downward, and the air is forced in by the piston, but is prevented from return ing by its elasticity, which closes the valve. III. Pressure of the Air. The pressure of the air is caused by its weight. The intensity of this force, and the fact that it operates equally in all di- rections, may be shown by the following experiments. 1. Downward Pressure of the Air. The down- ward pressure of the air results from its weight. Exp. Place the receiver upon the plate of the pump, and Illustrate this law. Describe the condensing pump. What is the cause of the pressure of the air 1 Illustrate its pressure. 164 NATURAL PHILOSOPHY. exhaust the air from it ; the downward pressure will be indicated by the firm- ness with which the receiver is held to the plate. If the receiver is large, the force is sufficient to lift a pump weighing two or three hundred pounds. Exp. Take a small receiver, open at both ends, F - 133 Fig. 133, called a hand glass, and place the hand over the upper end; on exhausting the air, the pressure will be so great that the hand can not be lifted with- out great effort. This is the principle- of cupping, for which purpose the skin is first slightly cut, and a small receiver is placed over that part from which it is intended to draw blood. Upon exhausting* the air, the press- ure upon the surrounding part is sufficient to force the blood from the veins, Exp. Tie a bladder over the open end of a receiver, Fig. 134, and exhaust the air ; the bladder will be bent inward, and, if struck when tensely stretched, will burst with a loud report. The Sucker. The pressure of the air is often illus- trated by a circular piece of leather with a string pass- Fig. 135. ed through the center, A, Fig. 135. When this is moistened and pressed down on any smooth surface, a weight of many pounds may be raised by the string in the center, in consequence of the pressure of the air upon its surface. Boys often use this to lift smooth stones and drag them along. Insects are enabled to walk upon the ceiling of a room be- cause their feet are formed like the sucker, and the upward pressure of the air holds them firmly to the ceiling. Animals drink and draw their milk by forming a vacuum with their lips, and the atmosphere forces the liquid into their mouths. What is called suction is nothing but the pressure of the air exerted upon the surface of a liquid, forcing it into a partial vacuum, which is formed by the mouth or by some other mechanism. 2. The Pressure of Air in all directions is beautifully illus- trated by the Magdeburg Hemispheres. These consist of two * The exhaustion in the case of cupping is usually made by simply burn- ing a little alcohol in the cup, which consumes the air in it, and then in- verting it suddenly over the part from which it may be desirable to force out the blood. What is the principle of cupping ? Describe the sucker. What experi- ments illustrate the pressure of the air in all directions. PRESSURE OF THE AIR. 165 Fig. 136. hemispheres, Fig. 136, and accu- rately fitted to each other. If they are 6 inches in diameter, on ex- hausting the air, they will be held ,, A.- , together so firmly that the strength of two men can not pull them asunder. In this case the press- ure must be in all directions ; there is an upward and lateral as well as downward pressure. 3. The ~Upward Pressure of the Air may be shown by filling a wine-glass with water, and laying a paper over the open end in. contact with the water. It may then be inverted, and the up- ward pressure of the air will prevent the escape of the water. If a tight vessel be filled with water and an aperture made in the bottom, the water will not run out because of the upward pressure of the air ; but, by making a small hole in the top, it will immediately flow ; hence the reason that a cask of beer or cider can not be emptied from the faucet unless a vent hole be made in the top. This fact, as well as the force of the upward pressure, may be illustrated in a more striking manner by the Weight Lifter. This consists of a glass cylinder, b, Fig. 137, closed at the top, with a piston, a, fitted to it. Exp. By means of a tube from c, connected with no the air pump, exhaust the air from b, and the upward pressure of . 138. ^ a j r b e i ow a will force the piston up with an attached weight. If the cylinder is six inches in diameter, it will raise more than two hundred pounds. 4. Amount of Atmospheric Pressure. The amount of atmospheric pressure is determined by counterbalanc- ing the pressure of the air by some liquid, as mercury or water, and then ascertaining the weight of the liquid. Thus : If we take a glass tube, a b, Fig. 138, some three feet in length, closed at one end, and, having filled it with c mercury, invert it in a vessel, c, containing the same liq- uid, the pressure on the outer surface of the mercury in the cup will sustain the mercury in the tube to the height of 30 inches. That it is the pressure of the air which sustains the col- umn of mercury can be proved Describe the weight lifter. What does it prove ? Fig. 137. & {^ ^>j ' b |_^ : LJZ_^, .^ LW 106 NATURAL PHILOSOPHY. Fig.UO. By placing the tube in a tall glass receiver, Fig. 139, J'fr 139. and exhausting the air, the mercury will gradually sink as the exhaustion proceeds, and will finally be nearly emptied from the tube. Upon the readmission of the air, it will rise to its former height. If water were used instead of mercury, the pressure would sustain a column about 34 feet in height. By this experiment we can determine, 5. The Weight of the Atmosphere, or the amount of pressure on any given surface. If the tube contain one square inch of surface, the weight of a column of mercu- ry thirty inches in height will be fifteen pounds ; and as the atmosphere sustains or balances this weight, it must also press with a force of fifteen pounds on every square inch of surface. This force is sufficient to press upon a man's body with a weight of fifteen tons ! The reason we do not feel it is, that there is air within the body, so that the inner and outer pressure is equalized. If, however, it be removed from one part, this enormous pressure will im- mediately be realized. The amount of atmospheric press- ure is measured by means of the Barometer. A tube filled with mercury, as in the above experiment, and supplied with a scale and some other fix- tures/is called a Barometer, Fig. 140. The uses of this in- strument are to determine not only the actual weight of the air, but also to indicate its variations in pressure ; and as the pressure diminishes in ascending above the level of the sea, it is also used to determine the height of mountains. It will be seen that when the tube is filled with mer- cury and inverted in a cup holding the same liquid, the mercury will sink to about the height of thirty inches, leav- ing the upper portion of the tube void of air. This is the most perfect vacuum possible, and is called V the Torricellian Vacuum, from the name of its Italian inventor, Torricelli. V is a screw to raise the mercury in the vessel to the point where the scale commences. This scale extends to How is the amount of atmospheric pressure determined ? What is the pressure of air on each square inch of surface? Describe the barometer. What are its uses ? VARIATION? OP ATMOSPHERIC PRESSURE. 167 Fig. 141. the upper portion of the tube, where it is graduated to inches and tenths of an inch, and, to indicate very slight variations, a verniei is applied to the scale, which carries the divisions to the hundredth of an inch. The Vernier is a small scale, v r, Fig. 141, fitted to slip up and down upon the princi- pal scale, b, but the divisions are a little larg- er. In the barometer scale an inch is divid- ed into ten parts, but the divisions of the vernier are such that ten of them are equal to eleven on the barometer scale, so that one division of the vernier is one hundredth larg- er than a division on the barometer scale. By placing the two scales together at 30 '2 inches, and moving the vernier up until it is at the exact height of the mercury, and then looking down the scale to the fourth division, it is opposite to one of the divisions of the barometer scale. As one division of the ver- nier is T o-th larger than one of the barometer scale, it has gained T |o tns of an inch, ana the mercury stands at 30-24 inches. In Stationary Barometers the mercury is contained in an open, wide basin ; but when it is intended for transportation from place to place, the mercury is sometimes in- closed in a leather bag, with a screw to force up the mercury into the tube to the height corresponding with the commencement of the scale ; for, in all kinds of barometers, the more mercury there is in the tube, the less there will be in the basin. Such a barom- eter can be transported without any danger to the instrument from the fluid condition of the mercury. When it is mounted in the form of a walking-cane, it is a convenient instrument for de- termining the height of mountains, and hence is termed the Mountain Barometer. 6. Variations of Atmospheric Pressure. By means of the barometer, the variations of pressure, at different times and in different situations on the earth's surface, may be accurately as- certained. The whole amount of variation of pressure at the Describe the vernier the stationary and mountain barometer, other uses of the barometer? What 168 NATURAL PHILOSOPbl. surface of the ocean is about three inches ranging from twenty- eight to thirty-one inches ; and as such variations indicate some changes in the atmosphere, the barometer becomes a iveather- glass, and enables us to predict, with tolerable certainty, storms, high winds, and other atmospherical phenomena. Generally, the rise of the mercury indicates fair, and its fall foul weather. During or just before a storm, the height will depend upon the position of the barometer in relation to the center of the storm. A high wind is also attended or preceded by a fall in the mer- cury. Of course its rise shows that the column of air at that place has become condensed, and its fall shows that the air is rarefied by some atmospheric changes, the cause of which is not fully understood. At the level of the sea the mean height of the barometer is found to be nearly the same, thirty inches ; but the oscillations are not equal for every degree of latitude. These variations are least in the tropics, and greatest between 30 and 60 of lati- tude. At New York city the variation of the barometer is less than two inches ; in London, about three inches ; while within the tropics its variation rarely exceeds a fourth of an inch. These variations are dependent in some degree upon moisture and temperature. Hence a thermometer is usually attached to the barometer, and the temperature of the place where the ob- servations are made carefully noted. There are also variations at different hours of the day, called horary variations, but these are very slight. At New York, by the observations of Mr. Redfield, the mean variation from ten A.M. to six P.M. is 0'39 inches. In ascending above the level of the sea, the column of air be- comes shorter, and the pressure is in consequence diminished. By numerous experiments it has been found that the mercury sinks about one tenth of an inch for every eighty-seven feet (see page 183). Hence the utility of the barometer to determine the height of mountains. The height of mountains is sometimes determined by the tem- What variations in the barometer at different latitudes ? What is the law of variation in the barometer as we ascend above the level of the sea ? peratures at wnicn water or alcohol boils in the valley and at their summits, for the pressure of the atmosphere upon the sur- . . face of liquids modifies their boiling temperatures, the pressure, the higher the temperature at which they boil ; and, on the other hand, if the pressure be removed, their boiling tem- peratures will be lowered. Thus water which boils at the sur- face of the ocean at 212 F., will boil at 72 F. in a vacuum. Alcohol will boil at 36, while ether boils below zero. Alcohol and ether, therefore, and some other liquids, would not exist in the liquid state at the ordinary temperature if the pressure of the atmosphere were removed, but would wholly pass into the state of vapor. \ Now, as we ascend above the level of the ocean, the pressure is diminished, and it is found that an ascent of about 550 feet will lower the boiling point of water one degree ;* and hence, by Fig. 142. means of tables constructed for the purpose, the height above the ocean may be readily ascer- tained by the temperature at which water boils at any given point. IV. MecJianical Pressure of Air on the Surface of Liquids. The pressure of air on the surface of water, in connection with its elasticity, produces many beautiful phenomena in nature, and is the source of much utility in the arts. Exp. To illustrate the pressure of air on liquids, take a glass fountain furnished with a stop-cock, Fig. 142, with a jet pipe, a, passing into the interior. Ex- haust the air, and then, having placed the lower end of the tube in a vessel of water, turn the stop-cock. The pressure of the air on the outer surface of the liq- uid will force the liquid into the fountain in a beauti- ful jet until it is nearly full. * In consequence of the diminished pressure, water on high mountains will boil at a temperature so low that in some cases it can not be used for culinary purples. This is said to be the case at the monastery of St. Ber- What other methods for ascertaining the height of mountains ? At what rate does the pressure diminish above the level of the sea ? What effect has the pressure of air upon liquids ? What illustrations of the mechanical pressure of air on the surface of liquids ? H 170 NATURAL PHILOSOPHY. a Exp. The experiment may be varied by placing a bolt- ^g- 143. head, a, Fig. 143, upon the top of a receiver, c, with a pipe extending into a vessel of water, B. On exhausting, the elasticity of the air in a will cause it to flow out through the water ; then, by allowing the air to flow into the receiver, it will force the water into the bulb a. If the water is colored in thJe experiment, the appearance is rendered much more striking and beautiful. If, instead of exhausting the air from any vessel before placing it over water, it be filled with a liquid heavier than water, the heavier liquid will flow out, and the atmospheric pressure will force the water in to supply its place. Thus, if a small tube be filled with mercury and inverted in a vessel of water, the mercury will flow out and the water will be. forced in to supply its place. It is on this principle that the slaves in the West Indies are said to steal rum. They fill a bottle having a long neck with water, and insert the neck in the bung-hole of the cask ; the water, being heavier than the spirit, falls down, and its place is filled by the lighter liquid, which is forced up. Lifting Pump. The common pump depends for its utility upon the pressure of the air, a vacuum being formed in the bar- rel by the piston as it is lifted up. Thus, let a b, Fig. 144, represent the bar- rel, with the piston and valves of the com- mon lifting pump. There is a valve, a, in the piston, opening upward, and one at b, in the lower part of the barrel, also opening up- ward, similar to the air pump. When the piston is raised by means of the handle, a vacuum is formed below it between a and b, and the pressure of the air on the water in the vessel below forces it up through the tube, lifts the valve, and causes it to follow the piston to the top. When the piston descends, the lower valve is closed and the upper valve opened, so that the nard, in Switzerland, where the monks find it difficult to qpk their vege- tables. In the process of refining sugar, where the heat may do injury, the sirup is sometimes evaporated in vacuo. The cost of fuel in this case is much diminished. Describe the lifting pump. How are its valves arranged ? LIFTING AND FORCING PUMP. 171 water passes above the piston. The next stroke closes the piston valve, and the water is lifted to the spout. The height of the lower valve can not be more than thirty- four feet from the surface of the water, because the pressure of the air is only sufficient to sustain a column of water at that height. Practically, the lower valve must be at a point a little less than thirty-four feet from the surface, in order that the wa- ter may pass through the valve of the piston as it descends. The Forcing Pump, c d, Fig. 145, differs from the lifting pump in two respects : the piston, c, is solid, and when it passes down it closes the lower valve, d, and forces the water through a pipe in the side of the cylinder, which has a valve opening inward. In some cases the water passes into an air chamber, e, and the elasticity of the air renders the stream from the spout constant. The Syphon depends on the same princi- pie. The syphon is' a bent tube, Fig. 146, with one arm longer than the other. If the tube be filled with water, and the short arm placed in a vessel of water, A B, as the column of water in E D falls out, the pressure on the surface of the liquid in the vessel will press it up through C to E with a force equal to the difference of the weight of water in the two arms of the tube, and the vessel will be en- tirely emptied. Tantalus's Cup acts on the same principle, b d l Fig. 147, is Fig. 147. the syphon tube contained in the cup c. When the cup is filled so as to cover the tube, the water passes up b and down d, and as the column in d is longer than that in b, and consequently heavier, as it flows out through a it tends to form a vacuum in the tube ; but this is prevent- ed by the pressure of 'the air, which forces the liquid through b until the cup is emptied. The syphon has been used to drain pits and mines, a tube being placed in the bottom of the pit, and conducted over the edges far enough to bring the other end below that in the well. The syphon is then filled, and the water will flow till the pit or mine How far from the surface of the water may the lower valve be placed ? Describe the forcing pump the syphon and Tantalus's cup. NATURAL PHILOSOPHY. is entirely drained. In this case the depth is limited to thirty- four feet, the greatest height to which the air will sustain a col- umn of water. Intermittent Springs depend upon the same principle. There are some springs which flow for a time and then cease. This is explained hy the fact that the water accumulates in caverns in the earth which have passages in the rocks from the source to the outlet in the form of the syphon. When these fountains are full they commence flowing, and do not cease till their whole contents have been discharged. They are then dry till the reser- voir is again filled, when they again begin to flow. The mode in which these springs are produced may be illus- trated by means of Tantalus's cup. Let the cup represent the cavern in the mountain which is filled with water from the rains, and let the tube d, instead of passing down through the cup, be carried through the side at a small distance from the top. This tube will represent the passage in the rocks from the fountain. Now, when the cup is filled, the water will begin to flow, and continue till the whole is emptied ; but if water is poured into it gradually, it will not begin to flow again until it is full, when it will be emptied a second time. V. Force exerted by Condensed Air upon Solids and Liquids. Hitherto we have considered the force of the air, its pressure and elasticity when in a natural state ; but if it is compressed into a small compass and allowed to expend its force, its elastici- ty will exert a far greater power than in its ordinary state. As air is perfectly elastic, it is highly advantageous for us to avail ourselves of this power in connection with several engines used in the arts. The condensing force may be exerted by a con- densing pump or a column of water. For experiments on the elastic force of air, we may employ the Air Fountain. This consists of a strong copper fountain, Fig. 148, with a tube, a d, extending from the top to the bottom, and with a stop-cock, c. To the end of this tube jets of any form nay be attached. By means of the condensing syringe, b, air I'ow sfi intermittent springs accounted for ? Illustrate the nature of in- v < litteiH: springs by Tantalus's cup. Describe the air fountain. What THE AIR FOUNTAIN. 173 may be forced into the fountain until it has attained a high degree of density. In fact, a force may be generated sufficient to burst the vessel if it is not very strong. It is the elasticity of carbonic acid gas which some- times bursts soda fountains, when too large quantities of this gas are forced into them, and condensed in the water with which they are nearly filled. If we force some air into the fountain, and then apply the revolving jet, the air, rushing out at the sides of the tube and removing the pressure, will cause the jet to revolve with great velocity. This action is similar to that of Barker's Mill (page 144). The Air Gun is similar to the fountain, only the bulb is smaller arid made very strong. If the air be compressed in it about 1600 times its volume, and then allowed to exert its elas- ticity upon the ball, it will propel it with the force of gunpowder. A ball is driven from the ordinary gun by the elastic force of the gases which are formed by igniting the powder. But the force of compressed air in the fountain is shown in a more satisfactory manner by partially filling the fountain itself with water, and then forcing into it a quantity of air. The elas- tic force of the air will be exerted upon the surface of the water, and by means of tubes which allow the water to pass through them, a beautiful jet may be formed, which will spout to a great height, and may be made to sustain a small ball placed upon its summit. A revolving jet may also be used. The water, in this case, will form a disc of spray, as shown in the figure. Sometimes it is desirable to make use either of the pressure of water or of its force through other mechanical media. In these cases the elasticity of air is often employed, by which water is raised to a great height, and made to flow in a continuous stream. Thus, in What is the principle of the air gun ? What is the force of gunpowder due to? How are jets of water produced by the air fountain? 174 NATURAL PHILOSOPHY. Hiero's Fountain, by the pressure of a column of water, a jet is thrown far above the level of the water in the fountain. The fountain consists of two globes of glass, A B, Fig. Fig. 149. 149, connected by tubes, a b. One of the tubes, a, passes, to the bottom of the lower globe, and ex- tends to the top of the plate or cup, D. A second tube commences near the top of the ball A, and extends into the top of the ball B. A third tube, with a jet, passes into the ball A and up through D. When the upper ball is filled nearly full of water, and a small quantity poured through the tube a, by which it descends into the lower ball, B, the air which it contains will be compressed, and the pressure will be communicated through the tube b upon the air in A. This pressure will be exerted upon the surface of the water in A, and force it out through the tube e in the form of a jet. As the water spouts up it falls back into the cup D, and runs down into the ball B, and by this means a constant pressure is kept up on the surface of the water in the lower bulb. The fountain will continue to play, therefore, until all the water is transferred through the jet pipe from A to B. To the forcing ^pump there is usually attached a small ball containing air (see Fig. 145). As the water is forced into this ball, the air is condensed, and by its elastic force the stream is kept constantly flowing. The Fire Engine combines the principle of the forcing pump in connection with the elasticity of compressed air. There is also usually connected with it a suction or lifting pump, to supply the well of the engine with water from some cistern or reservoir in the earth. Hungarian Machine. This apparatus was employed to drain a mine in Hungary, and depends for its action upon the elasticity of air, the compression being produced by a column of water, as in Hiero's Fountain. Thus p, Fig. 150, represents a tube, into the top of which water is made to flow from a small stream. The lower end of Describe Hiero's fountain. On what principle does it act ? Of what use is condensed air in the fire engine and forcing pump? Describe the Hungarian macnine. PROBLEMS. 175 Fig. 150. this tube passes nearly to the bottom of an air-tight box,/. Into the under side of the box a tube, d, passes down the side of the pit into the top of a similar box, which has a valve, a, in its bottom to admit the water. A third tube, g, also extends to the bottom of this box, so as to dip under the water, and passes over the sides of the mine, e. Now, when the water is let into the tube p, it fills the box f partially full of water, which con- denses the air in the upper part of it. This condensed air transmits its force through the tube d to the air in a, which presses upon the surface of the water, and forces it up through the tube g to the out- let of the pit. A pressure of 260 feet of water in the pipe p raises the water in the mine to the height of 96 feet, where it flows off by a side drain. PROBLEMS. 1. A gas bag, half full of air, was placed under the receiver of an air pump, and the air exhausted from the receiver until the expanded air filled the bag. What amount of pressure was re- moved from ach square inch of the surface of the bag ? Ans. 7* Ibs. 2. An EBronaut having filled his balloon three quarters full of gas, ascended till the gas expanded and filled the balloon. On the supposition that his body sustained a pressure of 14 tons at the surface, what pressure would it sustain at the height which he had then attained ? Ans. 10 tons. 3. A barometer at the foot of a mountain stood at 30 inches ; on carrying it to the top, it fell 10 inches. What was the den- sity of the air at its summit compared with its density at its foot ? Ans. fds. 4. Into an air fountain containing 1 cubic foot of space above the water, there was forced sufficient air to raise a column of water in a tube, the section of which was 1 square inch, to the height of 68 feet. What was the quantity of air forced into the fountain ? Ans. 2 cubic feet. 176 NATURAL PHILOSOPHY. 5. To what depth in the sea would it be necessary to sink a bag filled with air in order to compress it half of its volume ? Ans. 34 feet. 6. A receiver containing 1 cubic foot of air was exhausted till the mercury in the gauge stood at 20 inches. What portion of the original quantity of air still remained in the receiver ? 7. A barometer which stood at 29-5 inches at the foot of a mountain, was carried to its summit, where it stood at 27 inches. What was the height of the mountain above the valley ? Ans. 2175 feet. 8. At the foot of a mountain water was found to boil at a tem- perature of 210 degrees ; on going to the top it boiled at 200 F. What was the height of the mountain from its base, and what was the height of the base from the level of the ocean, on the supposition that the barometer stood at 30 inches ? Ans. Height of mountain, 5500 feet ; height of base above the ocean, 1100 feet. VI. Diffusion of Air through other Matter. In consequence of the great weight of the air, its perfect fluidity, and attraction for other matter, it penetrates among the atoms of all solid, liq- uid, and gaseous bodies whose pores permit it to enter. This fact may be proved and illustrated by numerous experiments. Thus, 1 . Air diffuses itself among the atoms of Solids. Exp. Take any porous body, as a piece of charcoal, and confine it at the bottom of a jar of water. Place the jar under the exhausted receiver of the air pump, and bubbles of air will be liberated from the solid and pass up through the water. An egg, a piece of bone, a piece of dry wood, and some mineral substances, will exhibit the same appearance. 2. Air is absorbed by Liquids, or diffuses itself among their particles. This is partly due to its pressure, and partly to an attraction which each has for the other. Exp. Take a jar of water, and, having placed it under the receiver, exhaust the air. As the pressure is removed from the surface of the water, fine bubbles of air will rise to the surface. If a glass of porter, or any other fermented liquor, be taken, Fig. 151, the bubbles of carbonic acid gas will be much larger, and the effect much more satisfactory. It is this acid which is contained in beers, in soda water, and in the waters of cer- tain springs, as at Saratoga (New York), and which gives them their pungent and pleasant taste. What experiments to show the diffusion of air through solids and liquids? DIFFUSION OF AIR. 177 It is owing to the air contained in water that fish are able to exist in it. If they are placed in a portion of water from which the air is removed, they will soon die, because the oxygen of the air is necessary to purify their blood. In performing the experi- ment upon fish under the receiver of an air pump, they will rise to the surface after a few strokes of the piston, owing to the ex- pansion of the air in the air bladder within them, and, by con- tinuing to exhaust the air, the bladder will burst, and they will sink to the bottom of the vessel. 3. Air diffuses itself through other Gases. The power of gases to diffuse themselves through each other is quite remark- able. The fact may be shown experimentally, with regard to any two gases, by confining them in jars, and allowing them to communicate with each other. Fig. 152. Thus, if we take a jar of hydrogen gas, H, Fig. 152, which is several times lighter than air, and invert it over a jar of air, C, the hydrogen will descend into the lower jar, and the air, at the same time, rise into the upper jar. In a short time they will be mingled, as may be proved by transferring the gases from each jar separately into a hydrogen pistol and explo<^g them. The same diffusion takes place when a jar of air ia placed over one of carbonic acid, though the air is much lighter than the acid. The law which governs them, as they mingle with each oth- er, has been ascertained by experiment, and it is found that The velocities with which Gases flow into each oilier are in- versely as the square roots of their densities. Hence the veloci- ty of the lighter gas is much greater than that of the heavier gas. Thus, if air were sixteen times as dense as hydrogen, it would flow with but one quarter of the velocity. This tenden- cy to diffusion is manifested most strikingly when there is a por- ous partition, as a stopper of plaster of Paris, between the two gases. Gases will also mingle through substances which are not considered porous. Hydrogen gas in a soap bubble will pass out, and air will pass in. How are fish enabled to exist in water ? What is the law when gases mingle with each other? Which has the greater velocity ? H2 178 NATURAL PHILOSOPHY. VII. Buoyancy of the Air.-^WQ have seen that water will float bodies specifically lighter than itself. The same is true of the air. This is due to its weight or pressure. Hence a balloon, Fig. 153, filled with hydrogen gas or with heated air, will be carried up into the atmosphere in the same manner that a cork when placed un- der water will rise to its surface. The heav- ier air surrounding the balloon lifts it up by its superior pressure ; hence, if the surface of a body is increased, while its quantity of matter remains the same, it will be buoyed up. If, therefore, a body be weighed in air, it will weigh less than if weighed in hydrogen gas or in a vacuum, just as a body will weigh less in water than in air. Now, as the power of any fluid to sustain bodies in it depends upon the sur- face exposed, the quantity of matter being the same, it will be easy to see that the same quantity of matter in its most concen- trated form, that of a sphere, would weigh in air more than when made into a large hollow balloon. Hence it is true that a 'J^ound of feathers is heavier than a pound of lead ;" that is, contains a larger quantity of matter. Exp. This principle may be illustrated by a thin glass globe, Fig. 154, balanced by a metal weight in air. When placed under the receiver, and the air exhausted, the glass will be seen to be the heavier. It is owing to the buoyancy of the air that smoke and clouds are borne up by it. VIII. Resistance of the Air. Air, as well as water, opposes a resistance to bodies passing through it. The force of resistance is as the square of the velocity. Hence, in rapid motions, as that of a cannon ball, this force becomes very great. It has been found difficult to give a cannon ball a velocity of 2000 feet per second. When the velocity is more than about 1280 feet per sec- ond, the resistance is suddenly augmented. This is due to the fact that the velocity of air flowing into a vacuum is about 1280 feet per second, and above this velocity the pressure is removed from the back of the ball, the air not flowing in to equalize the pressure. What example of the buoyancy of the air ? What is the law of resist- ance to bodies passing through the air? RESISTANCE' OP THE AIR. 179 It is owing to the resistance of the air that bodies falling through Fig. 155. it are retarded in proportion as their surfaces are enlarged. Were it not for this resistance, all bodies would fall from the same height in the same time, whatever their size or weight. Exp. To illustrate this principle, take a guinea and feath- er, or piece of paper, and suspend them in a long glass tube, Fig. 155. By allowing these to fall in the tube filled with air, it will be seen that the guinea falls with a much greater velocity than the feather. On exhausting the air, they will fall in the same time. It is owing to the resistance of the air that wind- mills, fans, and fan-mills are made to revolve. As the force of resistance depends upon the extent of surface exposed, their power may be increased with an increase of surface ; and by so arranging the wheels and floats that the rotary motion shall cause the fans to cut the air, while the propelling force of the wind strikes upon the broad surface of the fan, a large proportion of the force of the wind is made effective to turn the mill. To illustrate this difference, take two thin fans, fastened to an axis having two centers, so that it may revolve either flatwise or edgewise, and present first the broad surface and then the edges to the air, and turn them rapidly with the finger. In the former case they will soon stop, in the latter they will continue to re- volve for some time. Or two fan- wheels, Fig. 156, may be made to revolve first in a vacuum and then in the air ; one, b, with its broad surfaces ex- posed to the air in each case, and the other, a, with its edges, and their speed will be found to differ greatly in the air, but to be exactly equal in the vacuum. The sky-rocket, and many articles used in pyrotechny, depend upon the resistance of the air. As this resistance increases with the square of the velocity, it is found by What principle do the guinea and feather illustrate? How may the force of wind-wheels be increased ? Illustrate. Upon what force does the ascent of the sky-rocket depend ? Fig. 156. 180 NATURAL PHILOSOPHY. experiment that a train of cars running at the rate of fifty or sixty miles per hour, requires a very great addition of force to overcome the resistance of the air. Especially is this the case if the air is moving in the opposite direction. IX. Motion of the Air and other Gases. When air or any other gas is placed in any vessel, as in the air fountain, and an aperture made, it will flow out, provided its density is greater than the surrounding air. The laws by which its motion is reg- ulated through thin walls and through tubes are very similar to those which pertain to the efflux of liquids, which we have al- ready considered. When air is condensed in the air fountain and allowed to escape, its velocity decreases in a similar manner to that of a liquid spouting from an orifice near the bottom of a ves- sel filled with water, and allowed to empty itself. But if the compressing force is a column of water, which is kept constantly at the same height, as is the case in the gasometer, then the velocity of the efflux is constant, and is similar to that of a liquid spouting from a vessel kept constantly full of water. The Gasometer, Fig. 157, is simply a cylindrical vessel, G, open at the bottom, and sunk in a well, w, or similar cylinder open at the top, and filled with water. The gas is conducted through the water, and lifts the gasometer as it fills. A force r then may be applied, by means of weights, which shall cause the water to rise higher on the outside than on the inside of the gasometer, and, of course, as the gas flows out through an open- .*,, c, the weights cause the gasometer to sink, so that the height of the water is the same until the whole is discharged. The amount of condensation will depend upon the height of the water column, which may be increased or diminished by adding larger or smaller weights to the gasometer. A gauge, h i, is sometimes applied to pipes conducting air, for the purpose of ascertaining What conditions are necessary to the motion of gases? What laws regu- late the efflux of gases ? Describe the gasometer. What is the use of tha gauge ? Fig. 157. MOTION OF GASES. 181 the amount of pressure. The difference between the height of the column of water in the two arms of the gauge will indicate the amount of pressure. The velocity of gases and the quantity of efflux are determin- ed in the same way as in the case of liquids, but the degree of elasticity, which is the impelling force, is represented by a col- umn of water, since air is not of equal density. A column of water 34 feet high will reduce the volume of a confined portion of air one half, or will double its density. Now the velocity* of air thus condensed will be equal to that which a falling body would acquire in falling through a perpendicular height represented by the column of water. Water is about 770 times the density of air, so that the height in this instance would be 770 times 34 feet, or 26,180 feet ; and the velocity acquired by a body falling through this space would be about 1294 feet per second (see page 66). Now the pressure of the air at the surface in reference to a vacuum is precisely similar to the condensed air in the above example in relation to air at the common density, and hence air would flow into a vacuum about 1294 feet per second. The ve- locity is generally estimated, however, at 1280 feet, as air at its medium pressure will not sustain a column of water quite 34 feet in height, and, of course, the height of the air column would be less than in the above estimate. The velocity and quantity are influenced, also, by the orifice, as in the case, of liquids, so that the actual quantity discharged in a given time will be somewhat less than the theory requires. The lateral pressure of gases, as air, in conducting pipes, is similar to that of water. Long tubes, in consequence of friction, diminish the velocity and quantity of efflux. The resistance pro- duced by the friction is proportioned to the length of the tube ; but the larger the tube, the less the resistance, or the resistance * Let =the intensity of the force of gravity in the latitude of New York for one second =16 T V feet. Then we shall have the formula v=. SiVgh; h representing the height of the air column, which, of course, will vary with the degree of density of the compressed air. How is the velocity of air flowing into a vacuum determined ? What in- ftuence have conducting pipes upon the velocity of gases flowing through them? 182 NATURAL PHILOSOPHY. is inversely as the diameter of the tube, and increases as the square of the velocity of the flowing gas. There is also a " con- tracted vein," as in the case of liquids, though it can not be di rectly observed, and hence short tubes increase the quantity of efflux. When air is condensed and flows through an aperture in the side of a vessel, or through a tube which is terminated by a flat disc, there is produced the phenomenon of suction; that is, a partial vacuum is formed near the sides of the opening. Thus, if a tube, p, Fig. 158, with a disc, b c, be inserted in the air fountain, and a card or piece of metal, a, two thirds the diameter of the disc, placed upon it, directly over the aperture, the card can not be blown off by the force of the condensed air, but, after the first impulse, will vibrate at a very short distance from the aper- ture, while the air will rush out between it and the disc with considerable noise. A pin should be forced through the center of the card, extending into the aperture, to keep the card in its place. This singular fact is thus explained : As the air moves with greater velocity at the center than at the sides of the tube, the moment of its escape through the top of the disc, its lateral press- ure causes it to be spread in a thin layer between the disc and the card, by which a partial vacuum is formed around the side and over the disc, as represented in Fig. 158, and the external pressure of the air confines the card firmly to the disc. This principle is no doubt the cause of the effect produced by certain fixtures for the purposes of ventilation. SECTION II. THE ATMOSPHERE. METEOROLOGY. The atmosphere is that gaseous fluid which, surrounds, the earth. The description and explanation of its phenomena con- stitute the science of Meteorology. I. The iveight of the atmosphere is determined by means of the barometer, and is sufficient to counterbalance an ocean of mercury encircling tJib earth 2-5 feet in depth, and a similar ocean of water 34 feet in depth. How is the phenomenon of suction explained ? WEIGHT OF THE ATMOSPHERE. 183 II. The density of the atmosphere diminishes as we ascend from the surface of the earth in a geometrical ratio, as the height increases in an arithmetical ratio. . III. The Jieight of the atmosphere is about 50 miles. This is determined by the limit which is put to its elasticity by the weight of its particles at that height, and also by the phenomena, of the refraction of light. IV. The temperature of the atmosphere diminishes from the equator toivard the poles ; and, as we ascend above the surface of the earth, the thermometer sinks about one degree for every 352feet. V. The motions of the atmosphere, or the phenomena of winds, are occasioned by the unequal distribution of heat. Winds are variously named, as trade winds, land and sea breezes, hurri- canes, tornadoes, fyc. VI. The moisture of the atmosphere varies at different places, and at the same place at different times. The quantity of moist- ure is ascertained by means of the hygrometer. Its condensa- tion gives rise to dews, frosts, clouds, rain, snow, and hail. VII. Meteorolites and electrical phenomena may also be in- cluded in a description of the atmosphere. Also VIII. Its relations to animals, and to the principles of IX. 'Ventilation, or the laivs ivhich pertain to the draughts of chimneys, and the processes by which foul air is withdrawn from the apartments of buildings and pure air introduced. HAVING considered the properties of air, we are now prepared to study the phenomena of the atmosphere, its weight, density, height, relations to heat, moisture, winds and dews, electrical changes, &c. The description and explanation of the phenom- ena of the atmosphere constitute the science of Meteorology. I. Weight of the Atmosphere. The weight of a column of air of one square inch in surface, extending to the top of the atmo- sphere, is sufficient, as we have seen, to sustain a column of mer- cury two feet and five tenths in height, and a column of water thirty-four feet in height. This mercury weighs fifteen pounds, How is the weight of the atmosphere determined ? 184 NATURAL PHILOSOPHY. or, more exactly, fourteen and seven tenths. Knowing the weight of air pressing upon one square inch of surface, it is easy to cal- culate the weight of the whole atmosphere ; for if we can de- termine the number of square inches contained in the whole earth's surface, and then multiply these by fifteen, it will give us the absolute weight of the whole atmosphere. The number of square inches on the surface of our globe is found by multiply- ing the circumference by the diameter, or four times the square of the radius of the earth by 3*1416. The weight thus calcu- lated is found to be more than eleven trillions of pounds, or five thousand billions of tons. This weight would be sufficient to counterbalance an ocean of mercury encircling the earth 2' 5 feet in depth, or an ocean of water 34 feet deep. II. Density of the Atmosphere. The density of the atmos phere at the earth's surface is determined by the weight of a given quantity at the standard temperature and pressure, com- pared with an equal weight of water ; for, as atmospheric air is taken as a standard by which to compare other gases and vapors, its density must be determined by that of some other body of known density, as water or mercury. Air is found to be about TT i_^ths as dense as mercury, and T y oths as dense as water. It is not constant in its density ; at a medium pressure its density is Tj-i^th, the specific gravity of water being 1, that of mercury 13- 6. The density of the air is not equal throughout its whole ex- tent ; for, as the air is an elastic fluid, the lower strata are pressed upon by those above them, and, as we rise above the level of the sea, the density of the atmosphere diminishes in a definite ratio ; for, according to the law of Mariotte, The volume of the air is inversely as the compressing force ; and, as we ascend, the compressing force constantly diminishes. This decrease of pressure is indicated by the barometer. It is found by observation, aided by calculation, that at the height of seven miles it is but a quarter as dense as at the surface of the earth. Now, as this distance is doubled, the density is one quar- To what is it equal ? What is life density of air at the surface of the earth 1 Does it decrease in density ? According to what law 1 Illustrate the law of Mariotte. DENSITY OF THE ATMOSPHERE. 185 ter as great, or T Vt^ at three times the distance, ? ' T th as great. Hence, if we take the series 7, 14, 21, &c., we shall find that the density will "be , T V, Q\, &c. ; or, if the heights form an arithmetical series, the densities diminish in a geometrical ratio.* At the height of twenty-one miles, therefore, the atmosphere is sixty-four times rarer than at the surface of the earth, and at the height of one hundred miles one thousand million times rarer. On the other hand, if the atmosphere were allowed to enter the earth through an aperture in the direction of its center, its density would increase by the same law. At the depth of seven miles, it would be four times as dense as at the surface ; ' at four- teen miles, sixteen times as dense, giving the series 7, 14, 21, 28, 35, 42, 49, 56, 4, 16, 64, 256, 1024, 4096, 16384, 65536. The air would be denser than water at thirty-five miles, densei than mercury at forty-nine miles, and denser than platinum or any known body at fifty-six miles. Olmsted. If there were no disturbing causes, the exact density of the air at different heights might be accurately defined. But there are several facts not yet noticed which must be taken into account. The upper portions of the atmosphere are further from the earth's center ; and, therefore, as the force of gravity diminishes as the square of the distance, particles of air in the upper strata weigh less than those in the lower. The attraction of the sun and moon * The following table by Mr. Lubbock shows the constitution of the at- mosphere according to the most accurate observations hitherto made : Height in Miles. Pressure. Temperature. Density. 1 Inches. 30-00 24-61 Fahr. 4-50-0 35-0 1,00000 ,84611 2 20-07 19-5 ,71294 3 4 5 10 16-25 13-06 10-41 2-81 +3-4 13-3 30-6 126-4 ,59798 ,49903 ,41403 ,14499 15 45 240-6 ,03573 What would be the law of increase of density if the air extended toward the center of the earth ? What causes interfere with the law of the de- crease of density ? . 186 NATURAL PHILOSOPHY. is also greater the nearer the atoms are to diem, which will tend to render them lighter. In the upper regions of the atmosphere, too, heat and cold, and the formation of clouds interfere, in some degree, with the law. As heat expands, and cold contracts, and moisture diminishes its weight, in determining the exact density of the atmosphere, all these circumstances, except perhaps attraction, which is exceed- ingly small at ordinary heights, must be considered. III. Height of the Atmosphere.* If the air were of uniform density we could easily determine its height, since the heights of any two fluids are inversely as their specific gravities. Since, then, the specific gravity of air is to mercury as 1 to 11500, its height would be obtained by this proportion 1 : 11500 : : height of a column of mercury 30 inches : height of the atmosphere ; or, 1 : 11500 : : 2'5 ft. : 28750 =5 miles. On the other hand, if we apply the law, That the density diminishes in a geometrical ratio as the height increases by an arithmetical ratio, it is evident that the atmos- phere would be unlimited in extent, reaching to the most distant regions of space. But there are several reasons for believing that the atmosphere is limited, and that we may determine its height very nearly. 1 . The elasticity of the air is produced by a mutual repulsion between its particles ; but this repulsion is overcome in the high- er regions of the atmosphere by two causes, the increase of cold, and the attraction of gravitation ; for the force of gravitation de- creases but little at the height of fifty miles, while the elastic force is greatly decreased. At about this height the weight of the particles will overcome their repulsion, and thus prevent the further extension of the atmosphere. 2. This view is confirmed by reference to the phenomena of refraction. Light is not refracted higher than sixty miles, which shows that the space above is destitute of air. What effect have heat, cold, and moisture on the density of the atmos- phere ? How could the height of the atmosphere be determined if the air were of uniform density, and what would be its extent ? How far would the atmosphere extend by Mariotte's law ? What reason for believing that the atmosphere is limited in extent ? TEMPERATURE OF THE ATMOSPHERE. 187 IV. Temperature of the Atmosphere. The temperature of the atmosphere on the surface of the earth is very various. It gen- erally diminishes fi^n the equator toward the poles, but not equally. There are many disturbing causes which tend to in- crease the mean annual temperature* in the same parallel of latitude. Some of these disturbing causes are the situation of the land in reference to water, or to currents in the ocean ; the vicin- ity of deserts or high mountains, and the direction of the wind, also exert more or less influence upon the temperature. These variations are frequently represented on a chart thus : Through those places where the mean height of the thermom- eter is the same during the summer, lines are drawn called isoth- eral lines; and through those places in which the mean tem- perature during the winter is the same, similar lines are drawn, called isochimenal lines. These lines, owing to the various causes above alluded to, are somewhat irregular in their course around the earth, and places which have the same mean annual temper- ature often differ in the extremes of heat and cold during the year. Lines passing through such places are called isothermal. The temperature of the atmosphere as we ascend above the level of the sea is constantly diminishing, until we arrive at a point, varying in different latitudes, where water is congealed. Under the equator we reach this point at about the height of three miles. At the poles it is at the surface of the earth. The lower limit of this region is called ihe*curve of perpetual conge- lation. Hence mountains which rise above this limit are cover- ed with perpetual snow and ice. By numerous observations and calculations which have, been derived from the mean temperature and known decrease of heat at different heights, the line of per- petual congelation has been determined for every parallel of lati- tude from the equator to the poles. * By mean annual temperature is meant the mean height of the thermom- eter during the year. Thus we might ascertain the mean temperature for a single day by noting the height of the mercury for each hour, and then dividing this by 24. The mean annual temperature is sometimes ascertained approximately by the temperature of water in a deep well, which is nearly uniform during the whole year. Is the atmosphere of the same temperature throughout ? What is meant by the curve of perpetual congelation, and what is the form of this curve ? 188 NATURAL PHILOSOPHY. Thus, at the equator, Deg. Ht. in ft. 15577 10 15067 20 ..13719 30.. ..11592 Deg. Ht. in ft. 40 ^ 9016 50 m 6260 60 3684 80.. . 120 This line, it will be seen, approaches near the earth in a more rapid ratio as we approach the poles, though the greatest differ- ence is between forty and fifty degrees. The reason for the cold in the higher regions of the atmosphere is found in two well-known laws. 1. The air is not heated by the sun's rays passing directly through it, but by contact with the heated earth. 2. As each portion becomes heated, it rises up, but not to the top of the atmosphere. As it rises ft expands, and its capacity for heat increases and diminishes its temperature, so that it will soon arrive at a region where the air is of equal density, and there remain. By the heat of the sun, then, the atmosphere is heated only to a limited extent. Above this limit, as the pressure is less, its expansion is greater, and its capacity for heat increases. Hence the air must be colder the higher we ascend. This fact has also been confirmed by aeronauts, who experience the sensation of cold in proportion to their height above the surface. V. Phenomena of Winds. Winds are created by any disturb- ance of the equilibrium of the atmosphere. The principal agent in producing this disturbance is the heat of the sun, which acts unequally in different latitudes arid on different surfaces in the same latitude. The principle upon which winds are produced may be illustrated by reference to very common phenomena. By holding a lighted taper in the crevice of a door when there is a fire in the room, it will be observed that there is a current of air inward at the bottom and outward at the top. The draft of a chimney also illustrates the same fact. When a fire is made, the heated air rises, the colder air of the room flows toward the fire, and the smoke is carried up by the current of air thus produced. When the air in the room is warmer than that What is the cause of the cold in the higher regions of the atmosphere 1 How are winds produced 1 Illustrate the manner in which air is made to circulate in chimneys, &c. WINDS TRADE WINDS. 189 in the chimney, there is a downward current. On this principle, mines are sometimes kept cool and purified of foul air by two shafts, one longer than the other, situated at either extremity of the mine. The air in summer will moVe down the longer shaft and outward at the shorter one. In winter the external air is cooler than that in the mine, and it flows down the shorter and out at the longer shaft. In the spring and fall the air is station- ary, and then the miners complain of bad air. It requires but a slight difference of temperature to produce a draft ; thus, if we take a syphon tube, and put a piece of ice into the long arm, cur- rents of air will circulate through the longer and out at the shorter arm of the tube. The equatorial regions receive the direct rays of the sun ; and the atmosphere, being more heated in those regions, expands and rises up, while the colder air from either pole flows toward the equator to supply its place. Hence we should suppose that the winds would follow the apparent course of the sun. Such is found to be the fact. As such winds flow in definite directions, navigators take advantage of them in crossing the ocean, and hence they are called 1. Trade Winds. The trade winds on the north of the equator are from the northeast, and on the south side from the southeast, extending over a belt of the earth of about sixty de- grees, thirty on each side of the equator. The reason that these currents do not move directly toward the equator, the place of greatest rarefaction, is, that the atmos- phere moves with the earth from west to east, but the velocity is less the further we go from the equator. A current starting at sixty degrees north of the equator, and flowing directly south, passes over portions of the earth whose velocity is constantly in- creasing, and hence the wind, moving toward the east with less velocity than the portions of the earth over which it is flowing, appears to move from the northeast to the southwest ; and, owing to the fact that the earth is moving toward the east faster than the wind is, the latter is in the condition of a body acted upon How are the trade winds produced ? What is the direction of the trade winds ? What causes appear to alter their course ? 190 NATURAL PHILOSOPHY. by two forces, and it describes the diagonal of a parallelogram, or moves in a southwest direction ; for a similar reason, the currents which flow from the south are deflected, and flow in a northwest direction toward the equator. When the northeast trade wind meets the southeast trade wind, they unite and flow toward the west ; but, in consequence of the velocity with which the heated air rises up, their westerly motion is almost perfectly neutralized, and hence there is formed a zone called the region of calm?,. The center of this zone lies a little north of the equator, and varies at different seasons of the year. The air which rises up at the equator flows toward the poles, forming upper trade winds,, which flow in an opposite direction to those below, and as they descend toward the earth, constitute southwest winds in the northern, and northwest in the southern hemisphere. North of the equator, northeast and southwest winds prevail until we reach high latitudes, where they seem to change their direction. The existence of these winds has been ascertained by the direction given to the ashes in volcanic erup- tions when they have risen to a great height, and by the direction of the wind on the summits of high mountains in the region of the trade winds. Thus, at the summit of the Peak of Teneriffe, the winds are almost always from the west, or in a direction op- posite to the trade wind below. 2. Monsoons. Owing to the peculiar configuration of the land surrounding the Indian Ocean, the trade winds are subject to some modification. Thus, in the southern part of this ocean, be- tween New Holland and Madagascar, the southeast trade wind continues during the whole year ; but in the northern part, the wind from October to April is from the northeast, and from April to October from the southwest. These are called monsoons. A series of observations are in progress by Professor J. H. Coffin, which promise to throw much light on the direction of these and other winds. 3. The Simoon, a hot and destructive wind, which prevails in Where is the region of calms, and what is the cause ? How do the up- per trade winds move ? How are monsoons produced ? Describe the si- moon and its cause. LAND AND SEA BREEZES. 191 the deserts of Asia and Africa, is produced by the air becoming in- tensely heated over the sands of the desert. When this air attains considerable velocity, it takes up the fine sand, which, being ex- ceedingly dry, becomes very injurious to travelers in those regions. There are also very dry and cold winds, called the Puna Winds, which prevail on the high table lands of the Cordilleras in Peru. 4. Land and Sea Breezes are due to the unequal action of the rays of heat upon the land and water. During the day the land and sea receive equal quantities of caloric from the sun, but the land becomes more heated than the water, and, consequently, the air over it is more expanded and rises up, while the cooler air from the sea flows in to maintain the equilibrium. During the night the earth radiates its heat more rapidly than the sea, and as it grows cooler, the atmosphere is condensed and flows toward the sea. These changes near the sea are very grateful during the warm season. The sea breeze does not set in till near midday or after, nor the land breeze till after midnight, as it requires some time for the change to take place. Between the two there is general- ly a calm, showing that there is an equilibrium in the tempera- ture of sea and land. 5. Hurricanes are produced by the meeting of opposite cur- rents of air, and by upward currents. They prevail most exten- sively in tropical latitudes. They have, at the same time, a rota- ry and a progressive motion. According to the observations of Mr. Pvedfield, the Atlantic hurricanes originate a little east of the Caribbean Islands, and pass in a northwest direction to the tropic, and from thence their course is northeast. They rotate in a direction opposite to the apparent motion of the sun. South of the equator they observe a similar law, but move in exactly opposite directions, passing toward the southwest till they arrive at the southern tropic, and from thence toward the southeast, and rotating in the same direction with the sun. Explain the manner in which land and sea breezes are produced. How are hurricanes produced ? Where do the Atlantic hurricanes commence, and what is their course ? 192 NATURAL PHILOSOPHY. All our northeast storms are great whirlwinds. They are spread over large areas, often extending for thousands of miles. Their velocity varies from 7 to 30 or 40 miles per hour, and hence the mechanical effects which they produce are very various. In consequence of their rotary motion, the air in their center becomes rarefied, and that on the edges of the storm condensed. If the center' of the storm pass over the place where the experi- ment is tried, the barometer will rise at the commencement, will fall at the middle, and rise again at the close of the storm. The wind, also, will change to all points of the compass, and hence sailors generally know when they pass into the center of the whirlwind, from the sudden calm which exists, called the lull of the tempest. 6. Tornadoes are whirlwinds of limited extent, in which the rotary motion becomes so violent as to tear up trees, overturn buildings, and level every 'thing in their course. They sometimes move at the rate of 60 miles per hour. They occur mostly in the torrid zone. The rate at which winds move is very various. A gentle breeze moves from 6 to 10 miles per hour ; a storm, 30 ; a tor- nado and hurricane, 60 miles per hour. 7. Water Spouts result from whirlwinds passing over water By their rotary motion they take up the water in a large column in the same way that they take up straws and light bodies on the earth's surface. These whirls seem to originate in the upper Fig. 159. Fig. 160. Fig. 161. What are our northeast storms? How do they affect the barometer? What are tornadoes? At what rate do winds move? How are water spouts formed ? MOISTURE OF THE ATMOSPHERE. 193 regions of the atmosphere. They are conical or funnel-shaped. Sometimes their points do not reach the earth. Usually they appear in the form of a dark cloud, as in Fig. 160, which comes down to the water, and carries up a column, giving a loud and hissing sound, due to the violent agitation of the water in the whirling spout. The forming spout is represented at Fig. 159, the spout when fully formed at Fig. 160, and the spout as it breaks and passes away in Fig. 161. VI. Moisture of the Atmosphere. The atmosphere contains variable quantities of watery vapor, which rises up from evapo- ration. This process, which is very active in warm climates, is carried on at all places on the earth's surface, even from the po- lar snows. The quantity of vapor depends simply upon the tem- perature ; and as the temperature becomes rapidly cooler in the upper regions, the moisture is deposited in the form of clouds, which consist of hollow vessels of water. ' When these unite they produce rain, hail, or snow, according to the temperature of the region and the circumstances under which they are formed. The quantity of watery vapor in the atmosphere is constantly varying, and the amount at any time may be determined by means of Hygrometers. These are of several kinds. That invented by Saussure depends upon the property which the human hair has of contracting when dry, and lengthening when exposed to moist- ure. But the one commonly used is DanielVs Hygrometer, which depends for its action upon the temperature at which dew is formed, called the Dew Point. If the air requires to be cooled but slightly before it will deposit dew, then it is very moist ; if it require to be cooled a number of de- grees before the dew is deposited, it is dry. By ascertaining, then, the difference between the temperature of the atmosphere and the dew point, we may determine the quantity of moisture which the atmosphere contains. Darnell's hygrometer, by which the dew point is ascertained, W hat causes the moisture of the atmosphere ? What condenses it ? How is the quantity determined ? Describe the principle of hygrometers. De- scribe Daniell's hygrometer. 194 NATURAL PHILOSOPHY. Fig. 162. consists of a tube with two bulbs, a b, Figure 162. The bulbs are free from air, and one of them, b, made of black glass, is about half full of ether. A thermometer, d, is placed in the stem c, just dipping into the ether, to ascertain the temper- ature of the bulb, and another thermometer is placed on the standard to measure the tem- perature of the air. The bulb a is covered with a piece of muslin. Now, on pouring upon a a small quantity of ether, it will become cool by the evap- oration, and the vapor of ether within it will be condensed. This will remove the pressure from the ether in #, and it will evaporate, absorbing caloric from the bulb, by which its temperature will be diminished. The temperature of c d at the moment that dew begins to form on the surface of the black glass is the temperature of the dew point ; the temperature of the air is indicated by the thermometer on the standard; and from these observations, by means of tables constructed for the purpose, we can determine the quantity of moisture in the atmosphere. Thus it has been found by experiment that in 35.3+ cubic feet of air, at a temperature of 172 F., 264*93 grains of water may be contained. The air is then exactly saturated with wa- ter, and this is the dew point. Now, by repeating the experiment for each degree of tempera- ture, and ascertaining the quantity of water which the 35'3-f- cubie feet of air is capable of containing, we may construct a table by which the quantity of moisture in the atmosphere at any given time may be determined. As the quantity of water in the atmosphere depends upon the temperature, there is more in the summer than in the winter ; What is the dew point, and how does it show the state of the atmosphere as it respects its moisture ? How are the tables made out to ascertain the quantity of water in the atmosphere by the hygrometer ? When does the Atmosphere contain most moisture ? DEWS MISTS CLOUDS. 195 though, from the fact that the heat causes the warm air to ascend to a greater height in the summer, the difference near the surface is not easily detected ; in fact, owing to the greater diffusion of the moisture, the air is generally drier in summer than in winter. The absolute quantity of water is at its minimum in January, and at its maximum in July. The quantity also varies during the day. As the heat in- creases, larger quantities are evaporated ; but, owing to its great- er diffusion, it is drier from 9 A.M. to 4 P.M. than during the remaining 24 hours. The air over places near large bodies of water, as the sea-shore, generally contains more moisture than that in the interior of the country. The moisture also diminishes in going from the equa- tor to the poles. 1 . Dew. The formation of dew depends upon principles al- ready stated. The earth cools during the night, and the strata of air, saturated with moisture, come into contact with the cold earth, and a portion of the vapor is condensed. As all bodies do not radiate heat with equal facility, the dew will be deposited un- equally. Grass and leaves cool more rapidly than mineral sub- stances, and hence receive a greater quantity of dew. When clouds are formed, they impede the radiation of heat from the surface, and little or no dew is deposited. A brisk wind also in- terferes with the formation of dew by bringing the warm cur- rents of air in contact with the surface. 2. Hoar-frost is frozen dew. Mist, fog, and clouds consist of vesicles of water suspended in the air. 3. Mists and Fogs are produced over rivers and lakes in con- sequence of the difference of the temperature of the air. When the water is warmer than the air adjacent to it, the mingling of colder air will cause a deposit of fog ; or when the air over the water is colder than that upon the land, a similar deposit takes place by the intermingling of warm and cold currents. 4. Clouds are nothing but mist deposited in the higher regions of the atmosphere. They consist of small hollow vesicles which How does the moisture vary at different places ? What is the cause of devr of hoar-frost ? What are clouds 1 196 NATURAL PHILOSOPHY. are a little heavier than the air, but they sink very slowly, and, on reaching lower strata, they are dissolved from increase of tem- perature, and are borne about by the currents of air. They are constantly forming in consequence of the cold and warm currents which are intermingling, or from the upward currents of air, which become cooler as they ascend, and deposit their moisture. This is the reason that clouds are formed on the tops of mount- ains. The air, in passing up their sides, becomes cooler, arid its moisture is deposited, and forms a cap or wreath upon their summits Clouds are distinguished by several epithets, as Feathery Cirrus, which are the highest ; Cumulus, which are more dense ; Stratus, consisting of horizontal streaks ; Fleecy, Rainy or nimbus, &c. The height of the feathery clouds has been determined in some places to be at least 20,000 feet, and the vertical depth of some was ascertained to be from 1200 to 1400 feet. 5. Rain. When, by the condensation of vapor in the atmos- phere, the vesicles of mist become more and more dense, they be- gin to fall rapidly, and, uniting with others in their descent, form into drops, which descend to the earth in showers of rain. The formation of rain, then, is precisely similar to that of clouds and mist, the mingling of cold and warm currents of air. Quantity of Rain. The quantity of rain which falls at any place during the year may be determined by means of a rain- gauge. This consists of a cylinder of a given diameter, in which another cylinder is placed with an aperture in its bottom, through which the water that falls may pass into the first cylinder, and the quantity measured by means of a gauge for that purpose. The quantity of rain varies in different latitudes, generally de- creasing as we go from the equator to the poles. There is also more in summer than in winter. Within the tropics there are alternate seasons of rainy and dry weather, which continue from four to six months each. Some countries are so situated, as Egypt, that no rain ever falls, and others where it rains most of the year. Why do they form and disperse so rapidly? Why are mountains often capped with clouds ? Mention the different kinds of clouds. How is rain formed ? How is the quantity of rain which falls in a given time ascer- tained ? What variations in different latitudes ? RAIN SNOW HAIL. 197 In the south of Europe there are annually about 120 rainy days ; in central Europe, 146 ; and in the northern portions, about 1 80 rainy days. But the quantity does not depend upon the number of rainy days ; for, though the number increases as we go north, yet the quantity of rain is greater near and within the tropics. 6. Snow. Snow is produced by the condensation of vapor, but exactly how the flakes are formed is not ascertained. It is probable that the mist is not in the form of vesicles, but of small ice crystals, which in their descent enlarge and fall in snow-flakes. The form of the snow-flake is very various, yet they are all ref- erable to a hexagonal star, belonging to the same system of crys- tals as quartz or the rock crystal. These forms are not only va- rious, but exceedingly beautiful, especially when examined by a microscope. Snow is sometimes colored red and at others green. This is found to be due to a certain species of plant, a fungus which has the power of vegetating in the region of eternal frosts and snows with the same luxuriance that other plants manifest when placed in the more congenial earth. 7. Hail is usually formed just before a thunder storm. The stones consist of a nucleus with concentric layers of ice. It is difficult to explain exactly how they can be retained in the at- mosphere until they have attained so large a size ; some have been found weighing 12 ounces. Their occurrence is attended with very sudden changes of temperature, and also with thunder and lightning. Volta has suggested that there are two clouds situated above each other, and the hail which is first formed in the upper cloud falls to the lower, which is highly electrified ; then the stones, be- coming also electrified, are repelled, and sent back to their start- ing point, and thus they are passed back and forth until their size becomes so great that they fall to the earth. It is difficult, however, to conceive how^ the electricity of the What is snow, and how is it formed? What is the cause of its color? Under what circumstance* is hail formed ? How is its formation explained ? What objection to Volta'i theory? 198 NATURAL PHILOSOPHY. two clouds could exert such a force without passing through the air and forming an equilibrium, which of course would destroy their power of sustaining the hail in accordance with the above theory. There is no doubt, however, that hail is produced by sudden condensation of vapor, in connection with very cold strata of air through which it falls. The size of the stones would nat- urally increase by the condensation of moisture upon their sur- faces as they descend toward the earth. VII. Meteorolites. The atmosphere is the occasion of phenom- ena, in consequence of bodies passing through it or undergoing changes in it, which have been described under the terms Fall- ing Stars, Fire-balls, arid Meteoric Stones. 1. Falling Stars are so called because they resemble stars, though their light is rather more diffused. They fall through the atmosphere from a height of from 20 to 30 miles, with a velocity of 15 or 20 miles per second. The most remarkable circumstance to be noticed is, that they are more. or less periodical, the periods returning annually about the 13th of November and the 10th of August. One of the most remarkable of these showers of stars occurred on the 13th of November, 1833, in which, during the space of 9 hours, there fell, according to calculation, about 240,000 meteors. They ap- peared to radiate in all directions from a point a little south of the zenith, and flowed down like flakes of snow toward the hori- zon ; some of them passing below the horizon, and others going out after passing a short distance from their starting point. Va- rious theories have been proposed to account for them, but their origin is not yet fully known. 2. Fire-balls appear to be of the same nature, and only differ from falling stars in their greater size. They sometimes appear as large as the full moon, and pass in all directions through the atmosphere. They explode with one or more reports, and send down to the earth masses of matter called Meteoric Stones, which fall with great velocity and bury themselves in the earth. When first fallen they are very hot, and exhibit marks of fusion. They have a peculiar appearance by which they are easily distinguish- What are moteorolites, falling stars, and fire-balls 1 METEOROLITES. 199 ed. They generally contain, a portion of native iron and a bitu- minous crust. The iron is not always pure, but alloyed with a small quantity of nickel. 3. Stony masses have been found, of great weight, in different parts of the earth, whose origin has been ascribed to the same cause, and hence are called Aerolites. They weigh from a few ounces to several hundred pounds. These stones appear to be solid bodies circulating about the earth, and when they are brought within the atmosphere, their great velocity compresses the air, and its latent heat becoming developed, gives rise to the light, heat, and consequent explosion which usually attend their appearance. By this means a portion or the whole of the mass is precipitated to the earth. The Color of the Atmosphere is due to the refraction and re- flection of light. There are other phenomena of the atmosphere, such as halos, the rainbow, thunder and lightning, which are con- nected with electricity and light, and will be better understood in connection with those subjects. VIII. Relations of the Atmosphere to Animals and Vegeta- bles. The relations of the atmosphere to organic nature are most t intimate and highly important. Its density and perfect fluidity are such that animals move about in it without any sense of its presence, unless it is in rapid mo- tion, and yet its influence is constant, and absolutely essential to the existence of animal and vegetable life. 1. The inhabitants of countries situated far above the level of the ocean, where the air is more rare, have generally larger chests, in order to obtain the requisite quantity of oxygen. On ascend- ing high mountains, where the air is rare, a difficulty is often ex- perienced in respiration, due to diminished pressure and the small- er quantity of oxygen ; and in descending in a diving-bell, where ^ the air is compressed by a column of water, the quantity of ox- ygen taken into the lungs increases too much the circulation. This gives an increase of strength, but, if continued long, is in- Describe the meteoric stones and the manner of their production ? To what is the color of the atmosphere due ? What are the relations of the at- mosphere to animals ? What difficulty do persons experience in ascending high mountains or in descending in a diving-bell ? 200 . NATURAL PHILOSOPHY. jurious to health. The density at the surface seems best adapt- ed to the purposes of life. 2. Not only the constitution of the atmosphere, but its com- position, is such as to adapt it to the structure of the lungs of an- imals, and to the important changes which are effected through its agency upon the processes of life. The atmosphere consists chiefly of about 21 parts of oxygen and 79 of nitrogen in 100. The oxygen enters the lungs of all air- breathing animals with the nitrogen, and, passing into the circu- lation, combines with those parts of the body which have served their purpose, and must be ejected, and with that portion of the food which can not be assimilated, forming carbonic acid and water. These substances are ejected along with the nitrogen at each expiration. By this process the functions of life are sustain- ed. In animals living in the water, a portion of air is conveyed through the medium of water to their gills, and the process of purification performed in a similar way. The atmosphere contains variable quantities, as we have seen, of watery vapor, which rises up continually from the surface of the ocean and the land, and is precipitated again over the whole earth to supply the wants of organic life. There is also a variable quantity of carbonic acid in the at- mosphere, which is produced by several causes, such as the respi- ration of animals, combustion, decay, arid changes going on among the rocks. This acid is injurious to animals, but is the proper food of vegetables, whose leaves and roots absorb it, appropriate its carbon under the influence of solar light, and return the oxy- gen to the atmosphere for the use of animals. It is by this pro- cess that the purity of the atmosphere and its uniformity of com- position are constantly maintained. As the oxygen in confined apartments is constantly consumed by the power of respiration, and as the carbonic acid thus produced is not fit to support respi- ration, it becomes necessary to remove this foul air by some me- chanical arrangements. IX. Ventilation. The principle upon which a draught is pro- What is the composition of the atmosphere ? What are the causes which produce carbonic acid in the atmosphere ? VENTILATION. 201 Wig. 163. duced in a chimney may be illustrated by plac- ing a lamp, a b, Fig. 163, in a tube. The com- bustion of the oil in a b will not only consume a portion of the air, but heat it and make it spe- cifically lighter than the surrounding air. This lighter air will be forced up by the pressure of j the more dense portions, and a current will de- scend through c d and up b a. The chimney is the same as the tube, the fire is the lamp, and as the column of air in it becomes heated, the air of the room, which gains access in various ways, being more dense, flows through the fire, and thus a constant draught is kept up. It requires but a slight variation of temperature to determine the direction of the cur- rent. The air in the chimney must therefore be lighter than that in the room, or the draught will be in the opposite direction. This is often the case when a fire is first built. The external air be- ing more dense than that in the apartment, a current of air flows down the chimney, and the smoke at first does not ascend ; or the chimney may be so large that a sufficient body of air can not be heated to produce an upward current, and in this case the fire will smoke ; or the room may be too tight, so that air can not gain admission through the doors or windows, and in that case two currents may be established in the chimney, the one outward and the other inward, which will interfere with its draught. The chimney may be too broad at its entrance, or too high from the hearth, or too short, so that the ascending current will not attain sufficient velocity to counteract the external pressure of the cold- er air from its top ; or, finally, the top may be so situated as to be influenced by irregular currents of air. To remedy these defects, the chimney may be contracted at the bottom and also at the top. The heated air and smoke will then attain a greater velocity. Or its height may be increased. The higher it is, provided it is not too large, the greater will the velocity of the upward currents become. Hence, in some furna- ces and manufactories, where a strong draught is requisite, chim- neys are made very high. What is the principle upon, which a draught is formed in a chimney? What are the causes which interfere with the draught ? I 2 202 NATURAL PHILOSOPHY. Fig. 165. Sometimes one chimney enters another at nearly Fig , 164> right angles, and in this case the draught of one will generally be injured. The more rapid ascending cur- rent will interfere with, and nearly prevent the motion of the current which it meets. Thus, if we take two tubes, a b, Fig. 164, the one entering the other at near- ly right angles, if the current in the tube a, produced by a strong heat, meet the current in b, produced by a less heat, the latter will be overpowered by the former ; or if the stronger current is in b, that in a will be over- come. The flues, therefore, should enter each other at a very acute angle, or, rather, there should be separate flues for each fire carried to the top of the chimney, and then their cur- rents will not interfere. The draught of a chimney may be aided by mechanical contriv- ance, and by the form given to its top. We may assume that the "wind will strike the chimney near- ly at right angles to the direction of the smoke. If, therefore, the top is conical, and slightly con- tracted at its summit, the air, strik- ing upon the sides of this cone, will bound over and around it, Fig. 165, and produce a partial rarefac- tion, as at v, which will have a tendency to draw the smoke up arid increase the draught. Turncaps have also been ap- plied to chimneys to increase the draught, which we will more es- pecially consider in pointing out the methods of taking out foul air from apartments, and introducing cold or warm air accord- ing to the season. In a room where a number of individuals remain for any time, especially in public halls and school-rooms, the draught from the chimney is not sufficient to carry off all the foul air ; and partic- ularly is this the case when rooms are heated by furnaces or tight stoves. How should flues be built? In what other ways may the draught be *ided? VENTILATION. 203 In such cases chimneys may be built in the walls, or tubes in- troduced for the escape of the vitiated air. In order to promote this, certain arrangements may be made to increase the draught. The tubes to take out this air should be proportioned to the size of the room and to the number of persons who may be in it. The arrangement most easily made is to have a chimney built in the wall, with apertures, c, b, Fig. 166, one near the top and the other near the bottom of the room. Registers fitted to these apertures may be opened or closed at pleasure. The object of this is to close the upper register when the warm air is first admitted, as it will rise to the top of the room, and open the lower register to allow the cold air to escape through it ; but, after the room is occupied for a time, the impure air will rise to the ceiling, and the top register should then be opened to let it flow out. The draught may be increased by fixtures upon the top, as in the case of an ordinary chimney. By numerous experiments upon turncaps of various forms, that represented in Fig. 166, a, is found to be the best ; it consists of a tube, with the small end constantly turned toward the wind by means of a vane, while the smoke A passes out through the larger end. The wind fl "T 1 passes over the mouth of the chimney through the smaller portion of the tube. By this action a rarefaction will be produced upon the chim- ney, which will be greater or less in proportion to the force of the wind, and the draught will thereby be increased. This principle is similar to that described page 180. As the air which is passing through the smaller end is constantly ex- panding through the larger, it draws up the air from the chim- ney to fill the partial vacuum thus occasioned. A ventilator has been lately invented 5 * which combines the principle of the cone with some additions. This is said to be * Patented by F. Emerson, Esq., Boston. How should the registers be arranged ? When should they be opened, and when closed ? 204 NATURAL PHILOSOPHY. very effective for increasing the draught of chimneys. The fol- lowing is a representation of it : It consists of a tube, c, Fig. 167, inserted in Fig 167 the top of the chimney, upon which there is mounted a cap, a, like the frustum of a cone, with a plate, b, at a small distance from the opening, to prevent air and rain from entering the chimney. For the purpose of introducing pure air, an injector is employed. When we remember that each individual in an apartment consumes or renders unfit for res- piration about 12 cubic feet of air per hour, it becomes obvious that in a crowded hall a large quantity of pure air should be introduced, and that the means of expelling that which is impure should be most ample. But this is not all. The lights in the room also consume oxygen and pro- duce carbonic acid. Watery vapor and carbonic acid also flow into the room from perspiration and from respiration, so that each individual should have at least 16 cubic feet of pure air per hour. Pure air is better if taken from the top of the building, and in- troduced by means of tubes through numerous apertures in the room, as thereby it is more equally diffused, and cold and hot currents, which are highly injurious to health, are prevented. The proper ventilation of the hold, cabins, and timbers of a ship is an object of great importance. The plan of Mr. Emer- son, in the use of his "corresponding ventilators" the injector and ejector for the hold and cabins, as above described, is said to be very effective. We have lately seen a plan* for ventilating the timbers of a ship which appears to be both practicable and effective. Between the ribs of a ship there is an open space, produced by the planking on the outside and the ceiling on the inside of the vessel ; and near the keel water always accumu- lates, called bilge ivater, which not only becomes very offensive and injurious to health, but, added to the foul atmosphere, causes * Patented by Captain Knight, Ne 7f York. How much pure air ought each individual to have per hour? Describe the process of ventilating the timbers of a ship. UNDULATIONS. 205 the decay of the timbers. This space between the timbers is usually closed at the top by the plank sheer or railing, and at in- tervals by salt stops. Now, if apertures were made through the railing and salt stops, so that the air could circulate, this water would be less offensive and destructive. Ftff.168. Thus, let Fig. 168 represent two ribs of a ship, and a b bilge water. As the ship always rolls more or less at sea, the water will be thrown up on one side, b d, forcing out the im- C\\. ^/d P ure a i r > an d the P ure a i r will flow down on the other, c a. By flowing down on each side alternately, pure air is made to circulate, and to keep the water from becoming stagnant. Pure air is often introduced into the hold of a vessel by meana of a sail, made into a conical form. But we must refer the stu- dent to works which treat of ventilation for a fuller view of the subject. CHAPTER V. OF UNDULATIONS. L There is a class of motions called undulations, which arise from any disturbance among the ato?ns of an elastic substance. The causes of undulatory motions are gravity and elasticity. Undulations are progressive and stationary. II. 1. The, number of vibrations of an elastic rod is inversely as the square root of its length, and the vibrations, whether larg- er or smaller, are all performed in the same time. 2. The vibrations of a stretcJied cord are also isochronous. But the number in a given time increases with the tension of the string ; it is as the square root of the stretching weight, and with a given tension is inversely as the length of the string. When strings of the same material but of different thickness are compared, the number of vibrations is inversely as their diame- ters. Vibrating strings are disposed to divide themselves into definite parts, ivith points of rest called nodes. 206 NATURAL PHILOSOPHY. 3. Elastic planes, when made to vibrate, divide themselves into parts with nodal lines, and observe the same laws as vibrat- ing rods. III. Undulations in liquids, or water waves, are generally produced by air and gravity. They have a progressive motion, due to the rising and sinking of the particles of water in a ver- tical plane. When they fall upon surfaces they are reflected, and interfere with each other, producing standing vibrations. W^hen two si/stems encounter each other, they may produce par- tial or total interference, or unite and form a wave of greater 'magnitude. IV. 1. Waves are produced in the air by any disturbance of its density. An air-wave consists of a rarefied and condensed por- tion. Their length depends upon the number of vibrations in a given time, and their intensity upon the degree of condensa- tion; but, wliether feeble or intense, all air -waves move with the *ame velocity. 2. Air -waves are reflected, interfere with each other, form nodes of vibration, and have a definite relation to the length of pipes in which they may be formed. IN treating of motion and its laws, we have omitted to consider a class of motions which, from their peculiar character, are call- ed undulations, and also vibrations. Undulations consist of a tremulous motion, which passes in a vibratory or wave-like manner through some elastic medium. When such motions take place through the medium of solid, liquid, or gaseous bodies, they give rise to different waves, as wa- ter-waves, waves of sound, musical tones, &c. ; and when simi- lar motions take place in what is called the ether, a substance which is now believed to pervade all matter and to extend throughout space, they are supposed to give rise to the phenom- ena of light, heat, and possibly to electricity. A knowledge, therefore, of the origin, laws, and effects of such undulatory movements, is highly important in order to a full What are undulations, and how are they produced ? To what do they give rise ? UNDULATIONS. 207 comprehension of the remaining branches of Natural Philoso- phy- I. Origin of Undulations. Undulations arise from any dis- turbance among the atoms of an elastic substance. This disturb- ance may have a great variety of causes, as a sudden blow or impulse. Chemical, mechanical, or any other force which is capable of acting upon matter may give rise to it. But, whatever be the cause of this disturbance, the undulations themselves, in the three forms of matter which we have consid- ered, depend either upon elasticity or gravity, or upon both unit- ed ; ibr one or both of these forces, which constantly strive to re- store the disturbed parts to a state of rest, are essential to the commencement, and the sole causes of the continuance of undu- latory motion. Undulations are either stationary or progressive. 1. Stationary Undulations are those which are performed when all the parts of a vibrating body simultaneously swing back and forth within certain limits in exactly the same time, as is exemplified in the pendulum of a clock, or in a string fastened at the two extremities, and motion given to it by pulling the middle to one side, and then leaving it to exert its elastic force. The vibrations of such a string are also said to be transverse. 2. Progressive Undulations are such as are formed on the sur- face of water when it becomes agitated by the wind, or such as are produced by a cord fastened at one end, while the other end is moved up and down, until a wave-like motion is given to it. There is, however, no progressive motion of the parts of the cord or of the particles of water, but a successive rising and falling in the same plane. This is shown in water waves by the fact that light bodies floating on the surface of water are not carried along in the direction in which the wave is moving, but simply rise and fall as the wave passes under them. When the wave has reached its limit, it returns with an inverted motion, and continues to pass back and forth until all the parts are restored to a state of rest. What is the origin of undulations ? What are the causes of this disturb- ance ? What are stationary undulations ? transverse ? What are progress- ive undulations ? 208 NATURAL PHILOSOPHY. Thus, in Fig. 169, we have D &* a representation of the pro- j m J >>^--r- gressive undulations of the P one wave length, passing from nw - **" * s *-^__ ^ 6 left to right, m D n is the elevation, n E o the depres- Him - - iZZZZ^s^^^t sion, j9 D the height, and q E the depth of the wave. Nos. -p^ /^*L^ -- "^f I., II., represent the success- ive positions of the advancing *-*. ___ -^ _ wave from left to right, and "<- ' III., IV., V., those of its return from right to left. Both standing and progressive undulations may take place in liquids and gases as well as in solids. Let us now proceed to examine the laws which govern them in each of the three forms of matter. II. Laivs of Undulations in Solids. For the purpose of ex- hibiting the laws of vibration in solids, we may divide them into rods, strings, planes, and masses. 1. Rods. In the vibrations of a pendulum, all the particles of which it is composed maintain their position in reference to each other unchanged ; but if a steel spring or elastic rod, which is fastened at one end, is bent in any direction, its particles are slightly disturbed, and tend to restore themselves by the force of their elasticity ; but in the effort to regain a state of equilibrium, they cause the free portion of the spring to make a series of vi- brations, which grow less and less until the whole is brought to a state of rest. In this case we may notice the motion of the spring as a whole, which is similar to that of a pendulum with the exception that the motion of the top, Fig. 170, is sometimes curvilinear, as is shown when a bead is fasten- ed upon the end of a steel rod and also the motions of the individual particles which compose it. All the parts of the rod, and each separate particle, pass back and forth in the same time, though the amplitude of their motion, or the distance they pass on each side of their line of rest, is Illustrate by the diagram. How do vibrating rods differ from the pen- dulum ? UNDULATIONS OF STRINGS. 209 very different. The passage of the rod back and forth is called a vibration. (I.) The number of vibrations which a steel rod will execute in a given time is inversely as the square root of its length. Thus a rod which will make 16 vibrations in a second, will make four times as many, or 64 vibrations, in the same time, if reduced to one half of its length, and but one quarter as many, or 4, if its length is doubled. (2.) A rod thus fastened at one end performs all its vibrations in exactly the same time. In this respect the law is the same as that of the pendulum (page 102). 2. Strings. The vibrations of strings, whatever their mate- rial may be, are generally transverse. That is, the string is stretched between two fixed points, and its motion takes place on each side of the line of rest. Jflfr.m. Thus, let a b, Fig. 171, be a stretched cord or wire, and the point /drawn out to d, and then let go ; it will perform a series of vibrations between c and d. This effect is due to its elasticity ; for, when it has ar- rived at/, its inertia will carry it to c, its elasticity will bring it back again to/, and then its inertia will carry it to d again. These vibrations will be continued until the resistance of the air and the slight friction at the ends destroy its motion or bring it to a state of rest. It will be noticed that all the parts of the string reach their maximum distance on each side of the line of rest, a b, and pass this line at the same moment. The motion from d to c and back again to d is one vibration ; c d is the am- plitude or intensity of the vibration. The vibrations of stretched strings are governed by the four following laws : (1.) The vibrations of a stretched cord, whatever be their am- plitude, are performed in equal times. The reason of this law is similar to that given for the oscillations of the pendulum (page 102) ; for, the greater the amplitude of the vibrations, the greater the velocity of the several parts of the string ; or, in the longer What is the law of vibration in an elastic rod ? How do strings vi- brate ? Mention the four laws which govern the vibrations of a stretched cord. 210 NATURAL PHILOSOPHY. vibrations, the velocity is so much greater than it is in the short- er, that they are performed in the same length of time. (2.) The number of vibrations in a given time increases with the tension of the string, and is as the square root of its elastic force, or stretching weight. Thus, if the stretching weights are made 4, 9, and 16 times as great, then the number of vibrations will be as the square roots of these numbers, or 2, 3, and 4 times as many in the same time. (3.) The number of vibrations of a string is inversely as its length. That is, if the string of a violin or any other instrument make a given number of vibrations per second, then, if the ten- sion remain the same, it will make twice as many vibrations if but half of the string is allowed to vibrate ; 3, 4, and 5 times as many if the vibrations are performed by d, th, or th of the whole length of the string. (4.) The number of vibrations of different strings of the same 'material is inversely as their thickness or diameter. Thus, if a wire Y^o-th of an inch in diameter make 32 vibrations per sec- ond, another wire of the same material, which has twice the di- ameter, under the same tension will vibrate but half as fast, or 16 per second, while a wire whose diameter is but half the form- er will perform double the number of vibrations, or 64 per second. There are, however, three kinds of vibration which a stretch- ed cord or wire may be made to perform. Thus, let a twisted wire be suspended, as in Fig. 172, and stretched by means of a heavy ball. If the lower end is secured, it will execute transverse vibrations ; if the ball be raised up and let fall, its vibrations will be longitudinal ; and if it be twisted and then left to move, its vibrations will be ro- tary. Nodes and Standing 'Vibrations. A stretched string, during its vibrations, will, under certain circumstances, divide itself into two or more parts, which have a definite ratio to its length. Thus, if we take a How are transverse, longitudinal, and rotary vibrations produced 1 Fig. 172. UNDULATIONS OF SOLIDS. 211 small cord, and stretch it between two fixed points, and then, cause it to vibrate by pulling it to one side at a point one sixth of its length from the end, we may see its vibrations, and that there are one or more points of the cord, at equal distances from Fig ns each other, which are at rest, as m n, Fig. 173. These points of rest are termed nodes, and the swelling of the string be- tween the nodes bellies. These nodes may be readily formed by drawing a violin bow across a tensely-stretched string at differ- ent points. Sometimes several nodes may be formed at equal distances from each other, giving rise to standing vibrations be- tween each node. If we examine the lengths of the vibrating parts, we shall find that they are ?, ^d, th, &c., of the length of the string, and hence that the number of their vibrations are 2, 3, and 4 times as many, in the same time, as would be performed if the whole length of the string were made to vibrate. An elastic rod, also, when fixed at one end, divides itself into Fig. 174. two or more parts. Thus, if the rod a ^ c' c ft a b, Fig. 174, is fixed at a, and made to vibrate, it will divide itself into parts, with nodes, c' c. The parts a c 1 and c' c are equal, but c b is but half as long ; that is, the distance from the free extrem- ity to the first nodal point, c, is but half that between any two nodal points, as c c'. 3. Planes, Discs, &c. Elastic planes, whatever their form, as a plate of glass or metal, may be made to vibrate in several ways. 175 - The best way is to fasten them firm- ly by means of a vice, and then to draw a bow across their edges. A plate thus B fixed may be thrown into a series of vibrations, and if some black sand be sprinkled over the plate, it will arrange itself as in the accompanying figure (175). The lines where the sand col- lects are termed nodal lines, which di- What are nodes, and how may they be produced? What is meant by standing vibrations? How may elastic planes be made to vibrate ? How are the nodal lines shown ? 212 NATURAL PHILOSOPHY. vide the plate into spaces, any two adjacent spaces being in op- posite states of vibration, as shown by the signs -f- and . If we examine these lines and spaces, we find that those at the ends are but half the size of those in the centre ; hence the plate is similar to a vibrating rod, and may be regarded as com- posed of a series of rods simultaneously thrown into a state of vibration. The form of the figures which a plate is capable of producing, or the manner in which it divides itself, will depend upon its form, the point of support, the part across which the bow is drawn, and the point which is touched by the finger during its oscillations. By varying these conditions, we may produce what have been termed by Chladni, their discoverer, Sound Figures. Thus, let #, Fig. 176, be the point at which the several plates from I. to II. are fastened by the screw of the vice, b the part of the edge across which the bow is drawn. The sand will then be arranged on the nodal lines, which are in a state of re- pose, exhibiting different sound figures. If, however, one plate, as V., be fastened at the point a, while What relation do the spaces bear to each other? Describe the process by which different sound figures may be formed. UNDULATIONS OP LIQUIDS. 213 the finger is placed at w, and the bow drawn across the edge at b, the nodal lines represent figures which appear to be a combi- nation of all the preceding. If the plate is circular and fastened at its center, and a bow drawn across any part of its edge, while the finger is placed at 45 from it, the figure will be in the form of a cross, No. III. ; but if the finger be placed at 60, 30, or 90 from the point where the bow is applied, the nodal lines will give a figure of six rays, as in IV. It will be seen that the vibrations in the above rectangular planes are transverse; that is, perpendicular to the plane. The laivs of vibrating planes are the same as those of vibrat- ing rods. III. Undulations of Liquids. Water- Waves. 1. Water- waves are generally produced by the combined agency of air and gravity ; but, whatever the disturbing cause may be, any eleva- tion or depression of the surface of a liquid is propagated to a considerable distance from the point of disturbance. Thus, if a stone be thrown into a pond of water, circular waves will be formed, which consist of elevations and depressions, that follow each other with considerable rapidity, and spread themselves with uniform velocity to a greater or less distance over the surface of the pond. Such waves have a progressive motion, but the water does not move in the direction of the wave, but only rises up and down in a vertical plane. That there is no progressive motion of the wa- ter is shown by the fact that light bodies floating upon its sur- face do not advance with the wave, but only rise and fall in a vertical line as the wave elevations and depressions pass under them. The force which propels the wave is gravity. The par- ticles on the top of the wave are drawn down by this force with such velocity that they sink below the general level of the sur- face, and cause the particles which are adjacent in the advance of the wave to rise up and form another elevation, and gravity again draws them down and makes a second depression. Hence, How are water-waves produced ? What is the cause of their motion ? Does the water advance with the wave ? How is this proved ? 214 NATURAL PHILOSOPHY. after one elevation or depression, the force of gravity, which con- stantly strives to restore all the particles to a horizontal plane, causes them to perform a series of oscillations in vertical planes at right angles to the surface. In order, however, to understand the laws of water undula- tions, we must examine the connection of the wave with the mo- tion of the separate particles of water concerned in its propaga- tion. As soon as the wave begins to move, the particles of water on its surface begin to describe curves, which return into themselves, and, if the undulations are very regular, the curve is a circle. Each particle completes one entire revolution in its own circle during the time of passing from its highest to its lowest point of vibration and back again, or during the time it is passing from the surface above and below, and returning, to the point from which it commenced its motion ; and the distance the wave advances during one revolution determines the length of the wave, and the distance that each particle rises and sinks is its intensity or am- plitude of vibration. Thus, let there be a row of eight particles on the surface of a liquid, Fig. 177, and a wave pass in the direction of the arrows from left to right. Fig. 177. Suppose that the particle a, which lies upon the surface, is at rest when the descending wave strikes it. It will be depressed, and begin to revolve in a vertical circle, its radius assuming the different positions represented in a b c d, &c., to on, during the time of one oscillation. Now, if we consider eight such particles to be situated on the line a m, as a b c, &c., and that each particle begins its motion one eightn of a revolution later than the preced- ing, during the time that a is completing one revolution each suc- ceeding particle will move through a portion of its circle. When a has passed through one eighth of its circle, b begins to move, What motions do the particles of water make ? How is the length of the wave determined ? Illustrate by figure. REFLECTION OF WATER-WAVES. 215 and when a has completed an entire revolution, m begins its mo- tion. The particles between a and m are in the condition repre- sented in 7, 6, 5, 4, &c. ; that is, when m commences, h has com- pleted jth, g fths, / fths, e f ths, d fths, c |ths, b Jths, and a one entire revolution. The particles a and m are in the same condition, and the line which joins them is the length of the wave, and lies upon its surface. The diameter of the circle which each particle describes is the amplitude or intensity of the wave, c 6 its depth, and g 2 its height, each of which is equal to the radius of the circle which any particle describes during one oscillation. This radius is longer or shorter according to the amplitude of the wave. It is sometimes 20 feet, which makes a very high wave, perhaps the largest which ever occurs on the ocean in a violent storm, unless it be in cases where one wave mounts upon another in a manner which we shall presently ex- plain ; but the power of the wind is not believed to extend more than 20 feet below the surface, and hence waves are not in real- ity so high as they appear to be, since they rarely reach an am- plitude of 40 feet. 2. Reflection of Water-Waves. When the undulations of water fall upon any solid surface, they are reflected, and return in paths which depend upon the direction in which the incident wave meets the reflecting surface. Thus, if we consider a line of particles proceeding from the origin of the wave in the direc- tion of its motion, called a ray of undulation, we shall find, (1.) If it fall upon a plane surface perpendicular to the sur- face, it will be reflected and return in the same path. (^*) ^ ^ ^ a ^ u P on tne surface at any angle, as at c, in the direction d c, Fig. 178, it will be reflect- ed in the direction c a, and the angle which the incident ray d.c makes with a perpendicular to the surface, c b, is equal to that which the reflected ray, c a, makes with the same perpendicular ; that is, the angle d c b is equal to b c a, or the angle of incidence is equal to the angle of reflection the How is the amplitude determined ? What is the height and what the depth of the wave ? What is a ray of undulation ? What law do waves observe when reflected from surfaces? 216 NATURAL PHILOSOPHr. same law which is observed in the impact of solids (page 78). As the same law applies to all the rays which constitute the breadth of the wave, we may readily determine the path of the reflected wave by a knowledge of the form of the surface and the angle of incidence. If the wave is linear, that is, if a line resting upon the highest point of its elevation, at right angles to the direction in which it is moving, is a straight line, if such a wave meet a plane surface, it will be reflected and return in the same path. If it meet the surface at an angle of 20 or 30, it will be reflected at the same angles on the other side of the perpendiculars to the reflecting surface. But waves are generally circular or curvilinear, and we have to consider the law as applied to the reflection of such waves from surfaces either plane or curved. (1.) If the wave originate from the center of a cylindrical ves- sel, the rays of undulation will all be perpendicular to the sur- face, and will return, after reflection, to the center in exactly the same time. (2.) If the vessel is in the form of an ellipse, and a wave originate at one of the focii, all the rays will converge, after re- flection, to the other focus ; and if they proceed from the focus of a parabola, a, Fig. 179, they will be reflected in paral- lel lines, as b d, e d. (3.) If a circular wave fall upon a plane surface at right an- gles to it, then the different rays of undulation will meet the sur- face in successive moments of time, in consequence of which the form of the reflected wave will be the reverse of the incident wave ; that is, the rays which first strike the surface will be re- flected first, and will have returned to the same distance from the surface at the time the last rays meet it, that these last rays were at the moment the first were reflected. What is the form of waves ? How will the reflected wave move if it originate at the center of a circle ? How if it originate at the focus of an ellipse ? a parabola ? If a circular wave fall upon a plane surface, in what manner will it be reflected 1 INTERFERENCE OF WATER-WAVES. 217 ' 18 - Thus, suppose the wave 'g a d, proceeding from c, Fig. 179, meet the plane surface ef. The advance portions, as at a, will first be reflected, and will re- turn to k at the moment that the rays, at a and g reach the surface, and the form of the wave after reflection will be the same that it would have been had it proceeded from c', at the same distance on the other side ofef. 3, Interference of Water-Waves. When two waves on the surface of a liquid encounter each other under certain conditions, they destroy each other's effects, and are then said to interfere. This interference may be total or partial. Let us now determine the conditions under which total and partial interference takes place. Let A B, Fig. 180, be the surface of a liquid, A g the length of a wave, a b, c f the intensity or amplitude of its vibrations. Fig. 181. Let a second wave of equal length, which originated half a wave's length from A, and is moving in the same direction with equal intensity of vibration, meet it. Then this second wave from the point d will move in the direction d e g, exactly opposite to the wave afg. All the individual parts of each wave will move in opposite directions and with equal velocity, and hence they must counteract each other's motion, and a total interference will take place, so that the surface will remain at rest. (1.) The condition, therefore, under ivhicfi interference is pro- duced, is when the elevation of one wave falls into the depressions of another, and this will always occur when waves of equal lengths have come through paths of unequal ivave lengths. What are the conditions under which waves interfere with each other ? K 218 NATURAL PHILOSOPHY. If the spaces through which the second wave has passed are ?> l> 2| times a wave length of the first, then, when they meet, interference will be total. But it is evident that waves may originate a little less or a little more than half a wave length from each other ; they may also differ in intensity ; in which cases only partial interference will take place. Thus, let a g be the surface of the wave a m b s g, Fig. 181, m n, q s the intensity of its oscillations, and let another wave in- JF&.182. terfere with it at b, having the intensity q r, q t. As this second wave is moving in the direction q r, while the first is moving in the opposite direction q s, it will counteract a part of its motion, and the intensity of the vibrations of the resulting wave will be the difference between q s and q r, that is, q t. In this case the interference is partial, because only a part of the motion of the first wave is destroyed. (2.) If two systems of waves of equal lengths, which have pass- ed through equal spaces, or some multiple of their wave lengths, encounter each other, they unite, and increase the intensity of the resulting wave. Thus, let the wave a m p b, Fig. 183, whose intensity of vi- bration is represented by m n and o p, be met by another wave Fig. 183. at b, which has come through a space equal to once, twice, three times, &c., the wave length a b; then the elevations and de- pressions of the second wave will coincide with those of the first, and increase its force. When is the interference of waves partial, and when total ? When do waves increase each other's effects ? UNDULATIONS OF GASES. 219 If the intensity of the second wave is equal, q r, v w, then the intensity of the two combined will be represented by q t, v x, and the resultant wave by b t g x h. If the waves are of equal inten- sity when they meet, the amplitude of the resulting wave will be doubled. Although the force of the wind is supposed not to extend more than 20 feet below the surface of the water, yet, when several systems combine, we may understand how they may accumulate upon each other, and produce waves of much greater amplitude. 4. Standing Waves. It is evident that an incident and re- flected wave may meet under such conditions as to produce total interference, that is, the elevation of the reflected wave may fall into the depression of the incident wave, so that a line resting on the surface where they meet will be at rest. This will form a node of oscillation, and between this node and the reflecting surface there will be formed standing waves. 5. Inflection of Waves,. When water waves fall upon a soli^ surface, through which at any point there is an opening, as whei* they flow through a short channel between two arms of the sea, Fig. 184. they give rise to several systems of waves, adja- cent to the opening, which interfere with each other more or less and with the principal wave. Thus, suppose a wave fall upon a surface, and pass through the opening a b, Fig. 183, it will give rise to several waves, which, by crossing each other, produce various degrees of interference. This phenomenon is called the inflection of waves. IV. Undulations of Gases. Air-Waves. Undulations are produced in air by any disturbance of its density ; and though air- waves, like those of water, have a progressive motion, they differ from water-waves in several essential particulars. Air- waves are formed in the great air ocean which surrounds the earth, and not upon its surface. How high are waves formed in the ocean ? How are standing waves and nodes of oscillation produced ? What is meant by the inflection of waves ? By what means are waves produced in the air, and how do such waves dif- fer from water-waves ? 220 NATURAL PHILOSOPHY. Water-waves are due to gravity, air-waves to elasticity. In the water-wave the separate particles rise and fall at right an- gles to the direction or length of the wave. In air-waves the particles move back arid forth in a line with the advancing wave, and thus produce alternate condensations and rarefactions of the separate layers of air which make up the length of the wave. 1 . The nature and laivs of air- waves may be shown by means of open and covered pipes, in which the air is made to vibrate by any appropriate cause. J?^.18& A . 4 8 12 16 20 24 28 32 II II 1 1 II I II A 4 B C D 4 8 12 16 20 24 28 32 Let A B, Fig. 185, be an open tube, into which a piston, P, is accurately fitted, so that vibrations may be communicated to the air within it by a rapid motion back and forth. Let the air in the tube be divided into 32 equal layers. Suppose the piston move from. A to 8 and back, or let A 8 be the amplitude of its oscillations, and let the time of passing from 1 to 8, and back again to 1, be T Vth of a second, the piston will pass from 1 to 2, &c., in ^^th of a second. Each layer will therefore commence its motion -j 1 F^ n ^ a secon( i later than the preceding. Such a piston, however, will not move with uniform velocity, but its motion will be greatest midway between the limits of its course, or at 4. Hence, when it passes from 1 to 8, the air will be most condensed at 4, and when it returns it will be most rar- efied at the same point. When the piston has passed to 8, or the limits of its course, the 8th layer receives the impulse and com- municates it toward 16, and w r hen the piston has returned to 1, the 16th layer will begin its motion. The condensed part of the wave will be at 1 2, and the rarefied portion at 4 ; and when the piston commences to move the 1st layer the second time, the 16th layer will commence its motion. This determines the length of the wave. That is, the distance between two layers in similar states of vibration is the length of an air-wave. If, therefore, we ex- UNDULATIONS OF AIR. 221 amine this wave after one vibration of the piston, we shall find that it consists of a rarefied and condensed portion, the greatest condensation being at 12, and the greatest rarefaction at 4, and that the layers of air at 1 and 16 are at rest, while those between 1 and 8 are moving toward 1, and those between 8 and 16 toward 16. The condensed portion of the wave corresponds to the ele- vation, and the rarefied portion to the depression of a water-wave. C D represents the wave after one vibration. The wave will not stop, however, at 16, but will be propaga- ted to 32, the greatest condensation being at 28, and the greatest rarefaction at 20 ; and at the same moment the first wave will have changed its position, the greatest condensation occurring at 4, and the greatest rarefaction at 12. If the stroke of the piston is repeated, a succession of waves will be formed. Fig. 186 represents the condition of the air in. Fig. 186. 321 484440 36 322824- 20 l6 12 8 4 the tube after three strokes or vibrations of the piston, and the arrows show the direction in which the separate layers are moving. The length of the wave depends upon the time the piston is making an oscillation. The slower the motion the longer the wave, and the more rapid the motion of the piston the shorter the wave. Thus, if the time occupied by the piston in making an oscillation in the above example were T \ ths of a second instead of one, the wave length would have been doubled, and if it had performed an oscillation in half or a quarter, &c., of the time, the wave length would have been but half or a quarter, &c., as long. The intensity of the wave, however, depends upon the ampli- tude of the vibrations of the piston, because the air becomes more condensed and rarefied as the amplitude of its vibratory particles is increased. It will make no difference, however, in the progress- ive motion of the wave ; the shorter waves will vibrate so much Of what does an air wave consist ? How is its length determined ? Upon what does the length of the wave depend ? Upon what its intensity ? 222 NATURAL PHILOSOPHY. iaster than the longer that they will each traverse a given space in the same time. Hence, Air-waves, whatever their difference of length or intensity, are propagated with the same velocity and rjass over equal spaces in equal times. 2. Reflection of Air-Waves. If, instead of an open tube, we take one which is covered, that is, closed at one end, we may il- lustrate the manner in which air- waves are reflected, the relation which the length of the tube bears to the length of the wave, and the mutual influence of the incident and reflected portion of a fvave upon the character of its vibrations. Let the tube a b, Fig. 187, which is closed at one end, be a Fig. 187. a be d quarter the length of the air- wave, which enters it at its open ex- tremity. The moment that the layer 16 has reached the bottom, where it will be thrown back, the layer 12, which makes one quarter of the wave, enters it, and by the time this layer would reach the bottom, the layer 8 would enter the tube, and the lay- er 16 would have returned to the same point ; 8 and 16 are just half a wave length apart, and are, therefore, in opposite states of density, for we have seen that the distance between the point of greatest condensation and the greatest rarefaction is just half a wave length. At the open end of the tube, therefore, the great- est condensation and rarefaction take place at the same moment, and destroy each other's effects, or produce total interference; hence, at this point, the layer of air moves backward and forward without any change of density. 'Shis is termed a belly. All the layers of air in the tube commence their motion, reach their limits, and commence their return at the same moment of time. The layers near the bottom will be alternately condensed and rarefied, while those near the open extremity will not be changed in density. The air in the tube is thus thrown into standing vibrations. What law governs the propagation of air-waves ? Illustrate the reflec- tion of air-waves. How are standing vibrations produced 7 INTERFERENCE OF AIR-WAVES. 223 3. Interference of Air-Waves. Nodes. If now we take a tube, a d, Fig. 188, which is three quarters the length of the Fig. 188. &-* 7i *K C d **> c f <-s n' ci' air-wave, and divide it into three equal parts at the points n c, each division, as a n, will DC one quarter of the length of the air-wave. Suppose the wave to enter the tube, and pass to the bottom to d. The layers of the wave at a and c, which are re- moved one half the length of the wave from each other, are in opposite conditions of vibration. When the layer at a is most condensed, the layer at c is most rarefied, and the reverse. When the wave reaches the bottom, it is reflected, and, on its return, will reach c at the moment that the layer at that point, which is half a wave length, begins to move toward d; and as the two layers are in opposite states of vibration, they will interfere, and pro- duce a belly, as in the preceding case. If the wave had proceeded beyond d without reflection, there would have been a condensation at c' and a rarefaction at a', be- cause they are removed half a wave length from each other ; but, in consequence of the reflection at d, c' is thrown upon c, n' upon n, and a' upon a. At the point n, therefore, there will be a con- densation, owing to the meeting of the advancing and returning wave ; and as this is just one wave length, there will be alternate condensations and rarefactions. If, however, we examine the condition of the layer of air at d, we shall find that it is at rest, being acted upon by equal and opposite forces, produced by the layers of air moving simultane- ously to and from it ; d, then, is a node of oscillation, while there will be bellies at a and c, where the air is neither condensed nor rarefied, but merely moves back and forth. Under these conditions, the air in the tube is thrown into stand- ing vibrations, having a node at n which corresponds to the nodes we have already considered in the undulations of solid and liquid Describe the manner in which air- waves interfere and produce nodes. 224 NATURAL PHILOSOPHY. bodies. If the air-wave is much shorter, there may occur two or more nodes in the same tube. Nodes and standing vibrations are also formed in open tubes, provided the tube bear a certain relation to the length of the air- wave. The reflection, in this case, takes place from the open ex- tremities of the tube, in consequence of a condensed portion of the wave arriving at these points. The length of the tube, how- ever, bears a different relation to the wave. If the tube is one half the length of the wave, there will oc- cur a node in the center and bellies at each extremity. This is exemplified in Fig. 189, A B, which is a tube half the length Fig. 189. ft *" of the wave, n is the node, and the layers of air on each side simultaneously move to and from this point toward the open ex- tremities of the tube. The two conditions of the wave are rep- resented at n and n'. If the open tube were equal in length to the air-wave, then there would occur two nodes at n and n 1 , Fig. 190 ; and if the Fig. 190. L <** n b *> n -*M s n' n TV Y tube were two thirds the length of the wave, then there would be three nodes, one in the center, and the other two at one sixth of the length of the tube. The formation of regular air-waves in closed and open pipes, and the occurrence of one or more nodes of oscillation, give rise, as we shall see, to different tones, so that the same tube will emit notes of different pitch. We have considered the formation of regular air-waves in pipes, but waves formed in the air are precisely similar in char- acter, and observe the same laws. Air-waves thus excited are similar to water-waves in form ; that is, they are generally cir- How are nodes and standing vibrations produced in open tubes ? What is the relation of the length of the air-wave tq the tube in order to produce one or more nodes ? ACOUSTICS. 225 cular, and move with uniform velocity. Their intensity dimin- ishes as the square of the distance, and the extent to which they may be propagated is only limited by the extent of the atmos- phere. When they fall upon solid, or liquid, or even gaseous bodies, they are reflected, according to the same laws with those of water-waves. If a ray of undulation fall perpendicularly, it returns by the same path. If it fall upon a concave surface, its rays are collected to a focus. If rays proceed from one focus of an ellipse, they are reflected to the other focus. The further con- sideration of undulations, however, will be deferred till we come to treat of the effects of undulations upon the organs of sense, constituting the sensation of sound, music, light, &c. CHAPTER VI. ACOUSTICS. THE term Acoustics is derived from a Greek word, which means to hear. The object of this branch of Natural Philosophy is to investigate the nature and laws of Sound. As sound is the effect of undulations upon the organs of hearing, we propose to consider, 1st. The subject of sound in general ; and, 2d. That of musical tones. SECTION I. OF SOUND. Sound is a sensation produced by undulations of some elastic medium falling upon the organs of hearing. I. But only those undulations which are performed within certain limits as to number and time excite the sensation of sound. II. Sounds are various. A continued sound produced by the same number of vibrations per second is called a tone. III. Tones are high or low, feeble or intense; the lowest tone is produced by 16*5 vibrations per second, and the highest by about 16,000 vibrations per second. IV. An elastic medium is necessary to conduct sound. Solids 226 NATURAL PHILOSOPHY. are the best conductors, liquids rank next, and gases are the poorest conductors of sound. V. Sounds, whether high or loiv, feeble or intense, are conduct- ed in the same medium with equal velocity. The velocity of sound varies in solids, but is much greater than in liquids or gases. Water conducts sound 4708 feet per second; air con- ducts it at the rate of about 1120 feet per second. VI. Sound will travel to a great distance ; furthest in solids, and least in gases. VII. When sound is reflected, it gives rise to echoes, which are single or multiple. Upon the reflection of sound and its concen- tration the speaking and ear trumpets depend for their utility. VIII. Sound-waves may interfere with each other and 'pro- duce silence. SOUND is produced ivhen undulations which are propagated through some material medium fall upon the organs of hearing. Sound is a sensation, the effect of undulations in an elastic body. The origin of sound is therefore the same as that of undulations, which, as we have seen, are produced by the disturbance of the particles of an elastic substance. The medium through which undulations are conveyed to the organs of sense is principally the air. They may, however, be communicated through solids and liquids, or they may originate in solid or liquid bodies, be communicated to the air, thence to the external ear, and then pass again through solids and liquids to the auditory nerve. This is the ordinary mode in which the sensation of sound is produced. We have considered in the previous chapter the origin and laws of undulations in solids, liquids, and gases. It remains now to point out their relation to the phenomena of sound ; for, though all sounds are the effect of undulations upon the nerves of sense, yet all undulations do not impress these organs with the sensation of sound. I. Sound-waves are such as perform their vibrations within How is sound produced ? What is sound 1 What connection between undulations and sound ? Do all undulations produce the sensation of sound ? What, then, are sound-waves? UNDULATIONS PRODUCING SOUND. 227 certain limits as to time and number ; that is, the oscillations of the vibrating wave must reach a definite number in a given time in order to excite the sensation of sound, or, if they exceed a certain number in a given time, the ear will not be impressed by them, or will not be able to distinguish them. These limits must be determined by experiment. They are found to vary slightly when judged by different ears, as the organs of hearing are more perfect in some individuals than in others ; but, except in extraordinary cases, the variation is too slight to interfere with general laws. 1 . If we take an elastic cord, fixed at one end, and stretch it by attaching weights to the other, which will gradually increase its tension, and cause it to vibrate by pulling it to one side, we may see its vibrations until the increasing tension shall cause 16 - 5 to be made in one second ; then the intervals entirely dis- appear, and at the same moment we perceive the sensation of sound. It is found that the vibrations which produce the im- pression are from 16 to 17 per second. The same number of vi- brations per second will be impressed upon the air-wave which falls upon the organs of sense ; hence 16 -5 vibrations per second in a vibrating solid or fluid are the lowest number which the human ear can perceive, and produce the lowest tone that it is capable of hearing. 2. If now the number of vibrations be increased, which may be done by shortening the string or increasing its tension, or both, the tone will continue to rise until the number of vibrations has reached 16,000 per second, which will produce the highest tone which the ear can discriminate. If, therefore, the vibrations ex- ceed this number, human ears at least are not able to take notice of them, or, at any rate, can not distinguish the tone which they may produce. II. Varieties of Sound. The impressions made upon the or- gans of hearing by undulations are very various, and have re ceived distinctive names. How many vibrations per second are necessary to impress the organs of sense ? What is the effect of increasing the number of vibrations ? De- fine the several varieties of sound. 228 NATURAL PHILOSOPHY. When an elastic body is struck by a single blow, as when a bell is struck by its tongue or an explosion produced by gun- powder/ so that a sudden and intense air- wave is formed, the sound produced is called a report. When the blow is repeated at equal intervals of time, so that regular and equal waves are produced, falling upon the ear so rapidly that it can not distin- guish the intervals, it is called a tone ; and when the waves of sound are of unequal lengths, and the oscillations are repeated in such a manner as to interfere with each other, the sound pro- duced is called noise. III. Varieties, of Tone. Tones are distinguished as high and low, intense and. feeble. 1. The lowest tone which the ear can discern is produced, as we have seen, by a wave which makes 16'5 vibrations per sec- ond ; and by shortening the vibrating body, and increasing the number of vibrations, the tone rises higher and higher, until 16,000 vibrations per second give the highest tone. Those tones which are produced by the slower vibrations are low tones, and those produced by the more rapid vibrations are high tones. 2. The! intensity of the tone depends upon the amplitude of the vibrating particles, and not upon the length of its wave. If, for example, a stretched cord be made to vibrate, all its vibra- tions will be performed in the same time, but the distance through which the vibrating parts pass on each side of their line of rest may vary. If this distance is small, it will produce a. feeble tone; if large, a loud or an intense tone. 3. The quality of the tone is not so easily accounted for. The same tone may be produced by a violin, a trumpet, or the human voice, yet the tone differs very much in quality. It has been supposed to be due to the order in which the velocities and changes of density succeed each other in the sound waves which produce the tone. (Mutter.) IV. Conduction of Sound. We have seen in what manner undulations are conducted by means of elastic media ; it follows How are tones distinguished ? Upon what does the intensity of the tone depend ? What gives rise to the quality of the tone ? What is necessary in order to conduct sound T CONDUCTION OF SOUND. 229 that sound, using the term not only for jthe sensation, but for the undulations which produce it, must have some elastic medium for its conduction. 1. This fact may be readily proved by experiment; for if a body, as a bell, be made to vibrate in a vacuum, no sound will be perceived. Thus, Exp. Place a bell on some cotton wool in the receiver of an air pump, Fig. 191, and cause it to be rung by means of a sliding rod ; its vibrations will be communicated to the air in the receiver, and from thence to the receiver, which will pass them on through the external air to the ear, and the sound will be distinctly heard. Exp. Let the air now be exhausted, and the bell rung as before ; no sound will be heard, be- cause there is no medium to transmit its vibrations. Exp. While the bell is vibrating, admit the air slowly to the receiver, and sound will begin to be heard, at first feebly, and then gr-owing louder as the receiver is again filled with air. Other gases and vapors will also transmit the vibrations of sound ; for if, in the above experiments, a few drops of ether or water be introduced, after the air is exhausted they will rise up in vapor, and the sound of the bell will be distinctly heard. The experiment may be varied with hydrogen and other gases, but air is one of the best conductors. It follows, therefore, that no sound can be communicated beyond the limits of our atmosphere, be- cause there is nothing to continue the vibrations, nor can any sounds, however loud, reach the earth from any of the planetary bodies. The intensity of sound in air will be increased by con- densing it. Thus, if a bell be rung in a receiver of condensed air, .its tone will be much more intense ; and as air is rarefied, its power is diminished ; hence, on high mountains, the same vibra- tions give but a feeble sound. 2. Liquids, as water, are good conductors of sound. This is proved by the fact that persons under water are enabled to hear sounds which have originated at a great distance, and traveled through the intervening water. Water is a better conductor than air. 3. Solid bodies are still better conductors of sound than either How is this proved ? What bodies conduct sound best? 230 NATURAL PHILOSOPHY. of the preceding forms of matter. This may be shown by plac- ing the ear at one end of a long rod, while a pin is drawn across the other end. A slight blow on the end of a solid may be heard at the other end, though it may be several times the distance at which the same sound could be heard in the air. Solids, however, differ in their power of conduction. Only those which are elastic are capable of transmitting sound-waves. Inelastic bodies, as most soft bodies, obstruct the vibrations, and some wholly stop them. Glass, the metals, wood, and stretched cords are among the most elastic bodies which conduct sound. Very porous bodies, as wool, obstruct them. India rubber, and some other elastic substances, are destitute of conducting power. V. Velocity of Sound. 1 . The velocity of sound varies in dif- ferent media ; but in the same medium, all sounds, whether high or low, feeble or intense, are propagated with equal velocity. This law results directly from the nature of undulations pro- ducing sound. The length of each wave is proportioned to the number of vibrations in a given time, and whether the tones are feeble or intense, high or low whether they are produced by a violin, gunpowder, or the human voice, the undulations which give rise to them traverse a given space in the same time. This law is also proved by experiment and observation. When we listen to music at a distance, if we did not hear the high and low, the feeble and intense notes at the same moment, there would be no harmony, and we should hear nothing but a con- fused noise. A whisper is heard at the same moment with the loudest tone. There is a great difference in the actual distance at which a feeble and an intense tone may be heard, but no* dif- ference in the velocity with which they are propagated in the same medium. 2. Sound travels ivith different velocities in different media. (1.) Solid bodies transmit sound with different degrees of ve- locity. This is due to their elasticity and different densities. It has been found by experiment that sound passes in a bar of Upon what property does the conduction of sound depend ? What is the velocity of sound ? How is its velocity ascertained ? Does sound travel at the same rate in different media ? VELOCITY OF SOUND. 231 tin about 8400 feet per second, in a copper bar 13,440 feet, and in a solid tube of glass 19,040 feet per second. It passes through other solids with greater or less rapidity. This velocity is de- termined by noticing the time required for vibrations at one end of a bar to pass and be heard at the other end. (2.) Liquids, as water, transmit sound with much less veloc- ity than solids. According to the experiments of Colladon and Sturm, which were made on the waters of the Lake of Geneva, the velocity of sound in water is about 4708 feet per second. The velocity of sound in water is determined by two individuals placed at a known distance from each other : one of them commu- nicates vibrations to the water by striking two elastic bodies at a given instant, and the other, having his ear in contact with the wa- ter, notes the exact time when the sound is heard. The distance divided by the difference of time in seconds will give the velocity. (3.) The velocity with which air transmits sound has also been determined by experiment. Though, in consequence of the fact that the density, temperature, and moisture of the air vary at different times, there is a slight variation in the rate at which sound is propagated through it, yet at a medium pressure, and at a temperature of 60 F., sound travels about 1120* feet per sec- ond, or about one fourth as rapidly as in water, and only about one eighteenth the velocity with which it is transmitted in glass. The velocity of sound in air is determined by ascertaining the time required for it to pass over a known distance. In conse- quence of the almost instant passage of light through any con- siderable distance on the earth's surface, this may be effected by observing the flash of a musket at a certain distance, and noting the time which transpires before the report reaches the ear. * The velocity of sound through air was determined in France, at the tem- perature of 32 F., to be 1086-1 feet per second. Its velocity, as determin- ed about the same time in Holland, was 1089-42 feet per second; and, as- suming that its velocity is increased 1-14 feet per second for an increase of one degree of temperature, the velocity at a temperature of 62i F. would be, for the first, 1120-87, and for the second, 1124-19 feet per second; which latter is the rate which has been considered most correct. Accord- ing to this rate, sound travels 12| miles per minute, or 765 miles per hour. Which of the three forms of matter transmits sound with the greatest velocity ? How is the velocity of sound determined ? 232 N 7 ATURAL PHILOSOPHY. If the air is moist, the velocity is slightly increased. A wind in the same direction in which the sound travels will increase, and in the opposite direction will diminish its velocity. There is also a slight variation dependent on temperature. As the temperature is raised, the velocity of sound is increased about one foot (1-14 feet) for every degree. Sound, therefore, will travel faster in summer than in winter, faster during damp than during dry weather. In consequence of the known rate at which sound travels, we may determine the distance at which any report is made, provid- ed we are able to observe the cause of it. Thus we may ob- serve the blows of a man's ax felling a tree at a distance, and by noting how many seconds intervene after we see the stroke before the sound reaches us, the exact distance may be known. In this case, we often observe the, tree to fall before the last stroke reaches the ear. The distance of a flash of lightning may be determined in the same way by counting the number of sec- onds which intervene between the flash and the thunder. The number of seconds between the flash and the report of a cannon, multipled by 1120 feet, will give the distance it is from us. VI. Distance to which Sound may be propagated. An un- dulation communicated to the air or any elastic medium must travel to a great distance, but the intensity of the vibrations must constantly diminish. If the vibrations producing sound proceed from a center, they will observe the same law with any other in- fluence ; their intensity will be inversely as the square of the distance ; that is, at four times the distance, the sound will be but one quarter as loud ; so that, though we may not be able to set limits to the undulations, excepting that which terminates the medium, still they will, at a certain distance, become too fee- ble to produce the sensation of sound. The human voice is said to be heard at the distance of 700 feet. It has, however, been heard at a much greater distance. From Old to New, Gibraltar, a distance of ten miles, the watch- word "ALVs Well!" has been distinctly heard. How may distances be determined by means of sound 1 To what dis- tance will sound reach ? What law governs the intensity of sound? How far can a man's voice be heard ? REFLECTION OF SOUND ECHO. 233 The report of a musket may be heard about four miles, and the report of a volcanic eruption has been heard from 200 to 300 miles ; in the latter case, however, the ground aids in conducting the sound. The distance to which sound will travel is influenced by the smoothness or roughness of the surface ; it may be heard further across water than on the land, in a humid than in a dry atmos- phere, further in the night than in the daytime. Water trans- mits sound further than air, and solids further than liquids.* VII. Reflection of Sound. Echo. 1 . Air- waves, as we have already noticed, when they fall upon different surfaces, are reflect- ed, and the angle of incidence is always equal to the angle of re- flection. If they fall perpendicularly upon a smooth surface, they will be thrown back by the same path. If they meet the surface at any angle, they will be reflected at the same angle on the other side of a perpendicular to the re- flecting surface. It is not necessary, however, that the surface should be smooth. Sound is reflected from the sides of hills and rocks, from the sur- face of the earth and of water. Nor is it necessary that it should fall upon a solid or liquid body. Sound is reflected from the clouds, and even from the clear atmosphere, when currents of air of different densities are circu- lating. When sound-waves- are reflected from any surface, they may give rise to what is termed 2. An Echo. If the sound returns to the point from whence it originated, it must meet the surface at right angles, and in this case several syllables may be repeated. By a rapid utterance, * Sounds must be limited by the media in which they are propagated ; but when vibrations are once given to the air, they may continue long after they cease to affect the organs of sense ; in fact, vibrations in air may con- tinue, for aught which appears to the contrary, for years, so that, if those organs were sufficiently refined, we might be able still to hear the voices of friends long since passed away, or the songs of other days and of former generations, whose vibrations still float through the air. How far can a musket be heard ? What influences the distance ? What media transmit sound to the greatest distance ? How is the echo produc- ed 1 Under what conditions may several syllables be repeated 1 234 NATURAL PHILOSOPHY. eight syllables may be spoken in two seconds. If, therefore, we stand at the distance of 1120 feet from any reflecting surface } we may utter eight syllables, and they will be returned to us. If the distance is increased, the number may reach as high as fifteen syllables, which may be distinctly heard, the first returning at the moment the last is uttered. 3. Multiple Echoes. It is evident that the sound-wave may be reflected several times if it fall upon surfaces properly situated. Such echoes are known to exist in many places, particularly in winding valleys which lie between high bluffs or rocks. There is a valley on the Rhine, represented in Fig. 192, in Fig. 192. which the sound is repeated from the rocks on each side of the river, as shown at 1, 2, 3, 4. Near Milan there is a place where the sound is said to be re- peated thirty times. There was formerly an echo at Verdun, where the sound was reflected from the surface of two towers, so that the same sound would be repeated 12 or 13 times. 4. Whispering Galleries. If the surface from which sound- waves are reflected be a hollow sphere, and the waves proceed from its center, they will all return to the center. But if the wave fall upon a concave surface, it may be reflect- ed to a definite point. Mention examples of multiple echoes. How are whispering galleries constructed ? INTERFERENCE OF SOUND. 235 Fi 193 Thus, suppose a person to stand at the point g t Fig. 193, which is the focus of an ellipse, and another at c, the other focus, but separated by several hundred feet, the sounds which proceed from each focus fall upon the surface, as gf, c e, and are reflected to the opposite focus. Persons so situated may converse with each other in audible sounds or in whispers, and be distinctly heard, while those who may occupy the intervening space are unable to understand a single word. Hence such structures are called Whispering Galleries. 5. Speaking Trumpets. It is on the principle of the reflec- tion of sound that speaking trumpets are constructed. In these instruments the sound is reflected from the sides of the tube, and the intensity of the vibrating waves is greatly augmented. Thus the waves, Figure 194, are pass- ed from side to side through the tube, and reflected in parallel lines, so that nearly the whole force of the wave is projected in one direction. With a tube 20 or 25 feet in length, a man having a strong voice will make himself heard two or three miles. 6. Hearing Trumpets. The hearing trum- pet, Fig. 195, is similar in construction, only the sound-waves enter the larger end, and a greater number of rays are collected by reflection, and thrown upon the organs of hearing. The Stethoscope, an instrument to ascertain the condition of the organs of the chest, depends upon the conduction of sound. VIII. Interference of Sound. We have shown (page 223) that air-waves may interfere with each other so as to destroy their effects ; and hence, as sounds arise from such waves, there will necessarily occur interference of sound. This fact may be shown experimentally by passing air-waves of different lengths into a tube. Fig. 195. Describe the speaking trumpet. What is its use ? Describe the hearing trumpet. How may sounds interfere ? 236 NATURAL PHILOSOPHY. Thus, take a small jar, b, Fig. 196, and by means of two tuning forks, a d, of the same note, cause it to resound. A circular card must first be placed on one prong of each, and a drop of sealing-wax on one fork to increase its weight. The vessel must also be filled with water till it will give a clear note when either fork is held over its open extremity. If now both forks are held over it at the same time, there will be alternate periods of silence and sound, produced by the interference of the longer and shorter waves, which meet each other in the tube. Two sounds will in this way produce silence* This phenom- enon is not confined to sound-waves or water-waves. Two rays of light may produce darkness, and two rays of heat cold, as will be shown more fully when we come to speak of the interference of light/ SECTION II. MUSICAL TONES. HAVING considered the manner in which sound-waves are pro- duced and propagated, it remains now to investigate the relations which exist between different tones, and also between vibrations of the sounding body and the kind of tone it is capable of yielding. There are certain tones or combinations of tones which may succeed each other, or may coexist at the same time, and produce an agreeable impression on the ear, and hence are said to harmo- nize ; and when the vibrations which give rise to them are per- formed in equal times, to be in unison. There are other tones which strike upon the ear so as to produce a disagreeable sensa- tion, and hence they are said to be unharmoni&us or discordant. When several tones are harmonious, they are said to produce a chord. When such tones succeed each other, they give rise to what is called a melody, and a succession of chords produces what is termed a harmony. The different tones are called notes, or musical notes. * This fact may explain why it is that near the middle of a large hall if is often difficult to hear distinctly. By reflection, the sound-waves from the end of the hall interfere with those which proceed from the speaker's voice, and destroy their effects. When are musical tones said to harmonize ? to be in unison ? When dis- cordant ? What is a chord ? harmony ? melody ? VIBRATING STRINGS AND MUSICAL NOTES. 237 I. Relation betiveen a vibrating String and musical Notes. Let us first determine the relation which exists between a vibra- ting cord or wire and musical notes. For this purpose the sonometer or monochord may be employ- ed. It consists of a hollow box, Fig. 1 97, across which wires or Fig. 197. '8 i r Q * $ =| HT IT Q J g 5" strings may be stretched by means of weights, P. The cord is fastened at one end, C, and the other passes over a pulley, M, and is attached to the weight P. Two bridges, F F', are placed near each extremity. There is also a movable bridge, H H', which may be placed at any desirable point, so as to shorten the string at pleasure by pressing it upon this bridge with the finger. Such an instrument will enable us to ascertain the relation between the length, weight, and tension of cords and musical notes. We have seen, page 207, that 1 . The number of vibrations is inversely as the length of the string. 2. The number of vibrations is as the square root of its tension, or stretching weight. 3. The number of vibrations of strings of different thickness is inversely as their diameters. 1. In using the monochord we may employ one string at a time, and vary the size and length at pleasure. Suppose the cord C M be gradually stretched by the weight P, and a violin bow drawn across it. As long as the eye can Describe the sonometer. Repeat the laws of vibrating strings. 238 NATURAL PHILOSOPHY. trace the vibrations, no soimd will be heard, but as soon as its tension enables it to make 16*5 vibrations per second, the eye fails to perceive any intervals between them, and the ear is impressed with the sensation of sound, and this is the lowest tone which it is capable of discerning. This note is designated by Q. The string in this case must be loaded with metal, or be made very long, in order to vibrate with sufficient intensity to be heard. 2. If, now, the string be divided in the center, and the bow drawn across half of it, it will perform 33 vibrations per second, and the note is called an octave, and designated by C. If but one quarter of the string is allowed to vibrate, it will perform 66 vibrations per second, and yield a note which is a second octave, and is designated by C. If but one eighth of the string vibrate, it will perform 132 vibrations per second, and we shall have a note which is a third octave of C. In this way we may proceed dividing the string until we reach nine octaves, which include the whole number of sounds used in music. There is, however, a practical difficulty in consequence of the size of such a string, and, in order to obtain the higher notes, strings of less diameter and greater tension must be employed. We may attach a weight in the above case four times that which gave 16*5 vibrations, and obtain the octave, or 33 vibrations, and then, by adding four times this weight, we may reach the second octave, or 66 vibra- tions per second. 3. If the fundamental or lowest note which a string with a given tension will make be represented by 1, then the lengths of the string for the several octaves will be -, {th, }th, T Vth, &c. ; or, if the stretching weight be represented by 1 , the added weights for the octaves will be 4, 16, 64, &c. But there are eight notes in each octave, which are designated by the letters C, D, E, F, G, A, B, C, and called the Diatonic Scale. How many vibrations per second must a string make to yield the lowest note, or C ? If the string is but half as long, how many vibrations per sec- ond will it perform ? How are the octaves produced ? How must the tension be increased to answer the same purpose as halving the string? What are the relative lengths of strings to form the notes of the diatonic scale? D.ATON.C BCALB. The length of string necessary to produce th represent the length required for C by 1, will be C D E F G A B 1 I I * I i T 8 As the number of vibrations is inversely as the length of the string, if we call the number which gives C 1, then, by invert- ing the fractions representing the lengths, we shall be able to ex- press the relation which the number of vibrations of each note^n the octave bears to the others. Thus : CDEFGABC 1 f t I I 2; and, reducing these fractions to a common denominator, we have the series CDEFGABC 24 27 30 32 36 40 45 48. The string which gives the note C makes 24 vibrations, while that which yields the note D makes 27, E 30, F 32, &c. Now chords will occur whenever the vibrations of the several strings bear a definite relation to each other, or when their vibra- tions frequently coincide. Thus C makes 4 vibrations while E makes 5, C makes 3 while F makes 4, C makes 2 while G makes 3 ; and as the vibrations in this last note more frequently coin- cide with C, it is a more perfect chord ; it is called a fifth, being the fifth note from C. If we examine the intervals between the notes, we shall find that they are not all equal. Thus the in- terval between 24 and 27 is jth, between 27 and 30 th, &c., giving the series for the intervals between CDEFGABC I * TV * * I iV That is, there are three intervals of |th and two of th. The former are called full perfect tones, and the latter small perfect tones. The two intervals between E F and B C are each yjth, and, as they are nearly half as great as those between the oth- er notes, they are called semitones or hemitones. How may the relative number of vibrations for each note of the scale be expressed ? When will the more perfect chords be produced ? Are the intervals equal ? What are full tones, and what semitones ? 240 NATURAL PHILOSOrii * . 4. By shortening the string, diminishing its diameter, or in- creasing its tension, we might pass in the same manner through the several octaves, but it would be a repetition of a similar series, and we should find that though every eighth note from C would form a perfect chord with the lowest note which the string might give, yet the octaves of some of the other notes would cause a slight discord. Thus, while the key note C makes one vibra- tion, E, which is called the major third of C, makes f vibrations, and the major third of this note is of , or f f vibrations, and the major third of this last note is f of f of f , or ^V vibrations. This third note does not exactly accord with the octave of the fundamental note, which is represented by y 8 . When we as- cend, then, through full thirds, we fall below a pure octave. The same is true of the fifths, which rise above the pure octave of the key note, and hence musicians cause these notes to be raised or lowered a little to preserve the purity of the octaves. This is called temperament. 5. Intermediate notes are often wanted between those whose interval is a perfect tone. These notes take their name from the note above or below them, and are called sharped or flatted notes. Thus, the note between C and D is called sometimes C sharp, and sometimes D flat, according to circumstances. Between E and F, and between B and C, there can be no flatted or sharped note. 6. In the piano-forte the strings are of different lengths, differ- ent diameters, and some of them loaded ^with metal in order to yield the lower notes, the same string yielding but one tone. In the viol, tenor or bass, the tones are modified by the size and different degrees of tension given to the string, and the same string is made to yield several notes by shortening it with the fin- gers. In such instruments, all the strings being of the same length, those which yield the lower notes are also loaded with metal, to diminish the rapidity of vibration. In the harp the strings are varied in size, length, and tension II. Musical Tones in Pipes. Having considered the relation How may several octaves be attained by strings ? Under what condi- tions will the octaves form chords ? discords ? What are flats and sharps, and what is their use 1 How are the different notes produced in the piano- forte ? in the viol ? the harp ? MUSICAL TONES OF PIPES. 241 between stretched strings and the tones which they are capable of yielding, we proceed now to investigate the relations existing between air-waves and these same musical notes, for it is through the medium of air-waves that the vibrations of strings convey their impressions to the ear. We have seen that when air is made to vibrate in a covered or open pipe, the vibrations consist of successive condensations and rarefactions of the layers of air, the motion taking place in the direction of the length of the tube. ]Let us now ascertain the length of the air-waves necessary to produce given tones in connection with open and covered pipes. 1. Covered Pipes. If we take a covered pipe, a b, Fig. 198, Fig. 198. a be d 16 feet in length, and cause it to resound by bringing a vibra- ting string or plate, which makes 16 '5 vibrations per second, near its open end, it will yield the lowest note, Q, or the sound-wave which is formed will make 16-5 vibrations per second. Now we have seen that, in order that the air in such a pipe may be thrown into regular vibrations, the tube must be ^th, f ths, f ths, ^ths, &c., the length of the wave. The lowest note, therefore, which a covered pipe will yield must have an air- wave four times its length. The air-wave, then, which yields the lowest tone, C, must be 64 feet in length. The length of this wave, which gives the lowest note, may be confirmed by the rate at which sound travels. If we assume that the velocity of sound is 1120 feet per second, then a wave 64 feet in length would traverse a tube 16 feet in length 17'5 times in a second ; but the velocity of sound varies with the tem- perature. If we assume that the medium velocity of sound is 1056 feet per second, then a wave 64 feet in length would trav- erse a tube 16 feet long 16 - 5 times per second : 16'5 X 64 1056. A covered pipe, then, 16 feet long, will yield the lowest note, How are musical tones produced in pipes ? What is the length of an air-wave which yields the lowest note ? How is its length determined ? In what other manner is the length of the wave which yields the lowest note ascertained ? L 242 NATURAL PHILOSOPHY. and its wave length is 64 feet. This same pipe may yield other notes. The next higher note will have a wave length fds the length of the pipe, and the third note will have a wave length f ths the length of the pipe. The higher notes are produced by the formation of nodes of oscillation in the pipe, just as a string may give a higher note by dividing itself into parts, with nodes forming standing vibrations. If we diminish the length of the pipe, the key note will be raised. A covered pipe 4 feet long, which has a wave length of 16 feet, will yield the note C of the diatonic scale. Now the no.tes which combine with C, and make an agreeable impression upon the ear, are produced by air- waves whose lengths are |, fds, |ths, f ths, f ths of the length of the wave which yields C, and hence these notes may be produced by pipes which are |, fds, &c., the length of the pipe C. The time of oscillation is inversely as the wave lengths, so that these fractions inverted will express the relation between the number of vibrations of 'he several air-waves ; and hence, while C makes 1 vibration, the next note, f., will make 2. This note is the octave of C. The next note, whose wave length is |ds of C, will make 3 vibrations while C makes 2, and tin's is called the 5th of C, and is designated by G. The next note, f ths the wave length of C, makes 4 vibrations while C makes 3, and is the 4th of C, and designated by F. The note having a wave length ths of C, makes 5 vibrations to 4 of C, and is the major third of C, designated by E ; and the note whose wave length is |ths of C, makes 6 vibrations while C makes 5. This is the minor third of C, and marked E flat. We have, then, the following series of notes, making vibrations simultane- ously, according to the numbers : C E F G C 24 30 32 36 48. In order to complete the scale, E, F, and G must have their octaves, thirds, and fifths. The fifth of G makes 3 vibrations while G makes 2, and the next lower octave of this note makes Will the same pipe yield other notes ? What note will a covered pipe four feet long give ? How are the wave lengths of the several notes of the scale determined ? Describe the manner in which the several notes of the pcale are found, and the letters which designate them. ORGAN PIPES. 243 27 vibrations to 36 of G and 24 of C. This is D. The major third of G is B, which has 5 vibrations to 4 of G, or 45 of B to 36 of G. The fifth of F makes 48 vibrations while F makes 32. This is the octave of C ; and the major third of F makes 40 vibrations to 32 of F, and is designated by A. We have, then, the following series of notes, called the C gamut, whose simultaneous vibrations are CDEFGABC 24 27 30 32 36 40 45 48; and the wave lengths of these notes, representing the wave length of C by 1 , are, CDEFGABC I I which shows the same relations as exist between the length of cords and the notes which are yielded by them. Fig. 199- It is obvious that a series of pipes corresponding with the length of the air-waves above considered may be arranged so as to constitute a musical instrument. Organ pipes are arranged in accordance with these laws. The pipe, Fig. 199, consists of a pedal, P, which has a slit in it to admit the air from the bellows, and a tube with a mouth-piece, t. The air in the tube is thrown into vibrations by that which passes through the pedal, and strikes against the upper lip of the mouth-piece. The organ pipe is similar to a ^vh^stle. In flutes and similar ivind instruments, the several notes are produced by apertures placed so as to produce the same effect as shortening the tube ; and hence, in this t case, the tube, and consequently the air- waves, are length- ened or shortened by means of the fingers and keys, by which the apertures may be opened and closed at pleasure. 2. Open Pipes. Air- waves formed in open tubes may form a series of musical notes, provided the tubes bear a certain relation to the length of the waves. But in consequence of the How are the wave lengths represented, and what relation do they bear to the wave length of the key note, or C ? Describe the organ pipe. How are notes formed in flutes and similar wind instruments? NATUPtAL PHILOSOPHY. fact that the wave is not reflected at the bottom of the tuhe, but at the open extremities, the pipe, to produce the lowest note, C, must be 32 feet long, as the wave, which is 64 feet, will not be reflected until half of it has entered the pipe. In this case there will be a node of oscillation in its center, Fig. 200, and the three Jl Fig. 200. B C notes which such a pipe will give will have air- waves whose lengths are twice the length of the tube, once its length, and once and a half its length ; in the second note there are two nodes of oscillation, and in the third three nodes, Fig. 20 1 . The same Fig. 201. L ** n b a> n KM s n f n, TV Y relation exists between the air- waves and the length of a tube, whatever its key note may be. 3. Reed Pipes. In reed pipes a tongue is the vi- Fig. 202. brating body, which is set in motion by a current of air, and communicates its vibrations to the air in the pipe. The tongue consists of a flat piece of metal or elastic wood, r, Fig. 202, placed over a slit in the mouth-piece or hollow tube, c, and fastened at one end. A tuning wire, t, is made to slide up and down, so as to shorten or lengthen the tongue. In its vibrations it observes the laws of vibrating rods. In some forms the wind enters c through a pedal and bellows attach- ed to it, and in others it is forced in through the mouth. III. Transmission of Tones. We have seen that sound-waves may be transmitted from solids and liquids to air, and the reverse ; but, in passing from one medium to another, the sound is partially or wholly impeded. Thus the vibration of a tuning fork emits but a faint sound ; but the vibrations may be more readily communicated to the air by causing it to vibrate in contact with a larger vibrating sur- What relation between the wave lengths of notes and the length of open pipes ? What is the vibrating body in reed pipes? Describe the tongue. How may sounds be transmitted from one medium to another! ORGANS OF VOICE. 245 face, as a hollow box. A musical box will in this way transmit its vibrations to the air with more intensity if placed on some body, as the cover of a piano, to increase the vibrating surface. Air-waves falling on solid or liquid bodies are also impeded unless their length correspond with the length of the wave which the solid is capable of yielding. fig- 203. Thus, if a string, h as e d, Figure 203, stitched, and a bridge, b, placed at about one third of its length, and a bow be drawn across at a, the part b d will be thrown into vibrations, dividing itself into two parts, with a node at n yielding the same tone as e b. This is sometimes called the Sympathy of Sounds. The JEolian Harp produces its various notes by dividing it- self so as to be in sympathy with the varying force of the wind. We may notice the effect of an organ in a church. At the recurrence of certain notes, the pillars and whole building are shaken with vibrations. A speaker, the key note of whose voice corresponds to that of the room, will speak with much greater ease, as the vibrations of the room aid his voice. When certain notes are struck on a piano-forte, the lamps or crockery in the room will often vibrate. It is said that some musicians have the power of throwing a glass or china vessel into such violent vibrations, by sounding its key note, as to break it into many pieces. IV. Organs of Voice. The windpipe, through which air en- ters the lungs, is a tube made up of rings of cartilage, and termin- ated at its upper extremity by what is called the larynx, which constitutes the organ by which different tones are produced. Ar- ticulate sounds constituting speech are made principally by means of the tongue, palate, and lips, in connection with the action of the larynx. What is meant by sympathy of sounds ? When will the pillars of a church vibrate? What effect upon bodies to sound their key note near them ? By what organs are different tones produced ? What organs are concerned in articulate sounds? 246 NATURAL PHILOSOPHY. 204 - The larynx consists of four cartila- ges : a, Fig. 204, is called the cricoid cartilage, and surrounds the base of the larynx ; b b is called the thyroid carti- lage; c c, the two arytenoid cartilages; d is the epiglottis, which lies above the glottis, e. The edges of the glottis con- sist of very elastic tissue, forming what is called the chordce vocales, v, which may be more or less stretched by appro- priate muscles. The formation of notes is similar to reed pipes, the vibrations being performed by the chordae vocales, which, with the action of the other mem- branes, open and close the glottis with great rapidity, allowing the air to escape, and throwing it into vibrations, which yield tones high or low, intense or feeble, according to the tension of the vibrating tissues and force of the air from the lungs. For a full description of the organs of voice and of hearing, the student is referred to works which treat more at length of these organs. V. Organs of Hearing. The organs of hearing consist of three main parts : the external ear, the cavity of the tympanum, which is separated from the external ear by a membrane, and the labyrinth. The external ear consists of the pinna, C, and the meatus, M, Fig. 205, which convey the waves of sound to Fig. 205. Describe the larynx. What are the principal parts concerned in speak- j ? Of what do the organs of hearing consist ? CALORIC. 247 the membrane of the tympanum, D, which has attached to it on the inner side a small bone called the malleus, B, which is also connected with three other bones ; the second is called the incus, the third os orbiculare, and the fourth stapes, T, which closes the funestra ovalis. The tympanum cavity, V, is con- nected with the Eustachian tube, E, opening into the mouth, and the air in the labyrinth, K S, is put into vibrations by the vibrating bones, and communicates with the auditory nerve, N, where the sensation is conveyed to the mind. The use of the bones is not only to conduct the vibration, but to increase the tension of the membrane of the tympanum, so as to modify the intensity of the sound. CHAPTER VII. OF CALORIC OR HEAT. Heat or caloric exists in two states, Sensible and Insensible. I. Sensible caloric lias one general property, which is a tenden- cy to diffuse itself equally among the atoms of matter, and to form an equilibrium of temperature. This is effected by con- duction and radiation. II. Sensible caloric has one principal effect, which is a tenden- cy to expand all bodies, solid, liquid, and gaseous. III. Insensible caloric gives rise to the liquid and gaseous forms of matter, and produces the phenomena of liquefaction and vaporization ; hence, IV; By heating water it may be converted into steam, which, in connection with the steam-engine, is employed as a most use- ful and efficient mechanical power. THE subject of caloric belongs to Chemistry, but, as heat is a powerful mechanical agent, there is one branch of it which comes appropriately under the notice of the natural philosopher. Caloric exists in two states : 1 . Sensible, in which state it pro- Describe the several parts of this organ. Where is the sound perceived? To what science is caloric assigned ? In how many states does it exist ? 248 NATURAL PHILOSOPHY. duces the sensation of heat, and tends to expand all bodies into which it is introduced. 2. Insensible, in which condition it does not affect the temper- ature of bodies, but exists in them in greater or less quantities, and gives rise to the liquid and gaseous forms of matter. I. Sensible Caloric has one fundamental property, which is a tendency to diffuse itself equally through all bodies; that is, to bring all bodies to an equilibrium of temperature. This is effected in two ways : 1 . By conduction, in which case it passes from particle to par- ticle through any body. The rapidity with which it passes va- ries greatly in different substances. Solids are almost the only bodies which conduct heat at all. In liquids the power is very slight. In gases it is wholly wanting. Solids are heated by conduction, but liquids and gases are heat- ed by convection, that is, by contact of their particles against the surface of some heated solid. 2. By radiation, in which case caloric is thrown off in all di- rections from the surface of a heated body in right lines, and pass- es through air and other gases without heating them. When radiant caloric falls upon solid or liquid surfaces, it is either reflected, that is, thrown back from the surface in the same manner as a solid would be ; or it is absorbed, that is, passes into the body and heats it ; or transmitted, that is, passed directly through the body.^ II. Sensible Caloric produces one generic effect, Expansion. It expands all bodies, solids, liquids, and gases. In solids and liquids, the degree of expansion varies in different substances, and in the same substance at different temperatures ; but all gases are equally expanded by heat, whatever their temperature may be ; that is, equal additions of caloric expand them equally, and for every degree of Fahrenheit's thermometer they increase about * For a more extended view of conduction and radiation of caloric, see Gray's Chemistry, Caloric, p. 26. What is the fundamental property of sensible caloric ? How are solids heated? How liquids and gases ? Define conduction and radiation. What generic effect produced by caloric ? SENSIBLE AND INSENSIBLE CALORIC. 249 of what their volume would be at 32, on the supposition that they do not condense at that temperature. III. Insensible Caloric exists in different quantities in differ- ent substances, while their temperature is exactly the same ; and as any body changes its form, its power of retaining insensible caloric is increased or diminished, so that caloric will pass from its sensible to its insensible state, and the reverse, as the forms of matter change. The principal effects of insensible caloric are to produce lique- faction and vaporization. 1 . When sensible caloric is applied to a solid, as lead, at a cer- tain temperature, the solid melts, but after it has arrived at the melting point, which is always the same in the same substance, an additional quantity of caloric must be passed into an insensible state before liquefaction can be effected. Thus ice, when brought to the temperature of 32 F., its melting point, will still retain the solid state until sufficient caloric is added to raise it, if it continued ice, to 172 F., or 140 degrees of sensible caloric must pass into the insensible state before the ice will become water. 2. The same also takes place when liquids are heated to the point of vaporization. Before they assume the state of vapor, there must be added a large quantity of free caloric to pass into an insensible state. Thus water, if heated to 212, its boiling point, will not assume the state of vapor or steam until nearly 1000 of free caloric are supplied to pass into an insensible state. When vapors are condensed into liquids, and liquids are con- gealed to solids, this insensible caloric becomes free, or is driven out of the body, and appears again in the sensible state. IV. Steam. The formation of steam by the agency of caloric, and its employment as a mechanical power in connection with the steam-engine, render a knowledge of its properties essential to a clear understanding of the manner by which its useful effects are produced. 1 . Steam is formed at all temperatures, but it is only when it is formed at the temperature of the ebullition of water, and confined What is insensible caloric, and what are its effects? Illustrate these effects. What is steam, and how formed ? L 2 250 NATURAL PHILOSOPHY. in some appropriate vessel, that its force can be employed for any valuable mechanical purpose. When water is heated to 212 F. in an open vessel, it assumes the state of steam, in doing which it must exert a pressure equal to that of the atmosphere, or 15 Ibs. to every square inch. If a quantity of steam thus formed is conducted into a close vessel of the same temperature, 212, and heat applied to it, it will expand, or tend to expand, in precisely the same manner as atmospheric air ; for if it were placed in a bag, and the pressure of the atmosphere entirely re- moved, it would tend to expand indefinitely. If, however, we attempt to apply pressure to 1 steam at 212 F., or to remove pressure from it, it will be condensed, and return to the fluid state. At this point of condensation the steam is said to have its maximum of tension, and if it is formed at higher tempera- tures under the influence of pressure, at the point it would con- dense it has its maximum of tension ; hence The tension of steam will depend upon the temperature at ^vhich it informed. 2. But we can not determine the tension of steam, or its elastic force at different temperatures, without attending to the condi- tions under which it is formed in the boiler ; for, as the tempera- ture is increased, portions of steam are constantly added by the vaporization of the water, which renders it necessary to resort to experiment in order to ascertain its increase of tension with the increase of temperature. This may be effected by employing a strong boiler called a Digester, a, Fig. 206, partly filled with water. A thermometer, d, passes into the water to ascertain the temperature, and a glass tube, c, extends to the bottom, and dips into a quantity of mercury under the water. If now this bulb be heated by a spirit lamp, and the wa- ter be made to boil, the air being all let out by the stop-cock b, at the moment the water reaches its point of ebullition, 212 F., the tensioii of its steam will be just equal to that of the atmos- What law of expansion does stefcm observe on increase of temperature ? Upon what does the tension of steam depend ? How is the pressure of steam as the temperature rises ascertained ? Describe the digester TENSION OF STEAM. 251 phere ; and as that pressure is exerted by the air in the tube c, the mercury will remain at the same point as when the air was in the upper part of the globe instead of the steam. If now we raise the tempera ure to about 249 F., the mer- cury in the tube will be raised 1 1 the height of 30 inches, the pressure on the surface of the watei is doubled, and, of course, the elastic force of the steam, its tension, will be equal to two atmos- pheres of pressure, or 30 Ibs. to the square inch. By increasing the temperature, we shall find that the tension increases with increase of temperature, as in the following table : At the temperature of 212 F., the tension is equal to 1 atmosphere. 249 293 320 .341 359 392 438 456 2 4 6 8 10 15 25 30 (Mutter,} If water is confined under the pressures indicated in the above table, its boiling temperature will vary according to the same law of temperature as the tension of its vapor, so that its boiling point under a pressure of 30 atmospheres would be 456 F. It will be seen by inspecting the above table that the tension of steam increases much more rapidly in the higher than in the lower temperatures. Thus, between 212 and 249 F., a rise of 37 only doubles the tension, or renders it equal to 2 atmospheres ; but from 438 to 456 F., a jise of 18, the increase of tension is equal to 5 atmospheres. This rapid increase of tension is due to the greater density of the steam, which gives it a greater elastic force. This is shown by the fact that a cubic inch of water, when converted into steam at 212, will occupy a space equal to 1700 cubic inches ; but if it is converted into steam at a temperature of 249 F., it will only yield 897 cubic inches ; and if the tem- perature be 359 when it is converted into steam, it will then oc- cupy only 207 cubic inches. Hence, as it occupies much less space, its density must be much greater when formed at high than at low temperatures ; and if there were no additional steam added, What effect has pressure upon the boiling point of water? 252 NATURAL PHILOSOPHY. there would be an increase of tension from an increase of tem- perature. For these two reasons, therefore, the tension increases more rapidly as the temperature is higher. 3. When steam is formed at any temperature, at its maximum of tension a sudden and slight reduction of temperature will con- dense it. By means of a jet of cold water, the steam in the cyl- inder of the low pressure steam-engine is condensed, and it is due to this property of steam that low pressure engines are capa- ble of being worked. From this rapid increase of tension or pressure as the temper- ature is higher, there would seem to be a practical advantage in using steam under high pressure ; that is, if we wish to pro- duce a given constant force, it can be done with much less fuel under a high than under a low temperature ; for the insensible caloric diminishes as the temperature increases, so that in the same weight of steam the sum of sensible and insensible caloric is constant, and yet there is so much danger at such high tem- peratures of bursting the boiler as to render it impracticable to secure the advantage. A pressure of two or three atmospheres is sufficient for the ordinary purposes to which steam power is applied. V. Steam- Engine. The steam-engine owes its present perfection to Mr. James Watt. In or- der to understand the principle by which steam is applied in the engine, it is only necessary to take a glass tube, with a bulb and solid piston capable of working up and down in the tube, A^B, Fig. 207. By heating the water in A with a spirit lamp, the steam formed will raise the piston to the top ; then, by immersing the bulb, A, in cold water, it will condense the steam, and the force of the at- mosphere will drive the piston to the bottom. Now if, by means of a tube connected with a steam boiler, the steam be admitted at the bottom below the piston, it will raise it up as before ; but, in order to condense it, its temperature must be reduced. This may be effected by stopping the supply of steam ; and, by How may steam be condensed ? By what experiment may the princi- ple of the steam-engine be illustrated 7 LOW AND HIGH PRESSURE ENGINES. 253 means of a tube in the side, introducing a small jet of cold wa- ter, the pressure of the atmosphere will again force the piston to the bottom ; on readmitting the steam, it will be forced up. This may illustrate one form of the Zo^-pressure engine. It will be seen that the piston must be forced up against the pressure of the atmosphere, and hence the steam must have considerable tension ; but if the piston rod is made to move through a steam- tight collar, and the steam introduced and condensed at the top of the cylinder as well as at the bottom, the same motion may be produced with much less power ; as the whole pressure of the atmosphere is removed, the piston will be forced up by a force less by 15 Ibs. to the square inch, but when it is at the top we must apply the same force to press it to the bottom. Hence, as the engine is worked with a lower power of steam, it is called a low-pressure engine, and the improvement of Watt consisted chiefly in condensing the steam in a separate vessel called a con- denser, so that the temperature of the cylinder was kept uniform. The high-pressure engine is the same in all respects, except- ing that the steam is not condensed, but is passed out at the bot- tom and top of the cylinder, through appropriate valves, which are opened and closed by the motion of the piston. The same motion also admits and shuts off the steam at the bottom and top of the cylinder. As these engines work against the pressure of the atmosphere, they require a high tension of steam, and hence are called high-pressure engines. High-pressure engines are used in the steam -boats on our West- ern rivers and lakes, whether this is due to the opinion that the mud which collects in the boiler and other parts of the machinery is more inconvenient in low than in high-pressure engines, or whether it arises from some other cause. We have lately seen an invention which will remedy the inconvenience, by filtering the water as it enters the boiler. When the steam escapes it gives rise to successive puffs, which may be heard at a great distance. Locomotives have also high-pressure engines. One reason for this is, they may be made to occupy less space. Low-pressure Describe the low-pressure engine ; the high-pressure. What engines are used on our Western waters ? What kind of engines are used in locomotives ? NATURAL PHILOSOPHY. engines have a more complicated apparatus attached to them for condensing the steam, and are generally used in all large stearu vessels. Connected with the cylinder and piston there is a very compli- cated apparatus, as a boiler, pumps, wheels, &c., "which consti- tute what is called the Steam-Engine. 1. The Boiler. The steam boiler is made in the form of a cylinder, out of plates of sheet iron strongly riveted together. Sometimes tubes extend through the boiler, to allow the heat to be more readily and equally diffused. The following cut, Fig. 208, will give a very good idea of the boiler and its fixtures. Thus, B B is the boiler, the lower part containing water, and the upper portion, S S, steam ; F B is the fire. When coal is used, the fire is kept up by means of a blower, consisting of a fan- wheel, which, being rapidly turned by the machinery, forces the air through a tube constructed for the purpose. (1.) To determine the elastic force of the steam, or pressure, as it is called, there is both a barometer gauge at M, and a safe- ty valve in the center, e a b. This valve, which is of a conical Describe the boiler. How is the pressure determined 1 THE STEAM BOILER. 255 shape, is attached to a rod, connected with a lever of the third kind, e being the fulcrum, a the point where the force of the steam is applied, and w the weight capable of sliding on a b. As this lever is graduated like a steelyard, the force of the steam may be accurately weighed. It also serves another, which is its princi- pal purpose, that of a safety valve; for when the pressure arrives at a certain degree of intensity, the valve is forced up and the steam rushes out, and thus the boiler is protected from being burst by the elastic force of the steam. (2.) But it sometimes liappens that the steam loses its tension, or becomes condensed by the addition of too much cold water, and the boiler then is liable to be forced in by the pressure of the atmosphere. To guard against this, there is another valve at U, which opens downward, and allows the air to rush in whenever the boiler is exposed to a collapse. L is a large opening, firmly closed excepting when it is desirable to clean the boiler, as it be- comes incrusted with salt or mud. (3.) To determine the height of ivater in the boiler, two tubes, with stop-cocks, c d, are inserted; one of them dips just below the water level, and the other passes into the steam just above the water level ; if the water sinks too low, steam will issue from each pipe ; if too high, water will be forced through both of them. (4.) To regulate the supply of ivater as it is constantly passed off in steam, there is a feed-pipe. This consists of a pipe, v o, which extends nearly to the bottom of the boiler, having a valve, v, which is opened and closed by the lever b c a. The lever has attached to it a rod, which passes into the boiler, and is ter- minated by a square block or stone, B, resting on the surface of the water in the boiler, and counterpoised by a weight, p. This lever turns upon the fulcrum c. If the water rises in the boiler, it lifts the end of the lever , and closes the valve v, which pre- vents the water from flowing in through the pipe ; but if the wa- ter sinks, it depresses a, which lifts the valve, and allows a sup- ply to flow into the boiler. By this means the water in the boil- er is kept at the same height. How may a collapse be prevented ? By what arrangement can the height of the water in the boiler be ascertained ? How is the supply of water regulated ? NATURAL PHILOSOPHY. (5.) To convey the steam to the engine there is a steam-pipe, s, with a valve, v, which may be used to regulate the supply of steam by opening and closing it with the hand, or by means of the governor, which is attached to the revolving parts of the ma- chinery (see page 255). 2. The Steam-Engine, Fig. 209. Fig. 209. (1.) The steam is conducted through the steam -pipe, s, which comes from the boiler through the four-way cock, a, where the tube branches, one pass- ing into the cylin- der, c, near the bot- tom, and the other near the top, so that by means of a valve connected with the levers yy, the steam may be sent altern- ately above and be- low the piston as the machinery is put in motion. The pis- ton-rod is attached to the end of the working-beam, B F, which moves upon the fulcrum or pivot, A. A rod, F R, is also attach- ed, either to the crank of the fly-wheel, H H, with which the other revolving parts communicate, or directly to the crank of the wheel, which, as in the steam-boat, bears the floats upon the ex- tremities of its axle. (2.) Escape of Steam. In the high-pressure engine, after the steam admitted into the lower part of the cylinder has raised the piston, it passes out through a valve in the bottom, which opens at the moment the steam is let in at the top to force the piston down ; a similar valve discharges the steam which is above the piston as it rises. In the low-pressure engine, the steam above and below the piston is condensed at each stroke. (3.) Condenser. For this purpose there is a condenser, J, im- How i3 the supply of steaai regulated ? How is the steam introduced into the cylinder ? What becomes of the steam in high-pressure engines ? How is it disposed of in low-pressure engines ? THE STEAM-ENGINE. 257 mersed in a cistern of cold water, and with pipes, ff, which are connected with the bottom and top of the cylinder, to allow the steam to flow into it as the piston works up and down in the cylinder. In this vessel the steam is condensed by a jet of cold water, which is thrown from the injection cock. The water thus con- densed is pumped by the air pump, O, into the well, W, from whence it is again pumped into the pipe i i, which leads to the feed-pipe. By this means warm water is constantly supplied to the boiler, and this occasions a great saving of fuel in work- ing the engine. (4.) Regulation of the Steam. The supply of steam is regu- lated by the governor, G (p. 111). The valves which admit the steam above or below the piston in the cylinder are closed, and the steam shut off when the piston has traversed half or three quarters of the distance from the top to the bottom or the bottom to the top. If the steam were to flow till the piston had reach- ed its highest or lowest point, there would be an irregularity in its motion, and a sudden jar at each stroke ; but by shutting off the steam at a certain point, the motion is quite uniform. There is also a great saving of power, as it requires much less steam to work the piston. (5.) The power of the engine depends very much upon the size of its cylinder and the length of the stroke. If we know the tension or pressure of the steam and the area of a section of the cylinder, we may determine the force of its stroke, or the force which is exerted upon it by the steam. It is found, however, that much of this force is lost before it is transmitted to the re- volving parts of the machinery. The power is estimated by com- paring it with horse power, on the supposition that a horse will exert a force in the space of one minute which will raise 33,000 Ibs. one foot in height. Thus we have engines of 2, 5, and 20 horse power. " The steam-engine appears to be a thing almost endowed with intelligence. It regulates with perfect accuracy and uniformity the number of its strokes in a given time, counting and record- ing them, moreover, to tell how much work it has done, as a clock records the beats of its pendulum. It regulates the quan- How is the steam condensed in the low-pressure engine ? How is the power of the engine estimated t 258 NATURAL PHILOSOPHY. tity of steam admitted to work ; the briskness 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 which may accidentally enter into parts which should be vacuous ; and when any thing goes wrong which it can not of itself rectify, it warns its attendants by ringing a bell. Yet with all these tal- ents and qualities, and even when exerting the force of hundreds of horses, it is obedient to the hand of a child. Its aliment is coal, wood, charcoal, or other combustibles. It consumes none while idle. It never tires, and wants no sleep. It is not sub- ject to malady when originally well made, and only refuses to work when worn out with age. It is equally active in all climes, 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, &c. ; and a small engine, in the character of a steam pony, may be seen dragging after it on a rail-road a hundred tons of merchan- dise, or a regiment of soldiers, with thrice the speed of our fleet- est horse coaches. It is a king of machines, and a permanent realization of the genii of Eastern fable, submitting supernatural powers to the command of man," Arnott. CHAPTER VIII. ELECTRICITY. THE term electricity is derived from the Greek- name* of am- ber, a substance which, on being rubbed with a woolen or silk cloth, has the property of attracting light bodies. History.- The first recorded discovery of this property was made by Thales of Miletus, who lived about six hundred years before the Christian era ; but nothing important was known of the subject until the commencement of the seventeenth century. Dr. Gilbert, in 1600, made some few observations. Boyle, a Meaning of electricity. History of electricity. ELECTRICITY. 259 half century later, made a few additional discoveries ; but the science was not systematized until the time of Franklin, Gray, and Du Fay, between the years 1730 and 1760. Since this time electricity has attracted much of the attention of philoso- phers, and is now one of the most beautiful and interesting branches of physical science. Amber is not the only substance capable of exhibiting the phenomena of attraction when friction is employed, but a great many other substances have this same property. Glass and res- inous substances, as a glass rod or a piece of sealing-wax, when rubbed, furnish, perhaps, the readiest means for exhibiting the presence of the electric fluid, as the unknown cause of this pecu- liar attraction is called. When any body is rubbed and electricity is produced, it is said to be excited, or electrically excited ; and if any other body re- ceive the fluid from it, that body is said to be electrified. Electricity is excited, however, in a variety of ways, and there are found to be certain modifications of its properties, dependent upon the mode of generating it. The two methods which pro- duce the greatest difference are friction arid chemical action. The former gives rise to Statical or Common Electricity, and the latter to Voltaic Electricity, or Galvanism. SECTION I. STATICAL OR COMMON ELECTRICITY. I. Electricity is excited by friction, by change of form and temperature, by pressure, and by chemical and vital action. II. Electricity is detected by electroscopes, and its force meas- ured by electrometers. III. It consists oftivo kinds, called positive and negative, also vitreous and resinous. The positive is produced by rubbing glass and other vitreous bodies, and the negative by friction upon amber and other resinous matter. These substances are called non-conductors, while the metals, water, and some other bodies are termed conductors. IV. The generic property of the electric fluids is, that each What other substances yield it ? Meaning of electrically excited and electrified. 260 NATURAL PHILOSOPHY. repels itself and attracts the other, so that the presence of the one induces that of the other, a process called induction. V. Free electricity resides on the surface of conductors, and does not penetrate their substance ; hence the quantity will de- pend upon the extent of surface. In a sphere it is equally dis- tributed, but in a spheroid it accumulates near the extremities, and floivs into the air from points, so as to prevent a pointed conductor from retaining it. VI. In the Ley den jar, the two electricities are held on opposite sides of glass by the force of their mutual attraction, by which arrangement electricity may be accumulated in much greater quantities, and made to exhibit its effects with greater power. VII. Electricity is capable of producing powerful effects, me- chanical, chemical, and vital.. VIII. The atmosphere is ahuays electrified in various degrees. In it the most sublime displays of electricity are witnessed in the phenomena of thunder storms ; and as electricity often pass- es from the clouds to the earth, its injurious effects may be avoid- ed by means of lightning rods, which will convey it silently to the earth, and thus prevent buildings from being rent by the " lightning stroke." I. Modes of producing Electricity . 1. By fric- fig- mo- tion of one body upon another electricity is always generated. Thus the friction of two solids, as woolen cloth on a rod of glass or resin, a, Fig. 210, causes both bodies to be excited, and they will attract light bod- ies, as b, if brought near to them. The effect of friction on different bodies is very dissimilar. Some retain the fluid on their surfaces, and do not permit it to pass from one point to another. Hence they are called non-con- ductors and insulators. All vitreous and resinous bodies, such as sulphur, silk, wool, feathers, and dry wood, arc non-conduct- ors. Others permit it to pass with greater or less facility over their surfaces, take it readily from non-conducting substances, How is electricity produced ? What are conductors and non-conductors of electricity ? MODES OF PRODUCING ELECTRICITY. 261 and impart it to other conductors with little or no obstruction. Bodies of this class are called conductor?, of electricity. Met- als are the best conductors ; and, though the effect of friction upon them is to excite electricity, yet it passes off readily unless they are surrounded by insulators. Resinous and vitreous bodies are those generally employed for exciting electricity, and hence are called electrics* 2. The friction of tivo liquids, or a liquid with a solid, also excites electricity ; but, as most liquids are good conductors, it is conveyed away as fast as it is- produced. Gases, also, by friction upon each other, or upon solid or liq- uid bodies, develop this fluid ; thus, when the air blows over the frozen ground, or when steam of high tension issues from a steam boiler, great quantities are produced. But friction, though the best and most common mode of exciting electricity, is not the only mode. 3. Electricity is excited by change of form in bodies. Thus, when water congeals or ice melts, or when water evaporates or is condensed in the atmosphere, large quantities of electricity are excited. The same is true of all other bodies which undergo a change of state. 4. Electricity is excited by the pressure of one body upon an- other, or by mere contact, so that we can not place our hand upon any substance without exciting the electric fluid, though in a degree requiring a special apparatus in order to detect it. 5. Electricity is also excited by chemical action, or by the decomposition of bodies. Thus, if a copper and zinc plate be immersed in acidulated water, Fig. 211, and their edges be brought together by means of a wire, d, electricity will be excited in currents flowing from one plate to the other. This kind of electricity is called Galvanic or Voltaic Electricity, and possesses many peculiar properties which distinguish it from the preceding kinds. 6. Heat is another means of producing electric currents. 7. Some animals also have the power of generating electricity by means of organs which resemble the galvanic battery. Why are not liquids used to generate electricity ? How is electricity excited by gases? Mention the other modes of exciting electricity. 262 NATURAL PHILOSOPHY. The three latter 'modes will be considered under Galvanism. From the above statements, it is evident that electricity per- vades all matter, liquids, solids, and gases, though it sustains very different relations to two great classes of bodies, which are distin- guished by the terms conductors and non-conductors, or insulators. No substance, however, is a perfect non-conductor. The pow- er of insulating and of conducting electricity is^possessed by the two classes of substances in very different degrees. The follow- ing table exhibits the most important substances in the two classes : Conductors. The Metals are the best. Charcoal, Plumbago, Pure Water, Moist Snow, Steam and Smoke, Vegetables, Animals. Non-Condnctors. Resins, Shell-lac are the best. Amber, Sulphur, Wax, Fat, Glass and precious Stones, Silk, Wool, Hair, Feathers. Cotton, Paper, Diy Air, Baked Wood, Indii Fig. 214. Lia Rubber. II. Modes of detecting Electricity. The instruments by which the presence of electricity is detected are called electro- Fig. 213. scopes. Those by which its force is measured are term- ed electrometers. But the term electrometer is generally used for both kinds. An electrometer may be a pith ball suspended to a rod by a thread, called the Pendulum Electrometer, or a pith ball on the end of a pointer, attached to an index, called the Quadrant Electrometer, Fig. 213, or two strips of metal, as gold leaf, called the Gold Leaf Electroscope. This instrument consists of a glass jar, d, Fig. 214, in which two strips of gold leaf are hung side by side, attached to a metallic rod, b, which is terminated by a disc, a, or a knob ; a cup and point, c, may also be applied to the disc. Two pieces of tin foil are placed on the inside of the jar, as d, to discharge the electricity, if the leaves diverge sufficiently to touch them. The most delicate instrument for detecting small quantities of electricity is 'Bohnenberger 's Electroscope, Fig. 215, which con- What are electroscopes 1 electrometers ? Describe the gold leaf elec- troscope Bohnenberger's. ELECTROSCOPES. 263 Fig. 215. sists of one strip of gold leaf, arranged as above, and suspended between two metallic plates, p m. These plates are connected by wires to a dry pile, a b, which is formed by a series of small circu- lar plates, each consisting of gold leaf and zinc, with a piece of paper between them. They are packed closely in a glass tube, so that the metals shall alternate with each other. By this means electricity will be excited, so that the plates p and m will be constantly in opposite states, and the leaf, being equally attracted, remains suspended between them ; but by communicating the slightest trace of electricity to o n, the leaf will move to p or m, according to the kind of electricity which is applied. III. Electrical States produced by Friction of different Sub- stances. By means of the gold leaf electroscopes above describ- ed, or simply by pith balls suspended by silk threads, we may ex- hibit, experimentally, the first fundamental facts which were noticed in reference to the electric fluid. Fig. 216. Exp. If a glass rod is rubbed with silk or with a wool- x x en cloth, and brought near the pith ball electroscope, Fig. \ __ 216, the ball will be attracted toward it, remain in contact ~^) a moment, and then recede or be repelled. If a second ball C\ and the alkali at the negative or pole. If the poles are termina- ted by platinum foil, the effect will be rendered visible by the change of color. The alkali will turn the infusion green, and the acid will change it to red. In compounds thus decomposed, the add always goes to the positive, and the alkali to the negative pole; and as bodies oppo- To what is the light and heat ascribed, and why ? How may water be decomposed ? Epsom salts ? How are the electric states of the elements of these compounds ascertained 1 Fig. 252. THEORY OF DECOMPOSITION. 301 sitely electrified attract each other, the electric state of the oxy- gen in the case of water must be negative, and that of the hydro- gen positive ; and in the case of the salt, the state of the acid must be negative, and the alkali positive. These states are not constant ; for the same substance may be positive in one combina- tion, and negative in another. Oxygen, however, always assumes the negative state, and potassium the positive state. It is sup- posed that the electricities are neutralized during combination, and that the elements assume different electrical states when the currents circulate. Fig , 253. Theory of Decomposition. To un- derstand how a compound is decom- posed, suppose A B, Fig. 253, be sev- eral particles of water, placed between the two poles of a battery, +, . These particles are non-electric before the current circulates, but the moment the poles of the battery communicate with them, the oxygen of each particle turns toward the positive pole, represented by the light half, and the hydrogen toward the negative pole. As the atom of oxygen is liberated at the -f- pole, the next takes it place, and the third takes the place of the second, so that there is a row of atoms of oxygen passing from the negative to the positive pole, each one of which successively combines with the particles of hydrogen which are passing off in the opposite direction. The process is similar in all cases of decomposition by galvanism. Gilding. When a metallic salt is decomposed, the metal is precipitated upon the negative pole of the battery. In conse- quence of this, the baser metals may be covered with the precious in a permanent and perfect manner. Thus, let the object to be gilded, after being made clean, be attached to the negative pole of the battery of one of Smee's cups ; two cups are better for the purpose, a larger number being too powerful ; and then, after dipping the positive pole, which should be of gold or silver, into a solution of chloride of gold, place the article toj>e gilded in the same solution. In the course of a few Are the electric states of bodies constant? Mention the theory of the decomposition of water and other compounds. Describe the process of gilding theory of the change which takes place. 302 NATURAL PHILOSOPHY. minutes it will be covered with the purer metal, and may be coated as thickly as is desirable by continuing the process. A bent tube, represented in Fig. 252, may be used for the purpose of holding the solution. This is the most perfect process of gilding hitherto discovered. If the positive pole have a plate of the metal similar to that in the solution, and of equal size with the object, the solution will remain of constant strength, because as soon as the chlorine is liberated from the gold, which becomes attached to the object, it will attack the positive pole, and dissolve an equal quantity of gold, so as to keep constantly saturated. By varying the process slightly, we may obtain perfect molds of any object we may wish to copy. This process is called Electrography . The object of Fig. 254. which a mold or cast is desired, sup- pose it to be a coin, is attached to the negative pole of a battery, N, Fig. 254, inserted in a saturated solution of blue vitriol. The positive pole, term- inated by a zinc plate, C, is placed in dilute sulphuric acid, facing the coin, but separated from it by a porous par- tition, as a piece of bladder. In this case, both the water and the sulphate are decomposed ; the oxygen of the water combines with the zinc, and the sulphuric acid with the oxide thus formed ; and the hydrogen of the water unites with the oxide of copper which the acid leaves, by which pure metallic copper is attached to the ob- ject. This coat, when it is sufficiently thick, may be separated, and is a perfect mold of the coin, every line, and even the shades of polish being accurately copied. From this a cast may be formed. The same effect may be produced without a battery, if the zinc is connected by a copper wire with the coin. This process is very useful for multiplying coins and medallions. How is the strength of the solution preserved ? How may molds be made from coins, and what are the changes which take place ? MAGNETIC EFFECTS OF ELECTRICITY. 303 SECTION III. MAGNETIC EFFECTS OF ELECTRICITY. MAGNETISM, ELEC- TRO-MAGNETISM, AND MAGNETO-ELECTRICITY. I. Certain ores of iron are naturally magnetic. Hardened steel may be rendered magnetic in several ways. The most obvious property of a magnet is that of polarity ; and it is found that similar poles repel, and opposite poles at- tract each other. II. A. current of voltaic electricity causes the magnetic needle to move in a plane perpendicular to that in which the current moves, and to stand at right angles to the direction of the cur- rent ; and, by changing the direction of the current, rapid revo* lutions may be produced. III. Currents of electricity circulating in Jielices of insulated copper wire convert soft iron and steel laid within the coils into powerful magnets, Jiaving poles depending upon the direction of the positive current ; and by changing the polarity, rapid revolutions may be produced. IV. Currents of electricity circulating in an insulated copper ivire at the moment they commence to flow or cease flowing, in duce currents of electricity in surrounding bodies, called Volta Electric induction. V. Magnets have the power of inducing currents of electricity which produce all the effects of those from the galvanic battery a subject designated Magneto- Electricity. VI. The theory which best explains these phenomena is, that currents of electricity are developed in all magnetic bodies; and when two currents are parallel, and flowing in the same direc- tion, they attract, and when in opposite directions, they repel each other. VII. Electro-magnetism is applied to several useful purposes, the most important of which are the electro-magnetic telegraph, and the magnetic clock, or Electro- Chronograph. VIII. Voltaic electricity exerts a powerful effect upon animals. IX. Some animals have the power of generating the electric fluid. IT has long been known that common electricity influences 304 NATURAL PHILOSOPHY. the magnetic needle. But the discovery of Oersted (1819) opened a new field of investigation, which has led to the most useful and surprising results. I. Magnetism. Magnetism is so closely allied to electricity, that we have concluded to present a few of its fundamental facts in this connection. The fact that a magnet will induce currents of electricity, and that these same currents, as well as those from the battery, will induce magnetism, shows a close connection between them. 1. Magnetism is a peculiar attraction, which may be devel- oped in iron and some of its ores, and slightly in nickel and in cobalt. Certain ores of iron are found to be naturally magnetic, and hence are called Natural Magnets or Loadstones. But when the magnetic property is developed in a steel bar, by artificial processes, it is called an Artificial Magnet. When magnetism is induced in a bar of hardened steel, it is retained, and is then called a Permanent Magnet. Soft iron does not retain the magnetic property, though it may be rendered powerfully magnetic. 2. Magnetism manifests itself by attractions and repulsions. The most obvious property of a magnet is that of polarity ; that is, If iron filings be sprinkled upon a Fig. 255. magnet, Fig. 255, they will adhere mostly to its two extremities, d d, called its poles, where the power ap- pears to reside. The line which joins them is called its axis. If a sheet of paper be laid Fig. 256. upon a magnet, and iron filings sprinkled over it, they range themselves in curves, in Fig. 256. If a piece instead of the paper, be used, same effect will be produc The interposed bodies, the and the paper, have no tendency to destroy the force of attraction. Define magnetism. What are natural magnets ? What are artificial mag nets? How does magnetism manifest itself? MARINER S COMPASS. 305 Fig. 258. A magnetic needle is simply a magnetized piece of steel, balanced upon a pivot, Fig. 257, so as to move freely in a horizontal direc- tion When such a needle is free to move, one pole always points toward the north, and the other toward the south, and are called the north and south poles. A magnetic needle placed in a box with certain fixtures consti- tutes the Land Com- pass and the Mari- ner's Compass. In the latter, the nee- dle is attached to a circular card, Fig. 258, which is divided into thirty-two equal Q parts. The box containing the needle is sustain- ed in gimbals, which consist of two pairs of pivots, E F, p, fixed in the circumference of two rings, at right angles to each other, so that, whatever the motion of the ship, the compass-box main- tains a horizontal position. 3. The opposite poles of a magnetic needle attract, and simi- lar poles repel each other ; that is, a north pole will attract a south pole and repel a north pole, or a south pole will attract a north and repel a south pole. In these respects the magnetic needle bears the closest analogy to bodies similarly and oppositely electrified ; hence some have inferred the existence of two fluids, the northern called Boreal, and the southern called Austral magnetism. 4. Magnetism is developed by Induction. For if a piece of What is a magnetic needle ? Describe the mariner's compass. What is the principal property of the needle ? How is magnetism developed ? 306 NATURAL PHILOSOPHY. soft iron be brought near the poles of a magnet it becomes mag- netic, the north pole of the permanent magnet inducing a south pole on the end of the iron next to it ; but the iron loses its mag- netism when the magnet is removed. A hardened steel bar, when brought into contact with a magnet, becomes permanently magnetic. 5. The two poles of a magnet can not be separated, for if one pole be broken off, each portion will immediately assume north and south polarity. In this respect magnetism differs from elec- tricity, it being easy to isolate the two electricities from each other. 6. Magnetism, however, like free electricity, resides upon the surface, so that a hollow cylinder of steel will exhibit magnetic properties equally powerful with one which is solid. 7. The laiv of magnetic attraction and repulsion, as establish- ed by Coulomb with his torsion balance electrometer, is, that the force of attraction and of repulsion between two magnets is inversely as the square of the distance between them the same law which prevails in electricity, light, heat, and gravitation. 8. Magnets may be produced simply by taking a bar of hard- ened steel, placing the pole of an artificial magnet upon it about midway, and, inclining it to an angle of about 45, drawing it to- ward the end. When this has been repeated a few times, the steel will be rendered permanently magnetic. But the best mode of producing powerful magnets is by voltaic electricity. Magnets are often made in the form of a horse-shoe, Fig. 259, with a piece of soft iron placed across the ends of the poles, called an armature, which aids in preserving the magnetic power. The end of the armature next to the north or + pole has south or polarity, and the end in contact with the south pole has + or north po- larity. 9. Variation of the Magnetic Needle. The magnetic needle stands directly north and south in but a few places on the earth's surface, but varies to the east or west in different places. Lines Can the poles of a magnet be isolated ? What is the law of attraction and repulsion ? How may a magnet be produced 1 What is the best mode of producing magnets ? What is meant by the variation of the needle, and how does it vary ? ELECTRO-MAGNETISM. 307 connecting those places where the needle stands north and south are called lines of no variation. These lines, in fact, form but one, which entirely encircles the globe. There is a point in latitude 70 5' north and longitude 96 45' west, where the needle stands vertically. There is also a similar point in the southern hemisphere at 72 south latitude and 152 east longitude. There are also two points in the northern hemi- sphere called points of maximwn intensity. The stronger is in latitude 52 19' north and longitude 92 west. The weaker is in latitude 85 north and longitude 116 east. These have cor- responding points in the southern hemisphere. II. Electro-magnetism. The fundamental fact noticed by Oersted was, that a current of electricity, circulating in a copper wire, or any other conductor, produced certain definite motions of a magnetic needle, dependent upon the direction of the current. 1 . Influence of Voltaic Currents upon the Magnetic Needle. Fig 260 If a magnetic needle be freely sus- ~ ' '.>. pended, Fig. 260, with its north """"** pole pointing to the north, and a current of positive electricity passed from north to south directly above it in a vertical plane, the north pole of the needle will turn toward the east, and stand in the direction cd; or, if the current pass under the nee- dle from south to north, the same effect will be produced. By pass- ing an insulated wire several times around the needle the effect will be increased. An instrument thus constructed is called a Galvanom- eter, Fig. 261. But if the positive current be passed from south to north above the needle, the north pole will turn toward the west. This de- flection is never as much as 90, on account of the tendency of the needle to place itself in a north and south direction ; but if an astatic needle is used, that is, two needles with their north What were the facts noticed by Oersted? Describe the galvanometer. What is the effect of passing a positive current from north to south above the needle ? Why is the deflection less than 90 ? 308 NATURAL PHILOSOPHY. Wig. 262. and south poles united, the deflection will be 90 ; hence the tendency of a magnetic needle is to stand at right angles to the direction of a voltaic current, the needle moving in a plane per- pendicular to that in which the current moves. It will be no- ticed that this force acts tangentially, and in this respect differs from any force hitherto considered. 2. Revolutions of the Needle. When the needle turns toward the east, its inertia will carry it past that point, and then, if the direction of the current is changed, its north pole will turn to- ward the west, and will pass through the south point to reach it ; if then the current is again changed, it will complete a revo- lution, and in this way rapid revolutions may be given to the needle. If the needle is first made to turn to the west, it will revolve in the opposite direction. Revolutions may also be produced by passing currents of elec- tricity through the needle itself. Thus, if a magnet be placed upon its north pole, Fig. 262, and currents of positive electricity are passed through half its length, it will revolve rapidly, the direction depending upon the direc- tion of the currents. A little mercury must be placed in a cup at the center of the needle, and the connection made with B by a wire which dips into it. The two poles of the battery may be connected with B and C, which will send the currents through the lower half, or with A and B, which will send them through the upper half of the magnet, S N. 3. If the needle is made stationary, and the conducting wire attached to an axis, it will revolve rapidly, owing to the reaction of the magnet, provided the current is sent in opposite directions at each half revolution. How does a magnetic needle tend to stand in reference to a voltaic current ? How may revolutions be given to a needle ? How may revolu- tions be produced in the conducting wire ? THERMO-ELECTRICITY. 309 Fig. 263. Thus, let a copper wire, C, Fig. 263, wound in the form of a rect- angle, be attached to an axis, and placed between the poles of a per- manent horse-shoe magnet, the ends of the wires being soldered to two strips of silver on each side of the axis, so that, as the rectangle re- volves, the ends may be brought al- ternately in contact with springs of silver, which are connected with p and n, and these with opposite poles of a single battery, Smee's being the best for this purpose. As the positive current passes from north to south above the nee- dle, the side next to the north pole turns to the west, because the pole itself can not turn to the east, and when it has completed a quarter of a revolution, the other end of the wire receives the positive fluid, and the revolution continues until the rectangle has passed three quar- ters of a revolution, when the current is again reversed. It will be seen that the current is reversed every half revolution, as in the case of the magnet. 4. Two conducting wires may be made to revolve by sending currents through them in different directions ; those positive cur- rents which flow in the same direction will attract, and those which flow in opposite directions will repel each other. If the conducting wires are made of different metals, as bismuth and antimony, then the currents may be generated in them by heat, and revolutions produced. Electricity thus excited is termed, 5. Thermo-electricity. Thus, let #, Fig. 264, be a bar of antimony, and b, of bismuth, soldered together at the point c, and the other extremities Fig. 264. How may revolutions of two conducting wires be produced ? Describe the mode of exciting currents by boat, and of producing revolutions. 310 NATURAL PHILOSOPHY. Fig. 265. connected by wires. When the junction, c, is heated, a current of electricity will flow from the bismuth to the antimony, and when the junction is cooled, a current will flow in the opposite direction. The currents are feeble, but may be increased by uniting a series of bars, as in the compound voltaic circles. The existence of these currents may be shown by, 6. Thermo-electric Arches. Figure 265 represents two arches, s s, placed on the poles of a permanent magnet. Each consists of rectangular wires of silver, soldered to a circular wire of German silver. When the junctions are heated, currents of electricity flow from the German silver to the silver, passing up the heated side of the arch and descending the other side. These currents give polarity to the rectangle, and, by the influence of the pole of the magnet, the arch revolves, bringing the junctions successively into the flame, by which the direction of the current is changed in each rectangle every half revolution. The principle is the same as in the revolving rectangle. III. Influence of Voltaic Currents on Soft Iron and Steel. 1. If a bar of soft iron be inserted in a coil of insulated copper wire, and the two ends of the wire connected with the poles of a simple voltaic circle, it will be instantly converted into a magnet, but will lose its magnetism when the circuit is broken ; but if the bar is hardened steel, it will be ren- dered permanently magnetic. Thus, let C, Fig. 266, be a coil of wire, called a helix, and N S a bar of iron or steel" inserted in it. The poles of a battery, n p, may be attached by means of the cups which are in connection with the ends of the wire constituting the coil. While the currents are cir- culating, small nails or keys will be strongly attached to the two poles. What is the effect of currents of electricity on soft iron, and how may it be exhibited ? what upon steel ? Fig. 266. ELECTRO-MAGNETS. 311 267< If the soft iron is made in the form of two semicircles, Fig. 267, with handles attached, and placed within the coil, c, they will be held together with great force when the two ends of the wire, P N, are connected with a battery, but are easily separated when the circuit is broken. If the heliacal ring, c, is made with a small opening, it will cause small nails to adhere to it while the current is circulating, but as soon as the circuit is broken the nails will fall. The same effect will be produced if the wire is wound around the iron in the manner represented in Fig. 268. In this case it 1^.268. is called an Electro-magnet. An armature, connected with a steel-yard, being applied, the force of attraction is easily determ- ined. The longer the wire within certain limits, the greater the effect. Professor Henry, to whom we are indebted for many experi- ments on this subject, first succeeded in making electro-magnets which would sustain 1000, 2000, and even 3000 pounds. When pieces of hardened steel are drawn across the poles of an electro-magnet, we may obtain more powerful permanent mag- nets than by any other process. 2. The poles of the magnet in these experiments depend upon the direction in which the currents circulate. What is an electro-magnet ? pend? Upon what do the poles of the magnet de- 312 NATURAL PHILOSOPHY. Thus, if we take a coil of wire, represented in Fig. 266, place within it a bar of soft iron, the bar standing north and south, and then pass a current from the copper or positive pole of the battery around the bar from north to south, in a direction opposite to that in which the sun appears to move, the north end of the bar will be a north pole and the south end a south pole, as may be shown by its attracting the opposite poles of the magnetic needle. But if the positive current circulate in the same direction in which the sun appears to move, the south end will be the north pole, and the north end the south pole of the needle. 3. Revolutions of Electro-magnets. If by any means we can change the direction of these currents, so as to change the polar- ity of the iron bar, we may produce rapid revolutions. For this purpose, the bar is wound with insulated copper wire, and affixed to an axis between two poles of a per- Fig. 269. manent hwse-shoe magnet, or of an- other electro-magnet. This is the prin- ciple of Page's Revolving Magnet. It con- sists of a small electro-magnet, a, Fig. 269, fix*ed'to an axis, s, upon two sides of which, near the lower extremity, are two pieces -of silver, extending nearly around the axis, to which the two ends of the wire surrounding a are soldered. Two springs of silver, connected with the two cups, p r, press on each side of the axis in contact with the strips of silver. As these do not extend quite around the axis, there are two spaces which constitute a break, so that op- posite ends of the wire receive the cur- rent as the axis revolves, and by this means the polarity is reversed at each half revolution. The operation of this instrument depends upon the fact that opposite poles attract and the same poles repel each other. By the direction of the currents, two north and two south poles are made adjacent to each other, and there will be a mutual re- Describe Page's revolving magnet. How are the revolutions produced ? VOLTA-ELECTRIC INDUCTION. 313 pulsion. The electro-magnet will be repelled one quarter of a revolution, and then, because opposite poles attract, will be at- tracted one quarter of a revolution further. At this point the poles are reversed, and the repulsions and attractions continue. The rapidity of these revolutions is very remarkable. The poles are changed every half revolution, and yet instruments have been known to revolve more than 6000 times in a minute. To accomplish this, the current must pass through some 30 feet of wire twice each revolution. In order to measure the number of revolutions, a bell, b, is at- tached to this instrument, with a wheel, which is turned by an endless screw upon the axis, so that for every 100 revolutions the bell strikes. Many attempts have been made to apply this power to the propelling of machinery, and small engines have been constructed, but, as yet, without much success. 4. The attracting power, in case of electro-magnets, is not confined to the iron, but the conducting wire itself has the power of attracting iron filings. Nor does the attraction exist alone between tbe magnets or iron and the wire, but also between two wires conveying a cur- rent in the same direction. Thus, when a coil of wire has cur- rents of electricity sent through it, the separate coils will approach each other and render the coil shorter ; hence, 5. Two currents ivhichfloiu parallel and in the same direction attract each other, but if they jlow in opposite directions they repel each other, and from two such currents circulating in con- ducting wires we may produce all the attractions and repulsions exhibited by magnets. IV. Volta-electric Induction. Voltaic, like common electrici- ty, has the power of inducing electricity in surrounding bodies ; but lor this purpose a special apparatus is required. 1 If an insulated copper wire be wound around an electro- magnet, or around another coil of wire, and the inner coil be con- By what means is the velocity of revolutions determined? On what principle is it that the attractions and repulsions exhibited by magnets and conducting wires are explained ? What is meant by volta-electric iu- ductiou ? 314 NATURAL PHILOSOPHY. nected with the battery, the outer coil will have currents of elec- tricity induced in it as often as the battery current is broken or the circuit completed, and only at those times. Thus, let i y Fig. 270, be a coil of copper wire, the two ends Fig. 270. of which, A D, are connected with a battery, and let o be another coil, placed over the first, the two ends being represented by the two wires which are held in the hands. When the battery cur- rent is sent through the inner coil, and when the circuit is broken, there will be induced in the outer coil currents of electricity, which, if the ends of the wire are held in the hands, will produce powerful shocks. The electricity thus excited will produce light and heat, decompose compounds, and produce all the other effects of the battery current. This apparatus is called the Separable Helices, and is much used for medicinal purposes, as the shocks can be increased or diminished at pleasure by means of a bar of soft iron, or bundles of fine wires, w, placed in the inner coil. When the wires are inserted, the shocks are wonderfully in- creased through the inductive influence of the magnetism which is induced in them by the battery current. It is not necessary that the second coil should surround the first ; it may only be laid upon it or above it. Nor is the effect confined to the second coil ; but if a third or fourth coil be con- Desci ibe the separable helices. How may the second coil be placed ? SECONDARY AND TERTIARY CURRENTS. 315 nected with the second, currents of electricity will also "be induced in them at each interruption of the battery current. Thus, let A, Fig. 271, be an insulated copper ribbon connect- Fig. 271. ed with the battery, and B a second ribbon, the two ends of which are connected with a third, C, and a fourth coil of fine wire, W, placed over this, with the ends held in the hands. When the battery current is broken, currents will be induced in B and C, and when they cease they will induce currents in W, which will be manifested by giving a shock. 2. The currents in the several coils move in different directions. Thus, when the circuit is completed, a current in the second coil moves in the opposite direction, called the initial current, and, when it is broken, the induced current flows in the same direction, and is called the terminal current. The initial cur- rent in C will induce a tertiary current in W, flowing in the opposite direction, and the terminal current in C will produce a tertiary current in W, flowing also in an opposite direction. These tertiary currents are capable of producing currents in other helices of a fourth, fifth, and even the seventh order. The direction of these currents, produced by the. initial and terminal battery currents, are represented by the signs + and ; + when they flow with the battery current, and when they flow in opposite directions. Thus, the Initial. Terminal. Battery or primary current -j- -f- Secoridary current -f Tertiary current -f- Quaternary current -j- What will be the effect of a series of coils arranged as in Fig. 271 ? How do the currents circulate in the several bands? How are the directions of these currents indicated ? 316 NATURAL PHILOSOPHY. Fig. 272. These induced currents, which flow in opposite directions, re- act upon each other and upon the battery current, and diminish their effects. V. Magneto-electric Induction. Magnets have the power not only of inducing magnetism in iron and steel, but also currents of electricity in conducting wires. Thus, if one pole of a magnet be inserted in a coil or helix of copper wire, the ends of which are connected with a galvanome- ter, currents of electricity will be excited in the coil when it is inserted arid withdrawn, as will be indicated by the deflection given to the needle. But, for the purpose of exhibiting this effect in a more satis- factory manner, the Magneto-electric Machine may be employed. This consists of two horse-shoe magnets, placed parallel to each other, Fig. 272, with an axis between their poles, to which is at- tached two coils of cop- per wire, inclosing bun- dles of iron wire in each, constituting an arma- ture. The two ends of the copper wire forming the two coils are sol- dered to a silver ferrule or break-piece on each side of the axis, against which two silver springs connected with the two cups, a b, press. The armature is made to revolve by the wheel w. As the armature revolves, and the bundles of iron wire are brought near the poles of the magnets, they are rendered magnetic, their polarities being opposite to that of the magnets ; and when the wires pass between the poles they lose their polarity, and acquire opposite polarity as they pass again near the other poles of the magnet. When the polarity is changed, currents of electricity are induced in the wire, and are made to flow through it to the cups ; if the revolution is rapid, these currents flow in a con- What is meant by magneto-electric induction ? Describe the magneto- electric machine. Describe the manner in which currents of electricity are induced by this machine. AMPERE'S THEORY. tinuous stream, and may be made to produce tjesul those produced by electricity from the battery. But in order to obtain powerful shocks and rents must be interrupted, as in the battery current, and by this means secondary currents of much greater power are induced in the coil. This is effected by means of a steel spring connected with one cup, as , arid passing over pins in a wheel connected with the axis. When the spring is pressing upon the pins, the current flows in a continuous stream, and completes the circuit ; but when it passes by them the current is broken, and at that moment an induced secondary current is given off at the handles connected with the two cups, if they are in contact. All the effects of voltaic electricity may be produced by this apparatus. The sparks are very bright at each interruption of the wire, and the shocks too powerful to be endured but for a moment. This instrument may be employed for medicinal purposes, for decompositions, for producing magnetism arid revolutions of con- ducting wires and magnets. VI. Theory of Magnetism, Electro-magnetism, and Magneto- electricity. The most probable theory to explain the facts of magnetism, electro-magnetism, and magneto-electricity is that of INI. Ampere. This theory rests upon the supposition that all bodies are capa- ble of having circles of electricity excited in them, and when the circles in any two coincide or are parallel to each other they at- tract, and when tico move in opposite directions they mutually repel each other. \. In the case of steel, these currents are rendered permanent and constant in one direction : and in the case of soft iron, they are induced while the battery current is circulating ; but when it ceases, the currents move in all directions around the atoms of which it is composed, and neutralize each other's effects. By what arrangement are shocks and sparks produced? For what pur- poses may this machine he employed? What theory best accounts for magnetism, &c. ? State the facts on which the theory rests. Apply the theory lo explain the action of these currents on steel, iron, and the mag. uetic needle. 318 NATURAL PHILOSOPHY. 2. The reason, then, that the magnetic needle turns to the east when the positive current passes from north to south above it is, that positive currents are constantly circulating around the north pole of the needle in a direction opposite to that in which the sun moves, and hence the battery current opposes the current of the needle, and the north pole is repelled toward the east, so that both currents may coincide in direction ; and for the same reason, when the positive current passes from north to south be- low the needle, the north pole is repelled toward the west, that the currents may again coincide. 3. When currents of electricity pass around soft iron or steel, they induce currents in them which move in the same direction, and then, if two such pieces of steel are brought near each other, their north poles will repel, because their currents flow in oppo- site directions ; and for the same reason two south poles repel each other. But a north pole attracts a south pole because the currents coincide in direction. 4. When a magnet is brought near a piece of iron or steel, it converts it into a magnet, because it induces currents of electricity in it, which currents flow in opposite directions, and therefore a north pole always induces a south pole, and a south pole a north. This explains the tangential direction of the magnetic forces. 5. The tendency of the magnetic needle to stand north and south is readily explained, on the supposition that the heat of the sun and other causes produce currents of electricity, which follow the sun in his daily course from east to west, thus converting the earth into a magnet, with the pole, which corresponds to the north end of the needle, toward the south. These currents in- duce currents in the ores of iron, and thus produce the loadstone, and give the direction to the magnetic needle ; for it will be seen that it is only when the needle stands north and south that the currents in it and in the earth coincide in direction. 6. The dip of the magnetic needle is due to the fact that the currents forming circles around the earth are not at right angles What effect have currents of electricity on soft iron and steel ? Explain the reason lor the kind of polarity produced. Why does the magnetic needle point north and south 1 How is the dip of the magnetic needle ex- plained 1 TERRESTRIAL MAGNETISM. 319 Fig. 273. to its axis, but to a line which dips below the horizon, called the axis of the magnetic globe. The dip varies in different parts of the earth. To illustrate terrestrial mag- netism, let Fig. 273 be a globe, in the axis of which a magnet may be placed, and let a coil of wire, parallel to the equator, be passed around it. If the magnet is inserted in the globe, t oU "1-J TT;W, I ^Hc^ anc ^ a sma ^ magnetic needle k\\ *&?( ^nH^\l^] " placed in various parts, it will point in the direction of the poles, the north pole of the nee- dle toward the south pole of the magnet in the earth. North of the equator the north end will dip, and the south end south of the equator. If now the magnet be taken from the globe, and currents of electricity passed around under the small needle, it will have the same directive tendencies as when the magnet was inserted, and will stand toward the north and south poles. If it be moved north or south of the equator, it will ex- hibit all the phenomena of the dipping needle. These experiments appear decisive as to the fact that the mag- netism of the earth may be due to currents of electricity ; and in the fact that the heat of the sun must produce currents, we have all the conditions necessary to account for the effect. This theory, therefore, will explain all the phenomena of magnetism, a sub- ject which is usually considered a distinct branch of science.* * A theory of magnetism has been proposed by William A. Norton, and developed in the Journal of Science, vols. iv. and viii., in which it is as- sumed that " every particle of matter of the earth's surface, and to a cer- tain depth below it, is the center of a magnetic force, exerted tangentially to the circumference of every vertical circle that may be conceived to be traced around it. The direction of this force is such, that to the north of the acting particle the tendency is to urge the north end downward and the south end upward, and to the south of the same particle it is to urge the north end upward and the south end downward. " The intensity of the magnetic force of a particle of the earth at a g^iven distance is approximately proportional to its temperature or amount ot sen- sible heat." Illustrate the manner in which the magnetism of the earth may be ac- counted for by currents of electricity. 320 NATURAL PHILOSOPHY. VII. Application of Electro-magnetism to Useful Purposes. There are many processes in the arts which are now conducted by means of voltaic electricity, especially the processes of gilding and electrography. Attempts have also been made to construct machines which could be moved by electro-magnetic power, and although very rapid motions have been attained, the requisite power has not yet been so applied as to secure any very important results. The most useful, as well as astonishing application of electricity which has ever been made, is that of making it a mes- senger to convey intelligence from one place to another. The in- struments to effect this are called Magnetic Telegraphs. Of these there are at least three which are worthy of notice Morses, House's, and Bain's. Morses Magnetic Telegraph. This consists of three parts, a, battery to generate electricity, conducting ivires to convey it, and a register to record the signs which are used for letters. The register is represented in Fig. 274. Tig. 274. This theory, however, is consistent with the idea that the imponderable agents are the effects of different vibratory motions of the particles of mat- ter, and of the ethereal undulations caused by them ; and hence the force may be electrical. All these views are to be considered as theories, and not as settled facts. To what uses has voltaic electricity been applied? telegraph. Describe Morse's ELECTRO-MAGNETIC TELEGRAPH. 321 It consists of an electro-magnet, m m, an armature, a, which has a lever attached to it, at the end of which a steel pen, s, is placed, to make indentations in the paper, p p. The paper is moved by the clock-work, c, over a roller, against which the pen is lifted when the armature is attracted upon the magnet. W W are wires which are connected with the battery, at any distance from the register. Only one wire, however, is employed between any two stations. This is connected with one pole of the battery at one end, and with one cup of the register at the other. Wires are also connected with the other pole of the battery, and with the other cup of the register, and passed into the ground. To understand the operation of this instrument, suppose the register be placed in New York, and a wire extending to Wash- ington connected with a battery. The operator in Washington completes the circuit, and the electricity travels on the wire to New York, and passes around the electro-magnet, m m, by which it is rendered a magnet, and attracts the armature, a, which lifts the pen, s, against the paper, making a dot, or, if the paper is in motion, a line. Now as often as the circuit is broken the pen fails from the paper, and by completing and breaking the circuit a series of dots and dashes may be impressed upon it. As these stand for letters, words and sentences are readily communicated The following is the alphabet used by Professor Morse : 2 ---- - 3 ----- 4 ------ 5 --- 6 ------ 7 ---- 8 ----- 9 ---- - 02 A O _ 33 P C Q _ D R _ E - S F T G U H V I -- W j X K Y L Z M & _ . N 322 NATURAL PHILOSOPHY. House's Telegraph. This instrument is much more compli- cated than the preceding. Instead of signs, types are used, and each word is printed, so as to be read like any other print. Bain's Telegraph. This instrument does not depend upon magnetism, but the electricity is made to mark paper which is chemically prepared so as to be affected by it. All the above instruments are now in successful operation. Lines of telegraphic wires are rapidly extending throughout the United States and Canada. All the most important sea-ports and cities on the lakes are connected by them. In Europe, also, telegraphs are extensively employed. The news received from foreign countries may reach all parts of the United States at the same moment. The telegraph is liable to interruptions from several causes. 1. The wires may be broken by accident or intention. 2. Lightning sometimes strikes the wires, and even electric changes, as a thunder-shower near the line, will induce currents of electricity which will cause the register to work. A storm may also interfere with the regular communications. The telegraph has been employed not only to communicate in- telligence, but also to determine the longitude of different places, and to regulate time-pieces ; for as electricity passes instantaneous- ly to any distance on the earth's surface, the exact time, either as indicated by observation upon the heavenly bodies, or as kept by time-pieces, may be accurately determined, and the difference of longitude ascertained. Dr. Locke, of Cincinnati, has lately invented a clock called the Electro-chronograph, which, in connection with a register, is capable of marking y^th of a second of time. The clock breaks and closes the circuit in such a manner that the seconds are regis- tered in lines about one inch in length, with short breaks between them, and the exact time of any observation is registered by touch- ing a key. This invention will enable astronomical observers to note \vith great accuracy the time of observations, and record Describe House's and Baiu's telegraphs. What causes interfere with the operation of the telegraph? What other uses of the telegraph? Describe the electro-chronograph of Dr. Locke. ANIMAL ELECTRICITY. 323 them at any distance desired, and also to determine the difference of longitude. It will be of the greatest utility in the survey of coasts and harbors, and in all astronomical observations, where time is so important an element. VIII. Vital Effects of Electricity. The effects of voltaic and common electricity upon animals are similar, but the former is now more generally applied for medicinal purposes. Electricity exerts a salutary effect in many diseases, and has been supposed to be intimately connected with the living power. Some have gone so far as to assert that life may be generated by it. Its influence upon the vegetable kingdom is also most import- ant. The rocks and soils in connection with the living vegetable fulfill the essential conditions of the galvanic battery. The rocks, too, are brought under the influence of this wonder- ful power, and mineral veins are often distributed in accordance with the laws of voltaic action. IX. Animal Electricity. Some animals are capable of im- parting electric shocks, and, of course, of generating electricity. The electricity thus produced is similar to that produced by chemical action. This power is possessed by several species of fish. The principal are the torpedo and the gyninotus. The torpedo's power of imparting shocks was known to Aristotle and Pliny ; but Mr. Walsh, in 1773, made the discovery that its shock was precisely the same as that of the Leyden jar. The electrici- ty is generated by certain organs just back of the gills, on both sides of the body, about one third of its length. They resemble in some respects a galvanic pile, consisting of perpendicular col- umns, amounting in some cases to several hundreds. These col- umns are one fifth of an inch in diameter, and are divided into partitions by membranes, making cells somewhat like those of a galvanic battery. A new species of this genus has lately been taken at Wellfleet, Massachusetts (the Torpedo occidentalis), much larger than the European species, weighing from twenty to two hundred pounds. Their shocks are said to be sufficient to Mention the vital effects of electricity, and its relations to life. What is animal electricity? What animals are capable of imparting shocks ? De- scribe the torpedo. 324 NATURAL PHILOSOPHY. prostrate a man. The electrical organs are connected with a very large nervous apparatus, and their power seems to be de- pendent on the will of the animal. The Gymnotus or Surinam Eel, also, has the power of im- parting powerful shocks to other animals. Fish are paralyzed, and even the wild horses which are driven into certain lakes in South America are so paralyzed by the repeated shocks from the fish that they are sometimes drowned before they can recover. By these means the eels become exhausted, and are easily captured by the inhabitants. This animal has been subjected by Faraday to a series of experiments, and the power which it exercises has been shown to have a complete identity with the electrical fluid. The animal is found to be capable of imparting magnetism and sparks, producing heat and chemical decomposition at the time of imparting the shock. Portions near the head are found to be positive, and those near the other extremity negative. The large nervous apparatus of this animal seems to point out a close con- nection between electricity and nervous power. It has been sug- gested that nervous power may become electrical under a cer- tain state of the system. The Silurus Electricus, found in regions of Africa, possesses also a similar electrical power. Nature of Electricity. In exhibiting the phenomena of elec- tricity it seemed necessary to conceive of this agent as a fluid, but the more probable view is, as has already been stated, that electricity, light, and heat are dependent upon certain modifica- tions of the same substance called the ether ; that its production depends upon certain motions of this ether, and its transmissions upon its undulations, connected, it may be, with certain states or vibrations of ponderable matter. For a more extended treatise on magnetism and electro-mag- netism, the student is referred to Davis' s Manual of Magnetism, from which several of the diagrams in this work were taken. Describe the Surinam eel. What is the nature of electricity ? OPTICS. 325 CHAPTER IX. LIGHT, OR OPTICS. Optics is that branch of Natural Philosophy which treats of the nature and phenomena of light. This science properly embraces whatever relates to the origin and sources of light ; to the laws which govern its transmission ; to its relations to ponderable matter ; to color arid vision ; and to the theories by which its nature is illustrated and its phenomena are explained. Light, in its nature, as has already been indicated, is analo- gous to sound. It is produced by undulations of an ether which is supposed to pervade all space, and vision is the effect of these undulations upon the retina of the eye. The proof of this view of the nature of light will be adduced after considering its origin, and describing some of its obvious phenomena, such as radiation, reflection, refraction, decomposi- tion, absorption, &c. It is unnecessary to say that this constitutes a most interesting branch of natural science, whether we contemplate it in regard to the exquisite coloring of flowers, the opaline plumage of birds, the many-tinted leaves of the autumnal forest, the gorgeous hues imparted by the rising or setting sun to his attendant clouds, or to its boundless utility to man in the supply of his wants, and the preservation of his existence. " Man," says Arnott, "wherever placed in light, receives by the eye from every object around, nay, from every point in every object and at every moment of time, a messenger of light to tell him what is there, and in what condition. Were he omnipresent, or had he the power of flitting from place to place with the speed of the wind, he could scarcely be more promptly informed. Then, in many cases where distance intervenes not, light can impart at Define optics. What does the science embrace? What is said of the nature of light? 326 NATURAL PHILOSOPHY. once knowledge, which, by any other conceivable means, could come only tediously, or not at all. For example, when the illu- minated countenance is revealing the secret working of the heart, the tongue would in vain try to speak, even in long phrases, what one smile of friendship or affection can in an instant convey. Had there been no light, man never could have suspected the ex- istence of the miniature worlds of life and activity which, even in a drop of water, the microscope discovers to him ; nor would he have formed any idea of the admirable structure of many minute objects. It is light, also, which, pouring upon the eye through the optic tube, brings intelligence of events passing in the remotest regions of space." SECTION L ORIGIN OF LIGHT, AND THE LAWS WHICH GOVERN ITS TRANSMISSION. I. Light originates in ponderable matter, and is developed by heat, chemical and voltaic action, and by the presence of lu- minous bodies, as the sun and stars. II. Bodies may be divided into self-luminous and non-lumi- nous, opaque, transparent, and translucent. That ivhich trans- mits light is called a medium. III. In the same medium, rays of light move in straight lines. This is proved by the position of the images of bodies and by the phenomena of shadows. IV. The intensity of light radiating from a luminous point is inversely as the square of the distance. The intensity is de- termined, \. By the comparison of shadows ; 2. By equally il- luminated surfaces ; and, 3. By the power of causing a shadow to disappear. V. The velocity of light is about 195,000 miles per second. This has been ascertained in two ways : by observations upon the eclipses of the satellites of Jupiter, and by the aberration of the stars. I. Origin of Light. The existence of ponderable matter is as necessary to the production of light as to that of sound. A vacuum may transmit it, but can not generate it. Matter, as How does light originate ? SOURCES OF LIGHT. 327 has been seen, consists of minute atoms, and these individually are so closely connected with producing the phenomenon of light, that they may be considered as luminous points from which it emanates. All matter, when heated to a certain temperature, gives out light. In solids, this temperature is 977 Fahrenheit (Draper), but in gases it is much higher. The light emitted is at first of a dull red color ; but it increases in brightness, in a rapid ratio, as the temperature is raised, a body yielding, at 2600, a light of a dazzling whiteness, nearly forty times as intense as at 1000. Artificial light is usually produced by chemical action, as in ordinary combustion, and the light proceeding from voltaic elec- tricity. In this case, it is always connected with heat. There are some mineral, and certain decayed vegetable and animal substances, which shine in the dark, and are said to phos- phoresce a phenomenon which has been ascribed to slow com- bustion. Certain animals, also, as the glow-worm, emit light from their bodies, which may be seen in the dark. But the great source of our light is the sun, which sends it forth in all directions through the regions of space. The stars shine with their own light, and many of them, from their superior magnitude, pour forth floods of this dazzling fluid, much more in- tense than that which we receive from our sun, but their immense distance renders it faint and powerless to us. The moon and planets generate no light, but only reflect that which they receive from the sun. II. Bodies are divided into self-luminous, or such as shine by their own light, as the sun, stars, and terrestrial lights, and non- luminous, or those which only reflect, absorb, or transmit the light of luminous bodies. Those bodies which do not permit light to pass through them are called opaque ; those which offer little or no resistance to its passage are termed transparent ; and those which but partially transmit it are said to be translucent. Opaque bodies, when made into very thin leaves, are translucent, as gold and silver leaf. What are the sources of terrestrial light? What other sources of light? What division is made of bodies in their relation to light? 328 NATURAL PHILOSOPHY. That which transmits light is called a medium. Gases, liq- uids, and transparent solids impede its passage more or less, and are therefore imperfect media. A vacuum is a perfect or free medium. A ray of light is a line of luminous particles proceeding from a luminous point ; a beam of light is a number of parallel rays ; and a pencil of light is a collection of rays, radiating from a lu ruinous point. III. Laws of the transmission of light. 1 . In the same medium, rays of light proceeding from a luminous point move in straight lines, and with uniform ve- locity. (1.) That light moves in straight lines, is shown by the phe- nomena of images. If a ray of light be admitted through a small aperture into a dark room, it falls upon the wall at a point directly opposite the aperture and its source ; and if the air be agitated, the line of the ray may be distinctly seen by means of the floating moats which are illuminated by the ray. (2.) When a pencil of rays falls upon an opaque body, the form of the shadow shows that the lines described are straight lines. Thus, suppose a pencil of rays proceed from the point . A, Fig. 275, and fall upon the opaque ball, B, the lines A C and A D will be straight lines, as is shown by the limits of the shadow beyond B. The shadow in this case will be conical, and will increase in size the further it proceeds beyond B. If the luminous body have any considerable magnitude, there will be formed a half shadow on each side of the perfect shadow. That part of the central shadow which receives no light is called the umbra, while that which receives light from some parts of the luminous body and not from others, is termed the What is a medium? when is it free? Define a ray, a beam, and a pen oil of light. What is the law of the transmission of light? What is the umbra, and what the penumbra ? PHENOMENA OF ShADOWS. 329 Thus, let. A, Fig 276, be d luminous body, as the sun, and ii Ei an opaciue body. -^__ The space H B E receiving ~ "^^GSi) no light, will be the umbra. But the light from d will shine upon the space H B C, while that from f will be wholly obstructed ; and the same is true of the space H E D, which receives light from /, but riot from d ; hence these spaces will be partially illuminated. It will be noticed that the form of the penumbra is that of an inverted cone, and that it increases in diameter the farther it proceeds from the opaque body. But the umbra, or dark shadow, will have a form depending upon the relative magnitude of tbe luminous and the opaque body. If the luminous body is less than the opaque, it will increase in size as it proceeds, as in Fig. 275. - 277. If the two bodies are equal, it will be in the form of a cylinder, as in Fig. 277. If the luminous body is larger than the opaque, the umbra will converge to a point, as in Fig. 276. In all cases, the depth of the shadow is greatest and most clearly defined im- mediately behind the opaque body, for both the umbra and the penumbra fade away at a great distance from it. It is for this reason that the shadow of the point of a steeple is not accurately defined, while that of a hair, held near a white screen, is perfectly marked. Whatever the form of the shadow, the lines of light which limit it are always straight lines. That light moves with uni- form velocity, is proved by observations upon Jupiter's satellites. 2. When a luminous point or surface sends rays of light into a dark chamber upon a screen or reflecting surface, through a small orifice, there is formed an exact image of the luminous body, whatever the form of the aperture through -which it passes. This fact is easily shown by allowing rays of light to pass into a darkened room, through a small aperture in the shutter. How are the forms of shadows determined ? What is the form of the images formed by luminous objects ? 330 NATURAL PHILOSOPHY. Thus, if the direct rays of the sun **- 278 - be admitted into a room through a square aperture, as o, Fig. 278, a pencil of rays from each point of the sun's surface will enter through the aperture, and form square images upon the screen, as at c. As the sun is round, there will be a series of these quadrangular images, produced by rays from the circular edge of the sun, disposed in a circle upon the screen, while the light from the central parts of the sun will fill up the interior space with similar images, and the result will be a circu- lar illuminated figure, which will be an exact image of the sun. Hence, if the light which passes through the aperture be re- flected from an opaque body, we shall have an inverted image of the object upon the screen. It is on this principle that the hu- man eye and camera obscura, which will be described in a future section, are constructed. IV. Intensity of Light. The intensity of light, radiating from a luminous point, varies inversely as the square of the dis- tance. This may be proved mathematically and by experiment. Thus, if a luminous point be placed in the center of a hollow sphere, it will send rays to all parts of the inner surface. If the same quantity of light be placed in a sphere whose radius is two, three, or four times as great, it will be distributed over the entire surface. Now the surfaces of spheres are as the squares of their radii ; and hence, if the radius of one sphere be twice or three times greater than that of another, its surface will be four or nine times as great, and the same quantity of light being spread over this whole surface, its intensity will be only one fourth or one ninth as great.* This law may be shown experimentally, by allowing a ray of light to pass from a point, A, Fig. 279, upon square pieces of board, placed at the distance of 1, 2, 3, and 4 feet from it, as B, C, D, E. The first board, B, will obstruct all the light from C, or the same quantity of light which fell upon B would be * This law, as applied to the intensity of gra\ 7 itation, was demonstrated geometrically on page 37, Fig. 15. The same demonstration applies to the intensity of light, or to any influence radiating from a point. What is the law of the intensity of light at different distances 1 rilOTOMETHY. 331 spread over C, D, or E. These surfaces, C, D, and E 5 will be Fig. 279. B ODE found to contain four, nine, and sixteen times the surface of B ; and hence the light must be only {th, |th, and y^th as intense as at B. This proposition is strictly true, however, only when the light proceeds from a small surface or point, moves through a vacuum, and falls perpendicularly upon the surface. If the surface is oblique, it is evident that the same quantity of rays will be spread over a larger surface, as is exhibited in the falling of the oblique rays of the sun upon the northern and south- ern portions of the earth's surface. In passing through the at- mosphere, or any transparent medium, some of the rays of light are impeded ; therefore the intensity actually diminishes rather faster than the squares of the distances increase. Photometry. In order to measure the comparative intensities of different lights at the same distance, and of the same light at different distances, several methods have been employed. 1. It may be done by the comparison of shadows. This method depends upon the fact that the deeper the shadows cast by opaque bodies, the more intense must be the light. Fig. 280. ^ Thus, let A, Fig. 280, be a screen of white paper, d a rod, and C E two lights, placed at equal distances from the rod, so as to cast two IjXirT Pt shadows from it upon the screen. By observ- ing these shadows, it is easy to tell which is the darker. Then, by removing the light which casts the deeper shade, until the two shadows are equally dark, and measuring the distances of the lights from d, their illu- minating powers will be ascertained, for they will be as the squares What circumstances modify the intensity of light? How are the intensi- ties of different lights determined ? 332 NATURAL PHILOSOPHY. of their distances. If the two shadows are equally dark, and the light C is twice the distance of JE from the rod, then the light of C is four times as intense as that of E. If C is three or four times the distance of E, its light will be nine or sixteen times as bright. 2. A second method is by the equal illumitiation of surfaces. The instrument by which this is effected is called Ritchie's Photometer. It consists of a box, a b, Fig. 281, in the center of which is a wedge, cov- ered with white paper, f e g, and a conical tube in the top, through which the eye can look down on the screen, and which may be raised or lowered by the stand c. To determine the intensities of two lights, the one, m, is placed so as to illuminate the surface ef, and the other, n, the surface e g. The eye, at d, can observe both surfaces at the same time, and the lights are then placed at such distances that both sur- faces appear equally illuminated. The intensities of light they give out will be as the squares of their distances from the screen. Thus, if m be twice the distance of n, when both sides of the screen are equally illuminated, it gives out a light four times as intense. 3. There is still a third method, which is considered more val- uable than either of the preceding. It depends upon the principle that a shadow will be imperceptible in the presence of a light sixty-four times as intense as that by which it is cast. For ex- ample, take two lights whose intensities \ve wish to compare, and ascertain the relative distances at which they will cause the shadow cast by a third light to disappear, and their intensities will be as the squares of these distances. The eye can judge of the disappearance of the shadows more accurately than of the depth of the shadows, or of the intensity of the illumination. For this reason this method is the most accurate of an v hitherto invented. Mention the several methods of determining the intensities of different lights. Which is the best ? VELOCITY OF LIGHT. 333 V. Velocity of Light. The velocity of light has been determ- ined by two methods, entirely independent of each other. 1. Its velocity was first determined by Roemer, in 1676, from observations upon Jupiter's satellites. It was observed that when the earth was nearest Jupiter, one of the satellites of this planet appeared to enter its shadow, or to emerge from it, about 16 minutes sooner than when the earth was on the opposite side of its orbit, or at its greatest distance in its annual revolution. The distance between the two points of observation was the diameter of the earth's orbit, or about 190,000,000 miles, and therefore it was inferred that it took light a little more than 16 minutes to traverse this space. To illustrate, let S, Fig. 282, be the sun, E the earth, and T the Fig. 282. first satellite of Ju- piter. This satel- lite passes through the shadow of its primary, from T to T', in 42 hours 28 minutes, and the earth moves dur- ing the same time from E to E', a dis- tance of 2,880,000 miles. But the satellite actually emerges from the shadow fif- teen seconds later than it v/ould if the earth had remained at E ; and hence the light is fifteen seconds in passing from E to E', or 2,880, 000 miles, which would make its velocity 192,000 miles per second. That light moves uniformly at this rate, is shown by making the observations when the earth is in different parts of its orbit, either farther or nearer to Jupiter than is shown in the diagram. In all cases the rate per second will be the same. 2. Dr. Bradley, in 1725, confirmed this result by the aberra- tion of the stars, by which is meant an apparent change in regard to their actual place in the heavens. This is produced by the combined motion of light and of the earth in its orbit. By whom was the velocity of light first determined ? by what means? illustrate by diagram. What is the velocity of light as determined by this method ? 331 NATURAL PHILOSOPHY. It may be illustrated in the following manner : Fig. 283. Let S A and S' B, Fig. 283, be two rays of light coming from a star or the sun to the earth moving in its orbit in the direction A B. If now a telescope be held in the direction A S, the ray S A, in con- sequence of the motion of the earth from A toward B, will impinge upon the side of the tube before it reaches the bottom. But if the telescope be placed in the direction A E, so that A B shall be to A S as the velocity of the earth to the velocity of light, the ray will reach the bottom of the tube, passing through S' E A ; and hence the star will appear at S'when it is actually at S. The angle S A S' is called the angle of aberration. This amounts to 20 seconds for each star. By this method the velocity of light was found to be 195,000 miles per second, a result so nearly coinciding with that derived from Jupiter's satellites, as to leave no doubt that the true velocity of light is very accurately determined. SECTION II. REFLECTION OF LIGHT, OR CATOPTRICS. 1. When a ray of light is reflected, 1. The angles of inci- dence and of reflection are equal ; 2. When rays of light fall upon plane mirrors, the reflected rays have the same inclination as the incident rays have ; and, 3. The images formed by plane mirrors correspond with the objects, being at the same distance from the mirror, and like situated in every respect. 4. When two mirrors are placed at an angle, two o* more images of the object are formed. II. Rays of light falling on curved surfaces observe the same laiv ; hence, 1. Parallel rays falling upon a concave mirror are reflected to a point called the focus of parallel rays, ivhich is half way between the center of curvature and surface of the mirror. Concave mirrors give rise to images, whose position and magnitude will depend upon the position of the object. 2. Rays of light falling upon a convex mirror are rendered diverging ; and hence the images of such mirrors are less than the object behind the mirror, and nearer to it than the object. RAYS of light proceeding from a luminous body in the same What other method has been employed to ascertain the velocity of ligb* 7 Illustrate what is meant by the aberration of the stars. REFLECTION OF LIGHT. 335 medium, move, as we have seen, in right lines. But when they fall upon the surface of opaque bodies, they are either thrown back that is, reflected or taken up by the body, in which case they are said to be absorbed. When they fall upon transparent solid or liquid surfaces, or pass from one medium to another, they are turned from a straight line, and are said to be refracted. Let us first attend to the Reflection of Light. When a ray of light falls upon a smooth opaque surface, it is throivn back, and is said to be re- For instance, if a ray of light pass into a dark room, and fall upon a polished metallic surface, there is seen a bright spot upon it ; and if all the rays are reflected, the surface is not seen, but only the light. The surface of a perfectly polished substance is not visible. It is owing to the irregularity of reflected rays, arising from the irregularity of the surfaces from which they come, that any object becomes visible to the eye. Surfaces which reflect most of the rays of light are called mirrors. 1. Laws of Reflection. 1. A ray of light falling upon a smooth surface is reflected in such a manner, that the angle which the line described by the incident ray makes at the point of inci- dence with a perpendicular to tliat point is always equal to the angle made by the line described by the reflected ray and this same perpendicular ; or, in other words, the angle of incidence is equal to the angle of reflection, and is in the same plane. Fig. 284. Let c, Fig. 284, be a plane surface, d c the line /a described by the ray falling upon the surface at the point c, arid c b a perpendicular to that point. Then c a will be the path of the reflected ray, and the \ / angle d c b, called the angle of incidence, will be \ / ^ equal to the angle b c a, called the angle of c ' reflection. Light, in this respect, follows the same law as solid or liquid bodies, when they fall upon plane surfaces. Light may be reflected from plane or convex mirrors. 2. W hen rays of light fall upon plane mirrors, the reflected What is meant by reflection, refraction, and absorption of light? Illus- trate the reflection of light. What is the law of reflection ? 336 NATURAL PHILOSOPHY. Fig. 285. Fig. 286. rays have the same inclination to each other as the incident rays have. This fact is a direct result of the preceding law. The incident rays may be parallel, converging, or diverging. (1.) If the parallel rays, a c, b d, Fig. 285, fall upon the mirror, A B, the reflected rays, cf t d e, will also be parallel.* If the in- cident rays are in the same plane, the reflected rays will also be. (2.) If the rays, a c, b d, Fig. 286, fall converging upon the mirror, A B, the reflected rays will converge, as c e, d e, and meet in the point e. (3.) But if the rays e d, e c fall diverging upon the mirror, A B, then the reflected rays will diverge in the direction d b and c a ; that is, will have the same inclination as the incident rays. 3. Images formed by Plane Mirrors. In this case, the reflect- ed rays give rise to an image of the luminous point or object, which will appear as far behind the mirror as the object is be- fore it ; for the two reflected rays, c e, df, Fig. 287, if con- tinued back, will meet at a', arid by letting fall a perpen- dicular from a to the mirror, and continuing it to the same distance behind the mirror, it will meet the point a'.f On this principle it is possible to construct the image of any object as formed by a mirror. * For the angle a c f=b d c and/c B =.e d B being opposite exterior and interior angles, therefore c/is parallel to e d. t The two right-angled triangles, a c h and a' c h are equal, because they have a common side, h c, and the angle h c a = h c a 1 and c h a = c k a'; consequently, a h is equal to h a'. Mention the several laws of reflection from plane mirrors. Describe the nvmner in which images are formed by plane mirrors. By what rule may the image be constructed 1 2g7 IMAGES OF PLANE MIRRORS. 337 711 Thus, let A B, Fig. 288, be an object placed before a plane mirror, m' m. The rays, A g, A/, will be reflected in the direction f E, g o. These two lines produced will meet at a, and the perpendicular, A a, will meet in the same point. The same will be true of the rays from B ; they will be reflected to E and o as if they came from b ; and hence there will be an image of these two points at the same distance behind the mirror as the two points actual- ly are before, it. The same effect will be produced by the rays pro- ceeding from every part of the object between A and B : and hence the image a b will be at the same distance behind the mir- ror that the object A B is before it, and will be similarly situated in every respect. If, therefore, a plane mirror be placed at an angle of 45 to the horizon, an erect object placed before it will appear horizon- tal, and a horizontal object erect, because the image will have the same inclination to the mirror as the object ; and as each is 45 Q , taken together, they will amount to 90. When the object is twice the length of the mirror, and placed parallel to it, its image will be distinctly seen, for the angle of re- flection is equal to the angle of incidence, and these, taken to- gether, are double the angle of incidence. The surface, therefore, which reflects the rays from the object will be but half as long or as broad as the object ; hence a person may see his whole length in a mirror which is but half of his height. 4. The distinctness or brightness of the image increases as the angle of incidence increases. For example, if the light of a lamp fall nearly perpendicularly upon ground glass, polished wood, or varnished paper, we can not distinguish any flame ; but if the rays fall obliquely, the image will be distinctly seen ; that is, the intensity of the reflected rays is least at perpendicular incidence, and increases with the angle of incidence. The in- What relation does the image bear to the object? Upon what does the brightness of the image depend ? P 338 NATURAL PHILOSOPHY. "Fig. 289. tensity of the reflected rays is modified, also, by the medium in which they move, and the nature of the surface against which they impinge. 5. Angles of Reflection. When two mirrors are placed to- gether at certain angles, two or more images are formed. Thus, let A B, C B, Fig. 289, be two plane mirrors, placed at right angles to each other, and a a luminous point. The rays af and a g falling upon the two mirrors, will be reflected to I, and an eye at this point will see two images of a at E and b. But the ray a K will be reflected to c, and then, by a second re- flection, to I, so that the eye will perceive a third image at d ; that is, the image of a at K will send rays to c, and form by reflection a second image at d. By making the angle less than 90, the number of images will be increased, the image formed by one reflection constituting an object or radiant point for a second image, and this for a third. If the inclination of the mirrors be 60, 45, and 30, there will be six, eight, and ten images disposed in a circular manner. When the mirrors are parallel the number of images will be- come indefinite, and their situation will be in a direct line. In consequence of the diminution of light by repeated reflections, the images are less and less brilliant, until the light becomes too feeble for them to be perceived. This principle is illustrated in what is called The Endless Gallery, which consists of a box, having two plane mirrors placed parallel to each other in the opposite sides. When any object, as a candle, is placed in the box, there is pre- sented an endless succession of images. A person standing be- tween two mirrors placed upon the opposite walls of a room may see images of himself reflected in the same manner. How may several images of an object be formed ? What will be the ber of images when two plane mirrors are placed parallel to each other ? CURVED MIRRORS. 339 The Kaleidoscope is also constructed on the same principle. Two glass mirrors are inserted in a tube at an angle of 30 or 60, and pieces of colored glass are so placed as to exhibit an endless variety of images as the tube is turned. IT. Reflection from Curved Mirrors. Curved surfaces may be concave or convex. A hollow sphere, or the section of one, whose inner surface is polished, constitutes a concave mirror, and the same polished externally a convex mirror. The same law of reflection applies to curved mirrors as to plane, the angle of incidence being always equal to the angle of reflection. But, in consequence of the curvature, the reflected rays take the same direction that they would if they fell upon a plane which is tan- gent to the curve at the point of incidence. For illustration, let A r s B, Fig. 290, be a curved mir- ror, C the center of a sphere of which it forms a part, A B its diameter, in tn' its axis, passing through the middle of A B, and the lines C A and C B its aperture. Rays of light proceeding from C will fall perpendicularly upon the concave surface, and will be reflected to C ; or if they fall upon the convex surface, as a s, they will be thrown back in the same path. But rays of light proceeding from F to r will be reflected in the direction r o, on the other side of the perpen- dicular, C r, just as they would be if they fell upon the plane, k fc f , which is a tangent at the point r. If a ray fall upon the convex surface, as d s, it will be reflected in the direction s b, and, on the other side of the line, a s, perpendicular to the tangent at the point s. The path of the reflected ray is determined by making the angle b s a equal to d s a, or C r o equal to C r F. By ob- serving this law, we may determine with geometrical precision the path of any reflected ray. Let us apply this law to concave, and then to convex surfaces. Describe the kaleidoscope. Define a curved mirror. Illustrate the man- ner in which rays of light are reflected from curved surfaces. 340 NATURAL PHILOSOPHY. 1. Concave Mirrors. Let a c, Fig, 291, be a section of a concave mirror, C its center, and the line A B its axis ; we may then determine the path of the reflected rays when the radiant or luminous point is placed at different distances from the mirror. Suppose the radiant be so far TV removed that the ray h a shall be parallel to the axis A B ; it will be reflected to the point F, and this point is determined by making the angle C a F equal to C a h. Now the angles C a F and F C a are equal, and F a will be therefore equal to F C ; and if the ray h a is very near the axis, F a will be very nearly equal to F B ; or the ray h a will be reflected to a point half way between the center of the curve and the surface of the mir- ror. This point is called the principal focus, or the focus of parallel rays; for all the rays parallel with the axis and near to it will be collected very nearly in this point. Hence parallel rays of light falling upon a concave mirror, parallel to the axis, are reflected to a point called the principal focus, which is half way between the center of concavity and the surface of the mirror, Suppose the radiant to be placed at A, then the ray A a will be reflected to e, a point between the center of concavity and the principal focus. As A approaches C, the angle of incidence, A a C, will diminish, and, consequently, the angle of reflection, C a e, will diminish, and e will approach c, so that when the radiant is in the center of concavity, the angle of incidence being nothing, the reflected ray will return to C ; and if the radiant be removed toward F, the reflected rays will pass on the other side of the perpendicular, C a, and will cut the axis beyond C, along the line B A. When the radiant arrives at F, the reflected rays will become parallel. If the radiant be moved from F toward Illustrate the mode of determining the paths of rays reflected from a concave mirror when the radiant occupies different positions. How is the focus of parallel rays determined ? How far is the focus from the surface of the mirror? IMAGES OF CONCAVE MIRRORS. 341 B, 11 is evident that the reflected rays will diverge, as a d, more and more, until the radiant reaches the surface. Hence, (1.) Diverging rays radiating from a point of the axis farther from the mirror than the center of concavity, and falling upon a concave mirror, are reflected to the axis at a point between the center and the principal focus. (2.) Diverging rays radiating from the center of concavity are reflected hack again to the same point. (3.) Diverging rays radiating from any point between the cen- ter of concavity and the principal focus are reflected so as to cut the axis at points beyond this center. (4.) Rays diverging from the focus are reflected in parallel lines. (5.) .Diverging rays proceeding from any point between the principal focus and the surface of the mirror are reflected diverging. (6.) If converging rays fall upon the surface, it is evident that they will be converged to a point between the principal focus and the surface of the mirror. (7.) In all these cases the radiant is supposed to be situated in the axis, but the path of the reflected ray may be easily de- termined if the radiant is situated on either side of the axis. If the radiant is at d, Fig. 291, the ray d a will be reflected on the other side of the axis, at the same distance from it as d. 2. Images formed by Concave Mirrors. Having pointed out the method of determining the paths of reflected rays of light, Fig 292. when the position of the radi- ant is known, it is easy to de- termine the position and rela- tive magnitudes of the images which are formed by concave mirrors. Let M M', Fig. 292, be a concave mirror, F the princi- pal focus, C the center -of con- cavity, and D r its axis. Mention the several conditions under which rays of light may fall upon a concave mirror, and the paths of the reflected rays. Illustrate the mode in which images are formed by concave mirrors. 342 NATURAL PHILOSOPHY. Fig. 293. (1.) If the object be placed in the center of concavity, C, the image will coincide with it. This is seen when a mirror is held so that the eye is in its center, C. (2.) If the object be between the center and principal focus, as A B, the image will appear beyond the center, inverted and lar- ger, as a b ; and, consequently, (3.) If the object be beyond the center, the image will be be- tween the center and principal focus ; if a b is the object, A B wifl be the image. When the object is at an infinite distance the image will be in the prin- cipal focus. (4.) If the object is between the principal focus and the mir- ror, as A B, Fig. 293, the im- age will be behind the mirror, erect and larger, as a b. As concave mirrors generally form their images in front of the mirror, they were once employed to produce surprising appear- ances, the mirror being concealed in the wall to reflect an image of any object, so that it might appear in the air or upon a cloud produced for the purpose. Concave reflectors have been employed for telescopes for light- houses, either to concentrate the rays of light or throw them in a particular direction. 3. Convex Mirrors. In convex mirrors the path of the reflected ray is determined by the same law as that of con- cave mirrors. But as the rays fall upon the external surface of a sphere, such mirrors have only an imaginary focus. Let s s', Fig. 294, be a convex mirror, and c the cen- ter, c v its axis, and/ its focus. All these points are on the Fig. 294. What uses have been made of concave mirrors ? How is the path of the reflected ray determined in convex mirrors ? IMAGES OP CONVEX MIRRORS. 343 side opposite to that on which the light falls, but still it is equally easy to determine the direction of the reflected rays. (1.) If the rays converge toward the center of concavity, p s, p' s, they will return by the same paths, because they strike the plane, tangent to the parts at s s', at right angles. (2.) If the rays converge toward the principal focus, as t s, V s', they will be reflected in the direction s r, s' r f , in lines parallel tq the axis ; and hence parallel rays will be reflected in lines which, if continued, would meet in the principal focus ; hence they will diverge after reflection. Rays proceeding from any point of the axis, and falling upon the surface, will all be divergent after reflection. (3.) Images of Convex Mirrors. The images of convex mir- rors are situated behind the mirror, are less than the object, and symmetrical with it, whatever be the position of the object. Fig. 295. Thus, let M' M, Fig. 295, be a convex mirror, and A B an object placed before it. The rays from A and B will be re- fleeted to E as if they came from a b; hence an eye placed at E will perceive a diminish- ed image of the object, and the ME Bame will be true wherever the object is placed, because the reflected rays will diverge after re- flection in all positions of an. object, and will therefore appear to come from points behind the mirror, and nearer to its surface than the object ; hence the images must be smaller. 3. Spherical Aberration. When parallel rays of light fall upon a concave mirror, those rays near the axis are not converged to the same point as those further from it ; and hence pencils of rays from all parts of an object will not be collected at exactly the same points ; hence the image will be indistinct. By the crossing of the reflected rays, there is produced a curve more brilliant than other parts, called the caustic curve. To avoid the aberration produced by concave mirrors, they are sometimes ground in a parabolic form, and then all the rays which fall upon their surfaces are reflected accurately to a focal point. Point out the paths of the reflected rays. What kind of images are form- ed by convex mirrors ? Illustrate what is meant by spherical aberration. How may it be remedied ? What are caustic curves ? 344 NATURAL PHILOSOPHY. SECTION III. DIOPTRICS, OR REFRACTION OF LIGHT. I. When light passes obliquely from one medium to another of different density, it is refracted. 1 . If a ray of light pass from a rarer into a denser medium, it is bent toward a perpendicular to the refracting surface. 2. If from a denser to a rarer medium, it is bent from a per- pendicular to the refracting surface. The ratio between the sines of the angle of incidence and of refraction is called the index of refraction. 3. This ratio may be such that a ray will not pass from a denser to a rarer medium, and will give rise to what is called total reflection. 4. If a ray pass through a medium bounded by plane and par- allel surfaces, the incident and emergent rays will be parallel. II. When a beam of light passes through a triangular prism near the refracting angle, 1. It will be turned toward the back of the prism; 2. When rays from a single object fall upon sev- eral surfaces inclined to each other, several images of the object may be seen. III. 1. When parallel rays of light fall upon convex lenses, they are converged to a point called the principal focus, the dis- tance of ivhichfrom the lens will depend ttpon its form and com- position. 2. The action of concave lenses upon rays of light is just the opposite to that of convex lenses. 3. Convex lenses form inverted images of objects. 4. Concave lenses do not form convergent images of objects^ but, when looked through, we may see erect diminished images. 5. Owing to the laws of refraction, all the rays which fall upon a convex lens are not converged to the same point ; and hence we have what is called the spherical aberration of lenses. 6. Heat always accompanies solar light ; and hence convex lenses are burning glasses. IV. When a beam of light is passed through a prism it is separated into seven differently-colored rays, which are arranged in an invariable order, and called the solar spectrum. LAWS OF REFRACTION. 345 V. Certain appearances in nature are explained by the re' flection and refraction of light, such as the rainbow, twilight, haloes, and mirage. WE have seen that light moves in the same medium in straight lines, but when it passes from one medium to another of different density, as from air into water, it is, with few exceptions, bent from a direct course, and this deviation or change of direction is called Refraction. 1. To illustrate, let , Fig. 296, be a point from which a ray of light passes in the direction a S, and falls obliquely upon the surface of water, A B. At the point S the ray will be bent out of a straight line ; that is, in- stead of proceeding to/, it will be refract ed to e, or toivard a perpendicular, p p', to the refracting surface. The same law will always prevail wherever a ray passes from a rarer to a denser medium, excepting when the ray falls perpendicularly upon the surface of the medium, in which case no deviation will take place. 2. If a ray of light proceed from e, and pass out of the water into the air, it will be bent at the surface, S, and, instead of pro- ceeding to b, will be refracted toward a, or from a perpendicular to the refracting surface. 1. Laws of Refraction. It may be stated, then, as a general law, 1. That a ray of light, in passing from a rarer to a denser medium, is bent toward a perpendicular to the refracting sur- face ; and, 2. That a ray of 'light passing from a denser to a rarer me dium,is bent from a perpendicular to the refracting surface. There is but one exception to these laws, and that is when a ray falls perpendicularly upon the surface ; but the ray may fall so obliquely that, in passing into a rarer medium, the refraction is so great as to prevent it from entering, in which case it is re- flected at the surface. Define refraction of light. Illustrate by diagram. What is the law of refraction ? 346 NATURAL PHILOSOPHY. The line described by the ray before it meets the surface is called the incident ray, and that which it describes after refraction the refracted ray. The angle A S P is called the angle of incidence, e s p' the angle of refraction, and e sfihe angle of deviation. As objects are seen in the direction in which light from them meets the eye, it is easy to prove, both by experiment and from observation, the truth of the laws of refraction which have been given. Fig. 297. If we take a vessel, A B C D, Fig. 297, and lay a half dollar in the bot- tom at O, and place the eye at E, so that a ray of light proceeding direct- ly from the coin would have to pass through the sides of the vessel, O G Ei E, just below the top, it is evident that the coin would not be visible. But if the vessel be partly filled with water, the light from the coin will be bent from a perpendicular, P Q, at the point L, so as to pass over the edge of the vessel into the eye at E, and ren- der the coin visible. It will appear to be raised up, as at K, be cause E K is the apparent direction of the light. This is the reason that water in a river or pond, whose bottom may be seen, appears to be more shallow than it actually is, and that any object, as an oar, partly immersed in water*, appears bent at the surface. 2. Indices of Refraction. In order to exhibit the relation between the angles of incidence and of refraction, Let A P B, Fig. 298, be a globe half full of water, and C a point in its center, upon which a ray of light may fall from I, and be refracted to R, I C P will be the angle of incidence, and II C P the angle of refraction. The lines I m, H R, let fall from I and R upon P P, a perpendicular to the refracting surface, are called the sines of the angles of incidence and of refraction. Which is the angle of incidence, and which the angle of refraction ? What effect has refraction upon the position of objects? What is meaut by indi- ces of refraction ? Fig. 298. INDICES OF REFRACTION. 347 Now it is found by experiment that, with the same medium, the sines of the angles of incidence and of refraction bear to each other a constant ratio; that is, if the line I m is double that of H R, then I' m' will be double H' K/, or whatever the angle at which the ray meets the surface, the line representing the angle of incidence will always be double that which represents the an- gle of refraction. Thus, in the case of rays of light passing from air into water, the ratio of the sines of incidence #nd of refraction is as 1'366 to 1 ; that is, if H R be 1, 1 m wiU be 1-366 ; or if H' R' be 1, I" m' will be T366, and the same ratio would exist at whatever angle the ray might pass from air into water. But this ratio varies for different substances. From air into crown-glass these lines are in the ratio of T53 to 1, and into diamond as 2'487 to 1. These ratios, determined for each substance by experiment, are arranged in tables, and called Indices of Refraction. The following table contains the indices of refraction for sev- eral substances. The sine of the angle of refraction is called 1, and that of incidence is represented as follows : Indices of Refraction. Indices of Refraction. Chromate of lead 2-974 Diamond 2-487 Sulphur 2-148 Rock crystal 1-548 Crown glass 1-530 Flint glass 1-584 Water 1-366 Ice 1-309 If we would estimate rightly the refractive powers of different substances, we must regard their specific gravities or densities ; for if a less dense body is as refractive as one more dense, its ab- solute refractive power must be much greater. On this principle hydrogen gas, the lightest of any known substance, has an index of refraction over 3. Combustible bodies generally have the high- est indices of refraction. 3. Total Reflection. The constant ratio between the sines of the angles of incidence and of refraction renders it impossible for a ray of light to pass out of a denser into a rarer medium, when the angle of refraction causes the ray to make an angle with the surface equal to or exceeding 90. Are the indices of refraction the same for all bodies ? Under what con- ditions does total reflection take place ? 348 NATURAL PHILOSOPHY. For example, if the ray / e, Fig. 299, passing out of a dense medium, a b c, meet the surface, b e, so that the angle of refraction would cause the ray to make with the surface an angle of 90 or more, it is evident that it can not pass out of the me- dium, but will be reflected at its sur- face, and will be seen as at d. This is called total refection, because all the rays so situated must be reflected ; and this is the only case of a perfect mirror. In all other cases of reflection some of the rays are either absorbed, transmitted, or scattered. Such a surface, therefore, exhibits the highest possible brilliancy. The angle of total reflection will depend upon the indices of refraction. From water into air, it is 48 28' ; from glass, it is about 41 55' ; from diamond, 23 35'. 4. When light passes through any medium which is bounded by surfaces that are plane and parallel to each other, into the same medium in which it tvas moving before refraction, the emergent and incident rays are always parallel. Thus, if the rays r s, b c, Fig. 300, pass from air through the solid rectangu- lar piece of glass, A B, the emergent rays, d e, g f, will be parallel to the incident rays, r s, b c. The reason of this is, that the emergent rays at d g will be bent just as far from as the incident rays at s c were toward a perpendicular to the re- fracting surface. Hence, if the incident rays are parallel, the emergent rays will also be parallel ; if convergent, they will be convergent ; and if divergent, they will be divergent. Therefore, objects seen through such media, as through a pane of glass, will have the same mag- nitude, and will but slightly vary in position from their position when seen through air alone. If, however, diverging rays pass out of a denser into a rarer What is the law of incident and emergent rays when light is transmitted through bodies whose surfaces are plane and parallel ? What influence is exerted on convergent and divergent rays ? REFRACTION OP LIGHT BY PRISMS. 349 medium, a? they will be refracted from a perpendicular to the surface, their divergency will be increased. If they pass out of a rarer into a denser medium, they will diverge less than before, because they are refracted toward a perpendicular to the refract- ing surface. II. Refraction of Light by Prisms. An optical prism is a Fig. 301. transparent medium, bounded by two surfaces which incline to each other ; the line of their intersection is called the edge, and the angle which they make the refracting angle of the prism. A prism consists generally of a triangular piece of glass, a, Fig. 301, mounted upon a stand, b, and a joint, c, to enable us to place it in any position. 1 . When a ray of light passes through a prism near the re- fracting angle, it is turned toward the back of the prism, while the object is removed toward the refracting angle. Let ABC, Fig. 302, be a tri- angular prism, C the refracting an- gle, and a b a ray of light incident upon the surface, A C. The ray will first be refracted to/, and as it emerges on the side B C, it will again be refracted toward d, and an eye at this point would there- fore see the object removed down- ward to a 1 ; and if the refracting C angle were turned upward, all ob- jects would appear to be raised up from their actual position ; that is, the objects are always removed in the direction of the re- fracting angle of the prism. The intersection of the lines a b, f d, at e, ibrming the angle a e a', is called the angle of devia- tion. The larger the refracting angle, the greater the deviation. The refracting power of the substance, and the direction in which the rays fall upon the surface, influence the degree of de- viation. It is found by experiment and by calculation, that the angle of least deviation is equal to the index of refraction, mi- nus one, multiplied by the refracting angle of the prism. Define a prism. Illustrate the law of refraction in prisms. What is the angle of deviation, and to what is it equal 1 350 NATURAL PHILOSOPHY. 2. When light falls upon several surfaces, so that tttfe rays, after refraction, shall approach each other, several images are produced. Glasses constructed for this purpose are called Multiplying Glasses. Fig. 303. Thus, let a ray of light from a, Fig. 303, fall upon A F, and emerge from the five surfaces A B, B C, C D, D E, E F, so inclined to each other, that the rays, after re- fraction, shall meet at I, an eye situated at this point will see five images of a, and the number of images may be greatly increased by multiplying the number of faces. III. Refraction by Lenses. A lens consists of a transparent substance whose bounding surface is curved. There are six kinds of lenses, as seen in Fig, 304. The plano-convex lens, A, is bound- ed by one plane and one convex sur- face. The plano-concave, B, is bounded by one plane and one concave surface. The double or bi-convex lens, C, is bounded by two convex surfaces ; and F The double concave, D, by two concave surfaces. The concavo-convex lenses, E, F, have one concave and one convex surface. E is termed a meniscus lens. They differ from each other hi the fact that the concavity of the surface of F is less than the convexity, but in E it is equal or greater. A, C, and F are thicker at their centers than at the edges, and are convergent lenses ; while B, D, and E are thinner at, their centers than at the edges, and are divergent lenses. Lenses are generally made of glass, though sometimes of rock crystal and other precious stones, as the diamond. They are How may objects be multiplied by refraction 1 Describe the several kinds of lenses. Of what are lenses made ? REFRACTION BY LENSES. 351 ground to spherical surfaces, though there are elliptical, parabol ic, cylindrical, and other forms given to them. In the double convex lens, a b, Fig. 305, c and/ are the centers of the curva- ture, or geometrical centers ; d is the op- tical center, a b the aperture, c f the axis, and m n the secondary axis. All the rays which pass through the optical center, as m n, f c, are called principal rays. They are the central rays of each pencil of light, which proceeds from any luminous object. The refraction of light by lenses may be understood by means of a prism whose refracting angle is very small. The deviation in such a prism may be regarded as very nearly in proportion to the refracting angle ; that is, one prism whose refracting angle is twice as great as that of another, will produce twice the devi- ation. Each prism must have the same index of refraction. We have seen that light is bent toward the back of the prism. If, therefore, we put the backs of two prisms of very small refracting angles together, as a b c and c b d, Fig. 306, and let the parallel rays of light from f and g pass through them, they will be bent to F, where they will meet ; or, if rays proceed from F, they will be rendered parallel. Now we may regard a double convex lens as composed of an indefinite number of plane surfaces, situated so as to form a curve, upon which parallel rays may fall, and be converged to a focal point. In the same way, by uniting the re- fracting angles of two prisms, o r s, s t v, as in Fig. 307, and letting the parallel rays from e and /pass through them, the 71 rays will diverge as they emerge from the second surface to g and h. A double con- cave lens is precisely similar in its action upon light. Illustrate by diagram the axis, geometrical and optical centers, and aper- ture of lenses. What are principal rays ? How may the refraction of light by lenses be illustrated ? ff 352 NATURAL PHILOSOPHY. These two forms of lenses are exactly opposite in their effects upon light. 1. Convex Lenses. The action of all convex lenses is similar. The difference in their effects depends chiefly upon their degree of curvature, the deviation of a ray of light passing through them being greater in the double than in the plano-convex lens. In order to exhibit the laws of refraction in convex lenses, Let M N, Fig. 308, be a double convex lens, P a luminous Fig. 308. TSf point in the axis, A B, so placed that the rays falling upon the lens will be rendered convergent and meet the axis at D, at an equal distance on the other side of the lens. If the radiant be re- moved to C, the rays will be collected at G ; that is, as the radi- ant approaches the lens, the focal point recedes. On the other hand, if the radiant be removed beyond P, the rays will be col- lected at points nearer the lens than D ; and if the radiant be removed to such a distance that the rays are parallel, then they will be collected into a point called the principal focus. We may "determine the relative distances of the focal point and the point P in the following manner : Let the radiant be so placed at P that the rays shall converge to D, at an equal distance from the lens ; make the angle P M F equal to F P M, then the line P F will be equal to F M ; and as the angles of deviation of two rays, F M and P M, are equal, the angle D M H will be equal to P M F or M D F, the line P M being equal to M D ; hence the ray M H will emerge par- allel to the axis, 5 * and F is the focus of parallel rays. Now, when the rays are very near the axis, F M and F E may be regarded as equal to each other ; P is therefore twice the * For when two lines, as M H and F D, are cut by a third line, M D, making the alternate angles equal, the two lines will be parallel. Describe the action of a double convex lens upon rays of light. Illustrate the mode of determining the focus of parallel rays. How far is it from the lens ? CONCAVE LENSES. 353 distance of F from the lens. The principal focus, or focus of par- allel rays, is F ; and hence, if the radiant be placed at tiuice the distance of the principal focus of a convex lens, the rays will con- verge to a focus at an equal distance on the other side of the lens. If the radiant be moved from the focus, F, toward the lens, the rays will not converge to a focus, but will emerge diverging, though their divergency will be less than before refraction. The focal distance will depend upon the form of the lens, and also upon its index of refraction. In a double convex lens, the curvature of whose surfaces has an equal radius, and whose index of refraction is^f , the focus is found, by experiment, at the center of the spherical segments which form the lens. If the index of refraction is greater than f , the focus will be nearer ; if less than f , more remote. In a plano-convex lens, whose index of refraction is f , the focus is at a distance equal to twice the radius of curvature. 2. Concave Lenses. Concave lenses act upon light in a man- ner exactly the reverse of convex lenses ; that is, they separate the rays of light, causing parallel rays to diverge, diverging rays to diverge more, and converging rays to converge less than before. Fig. 309. (1.) Thus, let A B, Fig. A 309, be a double concave lens, and let the rays of light, e, k, c, fall upon it, parallel to the axis, D E. After refraction at the two B surfaces, they will diverge as if they came from the focal point, F. (2.) If the radiant be brought toward the lens, the rays, after refraction, will emerge still more divergent ; and the nearer the radiant, the nearer the imaginary focus, F, will be to the lens. (3.) If the rays converge toward the focus, F, as y z, v u, they will emerge, after refraction, parallel with the axis. At what distance from the lens will rays of light radiating from a point in the axis be brought to a focus ? What is the distance of the focus in a double convex lens ? plano-convex lens ? How do concave lenses act upon light ? Illustrate the manner in which rays of light are refracted by a double concave lens. 354 NATURAL PHILOSOPHY. (4.) If the rays converge toward a point farther from the lens than the focus, F, they will be rendered diverging. (5.) If to a point nearer the lens than the point F, they will converge less than before, and meet the axis at some point farther than this focus from the lens. 3. Secondary Axes. In the cases above considered, both of convex and concave lenses, the rays are supposed to be parallel to the axis, to radiate from or converge to some point in the axis of the lens ; but there may be an indefinite number of secondary axes, which are the central rays of each pencil, and these cut the principal axis in the optical center of the lens. Thus, let M N, Fig. 310, be a double convex lens, A B the mg. 310. B principal axis, any pencil of rays proceeding from any point with- out this axis, as from G, and falling upon the lens, will converge to F' ; the axis of this pencil will cut the principal axis in C, and all rays which pass through this point, both in convex and concave lenses, will be refracted in such a manner that the in- cident ray, G C, and the emergent ray, C F', will always be parallel to each other. In order to determine the position and character of the images which may be formed by means of lenses, it is only necessary to apply the principles already established. 4. Images of Convex Lenses. Convex lenses form inverted images of objects. Thus, let M N, Fig. 311, be a double convex lens, A B its principal axis, and C D an arrow placed beyond the principal focus, F. The pencil of rays emanating from C will be collected in G, and that from D will be collected in E, and those which proceed from the points between C and D will be collected in What are secondary axes ? Illustrate the manner of the formation of im- ages by convex lenses. IMAGES OF CONVEX LENSES. 355 corresponding points between G and E ; hence G E will be an E inverted image of the object. The reason for this inversion is, that the axis of each pencil must cross the principal axis in the optical center of the lens, as C G and D E. The size of the image, and its distance from the lens, will de- pend upon the distance of the object. (1.) If the object is twice the focal distance of the lens, the image will be of the same magnitude, and at the same distance from the lens. (2.) If the object approach the focus, the image will recede and increase in size ; and when the object arrives at the focus, the image will be at an infinite distance, as the rays will then go out parallel to each other. (3.) If the object be removed further than twice the focal dis- tance, the image will be nearer the lens than the object, and less in size ; hence The size of the object is to that of the image as the distance of the object from the lens is to the distance of the image from the lens. It will be seen to follow from this law that lenses of short focal distances will give images nearer the lens, and, consequent- ly, smaller than those which have a longer focal distance ; and that, at equal distances from the lens, the images will be. larger in proportion as the focal distance is shorter. (4.) If the object be placed nearer the lens than the focus, no convergent image can be formed, because the rays are in this case Upon what will the size of the image depend ? What ratio will the im- age bear to the object ? Why is the image enlarged ? What will be the effect if the object is placed nearer to the lens than the focus? 356 NATURAL PHILOSOPHY. rendered diverging, and yet ? ^- 3i '~- they are less diverging than before refraction ; and hence to an eye on the other side of the lens, M N, Fig. 312, the object A B appears to be magnified, erect, and fur- ther from the lens, as C D ; hence all objects seen through a double convex lens, placed nearer than the principal focus, are larger ; or, if the eye be placed nearer the lens than the principal focus, objects, for the same reason, will be magnified. This is the principle of the microscope. The ob- ject appears larger, because the lens, by causing the rays to con- verge, increases the angle of vision, which is the angle made by two lines coming from the extremities of the object and meeting in the eye. Thus, an eye at E, in Fig. 312, would perceive the object A B under the enlarged angle C E D ; and hence it would be magnified. 5. Images of Concave Lenses. As concave lenses cause ray of light to diverge, they do not give convergent images of objects ; but, on looking through such lenses, we see erect, diminished im ages. The reason of this is, they diminish the angle under which the object is viewed. Thus, let M N, Fig. 313, be a double concave lens, and C D an arrow. On look- through the lens from E, all the rays of light from the arrow will be rendered diverging, and appear to come from A B, which will therefore be a diminished image of C D. Concave lenses and convex mirrors give images smaller than the objects, while convex lenses and concave mirrors yield en- larged images of the objects placed before them. 6. Spherical Aberration of Lenses. In convex lenses as in concave mirrors, in order to form a distinct image, the rays of light must be very near the axis of the lens ; for, from the laws Fig. 313. How are images formed by concave lenses ? Illustrate spherical aberra- tion. DECOMPOSITION OF LIGHT. 3.77 of refraction, in all cases any two rays which meet the axis at the same point must be equally distant from the surface of the lens. Those rays, therefore, which fall farther from the axis will be collected at points farther from the optical center of the lens than those near the point where the axis meets it ; hence, in the pen- cils of light from any object, the rays which fall upon the surface of a convex lens will not all be converged to the same point in the axis of the pencil. This is called spherical aberration of lenses. The distance over which the rays are spread depends upon the form and thickness of the lens, and may be remedied by giving the lens " the form of a spheroid, whose major axis is to the dis- tance between its foci as the sine of incidence to the sine of refrac- tion." Rays parallel with this axis will meet in the remoter focus. 7. Burning Glasses. Convex lenses and concave mirrors not only collect the rays of light, but also those of heat into a focal point ; and hence they are called burning glasses. Fig. 314 represents a double convex lens, through which the rays of heat from the sun are made to pass, and are converged by it to a focus. The degree of heat will depend upon the diameter of the lens, and may be sufficient to melt the most refractory substances. A lens 3 feet in diameter has been known to melt cornelian in 75 sec- onds, and a piece of white agate in 30 seconds. IV. Decomposition of Light. 1. When a beam of solar light is passed through a prism, it is not only refracted at the two sur- faces, but separated into seven differently colored rays. Thi* fact may be shown experimentally by admitting a beam of light into a darkened room through a small orifice in the window shutter, and, after passing it through a prism, receiving the im- age upon a screen or apposite wall of the room. How may spherical aberration be remedied ? What are burning glasses ? What is the composition of light ? 358 NATURAL PHILOSOPHY. Thus, let m, Fig. 315, be a mirror to re- flect a beam of light from the sun through an aperture, O, in the shutter of a darkened room. There will be formed a circular im- age of the sun, directly opposite the aperture, upon the screen, S r. If now we intercept the beam by a triangular prism, P, it will refract the beam, and, instead of the white spot, we shall have a long, variously-colored surface, called the Solar Spectrum. If the beam is very small, we may distinguish seven differently- colored surfaces or images of the sun upon the screen, arranged as in Fig. 315, red, orange, yellow, green, blue, indigo, and vio- let. The red image is always nearest the white light, and the violet the farthest from it. The red ray, therefore, suffers the least, and the violet the greatest deviation, while the other colors are intermediate between these two extremes ; that is, 2. The differently-colored rays, are unequally refrangible. If each ray was equally refracted, we should have simply an im- age of white light, which, as we have seen, Fig. 278, p. 330, would be of the same form as the object which emits the rays in this case, an image of the sun ; and hence the solar spectrum must consist of seven differently-colored images of the sun, which slightly overlap each other, as represented in Fig. 315. By making the opening J^th of an inch in diameter, the refracting angle of the prism 60, and placing the screen 18 feet from the opening, the several colors are nearly distinct. The smaller the Jjeam, the purer the colors will appear. These colored bands are not equal in diameter. If we divide the spectrum into 360 equal parts, 45 will be red, 27 orange, 48 yellow, 60 green, 60 blue, 40 indigo, and 80 violet. These numbers, however, vary with the substance of the prism. , How is light decomposed ? spectrum ? How are the colors arranged in the solar THE SOLAR SPECTRUM. 359 To observe these colors, it is only necessary to look through a prism upon external objects, or even at the sky, when they will be seen in the same order as exhibited upon the screen. 3. White light, then, consists of seven colors, each one of which is simple. (I.) That each of the colored rays is simple, that is, not com- pounded of two or more colors, may be proved by the following Exp. Pass a ray of white light through a prism, and then separate one of the colors by means of a small slit in a screen, or by reflection from a mirror, and pass this isolated ray through a second prism. The ray will be refracted as before, but will suffer no change of color. Simple light was called by Newton homogeneous light. (2.) That white light consists of seven simple colors, may be shown by passing these colors, in the same proportion in which they exist in the solar spectrum, through a second prism with its refracting angle inverted. The rays will then be recomposed, and form a perfectly white image. Fig. 316. Thus, let the two prisms, S A A' and S' B B', Fig. 316, be so arranged that the refraction of the first shall be exactly counteract- ed by the second. We shall then have at M a white im- age, the same as would be U formed without the prisms. (3.) Newton further confirmed this fact by passing a beam of light, after it had been decomposed by a prism, through a double convex lens, and producing an image of perfectly white light. (4.) Muncfwiv attached clock-work to the prism, so as to give it a rapid motion. By this arrangement the solar spectrum was made to move rapidly back and forth upon the screen. The im- age then became white, slightly colored at the two extremities. By this means the different colors are so mixed that the eye fails to distinguish them, and the result is a sensation of whiteness. (5.) A similar effect may be -produced by taking a circular card, dividing it into seven sections in the proportion in which What is the proof that white light consists of seven simple colors ? Men- tion the experiments of Newton of Munchow ? 360 NATURAL PHILOSOPHY. the rays exist in the solar spectrum, and then painting them as nearly as possible with the seven prismatic colors. On causing the card to revolve rapidly the separate tints will disappear, and a grayish- white light will be reflected from its surface. If the colors applied were pure or simple, perfectly white light Fig. 317. would be the result. 4. Fixed Lines in the Spectrum. The solar spec- trum appears to be wholly colored when viewed at a little distance ; but when examined by a microscope, it is found to be crossed by dark lines, which are constant in position and magnitude when the same kind of prisrn is used, and the same kind of light, but vary slightly when the light is separated by different media. Solar, stellar, and artificial lights have each a different system. Some of the larger lines are represented in Fig. 317, and as they are fixed, they were represented by Fraun- hofer by the letters of the alphabet, commencing with A in the red. 5. Illuminating Power and other Properties of the Simple (1.) The several colored rays have been found to differ in their illuminating power. The yellow rays are the most brilliant ; that is, yellow impresses the eye more powerfully than any other color. This power diminishes gradually each way toward the red and violet. , (2.) It has been found, also, that the yellow rays exert a spe- cific influence upon vegetation, giving rise to the green color of the leaves and other parts of plants. (3.) The blue rays effect chemical changes in certain com- pounds, especially in the iodides and chlorides of silver, substances which are employed for producing photographic pictures. The more refrangible rays are also concerned in producing phosphor- escent light in bodies capable of yielding it. It has been sup- How can the same effect be produced by painting a card with the pris- matic colors ? Are there any dark lines in the spectrum ? how are they designated ? Which rays possess the greatest, and which the least illu- minating power? What rays influence vegetation and produce chemical changes ? COMPLEMENTARY COLORS. 361 posed that there were toward the violet end of the spectrum rays different from those of color, which are effective in producing chemical changes; and hence they have been termed chemical rays. (5.) Solar light is always accompanied by heat or calorific rays. These rays are less refrangible than those of color ; and hence the greatest heat is found in and near the red rays, and, in some cases, quite out of the spectrum, dependent upon the sub- stance of the prism. The intensity of the rays of heat diminishes rapidly toward the violet. 6. Complementary Colors. One color is said to be comple- mentary to another when their union will produce white light. When the simple colors are united in proper proportions they produce white light ; but if one color, as red, is wanting, the re- maining colors will yield a bluish tint, to which red is comple- mentary. Each color has its complementary color or colors, by the addition of which white light will be produced. For experiments on this subject, the apparatus represented in Fig. sis. Figure 318 may be employed. It consists of several plane mirrors with screens, mounted upon a frame, so that any two or more rays of homogeneous light may be isolated and reflected to the same spot on a screen. By this means the resulting colors may be clearly observed. Thus, Exp. If the red and blue rays are reflected to the same spot, they will yield a purple image. Red and yellow will form an orange, and yellow and blue a green tint, to which, if the remaining colors in each case are added, white light will be produced. Some opticians, as Dr. Brewster, have considered the solar spectrum to consist of but three simple colors, red, yellow, and blue, and that the other colors are produced by their combination. This theory supposes that some of the red rays extend to the Where are the rays of heat found ? What are complementary colors ? Of how many colors does the solar spectrum consist, according to Dr. Brewster ? Q 362 NATURAL PHILOSOPHY. violet, and also a portion of the yellow and blue rays, though each is most intense in certain portions of the spectrum. Whether this theory be true or not, it is easy to compound these three col- ors in such proportions as to produce nearly every variety of tint. 7. Natural Color of Bodies. If we look through a prism upon any colored object we shall be able to analyze the color which it reflects. Thus, if we take several narrow strips of colored paper such as is used by bookbinders for the titles of books is the best white, scarlet, orange, yellow, green, and blue, and, having arranged them near each other, observe them through a prism, we shall find that the white paper will yield all the prismatic colors. The yellow paper will exhibit colors nearest to the perfect spectrum, being wanting only in blue and violet, which, of course, are com- plementary to it. The orange yields a much less perfect spec- trum^ because the green, violet, and blue rays are wanting. The scarlet appears almost purely red, a slight tint of orange only being separated ; while the green and blue strips are almost entirely deficient in red rays. The light which is thus decomposed is that which is reflected from the body ; hence The different colors of natural objects depend upon the power of their surfaces to reflect certain rays and to absorb others. Few- bodies, however, have the power to absorb or to reflect all the rays of the spectrum, or of any color which may fall upon them. Objects which are bright scarlet absorb all but the red and a portion of the orange rays ; those which are white reflect all the rays ; and those that appear black absorb them all ; but most colored objects absorb a portion of all the rays, and reflect a por- tion of them ; hence we rarely see pure prismatic tints. It is this power of absorbing and reflecting the different colored rays of light which gives to each object in nature its distinctive color. Color, therefore, is a property of light, but not of matter. Material bodies only decompose the light, and reflect those rays which give them their color, while the complementary colors are absorbed. How may the natural colors of bodies be analyzed? On what does the color of natural objects depend ? What gives a body its distinct ive color 7 CHROMATIC ABEREATION. 363 Colored media may be employed to separate the rays of light, those rays only being transmitted which are of the color of the substance used, while the other colors are absorbed. Either col- ored glass or colored infusions may be used for this purpose. 8. Chromatic Aberration. The action of lenses upon light is the same as that of prisms ; that is, when white light is passed through a lens it is decomposed. As the red rays are less refran- gible than the violet, they will be brought to a focus in a convex lens farther from the lens ; and hence we shall have a colored image, so that objects seen through lenses will be fringed with the several prismatic colors. F&.319. To illustrate this, let A B, Figure 319, be a piano - convex lens, through which a beam of light, par- allel to the axis, is made to pass. The rays will be separa- ted ; the red will ap- pear at r, and the violet at v. The space r v is the chromatic aberration of the lens. This property of lenses was supposed by Newton to be incapa- ble of any remedy ; but, since his day, lenses have been construct- ed which almost entirely obviate the difficulty. The principle upon which chromatic aberration is avoided is founded in The different dispersive powers of substances whose indices of refraction are nearly equal. The power which a prism or lens has of separating the colored rays is called its dispersive power. Some substances possess this power in a much higher degree than others. Thus, flint glass will separate the rays nearly twice as far as crown glass, and three times as far as water ; and hence the breadth of its spectrum, and, of course, its dispersive power, will be in the same ratio.* But the indices of refraction * The dispersing power, however, is great in proportion to the difference between the indices of refraction in the red and violet rays. Thus, in wa- What is chromatic aberration, and on what principle may it be avoided ? What is meant by the dispersive |fcwer of a prism or lens ? 364 NATURAL PHILOSOPHY. (see p. 347) in crown and flint glass are nearly equal, being T53 in the former, and 1'584 in the latter. If now we combine these two kinds of glass a piece of flint glass, which has twice the dispersive power, with a piece of crown glass, whose refracting angle is made twice as great, and there- fore has the same dispersive power, but in an opposite direction we may wholly counteract the separation of the rays. Thus, let ABC, Fig. 320, be a prism 1^.320. of crown glass, and A C D a prism of flint A D glass ; let the refracting angle A C D be A / but half that of B AC, and let a beam ===== 7^p*^ a ^ of light be passed through this compound / y assaa * s ^ prism. B C It will be seen that the crown glass, whose angle of refraction is twice that of the flint, has, on this account, a dispersive power just equal to it. It will, therefore, disperse the rays in the di- rection of B C just as far as the flint glass will disperse them in the direction of A D, and thus the dispersive powers of the two glasses exactly counteract each other, and we shall have an im- age of white light ; but because the crown glass has twice the refracting angle of the flint, it will cause the beam to deviate to- ward B C twice as far as the flint glass will in the opposite direc- tion, so that the beam will still Fig. 321. Fig. 322. suffer considerable deviation in passing through the prism. By applying this principle to lenses, they are rendered achro- matic. This is done by using a convex lens of crown, and a concave lens of flint glass, Fig. 321, the curvatures of which correspond to the angles of the prism in the preceding diagram, ter, the index of refraction of the red ray is 1-330, that of the violet 1-344 ; the difference being 0-014. In flint glass the index of refraction in the red ray is 1-628, and the violet 1-671 ; the difference is 0-043, or a little more than three times that of water. Muller. How are lenses rencro*ed achromatic ? EXPLANATION OF THE RAINBOW. 365 the curvature of the crown glass being greater than the flint. Sometimes two double convex lenses of crown glass are combined with a double concave lens of flint glass, in which case the curva- tures may be exactly fitted to each other, Fig. 322. Rays of light passing through such lenses will converge to a focal point without dispersion. It is found difficult, however, in practice to produce perfect achromatism; and the best lenses give a slight tinge of color to the objects which are seen through them. V. Application of the laws of refraction and of reflection to the explanation of natural phenomena. There are certain appearances in nature which are of great beauty and sublimity, that find a ready explanation by the prop- erties of light, which have been hitherto considered, such as the rainbow, twilight, spectral apparitions, mirage, &c. 1 . The Rainbow. The rainbow is one of the most beautiful and striking phenomena in the natural world. It consists of one or more broad circular arcs of the prismatic colors painted upon the surface of the sky, opposite the sun. The bow is seen when the back is turned toward the sun, and forms the base of a cone, whose apex is the eye, and whose axis is a line passing from the sun through the eye, and also the center of the circle of which the bow is an arc. In order to understand how this arc is formed, it is neces- sary to examine the action of a drop of water upon the sun's rays. Drops of water have the properties of a lens and of a reflect- ing surface. Thus, let A H, Fig. 323, be a drop of water, S i parallel rays of light from the sun. These rays will be refracted at i to e, and the colored rays separated. At e a portion of them will be reflect- ed to/ and g, where, passing out of the drop, they will be again refracted to o and b, and an eye placed at these points will perceive the prismatic colors, red, or- ange, yellow, &c., painted beyond the drop, as at a. It will be seen that all the rays which are parallel when they What natural appearances may be explained by the reflection and refrac- tion of light ? Describe the rainbow. Explain the mot> of its production. 366 NATURAL PHILOSOPHY. fall upon the drop will not emerge from it parallel ; and hence, that the angles of deviation formed by the incident and emergent rays, as S a b, will not all be equal to each other. Now it is found that, of all the rays which fall upon the drop, only those which emerge nearly parallel, and make an angle of 42 30' with the incident rays, will reach the eye, and produce the sensation of light. As the drops of water are constantly fall- ing between the observer and the place of the bow, and rays of light falling upon them, only those drops which lie upon the sur- face of a cone, the radius of whose base subtends an angle of 42 30', will so refract and reflect the light as to reach the eye of the observer. To render this more distinct, let O P, Fig. 324, be a line 3 passing through the sun and the eye, and extending toward the center of the bow, and through this line pass a vertical plane. SECONDARY BOW. Through O draw the straight line O C in this plane, so that the angle P O C shall be equal to 42 30'. Let this plane be re- volved about the axis P O ; then all the drops which lie upon the surface of the cone, whose convex surface is described by the line O C, will send emergent rays of light to the eye of the observer at O, and hence he will perceive an arch of colored light. The arc of red light will be on the outer side of the bow, and will be about 30' in diameter, because the sun is not a point, but has an apparent diameter of 30' ; the violet band will be of the same width, but will occupy the inner portions of the bow, be- cause these rays make an angle of only 40 30' with the incident rays. The width of the bow will therefore be 2. The other bands will occupy the intermediate space between the red and violet, as in the solar spectrum. The position of the arc will depend upon the height of the sun above the horizon. When the sun is in the horizon and the observer at the level of the sea, the bow is an exact semicircle, with its center in the horizon. If the observer is upon a mountain, more than a semi- circle will be seen. In some cases a complete circle is observed, especially at certain waterfalls. If the sun is above the horizon, less than a semicircle is visible. The altitude of the bow will depend upon that of the sun. The higher the sun is, the lower the arc, until, at an altitude of 42 30', it becomes invisible, or sinks below the horizon. Secondary Boiv. In addition to this the primary bow, there is generally a second arc, somewhat larger, called the Secondary Bow, because it was at one time supposed to be produced from the first ; but it is due to the same laws of refraction and reflec- tion as the primary bow, and independent of it. There is, how- ever, this difference ; the rays which form this second arc are not only twice refracted, but twice reflected, and, on this account, the order of the colors will be exactly reversed, and the arc will be situated exterior to the primary bow. Where will the red light be situated ? What will be the breadth of the bow, and why ? Upon what will the position and altitude of the arc de- pend ? Describe the secondary bow. 368 NATURAL PHILOSOPHY. Fig. 325. To illustrate this, let a ray of light proceed from S, Figure 325, and fall upon a drop of water, it will be reflect- ed at I', and again at I" ; and, after two refractions, as in the primary bow, will meet the eye if it be properly situa- s ted. In this case the incident and emergent rays cross each other, and it is found that those emergent rays which make an angle with the former of about 50 will impress the eye with the sensa- tion of a colored image or bow. The red rays will be on the in- ner portions of the bow, making an angle of 50, while the violet will be on the exterior portion, making an angle of 53 30'. The breadth of the bow will, therefore, be 3 30', or 1 30' broader than the primary bow, but somewhat paler, because some rays are lost at each reflection within the drop. Similar bows are often produced by the light of the sun re- flected from the moon, called Lunar Bows, but they are very pale and indistinct. 2. Astronomical Refraction. Rays of light passing obliquely through the atmosphere are more or less bent from a direct course, by refraction, toward a perpendicular to the surface ; and hence the heavenly bodies seen in any other position than in the zenith are slightly elevated. To make this evident, let R, Fig. 326, be a star, S O S the surface of the earth, and a a, b b, c c, successive strata of air of different densi- ty. As the ray from R falls upon the stratum c c, in the direction R E, it is bent out of its course, and still farther deflected by the other strata, until it meets the surface of the earth at O. Now, as all objects are seen in the direction in which the light meets the eye, R will appear elevated to r. On this account the sun's rays are so refracted that we see his How do its size and position compare with the primary bow ? What are lunar bows 1 What is astronomical refraction ? Illustrate. z / ~~7~ 1^' **- IE O " TWILIGHT HALOS. 369 whole disc before he is above the horizon, and also after he is below the horizon when he sets. On this account, also, the day in the polar regions is nearly a month longer than it would other- wise be. The nearer the luminous body is to the horizon, the greater will be its elevation, because the rays traverse a denser medium. This is the reason that the sun and moon, when in the horizon, present an oval figure, the rays from the lower parts of their discs being more refracted than those from the upper parts. 3. Twilight. It is evident that some rays of light thus bent out of their course will reach the earth where the sun is below the horizon ; but, in addition to this, the atmosphere, with its watery vapor, not only refracts, but reflects the light more or less, and by this means gives rise to twilight. The degree of light will depend upon the distance of the sun below the hori- zon. The light gradually diminishes till the sun is 18 below the horizon, when it entirely ceases. This is the reason that twilight is enjoyed in the northern regions for months ; the sun, owing to the obliquity of his path to the horizon, is for a long time less than 18 degrees below it. 4. Halos. Parhelia . We often observe, when the sky is filled with watery vapor, just before a storm, colored rings encircling the sun and moon, which are called halos. These are pro- duced by the light falling upon the vapor or hollow vesicles of water, and are accounted for by the interference of the rays of light, which will be explained in a future section. There are also two other colored circles, often connected with bright spots or streaks of light, called parhelia, both of which have been ex- plained by supposing that small drops of water are formed into ice prisms, that partially decompose the light. 5. Color of the Sky. The blue color of the sky may be ex- plained on the principle that the blue rays of light only are re- flected to the eye by the particles of the atmosphere. Were no What effect has astronomical refraction upon the length of the day? How is twilight produced, and how does it vary in length? What are halos, and how are they explained ? How is the color of the sky account- ed for-? 370 NATURAL PHILOSOPHY. rays reflected by the atmosphere, the color of the sky would be perfectly black. The color differs at different times and places, and 'this is due to the condition of the atmosphere, the presence of vapor, or clouds. The gorgeous colors often witnessed in the evening and morn- ing sky are explained by the fact that the clouds transmit or re- flect only red and yellow rays. The evening sky is more brilliant than the morning, owing to the peculiar condition of the watery vapor, which at that period is on the point of condensation, while in the morning this vapor is condensed, and more rays are trans- mitted. This gives a grayish appearance to the sky ; but if the "morning is red," it shows that great quantities of vapor are in the air, and a storm is generally expected. 6. Mirage. In certain states of the atmosphere, when the lower strata are much rarefied by contact Fig. 327. with the heated earth, inverted images of Greets are often seen painted upon the face of the sky, near the horizon. Villages and vessels at sea are sometimes thus Tne appearance represented in Fig' 3Z7 was observed by Dr. Vince in 1789. The mast of a ship, A, was just visible at Ramsgate, and directly above it two im- ages of the same, B, C, one erect and the other inverted. This appears to be due to the extra- ordinary refraction and reflection 'of light, produced by strata of unequal density. A similar phenomenon may be witnessed by viewing a small object placed beyond a heated bar of iron. The glimmering which is seen in a hot day near the surface of the earth, and upon the surface of bright objects, is also due to hot and cool currents of air, which refra<$ and reflect the light as it passes through them. What is the cause of the brilliant colors of evening and morning ? What is mirage, and how is it explained ? VISION ITS CAUSE. 371 SECTION IV. OF THE EYE AND OPTICAL INSTRUMENTS. The sensation of light is due to the excitement of certain nerves which are spread over the interior coat of the eye, called the retina. Vision is the perception of an object by means of light. Eyes are of two kinds. I. Compound eyes, such as the eyes of most insects. II. Simple eyes, with convex lenses, as those of man and other vertebrate animals. III. Simple eyes have the power of perceiving near and dis- tant objects, there being certain limits beyond which objects be- come dim and invisible. IV. The impression made by light upon the organs of seme remains a short time after the object is removed. V. For the purpose of aiding the eye to perceive near and distant objects, or of presenting their magnified images, certain instruments have been invented, such as the camera obscura, the simple, compound, and solar microscopes, the magic lantern, and refracting and reflecting telescopes. 1 . THE sensation of light is produced by rays of light falling upon, and thereby setting in motion, certain delicate nerves, which are distributed over the interior coat of the eye, called the retina. The sensation of darkness is experienced when these nerves are at rest. There are, however, some other causes which produce this sensation, as a sudden blow, a rush of blood to the brain, an electrical discharge near the eye, &c. But there may be the sensation of light without vision. 2. By vision is meant the mind's perception of external objects through the medium of light. To produce vision, it is necessary that the object seen should be accurately depicted upon the retina. In order to this, a special apparatus is requisite, and this is found to be a strictly mechanical contrivance, founded upon principles already explained. In some animals this apparatus is wanting, and in such cases they may be able to distinguish light from darkness, but can have no perception of external objects. How is the sensation of light produced ? What is vision, and by what means is it produced ? 372 NATURAL PHILOSOPHY. 3. The apparatus by which the rays of light are made sub- servient to vision is very diverse among the different orders of animals ; but these differences may be reduced to two com- pound eyes, as those of most insects and crustaceans, and simple eyes ivith convex lenses. I. Compound Eyes. For our knowledge of the structure of this class of eyes, we are indebted to the investigations of Miiller. He has shown that such eyes consist of a great number of small cones, standing upon' the retina in such a way that only the light from external objects which is parallel with the axis of each cone can reach the retina, all the other rays, falling upon the inner sur- face of the eye, being absorbed by a dark-colored pigment which lines the sides of these cones. The distinctness of the image de- pends upon their number. The external membrane which covers them is divided into facettes, corresponding to the number of cones, which, in some cases, amount to 25,000. Spiders have eyes with convex lenses ; some insects have both kinds of eyes. II. Simple Eyes with Convex Lenses. Eyes of this kind be- long mostly to vertebrated animals. The images of .external ob- jects are formed on the retina of such eyes in precisely the same manner as they are formed by a double convex lens upon a screen. Thus, let a c, Fig. 328, be jFV-328. an object, and b b' b" the eye. The rays of light will pass into it at s s, and, after crossing ea,ch other, will be refracted by the lenses of the eye, and form an inverted image upon the inner membrane or retina, m n. The whole formation of the eye contributes to this effect. The outer coat of the eye, called the sclerotica, b b' b", is a strong membrane, covering the eye entirely, with the exception of a small round plate in front, bf, like the convex crystal of a watch, which is transparent, and called the cornea, and by which the rays of light begin to be refracted convergently on their en- trance into the eye. How many kinds of eyes are there, and what are they called ? Describe compound eyes. Where are such eyes found ? Describe simple eyes with convex lenses. DISTANCE OF DISTINCT VISION. 373 Immediately behind the cornea is the iris, which is a thin colored membrane stretched directly across the eye, having an aperture in its center, s s, called the pupil. Through this the rays are admitted to the crystalline lens, c c', which lies directly behind the iris, and by which they are converged still more. The space between this lens and the cornea is filled by a clear and somewhat saline fluid, called the aqueous humor ; and the whole space behind this lens is occupied by a transparent gelat- inous substance, called the vitreous humor, both of which exer- cise a converging refractive power upon light as it passes through them. Besides the outer or sclerotic coat there are two other mem- branes. The one next the sclerotica is called the choroid, and is covered on its inner surface with a black pigment, pigment- urn nigrum, for the purpose of absorbing any rays which might interfere with the distinctness of the image formed on the retina. The other membrane, lining the interior of the eye, d d', is the retina, upon which nerves, coming from the optic nerve o, are spread to receive the image m n, and convey the sensation fo the mind. That there is an exact inverted image of the object upon the retina may be proved by taking the eye of an ox, and, after re- moving the coats on the back of it, inserting it in an aperture of a window-shutter of a darkened room, when external objects will be seen by those in the room, perfectly painted upon the retina in the back part of the eye. The image will be more distinct if the eye of the white rabbit is employed, because it is destitute of pigment. III. Distance of distinct Vision. As the eye acts like a lens, when the object is near, the image is more distant than when the object is more remote. In order, therefore, for the eye to see objects distinctly at different distances, it must have the power of elongating or shortening the axis of the eye, or of making the lenses more or less convex. 1 . Olbers has shown that, if the curvature of the cornea were Mention the several parts of which the eye is composed, and the forma- tion of images within it. What is the distance of distinct vision? 374 NATURAL PHILOSOPHY. so altered that its radius should vary from '333 to '300 of an inch, the axis would be elongated about one line, and this would be sufficient to adapt the eye to distinct vision from four inches to infinity. Thus, at an infinite distance, the image is -8997 of an inch from the cornea. 2. The reason that objects at different distances are seen dis- tinctly may be explained by compression and change of position of the lens ; but neither explanation rests upon positive certainty as to the fact, and possibly both modes may be employed to pro- duce the effect. 3. There is a limit to distinct vision, which varies slightly in different eyes. The eye is capable of accommodating itself to the distance of an object, until it is within 8 or 10 inches ; and then, if brought nearer, the eye is obliged to make an effort to see it, and as it is brought nearer and nearer, it grows more and more dim until it becomes invisible. We involuntarily hold an object at the distance of distinct vision. If this distance is more than 8 inches, we are said to be long-sighted, if less, short-sighted. 4. When the object is too near, indistinct vision is produced, because the rays from it fall so diverging upon the eye that they can not be converged to a focus by the time they reach the retina, but fall upon it in a circle, the point where they would be brought to a focus being just behind the retina. Thus, If through two minute orifices in a card, we look at a pin head, held very near the eye, we shall see two distinct images of it, be- cause the pencil of rays which would be dispersed in a circle upon the retina is intercepted by the card, and only a few rays reach the retina at two points of this circle. But if the pin be removed to the distance of distinct vision, these two images will be merged into one. By means of this experiment, instruments are con- structed called opt&nieters, which enable us to define the distance of distinct vision. 5. In short-sightedness the eye is too convex, and the rays are brought to a focus too soon. In order to remedy this defect, con- Why do very near objects appear indistinct? By what means can the eye accommodate itself to objects at different distances ? How is short- sightedness remedied ? SHORT-SIGHTEDNESS AND LONG-SIGHTEDNESS. 375 cave glasses are used, which tend to separate the rays, so that by falling more divergent they are not brought to a focus before they reach the retina. Short-sightedness is often produced by habitually holding the object too near the eye. It generally occurs in early life, and ceases as the eye is flattened by advancing age. 6. In long-sightedness the eye is too flat, and the rays are not brought to a focus soon enough. To remedy this, convex glasses are worn, which render the rays so converging that they may be brought to a focus on the retina. Aged people become long-sight- ed in consequence of the flattening of their eyes, and are obliged to resort to convex glasses in order to see distinctly. 7. There is another limit of distinct vision depending upon the angle which the object subtends to the eye. When an ob- ject is situated at such a distance that the rays coming from its two extremities make an angle of 2", it can be distinctly seen, but if it be less, it is invisible. All objects, therefore, become in- visible if they are removed to a sufficient distance ; hence the apparent size of objects will depend upon the angle at which they are seen. Fig. 329. To illustrate this, let A C B, Fig. 329, be the angle under which the arrows i k, &c., are seen ; then the arrow i k will appear just as large as g h, ef t or those at the distance A B. B It is on this principle that convex lenses magnify objects, because they increase the angle under which they are seen. 8. The images of all objects are inverted on the retina, be- cause rays from the top of the object enter the pupil descending, and, continuing the same course, fall upon the lower part of the retina, and there form their image, while those from the bottom enter the pupil ascending, and, continuing their course afterward in the same direction, form their image on the upper part of the How is long-sightedness remedied ? What limit to distinct vision ? What influence has the angle of vision upon the size of objects ? Why are images of objects inverted ? 376 NATURAL PHILOSOPHY. retina. Why the object is seen erect, since its image id inverted, is not easily explained. It is supposed, however, that the image does not exist as a sensation, but that the mind projects it, as it were, in the direction in which the rays come to the eye. 9. It may be asked why, since the image of an object is formed on the retina of each eye, we do not see objects double. This question has been variously answered. It is supposed to be owing to the fact that the two images fall upon corresponding parts of the retina, and hence vision is single. If this relation is disturbed, as it may be by turning the eyes inward, two im- ages will be formed, or vision will be double. IV. Duration of the Impressions of Light. The sensation of light does not instantly cease when the object which produces it is removed. If a flaming torch be whirled rapidly around, we see a circle of light. In the rapid revolution of a wheel we are not able to distinguish the spokes, because the impression made by one remains till the next one arrives at the same place, and thus the impression of a solid wheel is given. If upon a green card an animal, or any figure, is painted in red, and the card is then moved quickly back and forth before the eye, the impression of the red color will remain upon the eye, and the animal will appear to move upon the green ground. There are many very amusing experiments in which figures of animals painted with different colors are made to perform vari- ous evolutions, all depending upon the duration of the impression of light. V. Optical Instruments. For the purpose of obtaining mag- nified images of objects near or remote, certain instruments have been invented which have greatly enlarged our ideas of the per- fection and greatness, as well as of the minuteness of the works of God. 1. The Camera Obscura. If an aperture is made in a win- dow-shutter, and the light from any external object, as an animal or a tree, Fig. 330, is admitted into a darkened room, an invert- Why do the images appear erect? Why are not objects seen double ? Does the impression of light remain airy time upon the retina ? How is this proved ? What is the object of optical instruments ? Describe the camera. OPTICAL INSTRUMENTS. Fig. 330. 377 ed image of the object will be painted upon the opposite wall. Such a room is a camera obscura. The manner in which this effect is produced was noticed on page 330. The rays of light from the bottom of the object pass through the aperture and form an image near the top of the room, while those from the top pass to the bottom of the room, the rays crossing each other in the aperture. The camera, as usually constructed, consists of a box, M N, Fig. 331, with a pro- jecting tube, d, containing a double convex lens, for the purpose of converging the rays and more highly illumin- ating the image, and a screen of ground glass, placed either on the back of the box where the image will be inverted, or upon the top, as a b, or bottom, upon which the image is thrown by means of a mirror, m, placed at an angle of 45, in which case the image will be in its natural position. The form of this instrument may vary to suit the manner of using it. If the object is to trace the picture, it is often thrown, by a mirror, upon a sheet of paper in the bottom of the box, and there traced with a pencil. Natural scenery may thus be ac- curately represented and delineated upon paper, or indelibly fix- ed on metallic plates, as in the Daguerreotype. 2. The Simple Microscope. This consists simply of a double convex lens, and when an object is placed a little nearer than the focal distance, and viewed through the lens, it appears magnified. Describe the simple microscope. 378 NATUfcAL PHILOSOPHY. Fig. 332. Let the object, c b, Fig. 332, c be placed on one side of a double convex lens, and be viewed by an eye, a, on the other side. The ray from c will be refracted, and will enter the eye as if it came from C ; and as the object is seen in the direction of the refracted ray, it will appear much larger than it really is. To estimate the power of such a lens of enlarging the dimen- sions of an object, we must take into consideration the following principle, alluded to above, that the apparent magnitude of an object depends upon the angle at which it is vieived; and the nearer it is, the greater is its apparent magnitude. Thus, if the focal length of the glass in this case is half an inch, and the ob- ject is seen distinctly, that may be considered the distance of the object from the eye. By comparing this with the distance of distinct vision, 8 inches, it will appear as much enlarged in any one direction as the distance of distinct vision is greater than the focal distance of the lens. The magnifying power of any lens may therefore be ascertained by dividing the distance of distinct vision, 8 or 10 inches, by the focal distance of tKe lens, in this case half an inch, which will increase each dimension twenty times. But this is not strictly true, for the object is not exactly in the focus, and the magnifying power is a little greater than this ratio would make it. It will be seen that the shorter the focal distance of the lens, the greater is its magnifying power. 3. The Compound Microscope. In this microscope there are two, and sometimes three, lenses. One forms the object-glass, as A B, Fig. 333, and one the 1^.333. eye-glass, as C D. When there is a third, as E F, the middle one is called ihejield- glass, because it enlarges the field of vision, by collecting the rays that otherwise would not fall upon C D. The ob- Why does the simple microscope magnify objects ? How is the magni- fying power of the microscope estimated ? Describe the compound micro- scope, and mention its uses. SOLAR MICROSCOPE. 379 ject is placed a little beyond the focus of the object-glass, by which an inverted image is formed near the focus of the eye-glass, which farther magnifies this image. Fig. 334. As the microscope is essentially composed of two glasses, its magnifying power is the product of the magnifying power of each of the glasses. Thus, if the object-glass magnify 10 times, and the eye-glass 20, then the diameter of the object will be in- creased 200 times, and its surface 40,000 times. It is evident that light will be de- composed by such instruments, and they therefore should be made achromatic. The annexed diagram, Fig. 334, rep- resents the compound microscope. The glasses are placed in the tube, as A B, I K, m n ; the mirror, V, is attached to il- ^ luminate the object, and sometimes a eon- [_!/ <-JL_Ji s] vex lens to concentrate the light upon it. 4. Solaf Microscope. This beautiful instrument consists of two parts, one for illuminating the object, and the other for mag- nifying it. It consists of a mirror, M, Fig. 335, placed on the outside of Fig. 235. a window, so as to reflect the sun's rays into a tube, T, in the end of which there is fixed a large convex lens, R, which partial- ly converges the rays. At the other end of the tube is another convex lens, U S, by which the rays are brought to a focus. A large quantity of light being thus concentrated, the object to be magnified is placed near this focus, and beyond it there is placed the object-glass, which magnifies the object, and throws its im- age upon a white wall or canvas in a darkened room. Describe the solar microscope. Why does it give enlarged images of objects ? 380 NATURAL PHILOSOPHY. The magnifying power will depend upon the focal distance of the lens, as in the simple microscope. The farther the screen is removed, the larger the image becomes. The oxyhydrogen blowpipe Drummond Light is sometimes use'd for all these instruments, instead of the light of the sun. 5. Magic Lantern. This is similar to the solar microscope, but more simple. It consists of a metallic lamp, A, Fig. 336, Fig. 336. a reflector, p q, and two lenses ; the one, m, to illuminate the ob- ject, and the other, n, to magnify it. By this arrangement an inverted image of the object is thrown upon a screen. This is used to give a magnified representation of objects painted on glass. 6. Telescopes. Telescopes are similar in their construction to microscopes ; but their glasses are so arranged as to produce a magnified image of distant objects, while the microscope is used to enlarge those that are near. Telescopes are of two kinds, refracting and reflecting. Of the refracting telescopes there are three principal varieties Galileo's, the astronomical, and the terrestrial. (1.) Galileo's Telescope. This consists of an object-glass, L N, Fig. 337, and an eye-glass, E E, which is a double concave lens, Fig. 337. B placed a little nearer than the focus of the object-glass. If, then, the lens L N would bring the rays from the object O B to a focus at M I, this lens will cause them to diverge so as give an erect image, i m. Opera-glasses are constructed in this way, be- cause it is desirable to have an erect image of the object. Describe the magic lantern. Of how many kinds are telescopes? REFRACTING TELESCOPES. 381 (2.) The Astronomical Telescope. In this telescope the eye- glass is a double convex lens, of small focal distance, as o, Fig. 338, for the purpose of viewing the image at c, which is made Fig. 338. A E by the object-glass, L. It is similar to the compound microscope. The image is inverted, and the power of the glass is found by di- viding the focal distance of the object-glass by that of the eye- glass. (3.) The Terrestrial Telescope. This is like the preceding, with two additional glasses, for the purpose of inverting the image so that objects may appear in an erect position. Fig- 339 Fig. 339. represents the arrangement in the land telescope or spy-glass. It will be seen that the two additional glasses, E E, F F, have the effect to invert the image formed by the object-glass, L N. These glasses are usually put into a little tube which is made to slide into that containing the object-glass, and the glasses are thereby adjusted to the object. It has been noticed, page 356, that convex lenses do not con- verge all the rays of a pencil which passes through them to the same focal point, and hence there is produced an indistinctness in the image formed. The greater the thickness and diameter of the lens, the greater the spherical aberration. The greatest aberration in a plano-convex lens is 4^- times its thickness. If, however, the light fall upon the convex surface, the least aberration is l T y th of its thickness. The aherration in a double convex lens of equal curvatures is of its thickness. If the convexities have radii which Describe the astronomical telescope. How does the terrestrial tele- scope differ from the astronomical ? What is the greatest aud least spheric- al aberration in a plano-convex lens ? What in a double convex lens ? 382 NATURAL PHILOSOPHY. are to each other as 1 to 6, and parallel rays of light fall upon the face whose radius is 1, the aberration is only l T ^th of its thickness, and this is the least to which the aberration can be reduced by a single glass, the case being excepted where the convex surface is ellipsoidal, a form somewhat difficult to give to lenses. As the lens is thinner, the aberration will be less ; and hence the object-glasses of large telescopes are thin lenses with long focal distances. In some cases they are composed of two glasses, so that the aberrations may counteract each other. In the eye- glasses, in consequence of their greater curvature, it is more dif- ficult to obviate their spherical aberration. By using very dense glass, or precious stones whose refracting index is very high, as the diamond, they may be made much flatter, and in this was the difficulty is in a great measure remedied. Opticians often correct this defect by grinding the surfaces and subjecting them to repeated trials, until, by actual experiment, the lenses are found to give distinct images. They also sometimes take a correct lens and make a mold of it, in order to obtain the same curva- tures. (4:.) Reflecting Telescopes. In reflecting telescopes the image of a distant object is formed by means of a concave mirror, arid viewed by a convex lens. The forms vary slightly, and have been named after their inventors. Newton's is represented in Fig. 340. A B is a concave mirror, placed in one end of a Fig. 340. A. T,! 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