CORNELL UNIVERSITY LIBRARY corneri university Library arV17815 A text-book on natural philosophy 3 1924 031 281 938 olin.anx Cornell University Library The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031281938 BY THE SAMI AUTHOR, % ®£jet-book on Cl)emt0tr|), FOR THE USE OF SCEOOLS AND COIIEGES. WITH NEARLY 300 ILinSTEATIONS. 12mo, SHEEP. PRICE 75 CENT, TEXT-BOOK NATUEAL PHILOSOPHY FOK THE USE OF SCHOOLS AND COLLEGES. CONTAINING THK MOST RECENT DISCOVERIES AND FACTS CO* PILED FROM THE BEST AUTHORITIES. ' BY JOHN WILLIAM DRAPER, M.D., TBOrSeSOR of CBBMISTSY in the CNIVEBSnT OF NKW TOBE, AND FOSMXIII.T rKOFESSOK OF ITATCSAL FHILOSOFHT AND CHEUIIITIIT IN HAUF- DBN SZONE7 COLLEGE, VIRGINIA. tXSl^ mavis Jfmiv f^uvcaria Sllustvattons. THIED EDITION. NEW YORK: HARPER &. BROTHERS, PUBLISHERS, 339 &. 331 PEARL STREET, FEANELIN SQUARE. Kntered, according to Act of Congress, in the year one thctsand eight hundred and forty-seven, by Harper & Brothers, ■D the Clerk's Office of the District Court of the Southern Distriu of New York. fRETACE. The success which has attended the publication of my " Text-Book on Chemistry," four large editions of it having been called for in less than a year, has induced me to publish, in a similar manner, the Lectures I for- merly gave on Natural Philosophy when professor of that science. It will be perceived that I have made what may appear an innovation in the arrangement of the subject ; and, instead of commencing in the usual manner with Me- chanics, the Laws of Motion, &c., I have taught the physical properties of Air and Water first. This plan was followed by many of the most eminent writers of the last century ; and it is my opinion, after an extensive experience in public teaching, that it is far better than the method ordinarily pursued. The main object of a teacher should be to communi- cate a clear and general view of the great features of his science, and to do this in an agreeable and short manner. Tt is too often forgotten that the beginner knows nothing ; and the first thing to be done is to awaken in him an interest in the study, and to present to him a view of the scientific relations of those natural objects with which he is most familiar. When his curiosity is aroused, he will readily go through things that are abstract and forbidding ; IV PREFACE. which, had they bean presented at first, would have dis- couraged or perhaps disgusted him. I am persuaded that the superficial knowledge of the physical sciences which so extensively prevails is, in the main, due to the course commonly pursued by teachers. The theory of Forces and of Equilibrium, the laws and phenomena of Motion, are not things likely to allure a beginner; but there is no one so dull as to fail being interested with the wonderful effects of the weight, the pressure, or the elasticity of the air. It may be more consistent with a rigorous course to present the sterner features of science first ; but the object of instruction ib more certainly attained by offering the agreeable. But though this work is essentially a text-book upon my Lectures, I have incorporated in it, from the most recent authors, whatever improvements have of late been intro- duced in the different branches of Natural Philosophy, either as respects new methods of presenting facts or the arrangement of new discoveries. In this sense, this work is to be regarded as a compilation from the best authori- ties adapted to the uses of schools and colleges. Disclaiming, therefore, any pretensions to originality, except where directly specified in the body of the work, I ought more particularly to refer to the treatises of Lame and Peschel as the authorities I have chiefly fol- lowed in Natural Philosophy ; to Arago, Herschel, and Dick in Astronomy. To the treatises of M. Peschel and the astronomical works of Dr. Dick I am also indebted for many very excellent illustrations. Those subjects, such as Caloric, which belong partly to Chemistry and partly to Natural Philosophy, and which, therefore, have been introduced in my text-book on the former subject, I have endeavored to present here in a different way, that those who use both works may have the advantage of seeing the same subject from dif- PREPAOE. ▼ ferent points of view. The laws of Undulations, now beginning to be recognized as an essential portion of this department of science, I have introduced as an abstract of what has been written on this subject by Peschel and Eisenlohr. It will, therefore, be seen that the plan of this work is essentially the same as that of the Text-Book on Chem- istry. It gives an abstract of the leading points of each lecture — ^three or four pages containing the matter gone over in the class-room in the course of an hour. The lengthened explanations and demonstrations which must always be supplied by the teacher himself are, therefore, except in the more difficult cases, here omitted. The object marked out has been to present to the student a clear view of the great facts of physical science, and avoid perplexing his mind with a multiplicity of details. There are two different methods in which Natural Philosophy is now taught : — Ist, as an experimental science ; 2d, as a branch of mathematics. Each has its own peculiar advantages, and the public teacher will follow the one or the other according as it is his aim to store the mind of his pupil with a knowledge of the great fiicts of nature, or only to give it that drilling which arises from geometrical pursuits. From an extensive compari- son of the advantages of these systems, I believe that the proper course is to teach physical science experi- mentally first — a conviction not only arising from consid- erations respecting the constitution of the human mind, the amount of mathematical knowledge which students commonly possess, but also from the history of these sciences. Why is it that the most acute mathematicians and metaphysicians the world has ever produced for two thousand years made so little advance in knowledge, and why have the last two centuries produced such a won- derful revolution in human affairs 1 It is from the lesson VI PREFACE. first taught by Lord Bacon, that, so^^iable to fallacy are the operations of the intellect, experiment must always be the great engine of human discovery, and, therefore, of human advancement. To teachers of Natural Philosophy I offer this book as a practical work, intended for the daily use of the class- room, and, therefore, so divided and arranged as to en- able the pupil to pass through the subjects treated of in the time usually devoted to these purposes. A great number of wood cuts have been introduced, with a view of supplying, in some measure, the want of apparatus or other means of illustration. The questions at the foot of each page point out to the beginner the leading facts before him. John William Draper. University, New York, July IG, 1847. CONTENTS. Ltctnra r^l I. Properties of Matter ,1 II. Properties of Matter and Physical Forces . . 4 in. Natural Pliilosopby — Pneumatics 11 IV, Weight and Pressure of the Air ... .17 V. Pressure of the Air 22 YI. Pressure and Elasticity of the Air . . .26 VIl. Properties of Air 31 VIII. Properties of Air (continued) 36^ IX. Hydrostatics — Properties of Liquids .... 41 X. The Pressures of Liquids 45 XI. Specific Gravity 60 XII. Hydrostatic Pressure 55 XIII. Flowing Liquids and Hydraulic Machines ... 60 XIV. Theory of Flotation 65 XV. Mechanics — Motion and Rest 69[ XVI. Composition and Resolution of Forces . . . 72 XVII. Inertia 77 XVm. Gravitation 81 XIX. Descent of Falling Bodies ^ 85 XX. Motion on Inclined Planes — Projectiles ... 90 XXI. Motion round a Center 94 XXII. Adhesion and Capillary Attraction .... 101 XXin. Properties of Solids 107 XXIV. Center of Gravity 110 XXV. The Pendulum 116 XXVI. Percussion 121 XXVII. The Mechanical Powers — ^the Lever .... 126 XXVin. The Pulley— the VPheel and Axle .... 131 XXIX. The Inclined Plane— VV'edge— Screw . . . .137 XXX. Passive or Resisting Forces ^X- XXXL Undulatory Motions • . Ifl" XXXII. Undulatory Motions (conlinutd) ISS XXXIII. Acoustics — Production of Sound 157 XXXIV. Phenomena of Sound 161 XXXV. Optics — ^Properties of Ught 169 XXXVI. Measures of the Intensity and Velocity of Light . 172 XXXVII. Reflexion of Light 178 XXXVUL Refraction of Light 184 Vlll COVTENTS. Lecture , Page, XXXIX. Action of Lenses 190 XL. Colored Light 195 XLL Colored Light {cmtinued) 200 XLIL Undulatory Theory of Light 205 XLIIL Polarized Light 210 XLIV. Double Refraction 215 XLV. Natural Optical Phenomena 221 ' XLVI. The Organ of Vision 227 XLVII. Optical Instruments— Microscopes 232 XLVIII. Telescopes 238 XLIX. Thermotics — the Properties of Heat .... 244 L. Radiant Heat 249 LI. Conduction and Expansion 253 LII. Capacity for Heat and Latent Heat .... 258 LIII. Evaporation and Boiling 262 LI7. The Steam Engine 267 LV. Hygrometry 272 LVL Magnetism 278 LVII. Terrestrial Magnetism 283 LVIII. Electricity 288 LIX. Induction and Distribution of Electricity .... 293 LX. The Voltaic Battery 298 LXI. Electro-magnetism 304 LXII. Magneto-electricity — Thermo-electricity , . . 309 LXIII. Astronomy 315 LXIV. Translation of the Earth round the Sun ... 321 LXV. The Solar System 328 LXVI. The Solar System (continued) ... . 334 LXVIL The Secondary Planets 340 LXVIII. The Fized Stars .346 LXIX. Causes of the Phenomena of the Sc lar System . . 353 LXX. TheTides ....'... .358 LXXL Figure and Motion of the Earth 363 LXXII. Of Perturbations .369 LXXIII. The Measurement of Tune . .... 373 INTRODUCTION. CONSTITUTION OP MATTER. LECTURE I. pROPERTiias OF Matter. — TJie Three Forms of Mat- ter. — Vapors. — The distinctive, essential, and accessory properties. — Extension. — Impenetrahility. — Unchangea- bility. — Illustrations of Extension. — Methods of measur- ing small spaces. — The Spherometer. — Illustration of Impenetrability. — The Diving-Bell. Material substances present themselves to us under three different conditions. Some have their parts so strongly attached to each other that they resist the intru- sion of external bodies, and can retain any shape that may be given them. These constitute the group of Sol IDS. A second c]ass yields readily to pressure or move- ment, their particles easily sliding over one another ; and from this extreme mobility they are unable of themselves to assume determinate forms, but always copy the shape of the receptacles or vessels in which they are placed — they are Liquids. A third, yielding even more easily than the foregoing, thin and aerial in their character, and marked by the facility with which they may be compress- ed into smaller or dilated into larger dimensions, give us a group designated as Gases. Metals may be taken as examples of the first ; water as the type of the second ; and atmospheric air of the third of these states or condi- tions, which are called " the three forms of bodies." In some instances the same substance can exhibit all three of these forms. Thus, when liquid water is cooled Under how many states do material substances occur? What are ■olids? 'What are liquids? What are gases? Give examples of each. Wliat is the technical designation given to these states ? Give an exam pie of a substance that can assume all tlL'jee forms. A 2 DISTINCTIVE PROPERTIES. to a certain degree, it takes on the solid condition, as i< or snow ; and when its temperature is sufficiently raised, it assumes the gaseous state, and is then known as steam. Writers on Natural Philosophy have found it convenient, for many reasons, to introduce the term Vapors, meaning by that a gas placed under such circumstances that it is ready to assume the liquid state. As the steam of water conforms to this condition, it is therefore regarded as a vapor. Under whichever of these forms material substances are presented, they exhibit certain properties: these are, first. Distinctive ; second, Essential ; third. Accessory. There is a certain bright white metal passing under the name of Potassium, the distinctive character of which is, Fig. 1. that, when thrown on the surface of water, it gives rise to a violent reaction, a beautiful violet-colored flame being evolved. A piece of lead, which, to external appearance, is not unlike the potassium when brought in contact with water, exhibits no such phe- nomenon, but, as every one knows, remains quietly, neither disturbing the water nor being acted upon by it. Such distinctive qualities are the objects of a Chemist's studies. It belongs to his science to show how some gases are colored and others colorless ; some supporters of com- bustion, while others extinguish burning bodies ; how some liquids can be decomposed by Voltaic batteries and some by exposure to a red heat. The general doctrines of af- finity, the modes in which bodies combine, and the char- acters of the products to which they give rise — all these oelong to Chemistry. But beyond these distinctive qualities of bodies, there are, as has been observed, certain other properties which are uniformly met with in all bodies whatever, and hence are spoken of as essential. They are. Extension. " Impenetrability. Unchangeability. By EXTENSION we mean that all sul)stances, whatevei Into what classes may the properties of bodies be divided ? Give an ex ample of distinctive properties. What is the object of the science of Chemistry? What are the essential properties of bodies? What if meant by extension 7 What by impenetrability? ESSENTIAL FSOFERTIES. their volume or figure may be, occupy a determinate por- tion of apace. We measure them by three dimensions — length, breadth, and thickness. Impenetrability points out the fact that two bodies cannot occupy the same space at the same time. If anai! is driven into wood, it enters only by separating the woody particles from each other ; if it be dropped into water, it ' does not penetrate, but displaces the watery particles : and even in the case of aerial bodies, through which masses can move with apparently little Fig. 2. "■esistance, the same observation holds good. Thus, if we take a wide-mouthed bottle, a, Fig. 2, and insert through its cork a funnel, b, with a narrow neck, and also a bent tube, c, which dips into a glass of water, d, on pouring any liquid into ' the funnel, so that it may fall drop by drop into the bottle, Ve shall find, as this takes place, that air passes out, bubble after bubble, through the water in d. The air is, therefore, not penetrated by the water, but displaced. The same fact may also be proved by taking a cupping-glass, a. Fig. 3, and im- mersing it, mouth downward, in a glass of water, b. If the aperture, c, of the cup- ping-glass be left open the air will rush out through it, and the water flow in below : but if it be closed by the finger, as the air can now no longer escape, the water is un- able to enter and occupy its place. Similar experiments establish the impenetrability ol liquids by solids. If in a glass of water, Fig. 4, ng. i. a leaden bullet is immersed, it will be seen that as the bullet is introduced the water rises to a higher level, showing, therefore, that a liquid can no more be penetrated by a solid than, as was seen in the former experiment, can a gas by a liquid. Two bodies cannot occupy the same space at the same time. The third essential property of matter is its unchange- Give an illustration that air is not penetrable by water. Give an illus- tration of the displacement of air by water. What is meant by ucchange- ability as a property of bodies 7 4 UNCHANGEABlIilTY OP MATTKB. ABILITY. This property may be looked upon as the foun- dation of Chemistry ; and though there are many phenom- ena which we constantly witness which seem to contradict it, they form, when properly considered, striking illustra- tions of the great tr'dth that material substances can nei- ther be created nor destroyed, and that the distinctive qualities which appertain to them remain forever un- changed. The disappearance of oil in the combustion of lamps, the burning away of coal, the evaporation of wa- ter, when minutely examined, far from proving the per- bhability of matter, afford the most striking evidence of its duration. Nor is a solitary fact known in the whole range of Chemistry,, Natural Philosophy, or Physiology, which lends the remotest countenance to the opinion that, either by the slow lapse of time or by any artificial pro- cesses whatever, can matter be created, changed, or de- stroyed. Even the bodies of men and animals, the struct- ures of plants, and all other objects in the fyorld of organ- ization, which seem characterized by the facility with which they undergo unceasing and eventually total change, are no exception to the truth of this observation. The bodies which we possess to-day are made up of particles \vhich have formed the bodies of other animals in former times, and which will again discharge the same duty for races that will hereafter come into existence. As illustrations connected with the extension and im- penetrability of matter, I may give the following in- stances : We are frequently required to measure the dimensions of bodies ; that is, to determine their length, breadth, or thickness. It is a much more difficult thing to do this ac- curatelythan is commonly supposed. It requires an artist of the highest skill to make a measure which is a foot or a yard in length, or which shall contain precisely a pint or a gallon. With a view of facilitating the measurement of bodies, a great many contrivances have been invented, such as verniers, spherometers, and screw machines of different kinds. The spherometer, which is a beautiful contrivance for measuring the thickness of bodies, is constructed as fol- ia there any reason to believe that new material particles can be ere ■ted by artificial processes, or old ones destroyed 1 THE SPHESOMETER. O lows : It has three horizontal steel branches, a, b, c, Fig. 5, which form with each other ^g 5. angles of 120 degrees. Prom the extremities of these branches there proceed three delicate steel feet, d, e,f, and through the cen- ter, where the branches unite, a screw, g, the thread of which is cut with great precision, and which terminates in a pointed foot, i, passes. The head of this screw carries a divided circle, m. Now, suppose the instrument is \ placed on a piece of flat glass, it will be supported on its three feet, which, are all in the same plane; but if in turning the screw we depress its point, i, beneath the plane of its feet, it can no longer stand with stability on the glass, but tot ters when it is touched, and emits a rattling sound. By altering the screw, therefore, we can give it such a posi- tion that both by the finger and the ear we discover that its point is level with the points d, e,f. Now let the ob- ject, the thickness of which is to be measured, be placed on the glass, and the screw turned until the instrument stands without tottering, it is obvious that its point must have been lifted through a distance precisely equal to the thickness of the object to be measured, and the movement of the head of the screw read off upon the scale, n, against which it works, indicates what that thick- ness is. This instrument, therefore, serves to show that in the measurement of small spaces, the senses of touch and hearing may often be resorted to with more effect than the eye. The spherometer is here introduced in connec- tion with these general considerations respecting the ex- tension of matter, as affording the student an illustration of the delicate methods we possess of determining the mi- nutest dimensions of bodies. As an illustration of the impenetrability of matter, the machine which passes under the name of the diving-bell Describe the spherometer. What is its use ? By what senses may we often form a better estimate of small spaces than by the eye ? D ACCESSORY PROPERTIES. may ^e mentioned. It consists of a vessel, a, a. Fig. 6, Fig. 6. of any suitable shape, and heavy enough to sink in vi^ater when plunged with its mouth downward. Owing to the impen- etrability of the air the water is excluded from the interior, or only finds access to such an e^ftent as corresponds to the press- ure of the depth to which it is sunk. Light is admitted to the bell through thick pieces of glass in its top, and a constant stream of fresh air thrown, into it from a tube, b, and forcing-pump above, the at- mosphere in the inside being suffered to escape through a stop-cock as it becomes vitiated by the respiration of the workmen. Diving-bells are extensively resorted to in submarine architecture, and for the recovery of treas- ure lost in the sea. LECTURE II. Properties of Matter. — The Accessory Properties oj Waiter. — Compressibility. — Expansihility. — Elasticity — Limit of Elasticity. — Illustrations of Divisibility. — Porosity und interstitial spaces. — Weight. Physical Forces. — Attractive and Repulsive Forces. — Molecular Attraction. — Gravitation. — Cohesion. — Con- stitution of Matter. Having disposed of the essential, we pass next to a con- sideration of the accessory properties of matter. They are. Compressibility. Expansibility. Elasticity. Divisibility. Porosity. Weight. That substances of all the three forms are compressi- ble is capable of easy proof. In the process of coining, pieces of metal are exposed to powerful pressure between the steel dies, so that they become much denser than be- Describe the diving-bell. On what principle does it act T Why must the air in its interior be renewed from time to time ? What are the acce» oiy properties of matter? EXPANSIBILITY AND ELASTICITY. 7 fore. By inclosing water or any other liquid in a strong vessel, and causing a piston, driven by a screw, to act upon it, it may be reduced to a less space, and gaseous substances, such as atmospheric air when inclosed in an India-rubber bag, or even a bladder, may be compressed by the hands. Under the influence of heat all substances expand. This may be proved for such solids Fig. 7. as metals by the apparatus represent- ed in Fig. 7. It consists of a stout board, a b, on which are fastened two "" brass uprights, c, d, with notches cut in them so as to re- ceive the ends of a metallic bar, e. This bar is slightly shorter than the whole distance between the notches, so that when it is set in its place it can be moved backward and forward, and emits a rattling sound. But if boiling water be poured upon it, it expands and occupies the whole distance, and can no longer be moved. The ex- pansion of liquids is well shown in the case of common thermometers, which contain either quicksilver or spirits of wine — those substances occupying a greater volume as their temperature rises. The air thermometer proves the same thing for gases. By elasticity we mean that quality by which bodies, when their form has been changed, endeavor to recover their original shape. In this respect'there are great dif ferences. Steel, ivory, India-rubber are highly elastic, and lead, putty, clay less so. Perfectly elastic bodies re- sist the action of disturbing causes without any ulterior change: thus a quantity of atmospheric air, compressed into a copper globe, recovers its original volume as soon as the pressure is removed, though it may have been shut up for years. By the limit of elasticity we mean the smallest force which is required to produce a permanent disturbance in the structure of an imperfectly elastic body. No solid is perfectly elastic. An iron wire, drawn a little aside, recovers its original straightness ; but if more violently bent, it takes a permanent set, because its. limit of elasticity is overpassed. The elasticity of a given Give; roofs that solids, liquids, and gases are all compressible. How can it be proved that solids, liquids, and gases are expansible ? What is meant by elasticity % Give examples of highly elastic and less elastir bodies What is meant by the limit of elasticity ? 8 DIVISIBILITY. substance can often be altered by mechanical processes, such as by hammering, or by heating and cooling, as in the process of tempering. The divisibility of matter may be proved in many ways. By various mechanical processes metals mayi^jften be re- duced to an extreme degree of tenuity : thus it is said that gold-leaf may be beaten out until it is only -g-^oVo t °^ an inch thick. By chemical experiments a grain of cop- per or of iron may be divided into many millions of parts. For certain purposes artists have ruled parallel lines upon glass, with a diamond point, so close to each other that ten thousand are contained in a single inch. The odors which are exhaled by strong-smelling perfumes, as musk, will for years together infect the air of a large room, and yet the loss of weight by the musk is imper ceptible. Again, there are animals whose bodies are so minute that they can only be seen by the aid of the mi- croscope. The siliceous shells of such infusorials occur in many parts of the earth as fossils. Ehrenberg has shown that Tripoli, a mineral used in the arts, is made up of these — a single cubic inch of it containing about forty-one thousand millions — that is, about fifty times as many individuals as there ai-e of human beings on the face of the globe. As substances of all kinds may be reduced to smaller dimensions, either by pressure or the influence of cold, and as it is impossible for two particles to occupy the same place at the same time, or even for one of them par- tially to encroach on the position occupied by the other, it necessarily follows that there must be pores or inter- stices even in the densest bodies. Thus quicksilver will readily soak into the pores of gold, and gases ooze through India-rubber. Writers on Natural Philosophy usually restrict the term " pore" to spaces which are visible to the eye, and designate those minute distances which sep- arate the ultimate particles of bodies by the term "inter- stices." All bodies have weight or gravity. It is this which How may the elasticity of a given substance be changed ? Give some illustrations of the great divisibilitjr of matter, derived from mechanical, chemical, physiological, and geological fads. How may it be proved that all bodies are porous ? What is meant By a " pore," and what by " inter- Bticos ?" FORCES OP ATTBACTION AND REPULSION. 9 causes them to fall, when unsupported, to the ground, or when supported, to exert pressure upon the supporting body. Nor is this property limited to terrestrial objects ; for in the same way that an apple tends to fall to the earth, so too does the moon ; and all the planets gravitate to- ward each other and toward the sun. It was the consid- eration of this principle that led M. Leverrier to the dis- covery of a nev? planet beyond Uranus — this latter star being evidently disturbed in its movements by the influ- ences of a more distant body hitherto unknown. Op Physical Forces. — AH changes taking place in the system of nature are due to the operation of forces. The attractive force of the earth causes bodies to fall, and a similar agency gives rise to the shrinking of substances — their parts coming closer together when they are expose <* to the action of cold. In like manner, when an ivorj ball is sufFeried to drop on a marble slab, its particles, which have been driven closer to one anotherby the force of the blow, instantly recover their original positions by repelling one another; that is to say, through the agency of a repulsive force. Of the nature of forces we know nothing. Their existence only is inferred from the effects they produce ; and according to the nature of those ef- fects, we divide them into Attractive and Repulsive FORCES — the former tending to bring bodies closer to- gether, the latter to remove them farther apart. It has been found convenient to divide attractive forces into three groups, according as the range of their action or the circumstances of their development differ. When the attractive influence extends only to a limited space, it is spoken of as molecular attraction ; but the attraction of gravitation is, felt throughout the regions of space. By cohesion is meant an attractive influence called into ex- istence when bodies are brought to touch one another. It is to be understood that these are only conventional dis- tinctions; and it is not improbable that all the phenomena of attraction are due to the agency of one common cause. Chemists have shown that, in all probability, material substances are constituted upon one common type. They What is meant by weight or gravity ? la it limited to terrestrial ob- jects X A/VTiat is meant by forces 1 How many varieties of them are there ! into what three groups are attractive forces divided ? What is the dis- tinction between them? A* 10 NATURE OP ATOMIC FOKCBS. are made up of minute, indivisible particles, called atoms, which are arranged at variable distances from each other. These distances are determined by the relative preva- lence of attractive and repulsive forces, resident in or among the particles themselves ; and so too is the form of the resulting mass. If the cohesive predominates over the repulsive force, a solid body is the result.; if the two are equal it is a liquid, and if the repulsive prevails it is a gas. There are many reasons which lead us to suppose that the repulsive force, which thus tends to keep the particles of matter asunder, is the agent otherwise known as heat. Whenever the temperature of a body rises it enlarges in volume, because its constituent particles move from each other, and on the temperature falling the reverse effect ensues. If, as many very eminent philosophers believe, heat and light are in reality the same agent, it follows, by a necessary consequence, as will be gathered from what we shall hereafter have to say on optics, that the atoms of bodies vibrate unceasingly, and that instead of there be- ing that perfect quiescence among them which a superfi- cial examination suggests, all material substances are the seat of oscillatory movements, many millions of which are executed in the space of a- single second of time ; the number increasing as the temperature rises, and- dimin- ishing as it falls. What is the true constitution of material substances ? What are the forces residing among the particles of bodies ? What are the conditions which determine Ihe solid, liquid, and gaseous forms ? What is probably the nature of the force of molecular repulsion? If light and heat are the name agent, what is the condition of the particles of bodies ? PNEUMATICS. 11 NATURAL PHILOSOPHY. PROPERTIES OF THE AIR. PNEUMATICS. LECTURE III. Vatural Philosophy. — Ohservationa on this branch of Science. Pneumatics. — General Relations of the Air. — Its connec- tion with Motion and Organization. — Limited Extent. — Constitution. — Compressibility. — Causes which Limit the Atmosphere. — Its Variable Densities. — Proportion- ality of its Elastic Force and Pressure. A VERY superficial knowledge of those parts of the world to which man has access readily leads to their class- ification under three separate heads — the air, the sea, and the solid earth. This was recognized in the infancy of science, for the four elements of antiquity were the di visions which we have mentioned, and fire. Natural Philosophy or Physical Science, which, in its extended acceptation, means the study of all the phe- nomena of the material world, may commence its inves ligations with any objects or any facts whatever. By pur- suing these, in their consequences and connections, all the discoveries which the human mind has made in this de- partment of knowledge might successively be brought forward. But when we are left to select at pleasure our point of commencement, it is best to follow the most nat- ural and obvious couise. All the advances made in our times by the most eminent philosophers, and our powers of appreciating and understanding them, depend on clear- ness of perception of the gi-eat fundamental facts of sci- ence — a perspicuity which can never arise from mere ab- stract reasonings or from the unaided operations of the What were the elementa of the ancients 1 What is Natural Philosophy t J 2 RELATIONS OP THE ATMOSPHERE. human intellect, but which is the natural consequence of a familiarity with absolute facts. These serve us as out points of departure, and in the more difficult regions of science they are our points of reference — often by their resemblances, and even by their differences, making plain what would otherwise be incomprehensible, and spread- ing a light over what would otherwise be obscure. In-ihe three divisions of material objects, which are so strikingly marked out for us by nature, we find traits that are eminently chai-acteristic. All our ideas of perma- nence and duration have a convenient representation in the solid crust of the earth, the mountains, and valleys, and shores of which retain their position and features un- altered for centuries together. But the air is the very type and emblem of variety, and the direct or indirect source of almost every motion we see. It scarce ever presents to us, twice in succession, the same appearance ; for the winds that are continually traversing it are, to a proverb, inconstant, and the clouds that float in it exhibit every possible color and shape. It is, in reality, the grand ori- gin or seat of all kinds of terrestrial motions. Storms in the sea are the consequences of storms in the air, and even the flowing of rivers is the result of changes that have transpired in the atmosphere. But the interest connected with it is far from ending here. The atmosphere is the birthplace of all those numberless tribes of creation which constitute the vege- table and animal world. It is of materials obtained frotn it that plants form their difierent structures, and, therefoj e, from it that all animals indirectly derive their food. It is the nourisher and supporter of life, and in those process- es of decay which are continually taking place during the existence of all animals, and which after death totally resolve their bodies into other forms, the air receives the products of those putrefactive changes, and stores them up for future use. And it is one of the most splendid discoveries of our times, that these veiy products which arise from the destruction of animals are those which are used to support the life and develop the parts of plants. They pass, therefore, in a continual circle, now belong- ing to the vegetable, and now to the animal world; What appears to be the leading characteristic of the atmosphere ? Whal are its relations to the organic world ? teXTENT OF THE ATMOSPHEBB. IS they come from the air, and to it they again are re- stored. It is not, therefore, the heautiful blue color whjch the air possesses, and which people commonly call the sky, or the points of light which seem to be in it at night, or" the moving clouds which overshadow it and give it such varied and fantastic appearances, or even those more im- posing relations which bring it in connection with the events of life and death, which alone invest it with a pe- culiar claim on the attention of the student. Connected as it is with the commonest every-day facts, it furnishes us with some of our most appropriate illustrations — those simple facts of reference of which I have already spoken, and to which we involuntarily turn when we come to in- vestigate the more difficult natural phenomena. Astronomical considerations show that the atmosphere does not extend to an indefinite region, but surrounds the earth on all sides to an altitude of about fifty miles. Com- pared with the mass of the earth its volume is quite insig- nificant ; for as it is nearly four thousand miles from the surface to the center of the earth, the whole depth of the atmosphere is only about one-eightieth part of that dis- tance. Upon a twelve-inch globe, if we were to^lace a representation of the atmosphere, it would have to be less than the tenth of an inch thick. Seen in small masses, atmospheric air is quite colorless and perfectly transparent. Compared with water and solid substances, it is very light. Its parts move among one another with the utmost facility. Chemists have proved that it is not, as the ancietits supposed, an ele- mentary body, but a mixture of many other substances. It is enough at present for us to know that its leading constituents are two gases, which exist in it in fixed quan- tities — they are oxygen and nitrogen — but other essential ingredients are present in a less proportion, such as car- bonic acid gas, and the vapor of water. Atmospheric air is taken by natural philosophers as the type of all gaseous bodies, because it possesses their general properties in the utmost perfection. In- dividual gases have their special peculiarities — some, for What is the altitude of the atmosphere ? What comparison does this bear to the mass of the earth ? What are its general properties ? What bodies constitute it ? Of what class is it the type ? 14 COMPRESSIBILITY OF AIR. ■example, are yejlow, some green, some purple, and some •ed. The first striking property of atmospheric air which we encounter, is the facility with which the volume of a given quantity of it can be changed. It is highly compressible and perfectly elastic. A quantity of it tied tightly up in a bladder or India-rubber bag, is easily forced, by the pressure of the hand, into a less space. The materiality of the air, and its compressibility, are simultaneously il- lustrated by the experiment of the diving-bell, described under Fig. 6. A vessel forced with its mouth downward under water, permits the water to enter a little way, be- cause the included air goes into smaller dimensions under the pressure ; but as soon as the vessel is again brought to the surface of the water, the air within it ex- pands to its original bulk. Fig. 8. This ready compressibility and expansibility may be shown in many other ways. Thus, if we take ^ a glass tube. Fig. 8, with a bulb c, at its upper end, the lower end being open and dipping into a vessel of water, d, and having previously partially filled the tube with water to the height, a, it will be found, on touching the bulb with snow, or by pour- ing on it ether, or by cooling it in any manner, that the included air collapses into a less bulk. It is therefore compressible, and on warming the bulb with the palm of the hand, the air is at once dilated. It is this quality of easy expansibility and compressi bility which distinguishes all gaseous substances from sol- ids and liquids. It is true the same property exists in them, but then it is to a far less degree. X)n the hypoth- esis that material bodies are formed of particles which do not touch one another, but are maintained by attractive and repulsive forces at determinate distances, it would appear that, in a gas like atmospheric air, the repulsive quality predominates over the attractive ; while in solids the attractive force is the most powerful, and in liquids the two are counterbalanced. Again, as respects relative weight, the gases, as a tribe, are by far the lightest of bodies ; and, indeed, it is How may it be proved to be compressible ? What does the diving-bell prove ? Describe the experiment, Fig. 8. In gaseous bodies does the at- tractive or repulsive force predominate ? ELASTICITV OP AIR. 15 am -ag tliem that we find the lightest substance in nature — ^hydrogen gas. They are, moreover, the only perfectly elastic substances that we know. Thus, a quantity of at- mospheric air compressed into a metal reservoir will re- gain its original volume the moment it has the opportuni- ty, no matter how great may be the space of time since it was first shut up. Under a relaxation of pressure this perfect elasticity displays itself in producing the expansion of a Fig. 9. gas. If a bladder partially full of atmospheric air be placed under an air-pump receiver, as the pressure is removed it dilates to its full extent, and might even be burst by the elastic force of the air confined within. The force with which this expansion takes place is very well display- . ed by putting the bladder in a frame, as shown in Fig. 10, and loading it with heavy weights ; as it Fig. lO expands by the spring of the air, it lifts up all the weights. If we were to imagine a given volume of gas placed in an immense vacuum, or under such circumstances that no extraneous agen- cy could act upon it, it is very clear that its expansion would be indefinitely great — the repulsive force of its own particles predom- inating over their attraction, and there being nothing to limit their retreat from one another. But when a gas- eous mass surrounds a solid nucleus, the case is diiferent — an expansion to a determinate and to a limited extent is the result. And these are the circumstances under which the earth and every planet surrounded by an elas- tic atmosphere exists ; for in the same way that our globe compels an unsupported body to fall to. its surface, and makes projectiles as bomb-shells and cannon-shot — no matter what may have been the velocity with which they were urged — return to the ground, so the same attractive force restrains the indefinite expansion of the air, and keeps the atmosphere, instead of difiusing away into empty space, imprisoned all round. Besides this cause — gravitation to the earth — a second Are gases perfectly elastic ? What does experiment Fig. 9 prove ? What would happen to a volume of gas placed in an indefinite vacuum 7 What limits the atmosphere to the earth ? 16 VARIABLE DENSITY OF THE ATMCSl'HEEE. one, for the limited extent of the atmosphere, may also be assigned — contraction — arising from cold. Observa- tion has shown that, as we rise to greater altitudes in the air, the cold continually increases ; and gases, in common with all other forms of body, are condensed by cold. The attempt at unlimited expansion which the atmos- phere, by reason of its gaseous constitution exerts, is therefore, kept in bounds by two causes — the attractiv force of the earth and cold — and accordingly its altitude does not exceed fifty miles. From the circumstance that air is thus a compressible body, we might predict one of the leading facts respect- ing the constitution of the atraosphei-e — it is of unequal densities at different heights. Those portions of it which are down below have to bear the weight of the whole su- perincumbent mass ; but this weight necessarily becomes less and less as we advance to regions which are higher and higher; for in those places, as there is less air to press, the pressure must be less. And all this is verified by ob- servation. The portions which rest on the ground are of the greatest density, and the density steadily diminishes as we rise. Moreover, a little consideration will assure us that there is a very simple relation between the press- ure which the air exerts and its elastic force. Consider the condition of things in the air immediately around us : if its elastic force were less, the weight of the superincum- bent mass would crush it in ; if greater, the pressure could no longer restrain it, and it would expand. It fol- lows, therefore, in the necessity of the case, that the elas- tic force of any gas is neither greater nor less, but pre- cisely equal to the pressure which is upon it. What is the agency of cold in this respect ? Why is the atmospl ere of unequal density at different heights 7 What relation is there between ita pressure and its elastic force ? THE AIR-PUMP. n LECTURE IV. Weight and Pressure op the Air. — Description of the Air-pump. — Its Action. — Limited Exhaustion. — Fun- damental fact that Air has weight. — Relative weight of other Gases. — Weight gives rise to Pressure. — Experi- ments illustrating the Pressure of the Air. In the year 1560, Otto Guericke, a German, invented an instrument whicbj from its use, passes under the name of the air-pump, and exhibited a number of very striking experiments before the Emperor Ferdinand III. This incident forms an epoch in physical science. Otto Guericke's instrument was imperfect in construc- tion and difficult of management. The apparatus re- quired to be kept under water. More convenient ma- chines have, therefore, been devised. The following is a description of one of the most simple : Upon a metallic fcasis, ff Fig. 11, Fig.n. are fastened two ex- hausting syringes, a a, which are worked by means of ahaiidle-, h, the two screw col- umns, d- d, aided by the cross-piece, e e, tightly compressing them into their pla-; ces. A jar, c, called aBe6eiver,the mouth of which is carefully ground true, is pla- ced on the plate of the pump, ff which is formed of a piece of metal or glass ground quite flat. This pump-plate is perforated in its center, from which air-tight passages lead to the bot- When and by whonu was the air-pump invented ? Give a description o Its genera! external appearance. What is the receiver ? What is tha pump-plate ? What passages lead from the center of the plate '{ , What IS the use of the screw 5 ? 18 STEUCTCRE OP THE AIR-PUMP. torn of each syringe, and wLen the handle, h, is moved the syringes withdraw the air from the interior of the jar From the same central perforation there is a third pass age, which can be opened or closed by the screw at g, so that when the experiments are over, by opening it the air can be readmitted into the interior of the receiver. So far as its exterior parts are concerned, this air-pump consists of a pair of syringes worked by a handle, and producing exhaustion of the interior of a jar, with a vent which can be closed or opened for the re^dmission of air. mg.x'i. The syringes are constructed exactly alike. The glass model represented in Fig. 12 exhibits their interior; each consists of a cylinder, a a, the interior of which is made perfectly true, so that a piston or plunger. A, introduced at the top may be pushed to the bot- tom, and, indeed, work up and SHv down without any leakage. There ^^ is a hole made through the piston, i, and over it a valve is laid. This consists of a flexible piece of mem- brane, as leather, silk, &c., which being placed on the aperture opens in one direction and closes in the other. Such a valve is in the pis- ton, and there is another one, c, resting on an aperture in the bottom of the cylinder. To understand the action of this instrument, let us sup- pose a glass globe fuU of atmospheric air to be fastened air-tight to the bottom of such a syringe, and the piston then lifted to the top of the cylinder. As it moves with- out leakage, it would evidently leave a vacuum below it were it not that the air in the globe, exerting its elastic force, pushes up the valve c, and expands into the cylin- der. In this way, therefore, by the upward movement of the piston, a certain quantity of air comes out of the globe and fills the cylinder. The piston is now depressed: the moment it begins to descend, the valve c, which leads What are the parts of each syringe ? How many valves has it X Which way do they open 7 Describe what takes place during the upward motion of the piston. What takes place during the downward motion ? • | fe0=:ii-T STRUCTURE OF THE AIR-PUMP. 19 into the globe shuts ; and now as the piston comes down it condenses the air below it, and as this air is condensed it resists exerting its elastic force. The piston-valve, d, under these circumstances, is pushed open, and the com- pressed air gets away into the atmosphere. As soon as the piston has reached the bottom of the cylinder all the aiir has escaped, and the process is repeated precisely as before. The action in the syringe is, therefore, to draw out fi-om the globe a certain quantity of air at each up- ward movement, and expel this quantity into the air at each, downward movement. For reasons connected with the great pressure of the air, and also for expediting the process of exhaustion, two syringes are commonly used. To their pistons are at- tached rods which terminate in racks, h h; between these there is placed a toothed wheel, which is turned on its axis by the handle, its teeth taking into the teeth of the racks. When the handle is set in motion and the wheel made to revolve, it raises one of the pistons, and at the same time depresses the other. The ends of these racks are seen in Fig. 12. The wheel is included in the transverse wooden bar, e e. Fig. 11. By the aid of this invaluable machine numerous striking and important experiments may be made. The form de- scribed here is one of the most simple, and by no means the most perfect. For the higher purposes of science more complicated instruments have been contrived, in which, with the utmost perfection of workmanship, the valves are made to open by the movements of the pump itself, and do not require to be lifted by the elastic force of the air. In such pumps a far higher degree of rare- faction can be obtained. No air-pump, no matter how perfect it may be, can ever make a perfect vacuum, or withdraw all the air from its receiver. The removal of the air depends on the ex- pansion of what is left behind, and there must always be that residue remaining which has forced out the portion last removed by the action of the syringes. The fundamental fact in the science of Pneumatics is, that atmospheric air is a heavy hody, and this may be How are the pistons moved by the rack ? What contrivances are intro- duced in the more perfect air-pumps 1 Can any of these instrumenta make a perfect var-uum 1 What is the cause of this 7 20 WEIGHT OF THE AIR. Fig. 13. proved in a very satisfactory manner by the aid of the pump. Let there be a glass flask, a, Fig. 13, the mouth of which is closed with a stop-cock, through which the air can be re- moved. If from this flask we ex- haust all the air, and then equi- poise it with weights at a balance as soon as the stop-cock is open- ed and the air allowed to rush in the flash preponderates. By add- ing weights in the opposite scale, we can determine how much it requires to bring the balance ' back to equilibrio, and there- fore what is the weight of a vol- ume of air equal to the capacity' of the flask. Upon the same principles we can prove that all gases, as well as atmospheric air, have weight; ' It is only requisite to take the exhausted flask, and hav-r ing counterpoised it as before, screw it on to the top of a jar, c, Fig. 14, containing the gas to be tried. On opening the stop-cocks, e d, the gas flows out of the jar and fills the flask,' which, being removed, may be again counterpoised at the bal- ance, and the weight of the gas filling it determined. There are very great differences among gases in this respect. Thus, if we take one hundred cubie inches of the following they will severally weigh : Hydrogen 2'1 grains. Nitrogen 30-1 " Atmospheric air 31-0 " Carbonic acid 47"2 " Vapor of Iodine 269'8 " What is the fundamental fact in Pneumatics ? How may the weight of the air be proved? How do other gases compare with it in this respect? Mention some of them. Fig. 14. PRKSSURE OP THE AIR- 21 From the fact that the air has weight, it necessarily follows that it exerts pressure on all thoseportions that are in the lower regions, having to sustain _ the weight of the masses above. And not only does this hold good as respects the aerial strata themselves, it also holds for all objects immersed in the air. In most oases, the resulting pressure is not detected, because it takes effect equally in all directions, and pressures that ai-e equal and opposite mutually neutralize each other. But when by the air-pump we remove the pressure from one side of a body, and still allow it to be exerted on the other, we see at once abundant ^?- '*• evidence of the intensity of this force. Thus, if we take a jar. Fig. 15, open at . both ends, and having placed it on the pump-plate, lay the palm of the hand on the mouth of it ; on exhausting the air the hand is pressed in firm contact with the jar, so that it cannot be lifted without the exer- tion of a very consiierable force. In the same way, if we tie over ajar a piece of blad- der, and allow it to dry, it assumes, of course, a perfectly horizontal position ; but on exhausting the air within very slightly, it becomes deeply depressed, and is Fig. 16 . soon burst inward with a loud' explosion. This i simple instance illustrates, in a very satisfacto- ry way, the mode in which the pressure of the air is thus rendered obvious ; for so long as the jar was not exhausted, and had air in its interior, the downward pressure of the atmosphere could not force the bladder inward, nor disturb its position in any manner : for any such disturbance to take place the pressure must overcome the elastic force of the air with- in, which resists it, pressing equally in the opposite way But on the removal of the air from the interior, the press- ure above is no longer antagonized, and it takes effect at once by crushing the t)ladder. Why does the air flxert pressure ? What follows on removing the press- nre from one side of a uodv 1 Describe the experiment in Figt. 15 and 16. Wliy is not the bladder crushfld in uctil the air is exhausted? 22 PRESSURE OF THE AIR. LEOTLRE V. The Press dre op the Air. — The Magdeburg Hermt- pheres. — Water supported hy Air. — The Pneumatic Trough. The Barometer. — Description of this Instrument. — Cattst of its Action. — Different lands of barometers. — Meas- urement of Accessible Heights. Many beautiful experiments establish the fact that the atmosphere presses, not only in the downward direc- tion, but also in every other way. Thus, if we take a pair Fig. 17 of hollow brass hemispheres, a b. Fig. 17, which (S) fit together without leakage, by means of a flange, \ kd and exhaust the air frond their interior through a , stop-cock aflixed to one of them, it will be found that they cannot be pulled apart, except by the exertion of a very great force. Now it does not matter whether the handles of these hemispheres are held in the position represented in the fig- ure, or turned a quarter way round, or set at any an- gle to the horizon they adhere with equal force togeth- er; and the same power which is required to pull them asunder in the vertical direction, must also be exerted in all others. This, therefore, proves that the pressure of the air takes effect equally in every direction, whether up- ward, or downward, or laterally. Fig. 18. In Fig- 18 a very interesting experiment is rep- resented. We take a jar, a, an inch or two wide and two or three feet long, closed at one end and open at the other, and having filled it entirely with water, place over its mouth a slip of writing pa- ' per, b. If now the jar be inverted in the position represented in the figure, it will be seen that the column of fluid is supported, the paper neither ^^ dropping off nor the water flowing out. This remarkable result illustrates the doctrine of the up- ward pressure of the air. Nor does it even require thai ProT'i that the air presses equally every way. Describe the apparatu ■« in Fig. 18. Why does not the paper fall from the mouth of the jar? - PRESSURE OP THE AIR. 83 a piece of paper should be used provided the glass has the proper form. Thus, let there be a bottle, a, ^s- 19- Fig, 19, in the bottom of which there is a large aperture, b. If the bottle be filled with water, and its mouth closed by the finger, the water will not flow out, but remain suspended. And that i this result is due to the upward pressure of the ' air is proved by moving the finger a little on one side, so as to let the air exert its pressure on the top as well as the bottom of the water, which immediately flows out. If we take ajar, a, Fig. 20, and having filled it full of water, invert it as is represented, in a ^e- 20- ^ reservoir or trough : for the reason ex- plained in reference to Fig. 18, the water will remain suspended in the jar. Such an arrangement forms the pneumatic trough of chemists. It en- ables them to collect the various gas- es without intermixture with atmos- pheric air; for if a pipe or tube through which such a gas is coming be depressed beneath the mouth of the jar a, so that the bubbles may rise into the jar, they will displace the water, and be collected in the upper part without any admixture. If in this experiment we use mercury instead of water, the same phenomenon ensues — the mercury being support- ed by the pressure of the air. Now it might be inquired, as the atmosphere only extends to a certain altitude, and therefore presses with a weight which, though great, must ne^cessarily be limited, whether that pressure could sus- tain a column of mercury of an unlimited length 1 If we take a jar a yard in length, and fill it vyith mercury, and invert it in a trough, it will be seen that the mercury is not supported, but that it settles from the top and de- scends until it reaches a point which is about thirty inches above the level of the mercury in the trough. Of course, as nothing has been admitted, there must be a vacant Will the same take place without any paper? Prove that it is due tc the apward pressure of the air. What is the pneumatic trough ? On what principle does it depend? Will the same take place if mercury i« used instead of water ? What takes place when the jar is more than tbirlir inches high ? 84 THE BAROKTETER. space or vacuum between the top of the mercury and tne top of the jar. Fig^i.\. This experiment which, as we are soon to see, is a very important one, is commonly made with ffi* a tube, a b. Fig. 21, instead of a jar — the tube being more manageable and containing less mer- cury. It should be at least thirty-two inches long, and being filled with quicksilver, may be inverted in a shallow dish containing the same metal, c. It is convenient to place at one side of the tube a scale, d, divided into inches, these inches being counted from the level of the mercury in the dish, ' c. Such an instrument is called a Barometer, or measurer of the pressure of the air. Let us briefly investigate the agencies which operate in the case of this instrument. If, having closed the mouth of the tube b with the finger, we lift it out of the dish c, it will be found that we must exert a considerable degree of force in order to sustain the column of mercury, which presses against the finger with its whole weight, and tends to push it away. Consequently, the mercury is continu- ally exerting a tendency to flow out, and therefore two forces are in operation : on the one hand, the weight of the mercury attempting to flow out of the tube into the dish ; and on the other, the weight or pressure of the at- mosphere attempting to push the mercury up in the tube. Fig. ss. If the pressure of the air were greater, it would push the mercury higher; if less, the mercury would flow out to a corresponding extent. Thus, the length of the mercurial column equilibrates the pressure of the air, and we therefore say that the atmospheric pressure is equal to so many inches of mercury. That the whole thing depends on the pressure of the air may be beautifully proved by putting the barometer under a tall air-pump receiver, as represented in Fig. 22, and exhaustingfT As the pressure of the air is reduced the mercurial col- ' umn falls ; and if it were possible to make a par- How is this experiment commonly made ? Describe a barometer. What ore the forces which operate in this instrument ? What does the mercu rial column equilibrate 1 What is it equal to 1 How may it be proved to depend on the pressure of the air ■" THE BABOMETER. 25 feet vacuum by such means, the mercury would sink in the tube to its level in the dish. On readmitting the air the mercury rises again, and when the original pressure is regained it stands at the original level. There are many different forml of barometers, *%• 23. tuch as the straight, the syphon, &c., but the prin- ^ ciple of all is tie same. The scale must uni- formly commence at the level of the mercury in the reservoir. ^Now it is plain that this level changes with the height of the column ; for if the metal flows out of the tube it raises the level in the reservoir, and vice versa. In every per- fect barometer, means, therefore, should be had to adjust the beginning of the scale to the level for the time being. In some barometers, as in that represented in Fig. 23, this is done by hav- ing the mercury in a cistern with a movable bot- tom, and by turning the screw V, the level can be ' precisely adjusted to that of the ivory point, a. A barometer kept in the same place under- goes variations of altitude, some of which are reg- ular and others irregular. The former, which depend on diurnal tides in the atmosphere, anal- ogous to tides in the sea, occur about the same time of the day-— the greatest depression being commonly about four in the morning and eve- ning, and the greatest elevation about ten in the morning and night. In summer, however, they occur an hour or two earlier in the morning, and ^ as much later at night. The irregular changes depenc on meteorological causes, and are not reduced as yet to any determinate laws. In amount they are much more extensive than the former, extending from the twenty-sev- enth to more than the thirtieth inch, while those are lim- ited to about the tenth of an inch. A very valuable application of the barometer is for the determination of accessible heights. The principle upon which this depends is simple — the barometer necessarily What would eneue if a perfect vacuum could be made ? What takes Elace on readmitting the. air? From what point should the scale of the arometer commence ? What are the regular barometric changes? What is the extent of the irregular ones ? How is the barometer applied to the measurement of heights 7 B 26 MEASCEE OP ATMOSPHERIC PRESSURE. standing at a lower point as it is carried to a higher posi- tion. In practice it is more complicated, and to obtain ex- act results various methods have been given by Laplace, Baily, Littrow, and others. LECTURE VL The Pressure of the Air. — Measure of the Force with which the Air presses. — Different Modes of Estimating it. — Experiments Illustrating this Force. Elasticity of the Air. — Experimental Illustrations. — The Condenser. Having, in the preceding lecture, explained the cause and illustrated the pressure of the air, we proceed in the next place to determine its actual amount. Fig-^i- There are many ways in which this may be done. The following is simple : Take a pair of Magdeburg hemis- pheres, the area of the sec- tion of which has been pre- viously determined in square inches; exhaust them as per- fectly aspossible at the pump; and then, fastening the lower handle, a, to a firm support, hang the other, h, Fig. 24, to the hook of a steelyard, and move the weight until the hemispheres are pulled apart. It will be found that this commonly takes place when the weight is sufficient to overcame a pressure of fifteen pounds on every square inch. This may serve as an elementary illustration, but there are other methods much more exact. Thus, by the ba- rometer itself we may determine the value of the pressure with precision. If we had a barometer which was ex- actly one square inch in section, and weighed the quanti- ty of mercury it contained at any given time, it would What may the Magdeburg hemisphere be made to prove ? How maj the same be proved by the barometer ? What is the pressure of the aii on one iquBre inch 7 PRESSURE OF THE AIR. 27 give us the value of the ^.tmospheric pressure on one square inch, because the weight of the mercury is equal to the pressure of the air. And by calculation we can, in- like manner, obtain it from tubes of any diameter. The phenomena of the barometer teach us that this pressure is not always the same, but it undergoes varia- tions. It is commonly estimated at fifteen pounds on the square inch. There are two other ways in which the value of the pressure of the air is stated. It is equal to a column of mercury thirty inches in length, or to a column of water thirty-four feet in length. We are now able to understand the reason of the great effects to which, the pressure of the air may give rise. In most instances these effects are neutralized by counter- vailing^^ pressures. Thus, the body of a man of ordinary size has a surface of about two thousand square inches, the pressure upon which is equal to thirty thousand pounds. But this amazing force is entirely neutralized, because, as we have seen, the atmospheric pressure is equal in all directions, upward, downward, and laterally. All the cavities and the pores of the body are filled JFii^. 25. with air, which presses with an equal force. The following experiments may further illustrate the general principle of atmospher- ic pressure : On a small, flat plate, a. Fig. 25, furnished with a stop-cock, S, which terminates in a narrow pipe, c, let there be placed a tall re- ceiver, fi:om which the air is to be exhausted by the pamp. 'The stop-cock h being clo- sed, and the instrument being removed from i the pump, b is to be opened, while the lower portion of its tube dips into a bowl of water. Under these circumstances the water is pressed up in a jet through c, and forms a fountain in vacuo. On the top of a receiver. Fig, 26, let there be cemented, air-tight, a cup of wood. What is the length of an equivalent cplBmn of mercury 1. What is it in the case of water? What amount of pressure is there on the body of a man ? By what is this counteracted ? Describe the fountain ir. vacua How may mercury be pressed through the pores of wood '• 28 ELASTICITY OF AIR. Fig.ae. a, terminating in a cylindrical piece, h, the pores of vvrhich run lengthwise. Beneath this let there be placed a tall jar, c. Now, if the wooden cup be filled with quicksilver, the jar being previously placed on the pump, and ex- haustion made, the metal will be pressed through the pores of the wood and descend in a silver shower. The jar, c, should be so placed as to prevent any of the quicksilver getting into the interior of the pump. There are many substances which exist in the liquid condition, merely because of the press- ure of the air. Take a glass tube. A, Fi0. 27, closed at one end and open at the other, and having filled it with water, invert it in ajar, B; introduce into it now a little sulphuric ether, which will rise, because of its lightness, to the top of the tube, at a. Place the apparatus be- neath the receiver of the air-pump, and exhaust. The ether will now be seen to abandon the liquid and assume the gaseous form, filling the entire tube and looking like air. On allowing the pressure again to take efiPect, it again relapses into the liquid form. Fiff. 28. The following experiments illustrate the elas- ticity of the air : Take a glass bulb, a, Fig. 28, which has a tube, b, projecting from it, the open extremity of which dips beneath some water in a cup, c; the tube and the bulb being likewise full of , vsrater, except a small space which is occupied by a bubble of air at a. Invert over the whole ajar, d, and, placing the arrangement on the pump, ex- haust. It will be found, as the exhaustion goes on, that the bubble a steadily increases in size until it fills all the bulb, and even the tube. On readmitting the press- ure the bubble collapses to its original size. The air is, therefore, dilatable and condensible — that is, it is elastic. If a bottle, the sides of which are square and the mouth hermetically closed, be placed beneath a receiver, and Why does s Iphuric ether retain the liquid state ? When the pressure is removed what becomes of the ether ! What does experiment Fig. 28 prove ' * THE CONDENSER. 29 JV^. 29. Fig. 30. C the pressure remove4, the air imprisoned in the interior exerting its elastic force, will vio- lently burst the bottle to pieces. It is, there- fore, well to cover it with a wire cage, as rep- resented in Fig. 29. The elastic force of the air increases with its density. Powerful effects, therefore, arise by condensing air into a limited space. The con- denser, which is an instrument for this pur- pose, is represented in Fig. 30. It consists of a tube, a b, in which there moves by a handle, g, a pistonyi In one Side of the tube, at c, there is an aperture, and at the lower part, d, there is a valve, e, opening down- ward. On pushing the piston down; the air be- neath it is compressed, and, openingthe valve e, by its elastic force, accumulates in the re- , ceiver, R. When the piston is pulled up a vacuum is. made in the tube ; but as soon as it passes the aperture, c, the air rushes in. Another downward movement drives this through the valve into the receiver, and the process may be continued until the elas- tic force of the included air becomes very great. If the receiver be partly filled with water, and there be placed in it a piece of wax, B.n-.egg, or any yielding or brittle bodies, it will be found impossible to alter their figure by condensing the air to any extent whatever. And this arises from the circumstance already explained — that the pressure generated is equal in .all direc- tions. The Cartesian image is a grotesque figure, made of glass, Fig. 31, hollovr within and filled with water to the height c d. The upper part, a, is filled with air. The water is introduced through the tail, h, and the quantity of it is so adjusted that the figure just floats in water. If, therefore, it be placed in a deep Fig.il Under what circumstances may flat bottles be broken ? What relation IS there between elastic force and density ? Describe the condenser. Why are not brittle bodies broken in such an instrument ? What is the reason of the motions of the Cartesian images ? 30 MISCELLANEOUS EXPERIMENTS. J I A Fig. 33. jar quite full of that liquid, and a cover of India-rubber Fig.3i.. or bladder tied on, as seen in Fig. 32, the fig- ure floats up at the top ; but by pressing with the finger on the cover, more water is forced into its interior, through the tail, b, and it descends to the bottom. On removing the finger the elastic force of the air, a, drives out this excess of wa- ter, and the image, becoming lighter, reascends. If the tail be turned on one side, as represent- ed, the efflux of the water taking effect in a lat- eral direction, the figure spins round in its move- ments and performs grotesque evolutions. On pieciaely the same principle, if a small bladder, only partly full of air, be sunk by a weight. Fig. 33, to the bottom of a deep glass of water, on covering the whole with a re- ceiver and exhausting, the elastic force of the included air dilates the bladder, which rises to the top, carrying with it the weight. When the pressure is readmitted the blad- der collapses and descends again to the bot- tom of the jar. There are numerous machines in which the elastic force of air is brought into operation, such as the air-gun, blowing tnachines, &c. Indeed, the various applications of gunpowder itself depend on this principle — that ma- terial on ignition suddenly giving rise to the evolution of an immense quantity of gas, which exerts a great elastic force. What is the cause of the ascent and descent of the little bladder, Fig. 33 ? On what do the air-gun and the action of gunpowder depend f mareiotte's law 31 LECTURE VII. Properties op the AiR.-^-Marriotfe's Law. — Proof Jbr Compressions and Dilatations. — Case in. which it Fails. — Resistance of the Air to Motion. — The Parachute. — The Air transmits Sound; -supports Animal Life, Com- bustion, and JgnitioA. — Exists in the pores of some Bodies and is dissolved in others. Atmospheric air being thus a highly compressible and expansible substance, we have next to inquire -what is the amount of its compressibility under diffei-ent degrees of force 1 This has been determined experimentally by different philosophers, the true law having first been dis- covered by Boyle and Marriotte. The density and elasticity of air are directly as the force of compression. The volume which air occupies is inversely as the press- ure upon it. To illustrate, and at the same time to prove these laws, we make use of a tube, a d-c h, so bent that it has Vt^- 34. two parallel branches, a and b. It is closed at b, Ba and has a funnel-mouth at a. Sufficient mercury is poured into the tube to close the bend and to insu- late a volume of air \nb d. Of course this air ex- ists under a pressure of one atmosphere equal to a column of mercury thirty inches long. Through the funnel, a, mercury is now to be poured ; as it accu- | /-ij raulates it presses upon the air in d b, and re- i yS duces its volume to c. If, in this manner, a column thirty inches long be introduced, it will be found that the air in b d\s reduced to half. There are, therefore, now two atmospheres pressing on the included air — the atmos- phere itself being one, and the thirty inches of mercury the other. Two atmospheres, therefore, reduce a given quantity of air into half its volume. In the same manner it could be proved, if the tube What is Marriotte's law ? Describe Marriotte's instrument. What is its use 1. When the pressure on a gas is doubled, tripled, quadrupled, what lume does it assume ? 32 RESISTANCE OF AIK. a, I'l f were long enough, that the introduction of another thirty inches of mercury, giving a pressure of three atmospheres, would condense the air to one-third, that four would com- press it to one-fourth, five to one-fifth, &c. Fig. 35. The truth of this law may be proved for rare- factions as well as condensations. For this purpose let there be taken a long tube, a h. Fig. 35, open at the end, h, and closed at a, with a screw ; a jar, A, filled with mercury to a sufficient height, is also to be provided. Now jjj«rra let the screw at a be qpened and the tube de- ll pressed in the mercury until the metal, by ^ ijj rising, leaves in the tube a few inches of air. The screw is now to be closed and the tube lift- ed. The included air at once dilates and a col- umn of mercury is suspended. It will be found that when the air has dilated to double its vol- ume, the length of the mercurial column in the tube will be fifteen inches — that is, half the ba- rometric length. By such experiments, it therefore appears that Marriotte's law holds both for condensations and rarefac- tions. This law has been verified until the air has been condensed twenty-seven times and rarefied one hundred and twelve times. In the case of gases, which easily as- sume the liquid- form, it is, however departed from as that point- is approached. Besides the properties already de- scribed, atmospheric air possesses others which require notice. Among these may be mentioned its resist- ance to motion. This property may be exhibited by means of the two wheels, a b, Fig. 36, which can be put in rapid rota- tory motion by the rack, d, which moves up and down through an air- tight stuffing-box, e. The wheels are so arranged that the vanes of a move through the air edgewise, but How may this be proved for rarefactions 7 To what extent has this law been verified ? How may the resistance of the air be proved ? In a vacu um is there any resistance ? Fig. 36. EESISTANCE OF AIE. 3S Fig. 37. those of b with their broad faces. On pushing down the rack, d, and making the wheels rotate with equal rapid- ity in the atmospheric air, one of them, a, will be found to continue its motion much longer than the other, b: and that this arises from the resistance which b experiences from the air is proved by making them rotate in the receiver from which the air has been exhausted, when b will continue its motion as long as a, both ceasing to re- volve simultaneously. The water-hammer affprds another instance of the same principle. It consists of a tube a foot or more long and half an inch in diameter. In it there is included a small quantity of water, but no atmospheric air. When it is turned upside down the water drops from end to end, and emits a ringing, metallic sound. If there was any air iu the tube, it would resist or break the fall of the water. A well-made mercurial thermometer exhibits the same fact. If there is a perfect vacuum in its tube, on turning the instrument upside down the metal drops like a hard, solid body against the closed end. The Parachute is a machine Dy which aeronauts may de- scend from a balloon to the ground in safety. It bears a general resemblance to an umbrella, and consists of a strong but light surface, a a. Fig. 37, from which a car," b, is suspended. When it IS detached from the bal- loon, it descends at first with an accelerated velocity, but this is soon checked by the resistance of the air, and the machine then falls at a rate nearly uniform, and very mod- erate. In virtue of its elasticity, atmospheric air is the common medium for the transmission of sounds. Underthe receiv- er of an air-pump let there be placed a bell, a, Fig. 38, the nammer, b, of which can be moved on its pivot, c, by means Describe the parachute and its mode of action. How may it be proved ■hat atmospheric air^ransmits sound ? B* 34 AIR SUPPORTS LIFE. of a lever, li, which is worked by a rod passing through Fig.'Si the stuffing-box, e. The bell is placed on a leather drum, g, and fastened down to the pump-plate by means of a board, d. While the air is yet in the receiver, the sound is quite audible, but on exhausting it becomes fainter and fainter, and at last can no longer be heard. On readmitting the air the sound gradually increases, and at last acquires its original intensity. The leather cushion,^, is necessary to prevent the transmission of the sound through the solid part of the pump. The air also is absolutely necessary for the support of fig. 39. life. The higher warm-blooded animals die when the air is only partially rare- fied. A rabbit, or other small animal, placed undei an air-pump jar may re- main there several minutes without being much disturbed ; but if we commence withdrawing the air the animal instantly shows signs of distress, and if the exper- iment is continued, soon dies. So, too, if a jar containing some small fishes be placed under an exhausted re- ceiver, the animals either float on their backs at the surface of the water, or descend only by violent muscular exertions. Fishes respire the air which is dissolved in water, and hence it is somewhat remarkable that they continue to live for a considerable length of time in an exhausted re- ceiver.' The air is also necessary to all processes of combustion. If a lighted candle be placed under a receiver, it will burn for a length of time ; but if the air be withdrawn by the pump, it presently dies out. The smoke also descends to the bottorri of the receiver, there being no air to buoy it up. Why is it necessary that the bell should rest on a cushion ? Prove that air is necessary for the support of life. Do fishes die at once in an ex- hausted receiver ? Prove that the air is necessary to support combus- AIR EXISTS IN PORES. 35 Fig. 40. If a gun-lock be placed in an exhausted receiver, and the flint be made to strike, no sparks whatever appear ; and, consequently, if there were powder in the pan, it could not be exploded. Tlie produc- tion of sparks by the flint and steel is due to small portions of the latter which are struck off by the percussion burn- ing- in the air, and when the air is re- moved that combustion can, of course, no longer take place. By taking advantage of the expansi- bility of the air, we are able to prove ji^. 41. that it is included in the pores of many bodies. Thus, if an egg is dropped into a deep jar of water, and this covered with a receiver as soon as exhaustion is made, a multi- tude of air bubbles continually ascend through the water. Or if a glass of porter be placed beneath such a receiver, its surface is covered jis^. 42. with a foam, the carbonic acid gas, which is the cause of its agreeable briskness, escaping away. And even com- mon river or spring water treated in the same manner exhibits the esqape of a considerable quantity of gas, which ascends through it in small , bubbles, and gives it a sparkling ap- pearance. Why does a gun-lock fail to give sparks in vacuo ? Hovf may Hie pres- ence of air in the pores of bodies be proved 1 Does water contain dig- Eolved air ? , 3fi LOSS OP WEIGHT IN AIK. LECTURE VIII. Properties op the Air. — Loss of Weight of Bodies in the Air. — Theory of Aerostation. — The Montgolfiei Balloon. — The Hydrogen Balloon. — Mode of Controll- ing Ascent and Descent. — Artificial and Natural Cur- rents in the Air. — Velocity with, which Air flows into a Vacuum. — Velocity of Efflux of different Gases. — Prin- ciples of Gaseous Diffusion. — These Principles regulate the Constitution of the Atmospliere. On principles which will be fully explained when we come to speak of specific gravity, it appears that a solid immersed in a fluid loses a portion of its weight. It foUows, of course, that a substance weighs less in the air than it does in vacuo. To one arm of a balance, a, Fig. 43, let there be hung Fig. a. a light glass globe, c, coun- terpoised in the air on the other arm, h, by means of a weight. If the apparatus be placed beneath a receiver, and the air exhausted, the I globe c, descends, but on re- admitting the air the equi- librium is again restored. This instrument was former- ly used for determining the density of the air. A substance that has the same density as atmospheric air, when it is immersed in that medium, loses all its weight, and will remain suspended in it in any position in which it may be placed. But if it be lighter, it is pressed upward by the aerial particles, and rises upon the same principle that a cork ascends from the bottom of a bucket of water. And as the density of the air con- What difference is there in the weight of a body in the air and in vacuo I What fact is illustrated by the instrument, Fig. 43 ? Under what circum stances does a substance in the air lose all its weight ? On what principle do air balloons depend ? AIR BALLOON. S"? tinually diminishes as we go upward, it is evident that such a body, ascending from one stratum to another, will finally attain one having the same density as itself, and there it will remain suspended. On these principles aerostation depends. Air balloons are machines which ascend through the atmosphere and float at a certain altitude. They are of two kinds : 1st, Montgolfier or rarefied air balloons ; and, 2d, Hydrogen gas balloons. The Montgolfier balloon, which was invented by the person whose name it bears, consists of a light bag of paper or cotton, which may be of a mg.u. spherical or other shape ; in its lower portion there is an aperture, with a basket suspended beneath for the pur- pose of containing burning material, as i straw or shavings. On a small scale, a \ paper globe two or three feet in diam- eter, with a piece of sponge soaked in spirits of wine, answers very well. The hot air arising from the burning matter enters the aperture, distending the balloon, and makes i' specifically lighter than the air, through which, of course, it will rise. The hydrogen gas balloon consists, in like manner, of a thin, impervious bag, filled either with hydrogen or com- mon coal gas. The former, as usually made, is from ten to thirteen times lighter than air ; the latter is somewhat heavier. A balloon filled with either of these possesses, therefore, a gi'eat ascentional power, and will rise to considerable heights. Thus, Biot and Gay Lussac, in 1804, ascended in one of these machines to an elevation of 23,000 feet. When the balloon first ascends, it ought not to be full of gas, for as it reaches regions where the pressure is diminished, the gas within it is dilated, and though flaccid at first, it will become completely distended. If it were full at the time it left the ground, there would be risk of its bursting open as it arose. The gas balloon squires a valve placed at its top, so that gas may be How many kinds of them are there I Describe the Montgolfier balloon. Describe the hydrogen balloon. What is the relative weight of hydrogen and air T Whyjmist not the machine be full when it leaves the giound 7 How is it made to ascend and descend ? 38 CURRENTS IN THE AIR. discharged at pleasure, and the machine made to descend. The aeronaut has control over its motions by taking up with him a quantity of sand in bags, as ballast. If he throws out sand the balloon rises, and if he opens the valve and lets the ga§ escape, it descends. The rarefaction which air~ undergoes by heat makes it, of course, specifically lighter. Warm air, therefore, as- cends, and cold air descends. When the door of a room which is very warm is open, the hot air flows out at the top, and the cold enters at the floor: these currents may be easily traced by holding a candle near the bottom and top of the door. In the former position the flame leans inward, in the latter it is turned outward, following the course of the draught. The drawing of chimneys, and the action of furnaces and stoves depends on similar principles : the column of hot air contained in the flue ascending, and cold air replacing it below. Similar movements take place in the open atmosphere. When the sun shines On the ground or the surface of the sea, the air in contact becomes warm, and rises ; it is replaced by colder portions, and a continuous current is established. The direction of these currents is changed by a variety of circumstances, as the diurnal rotation of the earth and other causes less understood. On these depend the various currents known as Breezes, Trade- winds, Storms, Hurricanes. The atmosphere does not rush into avoid space instan- taneously, but, under common circumstances of density and pressure, with a velocity of about 1296 feet in one second. Its resisting action on projectiles moving through it with great velocities is intimately connected with this fact. A cannon-ball, moving through it with a speed of two or three thousand feet, leaves a total vacuum behind it, and condenses the air correspondingly in front. It is, therefore, subjected to a very powerful pressure continu- ally tending to retard it. The rush of the air flowing into the vacuous spaces left by moving bodies is the cause of the loud explosions they make. How does increase of heat affect the air ? How may the currents in a warm room be traced ? What is the principle on which furnaces and stove depend ? How do winds and currents in the air arise ? What is the rea son that a cannon-ball moving in the air has its velocity rapidly reduced' DIFFUSION OF GASES. 39 Fig. 45. "When gases of difFerent densities flow from apertures of the same size, the velocities with which they issue are different, and are inversely as the square roots of their densities. The lighter a gas is the greater is its issuing velocity ; and therefore .hydrogen, which is the lightest body, moves, under such circumstances, with the greatest speed. The _ experiment represented in Fig. 45 illustrates these principles. Let there be a tube, a b, half an inch in diameter and six inches long, the end, b, being open and a closed with a plug of plaster of Paris, which is to be completely dried. Counterpoise this tube on the arm of a balance, and fill it with hydrogen gas, taking care to keep the ^ plug dry, letting the open end, b, of the tube dip just be- neath the surface of some water contained in a jar, C. In a very short time it will be discovered that the hydro- gen is escaping through the plaster of Paris, and the tube, filling with water, begins to descend ; and after a few min- utes much of the gas will have gone out, and its place be occupied partly by atmospheric air, which comes in in the opposite direction, and partly by the water which has risen in the tube. Even vvhen gases are separated from eac'n other by barriers, which, strictly speaking, are not porous, the same phenomenon takes place. Thus, if with the finger we spread a film of soap-water over the mouth of a bottle, a, and then expose it under a jar to some other Fig.ie. gas, such as carbonic acid, this gas percolates rap- idly through the film, and, accumulating in the bot- tle, distends the film into a bubble, as represented in Fig. 46. Meanwhile, a little atmospheric air es- capes out of the bottle through the film in the op- posite direction. What is the law under which gases flow out of apertures ? How may it be proved that gases can percolate through porous bodies, such as plugs of stucco? How majr it be proved that the; pass through films of water ? 40 DIFFUSION OP GASES. This propensity of gases to diffuse into each other is Fiff.^^. clearly shown by filling a bottle, H, Fig. 47, with a very light gas, as hydrogen ; and a second one, C, with a heavy gas, as carbonic acid, and putting the bottles mouth to mouth. Diffusion takes place, the light gas descending and the heavy one rising until both are equally com mixed. We see, therefore, that this property oi gases is intimately concerned in determining the constitution of the atmosphere, which is made up of different substances, some of which are light and some heavy — the heavy ones not sinking, nor the light ones ascending, but both kept equally commixed by diffusion into each other. Do the same phenomena ensue when no boundaries or barriers inter vene ? What have these principles to do with the constitution of the at mosphere ? * PROPERTIES OP LiaUIDS. 41 PROPERTIES OF LIQUIDS. HYDROSTATICS AND HYDRAULICS LECTURE IX. Properties op Liquids. — Extent and Depth of the Sea, — Its Influence on the Land. — Production of Fresh Wa- • ters. — Relation of Liquids and Gases. — Physical Con- dition of Liquids. — Different Degrees of Liquidity. — Florentine Experiment on the Compression of Water. — Oersted's Experiments. — Compressibility of otTier Li- quids, Having disposed of the mecbanical properties of at- mospheric air, which is the type of gaseous bodies, in the next place we pass to the properties of water, which is the representative of the class of Liquids. About two thirds of the surface of the earth are covered with a sheet of water, constituting the sea, the average depth of which is commonly estimated at about two miles. This, referred to our usual standards of comparison, im- presses us at once with an idea of the great amount of water investing the globe ; and, accordingly, imaginative writers continually refer to the ocean as an emblem of immensity. But, referred to its own proper standard of compari- son — ^the mass of the earth — ^it is presented to us under a very different aspect. The distance from the surface to the center of the earth is nearly four thousand miles. The depth of the ocean does not, therefore, exceed ^^^ part of this extent : and astronomers have justly stated, that were we on an ordinary artificial globe to place a What are the estimated dimensions of the seaT How dc ■'*"se com pare with the size of the earth itself 7 12 THE SEA. representation of the ocean, it would scarcely exceed in thickness the film of varnish already placed there by the manufacturer. In this respect the sea constitutes a mere aqueous film on the face of the globe. Yet, insignificant as it is in reality, it has been one of the chief causes engaged in shaping the external surface, and also of modeling the interior to a certain depth — for geological investigations have proved the former action of the ocean on regions now far removed from its influence, in the interior of conti- nents ; and also its mechanical agency in the formation of the sedimentary or stratified rocks which are of enor- mous superficial extents and often situated at great depths. Besides the salt waters of the sea, there are collections of fresh water, irregularly disposed, constituting the dif- ferent lakes, rivers, &c. The direct sources of these are springs, which break forth from the ground, the little streams from which coalesce into larger ones. But the true Source of all our terrestrial waters is the sea itself By che shiaing of the sun upon it a portion is evaporated into the air, and this, carried away by winds and condensed again by cold, descends from the atmosphere as showers of rain, which, being received upon the ground, perco- lates until it is stopped by some less pervious stratum, and flowing along this at last breaks out wherever there is opportunity in the low grounds — thus constituting a spring. Such streamlets coalesce into rivers, which find their way back again to the sea, the point from which' they originally came — an eternal round, which is repeat- ed for centuries in succession. From these more obvious phenomena of nature we dis- cover a relationship between aerial and liquid bodies — the one passing without difficulty into the other form — and, indeed, many of the most important events around us depending on that fact. Experiment also shows that, in many instances, substances which under all common circumstances exist in the gaseous condition, can be made to assume the liquid. Thus, carbonic acid, which is one of the constitutents of the atmosphere, can by pressure be reduced to the liquid form, and can even be made to What great phenomena have arisen from the action of the sea ? To what source are rivers and springs due ? How is it they are formed ? What lO lation is there between gases and liquids ? DEGREES OF LiaUIDITY. 43 assume that of a solid. The main agents by which such transmutations are affected are cold and pressure. The parts of liquids seem to have little cohesion. View- ing the forms of matter as being determined by the rela- tion of those attractive and repulsive forces which are known to exist among particles, it is believed in that now under consideration — the liquid — that these forces are in equiMbrio. For this reason, therefore, tne parti- cles of such bodies move freely among one another; and liquids, of themselves, cannot assume any determinate shape, but conform their figure to the vessels in which they are placed. Portions "of the same liquid added to one another readily unite. Among liquids we meet with what may be termed dif- ferent degrees of liquidity. Thus the liquidity of molasses, oil, and water, is of different degrees. It seems as though there was a gradual passage from the solid to this state, a passEige often exhibited by some of the most limpid substances. Thus alcohol, when submitted to an extreme degree of cold, assumes that partial consistency which is seen in melting beeswax, yet at common temperatures it is one of the most mobile bodies known. So, too, that compound of tin and lead which is used by plumbers as a solder, though perfectly fluid at a certain heat, passes, in the act of cooling, through various successive stages, and at a particular point becomes plastic and may be molded with a cloth. If a quantity of atmospheric air is pressed upon by any suitable contrivance, it shrinks at once in volume. We have already proved this phenomenon and determined its laws. If water is submitted to the same trial, the result is very different — it refuses to yield : for this reason, inas- much as the same fact applies to the whole class, liquids are spoken of as incompressible bodies. It was at one time thought that the experiment of the Florentine academicians, who ^filled a gold globe with water, and on compressing it with a screw found the wa ter ooze through the pores of the gold, proved completely the incompressibility of that liquid. ? But more recent ex- Do the parts of liquids cohere ? What is the relation between their at- tractive and repulsive forces ? Mention some of the distinctive qualities of liquids. Give examples of dififerent degrees of liquidity. What ezper jment has been supposed to prove that water is incompressible ? 44 COMPRESSIBILITY OF LiaUIDS. periments have shown, beyond all doubt, that liquids are compressible, though in a less degree than gases. Thus, it is a common experiment to lower a glass bottle, filled with water and carefully stopped with a cork, into the sea. Fig. 48. On raising it again the cork is often found forced in, and the water is uniformly brackish. But in a more exact manner the fact can be provec, and even the amount of compressibility meas- ured, by CErsted's machine. This consists of a strong glass cylinder, a a, Fig. 48, filled with water, upon which pressure can be exerted by a piston driven by 3, screw, b. When the screw is turned and pressure on the liquid exerted, it contracts into less dimensions, but at the same time the glass, a a, yielding, distends, and the contraction of the water becomes complicated with the expansion of the glass in which it is filaced. To enable us to get j-id of this difficulty, the instru- Fig. 49. ment. Fig. 49, is immersed in the cylinder of water, as seen at Fig. 48. This consists of a j,v glass reservoir,'e, prolonged into a fine tube, e J", M with a scale, x, attached to it. The reservoir and part of the tube are filled with water, and a little "^ column of quicksilver, x, is upon the top of the wa- ter, serving to show its position. On one side there is a gage, d, partially filled with air. It serves to measure the pressure. % Now when the instrument. Fig. 49, is put in the cylinder in the position indicated in Fig. 48, and pressure made by the screw, b, it is clear that the water in the reservoir will be compressed, and the glass which contains it,being pressed upon equally, internally and externally, will yield but very little. Mak- ing allowance, therefore, for the small amount of con#' pression which the glass thus equally pressed upon un- dergoes, we may determine the compressibility of the water as the force upon it varies. It thus appears that water diminishes yswot P^""* °^ its volume for each at- mosphere of pressure upon it. In the same way the com- pressibility of alcohol has been determined to be tto oo- Mention some that prove the contrary. Describe CErsted's machine^ What is the amount of the compressibility of water ? HTDEOSTATIG PRESSURE. 40 LECTURE X. The Pressures op Liquids. — Divisions of Hydrodynam- ics. — Liquids seek their own Level. — Equality of press- ures. — Case of different Liquids pressing against each other. — General Lawqf Hydrostatics. — Hydrostatic Par- adox. — Law for Lateral Pressures. — Instantaneous com- mimication of Pressure. — Bramah's Hydraulic Press. To the science which describes the mechanical proper ties of liquids the title of Hydrodynamics is applied. It is divided into two branches, Hydrostatics and Hydraul- ics. The former considers the weight and pressure of liquids, the latter their motions in canals, pipes, &rc. A liquid mass exposed without any confinement to the action of gravity would spread itself into one continuous superficies, for all its parts gravitate independently of one another, each part pressing equally on all those around it, and being pressed on equally by them. A liquid confined in a receptacle or vessel of any kind conforms itself to the solid walls by which it is sun-ound- ed, and its upper surface is perfectly plane, no part being higher than another. This level of surface takes phice even when different vessels communicating with each other are used. Thus, if into a glass of water we dip a tube, the upper orifice of which is temporarily closed by the finger, but little water will enter, owing to the impenetrability of the air; but, as soon as the finger is removed, the liquid instantly rises, and finally settles at the same level inside of the tube that it occupies in the glass on the outside. This result obviously depends on the equality of press- ure just referred to, and it is perfectly independent of the form or nature of the vessel. If we take a tube bent Into what branches is Hydrodynamics divided ? Under the action of gravity what form does a free liquid assume ? What is the effect when it is inclosed in a vessel ? Give an illustiation of the equality of pressure. 46 PRESSURE OP DIFFERE.VT LIQUIDS. Fig. 50. in the form of the letter U, and closing one of its branches with the finger, pour water into the other, as soon as the finger is removed the liquid rises in the empty branch, and, after a few oscillatory movements, stands at the same level in both. If one of the branches of such a tube is much widei than the other, the same result still ensues. Thus, as in Fig. 50, we might have a reser- voir,.A I, exposing an area of ten, or a hun- dred, or ten thousand times that of a tube rising from it, B G C H, but in the latter a liquid would rise no higher than in the former, both being at precisely the same level, A D. We perceive, therefore, from such an experiment, that the pressure of liquids does not depend on their absolute weight, but on their vertical altitude. The great mass of liquid contained in A exerts no more pressure on C than would a smaller mass contained in a tube of the same dimensions as C itseif. A variation of this experiment will throw much light upon the subject. Instead of using one, let there be two liquids, of which the spe- cific gravities are different. Put one in one of the branches of the tube,aZic, JF'zjO'.51, and the -14 other in the other. Let the liquids be quicksil- pis ver and water. It will be found, under these ■ circumstances, that the water does not press - the quicksilver up to its own level, but that, - for every thirteen and a half inches vertical '-B height that it has in one of the branches the 1 1 quicksilver has one inch in the pther. Of i ;;_ course, as they communicate through the hori- zontal branch, b, the quiclisilver must press ^ against the water as strongly as the water presses against it ; if it did not, movement would ensue. And such experiments, therefore, prove that it is the prin- ciple of equality of pressures which determines liquids to seek their own level. From this it therefore appears that a liquid in a vessel Does this depend on the mass of a liquid? Prove that it depends on its height. What takes place when liquids of different densities are used? In what directions do liquids press ? Fig. 51. HYDROSTATIC PRESSURES. 47 not only exerts a pressure upon the bottom in the di- ection in which gravity acts, but also laterally and up- ward. From what was proved by the experiment represented in Fig. 50, it follows that these pressures are by no means ne- cessarily as the mass, but in proportion to the vertical height. If one hundred drops of water be arranged in a vertical line, the lowest one will exert on the surface on which it rests a pressure equal to the weight of the whole. And from Buch considerations we deduce the general rule for esti- mating the pressure a liquid exerts upon the base of a vessel. " Multiply the height of the iluid by the area of the base on which it rests, and the product gives a mass which presses with the same weight." Thus in a conical vessel, E C ^'B- 53' D F, Fig. 52, thebase,C D, sus- tains a pressure measure^ by-^1 the column A B C D. For. all the rest of the liquid only presses on ABCD laterally, and resting on the sides EC and F D, cannot contribute any tlSng to the pressure on the base, CD But in a conicalvessel, EC D F, Fig. 53, the pressure on A Bis measured by A B CD, as before ; but the other por- tions of the liquid, not rest- ing upon the sides, press also upon the bottom, E F, and the result, therefore, is the same as if the vessel e^ were filled throughout to the height C A. This law is nothing more than an expression of the fact that the actual pressure of a liquid is dependent on its vertical height ^and the area of its base. Its applications give rise to some singular results. Thus, the Hydro- static bellows consists of a pair of boards. A, Fig. 54, Sig. 53. Give the rule for finding the pressure of a liquid on the base of the vea- wl containing it, Describe the hydrostatic bellows. 48 HYDKOSTATIC PARADOX. Fig-. 54. united together by leather, and from the lower one there rises a tube, e B e, ending in a funnel-shaped termination, e. If heayy weights, bed, are put upon the upper board, or a man stands upon it, by pour- ing water down the tube the weight can be raised. It is immaterial ho^ slender the tube, and, therefore, how small the quantity of water it contains, the total pressure resulting depends on the area of the bellows-boards, multiplied by the ver- tical height of the tube. Theoretically, therefoj-e, it appears that a quantity of water, however small, cafl lift a weight however great — -a principle sometimes spoken of as the hydrostatic paradox. But liquids exert a pressure against the sides as well as upon the bases of the containing vessel — the force of that pressui'e depending on the height. The law for estima- ting such pressure is, " The horizontal force exerted against all the sides of a vessel is found by multiplying the sum of the areas of all the sides into a height equal to half that at which the liquid stands." When bodies are sunk in a liquid, the liquid exerts a pressure which depends conjointly on the surface of the solid and the depth to which its center is sunk. Thus, if into a deep vessel of water we plunge a bladder, to the neck of which a tube is tied, the bladder and part of the tube being filled with colored water, it will be seen, as the bladder is sunk, that the colored water rises in the tube. A pressure exerted against one portion of a liquid is instantly communicated throughout the whole mass, each particle transmitting the same pressure to those around. A striking illustration of this is seen when a Prince Ru- pert's drop is broken in a glass of water, the glass being instantly burst to pieces. Bramah's press, or the Hydrostatic press, is an illus- tration of the principle developed in this lecture — that every particle of a fluid transmits the pressure it receives, in all directions, to those around. It consists of a i What is meant by the hydrostatic paradox ? Give the rule for finding lateral pressures. Prove that a liquid exerts a pressure on bodies plungeu in it. Give an illustration of the instantaneoui ':ominunication of pressure THE HYDRAULIC PRESS. 49 metallic forcing-pump, a. Fig. 55, in which a piston, s, is worked by a lever, cbd. This little pump communicates with a strong cyl- indrical reser- voir, A, in which awater-tightpis- ton, S, moves, having a stout flat head, P, be- tween which and a similar plate, R, supported in a frame, the sub- stance to be com- pressed, W, is placed. The cyl- inder, A, and the forcing-pump, with the tube communicating between them, are filled with water, the quantity of which can be in- creased by working the lever, d. Now it is obvious that any force, impressed upon the surface of the water in the small tube, a, will, upon the principles just described, be transmitted to that in A, and the piston, S, will be pushed up with a force which is proportional to its area, compared with that of the piston of the little cylinder, a. If its area is one thousand times that of the little one, it will rise with a force one thousand times as great as that with which the little one descends — ^the motive force ap- plied at d, moreover, has the advantage of the leverage in proportion as c cZ is greater than e b. On these princi- ples it may be shown that a man can, without difficulty, exert a compressing force of a million of pounds by the aid of such a machine of comparatively small dimensions. Describe the hydraulic press. c so SPECIFIC GRAVITY. LECTURE XI. PECiFic GrRATiTY. — Definition of the term. — The Stand- ards of Comparison. — Method for Solids. — Case when the Body is Lighter than Water. — Method for Liquids by the Thousand- Grrain Bottle. — Effects' of Temperature. — Standards of Temperature. — Other Methods for Li- qudds. — Method for Gases. — Effects of Temperature and Pressure. — The Hydrometer or Areometer. By the specific gravity of bodies we mean the propor- tion subsisting between absolute weights of the same vol- ume. Thus, if we take the same volume of water and copper, one cubic inch of each, for example, we shall find that' the copper weighs 8vS times as much as the water: and the same holds good for any other quantity, as ten cubic inches or one cubic foot. When of the same vol- ume the copper is always 8'6 times the weight of the water. Specific gravity is, therefore, a relative affair. We must have some substance with which others may be compared. The standard which has been selected for solids and liquids is water ; that for gases and vapors, atmospheric air. When we speak of the specific gravity of a substance which is of the liquid or solid kind, we mean to express its weight compared with the weight of an equal volume of water. Thus, the specific gravity of mercury is 13*5; that is to say, a given volume of it would weigh 13'5 times as much as an equal volume of water. Apparently the simplest way for the determination of specific gravities of solids, would be to form samples of a uniform volume ; as, for instance, one cubic inch. Their absolute weight, as determined by the balance, would be their specific gi'avities. But in practice so many difficulties would be encoun- tered in such a process that its results would be quite in- What is meant by specific gravity 1 What are the standards of com- parison ? Describe an apparently simple method of determining the spe- cific gravity of solids. THOUSAND-GRAIN BOTTLE. 51 exact ; and tbe principles of hydrostatics furnish us with far more accurate means for resolving such problems. To determine the specific gravity of a solid body, it is to be weighed first in air and then in water. In the latter instance it will weigh less than in the former, because it displaces a quantity of the water equal to its own volume, and this deficit in weight is the weight of the water so displaced. The weight in air and the loss in water being thus determined, to find the specific gravity, " Divide the weight in air by the loss in water, and the quotient is the Specific gi-avity." If the body be lighter than water, there must be affixed to it some substance sufficiently heavy to sink it, the weight of which, and also its loss of weight in water are previously known. Deduct this weight from the loss of the bodies when immersed together, and divide the abso- lute weight of the light body by the remainder ; the quo- tient gives the specific gravity. For the determination of the specific gravity of liquids several methods may be resorted to. One of the most simple is by the Thou- sand-grain Bottle. This consists of a light glass flask, a, Fig. 56, the stopper of which is also of glass with a fine per- foration, b, through it. When the bot- tle is filled with distilled water, and the stopper inserted in its place, any excess of liquid is forced through the perfora- tion, and the bottle, on being weighed, should be found to contain one thousand grains of the Hquid exactly. If any other liquid be in like manner placed in this bottle, by merely ascertaining its weight we at once de- termine its specific gravity. Thlas, if it be filled with oil, of vitrol or muriatic acid, it will be found to hold 1845 grains of the ,'brmer and 1210 of the latter. Those num- bers, therefore, represent the specific gravities of the bodies respectively. This instrument enables us to illustrate, in a very satis- factory manner, the effect of temperature on specific grav Give the general hydrostatic method. What is done when the body ia lighter than water ? Give the method in the case of liquids by the Tbou- Band-grain Bottle. 52 STANDARDS OF TEMPERATURE. ity. It has been said that the Thousand-grain bottle is so called from its containing precisely one thousand grains of water ; but very superficial consideration satisfies us that this can only be the case at a particular temperature. Suppose the bottle is of such dimensions that at 60° Fah- renheit it contains exactly one thousand grains, if we raise its temperature to 70° FaKrenheit, the water will expand, or if we lower it to 50° Fahrenheit it will contract exact- ly as if it were a liquid in a thermometer. It is, there- fore, very clear that temperature must always enter into these considerations, and that before we can express the relation of weight between any substance, whether solid or liquid, and that of an equal volume of water, we must specify at what particular temperature the experiment was made. For many purposes 60° Fahrenheit is select- ed, and for others 391° Fahrenheit, which is the temper- ature of the maximum density of water. There is a second method by which the specific gravity of fluids may be known. It is to weigh a given solid (as a mass of glass) in the fluids to be tried, and determine the loss of weight in each case. Inasmuch as the solid displaces its own volume of the different liquids, the losses it experiences when thus weighed will be proportional to the specific gravities. The follovidng rule, therefore, ap- plies : " Divide the loss of weight in the different liquids by the loss of weight in water, and the quotients will give the specific gravities of the liquids under trial." For the determination of the specific gravities of gases a plan analogous in principle to that of the Thousand-grain bottle is resorted to. A light glass flask, g, exhausted of air, is attached by means of the stop-cocks, e d, to the jar, c, containing the gas to be tried. This gas has been _ passed through a drying-tube, a, by means of a bent pipe, h, into the jar, c, over mercury. On Describe the effects of temperature on specific gravity. Give another method for determining the density of liquids. Hov^ is that of gases dis- covered ? Fig. 57. THE HYDROMETER. 53 opening the stop-cock the gas flows into g, and its weight may then be determined by the balance. From the greater dilatation of gages by heat, all that has been just said in relation to the effect of temperature on specific gravity applies here still more strongly. It is to be recollected that this form of bodies is compared with atmospheric air taken as the standard. For gases another disturbing agency beside tempera- ture intervenes — it is pressure. Atmospheric pressure is incessantly varying, and the densities of gases vary with it. It is not alone the thermometer, but also the Barom- eter which must be consulted, and the temperature and pressui'e both specified. Besides, great care must be taken in transferring the gas from, the jars in which it is con- tained, that it is not subjected to any accidental pressures in the apparatus itself, and that the flask in which it is weighed is not touched by the hands or submitted to any other warming or cooling influences. For the determination of the densities of liquids there is still another method, 'often more convenient than the former, and very commonly resorted to, it is by the aid of instruments which pass under the name of Hydrometers or Areometers. The principle on which these act is, that when a body floats upon water, the quantity of fluid displaced is equal in volume to the volume of the part of the body immersed, and in weight to the weight of the whole body. Thus, a piece of cork floating on the surface of quick- silver, water, and alcohol, sinks in them to very different depths : in the quicksilver but little, in the water more, and in the alcohol still deeper; but in every instance the weight of the quantity of the liquid displaced is equal to that of the cork. It is plain, therefore, that to determine the specific gravity of a liquid, WJ have only to determine the depth to which a floating body will be immersed in it. , The hydrometer fulfills these conditions. It consists of a cylin- drical cavity of glass, A, Fig. 58, on the lower part of which a spherical bulb, B, is blown, the latter being filled with a suitable quantity of small shot or quicksil- What clisturbing effects are encountored in the case of gases ? On what principle is the hydrometer constructed. 54 THE HYDROMETKR. ver. From the cylindrical portion, A, a tube, C, rises, in the interior of which is a paper scale bearing the divisions. Ffff. 58 The whole weight of the instrument is such that it floats in the liquid to be tried, and if that liquid is to be compared with water, and is lighter than water, the zero of the divided scale is toward the lower end of the paper; but if the liquid be heavier than water, the zero is toward the top of the scale. Tables are usually constructed so that, by their aid, when the point at which the hydrometer floats in a given liquid is determined in any experiment, the specific gravity is ex- pressed opposite that number in the table. Of these scale-hydrometers we have several different kinds, according as they are to deter- mine different liquids. Among them may be mentioned Fig. 59. Beaume's hydrometer, an instrument of con- stant use in chemistry. In the finer kinds of areometers the weighted sphere, B, Fig. 58, forms the bulb of a delicate thermometer, the stem of which rises into the cavity, A. This enables us to determine the temperature of the liquid at the same time with its specific gravity. Nicholson's gravimeter is a hydrometer which enables us to determine the density either of solids or liquids. It is represented at Fig. 59. Describe the hydrometer. HYDROSTATIC PRESSURE. 55 LECTURE XII. Hydrostatic Pressures and Formation op Fount- ains. — Fundamental Fact of Hydrostatics — holds also for Gases. — Illustrations of Upward Pressure. — . Determination of Specific Gravities of Liquids on these Principles. — Theory of Fountains. — Cause of Natural Springs. — Artesian Wells. The fundamental fact in hydrostatics thus appears to be, that as each atom of a liquid yields to the influence of gravity without being restrained by any cohesive force, all the particles of such a mass must press upon those which are immediately beneath them, and therefore the pressure of a liquid must be as its depth. The same fact has already been recognized for elastic fluids, in speaking of the mechanical properties of the earth's atmosphere, which, for this very reason, and also from the circumstance that it is a highly compressible body, possesses different densities at different heights The lower regions have to sustain or bear up the weight of all above them, but as we go higher and higher diis wei^t tecomes less and less, until at the surface it ceases to exist at all. We have already shown from the nature of a fluid such pressures are propagated equally in all directions, up- ward and laterally, as well as downward. This important principle deserves, how- ever, a still further illustration from the consequences we have now to draw from it. Let a tube of glass, a b. Fig. 60, have its lower end, b, closed writh a valve slightly weighted and opening upward, the end, a, being open. On holding the tube in a vertical position, the valve is kept shut by its own weight. But if we depress it in What is the fundamental fact in hydrostatics ? Does this hold for elastic fluids ? Describe the illustration represented in Fig. 60. How mav it be made to prove ths downward pressure of water f lig.W. 56 LiaUIDa SEEK THEIR LEVEL. Pig. 61. a vesBel of water, as soon as a certain depth is reached the upward pressure of the water forces the valve, and the tube begins to fill. Still further, if before immersing the tube we fill it to ike height of a few inches with water, we shall find that it must now be depressed to a greater depth than before, because the downward pressure of the included water tends to keep the valve shut. From the same principles it follows, that whfenever a liquid has freedom of motion, it will tend to arrange itself so that all parts of its surface shall be equidistant from the center of the earth. For this reason the surface of water in basins and other reservoirs of limited extent is always in a horizontal plane ; but when those surfaces are of greater extent, as in the case of lakes and. the sea, they necessarily exhibit a rounded form, conforming to the figure of the earth. It is also to be remembered that, when liquids are included in narrow tubes, the phenomena of cap- illary attraction disturb both their level and surface-figure. All liquids, therefore, tend to find their own level. This fact is well illustrated by the instrument, /J Fig. 61, consisting of a cylinder H of glass, a, connected by means of // a horizontal branch with the tube, '.' b, which moves on a tight joint at, ' c. By this joint, h can be- set par- allel to a, or in any other position. If a is filled with wa- ter to a given height, the liquid immediately flows through the hori- zontal connecting pipe, and rises to the same height in b that it occupies in a. Nor does it matter whether b be parallel to a, or set at any inclined position, the liquid spontaneously adjusts itself to an equal altitude. The same liquid always occupies the same level. But when in the branches of a tube we have liquids, the specific gravities of which are different, then, as has already been stated in Lecture What is the surface-figure of liquids ? Describe the illustration given in Fig. 61. What is the law of different liquids pressing on each other in a tube 7 Fig. m c f .14 - :i3 -10 a n -s A _x 0%^ FORMATION r, FOUNTAINS. 51 Fig.es X.,they rise to difFei-ent liBights. The law which deter- mines this is, "The heights of different fluids are inversely as their specific gravities." If, therefore, in one of the branches of a tube, a h. Fig. 62, some quicksilver is poured so as to rise to a height of one inch, it will require in the other tube, b c, a, column of water l^h inches long to equilibrate it, because the specific gravities of quick- silver and water are as 13| to 1. A very neat instrument for illustrating these facts is shown in Fig. 63. It consists of two long glass tubes, a h, which are con- nected with a small exhausting-syringe, c, their lower ends being open dip into the cups, w a, in which liie liquids whose. spe- cific gravities are to be tried are placed. Let us suppose they are water and alcohol. The syringe produces the same degree of partial exhaustion in both the tubes, and the two li- quids equally pressed up by the atmospher- ic air, begin to rise. But it will be found that the alcohol rises much higher than the vvater — to a height which is inversely pro- portional to its specific gravity. When in the instrument. Fig. 61, we bend the tube, b, upon its joint, so that its end is below the water-level in a, the liquid now be- gins to spout out: or if, instead of the jointed tube, we have a short tube, C e D, Fig. 64, proceeding from the reservoir, A B, the wa- ter spouts from its termination and forms a fountain, E F, which rises nearly to the same height as the water-level. The resistance of the air and the descent of the falling drops shorten the altitude, to which the jet rises to a certain extent. On the top of the fountain a cork ball, G, may be s spended by the play- ing water. The same instrument may be used to show B the equality of the vertical and lateral press- uies at any point. For let the tube, D'E, be removed s At what heights will quicksilver and water stand ? Describe the instru- ment, Fig. 63. What fact does it show ? Under what circumstances doei a liquid spout t How may a fountain bs formed ? mm. 58 FORMATION OF FOUNTAINS. as to leave a circular aperture at e; also let C be a plug closing an aperture in the bottom of exactly the same size as e. Now if the reservoir, A B, be filled to the height g, and kept at that point by continually pouring in water, and the quantities of liquid flowing out through the lateral aperture, e, and the vertical one, C, be measured, they will be found precisely the same, showing, therefore, the equality of the pressures ; but if an aperture of the same size were made at J", the quantity would be found corre- spondingly less. It is upon these principles that fountains often depend. The water in a reservoir at a distance is brought by pipes Fig. 65. to the jet of the fountain, and there suffered to escape. The vertical height to which it can be thrown is as the height of the reser- voir, and by having several jets variously ar- ranged in respect of one another, the fount- ain can be made to give rise to different fan- ciful forms, as is the case with the public fountains in the city of New York. A simple method of exhibiting the fount- ain is shown in Fig. 65. A jar, G-, is filled with water, and a tube, bent as at a b c, is dipped in it. By sucking with the mouth at a, the water may be made to fill the tube, and then, on being left to itself, will play as a fountain. On similar principles we account for the occurrence of springs, natural fountains, and Artesian wells. The strata composing the crust of the earth are, in most cases, in po- sitions inclined to the horizon. They also differ very greatly from one another in permeability to water — sandy and loamy strata readily allowing it to percolate through them, while its passage is more perfectly resisted by tenacious clays. On the side of a hill, the superficial strata of which are pervious, but which rest on an imper- vious bed below, the rain water penetrates, and being guided along the inclination, bursts out on the sides of the hill or in the valley below, wherever there is a weak place or where its vertical pressure has become sufficiently pow erful to force a way. This constitutes a common spring. Prove the equality of vertical and lateral pressures by the instrument, ^ig. 64. What is the principle of fountains ? Describe the apparatus. Fig W. On what priacipU do springs flow from the groMnd ? ARTESIAN WELLS. 59 The general principle of the Artesian or overflowing wells is illustrated in Fig. 66. Let V h c d, be the sur- face of a region of country the strata of which, b b' and Fig 66. d d', are more or less impervious to water, while the in- ter-mediate one, c c, of a sandy or porous constitution, al- lows it a freer passage. When in the distant sandy coun- try at c, the rain falls, it percolates readily and is guided by the resisting stratum, d d'. Now if at a, a boring is - made deep enough to strike into c c or near to d' on the principles which we have been explaining, the water will tend to rise in that boring to its proper hydrostatic level, and therefore, in many instances, will overflow at its mouth. The region of country in which this water ori- ginally fell may have been many miles distant. It follows, from the action of gravity on liquids, that if we have several which differ in specific gravity in the same vessel, they will arrange themselves according to their densities. Thus, if into a deep jar we pour quick- silver, solution of sulphate of copper, water, and alco- hol, they will arrange themselves in the order in which they have been named. What are Artesian wells 1 When several liquids are in the same vessel, how do they arrange themselves ? fiO or FLOWING LiaUIDS. LECTURE XIII. Op Flowing Liquids and Hydraulic Machines. — Laws of the Flowing of Liquids. — Determination of the Quan- tity Discharged. — Contracted Vein. — Parabolic Jets. — Relative Velocity of the Parts of Streams. — Undershot, Overshot, Breast- Wheels. — Common Pump. — Forcing- Pump. — Vera's Pump. — Chain-Pump. If a liquid, the particles of which have no cohesion, flows from an aperture in the bottom of its containing ves sel, the particles so descending fall to the aperture with a velocity proportional to the height of the liquid. The force and velocity with which a liquid issues de- pend, therefore, on the height of its level — the higher the level the greater the velocity. As the pressures are equal in all directions, and as it is gravity which is the cause of the flow, " The velocity which the particles of a fluid acquire when issuing from an orifice, whether sideways, upward, or downward, is equal to that which they would have acquired in falling perpen- dicularly from the level of the fluid to that of the orifice." When a liquid flows from a reservoir which is not re- plenished, but the level of which continually descends, the velocity is uniformly retarded : so that an unreplen- ished reservoir empties itself through a given aperture in twice the time which would have been required for the same quantity of water to have flowed through the same aperture, had the level been continually kept up to the same point. The theoretical law for determining the quantity of wa- ter discharged from an orifice, and which is, that " the quantity discharged in each second may he obtained by mul- tiplying the velocity by the area of the aperture" is nut found to hold good in practice — a disturbance arising from the adhesion of the particles to one another, from their On what does the velocity of a flowing liquid depend ? What is that ve locity equal to ? What is the difference of flow between a replenished am' an unreplenished reservoir? Why does not the theoretical law for the dis charge of water hold good ? THE CONTRACTED VEIN. 61 friction against the aperture, and from the formation of what is designated " the contracted vein." For when wa- ter flows through a circular aperture in a plate, the diam- eter of the issuing stream is contracted and Kg-. 67. reaches its minimum dimensions at a distance about equal to that of half the diameter of the aperture, as at s s. Fig. 67. This effect arises from the circumstance that the flowing water is not alone that whichis situated perpendicularly above the orifice, but the lateral portions likewise move. These, therefore, going in oblique directions, make the stream depart from the cylindrical form, and contract it, as has been described. By the attachment of tubes of suitable shapes to the ap- ertui-e, this effect may be avoided, and the quantity of flowing water very greatly increased. A simple aperture and such a tube being compared together, the latter was found to discharge half as much more water in the same space of time. As the motion of flowing liquids depends on the same laws as that of falling solids, and is determined by gravi- ty, it is obvious that the path of a spouting jet, the direc- tion of which is parallel or oblique to the horizon, will be a parabola ; for, as we shall hereafter see, that is the path of a body projected under the influence of gravity in vacuo. When a liquid is suffered to escape in a horizontal direc- tion through the side of a vessel, it may be easily shown to flow in a parabolic path, as in Fig. 68. The maximum distance to which a jet Can ^*s- 68. reach on a horizontal plane is, when the opening is half the height of the liquid, as at C, and at points B and D equidistant from C, it spouts to equal distances. To measure the velocity of flowing water, floating bodies are used : they drift, immersed in the stream un- der examination. A bottle i What is meant by the " contracted vein ?" From what does this arise ? How may the quantity of flowing water be increased ? What is the path }f a spouting iet? 62 WATER-WHEELS. partly filled with water, so that it will sink to its neck, with a small flag projecting, answers very well; or the num- ber of revolutions of a wheel accommodated with float- boards may be counted. In any stream the velocity is greatest in the middle (where the water is deep- est), and at a certain distance from the surface. From this point it diminishes toward the banks. Investigations of this kind are best made by Pictot's stream- measurer. Fig. 69. It consists of a ver- tical tube with a trumpet-shaped extrem- ity, bent at a right angle. When plung- ed in motionless water the level in the tube corresponds with that outside, but the impulse of a stream causes the water to rise in the tube until its vertical press- ure counterpoises the force. The force of flowing water is ofl:en employed for various purposes in the arts. We have several different kinds of water-wheels, as the undershot, the overshot, and the breast-wheel. The first of these consists of a wheel or drum revolving upon an axis, and on the periphery there are placed float- , boards, a h c d, &c. It is to be fixed so that its lower floats are immersed in a running stream or tide, and is driven round by the momentum of the current. Fig.71. The overshot-wheel, in like manner, consists of a cylinder or drum, with a series of cells or buckets, so arranged that the water which is delivered by a trough, A B, on the upper- most part of the wheel, may be held by the de- scending buckets as long as possible. It is the weight How may the velocity of flowing water be measured ? Describe the stream-measurer. What is the undershot-wheel ? What is the overshot wheel? 63 on its Fig. 12. mg.i3. COMMON PUMP. of this water that gives motion to this wheel axis. The breast-wheel, in like manner, con- sists of a drum work- ing on an axis, and having flc at - boards on its periphery. It is placed against a wall of a circular form, and the water brought to it fills the buckets at the point A, and turns the wheel, partly by its momentum and partly by its weight. Of these three forms the overshot-wheel is the most powerful. There are a great mariy con- trivances for the purpose of rais- ing water to a higher level. These constitute the different varieties of pumps. The common pump is repre- sented in Fig. 73. It consists of three parts : the suction-pipe, the barrel, and the piston. The suc- tion-pipe,ye, is of sufficient length to reach down to the water, A, proposed to be raised from the reservoir, L. The barrel, C B, is a perfectly cylindrical cavity, in which the piston, Gr, moves, air- tight, up and down, by the rod, d. It is commonly moved by a lever, but in the figure a rod and han- dle, D E, are represented. On one side is the spout, P. . At the top of the suction-pipe, at H, there is a valve, b, and also one on the piston, at a. They both open upward. When the piston is raised from the bottom of the barrel and again depressed, it exhausts the air in What is the breast-wheel 7 Which of these ia the most powerful t Deicribe the lifting-pump. 64 THE FORCING-PVMP. the suction-pipe, and the water rises from the reservoir, pressed up by the atmosphere. After a few movements of the piston the baiTel becomes full of water, which, at each successive lift, is thrown out of the spout, F. The action of this machine is readily understood^ after what has been said of the air-pump, which it closely resembles in structure. In the forcing-pump the suction pipe, e L, is commonly short, and the piston, g, has no valve. On the box at H, there is a valve, b, as in the former machine, and when the piston is moved upward in the barrel, C B, by the handle, E, and rod, D d, the water. A, rises from the reser- voir, L, and enters the barrel. During the downward move- ment of the piston the valve, h, shuts, and the water passes by a channel round m, through the lateral pipe, M O M N, into the air vessel, K K. The entrance to this air-vessel at P, is closed by a valve, a, and ll -e proceeds from it a ver- l 1 tube, H G, open at both e Is. After a few movements 1 the piston, the lower end, T if this tube becomes cov- e i with water, and any fiir- rl • quantity now thrown in compresses the air in the space, H G, which, exerting its elastic force, drives out the water in a continuous jet, S. The reciprocating motion of the piston may, therefore, be made to give rise to a continuous and unintermitting stream by the aid of the air-vessel, K K. Among other hydraulic machines may be mentioned Vera's pump, more, however, from its peculiar construe lion than for any real value it possesses. It consists of » Describe the forcing-pump. THE OHAIN-PUMP. 65 pair of puTJgys, over which a rope is made to run rapidly, the lower one is immersed in the wa- Fig.is. ter to be raised. By adhesion a por- tion of the water follows the rope in its movements, and is discharged into a receptacle placed above. The chain-pump consists of a series of flat plates held together by pieces ^^ of metal, so arranged that, by turning ^j^' an upper wheel, the whole chain is & made to revolve, on one side ascending / and on the other descending. As the flat plates pass upward they move through a trunk of suitable shape, and ' therefore continually lift in it a column of water. The chain-pump requires deep water to work in, and cannot completely empty its reservoir, but it has the advantage of not being liable to be choked. LECTURE XIV. Hydraulic Machines. — Theory op Flotation. — Archi- medes' Screw, — The Syphon acts by the Pressure of Air. — The Descent, Ascent, and Flotation of Solids in Liquids. — Quantity of Water displaced by a Floating Solid. — Case where fluids of different densities are used. — Equilibrium of Floating Solids. The screw of Archimedes is an ancient contrivance, invented by the philosopher whose name it bears, for the purpose of raising water in Egypt. It consists of a hol- low screw-thread wound round an axis, upon which it can be worked by means of a handle. The lower end of this spiral tube dips in the reservoir from which the water is to be raised, and by turning the handle the water con- tinually ascends the spire and flows out at its upper extremity. The syphon is a tube with two branches, C E, D E, What is Vera's pump ? Describe the chain-pump. Describe the screw of Archimedes. What is a syphon ? 60 THE SYPHON. Fig. 76, of unequal length, often employed in the arts for p- yg the purpose of raising or decanting liquids. The method of using it is first to fill it, and then placing the shorter branch in the vessel, B, to be decanted, the liquid ascends to the bend and runs down the longer branch. It is obvious that this mo- tion arises from the inequality of weight of the columns in the two branches. The long column over- balances the short one, and deter- mines the flow ; but this cannot take place without fresh quantities rising through the short branch, impelled by the pressure of the air. The syphon, therefore, is kept fiill by the pressure of the air, and kept running by the inequality of the lengths of the columns in its branches. This inequality is not to be measured by the actual lengths of the glass branches themselves, but it is to be estimated by the difference of level, A, of the liquid in the vessel to be decanted and the free end, D, of the Syphon. That this instrument acts in consequence of the press- ure of the air is shown by making a small one discharge quicksilver under an air-pump receiver. Its action will cease as soon as the air is removed. By the aid of a syphon liquid^ of different specific gravities may be drawn out of a reservoir without dis- turbing one another, and those that are in the lower part without first removing those above. Upon the same prin- ciple water may also be conducted in pipes over elevated grounds. Of the Floating of Bodies in Liquids. A solid substance will remain motionless in the interior of a li juid mass when it is of the same specific gravity. Under these circumstances the forces which tend to make it sink are its own weight and the weight of the column Why does water ascend in its short branch ? Why does it run from the longer 1 How is the inequality of the branches measured ? How can it be proved that its action depends on the pressure of the air ? What are the uses of the syphon t Under what circumstances will a solid remain motionless in a liquid? OF FLOATING BODIES. 67 of water which is above it. But as its weight is the same as that of an equal volume of the liquid in which it is immersed, this downward tendency is counteracted and precisely equilibrated by the upward pressure of the surrounding liquid. Consequently the solid remains mo- tionless in any position, precisely as a similar mass of the liquid itself would be. But if the density of the immersed body is greater than that of an equal bulk of the liquid, then the downward forces preponderate over the upward pressure, and the solid descends. If, on the other hand, the solid is hghter than an equal volume of the liquid, the upward pressure of the sur- rounding liquid overcomes the downward tendency, and tl^ body rises to the surface and floats. In the act of floating, the body is divided into two regions : one is immersed in the liquid and the rest is in the air. The part which is immersed under the surface of the liquid is siuih as displaces a quantity of that liquid as is precisely equal in weight to the Tig. 77. floating solid. This may be proved experimentally. Fill a glass. A, with water until it runs off through the spout, a, then immerse in it a floating body, such as a\Svooden ball; the ball will displace a quantity of water, which, if it be collected in the receiver, B, and weighed, will be found precisely equal to the weight of the wood. In any fluid a solid body will therefore sink to a depth which is greater as its specific gravity more nearly ap- proaches that of the liquid. As soon as the two are equal the solid becomes wholly immersed. In fluids of different densities any Abating body sinks deeper in that which has the smallest density. It will be recollected that these are the principles which are in- volved in the action of hydrometers. They are also applied in the case of specific-gravity bulbs, which are small glass bulbs, with solid handles, adjusted by the Under what will \\, rise, and under what will it sink ? What portion of the floating body is immersed 1 How may this be proved ? How do the specific gravities of the solid and the liquid on which it floats affect the phenomenon T 68 THE BALL-COCK. maker, so as to be of different densities. When a num ber of these are put into a liquid some will float and some will sink ; but the one which remains suspended, neither floating nor sinking, has the same specific gravity as the liquid. That specific gravity is determined by the mark engraved on the bulb. When a body floats on the surface of water it tends to take a position of stable equilibrium. The principles brought in operation here will be more fully described when we come to the study of the center of gravity of bodies. For the present, it is sufficient to state that sta- ble equilibrium ensues when the center of gravity of the floating solid is in the same vertical line as the center of gravity of the portion of fluid displaced, and as respects position beneath it. These considerations are of great im- portance in the art of ship-building, and also in the right distribution of the cargo or ballast of a ship. Pig. 78. The principle of flotation is in- geniously applied in the ball-cock, an instrument for keeping cisterns or boilers filled with a regulated amount of water. Thus, suppose that m 71, Fig. 78, be the level of the water in the boiler of a steam- engine ; on its surface let there float a body, B, attached by means of a rod, F a, to a lever, a c b, which works on the fulcrum c ,• on the other side of the lever, at h, let there be attached, by the rod b Y, a. valve, V, allowing water to flow into the boiler, through the feed-pipe, V O. Now, as the level of the water, m n, in the boiler lowers through evaporation, the float, B, sinks with it, and de- presses the end, a, of the lever ; but the end, b, rising, lifts the valve, V, and allows the water to go down the feed- pipe; and as the level again rises in the boiler the valve, V, again shuts. Instead of a piece of wood or hollow cop- per ball, a flat piece of stone, B, is commonly used ; and to make it float it is counterpoised by a weight, W, on the opposite arm of the lever. How are specific-gravity bulbs used ? What is the position of stable ' equilibrium in a floating body ? Describe the construction and action of the ball-cock. MOTION AND REST. 69 OF REST AND MOTION. MECHANICS. LECTURE XV. Motion and Rest. — Causes of Motion. — Classification of Forces. — Estimate of Forces. — Direction and Intensity. — Uniform and Variable Motions. — Initial and Final Velocities. — Direct, Rotatory, and. Vibratory Motions. All objects around us are necessarily in a condition either of motion or of rest. We shall soon find that mat- ter has not of itself a predisposition for one or other of these states ; and it is the business of natural philosophy to assign the paiticular causes which determine it to either in any special instance. A very superficial investigation soon puts us on our guard against deception. Things may appear in motion which are at rest, or at rest when in reality they are in motion. A passenger in a railroad car sees the boiises and trees in rapid motion, though he is well assured that this is a deception — a deception like that which occurs on a greater scale in the apparent rev- olution of the stars from east to west every night — the true motion not being in them, but in the earth, which is turn ing in the opposite direction on its axis. If deceptions thus take place as respects the state of motion, the same holds good as respects the state of rest. On the surface of the earth even those objects which seem to us to be quite stationary are not so in reality. Natu- ral objects, as mountains and the various works of man, though they seem to maintain an unchangeable relation as respects position with all the world for centuries together, are but in a condition of relative rest. They are, of What two states do bodies assume ? What deceptions may occur in le lation to motion and rest ? What is meant by relative and what by abaO' lute rest ? 70 MOTION AND REST. course, affected by the daily revolution of the earth on its axis, and accompany it in its annual movements round the sun. Indeed, as respects themselves, their parts are con- tinually changing position. Whatever has been affected by the warmth of summer shrinks into smaller space through the cold of winter. Two objects which maintain their position toward each other are said to be at rela- tive rest ; but we make a wide distinction between this and absolute rest. All philosophy leads us to suppose that throughout the universe there is not a solitary parti- cle which is in reality in the latter state. Whenever an object, from a state of apparent rest, com- mences tr mo ye, a cause for the motion may always be assigneu. And inasmuch as such causes are of different kinds, they may be classified as primary or secondary motive powers. The primary motive powers are univer- sal in their action. Such, for instance, as the general at- tractive force of matter or gravity. The secondary are transient in their effects. The action of animals, of elas- tic springs, of gunpowder, are examples. Of the second- ary forces, some are momentary and others more perma- nent, some giving rise to a blow or shock, and some to effects of a continued duration. Forces may be compared together as respects their in- tensities by numbers or by lines. Thus one force may be five, ten, or a hundred times the intensity of another, and that relation be expressed by the appropriate figures. In the same manner, by lines drawn of appropriate length we may exnibit the relation of forces ; and that not onlj as respects their relative intensity, but also in other par- ticulars. The direction (^motion resulting from the appli- cation of a given force may always be represented by a straight line drawn from the point at which the motioD commences toward the point to which the moving body is impelled. The point at which the force takes effect; upon the body is termed the point of wpplicatimi ; and the direction of motion is the path in which the body moves. To this special designations are given appropri- Is any object in nature in a state of absolute rest ? How may motive powers be classified ? What are primary motive powers ? Give examples of some that are secondary. How .may forces be compared together ? How may forces be represented ? What is rr.eant by the point of appli- cation 7 DIFFERENT KINDS OP MOTION 7) ate to the nature of the case, such as curvilinear, rectilin ear, &c. Moving bodies pass, over their paths with different de grees of speed. One may pass through ten feet in a sec ond of time, and another through a thousand in the sam« interval. We say, therefore, that they have different ve lodties. Such estimates of velocity are obviously ob tained by comparing the spaces passed over in a givei unit of time. The unit of time selected in natural phi losophy is one second. A moving body may be in a state of either uniform oj variable motion. In the former case its velocity contin- ually remains unchanged,- and it passes over equal dis- tances in equal times. In the latter its velocity under- goes alterations, and the spaces over which it passes ip equal times are different. If the velocity is on the in- crease it is spoken of as a uniformly accelerated motion. If on the decrease as a uniformly retarded motion. In these cases we mean by the term initial velocity the ve- locity which the body had when it commenced moving, as measured by the space it would then have passed over in one second ; and, by the final velocity, that which it pos- sessed at the moment we are considering it measured in the same way. The flight of bomb-shells upward in the air is an instance of retarded motion ; their descent down- ward of accelerated motion. The movement of the fingers of a clock is an example of uniform motion. There are motions of different kinds : 1st, direct ; 2d, rotatory ; 3d, vibratory. 1st. By direct motion we mean that in which all the parts of the whole body are advancing in the same direc- tion vdth the same velocity. 2d. By rotatory motion we imply that some parts of the body are going in opposite directions to others. The axis of rotation is an imaginary line, round which the parts of the body turn, it being itself at rest. 3d. By vibratory movement we mean that the body which changes its place returns toward its original posi lion with a motion in the opposite direction. Thus, the How are velocities measured 7 What is the unit of time ? What v meant by unifoim and what by variable motion ? What by initial and final velocity f What varieties of motion are there? Wliat is direct motion ? What is rotatory motion 1 What is vibratory motion 7 72 COMPOUND MOTION. particles of water which form waves alternately rise and sink, and the pendulum of a clock beats backward and forward. These are examples of vibratory or oscillatory movement. LECTURE XVI. Op the Composition and Resolution op Forces. — , Compound Motion. — Equilibrium. — Resultant. — 77ie Parallelogram of Forces. — Case where there are more Forces than Two. — Parallel Forces. — Resolution of Forces. — Equilibrium, of three Forces. — Curvilinear Motions. When several forces act simultaneously on a body, so as to put it in motion, that motion is said to be com- pound. In cases of compound motion, if the component or con- stituent forces all act in the same direction, the resulting eflfect will be equal to the sum of all those forces taken together. If the constituent forces act in opposite directions, the resulting effect will be equal to their difference, and Fig. 79. ' its direction will be that of the greater force. Thus, if to a knot, a. Fig. 79, we attach sev- eral weights, b c, by means of a string passing over a pulley, e, these weights will evidently tend to pull the knot from a to e. But Jh ^f '^ ^'^ '^^ same knot we attach a 'W weight,yj by a string passing over the pulley g, this tends to draw it in the opposite direction. When the weights on each side of the knot act conjointly, they tend to draw it oppo- site ways, and it moves in the direction of the greater What is compound motion? When the component forces all act in the same direction, what is their effect equal to ? What isi the result when they act in opposite directions I Under what circumstances are forces in equilibrio ? TA:; '. LLBLOGRAM OF FORCES. 73 If two forces of equal intensity, but in opposite direc- tions, act upon a given point, that point remains motion- less, and the forces are said to be in, (squilibrio. When there are many forces acting upon a point in equilibrio, the sum of all those acting on one side must be equal to . the sum of all the rest which act in the opposite direction. By the resultant offerees we mean a single forco which would represent in intensity and direction the conjoint action of those forces. If the constituent forces neither act in the same nor in opposite directions, but at an angle to each other, their resultant can be found in the following manner : — Let a be the point on which the forces act ; let one of them be represented in intensity and di- rection by the line a b, and the other likewise in intensity and direction by the line a c. Draw the lines b d, c d, so as to com- plete the parallelogram a b c d; draw also the diagonal, a d. This diagonal will be the resultant of the two forces, and will, therefore, represent their conjoint action in intensity and direction. The operation of lig.ei, pairs of forces upon a - point is readily under- 1^^' ^.^ - — — — _ a stood. Thus, 1st. On ^^ "^-^ __— — "^^ ■ a point, a, Mg. 81, let o two forces, a b, a c, act. Complete the parallelogram ab d c, and draw its diagonal, a d. This line will rep- resent in intensity and direction the resultant force 2d. On a point, a. Fig. 82, Fig.tn. let two forces again repre- sented in intensity and di- rection by the lines ab,ac, ^~ act. Complete the paral- lelogram abed, draw its diagonal, a d, which is the resultant, as before. Now, on comparing Fig. 81 with Fig. 82, it read ily appears that the resultant of two forces What is meant by a resultant ? Describe the parallelogram of forces. Give illustrations of the case in which the forces act nearly in the sams and also of that in which they act nearly in opposite directions. 74 ANGULAR AND PARALLEL FORCES. is greater as those forces act more nearly in the same direction, and less as those forces act more nearly iu op'posite directions. Many popular illustrations of the parallelogram of forces might be cited. The following may, however, suifice. If a boat be rowed across a river when there is BO current, it will pass in a straight line from bank to bank perpendicularly ; but this will not take place if there is a current, for as the boat crosses it is drifted by the stream, and makes the opposite bank at a point which is lower according as the stream is more rapid. It moves in a diagonal direction. On the same principles we can determine the common, resultant of many forces acting on a point. Two of the forces are first taken and their resultant found. This resultant is combined with the third force, and a second resultant found. This again is combined with the fourth force, and so on, un- ^/. til the forces are exhausted. The "*e final resultant represents the con- joint action of all. Thus, let there be three forces applied to the point a, represented in intensity and direction by the lines a h, ac,ad, Fig. 83, respectively ; if o S and a c be combined, they give as their resultant a e, and if this resultant, a e, be combined with the third force, a d, it yields the resultant af, which, therefore, represents the common action of all three forces. ^ie 84. The resultant of two paral- a p a' lei forces applied to a line, and on the same side of it, is equal to their sum and parallel to their direction. Thus, the forces a b, a' b' applied to the line a a', ,1 / It'- give a resultant, p r, parallel * 'to their common direction and equal to their sum. Give an illustration of the diagonal motion of a body under the influence of two forces. How may the resultant of more forces than two be found f What is the resultant of parallel 'brce" applied to a line on tbo same, 'vA on opposite sides ? RESOLUTION OF FORCES. 75 But when parallel forces are applied on opposite sides of a line, the resultant is equal to their difference, and its direction is parallel to theirs. In this, as also in the fore going case, the point at which the resultant acts is at a distance from the points at which the two forces act, inversely proportional 'to their intensities. In the fore- going case this point falls between the directions of the two forces, and in the latter on the outside of the direction of the greater force. The parallelogram of forces not f^g- 85. only serves to effect the composi- w^ jj' tion of several forces, but also the jr^" resolution of any given force ; that is to assign several forces which in their intensities and directions shall i^ be equivalent to it. Thus, let a f. Fig, 85, be the given, force; by '"-•v^^ ^\f making it the diagonal of a paral- e" lelogr^m it may be resolved into its components, ad,ae; in the same manner, a e, may be resolved into its compo- nents, a c, a b. Thus, therefore, the original force is resolved into three cpmpoheftts, ab, a c, a d. Upon similar principles, itfirtts^ be readily proved that two forces acting at any angle .upon a point can never maintain that point in equilibrio — but three forces may ; and in this instance, they will be. represented in intensity and direction by the thre^ ^des of a triangle, perpendic- ular to their respective directions. If two forces act upon a point in the direction of and in magnitude proportional to the, sides of a parallelogram, that point will be kept-, in equilibrio by a third force op- posed to them in the direction of the diagonal and pro- portional to it. On the table, a d, place a circular piece of paper, on which there-^is drg,wn any triangle, abc, c coin- ciding with the center of the tab1»; and let us suppose that the sides of this triangle are, as shown in the figure, in the proportion to one anothei-, as 2 3 4 ; draw upon the paper, c e, parallel to a b, and prolong a ctod. Take three strings, mdsing a knot at the point c, and by means of tha What is meant by the resolution of forces ? How does the parallelogram of forces serve for this purpose ? Can two forces acting at an angle upon point keep it in equilibrio? Can three? In this case what must be heir relation ? 76 COMPOSITION OP FORCES. *"»«■■ 86. movable pullies, ttt, stretch the Bti'ings over the lines c b, c d, c e ; at the end oi c d suspend a weight of four pounds, at the end of c e one of three pounds, and at the end of c 5 one of two pounds. The knot will remain in equilibrio, proving, there- fore, the proposition. In the composition of forces power must always be lost. Thus, in this experiment we see that a weight of three pounds and one of two pounds equipoise a weight of four pounds only. If of two forces acting upon a point one is momentary and the other constant, the point may move in a curve. Thus, if in Fig. 87, a shot be projected obliquely up- ward from a gun, it is under the ac- tion of two forces — the momentary force of the explosion of the gun- powder and the constant effect of t1}%fn attraction of the earth. It- describes, therefore, a curvilinear path, a b c, the direction of which continually declines toward the di- ■ rection af the constant force. It is only when a force acts' in a direction perpendicu- lar to a body that its full effect is obtained. This is easi- ly proved by resolving an oblique force into two others, one of which is perpendicular aiJd the other parallel to the side of the body acted upon. This Tatter force is, of course, lost. Why in the composition of forces is power always lost ? What is the result of the action of a momentary and a constant force upon a point 7 fn what direction must a force act to obtain its full «ffect ? INERTIA. 77 LECTURE XVII. Inertia. — Inertia a Property of Matter. — Indifference to Motion and Rest. — Moving Masses are Motive Powers. — Determination of the Quantity of Motion:— Momen- tum. — Action and Reaction. — Newton's Laws of Mo tion. — BoJinenherger's Machine. All bodies have a tendency to maintain their present condition, whether it be of motion or rest. It is only by the exertion of force that that condition can be changed. A mass of any kind, when at rest, resists the application of force to put it in motion, and when in motion resists any attempt to bring it to rest. This property is termed INERTIA. It is illustrated by many familiar instances : thus, loaded carriages require the exertion of far more force to put them in motion than is subsequently required to keep them going, and a train of railroad cars will run for a great distance after the locomotive is detached. Universal experience shows that inanimate bodies have' no power to produce spontaneous changes in their con- dition. They are wholly inactive. Even when in motion they exhibit no tendency whatever to alter their state. Thus, the earth rotates on its axis at the same rate which it did thousands of years ago, and the planetary bodies pursue their orbits with an unchangeable velocity. A moving mass can neither increase nor diminish its rate of speed, for if it could do the former it must necessarily have the power spontaneously to put itself in motion if it were in a condition of rest. Nor can such a mass, if in motion, change the direction of its movement any more than it can change its velocity. Such a change of direc- tion would imply the operation of some innate force, which of itself could have put the mass in movement. When ever, therefore, we discover in a moving body changes in direction or changes in velocity, we at once impute them What is meant by the terai inertia ? Give an illustration of inertia. What illustration have we that when bodies are in motion they do not spontaneously tend to come to rest? Can a moving mass increase or di- minish its rate^fj^qg^l Can it change its direction of itsel'7 ra MOMENTUM. to the agency of acting forces, and not to any innate power of the moving body itself ^s- 88. If an ivory ball, a. Fig. 88, ^ ^ be laid upon a sheet of paper, w. b c, on the table, and the paper " C suddenly pulled avyay, the ball does not accomp'any the movement but remains in the same place on the table. A person jumping from a carriage in rapid motion falls down, -because his body, still participating in the motion of the carriage, follows its direction after his feet have struck the earth. By the mass of a body we mean the quantity of mat- ter contained in it — that is, the sum of all its particles. The mass of a body depends on its volume and density. In consequence of their inertia, masses in motion are themselves motive powers. Such a mass impinging on a Kff-89. second tends to set it in motion. —^ _^ Thus, if a ball a, Fig. 89, moving w t w toward c, impinge upon a second ^ 6 , C ^all, h, of equal weight, the two will move together toward c, with a velocity one half of that which a originally had. In this case, therefore, a has acted as a motive force upon b, and it is obvious that the intensity of this action must depend on the magnitude and velocity of a, increasing as they increase and dimin- ishing as they diminish. The ball a is said, therefore, to have a certain momentum or moment, which depends part- ly upon its mass and partly upon its velocity; and the mo- ments of any two bodies may he compared by mvltiplying together the mass and velocity of each. Thus, if a body, A, has twice the mass of another, B, and moves with the same velocity, the momentum of A wHill be twice that of B ; but if A, having twice the mass of B, has only half its velocity the moments of the two will be equal. It is upon this principle that heavy masses moving very slowly exert a great force, and that bodies comparatively light, moving with great speed, produce striking effects. The battering-rams of the ancients, which were heavy masses moving slowly, did not produce more powerful Give an experimental illustration of inertia. How is it that moving bodies are themselves motive powers ? How is the quantity of motion or momentum of a body ascertained ? ACTION AND REACTION. 79 effects than cannon-shot, which, though comparatively light, move with prodigious ^peed. From the foregoing considerations, jt therefore appears that the amount of motion depends neither upon the mass alone nor the velocity alone. A certain mass, A, moving with a given velocity, has a certain momentum or quanti- ty of motion. If to A a second equal mass, B, with a sim- ilar velocity be added, the two conjointly will, of course, possess double the momentum of the first — the mass has doubled, though the speed is the same, and therefore the quantity of motion has doubled. Again, if a certain mass, A, moves with a given speed, arid a second one, B, moves with a double speed, it is obvious that this last will have twice the quantity of motion of the former. Here the masses are the same, but the velocities are different. The quantity of motion or momentum which a body possesses is, therefore, obtained by multiplying together the num- bers which express its mass and its velocity. Action and reaction are always equal to each other. The resistance which a given body exhibits is equal to the effect of any force operating upon it. This equality of action and reaction may be shown by an apparatus represented in Fig. 90, in which ^s- ^■ two balls of clay or putty, a b, are suspended by strings so as to move over a graduated arc. If one of the balls be allowed to fall upon the other, through a given number of degrees, it will com- municate to it a part of its mo- tion, and the following facts may be observed : 1st. The bodies, af- ter collision, move on together, and therefore have the same velocity. 2d. The quantity of motion remains unchang- ed, the one having gained as much as the other has lost, so that if the two are equal they will have half the veloc- ity after impact that the moving one had when alone. 3d. If equal, and moving in opposite directions with equul, velocities, they will destroy each other's motions and come Does the mass or the velocity, taken alone, measore the amount of mo- tion ? What is the relation between action and reaction ? What is the apparatus rnpresented in Fig. 00 intended to illustrate? Mention some oi the results. 80 NEWTONS LAWS. to rest. 4£h. If unequal, and moving in opposite direc- tions, they will come to rest when their velocities are in- versely as their masses. The following three propositions are called " Newton's laws of motion." They contain the results depending on inertia : — I. Every body must persevere in its state of rest or of uniform motion in a straight line, unless it be compelled . to change that state by forces impressed upon it. II. Every change of motion must be proportional to the impressed force, and must be in the direction of that straight line in which the .force is impressed. III. Action must always be equal, and contrary to re- action, or the action of two bodies upon each other must be equal and directed to contrary sides. As an example of the operation of inertia, and illustra- ting the invariability of position of the axis of the earth ^e- 91- during its revolution, I here describe Bohnenberger's machine. It consists of three movable rings, AAA, Fig. 91, placed at right angles to each other, AH I "^B IB and in the smallest ring there is a heavy metal ball, B, supported on an axis, which also bears a little roller, c. A thread being wound round this roller and any particular position being given to the axis, by quickly pulling the "^*" thread the ball may be set in rapid ro- tation. It is now immaterial in what position the instru- ment is placed, its axis continually maintains the same di- rection, and the ring which supports it will resist a con- siderable pressure tending to displace it. What are Newton's three laws of motion ? Describe Bohnenberger*' machine. What does it illustrate ? GRAVITATION. 81 LECTURE XVIIi; Gravitation. — Preliminary Ideas of Motions of Attrac- tion. — The Earth and Falling Bodies. — Laws of At- traction, as respects Mass and Distance. — Nature of Weight. — Absolute and Specific Weight.-^-The Plumb- Line. — Convergence of such Lines toward the EartVs Center. — Action of Mountain Masses. All material substances exert upon each other an at- tractive force. To this the designation of Gravity or Gravitation has been given. It was the great discovery of Sir I. Newton that the same force which prpduces the descent of a stone to the ground holds together the plan- ets and other celestial bodies. To obtain a preliminary idea of the nature an4 opera- tion of this force, let us suppose that two balls of equal weight be placed in presence of each other, and under such circumstances that no extraneous agency supervenes to interfere with their mutual action. Under these cir- cumstances, all the phenomena of nature prove that the two balls will commence moving toward each other with equal speed, their velocity continually increasing until they come in contact. Inasmuch, the^refore, as their masses are equal and their velocities equal, the quantities of motion they respectively possess will also be equal, as is proved in Lecture XVII. Again, let there be two other balls situated as before, but let one of them, B, be twice as large Ffg. 92. as A. Motion will again ensue by reason .„ of their mutual attraction, and they will ^ approach each other with a velocity con- W tinually increasing. In this instance, however, their speed will not be equal, the larger body, B, having a correspondingly less velocity than the smaller one, A. If, as we have supposed, it is twice as large, its What is meant by gravity? Give an explanation of the phenomena of he attraction of tvfo equal balls. Give a similar explanation in the case ■vbare the balls are unequal. 82 LAWS OF GRAVITATION. velocity vi^ill -be only one half. But in this, as in the former case, the quantity of motion that each possesses is the same, for that depends on velocity and mass con- jointly. Further, if of the two bodies one becomes infinitely great as respects the other, then it is obvious- that the lit- tle one alone will appear to move. This condition is what actually obtains in the case of our earth and bodies sub- jected to its influence. A mass of any kind, the support of which is suddenly removed, falls at once to the ground, and though in reality the earth moves to meet it just as much as it moves to meet the earth, the difference in these masses is so immeasurably great that the earth's motion is imperceptible and may be wholly neglected. The force by which bodies are thus solicited to move to the earth is called terrestrial gravity or gravitation. The force of gi-avity depends on two diffeifent condi- tions : 1st, the mass'; 2d, the distance. 1st. The intensity of the force of gravity is directly as the mass. That is to say, that, for example, in the case of the earth, if its mass were twice as large its force of attraction would be twice as great ; or if it were only half IS large its attraction would be only half as much as it is. 2d. In common with all other central forces, gravity diminishes as the distance increases. The law which de- Lormines this is expressed as follows : " The fojce of gravity is inversely as the square of the distance;" that is to say, if a"b6dy be placed two, three, four, five times its original distance from another, the force attracting it will continually diminish, and in those different instances will successively be four, nine, sixteen, twenty-five times less than at first. When a body, instead of being allowed to fall freely to the earth, is supported, its tendency to descend is not anni- hilated, but it exerts upon the supporting surface a degree of pressure. This pressure we speak of as weight. And inasmuch as the attractive force upon a body depends on its mass, it is obvious that, if the mass is doubled, the weight is doubled ; if the mass is tripled, the weight is Wliat is the relation in this respect between falling bodies and the earth ? On what two conditions does the Intensity of gravity depend ? What ia the law for the mass ? What is the law for the distanco ? What is weight ? ABSOLUTE AND SPECIFIC WEIGHT. 83 rriplod. Or, in other words, the weight of bodies is al- ways proportional to their mass. ' The absolute weight of a given body at the same place on the earth's surface is always the same ; for the mass, and, therefore, the attractive force of the earth never changes. If by any means the attractive influence of the earth could be doubled, the weight of every object would change, and be doubled correspondingly. The absolute weight of bodies is determined by bal- ances, springs, steelyards, and other such contrivances, as will be explained in their proper place. Difierent units of weight are adopted in dififerejit countries, and for dif- ferent purposes, as the grain, pifice, pound, gramme, &c. In bodies of the same nature the absolute weight is pro- portional to the voluipe. Thus a mass of iron which is twice the volume of another mass will also have twice its weight. But when we examine dissimilar bodies the result is very difierent. A globe of water compared with one of copper, or lead, or wood of the same size will have a very difierent weight. The lead^will weigh more than the water, and the wood less. This fact we have already pointed out by the term "specific gravity," or specific weight of bodies. And, inasmuch as it is obviously a relative thing or a matter of comparison, it is necessary to select some substance which Bhall serve to compare other bodies with : for solids and liquids water is taken as the unit or standard of compari- son. And we say that iron is about seven, lead eleven, quicksilver thirteen times as heavy as it ; or that they have specific gravities expressed by those numbers. The unit of comparison for gaseous and vaporous bodies is atmospheric air. When an unsupported body is allowed to fall its path is in a vertical line. If a body be suspended by a thread the thread represents the path in which that body would have moved. It occupies a vertical dftection, or is per- pendicular to the position which would be occupied by Is it constant for the same body t How is absolute weight determined? What units are employed? What connection is there between weight and volume in bodies of the same kind ? What is meant by specific grav ity ? What substance is the unit fo» solids and liquids ? What is the nnit for gases and vapors? 84 THE PLUMB-LINE. a surface of stagnant water. Such a thread is termed a plumb-line.. It is of constant use in the arts to determine horizontal and vertical lines. Fig. 93. If in two positions, A B, Fig. 93, on the earth's surface plumb-lines were sus- pended, it would be found that, though they are perpendicular as respects that surface, they are not parallel to one an- other, but incline, at a small angle, A C B, to each other. If their distance be one mile this convergence would amount to one minute; and if it be sixty miles the convergence would be one degree. Now, as the plumb-line indicates the path of a falling body, it is easily understood that on different parts of the earth's surface the paths of falling bodies have the inclinations just described. A little consideration shows that the de- scent of such bodies is in a line directed to the center, C, of the earth. That center we may therefore regard as the active- point, or seat of the whole earth's attractive influence. When examinations with plumb-lines are made in the neighborhood of mountain masses those masses exert a disturbing agency on the plummet, drawing the line from its true vertical position. But this is nothing more than what ought to take place on the theory of universal gravitation ; for that theory asserting that all masses ex- ert an attractive influence, the results here pointed out must necessarily ensue, and the lateral action of the moun- tains correspondingly draw ihe plummet aside. What is a plumb-line ? At considerable distances from one another are plumb-lines parallel ! What conclusion is drawn from this fact 1 Wh«t u the effect of mountain masses ? OF FALLING BODISS. 85 LECTURE XIX. The Descent op Falling Bodies. — Accelerated Motion. — Different bodies fall with equal velocities. — Laws of DesceM as respects Velocities, Spaces, Times. — Prin- ciple of Attwood's Machine. — It verifies the Laws of Descent — Resistance of the Atmosphere. Observation proves that the force with which a falling body descends depends upon the distance through which it has passed. A given weight falling through a space of an inch or two may give rise to insignificant results ; but if it has passed through many yards those results become correspondingly greater. Gravity being a force continually in operation, a falling body must be under its influence during the whole period of its descent. The soliciting action does not take effect at the first moment of motion and then cease, but it con- tinues all the time, exerting as it were a cumulative effect. The falling body may be regarded as incessantly receiv- ing a rapidly recurring series of impulses, all tending to drive it in the same direction. The effect of each one is, therefore, added to those of all its predecessors, and a uni- formly accelerated motion is the result. Falling bodies are, therefore, said to descend with a uni- forml'^ accelerated motion. As the attraction of the earth operates with equal in- tensity on all bodies, all bodies must Jail with equal ve- locities. A superficial consideration might lead to the erroneous conclusion that a heavy body ought to descend more quickly than a lighter. But if we have two equal masses, apart from each other, falling freely to the ground they will evidently make their descent in equal times or with the same velocity. Nor will it alter the case at all if we imagine them to be connected with each other by an inflexible line. That line can in" no manner increase or diminish their time of descent. What is the diflerence of effect when bodies have fallen through differ-: ent spaces ? Why does gravity produce an accelerated motion r Do all bodies fall to the earth with the same' or different velocities 7 56 LAWS OF FALLING BODIES. The spade through which a body falls in one second of time varies to a small extent in different latitudes. It is, however, usually estimated at sixteen feet and one tenth. As the effect of gravity is to produce a uniformly accelerated motion, the final velocities of a descending body will increase as the times increase; thus, at the end of two Beconds, that velocity is twice as-great as at one ; at the ead of" three seconds, three times as great ; at the end of four, four times, and so on. Therefore the final velocity dt the end Of the first second is 32^ feet " second " 64^ " " third " . • 96| • &c., l&C. The spaces through which the hody descends in equal successive portions of time increase as the numbers 1.3.5.7, &c. ; that is to say, as the body descends through sixteen feet and one tenth in the first second, the subsequent spaces will be For the first second I63V feet. " second " " third " &c.. 48^ ." 8OA " &c. and these numbers are evidently as 1.3.5, &c. The entire space through which a body fall^ increases as the squares of the times. Thus, the entire space is. For the first second , . . . 16^ feet. " second " . . 64| " " third " ■ ■ 144A " &c., &i. and these numbers are evidently as 1.4.9, &c., which are themselves the squares of the numbers 1.2.3, &c. If a hody continued falling with the final velocity it hao, acquired after falling a given time, and the operation of gravity were then suspended, it would descend in the same length of time through twice the space it fell through before relieved from the action of gravity. Is the space through which a body descends every where the same ? What is the relation between final velocities and times ? What relation is there between the spaces and times ? What between the entire spaces and times ? Suppose a body continues to fall, gravity being suspended, what is the relation of the space through which it will move with that it has already fallen through, the times being equal? ATWOOd's MACHINP. 87 The following table imbodies the results of the three P»st laws. I Times .... . . 1.2.3.4.5.6.7, &c. p^nal velocities 2.4.6.8.10.12.14, &c Space for each time .... 1.3.5.7.9.11.13, &c. Whole spaces . . . . . 1.4.9.16.25.36.49, &c. It would not be easy to confirm these results by ex periments directly made on falling bodies, the space described in the first second being so great (more thai sixteen feet), and the spaces increasing as the squares of the times. There is an instrument, however, known as Attwood's machine, in which the force of gravity being moderated without any change in its essential characters, we are enabled to verify the foregoing laws. The principle of Attwood's machine is this. Over a pulley, A, Fig. 94, let there pass a fine silk Fig- 94- line which suspends at its extremities equal j^l weights, b c. These weights, beiiig equally i ^[\v acted upon by gravity, will, of course, have OO* no disposition to move ; but now to one of the ^•-^ weights, c, let there be added another much smaller weight. A, these conjointly prepon- derating' over h, will descend, S at the same time rising. It might be supposed that the small additional weight, d, under these cir- cumstances, would fall as fast as if it were ' ©'' Unsupported in the air ; but we must not forget that it has simultaneously to bring down with it the weight to which it is attached, and also to lift the opposite one. By its gravity, therefore, it does descend, but with a velocity which is less in proportion as the difierence between the two weights to which it it affixed is less than their sum. It gives us a force precisely like gravity — indeed it is gravity itself — operating under such conditions as to allow a moderate velocity. To avoid friction of the axle of the pulley, each of its ends rests upon two friction-wheels, as is shown at Q,, Fig. 95 ; P is the pillar which supports the pulley. One of the weights is seen at 5, the other moves in front of the divided scale c d. This last weight is made to pre- What is the principle of Attwood's machine ? Why does not the addi- tional weight fall as fast as if it fell freely ?. Describe the construction of the machine 88 ATTWOODS MACHINE. Fig. 95. ponderate by means of a rod. There is a shelf which can be screwed opposite any of the di visions of the scale, and the arrival of the descending weight at that point ia indicated by the sound aijising from its striking. A clock, R, indicates the time which has elapsed. To en- able us to fulfill the condition of sus- pending the action of gravity at any moment, a shelf, in the form of a ring, is screwed upon the scale at the point required. Through this the descend- ing weight can freely pass, but the rod which caused the preponderance is intercepted. The equality of the two weights is, therefore, reassumed, and the action of gravity virtually sus- pended. By this machine it may be shown that, in order that the descending weight shall strike the ring at inter- vals of 1, 2, 3, 4, &c., seconds, count- ing from the time at which its fall commences, the ring must be placed at distances from the zero of the scale, which are as the number^ 1, 4, 9, 16, &c. ; and t ese are the squares of the times. And in the same manner may the other laws of the falling of bodies be proved. When a body is thrown vertically upward it rises with an equably retarded motion, losing 32i feet of its original velocity every second. If in vacuo, it would occupy as much time in rising as in falling to acquire its original velocity, and the times expended in the ascent and descent would be the same. Forces which, like gravity, in this instance, produce a ietardation of motion are nevertheless designated as ac- celerating forces. Their action is such that, if it were brought to bear on a body at rest, it would give rise to an accelerated motion. Give an ilMistration of its use. What is the effect when a body Is thrown vertically upward ? Under what signification is the term " accelerating forces" sometimes used ? RESISTANCE OF THE AIR. 89 In rapid movements taking place in the atmosphere, a disturbing agency arises in the resistance of Fig. 96. the air — a disturbance which becomes the more striking as the descending body is lighter, or exposes more surface. If a piece of gold and a feather are suffered to drop from a certain height, the gold reaches the ground much sooner than the feather. Thus, if in a tall air-pump receiver we allow, by turning the button, a, Fig. 96, a gold coin and a feather to drop, the feather occupies much longer than the coin in effecting its descent ; and that this is due to the resistance of the air is proved by withdrawing the air from the receiver, and, when a good vacuum is obtained, making the coin and the feather , fall again. It will now be found that they descend in the same time precisely. Nor is it alone light bodies which are subject to this disturbance : it is common to all. Thus it was found that a ball of lead dropped from the dome of St. Paul's Cathe- dral, in London, occupied 4^ seconds in reaching ths pavement, the distance being 272 feet. But in that time it should have fallen 324 feet, the retardation being dus to the resistance of the air. It has been observed that the force of gravity is not the same on all parts of the earth. The distance fallen through in ,one second at the pole is 16'12 feet; but at the equator it is 16*01 feet. This arises from the circumstance, that the eai'th is not a perfect sphere, its polai: diameter being shorter than its equatorial and, therefore, bodies at the poles are nearer to its center than they are at the equator. Thus7 in Fig. 97, let N S represent the globe of the earth, N and S being Fiff- 97. N What cause interferes with these results 7 How can it be proved that these effects are due to the resistance of the air 1 Is this disturbance lira ited to light bodies ? What is the distance through which a falling body descends at the equator and at the poles ? What is the reason of this difference ? 90 MOTION ON PLANES. the north and south poles, respectively.- Owing to its polar being shorter than its equatorial diameter, bodies situated at different points on the surface may be at very different distances from the center, and the force of grav- ity 'exerted upon them may be correspondingly very»dif- ferent. LECTURE XX. Motion on Inclined Planes. — Case of a Horizontal,, a Vertical, and an Inclined Plane. — Weight expended partly in producing pressure and partly motion. — Laws of Descent down Inclined Planes. — Systems of Planes. — Ascent up Planes. Projectiles. — Parabolic theory of Projectiles. — Disturb- ing agency of the Atmosphere. — Resistance to Cannon- shot. — Ricochet. — Ballistic Pendulum. When a spherical body is placed on a plane set hori- zontally, its vphole gravitation is expended in producing a pressure on that plane. If the plane is set in a vertical position the body no longer presses upon it, but descends vertically and unresisted. At all intermediate positions which may be given to the plane the absolute attraction will be partly expended in producing a pressure upon that plane, and partly in producing an accelerated de- scent. The quantities of force thus relatively expended in producing the pressure and the motion will vary with the inclination of the plane : that portion producing press- ure increasing as the plane becomes more horizontal, and that producing motion increasing as the plane becomes more vertical. Let there be a ball descending on the surface of an in- clined plane, A B, Fig. 98, and let the line d e represent its weight or absolute gravity. . By the parallelogram of forces we may decompose this into two other forces, dj What are the phenomena exhibited by a spherical body placed on planet of different inclinations? Into what forces may the absolute gravity of the body be resolved ? t MOTION DOWN INCLINED PLANES 91 and d g, one of which is Fig.W- perpendichlar to the plane and the other parallel to it. The first, therefore, is expended in producing pressure upon the plane, and the second in pro- ducing motion down it. The following are the laws of the descent of bodies down inclined planes. • The pressure on the inclined plane is to the weight of the body as the base, B C, of tlfe inclined plaiie is to its length, A B. The accelerated motion of a descending body is to that which it would have had if it fell freely as the height, A C, of the plane is to its length, A B. The final velocity which the descending body acquires is equal to that which it would have had if it had fallen freely through a distance equal to the height of the plane ; and, therefore, the velocities acquired on planes of equal height, but unequal inclinations, are equal. The space passed through by a body falling freely is to that gone over an inclined plane, in equal times, as the length of the plane is to its height. If a series of inclined planes be represented, in position and length, by the chords of a circle' termi- nating at the extremity of the verticaLdiame- A ter, the .times of descent down each will be equal, and also equal to the time of descent through thai; vertical diameter. Thus, let A D, A Gr, D B, Gr B be chords of a circle ter- minating at the extretriities, A B, of the ver- tical diameter; and, regarding these as inclin- ed planes, a body will descend from A to D, or A to G-, or D to B, or G to B in the same time that it would fall from A to B. If a body descend down a system of several planes, A Fig. 99 What effects do those forces respectively produce ? What lelation is there between the pressure on the inclined plane and the weight of the 3ody ? What is the' relation between the velocities in descent down a plan§ and free falling ? What is the final velocity equal to 7 What is the elation of the space passed through ? What is Fig. 99 intended to illus- . ate? 92 PROJECTILES. C, Fig. 100, with Jifferent inclinations, it will acquire Fig. 100. the same velocity as it would have had in descending through the same vertical height, A B, though the times of descent are unequal. If a body which has descended an inclined plane meets at the foot of it a second plane of equal alti- tude, it will ascend this plane vnth the velocity acquired in coming C down the first, until it has reached the same altitude from which it descended. Its velocity being now expended , it will re-descend, and ascend the first plane as before, oscillating down one plane, up the other, and then back again. The same thing will take place ^s 101. if^ instead of being over an inclined plane, the motion be made over a curve, as in Fig. 101. In practice, however, the resistance of the air and friction soon bring these motions to an end. In the motions of projectiles two forces are involved — the continuous action of gravity, and the momentary force which gave rise to the impulse — such as muscular ex- ertion, the explosion of gunpowder, the action of a spring, &c. The resulting effects of the combination of these forces will differ with the circumstances under which they act. If a body be projected downward, in a vertical line, it fol- lows its ordinary course of descent, its accelerated motion arising from gravity being conjoined to the original pro- iectile force. But if it be thrown vertically upward, the action of gravity is to produce a uniform retardation Its velocity becomes less and less, until finally it wholly ceases. The body then descends by the action of the earth, the time of its descent being equal to that of its as cent, its final velocity being equal to its initial velocity. But if the projectile force forms any angle with xhf direction of gravity, the path of'the body is in a para bolic curve, as seen in Fig. 102. If the direction o^ Describe the phenomena of motion on curves. What forces are involv ed in the motion of a projectile? What are the effects in vertical projec 4on upward and downward? What is the theoretical path in angula orojection ? PARABOLIC THEORY. 93 the projection be horizontal, the path 3escribed will be half a para- bola. This, which passes under the title of the parabolic theory of projec- tiles, is found to be entirely de- parted from in practice. The curve described by shot thrown from guns is not a parabola, but another curve, - the Ballistic. In vertical projections, instead of the times of ascent and descent being equal, the former is less. The final velocity is not the same as the initial, but less. Nor is the descending motion uniformly accelerated ; but, after a certain point, it is constant. Analogous differences are discovered in angular projections. The distance through which a projectile could go upon the parabolic theory, with an initial velocity of 2000 feet per second', is about- 24 miles : whereas no projectile has even been thrown farther than five miles. In reality, the parabolic theory of projectiles holds only for a vacuum. And ■ the atmospheric air, exerting its resisting agency, totally changes all the phenomena — not only changing the path, but whatever may have been the initial velocity, bringing it speedily down below 1280 feet per second. The cause of this phenomenon ^- ""• may be understood from Fig. ^_ , . 103. Let B be a cannon-ball, ^ •' "" moving from A to C with a ve- ^ ' {]f. - C locity more than 2000 feet per second. In its flight it removes a column of air between A and B, and as the air flows into a vacuum only at the rate of 1280 feet per second, the ball leaves a vacuum behind it. In the same manner it powerfully compresses the air in front. This, therefore, steadily presses it into the vacuum behind, or, in other words, retards it, and soon brings its velocity down to such a point that the ball moves no faster than the air moves — that is, 1280 feet per second. ' Is this the path in reality ? Mention some of the discrepancies between the theoretical and actual movements of projectiles. What are these dis- crepancies due to ? Describe the nature of the resistance exerted on a cnnnon-shot in its passage through the air. y4 ^, ._, ' i MOTION HOUND A CENTER. A shot thrown with a high initial velocity not only de viates from the parabolic path, but also to the rigBt and left of it, perhaps several times. A ball striking on the earth or water at a small angle, bounds forward or rico- eheU, doing this again and again until its motion ceases. Fig. 104. The initial velocity given by gunpowder to a ball, and, therefore, the explosive force of that material may be de- termined by the Ballistic pen- dulum. This consists of a heavy mass, A, Fig. 104, sus- pended as a pendulum, so aa to move over a graduated arc. Into this, at the center of per.' cussion, the ball is fired. The pendulum moves to a corresponding extent over the grad- uated arc, with a velocity which is less according as the weight of the ball and pendulum is greater than the weight of the ball aloiie. The explosive force of gunpowder is equal to 2000 at- mospheres. It expands with a velocity of 5000 feet per second, and can communicate to a ball a velocity of 2000 feet per second. The velocity is greater with long than short guns, because the influence of the powder on the ball is longer continued. LECTURE XXI. Op' Motion RouNb a Center. — FecvMarity of Motion on a Ckrve. — Centrifugal Force. — ^Conditions of Free Cur- vilinear Motion.— Motion of the Planets. — Motion in a . Circle. — Motion in an Ellipse. — Rotation on an Axis. — ^ Figure of Revolution. — Stability of the Axis of Rota' tion. In considering the motion of bodies down inclined planes, we have shown that the action of gravity upon What is meant by ricochet ? Describe the ballistic pendulum. What IS the estimate of the explosive force of gunpowder ? What is the veloci tv of its expansion 7 What is the velocity it can communicate tu a ball f MOTION ON A CURVE. 95 them may be divided into two portions — one producing Dressure upon the plane, and therefore acting perpendic- ularly to its surface; the other acting parallel to the plane, and therefore producing motion down it. * It has also been shown that, in some respects, there is an analogy between movements over inclined planes and over curved lines, but a further consideration proves that be- tween the two there is also a very important difference. A pressure occurs in the case of a body moving on a curve which is not found in the case of one moving on a plane. It arises from the inertia of a moving body. Thus, if a body commences to move down an inclined plane, the force producing the motion is, as we have seen, parallel to the plane. From the first moment of motion to the last the direction is the same, and inasmuch, as the inertia of the body, when- in inotion, tends to continue that mo- tion in the same straight line, no deflecting agency is en- countered^ But it is very differejjit with Fig. 105. motion on a curve. llere the direction of descent from A to B is perpetually changing ; the curve from its form -resists, and therefore deflects the falling oody. At any point its inertia tends to continue its motion in a straight line : thus, at A, were it not for the curve it would move in the^line A a, at B in the line B b, these lines being tangents to the curve at the points A and B. The curve, therefore, continually de fleeting the falling body, experiences a pressure itself-^a pressure which obviously does not occur in the case of an inclined plane. This pressure is denominated " cen- trifugal force," because the moving body tends to fly from the center of the curve. In the foregoing explanation we have regarded the Dody as being compelled to move-in a curvilinear path, by means of an inflexible- and resisting surface. But It may easily be shown that the same kind of motion will Explain the difference between motion on inclined planes and motion on curves. What is meant by centrifugal force 1 Under what circumstances can curvilinear motion ensue without the intervention of a rigid curve ? 96 CURVILINEAR MOTION, ensue without any such compelling or resisting surface provided the body be under the control of two forces, one of which continually tends to draw it to the cen- ter' of the curve in which it moves, while the other, as a momentary impulse, tends to carry it in a different di- rection. Thus, let there be a body, A, Fig. 106, attract- ed by another body, S, and also subjected to a projectile force tending to carry it in the direction A H. Under the con- joint influence of the two forces it will describe a curvilinear orbit, A T W. The point to which the first force solicits the body to move is termed the center of gravity — that force itself is desig- nated the centripetal force, and the momentary force passes imder the name of tangential force. The following experiment clearly shows how, under the action of such forces, curvilinear motion arises. Let there be placed upon a table a ball. A, and from the top of the room, by a long thread, let there be suspend- ed a second ball, B, the point of suspension being verti cally over A. If now we re move B a short ^distance from A, and let it go, it falls at once on A, as though it were attracted. It may be regarded, therefore, asunder the influence of a centripetal force emanating from A. What must the nature of the two forces be ? What is the center of gravity? What is the centripetal force ? What is the tangential force i Describe the experiment illustrated in Fig. 107. Fig. 107. CURVILINEAR MOTIONS. 97 But if, instead of simply letting B drop upon A, we give it an impulse in a direction at right angles to the line iv which it would have fallen, it at once pursues a curvilin- ear path, and may be- made to describe a circle or an el- lipse according to the relative intensity of the tangential force given it. This revolving ball imitates the motion of the planetary bodies round the sun. To understand how these curvilinear motions arise, let C be the center of gi-avity, and sup- pose a body at the point a. Let a tan- gential force act on it in such a man- ner as to drive it from a to b, in the same time as it would have fallen from a to d. By the parallelogram of forces "i it will move to J". When at this point, f, its inertia would tend to carry it in the directiony^, a distance equal to a j^ in a time equal to that occupied in passing from u to f; but the constant attractive force still operating tends to bring it to h; by the parallelogram of forces it therefore is carried to k ; and Dy similar reasoning we might show that it will next be found at n, and so on. But when we consider that the centripetal force acts continually, and not by small interrupted impulses, it is obvious that, in- stead of a crooked line, the path which the h)ody pursues will be a continuous curve. The planets move in their orbits round the sun, and the satellites round their planets, in consequence of the action of two forces — a centripetal force, which is gravi- tation, and a tangential force originally impressed on them. The centrifugal force obvioi(sly arises from the action of the tangential. It is the antagonist of the centripetal fotce. The figure of the curve in which a body revolves is de- termined by the relative intensities of the centripetal and tangential forces. If the two be equal at all points the curve will be a circle, and the velocity of the body will Explain why this curvilinear motion ensues. What forces direct the motions of the planets ? What is the relation between the centripetal and centrifugal force ? E 98 CDEVILINEAR MOTIONS. be uniform. But if the centrifugal force at different points of the body's orbit be inversely as the square of its distance from the center of gravity, the curve will be an ellipse and the velocity of the body variable. In elliptical motion, which is the motion of planetary bodies, the center of gravity is in one of the foci of the ellipse. All lines drawn from this point to the circumfe- rence are called radii vectores, and the nature of the mo- tion is necessarily such that the radius vector connecting the revolving body with the center of gravity sweeps over equal areas in equal times. The squares of the velocities are inversely as the dis- tances, and the squares of the times of revolution are to each other as the cubes of the distances. Fig. 109. Let A B D E be an elliptical orbit, as, for example, that of a planet, the longest diameter being A B, and the short- est D E. The points F and G are the foci of the ellipse, and in one, as F, is placed the center of gravity, which, in this instance, is the sun. The planet, therefore, when pursuing its orbit, is much nearer to the sun when at A than when at B. The former point is, therefore, called the perihelion, the latter the aphelion, and D and E points By what circumstance 18 the figure of the curve determined? Under what circumstances is it a circle ? Under what an ellipse 1 What is the .-adius vector 1 Wliat are the laws of elliptic motion ! FIGURE OF EEVOLUTION. 99 of mean distance. The line A B, joining the perihelion and aphelion, is the line of the af sides ; it is also the gi'eat- er or transverse axis of the orbit, and D E is \!t\er conju- gate or less axis. A line drawn from the center of grav- ity to the points D or E, as F D, is the mean distance, F is ihe-lower focus, Gr the higher focus j K the lower apsis, B the higher apsis, and F C or G C — that is the distance of either of the foci from the center — the excentricity. When a body rotates upon an axis all its parts revolve in equal times. The velocity of each particle increases with its perpendicular distance from the axis, and, there- fore, so also does its centrifugal force. As long as this force is less than the cohesion of the particles, the rotating body can preserve itself, but as soon as the centrifugal force overcomes the cohesive, the parts of the rotating mass fly oiF in directions which are tangents to their circular motion. There are many familiar instances which are examples of these principles. The bursting of rapidly rotating masses, the expulsion of water from a mop, the projec- tion of a stone from a sling. If the parts of a rotating body have freedom of motion among themselves, a change in the figure of that body may ensue by reason of the difference of centrifugal force of the different parts. Thus, in the case of the earth, the figure is not a perfect sphere, but a spheroid, the diame- ter or axis upon which it revolves, called its polar diam- eter, is less than its equatorial, it having assumed a flat- tened shape toward the poles and a bulging one toward the equator. At the equator the centrifugal force of a particle is ^i^ of its gravity. This .^ji^. no. diminishes as we approach the poles, where it becomes 0. The tendency to fly from the axis of motion has, therefore, given rise to the force in question. Et In Fig. 110, we have a repre- sentation of the general figure of the earth, in which N S is the polar diameter and also the axis of rotation, E'E, the equatorial diameter. Define the various parts of an elliptic orbit. Describe the phenomena of rotation on an axis. What figure does a movable rotating mass tenower is to the weight as the breadth of the worm is to the circumference described by that point of the lever to which the power is attached. When the end of the screw is advancing through a nut, this law evidently becomes that the power is to the weight as the circumference described by the power is to the space through which the end of the screw advances. It is obvious, therefore, that the force of the screw increases as its threads are finer, and as the lever by which it is urged is longer. When the thread of a screw works in the teeth of a M^ 162. wheel, as shown in Fig. 162, it constitutes an endless screw. An important use of this contrivance is in the engine for dividing grad- • uated circles. The screw is also used to produce slow motions, or to measure by the advance of its point, minute spaces. In the spherome- ter, represented in Fig. 5, we have an example of its use. For all these purposes where slow motions have to be given, or minute spaces divided, the eificacy of the screw will increase with the closeness of its thread. But there is soon a practical limit attained ; for, if the thread be too fine it is liable to be torn off. To avoid this, and to attain those objects almost to an unlimited extent, Huntev's screw is often used. It may be understood from Fig. 163. It consists of a screw. A, working in a nut, C. What is the worm and the spire ? What is a nut? What is the law of equilibrium of the screw ? When the end of the screw advances wha* does this law become ? Describe an endless screw. PASSIVE FORCES. 141 To a movable piece, D, a second Bcrew, B, is affixed. This screw works in the interior of A, which is hollow, and in which a corre- sponding thread is cut. While, therefore, A is screwed down- ward, the threads of B pass up- wardi and the movable piece, D, advances through a space which is equal to the difference of the breadth of the two screws. In this way very slow or minute -motions may be obtained with a screw, the threads of which are Vig. 163. LECTURE XXX. Op Passive ok Resisting Forces. — Difference between the Theoretical and Actual Results of Machinery. — Of Impediments to Motion. — Friction. — Sliding and Roll- ing Friction. — Coefficient of Friction. — Action of Un- guents. — Resistance of Media. — General FhcTwrnena of Resistance. — Rigidity of Cordage. It has already been stated, in the foregoing Lectures, hat the properties of machinery are described without taking into account any of those resisting agencies which 60 greatly complicate their action. The results of the theory of a machine in this respect differ very widely from its practical operation. There are resisting forces or impeding agencies which have thus far been kept out of view. We have described levers as being inflexible, the cords of pulleys as perfectly pliable, and machinery, gen- erally, as experiencing no friction. In the case of one of the powers, it is true that this latter resisting force must necessarily be taken into account ; for it is upon it that the efficacy of the wedge chiefly depends. Describe Hunter's screw. What is meant by passive or resisting forces X Why does the theoretical action of a machine differ from its practica> operation ? 14-4 FRICTION. So, too, in speaking of the motion of projectiles, it has been stated that the parabolic theory is wholly departed from, by reason of the resistance of the air; and that not only is the path of such bodies changed, but their range becomes vastly less than what, upon that theory, it should be. Thus, a 24-pound shot, discharged at an elevation of 45°, with a velocity of 2000 feet per second, would range a horizontal distance of 125,000 feet were it not for the resistance of the air ; but through tnat resistance its range is limited to about 7300 feet. Of these impediments to motion or passive or resisting forces, three leading ones may be mentioned. They are, 1st, friction; 2d, resistance of the media moved through ;' 3d, rigidity of cordage. OP FRICTION. Friction arises from the adhesion of surfaces brought into contact, and is of different kinds — as sliding friction, when one surface moves parallel to the other, rolling friction, when a round body turns upon the surface of another. By the measure of friction, we mean that part of the weight of the moving body which must be expended in overcoming the friction. The fraction which expresses this is termed the coefficient of friction. Thus, the coef- ficient of sliding friction in the case of hard bodies, and when the weight is small, ranges from one seventh to one third. It has been proved by experiment that friction increases as the weight or pressure increases, and 'as the surfaces in contact are more extensive, and as the roughness is greater. With surfaces of the same material it is nearly proportional to the pressure. The time which the sur- faces have been in contact appears to have a considerable influence, though this differs much with surfaces of differ ent kinds. As a general rule, similar substances give rise to greater friction than dissimilar ones. On the contrary, friction diminishes as the pressure is Give an illustration of resisting force in the case of projectiles. How many of these impediments may be enumerated ? What varieties of fric- tion are there ? What is the coefficient cf friction ? Mention some of tha conditions whiph increase friction RESISTANCE OF MEDIA. 143 less, as the polish of the moving surfaces is rnore perfect, and as the surfaces In contact are smaller. It may also be diminished by anointing the surfaces with some suita- ble unguent or greasy material. Among such substances as are commonly used are the different fats, tar, and black lead. By such means, friction may be reduced to one fourth. Of the friction produced by sliding and rolling motions, the latter, under similar circumstances, is far the least. This partly arises from the fact that the surfaces in con- tact constitute a rnere line, and partly because the asperi- ties are not abraded or pushed aside before motion can ensue. The nature of this distinction may be clearly un- derstood by observing what takes place when two brushes with stiff bristles are moved over one another, and when a round brush is rolled over a flat one. In this instance, the rolling motion lifts the resisting- surfaces from one another ; in the former, they require to be forcibly pushed apart. Though, in many instances, friction acts as a resisting agency, and diminishes the power we apply to machines, in some cases its tsffects are of the utmost value. Thus, when nails or screws are driven into bodies, with a view of holding them together, it is friction alone which main- tains them in their places. The case is precisely the same as in the action of a wedge. ItBSISTANCE OP MEDIA. A great many results in natural philosophy illustrate the resistance which media offer to the passage of bodies through them. The experiment known under the name of the guinea and feather experiment establishes this for atmospheric air. In a very tall air-pump receiver there are suspended a piece of coin and a feather in such a way that, by turning a button, at a. Fig. 164, the piece on which they rest drops, and permits them to fall to the pump-plate. Now, if the receiver be full of atmospheric air, on letting the objects fall, it will be found that, while the coin descends with rapidity, and reaches, in an instant. Mention some that diminish it. What is the difference of effect be- tween sliding and rolling friction ? Give an illustration of this. Undei what circumstances does advantage arise from friction? 144 RESISTANCE OF MEDIA. Fiff. 164. the pump-plate, the feather comes down leisurely, being buoyed up by the air, and the speed of its motion resisted. But if the air is first extracted by the pump, and the objects allowed to fall in vacuo, both pre- cipitate themselves simultaneously with equal velocity, and accomplish their fall in equal times. In the vibrations of a pendulum, the final stoppage is due partly to friction and partly to this cause. And in the case of motions taking place in water, we should, of course, expect to find a gi'eater resistance arising from the greater density of that liquid. The resisting force of a medium depends up- on its density, upon the surface which the mov ing body presents, and on the velocity with which it moves Water, which is 800 times more dense than air, will offer a resistance 800 times greater to a given motion Of the two mills represented in Fig. 36, that which goes with its edge first runs far longer than that which moves with its plane first. We are not, however, to~" understand that the effect of the medium, on a body moving through it, increases directly as the transverse section of the body; for a great deal depends upon its figure. A wedge, going with its edge first, will pass through water more easily than if impelled with its back first, though, in both in- stances, the area of the transverse section is of course the same. It is stated that spherical balls encounter one fourth less resistance from the air than would cylinders of equal diameter; and it is upon this principle that the bodies of fishes and birds are shaped, to enable them to move with as little resistance as may be through the me- dia they inhabit. The resistance of a medium increases with the velocity with which a body moves through it, being as the square of the velocity, so long as the motion is not too rapid ; but when a high velocity is reached, other causes come into operation, and disturb the result. Describe the guinea and feather experiment. What does it prove? What is the cause of the stoppage of a pendulum ? How does the density of a liquid affect its resistance ? How is resistance affected by figure f How by velocity ? RIGIDITY OP CORDAGE. 145 As with friction, so with the resistance of media, a great many results depend on this impediment to mo- tion ; among such may be mentioned the swimming of fish \;hrough water, and the flight of birds through the air. It is the resistance of the air which makes the para- chute descend with moderate velocity downward, and causes the rocket to rise swiftly upward. RIGIDITY OF CORDAGE. In the action of pulleys, in machinery in which the use of cordage is involved, the rigidity of that cordage is an impediment to motionr When a cord acts round a pulley, in consequence of imper- fect flexibility, it obtains a leverage c on the pulley, as may be under- stood from Fig. 165, in which let C K D be the pulley working on a pivot at O ; let A and B be weights suspended by the rope A C K D B. From what has been said respect- ing the theory of the pulley, the action of the machine may be regarded as that of a lever, COD, with equal arms, C O,, O D. Now, if the cord were perfectly inflexible, on making the weight A descend by the addition of a small weight to it, it would take the position at A', the rope being a tangent to the pulley at C ; at the same time B, ascending, would take the position B', its cord being a tangent at D'. From the new posi- tions, A' and B', which the inflexible cord is thus sup- posed to have assumed, draw the perpendiculars. A' E, B' F., then will O E, O F, represent the arms of the lever on which they act — a diminished leverage on the side of the descending, and an increased leverage on the side of the ascending weight is the result. In practice the result does not entirely conform to the foregoing imaginary case, because cords are, to a certain extent, flexible. As their pliability diminishes, the dis- turbing effect is greater. The degree of inflexibility de- Mention some of the valuable results which depend on it. Give a general ;dea of the action of rigidity of cordage What takes place in case of ab- solute! inflexibility, as in Fig. 165? On what does inflexibility depend ' G 146 RIGIDITY OF CORDAGE. pends on many casual circumstances, such as dampness or dryness, or the nature of the substance of which they are made. Inflexibility increases with the diameter of a cord, and with the smallness of the pulley over which it runs. UNDULATIONS. 147 OF UNDULATORY MOTIONS. LECTURE XXXI. Op X^ndulations. — Origin of Undulations. — Progressive and stationary Undulation. — Course of a progressive Wave. — Nodal Points.— Three different hinds of Vibra- tion. — Transverse Vibration of a Cord. — Vibrations of Rods. — Vibrations of elastic Planes. — Vibrations of Liquids. — Waves on Water. "When an elastic body is disturbed at any point, its particles gradually return to a position of rest, after exe- cuting a series of vibratory movements. Thus, vyhen a glass tumbler is struck by a hard body, a tremulous mo- tion is communicated to its mass, which gradually declines in force until the movement finally ceases. In the same manner a stretched cord, which is drawn aside at one point, and then suffered to go, is thrown into a vibratory or undulatory movement ; and, according as circumstances differ, two different kinds of undulation may be established, 1st, progressive undulations ; 2d, sta- tionary undulations. In progressive un Vig-iss. dulations the vibra- d tingparticlesofabody X-m, <^ j,"^ * '-—!, communicate theirmo- tion to the adjacent -^^__ particles ; a succes- sive propagation of movement, therefore, ™"'~ ensues. Thus, if a cord is fastened at one DTb^- end, and the other is moved up and down, -y-m. '*" ^^^ ^ e a wave or undulation, m D » E o, is produced. The part, jw D », is the elevation Under what circumstances do vibratory mofements arise ? How manj kinds of undulations are there ? Describe the nature of a progressive un- dulation. 148 KINDS OF VIBRATIONS. of the Nil ave, D being the summit, re E o is the depression, E being the lowest point, D p is the height, q E the depth, and m o the length of the wave. But, under the circumstances here considfered, the mo- ment this wave has formed, it passes onward, and suc- cessively assumes the positions indicated at I, II, III. When it has arrived at the other end of the cord, it at once returns with an inverted motion, as shown at IV and V. This, therefore, is a progressive undulation. Again, instead of the cord receiving one impulse, let it K^. 167. ^^ agitated equally at equal inter- vals of time ; it will then divide itself, as shown in Fig. 167, into equal elevations and depressions with in- tervening points, m n, which are at rest. These are sta- tionary undulations, and the points are called nodal points. The agents by which undulatory movements are estab- lished are chiefly elasticity and gravity. It is the elas- ticity of air which enables it to transmit the vibratory motions which constitute sound, and, for the same reason, steel rods and plates of glass may be thrown into musical vibrations. In the case of threads and wires, a sufficient degree of elasticity may be given by 'forcibly stretching them. Waves on the surface of liquids are produced by the agency of gravity. There are three different kinds of vibrations into which a stretched string may be thrown : transverse, longitudinal, and twisted. These may be illustrated by the in- strument represented at Fig. 168. It consists of a piece of spirally- twisted wire, stretched from a frame by a weight. If the lower end of the wire be secured by a clamp, on puU- ^ ing the wire in .the middle, and then ^ letting it go, it executes transverse __. vibrations. If the weight b^ gently "^ lifted, and then let fall, the wire per- forms longitudinal vibrations; and it Fig. 168. m *^^ ^ What is meant by the height, depth, and length of a wave '! Describe he Stati'^"5*^v vihrntinn "Rv whsl: norpnfa ni-o i->n,4..l_i lished ? wnac IS meant oy me neigui, aepcn, anc ^ „. „ ^y^yc ■ i^»io^..."w the stationary vibration. By what agents are undulatory motions estab- wie Biaiioiiary viuraiiun. ny wuat agenis are Undulatory motions estab- lished? How may elasticity be communicated to cords' Into how many kinds of vibration may a string be thrown ? How may this be illui trated by the apparatus represented in Fig. 168 ? TEAN3VERSE VIBRATIONS. 149 the wbight be twisted round, and then released, we have rotavorj vibrations. If we take astring, a b, Mg.lQ^, and.having stretched it be- tween two nxed points, a ptg. im. and b, draw it aside, and then let it go, it executes transverse vibrations, as a.« has already been de- Bcvibed. The cause of its motion, fropi the position we have stretched it to, is its own elasticity. This makes it return from the position, a c 5, to the straight line, afb, with a continually accel- erated velocity ; but when it has arrived in afb, it cannot stop there, its momentuipcan-ying it forward to a d 3, with a velocity continually decreasing. Arrived in this position, it is, for a moment, at rest ; but its elasticity again impels it as before, but in the reverse direction to af b ; and so it executes vibrations on each side of that straight line until it is finally brought to rest by the resistance of th« air. One complete movement, from a ch to a db and back, is called a vibration, and the time occupied in per forming it the time of an oscillation. The vibratory movements lof such a solid are isochro ^ous, or performed in equal lines. They increase in rapidity with the tension — that is, with the elasticity — being as the square root of that force. The number of vibrations in a given time is inversely as the length of the string, and also inversely as its diameter. The vibrations of solid bodies may be studied best un- der the divisions of cords, rods, planes, and masses. The laws of the vibrations of the first are such as we have jusl explained. In rods the transverse vibrations are isochronous, and in a given time are in number inversely as the squares of tha lengths of the vibrating parts. Thus, if a rod makes two vibrations in one second, if its length be reduced to half it will make four times as many — that is, eight ; if to on« fourth, sixteen times as many — that is, thirty-two, &c The motion performed by vibrating-rods is often very com Describe the transverse vibration of a string. What Is a vibration' What is the time of an oscillation ? What is meant by isochronous vibra tions? How are the vibrations of solid bodies divided ? What are ths laws for the vibrations of rods 7 160 VIBKATIONS OF PLANES. Fig 170 plex. Thus, if a bead be fastened on the free ex tretnity of a vibrating steel rod, Fig. 170, it will exhibit in its motions a curved path, as is seen at c. Rods may be made to exhibit nodal points. The space between the free extremity and the first nodal point is equal to half the length contained between any two nodal points, but it vibrates with the same velocity. Thus, a, Fig. 171, being the fixed, and b the free end F,g. 171. of such a rod, the part ^ ^ between b and c is half ^ INTERFERENCE OF WAVES. 155 therefore, arises a sphere of air, the superficies or shell of which has a maximum density. Reaction now sets in, the sphere contracts, and the returning particles come to their original positions. But as a disturbance on the sur- face of a liquid gives origin to a progressive wave, so does the same thing take place in the air. By the intensity of vibration of a wave we mean the relative disturbance of its moving particles, or the mag- nitude of the excursions they make on each side of their line of rest. Thus, on the surface of water we may have waves "mountains high," or less than an inch high; the intensity of vibration in the former is correspondingly greater than in the latter case. In aerial waves, precisely as in the surface-waves of water, interference arisea under the proper conditions. Thus, let a m p h, Fig. 178, be a wave advancing toward c, and let m n, o p he the intensity of its viiration, or the maximum distances of the excursions of its vibrating par- ticles. Then suppose a second wave, originating at h (a distance from a precisely equal to one wave length), the intensity of vibration of which is represented by q r. The motions of this second wave coinciding throughout its length with the motions of the first, the force of both sys- tems is increased. The intensity, therefore, of the wave, arising from their conjoint action at any point, q will be equal to the sum of their intensities, q r, q s — that is, it will be q t, and for any other point, v, it will be equal to the sum of v w and v u — that is, v x. So the new wave will be represented hy b t g x h. Now let things remain as before, except that the point of impact of the second wave, instead of being one whole wave from a, is only half a wave, the effects on any parti- What is meant by the intensity of vibration ? Trace the phenomena of interference represented in Figs. 178 and 179 respectively. 156 INTERFERENCE OF WAVES. cle, such as q, take place in opposite directions, the sec- ond wave moving it with the intensity and direction q Fig. 179. r, the first with q s — the resultant of its movement in in- tensity and direction, will, therefore, be the difference of these quantities — that is, q t. And the same reasoning continued gives, for the wave resulting from this conjoint action, b t g x h c. Under the circumstances given in Fig. 178, the systems of waves increase each other's force ; under those of Fig. 179, they diminish it ; or if equal to one another counter- act completely, and total interference results. Waves in the air, as they expand, have their superfi- cies continually increasing, as the squares of their radii of distance from the original point of disturbance. Hence the effect of all such waves is to diminish as the squares of the distances increase. Under what law does the effect of waves in the air diminish ? ACOUSTICS. 157 THE LAWS OP SOUND. ACOUSTICS. LECTURE XXXIII. Production of Sound. — The Note Depends on Frequen- cy of Vibration. — Distinguishing Powers of the Ear,— Soniferous Media. — Origin of Sounds in the Air. — Elas- ticity Required and Given, in the Case of Strings hy Stretching. — Rate of Velocity of Sounds. — All Sounds Transmitted with Equal Speed. — Distances Determined by it. — High and Low Sounds. — Three Directions of Vibration. — Intensity of Sound. — Quality of Sounds. — The Diatonic Scale. When a thin elastic plate is made to vibrate, one of its ends being held firm and the other being free, and its length limited to a few inches, it emits a clear musical note. If it be gradually lengthened, it yields notes of different characters, and finally all sound ceases, the vibrations be- coming so slow that the eye can follow them without dif- ficulty. This instructive experiment gives us a clear insight into the nature of musical sounds, and, indeed, of all sounds generally. A substance which is executing a vibratory movement, provided the vibrations follow one another with sufficient rapidity, yields a musical sound ; but when those vibrations fall below a certain rate, the ear can no onger distinguish the effect of their impulsions. The number of vibrations which such a plate makes in What is the nature of a musical sound ? Under what circumstances does the sound become inaudible ? What regulates the number of vibra- tions of an elastic plate ? 158 SOUND ARISES IN VIBRATIONS. a given time depends upon its length, being inversely as the square of the length of the vibrating part. Thus, if we take a given plate and l-educe its length, the vibra- tions will increase in rapidity ; when it is half as long it vibrates four times as fast ; when one fourth, sixteen times, &c. All sounds arise in vibtatory movements, and musical notes differ from one another in the rapidity of their vi- brations — the more rapidly recurring or frequent the vi- bration the higher the note. There is, therefore,' no difficulty in determining how many vibrations are required to produce any given note. We have merely to find the length of a plate which will yield the note in question, knowing previously what length of it is required to make a determinate number of vibra- tions in a given space of time. Thus it has been found that the ear can distinguish a sound made by 15 vibra- tions in a second, and can still continue to hear though the number reaches 48,000 per second. That all sounds arise in these pulsatory movements common observations abundantly prove. If we touch a bell, or the string of a piano, or the prong of a tuning- fork, we feel at once the vibratory action, and with the cessation of that motion the sound dies away. Fig. 180. But the pulsations of such a body are not alone sufficient to produce the phenomena of sound. Media must intervene between them and the or- gan of hearing. In most cases the medium is atmospheric air, and when this is taken away the effect of the vibrations wholly ceases. Thus, a bell or a musical snuff-box, under an exhausted receiver, as in Fig. 180, can no longer be heard; but on read- mitting the air the sound becomes audible. The sounding body, there- fore, requires a soniferous medium to propagate its im- pulses to the ear. Atmospheric air is far from being the only soniferous How may the number of vibrations which constitute any sound be de- termined ? How may it be proved that all sounds arise in vibratory move ments ? How may it be proved that a soniferous medium is required ? SONIFEROUS MEDIA. 159 medium. Sounds pass with facility through water ; the scratching of a pin or the ticking of a watch may be heard by the ear applied at the end of a very long plank of wood. Any uniform elastic medium is capable of trans- mitting sound ; but bodies which are imperfectly elastic, or have not an uniform density, impair its passage to a corresponding degree. The effect of a vibrating spring, or, indeed, of any vi- brating body on the atmospheric air, is to establish in it a series of condensations and rarefactions which give rise to waves. These, extending spherically from the point of disturbance, advance forward until they impinge on the ear, the structure of which is so arranged that the move- ment is impressed on the auditory nerves, and gives rise to the sensation which we term sound. Both the sonorous body and the soniferous medium must, therefore, be elastic, the regularity of the pulsa- tions of the former depends upon the uniformity of its elasticity. In the case of strings, we give them the re- quisite degriee of elastic force by stretching them to the proper degree. And, as the undulatory movements which arise in the soniferous medium are not instantaneous, but successive, it follows that the transmission of sound in any medium requires time. That this is the case, we may satisfy ourselves by remarking the period that elapses between seeing the flash of a gun and hearing the report. It is greater as we are removed to a greater distance. In different media, the velocity of transmission depends on the density and specific elasticity. It has been found, by experiment, that in tranquil air the velocity of sound at 60°, and at an average state of moisture, is H20 feet in a second. The wind accelerates or retards sound, ac- cording to its direction, damp air transmits it more slowly than dry, and hot air more rapidly than cold, the velocity increasing about 1"1 foot for every Fahrenheit degree. In a soniferous medium, all sounds move equally fast it is wholly immaterial what may be their quality or theil Mention some such soniferous media. How is it that sounds are finally Eerceived by the ear ? What condition is required both for the sounding ody and soniferous medium ? How may suflBcient elasticity be given in the case of strings ? Does the transmission ofsound require time? What is the Telocity of sound per second ? What is the effect of the wind, damj> ness, or change of temperature 1 160 VELOCITY OP SOUND. intensity. Thus, we know that even the most intricate music executed at a distance is heard without any discord, and precisely as it would be close at hand. Nor does it matter whether it be by the human voice, a flute, a bugle, or, indeed, by many different instruments at once, the relation of the difference of sounds is accurately preserv- ed. But this can only take place as a consequence of the equal velocity of transmission ; for if some of these sounds moved faster than others discord must inevitably ensue. The experiments of Colladon and Sturm on the Lake of Geneva show that the velocity in water is about four times that in air, being 4708 feet in a second. With re spect to solid substances, it is stated that the velocity in air being 1, that in tin is 7^, in copper 12, in glass 17. Advantage is sometimes taken of these principles to determine distances. If we observe the time elapsing between the flash of a gun and hearing the sound, or be- tween seeing lightning and hearing the thunder, every second answers to 1120 ieet. Sounds are of different kinds : some are low or high, grave or' acute, according as the vibrations are slower or faster. Again : the intensity of vibration or the magni tudes of the excursions which the vibrating particles make determine the force of sounds, an intense vibra- tion giving a loud, and a less vibration a feeble sound. The vibrations of a soniferous body may take place in three directions : they may be longitudinal, transverse, or rotatory vibrations ; or, indeed, they may all co-exist. Fig. 181. A body may be divided into vibrat- ing parts, separated from one another by nodal points or lines. Thus, if we take a glass or metal plate, and having strewed its surface with fine dry sand, and holding it firmly at one point between the thumb and finger, or in a clamp, as represented in Fig. 181, draw a violin bow across its edge, it yields a musical note, and the sand is thrown off those places which are in motion, and collects on the nodal points, which are at rest. The quantity, or strength, or intensity of a sound de What is the velocity of sounds in water ? Into what varieties may sound be divided ? In what directions may a sounding body vibrate I How may nodal lines on surfaces be traced ? NATURE OP SOUNDS. 161 pends on the intensity of the vibrations and the mass of the sounding body. It also varies with the distance, be ing inversely proportional to its square. Musical sounds are spoken of as notes, or as higji and lew. Of two notes, the higher is that which arises from more rapid, and the lower from slower vibrations. Besides this, sounds differ in their quality. The same note emitted by a flute, a violin, a piano, or the human voice is wholly different, and in each instance peculiar. In what this peculiarity consists we are not able to say. The several notes are distinguished by letters and names ; we shall also see pi-esently that they may be dis- tinguished by numbers. They are — CDEFGABC. Or, lit, re, mi, fa, sol, la, si, ut. Such a series of sounds passes under the name of the diatonic scale. LECTURE XXXIV. Phenomena op Sound. — Notes in Unison. — Octave. — In- terval of Sounds. — Melody. — Harmony. — The Mono- chord. — Length of Cord and Numher of Vibrations re- quired for each Note. — Laws of Vibrations in Cords, Rods, Planes. — Acoustic Figures on Plates. — Vibration of Columns of Air. — Interference of Sounds. — Whisper- ing Galleries. — Echoes. — Speaking and Hearing- Trtem- ^et. Two notes are said to be in unison when the vibrations which cause them are performed in equal times. If the one makes twice as many vibrations as the other, it is said to be its octave, and the relation or interval there is between two sounds is the proportion between their re- spective numbers of vibrations. There are combinations of sounds which impress om organs of sense in an agreeable manner, and others which On what does the intensity of sound depend ? What is it that determines the highness or lowness of notes 1 What is meant by the quality of soun/" i ? How may notes be distinguished ? When are notes in unison? Wha la an octave ? What is the relation or interval of sound* T 1«2 THE MONOCHORD. produce a disagreeable effect. In this sense, we speak of the former as being in unison, and the latter as being discordant. A combination of harmonious sounds is a chord, a succession of harmonious notes a melody, and a succession of chords harmony. "We have remarked in the last lecture that sounds may be expressed by numbers as well as by letters or names, and their relations to one another clearly exhibited. For this purpose, we may take the monochord or sonometer, C, Fig. 182, an instrument consisting of a wire or IHg. 182. ,r 1 = prr-r. "I-S C F ® H Bf !< -^ -liJ JLJ US 3 {a |M [I catgut stretched over two bridges, F F', which are fast- ened on a basis, S S' ; one end of the cord passes over a pulley, M, ,and may be strained to any required degree of weights, P. The length of the string vibrating may be changed by pressing it with the finger upon a movable piece, H, which carries an edge, T, and the case beneath is divided into parts which exhibit the length of the vi- brating part of the wire. The upper part o{ Fig. 1^2 shows a horizontal view of the monochord, the lower a lateral view. The instrument here represented has two strings, one of catgut and one of wire. Now, it is to be understood that the number of vibra- tions of such a cord are inversely as its length ; that is, if the whole cord makes a given number of vibrations in one second, when you reduce its length to one half it w \11 make twice as many ; if to one third, thrice as many, & z What is a chord, a melody, and harmony ? Describe the monochord VIBRATIONS OF CORDS 163 Suppose the cord is stretched so as to give a clear sound, which we may designate as C, and the movable bridge is then advanced so as to obtain successively the other notes of the gamut, D, E, F, G, A, B, C, it will be found that these are given when the lengths of the cord, com- pared with its original length, are — Name of note . . . CDEFGABP Length of cord . . . li f t z> Ti h J! TT' i- but as the number of vibrations is in the inverse ratio of the lengths of the vibrating cords, we shall have for the number of vibrations, if we represent by 1, the number that gives C, the following for the other notes : Name of note .. . CDEFGABC Number of vibrations . . 1, |, |, f, f, |, V 2. From C to G is an octave, and from this we gather that, in the octave, the higher note makes twice as many vibra- tions as the fundamental note, and that between these there are other intervals, which, heard in succession, are harmonious ; the eight, therefore, constitute a scale, com- monly called the diaConic scale. Musical instruments are of different kinds, depending on the vibrations of cords, rods, planes, or columns of air. It has already been stated, that the number of vibra- tions, of a cord is inversely as its length — the number also increases as the square root of the force that stretches it ; thus, the octave is given by the same string when stretch- ed four times as strongly ; the material of the string, whether it be catgut, iron, &c., also affects the note. In rods the height of the note is directly as the thick-' ness, and inversely as the square of the length. The quality, of the material also, in respect of elasticity, deter- mines the note. The foregoing observations apply to transverse vibra- tions of cords and rods; but! they may be also made to execute longitudinal and torsion vibrations, the conditions of which are different. In planes held by one point, and a bow drawn across at another, or struck by a blow, sounds are emitted, and by the aid of sand nodal lines may be traced. Thus, in Fig. 183, a is the point, in each instance, at which the What lengths of a cord are required to give the notes of the gamut ? What are the corresponding number of vibrations ? What is the diatonic scale ? What are the lavfs for the vibration of cords ? What in the case of rods ! 1B4 ACOUSTIC FIGURES. Dlate is held, and h that at which the bow is applied ; the sand arranges itself in the dotted lines. The two large figures are formed by putting together four smaller plates, in one instance bearing the nodal lines, represented at I, and, in the other, at II. They may, however, be directly generated on on6 large plate of glass by holding it at a, touching it at w, and drawing the bow across it at b. Fig. 183. I a J-5 ■l m n a Circular plates, a in III, may be made to bear a four- rayed star, by holding them in the center, drawing the bow at any point at J, and touching the plate at a point 45° distant from the bow ; but if the plate be touched 30°, 60°, or 90° ofi", it produces a six-rayed star, Fig. IV. Columns of air may be made to emit sounds by being thrown into oscillation, as in horns, flutes, clarionets, &c. In these the column of air, included in the tube of the in- strument, is made to vibrate longitudinally. The height of the note is inversely proportional to the length of the column, and therefore different notes may be obtained by having apertures, at suitable distances, in the side of the tube, as in the flute. Two sounds may be so combined together that they shall In the case of planes how may the nodal lines be varied ? How may columns of air be made to vibrate ? How is the length of the vibrating Golunin varied in different wind instruments 7 INTERFERENCE OF SOUNDS. left a 1 mutually destroy each other's effect, and silence result. This arises from .interference taking place in the aerial waves, the laws of which are those given in Lecture XXXII. The following instances will illustrate these facts. When a tuning-fork is made to vibrate, and is turned round upon its axis near the ear, four periods may be dis- covered during every revolution in which the sound in- creases or declines. If we take 'two tuning-forks of the same note, ad, Fig. 184, and fasten a circle of cardboard, half an inch in diameter, on one of the prongs of each, and make one of the forks a little heavier than the other, by putting on it a drop of wax, and then filling a jar, b, to such a J height with water, that either of the forks, when held over it, will make it resound, so m long as only one is held, there will be a con- ^B tinuous note, without pause or interruption ; JK^ but if both are held together, there will be periods ot silence and periods of soupd, according as the longer waves, arising from one of the forks, overtakes and inter- feres with the shorter waves, arising from the other. Sounds undergo reflexion, and may therefore be directed by surfaces of suitable figure. If, in the focus of a concave mirror a watch be placed, its ticking may be heard at a great distance in the focus of a second mirror, placed so as to receive the sound-waves of the first. On similar principles also whispering-galleries depend. These are so constructed that a low whisper uttered at one point is reflected to a focus at another, in which it may be distinctly heard, v/hile it is inaudible in other po- sitions. The dome of St. Paul's cathedral, in London, is an example. Echoes are reflected sounds. Thus, if a person stands in fi-ont of a vertical wall, and at a distance from it of about 6S^ feet, if he utters a syllable, he will hear a sound which is the echo of it. If there be a series of such ver- tical obstacles, at suitable distances, the same sound may be repeated many successive times. A good ear can dis- tinguish nine distinct sounds in a second ; and, as a sound Give some illustrations of the interference of sound. How may it be proved that sounds undergo reflexion ? What are whispering-galleries 1 Unde* what circumstances do echoes arisa? 166 ECHOES. travels 1120 feet in the same time, for the ech-3 to be clearly distinguished from its original sound, it nnust travel 125 feet in passing to and from the reflecting snrface, tha is, the reflector must be at least 62^ feet distant. Remarkable echoes exist in several place?. One ne» Milan repeats a sound thirty times. The ancients men tion one which could repeat the first verse of the Mnoi'. Fig. 185. eight times. On the banks of-'rivers — as, for example, on the Rhine, as represented in Fig. 185 — sounds are often echoed from the rocks, rebounding, as at 1, 2, 3, 4, from side to side. Speaking-trumpets depend on the reflection of sound. Fig. 1S6. The divergence is prevented by the sides of its tube ; and if the instrument is of a suitable figure, the rays of sound issue from it, as seen in Fig. 186, in a parallel direction. Its efiiciency depends on its length. It is stated that through such an instrument, from 18 to 24 feet long, a man's voice can be heard at a distance of three miles. Under common cir- cumstances, the greatest distances at which sounds have ■Why must two reflecting surfaces be at a certain distance t What is the construction of the speaking-tnimpet 1 HEARING-TRUMPETS 167 been heard are usually estimated as follows : the report of a musket, 8000 paces ; the march of a company of sol- diers at night, 830 paces; a squadron galloping, 1080 ; the voice of a strong man, in the open air, 230. But the ex- plosions of the volcano of St. Vincent were heard at Demerara, 345 miles ; and, at the siege of Antwerp, the cannonading was heard, in the mines of i^;;'. 187. Saxony, 370 miles. The hearing-trumpet is for the purpose of collecting rays of sound by reflexion, and transmitting them to the ear. Its mode of action is represented at Fig. 187. At what distaoce can sounds be heard? What is the construction cf the hearing-trumpet. 16S OPTICS. PROPERTIES OF LIGHT. OPTICS. LECTURE XXXV. PlloPERTiEs OP Light. — Theories of the Nature of Light. — Sources of Light. — Phosphorescence. — Temperature of a red Heat. — Effects of Bodies on Light. — Passage in straight Lines. — Production of Shadows. — Umbra and Penumbra. ^ Having successively treated of the general mechanical properties of gases, liquids, solids, and the laws of motion, we are led, in the next place, to the consideration of cer- tain agents or forces — light, heat, electricity. These, by many philosophers, are believed to be matter, in an im- ponderable state ; they are therefore spoken of as im- ponderable substances. By others their effects are re- garded as arising frorri motions or modifications impressed on a medium everywhere present, which passes under the name of the ether. Applying these views to the case of light, two diiferent hypotheses, respecting its constitution, obtain. The first, which has the designation of the theory of emission, re- gards light as consisting of particles of amazing minute- ness, which are projected by the shining body, in all di- rections, and in straight lines. These impinging eventu- ally on the organ of vision, give rise to the sensation which we speak of as brightness or light. To the othel theory, the title of undulatory theory is given ; it supposes that there exists throughout the universe an ethereal me- dium, in which vibratory movements can aiise somewhat analogous to the movements which give birth to sounds Name the imponderable substances. What other theory is there re epecting their nature ? What is the theory of emission ? What is thS foundation of I he undulatory theory? SOURCES OF LIGHT. 1C9 in the air; and these passing through the transparent parts of the eye, and falling on the retina', affect it with their pulsations, as waves in the air affect the auditory nerve, but in this case g^ve rise to the sensation of light, as in the other to sound. There are many different sources of light — some are astronomical and some terrestrial. Among the former may be mentioned the sun and the stars — among the lat- ter, the burning of bodies, or combustion, to which we chiefly resort for our artificial lights, as lamps, candles, gas flames. Many bodies are phosphorescent, that is to say, emit light after they have been exposed to the sun or any shining source. Thus, oyster-shells, which have been cal- cined with sulphur, shine in a dark place after they have been exposed to the light, and certain diamonds do the same. So, too, during processes of putrefaction, or slow decay, light is very often emitted, as when wood is mould- ering or meat is becoming putrescent. The source of the luminousness, in these cases, seems to be the same as in ordinary combustions, that is, the burning away of car- bon and hydrogen under the influence of atmospheric air; but, in certain cases, the functions of life give rise to an abundant emission of light, as in fireflies and glowworms ; these continue to shine even under the surface of water, and there is reason to believe that the phenomenon is to a considerable extent subject to the volition of the animal. All solid substances, when they are exposed to a cer- tain degree of heat, become incandescent or ernit light. "When first visible in a dark place, this light is of a red- dish color, but as the temperature is carried higher and higher it becomes more brilliant, being next of a yellow, and lastly of a dazzlihg whiteness. For this reason we sometimes indicate the temperature of such bodies, in a rough way, by reference to the color they emit : thus we speak of a red heat, a yellow heat, a white heat. I have recently proved that all solid substances begin to emit light at the same degree of heat, and that this answers to 977° of Fahrenheit's thermometer ; moreover, as the tem- Mention some of the sources of light. What is meant by phospho-, rescence? To what source may the light emitted daring putrefaction and decay be attributed ? What is there remarkable in the shining of glow- worms and fireflies ? What is meant by incandescence ? What succes- sion of colors is jierceived in self-lumiBous bodies 7 At what temnperature do all solids begm to shine ? H 170 PATH OF RAYS. perature rises the brilliancy of the light rapidly increases, so that at a temperature of 2600° it is almost forty times as intense aa at 1900°. At these high temperatures an ele- vation of a few degrees makes a prodigious difference in the brilliancy. Gases require to be brought to a far higher temperature than solids before they begin to emit light. Non-luminous bodies become visible by reflecting the light which falls on them. In their general relations such bodies may be spoken of as transparent and opaque. By the former we mean those which, like glass, afford a more or less ready passage to the light through them ; by the latter, such as refuse it a passage. But transparency and opacity are never absolute— they are only relative. The purest glass extinguishes a certain amount of the rays which fall on it, and the metals which are commonly looked upon as being perfectly opaque allow light to pass through them, provided they are thin enough. Thus gold leaf spread upon glass transmits a greenish-colored light. The rays of light, from whatever source they may come, move forward in straight lines, continuing their course until they are diverteJ'from it by the interposition of some obstacle, or the agency of some force. That this rectilinear path is followed maybe proved by a variety of facfs. Thus, if we intervene an opaque body between any object and the eye, the moment the edge of that body comes to the line which connects the object and the eye the object is cut off from our view. In a room into which a sunbeam is admitted through a crevice, the path which the light takes, as is marked out by the motes that float in the air, is a straight line. By a ray of light we mean a straight line drawn from the luminous body, marking out the path along which the shining particles pass. A shining body is said to radiate its light, because i' projects its luminous particles in straight lines, like radii, in every direction, and these falling on opaque bodies and being intercepted by them, give rise to the produc- tion of shadows. At what rate does the light increase as the temperature rises 3 Aia solids or'gases most readily made incandescent? How do non-luminoul bodies become visible ? What classes are they divided into ? Are trans' parency and opacity absolute qnalities ? Prove that rays move in straigh Unes. What is meant by radiation ? How are shadows produced ? SHADOWS. 171 If the light is emitted by a single luminous point, the Doundary of the shadow can be obtained by drawing straight lines from the lumi- Fig. 188. nous point to every point on the edge of the body, and pro- ducing them. Thus, let a, Fig. 188, be the luminous point, b c the opaque body ; by draw- ing the lines ab,ac, and pro- ducing them to d and e the boundary and figure of the shadow maybe exhibited. But if the luminous body, as in most instances is the case, possesses a sensible magnitude ; if it is, for example, the sun or a flame, an opaque body will cast two shadowSj which pass respect- ively under the names of the wmhra and penumbra — the former being dark and the latter partially illuminated. This may be illustrated by Fig. 189, in Fig. 189 which a b is the flame of a candle or any other luminous source, having a sensible magnitude, c d the opaque^ body. Now the straight lines, a c f, a dh, drawn from the top of the flame to the edges of the opaque body and produced, give' the shadow for that point of the flame ; attd the lines bee, b d g, drawn in like manner from the bottom of the flame, give the shadow for that point. But we see that the space between g and h, which belongs to the shadow for the top of the flame, is not perfectly dark, because it is so situated as to be partially illuminated by the bottom of the flame — and a similar remark may be made as respects the space,ye, which receives light from the top of the flame. But the remaining space, f g, re- ceives no light whatever — it is totally dark — and we there- fore call it the umbra, while the partially-illuminated i-e- gions.y e and g h, are the penumbra. Trace the shadow of a body formerby a luminous point. Trace the formation of a shadow when the luminous source is of sensible size. What Is the umbra? What is the penumbra 172 PHOTOMETRY. LECTURE XXXVI. Op the Measures of the Intensity and Velocity op Light. — Conditions of the Intensity of Light. — Of Pho- tometric Methods. — Rumford's Method by Shadows. — Ritchie^s Photometer. — Difficulties in Colored Lights. — Masson's Method. — Velocity of Light Determined by the Eclipses of Jupiter's Satellites. — The same by the Aber- ration of the Fixed Stars. By Photometry we mean the measurement of the brill- iancy of light — an operation which can be conducted in many different ways^ It is to be understood that the illuminating power of a shining body depends on several circumstances : First, upon its distance — for near at hand the effect is much greater than far off — the law for the intensity of light in this respect being that the brilliancy of the light is inversely as the square of the distance. A candle two feet off gives only one fourth of the light that it does at one foot, at three feet it gives only one ninth, &c. Secondly, it depends on the absolute intensity of the luminous surface : thus we have seen that a solid at different degrees of heat emits very different amounts of light, and in the same v^ay the flame of burning hydrogen is almost invisible, and that of spirits of wine is very dull when compared with an ordinaiy lamp. Thirdly, it depends on the area or surface the shining body exposes, the brightness being greater according as that surface is greater. Fourthly, in the absorption which the light suffers in passing the medium through which it has to traverse — for even the most transparent obstructs it to a certain extent. And lastly, on the angle at which the rays strike the surface they illuminate, being most effective when they fall per- pendicularly, and less in proportion as their obliquity in- What is photometry ? Mention some of the conditions which determiM .he brilliancy of light. What is the law of its decrease by distance? Whsl Has obliquity of surfaces to do with the result ? INTENSITY OF LIGHT. 173 The first and last of the conditions here mentioned, as controlling the intensity of light — the effect of distance and of obliquity — may be illustrated as follows : — Fig. 190. 1st. That the intensity of light is inversely as the squares of the distance. Let B, Fig. 190, be an aperture in a piece of paper, through which rays coming from a small illuminated point, A, pass ; let these rays be received on a second piece of paper, C, placed twice as far from A aa is B, it will be found that they illuminate a, surface which is twice as long and twice as broad as A, and therefore contains four times the area. If the paper be placed at D, three times as far from A as is B, the illuminated space will be three times as long and three times as broad as A, and contain nine times the surface. If it be at E, which is four times the distance, the surface will be sixteen times as great. All this arises from the rectilinear paths which the diverging rays take, and therefore a surface illumina- ted by a given light will receive, at distances represented by the numbers 1, 2, 3, 4, &c., quantities of light repre- sented by the numbers 1, J, i, ^, &c., which latter are the inverse squares of the fonner numbers. 2i. That the intensity of light is dependent on the an- gle at which the rays strike the receiving' surface, being most effective when they fall perpendicularly, and Jess in proportion as the obliquity increases. Let there be two surfaces, D C and E C, Fig. 191, on which a beam of light, A B, falls on the former perpendicularly and on the latter obliquely — the latter surface, in proportion to its obliquity, must have a larger area to receive all the rays which fall on D C. A given quantity of light, therefore. Give illustrations of the effect of distance and of obliquity. ' 174 EUMFOEDS FHOTOMETEU. FHg. 191. ts diffused over a greater surface when it is received ob- liquely, and its effect is correspondingly less. To compare different lights with one another, Count Rumford invented a process which goes under the name of the method of shadows. The principle is very simple. Of two lights, that which is the most brilliant will cast the deepest shadow, and with any light the shadow which is cast becomes less dark as the light is more distant. If, therefore, we wish to examine experimentally the brill- iancy of two lights on Rumford's method, we take a screen of white paper and setting in front of it an opaque rod, we place the lights in such a position that the two shadows arising shall be close together, side by side. Now the eye can, without any difficulty, determine which of the two is darkest ; and by removing the light which has cast it to a greater distance, we can, by a few trials, bring the two shadows to precisely the same degree of depth. It remains then to measure the distances of the two lights from the screen, and the illuminating powers are as the squares of those distances. Ritchie's photometer is an instrument for obtaining the same result, not, however, by the contrast of shadows, but by the equal illumination of surfaces. It consists of a box, a b, Fig. 192, six or eight inches long and one broad and deep, in the middle of which a wedge of wood, /eg, with its angle, e, upward, is placed. This wedge is covered over with clean white paper, neatly doubled to a sharp line at e. In the top of the box there is a conical tube, with an aperture, d, at its upper end, to which the What is the principle of Eumford's photometric process ? How is it applied in practice ? What is the illuminating power of the lights propor (ional to ? Describe Ritchie's photometer. RITCHIE S PHOTOMETEE.. 175 eye is applied, and the whole may be raised to any suitable height by means of p/g, 192. the stand c. On look- ^ ing down through ^ d, having previous- ly placed the two lights, m n, the in- . '/ I e ' tensity of which we desire to determine^ on opposite sides of iit the box, they illu- minate the paper surfaces exposed to them, e fUi m, and e g to », and the eye, at d, sees both those surfaces at once. By changing the position of the lights, we eventually make them illuminate the surfaces equally, and then measuring their distances from e, their illuminating powers are as the squares of those dis- tances. It is not possible to apply either of these methods in a satisfactory manner where, as is unfortunately often the case, the lights to be examined differ in color. The eye can form no judgment whatever of the relation of bright- ness of two surfaces when they are of different colors ; and a very slight amount of tint completely destroys the accuracy of these processes. To some extent, in Ritchie's instrument, this may be avoided, by placing a colored glass at the-.aperture, d. A third ^photometric method has recently been intro- iuced ; it 'has great advantages over either of the fore- going ; and difference of coloi", which in them is so se- rious an obstacle, serves in it actually to increase the ac- curacy of the result. The principle on which it is found- ed is as follows : If we take two lights, and cause one of them to throw the shadow of an opaque body upon a white screen, there is a certain distance to which, if we bring the second light, its rays, illuminating the screen, will totally obliterate all traces of the shadow. This dis- appearance of the shadow can be judged of with great What difBculties arise when the lights and the shadows they give are colored ? H iw n\ay these be avoided t Describe another procesa which is free from the foregoing difficulties. On what principle does it de- pend? 176 VELOCITY OF LIGHT. accuracy by the eye. It has been found that eyes of average sensitiveness fail to distinguish the effect of a light when it is in presence of another sixty-four times as intense. The precise number varies somewhat with dif- ferent eyes ; but to the same eye it is always the same. If there be any doubt as to the perfect disappearance of the shadow, the receiving screen may be agitated or moved a little. This brings the shadow, to a certain ex- tent, into view again. Its place can then be traced ; and, on ceasing the motion, the disappearance verified. When, therefore, we desire to discover the relative in- tensities of light, we have merely to inquire at what dis- tance they effect the total obliteration of a shadow, and their intensities are as the squares of those distances. ■! have employed this method for the determination of the quantities of light emitted by a solid at different temper- atures, and have found it very exact. Light does not pass instantaneously from one point to another, but with a measurable velocity. The ancients believed that its transmission was instantaneous, illustrat- ing it by the example of a stick, which, when pushed at one end, simultaneously moves at the other. They did not know that even their illustration was false ; for a certain time elapses before the farther end of the stick moves ; and, in reality, a longer time than light would re- quire to pass over a distance equal to the length of the stick. But in 1676, a Danish astronomer, Eoemer, found, from observations on the eclipses of Jupiter's satellites, that light moves at the rate of about 192,000 miles in one second. This singular observation may be explained as foUowe : Let S, Fig. 193, be the sun, E the earth, moving in the orbit E E', as indicated by the arrows j let J be Jupi ter and T his first satellite, moving in its orbit round him. It takes the satellite 42 hours 28 minutes 35 sec onds to pass from T to T' — that is to say, through the planet's shadow. But, during this period of time, the earth moves in her orbit, from E to E', a space of 2,880,000 miles. Now, it is found, under these circum Does light move with instantaneous velocity ? Who discovered its pro gressii* motion ? What is its actual rate ? ■ Describe the facts by whic> this has been determined. By whom and under what circumstances has this been verified ? roemee's and bradlet's discoveries. 177 dances, that the emersion of the satellite is 15 seconds Fig. 193. later than it should have been. And it is clear that this is owing to the fact that the light requires 15 seconds to pass from E to E' and overtake the earth. Its velocity, therefore, in one second, must be 192,000 miles. This, beautiful deduction was corroborated by Dr Bradley, in 1725, upon totally different principles, involv ing what is termed the aberration of the stars. The prin- ciple, which is somewhat dif- ng. 194. ficult to explain, is clearly il- lustrated by Eisenlohr as fol lows : Let M" N represent a ship, whose side is aimed at point blank by a cannon at a. Now, if the vessel were at Test, a ball discharged in this manner would pass through the points b and c, so that the three points, a, h, and c, would all be in the same straight line. But if the vessel itself move from M toward N, then the ball which entered at b would not come out at the opposite point, c, but at some other point, d, as much nearer to the stem, as is equal to the distance gone ovei by the vessel, from M to N, during the time of passage of the ball through her. The lines b c and b d, therefore, form an angle at b, whose magnitude depends on the po- sition of b c and b d. The greater the velocity of the ball, as compared with the ship, the less the angle. Next, What is meant by the aberration of the fixed stars ? Give an illustration of it. What is the vain e of the angle of aberration ? What is the velocity of light as thus determined ? 178 REFLEXION OP LIGHT. for the ship substitute in your mind the earth, and for the cannon any of the fixed stars ; let the velocity, b c, of the cannon-ball now stand for that of light, and let <^ c be the velocity of the earth in her orbit. The angle d b c, ia called the angle of aberration. It amounts to 20^ seconds for all the stars ; for they all exhibit the same alteration in their apparent position, being more backward than they really are in the direction of the earth's annual mo- tion, as Bradley discovered. By a simple trigonometri- cal calculation, it appears from these facts that the velo- city of light is 195,000 miles per second, a result nearly coinciding with the former. LECTURE XXXVII. Reflexion op Light. — Different kinds of Mirrors. — General Law of Reflexion. — Case of Parallel, Con- verging, and Diverging Rays on Plane Mirrors. — The Kaleidoscope. — Properties of Spherical Concave Mir- rors. — Properties of Spherical Convex Mirrors. — Spheri- cal Aberration. — Mirrors of other Forms.-;— Cylindrical Mirrors. When a ray of light falls upon a surface, it may be reflected, or transmitted, or absorbed. We therefore proceed to the study of these three incidents, which may happen to light, commencing with reflexion. Reflecting surfaces in optics are called mirrors; they are of various kinds, as of polished metal or glass. They differ also as respects the figure of their surfaces, being plane, convex, or concave ; and again they are divided into such as are spherical, parabolic, elliptical, &c. The general IdW which is at the foundation of this part of optics — the law of reflexion — is as follows : The angle of reflexion is equal to the angle of Incidence, the reflected ray is in the opposite side of the perpendicular, and the perpendicular, the incident, and the refected rays are all in the same plane. When a ray of light falls on a surface what may happen to it ? What ia meant bv reflecting surfaces ? What is the general law of reflexion? PLANE MIRRORS. 179 Thus, let c, Fig. 195, be the reflectuig sur- '^v- 195- face ; & c a perpendicular to it at any point, a c a ray incident on the same point ; the path of the reflected ray under the foregoing law will. he c d; such, that it is on the oppo- site side of the perpendicular to the incident ray, that ac,cb, and c d, are all in the same plane, and that the angle of incidence, a cb, ia equal to the angle of reflexion, bed. Reflexion from mirror surfaces may be studied under three divisions : reflexion from plane, from concave, and from convex mirrors. When parallel rays fall on a plane mirror, they will be reflected parallel, and divergent and convergent rays will respectively diverge and converge at angles equal to their angles of incidence. When rays diverging from a point fall on a min-or, they are reflected from it in such a manner as though they proceeded from a point as far behind it as it is in reality before it. This principle has already been ex- plained in Lecture XXXII, Fig. , ^v-'^^- 176. It is illustrated in J%. 196. Thus, if from the point a two rays, a b, a c, diverge, they will, under the general law, be respect- ively reflected along b d, c e ; and if these be produced they will in- tersect at a', as far behind the mirror as a is before it. The point a' is called the virtual focus. From this it appears that any object seen in a plane mirror ap- pears to be as far behind it as it is in reality before it. If an object is placed between two parallel plane mir- rors each VTiil produce a reflected image, and will also repeat the one reflected by the other. The consequence is, therefore, that there is an indefinite number of images produced, and in reality the number would be infinite Illustrate this law by Fig. 195. What three kinds of mirrors are there ? When parallel, divergent, or convergent rays fall on a plane mirror, what happens to them after reflexion ? AVhat does Fig. 196 Illustrate ' What is the eifect of two parallel plane mirrors ? 180 CONCAVE MIRRORS. were the light not gradually enfeebled by loss at each successive reflexion. The kaleidoscope is a tube containing two plane mir- rora, which run through it lengthwise, and are generally inclined at an angle of 60^. At one end of the tube is an arrangement by which pieces of colored glass or other objects may be held, aiid at the other there is a cap with a small aperture. On placing the eye at this aperture the objects are reflected, and form a beautifiil hexag- onal combination, their position and appearance may be varied by turning the tube round on its axis. Concave and convex mirrors are commonly ground to a spherical figure, though other figures, such as ellipsoids, parabaloids, &c., are occasionally used for special pur- poses. It is the properties of spherical concaves tbat we shall first describe. The general action of a spherical mirror may be under- Fig.wi. stood by regarding it as made up of a great number of small plane mirrors, as A, B, C, D, E, F,G,Fig.m. On such a combination of small mirrors, let rays emanating from R impinge. The different degrees of obliquity under which they fall upon the mirrors cause them to follow new paths after reflexion, so that they converge to the point S as to a focus. The problem of determining the path of a ray after it has been reflected is solved by first drawing a perpen- dicular to the surface at the point of impact, and then drawing a line on the opposite side of this pei-pendicular, making with it an angle equal to that of the angle of incidence of the incident ray. Thus, let r, s, Fig. 198, be an incident ray falling on any reflecting surface at s. To find the path it will take after reflexion, we first draw s c, a perpendicular to the surface at the point of impact, 8. And then draw the line s J" on the opposite side of the What is the kaleidoscope ? What is the ordinary figure of concave and convex mirrors ? How may the general action of these mirrors be con- ceived? Describe -the method for determining the path of rays aftei reflexion CONCAVE MIEEOKS. 181 perpendicular c s, such, that the angle c s f ia equal to the angle o s r. This is nothing but an application of the general law of reflexion, that the angles of incidence and reflexion are equal to one another, and are on oppo- site sides of the perpendicular. When rays of light diverge from the center of a spheri- cal concave mirrofj after reflexion they converge back to the same point. For, from the nature of such a surface, lines drawn from its center are perpendicular to the point to which they are drawn, every ray, therefore, impinges perpendicularly upon the surface and returns to the center again. When parallel rays of light fall on the surface of a sphe- Fig- 198. rical mirror, the aper- ture or diameter of which is not very large, they are re- flected to a point half way between the sur- face and center of the mirror. Thus, let r* / «* be parallel rays falling on the mirror * *', the aperture, s s', of which is only a few degrees, these rays, after refleiidon, will be found converging to the point _/) which is called the principal Jhcus, half way between the vertex of the mirror, v, and its center, c; for if we draw the "radii, c s c s", these lines are perpendiculars to the mirror at the points on which they fall ; then make the angles c syequal car, and c s'f equal c s' r', and it is easy to prove that the pointy is midway between v and c. But if the aperture, s s', of the mirror exceeds a few de- grees, it may be proved geometrically that the rays no longer converge to the focus,y but, as the aperture in- creases, are found nearer and nearer to the vertex, v, until finally, were it not for the opacity of the mirror, they would fall at the back of it. As this deviation is depend- ent on the spherical figure of the mirror, it is termed aberration of sphericity. When rays diverge from tha center of a spherical concave mirror, Vf here will they be found after reflexion 1 What is thf case virhen parallel rays fall on a spherical mirror 1 Why is the result Hmitedlo mirrors of small aperture ? What is meant by aberration of sphericity? i82 CONCAVE MIRRORS. Piff. 200. Conversely, if diverging rays issue from a lucid point, /, Fig. 198, half way between the vertex and center of a spheri- cal mirror of limited aperture, they will be reflected in parallel lines. Rays coming from any point, r, Fig. 199, at a finite distance beyond the center of the mirror, will be reflected so as to fall between the focus, J", and the center, c. Rays comingfrom a point, r, Fig. 200, between the focus, jT, and the vertex, v, will diverge after reflexion. Under such circumstances a virtual focus, f, exists at the back of the mirror. Concave mirrors give rise to the formation of images in their foci. This fact may be shown experimentally by placing a candle at a certain distance in front of such a mir- ror and a small screen of paper at the focus. On this paper will be seen an image of the flame, beautifully clear and distinct, but inverted. The relative size and position of this image varies according to the distance of the object from the vertex of the mirror. The second variety of curved mirrors is the convex; their chief properties are as follows : When parallel rays fall on the surface of a convex mir- ror, they become divergent after reflexion ; for let * s' be such a mirror, and r s r" s' rays parallel to its axis falling on it, let c be the center of the mirror, and draw c s c^, which will be respectively perpendicular to the mirror at the points s and s' ; then for the reflected rays, make the What is the case when diverging rays issue from the focus of a spherical mirror? What when they come from a finite distance beyond the center? What when they come from between the focus and the vertex ? How may it be proved that concave mirrors form images ? What is the second van- ety of mirrors ? When parallel rays fall on a convex mirror, what path do they take ? CONVEX MIRRORS. 18a Fig. 201. mgle, t s p, equal to p s r, and the angle, f s' p', equal to p' s' /- It may then de demonstrated, that not only do these re- flected rays diverge, but if they be producod through the mirror till they intersect, they will give a virtual focus at /, half way between the vertex of the mir- ror, V, and its center, c, so long as the mirror is of a limited aperture. In a similar manner it may be proved that diverging rays, falling on a convex mirror, become more divergent. To avoid the effect of spherical aberration, it has been proposed to give to mirrors other forms than the spherical. Some are ground to a paraboloidal, and others to an ellip- soidal figure. Of the properties of such surfaces I have already spoken, under the theory of undulations, in Lec- ture XXXII ; and the effects remain the same, whether we consider light as consisting of innumerable small particles, shot forth with great velocity, or of undulations arising in an elastic ether. In both cases parallel rays, falling on a paraboloidal mirror, are accurately converged to the fo- cus, whatever the aperture of the miixor may be ; and in ellipsoidal ones, rays diverging from one of the foci, are collected together in the other. Occasionally, for the pur poses of amusement, mirrors are gi'ound to cylindrical or conical figures ; they distort the appearance of objects presented to them, or reflect, in proper proportions, the images of distorted or ludicrous paintings. Why are paraboloidal and ellipsoidal mirrors sometimes used ? What is the effect of the former on parallel lays 1 What of the latter on rays is- suing from one of the foci ? What are the effects of cylindrical mirrors 1 184 REFKACTION OP lilGHT. LECTURE XXXVIII. Refraction op Light. — Refractive Action described.— Law of the Sines. — Relation of the Refractive 'Power with other Qualities. — Total Reflexion. — Rays on plane Surfaces. — The Prism. — Action of the Prism on a Ray. — The Multiplying- Glass. When a ray of light passes out of one medium into another of a different density, its rectilinear progress is disturbed, and it bends into a new path. This phenom- enon is designated the refraction of light. Tims, if a sunbeam, entering through a small hole in the shutter of a dark room, falls on the surface of some water contained in a vessel, the beam, instead of passing on in a straight line, as it would have done had the water not intervened, is bent or broken at the point of incidence, and moves in the new direction. ^s- 202. In tJie same way, also, if a ^ coin or any other object, 0, Fig. 202, be placed at the bottom of an empty bowl, A B C D, and the eye at E so situated that it cannot per- ceive the coin, the edge of the vessel intervening, if we pour in water the object comes into view ; and the cause of this is the same as in the for- mer illustration : for while the vessel is empty the ray is obstructed by the edge of the bowl, as at O G- E, but when water is poured in to the height F G, refraction at the point L, from the perpendicular, P Q,, ensues; and now the ray takes the course OLE, and entering the eye at E, the object appears at K, in the line ELK. For the same reason oars or straight sticks immersed in water look broken, and the bottom of a stream seeraa at a much less depth than what it actually is. What is meant by the refraction of light ? Explain the illustrations of this phenomenon as given in I'igs. 202 and 203. REFRACTION OP LIGHT. 185 Fig. 303. The same result ensues under the cifi^/umstances repre sented in Fig. 203, in which E represents a candle, the rays of which fall on a " rectangular box, ABC D, under such circum- stances as to cast the shadow of the side A C, so as to fall at D. If the box be now filled with water, every thing re- maining as before, the shadow will leave the point D and go to d, the rays undergoing refraction as they enter the liquid ; and if the eye. could be placed at d, it would see the candle at e, in the direction of d A produced. Let N O, Fig. 204, be a refracting surface, and C the G E point of incidence of a ray, B C, C E the course of the refracted ray, and C K the course the ray would have taken had not refraction ensued. With the point of inci- dence, C, as a center, describe a circle, N M O G, and from A and R draw the lines A D, R H at right angles to the perpendicular M G to the point C. Then ACM will be the angle of incidence, R C G the angle of refraction; A D is the sine of the angle of incidence, and H R the sine of the angle of refraction. Now in every medium Explain Fig. 204. What is the angle of incidence ? What is the angle of refraction ? Which are the sines of those angles ? 186 LAW OF SINES. Pig.SOS. poC / h /^SJH l/\ \/l W these lines have a fixed relation to one another, and jhe general law of refraction is as follows : — In each medium the sine of the angle of incidence is in a constant ratio to ike sine of the angle of refraction ; the in- cident, the perpendicular, and the refracted ray are all in the same plane,w7iic7i is always at right angles to the plane of the refracting medium. To a beginner, this law of the constancy of sines may be explained as follows : — Let C D, Fig. 205, be a ray falling on a medium, A B, in the point D, where it undergoes refrac- J tion and lakes the dii'ection D E. Its sine of incidence, as just explained, is C g, and its sine of refraction E e ; and let us suppose that the medium is of such a nature that the sine of refraction is one half the sine of incidence — that is, E e is half C g. Moreover, let there be a second ray, H D, incident also at the point D, and refracted along D F ; H h will be its sine of incidence, and F f its sine of re- fraction; and by the law Fy will be exactly one half H^. The proportion or relation between these sines differs when different media are used, but for the same medium it is always the same. Thus, in the case of water, the pro- portion is as 1.366 to 1; for flint-glass, 1.584 to 1; for dia- mond, 2.487 to 1. These numbers are obtained by ex- periment. They are called the indices of refraction of bodies, and tables of the more common substances are given in the larger .works on optics. No general law has as yet been discovered which would enable us to predict the refractive power of bodies from any of their other qualities ; but it has been noticed that inflammable bodies are commonly more powerful than incombustible ones, and those that are dense are more en- ergetic than those that are rare. When a ray of light passes out of a rare into a dense What relation do these sines bear to one another ? Explain the law of the constancy of the sines as givfen in Fig. 205. What is the rate for water, flint-glass, and diamond ? WTiat is meant by indices of refraction ? Istho refi-active power of bodies connected with any other property ? TOTAL REFLEXION 187 medium, it is refracted toward the perpendicular. Fig. 203 is an illustration — the rays passing from air into wa- ter. But when a ray passes from a dense into a rarer medium it is refracted from the perpendicular. Fig. 202 is an example — the rays passing from water into air. In every case when a ray falls on the surface of any medium whatever, it is only a portion which is transmit- ted, a portion being always reflected. If in a dark room we receive a sunbeam on the surface of some water, this division into a reflected and a refracted ray is very evi- dent : and when a ray is about to pass out of a highly re- fractive medium into -one that is less so, making the angle of incidence so large that the angle of refraction is equal to or exceeds 90°, total reflexion ensues. This may be readily shown by allowing the Fig. 206. rays from a candle, f, or any .3 other object, to fall on the sec- | ond face, 6 c, of a glass prism, a i^ \ ,a h c, Fig. 206 ; the eye placed atd will receive the reflected ray, d e, and it will be perceived that the face h c of the glass, when exposed to the daylight, ap- pears as though it were sil- vered, reflecting perfectly all objects exposed to its front, a c. As with the reflexion of light, so with refraction — ^it is to be considered as taking place on plane, convex, and concave surfaces. When parallel rays fall upon a plane refracting surface they continue parallel after refraction. This must neces- sarily be the case on account of the uniform action of the medium. If divergent rays fall upon a plane of greater refractive power than the medium through which they have come, they will be less divergent than before. Thus, from the point a let the rays ah, ah' diverge ; afl;er suffering re- fraction they will pass in the paths h c, V c, and if these When is light refracted toward and when from the perpendicular ? Is the whole of the light transmitted ? Under what circumstance does total reflexion take place ? What ensues when parallel rays fall on a plane surface ? What is the case with diverging ones ? 188 THE PRISM. lines be projected, they will inter- sect at a', but a' h, a' h' are less divergent than ah, a b'. If, on the contrary, rays pass from a medium of greater to one of less refractive power, they will be more divergent after refrac- tion. For thia reason bodies un- der water appear nearer the sur- face than they actually are. When parallel rays of light pass through a medium bounded by planes that are parallel, as through a plate of glass, they will continue still parallel to one another, and to their original direction, after refraction. For this reason, therefore, we see through such plates of glass objects in their natural positions and relation. The optical prism is a transparent medium, having Fig. 208. plane surfaces inclined to one another. It is usually a wedge-shaped piece of glass, a a. Fig. 208, which can be turned into any suita- ble position, on a ball and socket-joint, c, and is supported on a stand, h. As this instrument is of great use in optical researches, we shall describe the path of a ray of light through it more minutely. Let, therefore, ABC, Fig. 209, be such a glass prism ^'S- ^^- seen endwise, and let jL B ^^ a b he a, ray of light incident at b. As this ray is passing from a rarer to a denser me- dium it is refracted toward the perpendic- •-^o,' ular to an extent de- pendent on the refractive power of the glass of which the prism is composed, and therefore pursues a new path, b c, through the glass ; at c it again undergoes refraction, and now passing from a denser to a rarer medium, takes What is the case when parallel rays pass through media with plane and parallel surfaces ? What is a prism ? Describe the path of a ray of light through this instrument. * MDLTIPLYING-GLASS. 189 Mg. 210. B new course, c d. To an eye placed at d, and looking through the prism, an object, a, seems as though it were at a', in the straight line d c continued. Through this in- stniment, therefore, the position of objects is changed, the refracted ray, c d, proceeding toward the back, A B, of the prism. But the prism in actual practice gives rise to far more complicated and interesting effects, to be described here- after, when we come to speak of the colors of light. The multiplying-glass is a transparent body, having sever- al inclined faces. Its construc- tion and action are represented at Fig. 210. Let A B be a plane face, C D also plane and parallel to it, but A C and D B inclined. Now let rays come from any object, a, those, a h, which fall perpendiculai'ly on the two faces will pass with- out suffering refraction ; but those, ac,a S, which fall on the inclined faces will be refracted into new paths, e f, d f, these portions acting like the prigm heretofore described. Con- sequently, an eye placed aty will see three images of the object in the direction of the lines along which the rays have come — that is, at a', a, a". Hence the term nmlti- plymg-glass, because it gives as many images of an ob- ject as it has inclined surfaces. To what other phenomenon does the prism give rise? What is the multiplying-glass? Why does it give as many images of an object as it has faces ? 190 LENSES. LECTURE XXXIX. The Action op Lenses. — Different Forms of 'Lenses.-'-' General Properties of Convex henses. — General Proper- ties of Concave Lenses. — Analogy between Mirrors and Lenses. — Production of Images by Lenses. — Size and Distance of Images. — Visual Angle. — Magnifying Ef- fects. — Burning-Lenses. Transparent media having curved surfaces are called lenses. They are of six mg. an . different kinds, as repre- A ...^MMiMlllim*.. Plano-convex. sented in Fig. 211. The . plano-convex lens, A, has B one surface plane and the other convex, the piano- C ' concave, B, has one sur- Plano-concave Double Convex. Concavo-convex. face plane and the other ] ^ — Wii Double Concave. concave ; C is the double convex, D the double con- cave, E the meniscus, and F the concavo-convex. F , For optical uses lenses are commonly made of glass, but for certain purposes other substances are employed. For example, rock crystal is often used for making spec- tacle lenses ; it is a hard- substance, and is not, therefore, so liable to be scratched or in- jured as glass. In a lens the paint c is called the geometrical center, for all lenses are ground to spherical surfaces, and c is the center of their curvature ; the aperture of the lens is a b, and d is its opti- cal center ; few the axis, and any ray, m n, which passes through the optical center, is called a principal ray. What aje lenses ? How many kinds of lenses are there ? What are they commonly made of? What other substances are sometimes used ? What is the geometrical center? What is the optical center? What is a principal ray ? What is the aperture 1 ACTION OF LENSES. 191 The general action of lenses of all kinds may be under- stood after what has been said in relation to the prism, of which it was remarked that the refracted ray is bent toward the back. Thus, if we have Mg. 213. two prisms, a c e, b c e, ^ placed back to back, and allow parallel rays of light, m. m n, to fall upon them, these Tays, after refraction, C^ ^* S^^ being bent from their par- allel path toward the back W of each prism, will inter- sect each other in some point, as f. Now, there is obviously a strong analogy between the figure of the double convex lens and that of these two prisms; indeed, the former might be regarded as a series of prisms with curved surfaces, and from such consideration it is clear, that when parallel rays fall on a convex lens, they will converge to a focal point. Again, let us suppose that a pair of prisms be placed edge to edge, as shown in Fig. 214, and that parallel rays, m n, are incident upon them. These rays undergo refraction, as before, to- ^Y 214 ward the back of their re- spective prisms, b c, d e, and therefore emerge di- vergent, as at y and g. Now, there is an analogy between such a combina- tion of prisms and a con- cave lens, and we there- fore see that the general action of such a lens upon parallel rays is to make them divergent. By the aid of the law of refraction it may be proved that lenses possess the following properties. Evei-y principal ray which falls upon a convex lens of limited thickness is transmitted without change of direc- tion. How ma^ the general action of a double convex lens be deduced from that of a pair of prisms 1 Trace the same action in the case of a double concave lens. 192 PROPERTIES OF LENSES. Rays parallel to the axis of a double equi-convex glass lens are brought to a focus at a distance from the optical center equal to the radius of curvature of the lens. But if it be a plano-convex glass the focal distance is tvyice as great. The focus for parallel rays is called the principal focus. Eays diverging from the principal focus of a convex lens after refraction become parallel. Rays diverging from a point in the axis more distant than the principal focus converge after refraction, their point of convergence being nearer the lens as the point from which they radiated was more distant. Rays coming from a point in the axis nearer than the principal focus diverge after refraction. With respect to concave lenses, the chief properties may be described as follows : — Every principal ray passes without change of direction. f^g. 315. Rays parallel to the axis are made diver- gent. Thus, m n, Fig' ure 215, being parat lei rays falling on the double concave, a b, diverge after refrac- tion in the directions g d; and if they be produced give rise to a virtual or imaginary focus aty; By concave lenses diverging rays are made still more divergent. When the effects of lenses are compared with those of miiTors, it will be found that there is an analogy in the action of concave mirroi's and convex lenses, and of con- vex mirrors and concave lenses. It has already been remarked that concave mirrors give images of external objects in their focus. The same holds good for convex lenses. Thus, if we take a convex lens, and place behind it, at the proper distance, a paper screen, we shall find upon that screen beautiful images of What are the chief properties of convex lenses ? What are the chiet properties of concave lenses? What is the relation between mirrors and lenses in their effects ' FOKMATION OP IMAGES. 193 all the objects in front of the lens in an inverted position. The manner in which they form may be understood from Mg. 216. Where L' L is a double convex lens, M N Fig. 316. any object, as an arrow, in front of it, the lens will give an inverted image, n m, of the object at a proper distance behind. From the point M all the rays, as M L, M C, M L', after refraction, will converge to a focus, m ; and from the point N all rays, as N L, N C,.N L', will like- vrise converge to, a focus, n; and so, for every interme- diate point between M and.N, intermediate foci will form between m and n, and therefore conjointly give rise to an inverted image. The images thus given by lenses or mirrors may be made visible by being received on white screens or on smoke. rising from a combustible body, or directly by the eye placed in a proper position to receive the rays. They then appear as if suspended in the air, and are spoken of as aerial images. The distance of such images from a lens, and also their magnitude, vary with circumstances. If the object be very remote^ it gives a minute image in the focus of the len? ; as it is brought nearer, the im' age recedes farther, and becomes larger ; when it is at a distance equal to twice the focal distance, the image is equidistant from the lens on the opposite side, and is of the same size as the object. As the object approaches still nearer, the jmage recedes, and now becomes larger than the object. When it reaches the focus, the image is at an infinite distance, the refracted rays being parallel to one another. And, lastly, when the object comes be- tween the focus and the surface of the lens, an erect and Do convex lenses give rise'to the fonnation of images ? How does this effect arise ? How may such images be made visible 7 Under what circumstances do the size and distance of the image vary ? 194 MAGNIFYING POWER. magnified image of the object will appear on the same side of the lens as the object itself. Hence, convex lenses are called magnifying-glasses. From these considerations, it therefore appears that the Fig. 2:7. magnifying power of lenses is not, as is often popularly supposed, due to the peculiar nature of the glass of which they are made, but to the figure of their surfaces. The dimensions of all objects depend on the angles under which they are seen. A coin at a distance of 100 yards appears of very small size, but as it is brought nearer the eye its size increases ; and when only a few inches off, it can obstruct the view of large objects. Thus, if A rep- resent its size at a remote distance, the angle D E F, or the visual angle, is the angle under which it is seen ; when brought nearer, at B, the angle is G- E H ; and at C, in- creases to I E K. In all cases the apparent size of an object increases as the visual angle increases, and all ob- jects become smaller as their distances increase ; and any optical contriv;ginces, either of lenses or mirrors, which can alter the angle at which rays enter the eye and make it larger than it would otherwise be, magnify the objects seen through them. On these principles concave mirrors and convex ienses magnify, and convex mirrors and concave lenses minify. Fromtheirproperty of con verging parallel rays to afo- CHS, convex lenses and concave mirrors have an interesting application, being used for the production of high temper- atures, by converging the rays of the sun. Fig. 218 repre- sents such a burning-glass. The parallel rays of the sun Why are convex lenses magnifying-glasses ? On what does this mag Bifyii .g action depend ? What is the visual angle of an object ? eOLOREO LIGHT. 195 falling on it are made to con- Fig. sis. verge, and this convergence might be increased by a sec- ond smaller lens. At the focal point any small object being exposed its tempera- ture is instantly raised. In such afocus there are few sub- stances that can withstand the heat — ^brick, slate, and other such earthy matters instantly boil, metals melt, and even < volatilize away. During the last century some French chemists, using one of these instruments, found that when a piece of silver is held over gold, fused at the focus, it became gilded over by the vapor that rose from the melted mass. And in the same way gold could be whitened by the vapors of melt- ed silver. The heat attained in this way far exceeds that of the best constructed furnace. LECTURE XL. Op Colored Light. — Action of the Prism. — Refraction and Dispersion. — The Solar Spectrum. — Its Constituent Rays. — They pre-exist in White Light. — Theory of the D^erent RefrangiMlity of the Rays of Light. — Differ- ent Dispersive Powers. — Irrationality of _ Dispersion. — Illuminating Effects. — The Fixed Lines. — Calorific Effects. — Chemical Effects, In speaking of the action of a prism, in Lect. XXXYIII., it was observed, that it gives rise to many interesting results connected with colored lights. These, which con- stitute one of the most splendid discoveries of Newton, I next proceed to explain. Through an aperture, a. Fig. 219, in the shutter of a dark room let a beam of light, a e, enter, and let it be inter- cepted at some part of its course by a glass prism, seen What is a burning glass 1 Why does it give rise to the production of an intense heat ? Mention some of the effects which have been obtained Oy tliese instruments. Describe the action of a prism on a ray of light. 196 DECOMPOSITION OP LIGHT. endwise at h c. The light will undergo refraction, and Fig. 219. in consequence of what has beeft al- ready stated, will pass in a direction, d, toward the back of the prism. Now, for any thing that has yet ^ been said, it might appear that this refracted ray, on reaching the screen d e, would form upon it a white spot similar to that which it would have given at e, had not the prism inter- vened. But when the experiment is made, instead of the lighj going as a single pencil of uni- form width, it spreads out into a fan shape, as is indicated by the dotted lines, and forms on the screen an oblong image jf the most splendid colors. In this beautiful result, two facts, which are wholly distinct, must be remarked : 1st, the light is refracted or bent out of its rectilinear path ; 2d, it is dispersed into an oblong colored figure. On examining this figure or image, which passes under the name of the solar spectrum, we find it divided into seven well-marked regions. Its lowest portion, that is to say, the part nearest to that to which the light would have gone had not the prism intervened, is of a red color, the most distant is of a violet, and between these other colors may be seen occurring in the following order : — Fig. 220. Red, Orange, Yellow, Green, Blue, Indigo, Violet. truth In Fig. 220, the order in which they occur is indicated by their initial letters, e being the point to which the light would have gone had not the prism intervened. Now, from what source do these splendid colors come 1 Newton proved that they pre-existed in the white light, which, in reality, is made up of them all taken in proper proportions. There are many ways in which this important can be established. Thus, if we take a second Is the refracted light white t What two general facts are to be observ ed ? What color is the lowest portion of the Spectrum ? What is the color of the highest. Wliat is the order of the colors ? DECOMPOSITION OF. LIGHT. 191 pnsm, B B' S', Fig. Fig.m. 221, and put it in an in- verted position, as re- spects the first, A A' S, so that it shall refract again in the opposite direction the rays re- fracted by the first, they will, after this second refraction, reunite and form a uniform beam, M, of white light, in all respects like the original beam itself. If the production of color were due to any iiTegular action of the faces of the first prism, the introduction of two more faces in the second prism would only tend to increase the coloration. But so far from this, no sooner is this second prism introduced than the rays reunite and recompose white light. It follows as an inevitable conse- quence that white light contains fM the seven rays. But Newton was not satisfied with this. He further collected the prismatic colored rays together into one focus by means of a lens, and found that they produced a spot of dazzling whiteness. And when he took seven powders, of colors corresponding to the prismatic rays, and ground them intimately together in a mortar, he found, that the resulting powder had a whitish aspect ; or if, on the surface of a wheel which could be made to spin round very fast on its axis, colored spaces were painted, when the wheel was made to turn so that the eye could no longer distinguish the separate tints, the whole as- sumed a whitish-gray appearance. By many experiments Newton proved that the true cause of this development of brilliant colors from a ray of white light by the prism, is due to the fact that that in- strument does not refract all the colors alike. Thus, it could be completely shown, in the case of any transparent medium, that the violet-ray was far more refrangible than the red, or more j^sturbed by such a medium from its course. In this originated the doctrine of " the different refrangibility of the rays of light." How may it be proved by two prisms that all these colors pre-exist in white light ? What may be proved by reuniting the rays by alans ? What by colored powders or a painted wheel? What is the cause of this de velopment of colors 7 ?98 IRRATIONALITY OF DISPERSION. On examining the order of colors in the spectrum, we find, in reality, as in Fi^. 220, that the red is least dis- turbed from its course, and the other colors follow in a fixed order. The red, therefore, is spoken of as the least refrangible ray, the violet as the most, and the other col- ors as intermediately refrangible. We now see the cause of the development of these col- ors from white light, which contains them all. If the prism acted on every ray alike, it would merely produce a white spot at d, analogous to that at e, Fig.'220, but as it acts unequally it separates the colored rays from one another, and gives rise to the spectrum. On examining prisms of different transparent media, we find that they act very differently — some dispersing the rays far more powerfully than others and giving rise, un- der the same circumstances, to spectra of very different lengths. In the treatises on optics, tables of the disper- sive powers of different transparent bodies are given : thus it appears that oil of cassia is more dispersive than rock-salt, rock-salt more than water, and water more than fluor spar. Moreover, in many instances it has been found that if we use different prisms which give spectra of equal lengths, the colored spaces are unequally spread out. This shows that media differ in their refracting action upon particu- lar rays, some acting upon one color more powerfully than another. This is called irrationality of dispersion. The different colored rays of light are not equally lu- minous — ^that is to say, do not impress our eyes with an equal brilliancy. If a piece of finely-printed paper be placed in the spectrum, we can read the letters at a much greater distance in the yellow than in the other regions, and from this the light declines on either hand, and grad- ually fades away in the violet and the red. It has also been found that the colors are not continu- ous throughout, but that when delicate means of examina- tion are resorted to the spectrum is seen to be crossed with many hundreds of dark lines, irregularly scattered through it. A representation of some of the larger of these is To what doctrine did this discovery give rise ? Do different media dis- perse to the same or different extents ? What is meant by irrationality of dispersion ? Are all the rays equally luminous to the eye ? How may this be proved ? FIXED LINES. 199 given in Fig. 222. It is curious that though they exist in the sun-light, and in that of the planets, they are Ftg^"^ not found in the spectra of ordinary artificial jP" lighte ; and, indeed, the electric spark gives a light I which is crossed by brilliant lines instead of black I ones. The chief fixed lines are designated by the | letters of the alphabet, as shown in the figure. The light of the sun is accompanied by heat. Dr. Herschel found that the different colored pris- 1 matic spaces possess very different power over! the thermometer. The heat is least in the violet, I and continually increases as we descend through I the colors, the red being the hottest of them all. I But below this, and out of the spectrum, when! there is no light at all, the maximum of heat isl found. The heat of the sunbeam is, therefore, re- 1 frangible, but is less refrangible than the red ray | of light. Late discoveries have shown that every ray of light can produce specific changes in compound bodies. Thus it is the yellow ray which controls the growth of plants, and makes their leaves turn green ; the blue ray which brings about a peculiar decoroposition of the iodides and chlorides of silver, bodies which are used in photogenic drawing. Those substances which phosphoresce after ex- posure to the sun are differently affected by the different rays — the more refrangible producing their glow, and the less extinguishing them. Describe the fixed lines of the spectrum. How are they distinguished ? What are the calorific effects of the spectrum? Whicit is the hottest space? What are the chemical effects? 200 H0M06KNE0U3 LIGHT. LECTURE XLI. Op Coloeed Light. — "Properties of Homogme^zis Light,— Formation of Compound Colors. — Chromatic Aberration of Lenses.— Achromatic Prism. — Achromatic Lens. — Imperfect Achromaticity from Irrationality of Disper- sion. — Cailse of the Colors of Opaque Objects. — Effects of Monochromatic Lights. — Colors of Transparent Media. Each color of the prismatic spectrum consists of homo geneous light. It can no longer be dispersed into other colors, or changed by refraction in any manner. Thus, Tig. 223. let a ray of light, S, Fig, 223, enter through an aperture, F, into a dark room, and be dispersed by the prism, A B C ; through a hole, G, in a screen, D E, let the resulting spectrum pass, and be received on a second screen, d e, placed some distance behind ; in this let there he a small opening, g, through which one of the colored rays of the spectrum, formed by A B C, may pass and be received on a second prism, ab c. It will undergo refraction, and pass to the position M on the screen, N M. But it will not be dispersed, nor will new colors arise from it ; and it is immaterial which particular ray is made to pass the opening at g, the same result is uniformly obtained. Homogeneous or monochromatic colors, therefore, can- not suffer dispersion. By the aid of the instrument Fig. 224, which consists How may it be proved thatliomogeneous light undergoes no further dis- persion ? What IS the use of the instrument represented in Fig. 224 ? COMPOUND COLOBS. 201 of a series of little plane mirrors set upon a frame, we 'f'£>i a ^ s -w g — g — s- can demonstrate, in a very striking manner, the constitu- tion of different kinds of lights ; for if this instrument be placed in such a manner as to receive the prismatic spec trum, by turning its mirrors in a suitable position we can throw the rays they receive at pleasure on a screen. Thus, if we mix together the red and blue ray, a purple results ; if the red and yellow, an orange ; and if the ybUow and blue, a green. It is obvious, therefore, that of the color* we have enumerated in Lecture XL, as the seven pris- matic rays, the green, the indigo, and violet may be com- pound, or secondary ones, arising from the intermixture of red, yellow, and blue, which by many philosophers are looked upon as the three primitive colors. We have already remarked that there is an analogy be- tween prisms and lenses in their action on the rays of light, and have shown how rays become converging or di- verging in. their passage through those transparent solids In the same manner it also follows, that as prisms pro- duce dispersion as well as refraction, so, J^V- 225. too, must lenses: for, by considering the action of pairs of prisms, as in Fig. 225, or as we have already done in Lec- ture XXXIX., we arrive at the action of concave and convex lenses, and find that as refrangibility differs for different rays — being least for the red and most for the violet — a lens acting unequally will cause objects to be seen through it fringed with prismatic colors. This phenomenon passes under the title of chromatic aberra- tion of lenses. To understand more clearly the nature of this, let par- allel rays of red light fall upon a plano-convex lens, A Which of the colors of the spectram maybe regarded as compound, and which as simple ? How may it be shown that lenses produce colors as well as igisms { 202 CHROMATIC ABERRATION. B, Fig 226, and be converged by it to a focus in the point ••, the distance of which from the lens is measured. Then let parallel rays of violet light, in like manner, fall on the lens, and be converged by it to a focus, v. On being measured, it will be found that this focus is much nearer the lens than the other; and the cause of it is plainly due to the unequal refrangibility of the two kinds of light. The violet is the more refrangible, and is, therefore, more powerfully acted on by the lens, and made to converge more rapidly. But this which we have been tracing in the case of ho- mogeneous rays must of course take place in the com- pound white light. On the same principle that the prism separates the white light into its constituent rays by act- ing unequally on them, so, too, will the lens. Parallel rays of white light falling on a lens, such as Fig. 226, are not, therefore, converged to one common focus, as repre- sented in Lecture XXXIX, but in reality give rise to a series of foci of different colors, the red being the most remote from the lens, and the violet nearest. In some of the most important optical instruments it is absolutely necessary that this defect should be avoided, and that a method should be hit upon by which light may be refracted without being dispersed. Newton, who believed that it was impossible to succeed with this, gave up the improvement of the refracting telescope, in which it is required that images should be formed without chro- matic dispersion, as hopeless. But, subsequently, it was shown that refraction without dispersion can be effected. This is done by employing two bodies having equal re- fractive, but unequal dispersive powers. Those which What is the effect of a plano-convex lens on parallel rays rf red and blue light, respectively ' What is the effect on white light ? ACHROMATIC PRISM AND LENS. 203 are commonly selected are crown and flint glass, which refract nearly equally. The index for crown being about 1-53, and that of flint 1*60 ; but the dispersion of good flint glass is twice that of crown. If, now, we take two prisms, ABC, Fig. 227. Fig. 227, being of crown, and A C D, of flint glass, and place them, with their bases in opposite ways, the refracting angle, C, - of the latter being half that of A, the former, or, in other words, adjusted to d o their relative dispersive powers, it will be found that a ray of light passes through the compound prism, undergoing re- fraction, and emerging without dispersion ; £)r the incident ray, in its passage through the crown prism will be dis- persed into the colored rays, and these, falling on the flint prism — the dispersive power of which we assume to be double, and acting in the opposite direction — will be re- fracted in the opposite direction, and emerge undispersed Such an instrument is called an achromatic prism. The same principle can, of course, be Fig.S3a. used in the construction of lenses, between which and prisms there is that general analogy heretofore spoken of. The achro- matic lens consists of a concave lens of flint and a convex one of crown, the cur- , vatures of each being adjusted on the same 1 principle as the angles of the achromatic prism are determined. Such an arrange- ment is represented in Fig. 228. It gives in its focus the images of objects in their natural colors, and nearly devoid of fringes. But in practice, it has been found impossible, by any ■iuch arrangement, to effect the total destruction of color. The edges of luminous bodies seen through'such lenses ire fringed with color to a slight extent. This arises irom the circumstance that the dispersive powers of tha media employed are not the same for every colored ray. The simple achromatic lens, F^g. 228, will collect the ex- How may refraction without dispersion be performed 7 Describe the atructure of the achromatic prism ? what is its mode of action ? Describe the construction of the achromatic lens. Why are there with these lenses residual fimges ? 204 COLORS OF OBJECTS. treme rays together ; but leaves the intenrediate ones, to a small extent, outstanding. The theory of the compound constitution of light ena- bles us to account, in a clear manner, for the colors of natural objects. Those which exhibit themselves to us as white merely reflect back to the eye the white light which falls on them, and the black ones absorb all the in- cident rays. The general reason of coloration is, there- fore, the absorption of one or other tint, and the reflec- tion of the rest of the spectral colors. Thus, an object looks blue because it reflects the blue rays more copiously than any others, absorbing the greater part of the rest. And the same explanation applies to red or yellow, and, indeed, to any compound colors, such as orange, green, &c. That colored bodies do, in this way, reflect one class of rays more copiously than others may be proved by placing them in the spectrum. Thus, a red wafer seems of a dusky tint in the blue or violet regions, but of a brill iant red in the red rays. On the same principles we account for the singular re suits which arise when monochromatic lights fall on sur faces of any kind. Thus, when spirits of vrine is mixed wdth salt in a plate, and set on fire, the flame is a mono chromatic yellow — that is, a yellow unaccompanied by any other ray. If the variously colored objects in a room are illuminated with such a light they assume an extraor- dinary appearance : the human countenance, for exam- ple, taking on a ghastly and death-like aspect ; the red of the lips and the cheeks is no longer red, for no red light falls on it ; it therefore assumes a grayish tint. The colors of transparent bodies, such as stained glass and colored solutions, arise from the absorption of one class of rays and the transmission of the rest. Thus, there are red glasses and red solutions which permit the red ray alone to traverse them, and totally extinguish every other. But, in most cases, the colors of transpa- rent, and also of opaque bodies, are far from being mono- chromatiCk They consist, in reality, of a great number How may the colors of natural objects be accounted for ? What is the cause of whiteness and blackness 1 How can it be proved that bodies re- flect some rays in preference to others ? What is monochromatic light ? What is the cause of the singular appearance of objects seen by sjch lights f What is the cause of the colors of transparent bodies 7 UNDDLATOEY THEORY. 20f of different rays. Thus, common blue-stained glass trans- mits almost all the blue light that falls upon it, and, in ad- dition, a little yellow and red. LECTURE XLII. Undhlatort Theory of Light. — Two Theories of Light — Applications of ike Gorpusadar Theory. — Vndulatory Theory. — Length of Waves is the cause of Color. — De- termination of Periods of Vibration. — Interference of Light. — Explanations of Newton's Rings, and Colors of thin "Plates.— "Diffraction of Light. It has been stated that there are two different theories respecting the nature of light — the corpuscular and the undulatory. In accounting for the facts in relation to the production of colors, it' is assumed that, in the former, there are various particles of luminbus matter answering to the various colors of the rays, and which, either alone or by their admixture, give rise to the different tints we see. In white light they all exist, and are separated from one another by the prism, because of an attractive force which such a transparent body exerts ; and that at- tractive force being unequal for the different color-giving particles, difference of refrangibility results. The colors of natural objects on this theory are explained by supposing , that some of the color-giving particles are reflected or transmitted, and others stifled or 'stopped by the body on which they fall. The phenomena of reflection by pol- ished surfaces are therefore reduced to the impact of elastic bodies ; and in the same way that a ball is repel- led from a wall against which it is thrown, so these little particles are repelled, making their angle of reflexion equal to their angle of incidence. But while there are many of the phenomena of light, such as reflexion, re- fraction, dispersion, and coloration, which can be ac- counted for on these principles, there are others which What are the two theories of light ? What is the nature of the corpuscu lar theory 1 On its principles what is the constiiution of white light ? How does it account for difference of re&angibility and the colors of natura. objects 1 How does it account for the phenomena of reflexion ? 'iOG VIBRATIONS IN THE ETHER. the emanation or corpuscular theory cannot meet. These are, however, explained in a simple and beautiful manner by the other theory. The undulatory theory rests upon the fact that there exists throughout the universe an elastic medium called THE ETHER, in which vibratory movements can be estab- lished very much after the manner that sounds arise in the air. Whatever, therefore, has been said in Lectures XXXI, &c., respecting the mechanism and general princi- ples of undulatory movements applies here. Waves in the ether are reflected, and made to converge or di- verge on the same principles that analogous results take place for waves upon water or sounds in the air. It will have been observed already that the reflexions of undu- lations from plane, spherical, elliptic, or parabolic sur- faces, as given in Lecture XXXII, are identically the same as those which we have described for light in Lec- ture XXXVII. From the phenomena of sound we can draw analogies which illustrate in a beautiful manner the •phenomena of light : for, as the different notes of the gamut arise from undulations of greater or less frequency, so do the colors of light arise from similar modifications in the vibrations of the ether. Those vibrations that are most rapid im- press our eyes with the sensation of violet, and those that are slower with the sensation of red. The difierent col- ors of light are, therefore, analogous to the different notes of sound. In Lecture XXXIII it was shown how the frequency of. vibration which could give rise to any musical note might be determined, and it appeared that the ear could detect vibrations, as sound through a range commencing vidth 15 and reaching as far as 48,000 in a second. The frequen- cy of vibration in the ether required for the production of any color has also been determined, and the lengths of the waves corresponding. The following table gives these results. The inch being supposed to be divided into ten millions of equal parts, of those parts the wave lengths are: — On what does the undulatory theory rest? Do the general laws of undn lations apply to the phenomena of light ? What analogy is there be tween sound and ligot 7 How do the colors of light compare with the notes of sound ? TIMES or VIBRATION. 207 ir Red light . 256 Orange " 240 ■ Yellow " 227 Green « . 211 Blue 196 Indigo " 185 Violet " . . 174 More recent investigations have proved the remarkable fact that the length of the most refrangible violet wave being taken as one, that of the least refrangible red vnll be equEd to two, and the most brilliant part of the yellow one and a Half. Knowing the length of a wave in the ether required for the production of any particular color of light, and the rate of propagation through the ether, which is 195,000 miles in a second, we obtain the number of vibrations ex- ecuted in one second, by dividing the latter by the former. From this it appears that if a single second of time be divided into one million of equal parts, a wave of red light vibrates 458 millions of times in that short interval, and a wave of violet light 727 millions of times. Further, whatever has been said in Lectures XXXI XXXII, in reference to the interference of waves, must necessarily, on this theory, apply to light. Indeed, it was the beautiful manner in which some of the most incom- prehensible facts in optics were thus explained, that has led to its almost universal adoption in modern times. That light added to light should produce darkness, seems to be entirely beyond explanation on the corpuscular theory ; but it is as direct a consequence of the undula- tory, as that sound added to sound may produce silence. From a lucid point, p, Fig. 229, let rays of light fall upon a double prism, m n, the angle of which, at C, is very obtuse. From what has been said respecting the multiplying-glass (Lecture XXXVIII), it appears that an eye applied at a would see the point p double, as at p' and j/'. Between these images there is also perceived a number of bright and dark lines perpendicular to a line joining p' and p". On covering one half the- prism the lines disappear, and only one image is seen. What relation of wave length exists between the least, the intermediate, and the most refrangible rays? How may the frequency of vibrations be determined from the wave length ? What is that frequency in the case ol red and violet light ? Does interference of luminous waves take place ' How 18 this exhibited by the double prism, Fi);. 229? 308 INTERFERENCE OP LIGHT. This alternation of light and darkness is caused by ethereal waves from the points^' andy crossing one an- other, and giving rise to interference. If, therefore, with Fig. 289. those points as centers, we draw circular arcs, 0, 1, 2, 3, 4,'&c., these may represent waves, the alternate lines between them being half waves. It will be perceived that wherever two whole waves or two half waves en- counter, they mutually increase each other's effect ; but if the intersection takes place at points where the vibra- tions are in opposite directions, interference, and, there- fore, a total absence of light results, as is marked in the figure by the large dots. Wherever, therefore, rays of light are arranged so as to encounter one another in opposite phases of vi- bration, interference takes place. Thus, if we take a Fig.iao convex lens, of very long focus, and " press it upon a flat glass by means of screws, Fig. 230, at the point of con- tact, when we inspect the instrument by reflected light a black spot will be seen, surrounded alternately by light and dark rings. These pass under the name of Newton's colored rings. When the light is ho- mogeneous the dark rings are black, and the colored ones of the tint which is employed, but when it is common What IB the effect of two whole or two half waves encountering! When does interference take place ? Describe the process for forming Newton's colored rings. mPFKACTION OP LIGHT. 209 white light the central black spot is surrounded by a se- ries of colors. When the instrument is inspected by transmitted light, the colors are all complementary, and the central spot is of course white. These rings arise from the interference of the rays reflected from the ante- rior and posterior boundaries between the two glasses. The colors of soap-bubbles and thin plates of gypsum, are referable to the same cause. By the diffraction of light is meant its deviation from the rectilinear path, as it passes by the edges of bodies or Mg.sai. through apertures. It arises from the circumstance that when ethereal, or, indeed, any kind of waves im- pinge on a solid body, they give rise to new undulations, originating at the place of impact, and often producing interference. Thus, if a diverging beam of light passes through an ap- erture, a b. Fig. 231, in a plate of metal an eye placed beyond will dis- cover a series of light. and dark fringes. The cause of these has been already explained in Lecture XXXIL, in which it was shown that from the points a and h new systems of undulations arise, which interfere with one an- other, and also with the original waves. What is the cause of them? What is the cause of the colors of soap- bubbles and their films generally f What is meant by the diffraction of Kghtt 210 POLARIZATION OF LIGHT. LECTURE LXIII. Op Polarized Light. — Peculiarity of Polarized Lights- Illustrated by the Tourmaline. — Polarization by Reflex- ion. — General Law of Polarization. — Positions of no Reflexion. — Plane of Polarization. — Polarization by Refraction. — Application of the Undulatory Theory. — The Polariscope, When a ray of common light is allowed to fall on the surface of a piece of glass it can he equally reflected by the glass upward, downward, or laterally. If such a ray falls upon a glass plate at an angle or 66°, and is received upon a second similar plate at a sim- ilar angle, it will be found to have obtained new proper- ties : in some positions it can be reflected as before, in others it cannot. On examination, it is discovered that these positions are at right angles to one another. Again : if a ray of light be caused to pass through a Fig.vss. plate of tourmaline, c d, Fig. 232, in the direction a b, and J j jiiimi--- be received upon a second plate, '^fliiljl ^ placed symmetrically with ,the first, it passes through both with- out difficulty. But if the second plate be turned a quarter round, as at g A, the light is totally cut off". ' Considering these results, it therefore appears that we can impress upon a ray of light new properties by cer- tain processes, and that the peculiarity consists in giving" it different properties on different sides. Such a ray, therefore, is spoken of as a ray of polarized light. When light is polarized by reflexion, the effect is only completely produced at a certain angle of incidence, which therefore passes under the name of the angle of What is observed in the reflexion of ordinary light ? What occurs when light which has already been reflected at 56° is attempted to be re- flected again ? Describe the action of a tourmaline. What is meant l^ pola nzed light 1 Under what circumstances does maximum polarization take place ^ POLARIZATION OF LIGHT. 211 maximum polarization. It takes place when the reflected ray makes, with the refracted ray, an angle of 90°, Fig. 333. F^.234. Thus, let A B, Fig. 233, be a plate of glass, a i an inci- dent ray, which, at h, is partly reflected along h c and partly refracted along b e, emerging therefrom at e d. Now, maximum polarization ensues when c h e ia a right angle, from which it follows that the polarizing power is connected with the refractive, the law being that "the index of refraction is the tangent of the angle of polarization." Let A B, Fig, 234, be a plate of glass, on which a ray of light, a b, falls, and after po- larization is reflect- ed alongic; atclet it be received on a a second plate, C D, similar to the for- mer, and capable of revolving on c b, as it were on an axis. Let us now examine in what positions of this plate the polarized ray, b c, can be reflected, and in what it cannot. What is the law connecting refraction and polarization ? What are the relative positions of the reflecting plates when the ray cannot be re- flected? 212 PHENOMENA OF POLARIZATION. Experiment at once shows that when the plane of re- flexion of the first mirror coincides with the plane of re- Kg. S35. flexion of the second, the polarized ray un < dergoes reflexion;— but if they are at right angles to one another, it is no longer reflect- ed. To make this clear, let a b. Fig. 235, be the first mirror, and c d the second, so ar- ranged as .to present their edges, as setfn depicted on this page. Again : let ef be the first and g h the sec- F^I °'^^> '"'^ turned half way round, but still presenting its edge, in both those positions, the planes of incidence I \q and reflexion of both the mirrors coincid- ing, the ray polarized by a & or ey will be reflected. But if, as in i k, the sec- ond mirror, I, is turned so as to present its face, or, as in m n^\l is turned at o, so as to present its back, in these cases, the planes of incidence and reflexion of the two mirrors being at right angles, the polarized ray can no longer be reflected. We have, therefore, two posi- tions in which reflexion is possible, and two in which it is impossible, and these are at right angles to one another. By the plane of polarization we mean the plane in which the ray can be completely reflected from the second mirror. When a ray of light falls on the surface of a transparent medium, it is divided into two portions, as has already been said, one of these being reflected and the other re- fracted. On examination, both these rays are found to be polarized, but they are polarized in opposite ways, or What is the plane of polarization ? In the case of a transparent tab- dirnn, what is the relation between the reflected and refracted rays' EXPLANATION OF FOLABIZ. TION. 213 rather the plane of polarization of the refracted is at right angles to the plane of polarization of the reflect- ed ray. When it is required to polarize light by refraction a pile of several plates of thin glass is used, for polarization from a single surface is incomplete. On the undulatory theory we can give a very clear account of all these phenomena. Common light origi- nates in vibratory movements taking place in the ether ; but it differs from the vibrations in the air which consti- tute sound in this essential particular that, while in the waves of sound the movements of the vibrating particles lie in the course of the ray, in the case of light they are transverse to it. This may be made plain by considering the wave-like motions into which a cord may be thrown by -shaking it at one end, the movement being in the up-and-down or in the lateral direction, while the wave runs straight onward. The ethereal particles, therefore, vibrate transversely to the course of the ray. But then there are an infinite number of directions in which these transverse vibrations may be made : a cord may be shaken vertically or laterally, or in an infinite number of inter- mediate angular positions, all of which are transverse to its length. Common light, therefore, arises in ethereal vibrations, taking place in every possible direction transverse to the path of the ray ; but in polarized light the vibrations are all in one' plane. Thus, in the case of the tourmaline, when a ray passes through; it all the vibrations are taking place in one direction, and therefofe the ray can pass through a second plate placed symmetrically with the first ; but if the second be turned a jv 236 quarter round the vibrations can no ^ ' ^ longer pass, just, in the same way that^ rtlll] — -"] a sheet of paper, c d, may be slipped r,. ttt , through a grating, a b, while its plane coincides with the length of the bars; out can no longer go through-when it is turned as at ej", a quarter round. How is light to be polarized by refraction ? What is light according to the undulatory theory? In what directions are the vibrations made? How may this be illustrated by a cord ? In what directions xire the vibra- tions of polarized light 1 How is this illustrated iu i%. 236 ? 214 FOLAmZED RAYS. Again, in the case of polarization by reflexion, let A B, Fig. 237. Fig. 237, be the mirror on which a ray of common light, a b, falls at the prop- er angle of polarization, and is reflected in a polar- ized condition along h c. C D will be the plane in which the ■ ethereal parti- cles vibrate after reflection, and the curve line drawn on it may represent the intensities of their vibra ' tions. So, too, in Fig. 238, we have an illustration of polarization by refraction. Let A B be a bundle of glass plates, a h the incident, and c d the polarized ray; the plane C D at right angles to the plates is the plane of polarization, and the curve drawn on it represents the intensities with which the polarized particles move. In every instance the plane of polarization is perpendic- ular to the planes of reflexion and refraction. liTi^.239. The polariscope is an instru- ment for exhibiting the proper- ties of polarized light. There are many different forms of it : Fig. 239 represents one of 3® them. It consists of a mirror of black glass, a, which can be set at any suitable angle to the brass tube, A B, by means of a graduated arc, ey it can also be rotated on the axis of the tube B A, and the amount of that rotation read off on the What is the illustration given as respects reflected light in Fig. 2377 What is it for refracted light in Fig. 238 ? What is the constant position of the plane of polarization ? Describe the polariscope. DOUBLE EBrRACTION. 215 graduated circle h. At the other end of the tube theru is a second mirror of black glass, i, which, like a, can be arranged at any required angle, and likewise turned round on the axis of the brass tube, A B, the amount of its rotation being ascertained by the divided circle, c. Sometimes instead of this mirror of black glass, a bundle of glass plates in a suitable frame is used. The instru- ment is supported on a pillar, C. The fundamental property of light polarized by re- flexion may be exhibited by this instrument as follows : — Set its two mirrors, a and A, so as to receive the light which falls on them at an angle of 56°. Then, when the first, a, makes its reflexion in a vertical plane, the light can be reflected by i also in a vertical plane, upward or downward. But if d be turned round 90°, so as to attempt to reflect the ray to the right or lefk in a hori- zontal plane, it will be found to be impossible, the light becoming extinct and in intermediate positions; as the mirror revolves the light is of intermediate intensity. LECTURE XLIV. On Double Refraction and the Production of Col ORS IN Polarized Light. — Double Refraction of Ice- land Spar. — Axis of the Crystal. — Crystals with two Axes. — Production of Colors in Polarized Light. ^ Complementary Colors Produced. — Colors Depend on the Thickness of the Film. — Symmetrical Rings and Crosses. — Colors Produced by Heat and Pressure.-^ Circular and Elliptical Polarization. Bt double refraction we mean a property possessed by certain crystals, such as Iceland spar, of dividing a single incident ray into two emergent ones. Thus, let R r be a ray of light falling on a rhomboid of Iceland spar, ABC X, in the point r, it will be divided during its passaere through the crystals into two rays, r E, r O, the latter 'of How may this instrument be used to exhibit light polarized by reflexion . What is meant by double refraction? Describe the phenomena exhibitec by a crystal of Iceland spar. «1& DOUBLE REFRACTION. tig. 240. Fig. 241. which folio WB the ordi- H nary law of refraction, and therefore takes the name of the ordinary ray, the former follows a dif- ferent law and is spoke of as the extraordinary ray. Through such a crys- tal objects appear double. A line, M N, on a piece of paper viewed through it is exhibited as two lines, M N,»j n, the amount of separation depending on the thickness of the crystal. The emergent rays E e, O o, are parallel after they leave the surface X. A line drawn througfcthe crystal from (f one of its obtuse' angles to the other is " called the axis of the crystal, and if arti- ficial planes be ground and polished as n m, o p, perpendicular to this axis, a I, Fig. 241, rays of light falling upon this axis or parallel to it do not undergo double refraction. Fig. i4Si. Or, if new faces, o p, n m, Fig. 242, be ground and polished parallel to the axis a 5, a ray falling in the direction df also remains single. But if the refracting faces are neither at right angles nor parallel to the axis, double refraction al\yays ensues. While Iceland spar has only one axis of double refrac- tion, there are other crystals, such as mica, topaz, gypsum, &c., that have two. In crystals that have but , one axis there are differences. In some the extraordinary ray is inclined from the axis in others toward it when compared with the ordinary ray. The former are called negative srystals, the latter positive. The explanation which the undulatory theory gives of jhis phenomenon in crystals having a principal axis is, ihat the ether existing in the crystal is not equally elastic What is the axis of the crystal ? In what cases does an incident ray not indergo double refraction ? What crystals have two axes of double refrac- tion ? Wh^t are negative crystals ? What are positive ones ? COLORS IN POLARIZED LIGHT. 217 In every direction. Undulations are therefore propagated unequally, and a division of the ray takes place, those undulations v^hich move quickest having the less index of refraction. When the two rays emerging from a rhomb of Iceland spar are examined, they are both found to consist of light totally polarized, the one being polarized at right angles to the other. We have, therefore, several different ways in which light can be polarized — ^by reflexion, refraction, absorp- tion, and double refraction. When a crystal of Iceland spar is ground to a prismatic shape, and then achromatized by a prism of glass, it forms one of the most valuable pieces of polarizing apparatus that we have. Such a prism may be used to very great advantage instead of the mirror of tht apparatus, Fig. 239. If a ray of polarized light is passed through a thin plate of certain crystalized bodies, such as^ mica or gyp- sum, and the light then viewed through an achromatic prism or by reflexion from the second mirror of the polarizing machine, Fig. 239, brilliant colors are at once Fig. 243. developed. Thus, let E. A be a ray of light incident on the first mirror of the polariscope, A C the resulting polarized ray, and D E F G be a thin plate of gypsum or mica. If, previous to the introduction of this plate, the two mirrors A and C be crossed, or at right angles to one another, the eye placed at E will perceive no light ; What is the explanation of double refraction on the vindulatory theory? What is the condition of the emergent rays? In what ways may light be polarized? Under what circumstances are colors developed by poUr. ized light ? 218 COLORS IN POLARIZED LIGHT. but, on the introduction of the crystal, its surface appears to be covered with brilliant colors, which change their tints according as it is inclined, or as the light passes through thicker or thinner places. On further examination it will be found that there are two lines, D E and F G, which, when either of them is parallel or perpendicular to the plane of polarization, R A C or A C E, no colors are produced. But if the plate be turned round in its own plane a single color appears, which becomes most brilliant when either of the lines ah,c d, inclined 45°, to the former ones are brought into the plane of polarization. The former lines are called the neutral, and the latter the depolarizing axes of the film. This is what takes place so long as we suppose the two mirrors, A C, fixed; but if we make the mirror nearest to the eye revolye while the film is stationary, the phe- nomena are different. Let the film be of such a thickness as to give a red tint, and be fixed in such a position as to give its maximum coloration, and the eye-mirrqr to re- volve, it will be found that the brilliancy of the color de- clines, and it disappears when a revolution of 45° has been accomplished ; and now a pale green appears, which increases in brilliancy until 90° are reached, when it is at a maximum. Still continuing the revolution, it becomes paler, and at 135° it has ceased, and a red blush com- mences, which reaches its maximum at 180° ; and the same system of changes is run through in passing from 180° to 360° ; so that while the film revolves only one color is seen, but as the mirror revolves two appear. If, instead of using a mirror, we use an achromatic prism, we have two im- ages of the film at the same time, and we find that they exhibit comple- mentary colors — that is, colors of such a tint that if they be mixed togeth- er they produce white light. This effect is rep resented in Fig. 244, ■> '. — , What are the neutral axes of the film? What are its depolarizing axes What takes place when the film is stationary and the mirror revolves What is the relation of the two resulting colors to each other ? Fig. 214. KINGS AND CROSSES. 219 That the particular colars which appear depend on the thickness of the films, is readily established by taking a thin wedge-shaped piece of sulphate of lime, and etpos- ing it in the polariscope ; all the different colors are then seen, arranged in stripes according to the thickness of the film. When a slice of an uniaxial crystal cut at right angles to the axis is used instead of the films, in the foregoing experiment, very brilliant effects are produced, consisting Fig. 245. of a series of colored rings, arranged symmetrically and marked in the middle by a cross, which may either be light or dark — light if the second mirror is in the proper po- sition to reflect the light from the first, and dark if it be It right angles thereto. In crystals having two axes a complicated system of oval rings, originating round each axis, may be perceiv- Fig. 346. ed, intersected by a cross. Fig. 246, represents the ap- pearance in a crystal of nitrate of potash ; and in the same way other figures arise with different crystals. How can it be proved that the color is determined by the thickness of the film ? What phenomena are seen when slices from crystals are used 1 With rryntalffiriiifiit'^'nipTfniim ft i ifaillif i ''''"'''"""'' ' ? 220 EFFECTS OF PBESSUEE, ETC. If transparent noncrystalized bodies are employed in these experiments, no colors whatever aie perceived mg. 347. Thus, a plate of glass placed in the polariscope, gives rise to no such development ; but if the structure of the glass be disturbed, either by warming it or cooling it un- equally, or if it be subjected to unequal pressure from screws, then colors are at once developed. This proper- ty may, however, be rendered permanent in glass, by heat ing it until it becomes soft and then cooling it with rap- idity. All the phenomena here described belong to the divi- sion of plane polarization — but there are other modifica- tions which can be impressed on light, giving rise to very remarkable and intricate results : these are designated circular, elliptical, &c., polarization. The mechanism of the motions impressed on the ether to produce these re- sults is not difficult to comprehend ; for common light, as has been stated, originates in vibrations taking place in ejjgry direction transverse to the ray; plane polarized light arises from vibrations in one direction only : and when the ethereal molecules move in circles they originate circular- ly polarized light, and if in ellipses, elliptical. When glass is unequally Warmed or cooled, or subjected to une(]ual pressures, what is the result? How may these effects be made perma- oent ? What modification of the ether gives rise to plane polarization I What to circular and what to elliptical ? THE RAINBOW. 231 LECTURE XLV. Natural Optical Phenomena. — The Rainbow. — Condi tions of its Appearance. — Formation of the Inner Bow — Formation of the Outer Bow. — The Bows are Cir cular Arcs. — Astronomical Refraction. — Elevation of Objects. — The Twilight. — Reflexion from the Air. — Mi rages and Spectral Apparitions, and Unusual Refraction The rainbow, the most beautiful of meteorological phenomena, consists of one or more circular arcs of pris- matic colors, seen when the back of the observer is turn- ed to the sun, and rain is falling between him and a cloud, which serves as a screen on which the bow is depicted. When two arches are visible the inner one is the most brilliant, and the order of its colors is the same in which they appear in the prismatic spectrum — the red fringing its outer boundary, and the violet being within. This is called the primary bow. The secondary bow, which is the outer one, is fainter, and the colors are in the invert- ed order. When the sun's altitude above the horizon ex- ceeds 42° the inner bow is not seen, and when it is more than 54° the outer is invisible. If the sun is in the hori- zon, both bows are semicircles, and according as his alti- tude is greater a less and less portion of the semicircle is visible ; but from the top of a j;^v. a48. mountain bows that are larger tnan a semicircle may be seen. Theseprismatic colors arise from reflexion and refraction of light by the drops of rain, which are of a spherical figure. In the .primary bow there is one reflexion and two refrac- tions ; in the secondary there Under what circumstances does the rainbow form ! Of the two bows which is the most brilliant ? What is the order of the colors ? What is their order in the secondary bow ? What are the circumstances which de- termine the visibility of each bow ? When are thej semicircles ? Whfen more than semicircles ? How is the primary bow ''maai ? 22S THE RAINBOW. are two reflexions and two refractions. Thus, let S, JEHg, 248, be a ray of light, incident on a raindrop, a; on ac- count of its obliquity to the surface of the drop, it will be refracted into a new path, and at the back of the drop it will undergo reflexion, and returning to the anterior face and escaping it will be again refracted, giving rise to violet and red and the intermediate prismatic colors between, constituting a complete spectrum ; and as the drops of rain are innumerable the observer will see in- numerable spectra arranged together so as to form a cir- cular arc. jY^. 249. The secondary rainbow arises from two refractions and two re- flexions of the rays. Thus, let the ray S, Fig. 249, enter at the bottom of the drop, it passes in the direction toward I' after hav- ing undergone refraction at the front; from I' it moves to I", where it is a second time reflected, and then emerges in front, undergoing refraction and dispersion again. For the same reason as in the other case, prismatic spectra are seen arranged together in a circular arc and form a bow. In Fig. 250, let O be the spectator and O P a line drawn from his eye to the center of the bows. Then rays of the sun, S S, falling on the drops ABC, will produce the inner bow, and falling on D E F, the outer bow, the former by one and the latter by two reflexions. The drop A reflects the red, B the yellow, and C the blue rays to the eye ; and in the case of the outer bow, F the red, E the yello^w, and D the blue. And as the color perceived is entirely dependent on the angle under which the ray" enters the eye, as in the case of the interior bow, the blue entering at the angle COP, the yellow at the larger angle BOP, and the red and the largest A P, we see the cause why the bows are circular arcs. For out of the innumerable drops of rain which compose the shower, those only can reflect to the eye a red color which make the same angle, A O P, that A does with the line O P, and these must necessarily be arranged in What are the conditions for the formation of the secondary bow ? Whj are both bows circular arcs 1 THE RAINBOW. 223 a circle of which the center is P. And the same reason- ing applies for the yellow, the blue, or any other ray as //// //// iff/ .<■ ///;■ //<••/ well as the red, and also for the outer as well as the inner bow. Another interesting natural phenomenon connected with the refraction of light is what is called " astronomi- cal refraction," arising from the action of the atmosphere on the rays of light. It is this which so powerfully dis- turbs the positions of the heavenly bodies, making them appear higher above the horizon than they really are, and changes the circular form of the sun and moon to an oval shape. It also aids in giving rise to the twi- light. Let O be the position of an observer on the earth, Z, What is the cause of astronomical refraction ? 224 ASTRONOMICAL REFRACTION, Fie. 251. Fig. 251, will be his isenith, and let E be any star, the rays from which come, of course, in straight line?, such as R E. Now, when such a ray impinges on the atmosphere at s, it is refracted, and deviates from its recti- linear course. At first this refraction is fee- ble, but the atmos- phere continually in- creases in density as we descend in it, and therefore the deviation of the ray from its orig- inal path, R E, be- -^omes continually greater. It follows a curvilinear line, and finally enters the eye of the observer at O. This may perhaps be more clearly understood by supposing the concentric circles, a a,h b, c c, represented in the figure, to stand for concentric shells of air of the same density, the ray at its entry on the first becomes refracted, and pursues a new course to the second. Here the same thing again takes place, and so with the third and other ones successively. But these abrupt changes do not oc- cur in the atmosphere, which does not change its density from stratum to stratum abruptly, but gradually and con- tinually. The resulting path of the ray is, therefore, not a broken line, but a continuous curve. Now, it is a law of vision that the mind judges of the position of an object as being in the direction in which the ray by which it is seen enters the eye. Consequently the star, R, which emits the ray we have under consider- ation, will be seen in the direction, O r — that being the direction in which the ray entered the eye^and, there- fore, the eifect of astronomical refraction is to elevate a star or other object above the horizon to. a higher appa- rent position than that which it actually occupies. Astronomical refraction is greater according as the ob- ject is nearer the horizon, becoming less as the altitude Trace the path of a ray of light which impinges obliquely on the at- mosphere. Why is it of a curvilinear figure ? How does the mind judge of the position of an object ? What is, therefore, the effect of astronomical refraction ? What is the difference in this respect between ar. abject in the horizon and one in the zenith ? ASTRONOMICAL REFEACTION. 225 increases, and ceasing in the zenith. An ohject seen in the zenith is therefore in its true position. On these principles, the figure of the sun and moon, when in the horizon, changes to an oval shape ; for the lower edge being more acted upon than the upper, is therefore relatively lifted up, and those objects made less in their vertical dimensions than in their horizontal. Even when an object is below the horizon it may be BO much elevated as to be brought into view ; for just in the same way that a star, R, is elevated to r, so may one beneath the horizon be elevated even to a greater extent, because refraction increases as we descend to the hori- zon. Stars, therefore, are visible before they have ac- tually risen, and continue in sight after they have actually set. They are thus lifted out of their true position when in the horizon about thirty-three minutes. In the books on astronomy tables are given which represent the amount of refraction for any altitude. What has been here said in relation to a star holds also for the sun ; which, therefore, is made apparently to rise sooner and set later than what is the case in reality. From this arises the important result that the day is pro- longed. In temperate climates, this lengthening of the day extends only to a few minutes, in the polar regions - the dai/ is made longer by a month. And it is for this cause, too, that the morning does not suddenly break just at the moment the sun appears in the horizon, and the night set in the instant he sinks ; but the light gradually fades away, as a twilight, the rays being bent from their path, and the scattering ones which fall on the top of the atmosphere brought in curved directions down to the lower parts. The phenomenon of twilight is not, however, wholly due to refraction. The reflecting action of the particles of the air is also greatly concerned in producing it. The manner in which this takes place is shown in Fig. 252, where A B C D represents the earth, T R P the atmos- phere, and S O, S' N, S" A rays of the sun passing through it. To an observer, at the point A, the sun, at S", is just Why is the figure of the sun or moon oval in the horizon ? What is to be observed as respects the rising and setting of stars ? Wlat effect has he refraction of the air in producing twilight ? How is it that the reflec- 've power of the air aids in this effect ? 226 TWILIGHT. set, but the whole hemisphere above him, PUT, being his sky, reflects the rays which are still falling upon it, and gives him twilight. To an observer, at B, the sun Fig. 252. J4 has been set for some time, and he is in the earth's shad- ow, but that part of his sky which is included between P Q, B. a; is still receiving sun-rays, and reflecting them to him. To an observer at C, the illuminated portion of the sky has decreased to P Q, ar. His twilight, therefore, has nearly gone. To an observer at D, whose horizon is bounded by the line D P, the sky is entirely dark, no rays from the sun falling on it. It is, therefore, night. The action of the atmosphere sometimes gives rise to curious spectral appearances — such as inverted images, looming, and the mirage. The latter, which often occurs on hot sandy plains, was frequently seen by the French during their expedition to Egypt, giving rise to a decep- tive appearance of great lakes of water resting on the sands. It appears to be due to the partial rarefaction of the lower strata of air through the heat of the surface on which they rest, so that rays of light are made to pass in a curvilinear path, and enter the eye. In the same way at sea, inverted images of ships floating in the air are often discovered. Thus, "On the 1st of August, 1798, Dr. Vince observ- ed at Ramsgate a ship, which appeared, as at A, Fig. 253, the topmast being the only part of it seen above the hori- zon. An inverted image of it was seen at B, immediately above the real ship, at A, and an erect image at C, both of them being complete and well defined. The sea was Describe this effect in the four positions, A, B, C, D oiFig. 252. Men tion some remarkable appearances due to unusual refraction and reflex ion of the air. TBI! MISAGE. 227 Fig. 253. distinctly seen between them, as at V W. As the ship rose to the ho- rizon, the image, C, gradually dis- appeared ; and, while this was going on, the image B, descended, but the mainmast of B did not meet the mainmast of A. The two images, B C, were perfectly visible when the whole ship was actually below the horizon." These singular appearances, which have often given rise to superstitious legends, may be imitated artificially. Thus, if we take a long mass of hot iron, and, looking along the upper surface of it at an object not too distant, we shall see not only the object itself, but also an inverted image of it below, the second im- age being caused by the refraction of the rays of light as they pass through the stratum of hot air, as is the case of the mirage. The trembling which distant objects exhibit, more es- pecially when they are seen across a heated surface, is, in like manner, due to unusual aud irregular refraction taking place in the air. LECTURE XLVL The Organ of Vision. — The Three Parts of the Eye. — Description of the Eye of Man. — Uses of the Accessory Apparatus.-:!— Optical Action of the Eye. — Short and, Long-Sightedness. — Spectacles.' — Erect and Double Vis' ion.-r-Peculiarities of Vision. — Physiological Colors. Almost all animals possess some mechanism by which they are rendered sensible of the presence of light. In some of the lower orders, perhaps, nothing more than a difiiised sensibility exists, without there being any special How may the mirage be imitated ? How is it known that the lowest ani mats are sensible to light ? 228 TKE EYE. organ adapted for the purpose. Thus, many animalcules are seen to collect on that side of the liquid in which they Hve on which the sun is shining, and others avoid the light But in all the higher tribes of life there is a special me- chanism, which depends for its action on optical laws— it IS the eye. This organ essentially consists of three different parts— an optical portion, which is the eye, strictly speaking j a nervous portion, which transmits the impressions gather- ed by the former to the brain ; and an accessory portion, which has the duty of keeping the eye in a proper work- ing state and defending it from injury. In man the eye-ball is nearly of a spherical figure, be- ^'B-^ii- ing about an inch in di- ameter. As seen in front, between the two eyelids, d e. Fig. 254, it exhibits a white portion of a porce- lain-like aspect, a a,' a col- ored circular part, b b, which continually changes in width, called the iris ; and a central black por- tion, which is the pupil. When it is removed from the orbit or socket in which Fiff. 255. it is placed, and dissected, the eye is found to consist of sever- al coats. The white portion seen anteriorly at o « extends all round. It is very tough and resisting, and by its mechanical qualities serves to support the more delicate parts within, and also to give insertion for the at- tachment of certain muscles which roll the eye-ball, and direct it to any object. This coat passes under the name of the sclerotic. It is represented in Fig. 255, at a a a a. In its front there is a circular aperture, into which a transparent portion, b b, resembling in shape a watch-glass, is inserted. This Of how many parts does the eye consist ? What are the offices of these parts 1 What is the figure and size of the eye in man 7 What if the iris, the pupil, and the sclerotic coat 7 THE EYE. 229 This is called the cornea. It projects somewhat beyond the general curve of the sclerotic, as seen at h S, in the figure, and with the sclerotic completes the outer coat of the eye. The interior surface of the sclerotic is lined with a coat which seems to be almost entirely made up of blood-ves- sels, little arteries and veins, which, by there internetting, cross one another in every possible direction. It is called the choroid coat : it extends like the sclerotic as far as the cornea. Its interior surface is thickly covered with a slimy pigment of a black color, hence called pigmentum nigrum. Over this is laid a very delicate serous sheet, which passes under the name of Jacoh's membrane, and the optic nerve, O O, coming from the brain perforates the sclerotic and choroid coats, and spreads itself out on the interior surface as the retina, rrrr. The optic nervps of the opposite eyes decussate one another on their passage to the brain. These, therefore, are the coats of which the eye is com- posed. Let us examine now its internal structure. Be- hind the cornea, b h, there is suspended a circular dia- phragm, ef, black behind and of different colors in differ- ent individuals in front. This is the iris. Its color is, in some measure, connected with the color of the hair. The central opening in it, d, is the pvpil, and immediately be- hind the pupil, suspended by the ciliary processes, g g, is the crystaline lens, c c — a double convex lens. AH the space between the anterior of the lens and the cornea is filled with a watery fluid, which is the aqueous humor; that portion which is in front of the iris is called the an- terior chamber, and that behind it the posterior. The rest of the space of the eye, bounded by the crystaline lens in front and .the retina all round, is filled with the vitreous humor, V V. With respect to the accessory parts, they consist chiefly of the eyelids, which serve to wipe the face of the eye and protect it from accidents and dust; the lachrymal appara- tus, which serves to wash it with tears, so as to keep it What is the comea ? What are the choroid coat, pigmentum nigrum, and Jacob's membrane ? What are the optic nerve and retina ? What is the gosition of the iris ? Hovr is the lens supported ? Where is the aqueous umor 1. Where the vitreous ? What are the two chambers of the eye T WHat are the accessor; parts and their uses ? 230 SPECTACLES. continually brilliant ; and the muscles requisite to direct it upon any point. Of the nervous part of the eye, so far as its functions are concerned, but little is known — the retina receives the imjjressions of the light, and they are conveyed along the optic nerve to the brain. _ Now as respects the optical action of the eye, it is ob- viously nothing more than that of a convex lens, to which, indeed, its structure actually corresponds : and as in the focus of such a convex lens objects form images, so by the conjoint action of the cornea and crystaline, the images of the things to which the eye is directed form at the proper focal distance behind — that is, upon the retina. Distinct vision only takes place when the cornea and the lens have such convexities as to bring the images exactly upon the retina. In early life it sometimes happens that the curvature of these bodies is too great, and the rays converging too rapidly, form their images before they have reached the posterior part of the eye, giving rise to the defect known as short-sightedness — a defect which maybe remedied by putting in front of the cornea a concave glass lens of such concavity as just to compensate for the excess of the con- . vexity of the eye. In old age, on the contrary, the cornea and the lens be- come somewhat flattened, and they cannot converge the rays soon enough to form images at the proper distance be- hind. This long-sightedness may be remedied by putting in front of the cornea a convex lens, so as to help it in its action. Concave or convex lenses thus used in front of the eyes constitute spectacles. It is believed that this appli- cation was first made by Roger Bacon, and if unquestion- ably constitutes one of the most noble contributions which science has ever made to man. It hsis, given sight to mil- lions who would otherwise have been blind. As the image which is formed by a convex lens is in- verted as resipects its object, so must the images which form at the bottom of the eye. It has, therefore, been a What is the duty of the retina, and what that of the optic nerve ? To what optical contrivance is the eye analogous ? When does distinct vis- ion take place ? What is the cause of short-sightedness, and what is its cure ? What is the « ause of long-sightedness, and its cure 1 PECULIARITIES OF VISION. 231 questiob among optical writers, why we gee objects in their natural position, and also why we do not see double, inas- much as we have two eyes. Various explanations of these facts have been offered, chiefly founded upon optical prin ciples. None, however, appear to have given general sat- isfaction, and in reality the true explanation, I believe, will be found not in the optical, but in the nervous part of the visual organ. It is no more remarkable that we see single, having two eyes, than that we hear single, hav- ing two ears. It is the simultaneous arrival in the brain, that gives rise out of two impressions to one perception, and accordingly, when we disturb the action of one of the eyes by pressing on it, we at once see double. Among the peculiarities of vision it maybe mentioned, that for an object to be seen it must be of certain magni- tude, and remain on the retina a sufficient length of time; and, for distinct vision, must not be nearer than a certain distance, as eight or ten inches. This distance of distinct vision varies somewhat with different persons. The eye, too, cannotbear too brilliant a light, nor can it distinguish when the rays are too feeble ; though it is wonderful to what an extent in this respect its powers range. "We can read a book by the light of the sun or the moon ; yet the one is a quarter of a million times more brilliant than the other. Luminous impressions made on the retina last for , a certain space of tithe, varying from one third to one sixth of a second. For this reason, when a stick with a -spark of fire at the end is turned rapidly round, it gives rise to an apparent circle of light. By accidental or physiological colors we mean such as are observed for a short time depicted on surfaces, and then vanishing away. Thus, if a person looks steadfastly at a sheet of paper strongly illuminated by the sun, and then closes his eyes, he will see a black surface corre- sponding to the paper. So if a red wafer be put on a sheet of paper in the sun, and the eye suddenly turned on a white wall, a green image of the wafer will be seen. Spectral illusions in the same way often arise — thus, when Is there any thing remarkable respecting erect and double vision? What peculiarities respecting -vision may be remarked ? What is the distance of distinct vision ?^ To what range of intensity of light can the eye adapt itself? Why does a lighted stick turned round rapidly give rise to the appearance of a circle of fire ? What is meant by accidental colors? 232 OPTICAL INSTRUMENTS. we awake in the morning, if our eyes are turned at once to a window brightly illuminated, on shutting them again we shall see a visionary picture of every portion of the window, which after a time fades away. LECTURE XL VII. Op Optical Instruments. — The Common Camera Oh- scwra. — The "Portable Camera. — The Single Microscope — The Compound Microscope. — Chromatic and Spheri- cal Aberration. — T?ie Magic Lantern. — The Solar Mi- croscope, — The Oxyhydrogen Microscope. In this and the next Lecture I shall describe the more important optical instruments. These, in their external appearance, and also in their principles, differ very much according to the taste or ideas of the artist. The descrip- tions here given will be limited to such as are of a simple kind. The Camera Obscura, or dark chamber, originally con- sisted of nothing more than a double convex lens, of a foot or two in focus, fixed in the shutter of a dark room. Opposite the lens and at its focal distance, a white sheet received the images. These represent whatever is in front of the lens, giving a beautiful picture of the stationary and movable objects in their proper relation of light and shadow, and also in their proper colors. In point of fact, a lens is not required : for, if into a Fig. 256. What was the original form of the camera obsGura 7 CAMERA OBSCURA. 233 dark chamber, C D, Fig. 256, rays are admitted through a small aperture, L, an inverted image will be formed or a white screen at the back of the chamber, of whatever objects are in front. Thus the object, A B, gives the in- verted image, b a. These images are, however, dim, ow- ing to the small amount of light which can be admitted through the hole. The use of a double convex lens per- mits us to-have a much larger aperture, and the images are correspondingly brighter. pig. 257. The portable -^ camera obscura consists of an achromatic dou- <2|| ble convex lens, .a a', set in a brass mounting in the V front of a box consisting of two parts, of which c c slides in the wider one, b b'. The total length of the box is ad- justed to suit the focal distance of the lens. In the back of the part, c c', there is a square piece of ground glass, d, which receives the images of the objects to which the lens is directed, and by sliding the movable part in^ or out the ground glass can be brought to the precise focus. The interior of the box and brass piece, a a', is blackened all over to extinguish any stray light. The images of the camera are, of course, inverted, but they can be seen in their proper position by receiving them on a looking-glass, placed so as to reflect them up- ward to the eye. Objects that are near, compared with objects that are distant, require the back of the bpx to be drawn out, because the foci are farther oif. Moreover, those that are near the edges are indistinct, while the cen- tral ones are sharp and perfect. This arises from the cir- cumstance that the edges of the ground glass are farther from the lens than the central portion, and, therefore, out of focus. , OF MICROSCOPES. The single microscope. — When a convex lens is placed Is it necessary to have a lens ? What advantage arises from the use ol one ? Describe the portable camera obscjira. Why does the focal dis- tance vary for different objects ? Why are the images on the edges indi» tinct while the central ones are sharp f 234 THE MICROSCOPE. between the eye and an object situated a little nearer than its focal distance, a magnified and erect image will be seen. '^s- 258. The single microscope con- sists of such a lens, m, Fig, 258, the object, b c, being on one side and the eye, a, at the other, a magnified and ^>a^ erect image, B C, is seen. '•••■ ^ The linear magnifying pow- er of such a lens is found by jOyiding the distance of distinct vision by its focal length. T4c compound microscope conjmonly consists of three •ig. 259. lenses, A B, E F, C D, Fig. 259 ; A B being the object-glass, E F the field-glass, and C D the [eye-glass. Beyond the I object-glass is placed the object, at a dis- tance somewhat greater than the focal length ; a magnified image is, therefore, produced, and this* being viewed by the eye-glass is still further magnified, and, of course, seen in an inverted po- sition. The use of the field-glass is to intercept the ex- treme pencils of light, n m, coming from the object-glass, which would otherwise not have fallen on the eye-lens. It therefore' increases the field of view, and hence its name. In this instrument the object-glass has a very short fo- cus, the eye-glass one that is much larger ; and the field- glass and the eye-glass can be so arranged as to neutral- ize chromatic aberration. To determine directly the magnifying power of this in- strument, an object, the length of which is known, is placed 'jefore it. Then one eye being applied to the instrument, with the other we look at a pair of compasses, the points of which are to be opened until they subtend a space equal to that under which the Object appears. This space being divided by the known length of the object, gives the magnifying power. Describe the single microscope. How is its magnifying power found? Describe the compound microscope'. What is the use of the field lensl How may its magnifying power be found 1 COMPOUND MICROSCOPE. 235 In Fig'. 260, we have a representation of the compound microscope, as commonly made. A K^.260. B is. a sliding brass tube, which bears the eye-glass ; m n is the object- glass ; I K the field-glass ; S T a stage for carrying the objects. It can be moved to the proper focal dis- tance by means of a pinion. At V there is "a mirror which reflects the light of a lamp or the sky upward, to illuminate the object. The body of the microscope is supported on the pillar M, and it can be turned into the horizontal or any oblique po- sition to suit the observer, by a joint, N. To the better kind of instru- ments micrometers are attached, for the purpose .of determining the di- ^ mensions of objects. These are some- U/ '-^ — '■' vj times nothing more than a piece of glass, on which fine lines have been drawn with a diamond, forming divisions the value of which is known. , Such a plate may be placed either immediately beneath the object or at the diaphragm, which is between the two lenses. In microscopes the defective action of lenses, known as chromatic aberration, and described in Lecture XLI., interferes, and, by imparting prismatic colors to the edges of objects, tends to .make them indistinct. To overcome this difficulty, achromatic object-glasses are used in the finer kinds of instruments. Besides chromatic aberration, there is another defect to which lenses are subject. It arises from their spheri- cal figure, and hence is designated spherical aberration. Let P P, Fig. 261, be a convex lens, on which rays, E P, E P, E M, E M, E A, from any object, E c, are iticident, it is obvious that the principal ray, E A, will pass on, through B, to F without undergoing refraction. Now, rays which are near to this, as E M, E M, converge by the action of the lens to a focus at F ; but those which are more distant, and fall near the edges of the lens, as Describe the parts of the compound niicioscope represented in Fig. 260. What kind of micrometers may be used ? What are the effects of chro- matic and spherical aberration ? 236 MAGIC LANTERN, E N, E N, converge more rapidly, and come to a focus at G. Thus, images, F f, Gt g, are formed b3r the ex- treme rays, and an intermediate, series of them by the Sig. 261. intermediate rays, the whole arising from the peculiarity of figure of the lens. It is, indeed, the same defect as that to which spherical mirrors are liable, as explained in Lecture XXXVII ; and hence, to obtain perfect action with a spherical lens, as with a spherical mirror, its ap- erture must be limited. 1'he Magic Lantern consists of a metallic lantern. Fig. 262. A A' Fig. 262, in front of which two lenses are placed. One of these, m, is the illuminating lens, the other, n, the magnifier. A powerful Argand lamp is placed at L, and behind it a concave mirror, p q. In the space between the two lenses the tube is widened c d, or such an arrange- ment made that slips of glass, on which various figures are painted, can be introduced. The action of the in- strument is very simple. The mirror and the lens m Describe the magic lantern. What is the use of its condensing lens and mirror ? SOL^AR MICEOSCOFE. 237 illuminate the drawing as highly as possible ; for the lamp being placed in their foci, they throw a brilliant light upon it,, and the magnifying lens, n,, which can slide in its tube a little backward and forward, is placed in such a position as to throw a highly magnified image of the drawing upon a screen, several feet off, the precise focal distance being adjusted by sliding the lens. As it is an inverted image which forms, it is, of course, neces- sary to put the drawing in the slide, c d, upside down, so as to have their images in the natural position. Various amusing slides are prepared by the instrument-makers, some representing bodies or parts in motion. The fig- ures require to be painted in colors that are quite trans- parent. The Solar Microscope. — This instrument, like the Fig.W3. magic lantern, consists of two parts — one for illuminating the object highly, and the other for magnifying it. It consists of a brass plate, which can be fastened to an aperture in the shutter of a dark room, into which a beam of the sun may be directed by means of a plane mirror. In Fig. 263,'M is the mirror, to which movement in any di- rection may be given by the two buttons, X and Y, that rays from the sun may be reflected horizontally into the room. They pass through a large convex lens, R, and are con- converged by it ; they again impinge on a second lens, U S, which ■ concentrates them to a focus, the precise point of which may be adjusted by sliding the lens to the proper position by the button B. P P' is in apparatus, consisting of two fixed plates, with a movable one, Q,, be- tween them, Q, being pressed against P' by means of spiral springs. This apparatus is for the purpose of sup- porting the various objects which are held by the pressure Why must the slider be put in upside down 1 What are the two parts of the solar microscope? Describe the instrument as represented in Fig. 263. - ^38 OXYHYDROGEN MICROSCOPE. of Q, against P'. Immediately beyond this, at L, is the magnifying lens, or object-glass, which can be brought to the proper position from the highly illuminated object by means of the button B', and the magnified image result- ing is then thrown on a screen at a distance. The solar microscope has the great advantage of ex- hibiting objects to a number of persons at the same time. In principle, the oxyhydrogen microscope is the same as the foregoing, only, instead of employing the light of the sun, the rays of a fragment of lime ignited in the flame of a oxyhydrogen blow-pipe are used. These rays are converged on the object, and serve to illuminate it. The advantage the instrument has over the solar micro- scope is that it can be used at night and on cloudy days. LECTURE XLVIII. Of Telescopes. — Refracting and Reflecting Telescopes. — Galileo's Telescope. — Tke Astronomical Telescope. — TAe Terrestrial. — Of Reflecting Telescopes. — HersclieVs Newton^s, Gregory's. — Determination of their Magnify- ing Rowers. — The Achromatic Telescope. The telescope is an instrument which, in principle, re- sembles the microscope, both being to exhibit objects to us under a larger visual angle. The microscope does this for objects near at hand, the telescope for those that are at a distance. Telescopes are of two kinds, refracting and reflecting. Each consists essentially of two parts, the object-glass or objective, and the eye-piece. In the former, the objec- uve is a lens, in the latter it is a concave mirror. The distinctness of objects through telescopes is neces- Barily connected with the brilliancy of the images they give, and this, among other things, depends on the size of the objective. What advantage has the solar microscope over other forms of instru. ment ? What is the okyhydrogen microscope ? What is the telescope f Of howr many kinds are telescopes ? What are their essential parts % What is the objective in the refracting and reflecting telescope, re spectively ? On nrhat does the brilliancy deperjd ' GALILEO S TELESCOPE. 231 There are three kinds of refracting telescopes : — Is) Galileo's; 2d, the astronomical; 3d, the terrestrial. Galileo's Telescope, which is represented in Fig FV- 264. 264, consists of a convex lens, L N, which is the objec tive, and a concave eye-glass, E E. Let O B be a dis- tant object, the rays from which are received upon L N, and by it would be brought to a focus, and give the im- age, M I ; but, 'before they reach this point, they are in- tercepted by the concave eye-glass, E E, which makes them diverge, as represented at H K, and give an erect image, i m. This form of telescope has an advantage in the erect position of its image, which is usually presented with great clearness. Its field of view, by reason of the di- vergence of the rays through the eye-glass, is limited. When made on a small scale, it constitutes the common opera-glass. The Astronomical Telescope differs from the former mg.^ess. in having for its eye-piece a convex lens of short focus compared with that of the object-lens. In this, as in the former instance, the office of the objective is to give an image, and the eye-piece magnifies it precisely on the same principle that it would magnify any object. In Fig. 265, L N is the objective, and E E the eye-glass ; the rays from a distant object, O B, are converged so as to give a focal image, M I. This being viewed through the eye-lens, E E, is magnified, and is also inverted. The magnifying power of the telescope is found by di- How many kinds of refracting telescopes are there ? Describe Galileo's telescope. Why has it so small a field of view ? What are the essential parts of the astronomical telescope 7 Why does it invert J 240 TEEKBSTKIAL TELESCOPE. viding the focal length of the objective by that of the eye- lens. This telescope, of course, inverts, and therefore is not well adapted for terrestrial objects ; but for celestial ones it. answers very well. The Terrestrial Telescope consists of an object- Fig. 266. G ; F E -r I, B lens, like the foregoing, but in its eye-piece are three lenses of equal focal lengths. The combination is repre- eented in Fig. 266, in which L N is the object lens, and E E, F F, Gr Gr the eye-lenses, placed at distances from each other equal to double their focal length. The prog- ress of the rays through the object-lens and the first eye- glass to X is the same as in the astronomical telescope ; but, after crossing at X, they are received on the second eye-lens, which gives an erect image of them, atim, which is viewed, therefore, in the erect position by the last eye- lens, Gr Gr. As the distance at which the image forms from the ob- ject-lens is dependent on the actual distance of the object itself, one which is near giving its image farther off than one which is distant, it is necessary to have the. means of adjusting the eye-piece, so as to bring it to the proper dis- tance from the image, M I. The object-lens is there- fore put in a tube longer than its own focus, and in this a smaller tube, bearing the three eye-lenses, immovably fixed, slides backward and forward ; this tube is drawn out until distinct vision of the object is attained. Reflecting Telescopes are of several different kinds. They have received names from their inventors. Herschbl's Telescope consists of a metallic concave mirror, set in a tube in a position inclined to.the axis. It of course gives an inverted image of the object at its fo- cus, and the inclination is so managed as to have the im- age form at the side of the tubel There it is viewed by How is its magnifying power found ? Describe the terrestrial telescope. What is the action of its three eye-lenses ? Why must there be means of sliding the eye-piece ? How are reflecting telescopes designated ? De- scribe Herschel's telescope. Newton's and Gregory's telescopes. 241 an eye-lens, which shows it magnified and inverted. The back of the observer is turned to the object, and the in- clination of the mirror is for the purpose of avoiding ob- struction of the light by the head. Newton's Telescope consists of a concave mirror, A R, Fig. 267, with its axis parallel to that of the tube, D E Fig. 267 ^^ F G, in which it is set. The rays reflected from it are intercepted by a plane mirror, C K, placed at an angle of 45°, on a sliding support, m. They are, therefore, re- flected toward the side of the tube, the image, i m, form- 'ng at I M, an eye-glass at L magnifies it. The Gregorian Telescope has a concave mirror, A R, Fig, 268, with an aperture, L, in its center. The rays A from a distant object, O B, give, as before, an inverted image, M I. They are then received on a small concave mirror, K G, placed fronting the great one. This gives an erect image, which is magnified by the eye-lens, P. The magnifying power of any of these instruments may be roughly estimated by looking at an object through them Math one eye, and directly at it with the other, and com- paring the relative magnitude of the two images. In Her- schel's telescope the back of the observer is toward the object, in Newton's his side, but in G-regory's he looks di- rectly at it. The latter is, therefore, by far the most agreeable instrument to use. The largest telescopes hith- erto constructed are upon the plan of Herschel and Newton. When Sir Isaac Newton discovered the compound na- ture of light, by prismatic analysis, be came to the con- In what position does tl)e observer stand ? Describe Newton's telescope Pescribe the Gregorian telescope. How may the magnifying power of hese instruments be ascertained ? L 342 THE ACHROMATIC TELESCOPE. elusion that the refracting telescope could never be a per feet instrument, because it appeared impossible to form an image by a convex lens, without its being colored on the edges by the dispersion of light. He therefore turn- ed his attention to the reflecting telescope, and invented the one which bears his name. He even manufactured one with his own hands. It is still preserved in the cab- inet of the Royal Society of London. But after it was discovered that refraiction without dis- persion can be effected, and that lenses can be made to form colorless images in their foci, the principle was at once applied to the telescope ; and hence originated that most valuable astronomical instrument, the achromatic telescope. In this the object-glass is of course compound, consist- iwg, as represented in Fig. 269, of one crown and one Fig. 269. Fig. 270. flint-glass lens, or as represented in Fig. 270, of one flint and two crown-glass lenses. The principle of its action has been described in Lecture XLT. The great expense of these instruments arises chiefly from the costliness of the flint-glass, for it has hitherto been found difiicult to obtain it in masses of large size, perfectly free from veins or other imperfections. Nevertheless, there are instruments which have been constructed in Germany, with an aper- ture of thirteen inches. Some of these are mounted on What was it that led to the adoption of the reflecting telescope ? On what does the acb'-omatic telescope depend ? Of what parts are the dou ble and triple objet -glasses composed 1 What is the cause of the costli' ness of these instruments T ACHROMATIC TELESCOPES. 243 a frame, connected with a clock movement, bo that when the telescope is turned to a star it is steadily kept in the center of the field of view, notwithstanding the motion of the earth on her axis. Several large instruments of thi« description are now in the diff^rept ohsaiTf>tari«>« of tht- United States. 244 HEAT OR CALORIC. THE PROPERTIES OF HEAT. THERMOTICS. LECTURE XLIX The Properties of Heat. — Relations of hight and Heat. — Mode of Determining the Amount of Heat. — The Mercurial Thermometer. — Its Fixed Points. — Fahren- heit's, Centigrade, Reaumur's Thermometers. — The Gas Thermometer. — Differential Thermometer. — Solid Ther- mometers. — Comparative Expansion of Gases, Liquids, and Solids. Whatever may be the true cause of light, whether it DO undulations in an ethereal medium, or particles emit- ted with great velocity by shining bodies, observation has clearly proved that heat is closely allied to it. When a body is brought to a very high temperature, and then allowed to cool in a dark place, though it might be white-hot at first it very soon becomes invisible, losing its light apparently in the same way that its loses its heat. And we shall hereafter find the rays of heat which thus escape from it may be reflected, refracted, inflected, and polarized, just as though they were rays of light. In its general relations heat is of the utmost importance in the system of nature. The existence of life, both vege- table and animal, is dependent on it; it determines the dimensions of all objects, regulates the form they assume, and is more or less concerned in every chemical change that takes place. Every object to which we have access possesses a cer-« tain amount of heat, and so long as it remains at common What is observed during the cooling of bodies ? Why are the relation of heat of such philosophical importance 7 THE THERMOMETER. 245 temperatures, may be touched without pain ; but if a larg- er quantity of heat is given to it, it assumes qualities that are wholly new, and if touched it burns. To determine, therefore, with precision the quantity of heat which is present in a body when it exhibits any particular phenomenon, it is necessary that we should be furnished with some means of effecting its measurement. Instruments intended for this purpose are called ther- mometers. . , . Of thermometers we have several different kinds. . Some are made of solid substances, others of liquids, and others of gases. ; With a few exceptions, they all depend on the same iprinciple — 'the expansion which ensues in all bodies as their temperature rises. Of these the mercurial thermometer is the most ^g- 271 common, and for the purpose of science the most' generally available. It consists of a glass tube, Fig. 271, with a bulb on its lower extremity. The entire bulb and part of the tube are filled with quicksilver, and the rest of the tube,ihe ex- tremity of which is closed, contains a vacuum. This glass portion is fastened in an appropriate manner, upon a scale of ivory or metal, which bears. divisions, and the thermometer is said to be at, that particular degree against which its quick- silver stands on the scale. If we take the bulb of such an instrument in the hand, the quicksilver immediately begins to rise in the tube, and finally is stationary at some particular degree, generally the 98th in our ther- mometers. We therefore say, the temperature of the hand is 98 degrees. In effecting a measure of any kind, it is neces- sary to have a point from whicji to start and a point to which to go. The same is also necessa- ry in miaking a scale. • One of the essential qual- ities of a thermometer is to enable: observers in all parts of the world to indicate the same temperature by the same What is the use of the thermometer ? What different kinds of ther- mometers have we ? On what general principle do they all depend ? What form of thermometer is the most common ? What are the degrees ? What temperature does it indicate if held in the hand 7 Why are fixed point! necessary in forming; the scale ' 246 THKRMOMETRIC SCALES. degree. A common system of dividing the scale must, therefore, be agreed upon, that all thermometers may cor- respond. If we dip a thermometer in melting ice or snow, the quicksilver sinks to a certain point, and to this point it will always come, no matter when or where the experi- ment is made. If we dip it in boiling water, it at once rises to another point. Philosophers in all countries have agreed that these are the best fixed points to regulate the scale by, and accordingly they are now used in all ther- mometers. In the Fahrenheit thermometer, which is com- monly employed in the United States, we mark the point at which the instrument stands, when dipped in melting snow, 32°, and that for boiling water, 212°, and divide the intervening space into 180 parts, each of which is a de- gree ; and these degrees are carried up to the top and dovyn to the bottom of the scale. In other countries other divisions are used, adjusted, however, by the same fixed points. The Centigrade thermometer has, for the melting of ice, 0, and for the boiling of water, 100°, with the intervening space divid- ed in 100 equal degrees. In Reaumur's thermometer, the lower point is marked 0, and the upper 80°. The philosophical fact upon which the construction of the thermometer reposes, is that quicksilver expands by an increase of heat, and is contracted by a diminution of it ; and further, that these expansions and contractions are in proportion to the changes of temperature. Fig. 278. But for particular purposes, thermometers have been made of oil, of alcohol, and of a great many other liquid bodies, and give rise to the same gen- eral results. As an uniform law it may, therefore, be asserted that all liquids dilate as their temper- ature rises, and contract as it descends. But heat determines the volume of gases as well as of liquids. If we take a tube, o, Fig. 272, with a bulb at its upper extremity, b, and having partly ^c filled the tube with a column of water, colored, to make its movements visible, the lower end dipping What two fixed points have been selected ? What is the Centigrade Bcalp ? What is Reaumur's scale ? What is the fact on which the con- 8tr» .tion of the thermometer depends ? How may this be extended to otl' r liquids ? AIK THERMOMETER. 247 loosely into some of the same colored water, contained in a bottle, c; on touching the bulb, b, the colored liquid in the tube is pressed down by the dilatation of the air, and on cooling the bulb the liquid rises, because the air con- tracts. And were the bulb filled with any other gaseous substance, such as oxygen, hydrogen, &c., still the same thing would take place. So gases, like liquids, expand as their temperature rises, and contract as it descends. Such an instrument as Fig. 272, passes under the name of an air thermometer. Its indications are not altogether reliable, as may be proved by putting it under an air-pump receiver, when its column of liquid will instantly move as soon as the least change is made in the pressure of the air. It is affected, therefore, by changes of pressure as well as changes of temperature. ~ There is, however, a form of c mg.vni. air thermometer which is free from this difficulty. It is the dif- ferential thermometer. This in- strument consists of a tube, a b. Fig. 273, bent at right angles to- ward its ends, which terminate in two bulbs, c d. In the hori- zontal part of the tube is a little column of liquid marked by the black line, which serves as an index. If the bulb c, is touched by the hand, its air dilates and presses the index column over the scale ; if <£ is touched the same thing takes place, but the column moves the opposite way ; if both bulbs are touched at once, then the column, pressed equally in opposite directions, does not move at all. Of course, a similar reasoning applies to the cooling of the bulbs. The instrument is, therefore, called a dif^ ferential thermometer, because it indicates the difference of temperature between its bulbs, but not absolute tem- peratures to which it is exposed. In the same manner that we have thermometers, in which the changes of volume of liquids and gases are employed, to indicate changes of temperature, so, too, we have others in which solids are used. These generally consist of a strip of metal which is connected with an ar- How majr it be extended to all the gases ? Describe the air thermome- ter. Describe the diSerential thermometer. What does this instriment indicate 7 248 EXPANSION or LiaUlDS. rangement of level's or wheels, by which any variations in its length may be multiplied. The disturbing agencies, thus introduced by this necessary mechanism, interfere very much with the exactness of the^e instruments. And hitherto they have not been employed, except for special purposes, and can never supplant the mercurial thermom- eter. It being thus established that all substances, gases, liquids, and solids expand as their temperature i-ises, and contract as it falls, it may next be remarked that great (Jifferences are detected when different bodies of the same form are compared. There are scarcely two solid sub- stances which, for the same elevation of temperature, ex- pand alike. All do expand ; but some more and some less. In the case of crystalline bodies, even the same substance expands differently Jn different directions. Thus, a crystal of Iceland spar dilates less in the direc- tion of its longer than it does in the direction of its shprt- er axis. The same holds good for liquids. If a number of Fig. 274. thermometers, ab c, Fig. 274, of the same size be filled with different liquids, and all plunged in the same vessel of hot water, _/] so as to be warmed alike, the expansion they exhibit will be very different. Until recently, it was believed that all gases expand alike for the same ' changes of temperature, but it is now known that minute differences exist among them in this respect. For every degree of Fahrenheit's thermometer atmospheric air expands 5-1^ of its volume at 32°. Gases, liquids, and solids compared together, for the same change of temperature, exhibit very different changes of volume ; gases being the most dilatable, liquids next, and solids least of all. This, probably, arises from the ftijCt that the cohesive force, which is the antagonist of heat, is most efficient, in solids, less so in liquids, and still less in gases. Are thermometers ever made of soliil bodies ' What difficulties are in the way of their use ? Do bodies of the same form expand alike 7 What remarks may be made respecting Iceland spar? How may it be proved that different liquids expand diiSerently ? What is the expansion of aii for each degree ? Do other gases expand exactly like air ? Of gases, liquids, and solids, which expands most ? RADIANT HEAT. 249 LECTURE L. Op Radiant Heat. — Tath of Radiant Heat.— Velocity of Radiant Heat. — Eificts of Surface. — Law of Reflex- ion. — Reflexion by Spherical Mirrarsj-^Theory of Ex- changes of Heat, — Diathermanoiis and Athermanous Bodies. — Properties of Rock Salt. — Imaginary Colora- tion. Experience shows that whenever a hot body is freely exposed its temperature descends, until eventually it comes down to that of the surrounding bodies. There are two causes which tend to produce this result. They are radiation and conduction. All bodies, whatever their temperature may be, radiate heat from their surfaces. It passes forth in straight lines, and may be reflected, refracted, and polarized like light. The rate at which radiant heat moves is, in all proba- bility, the same as the rate for light. It, has been asserted that its, velocity is only four fifths that of light, but this seems not to rest upon any certain foundation. As respects the rapidity or facility with which radi- ation takes place, much depends on the nature of the sur- face. The experiment9,^of Leslie show that, at equal temperatures, such as are smooth are far less effective than such as are rough. This result he established by taking a cubical meteil- lic vessel, a, filled with hot water, the four verti- cal sides being in differ- ent physical conditions — one being polished, a sec- ond slightly roughened, a third still more so, and the fourth joughened and black- ened. Under these circumstances, the rays of heat es- What causes tend to produce the cooling of bodies ? In what direction does radiant heat pass 1 What is the velocity of its movement ? How is the rapidity of radiation controlled by surface? Of smooth and roiigli bodies which are the best radiators ? Kff.275. caping from each surface as it was turned in succesBior toward a metallic reflector, M, raised a thermometer, d, placed in the focus, to very different degrees, the polished one producing the least effect. Just as light is reflected, so, too, is heat. If we take a plate of bright tin and hold it in such a position as to re- flect the light of a clear fire into the face, as soon as we see the light we also feel the impression of the heat. The law for the one is also the law for the other, " the angle of reflexion is equal to the angle of incidence," and con- sequently mirrors with curved surfaces act precisely in one case as they do in the other. We have already shown, Lecture XXXVII, how rays diverging from the focus of a mirror' are reflected parallel, and how parallel rays falling on a mirror are converged. And it is upon that principle that we account for the following striking experiment. In the focus of a concave metallic mirro' Pig. 376. -^ ^ let there be placed a red hot ball, a, IHg. 276, the rays of heat diverging from it in right lines, a c, a d, a e, a J will be reflected parallel in the lines c g, dh,e i,fk, and, striking upon the opposite min-or, will all converge to h, in its focus. If, therefore, at this point any small com- bustible body, as a piece of phosphorus, be placed, it will instantly take fire, though a distance of twenty or fifty feet may intervene between the mirrors. Or, if the bulb of an air thermometer be used instead of the phosphorus, What is the law for the reflexion of heat ? How do curved mirrors act on radiant heat? Describe the experiment represented by Ji%. 276 THEORY OF THE EXCHANGES OF HEAT. 251 it will give at once the indication of a rapid elevation of temperature. But this is not all ; for, if still retaining the thermome- ter in its place, we remove away the red hot ball and re- place it by a mass of ice, the thermometer instantly indi cates a descent of temperature, the production of cold. At one time it was supposed that this was due to cold rays which escaped from the ice, after the same manner as rays of heat, but it is now admitted that the effect arises from the circumstance that the thermometer bulb, being warmer than the ice, radiates its heat to the ice, the temperature of which ascends precisely in the same manner as that in the former experiment, the red hot ball being the warmer body, radiated its heat to the ther- mometer. In fact, these experiments are nothing more than illus- trations of a theory which passes under the name of " the Theory of the Exchanges of Heat." This assumes that all bodies are at all times radiating heat to one another ; but the speed with which they do this depends upon their temperature, a hot body giving out heat much faster than one the temperature of which is lower. If thus, we have a red hot ball and a thermometer bulb in presence of one another, the ball, by reason of its high temperature, will give more heat to the bulb than it receives in return ; its temperature will, therefore, descend, while that of the bulb rises. But if the same bulb be placed in presence of a mass of ice, the ice will receive more heat than it gives, because it is the colder body of the two, and the temperature of the thermometer therefore declines. All bodies are at all times radiating heat, their power of radiation depending on their temperature, increasing as it increases, and diminishing as it diminishes. As is the case with light, so, too, with heat : there are substances which transmit its rays with readiness, and others which are opaque. We therefore speak of dia- thermanous bodies which are analogous to the trans- parent, and athermanous which are like the opaque What ensues if a piece of ice is used instead of a hot ball ? How was this formerly explained ? What is the true explanation of it? What is meant by the Theory of the Exchanges of Heat ? On what does the rate of ra diation depend 1 What are mathermanous bodies ? What are atherma- nous ones? 252 REFRACTION OP HEAT. Among the former a vacuum and most gaseous bodioa may be numbered ; but it is remarkable that substances which are perfectly transparent to light are not necessa- rily so to heat. Glass, which transmits with but little loss much of the light which falls on it, obstructs much of the heat ; and, conversely, smoky quartz and brown mica which are almost-opaque to light transmit heat readily. But of all solid substances, that which is most transparent to heat, or most diathermanous, is rock-salt ; it has there- fore been designated as the glass of radiant heat. If a prism be cut from this substance, and a beam of radiant heat allowed to fall upon it, it undergoes refraction and dispersion precisely as we have already described as occurring under similar circumstances with a glass prism for light in Lecture XL. And if convex lenses be made of rock-salt they converge the rays of heat to foci, at which the elevation of temperature maybe detected by the thermometer. Heat, therefore, can be refracted and dispersed as easily as it can be reflected. If we take a convex lens of glass and one of rock-salt, and cause them to form the image of a burning candle in their foci, it will be found on examination that the image through the rock-salt is hot, but that through thet glass can scarcely affect a delicate thermometer. This, experi- ment sets in a clear light the difference in the relations between glass and salt, the former permitting the light to pass but not the heat, the latter transmitting both together. When light is dispersed by a prism the splendid phe- nomenon of the spectrum is seen. But in the case of heat our organs of sight are constituted so that we cannot discover its presence, and therefore fail to see the cor- responding result. But it is now established beyond all doubt, that in the same manner that there are modifica- tions of light giving rise to the various colored rays, so, too, there are corresponding qualities of radiant heat Moreover, it has been fully proved that, as stained glass and colored solutions exert an effect on white light, ab- sorbing some rays and letting others pass, the same takes place also for heat. In the case we have already con- <» Mention some of the former. Of all solid bodies which is the most diathermanous? What is to be observed when rock-salt and glass an compared ? IMAGINARY COLORATION. 253 Bidered of the imperfect diathermancy of glass — the true cause of the phenomenon is the cciloi'ation which the glass possesses as respects the rays of heat, and inasmuch as a substance may be perfectly transparent to one ^of these agents and not so to the other, so, also, a body may stop or absorb a given ray for the one and a totally dif- ferent one for the other. Glass allows all the rays of light to pass almost equally well, but it obstructs almost completely the 'blue rays of heat. The coloration of bodies, which has already been described as arising from absorption, may, therefore, be wholly different in the two cases ; and as our organs do not permit us to see what it is in the case of heat, and we have to rely on indirect evidence, we speak of the imaginary or ideal coloration of bodies. If heat like light, as there are reasons for believing, arises in vibratory movements which are propagated through the ether, all the various phenomena here de- scribed can be readily accounted for. The undulations of heat must be reflected, refracted, inflected, undergo interference, polarization, &c., as do the undulations of light, the mechanism being the same in both cases. LECTURE LI. Conduction and Expansion. — Good and Bad Conductors of Heat. — Differences among the Metals. — Gbnduction , and Circulation in Liquids. — Point of Application of Heat. — Case of Gases. — -Expansion q/" Gases, Liquids, ^ and Solids.- — Irregularity of Expansion in Liquids and Solids. — Regularity of Gases. — Point of Maximum Density of Water. "When one end of a metallic bar is placed in the fire, after a certain time, the other has its temperature ele- vated, and the heat is said to be" conducted. It finds its What reasons are there for supposing that radiant heat is colored ? Do natural bodies possess a peculiar coloration for heat! What is meant by ideal or imaginary coloration I If heat consists of ethereal undulations te what effects must it be liable ? What is meant by the conduction of beat? 254 CONDUCTION OP HEAT. way from particle to particle, from those that are hot to those that are cold. But if a piece of wood or of earthenware he suhmitted to the same trial a very different result is obtained. The farther end never becomes hot, proving, therefore, that some bodies are good and others bad conductors of heat. The rapidity with which this conduction from particle to particle takes place, depends, among other things, upon their difference of temperature. Thus, when the bulb of a thermometer is plunged in a cup of hot water, for the first few moments its column runs up with rapidity, but as the thermometer comes nearer to the temperature of the water, the heat is transmitted to it more slowly. Of the three classes of bodies solids are the best con- ductors, liquids next, and gases worst of all. Of solids the metals are the best, and among the metals may be mentioned gold, silver, copper. Among bad solid con- ductors we have charcoal, ashes, fibrous bodies, as cotton, silk, wool, &c. That the metals differ very much in this respect from one another may be satisfactorily proved by taking a rod of copper, one of brass, and one of iron, h c dfFig. 277, Fir 277. of equal length and diameter, and screw- ij . - ing them into a solid metallic ball, a, hav- ing placed on their farther extremities at h c d, pieces of phosphorus, a very com- j a bustible body. Now, if a lamp be placed oj under the ball, it will be found that the heat traverses the metallic bars with very different degrees of facility, and the phos- phorus takes fire in very different times; the first that inflames is that on the copper, then follovi^ that on the brass, and a long time after that on the iron. Liquids are, for the most part, very indifferent conduct- ors of heat. This may be established, for example, in the case of water, by taking a glass jar, a, Fig. 278, nearly filled with that substance, and introducing into it the bulb of a delicate air-thermometer, c, so that a very short space How may it be proved that different bodies conduct heat with different degrees of facility ? How is this affected by difference of temperature ? Of the three classes of bodies which conduct heat best? How may dif- ference ol conduct>^>i am ?ng metals be proved? CIRCULATION. 255 intervenes between the top of the bulb and the Fig.srs surface of the liquid. If now some sulphuric ether be placed on that surface, and set on fire, it will be found that the thermometer remains mo- tionless, and we therefore infer that the thin stratum intervening between the burning ether and the thermometer cuts oiF the passage of the heat. More delicate experiments have, however, proved that the liquid condition is not, in itself, a necessary obstruction. Even water does conduct to a certain extent; and quicksilver, which is equally a liquid, conducts very well. But experience assures us that, under common circum- stances, heat is uniformly disseminated -through liquids with rapidity. This, however, is due to the establishment of currents in their mass. We have seen how readily this class of bodies expands under an elevation of tempera- ture, and this explains the nature of the passage of heat through them. When the source of heat is applied at the bottom of a vessel containing vrater, those particles which are in immediate contact with the bottom become warm- ed by the direct action of the Bre, and they therefore ex- pand. This expansion makes them lighter, and they rise through the stratum above, establishing a current up to the surface. Meantime their place is occupied by colder particles, which descend, and these in their turn becom- ing warm follow the course of the former; Circulation, therefore, takes place throughout the liquid mass, in con- sequence of the establishment of these currents; jv^.are. and all parts being successively brought in con- tact with the hot surface, all are equally heat- ed. That thes^ movements do take place, majf be proved by putting into a flask of water, aji Fig. 279, a number of fragments of amber, adding a little glauber salt to make their spe- cific gravity of the liquid more nearly that of the amber, and then applying a lamp, currents are soon set up, and the amber, drifting in them, marks out their course in an instructive manner. How may it be proved that liquldf are bad conductors of heat ? Is the liquid state a necessary obstruction ? Mention a liquid which is a good conductor. How is beat then transmitted through liquids ? On what do these currents depend ? How may they be illustrated by means of amber ? 256 CIRCULATION IN GASES. Such currents, however, wholly depend oii the point of application of the heat. If the fire, instead of being ap- , plied at the bottom' of the vessel, is applied at the top, aa in Fig. 278, then the liquid can never be warmed. The cause of the movements of particles is their becoming lighter-^they therefore float upward ; but if they a:re al- ready situated on the surface of course no movement can take place. With respect to gases we observe the same peculiari- ties that we do with liquids. Strictly speaking, they are Fig. 280. very bad conductors of heat; but from the mo- ~ bility of their parts, it is very easy to transfer heat readily through them, provided it is right- ly applied. The experiment represented in Fig. 280, shows how easily circulation takes place in them. If a piece of burning sulphur be put in a cup, a, and a jar full of oxygen be inverted over it, the combustion goes on with rapidity, and the light smoke that rises marks out very well the path of the moving air. It rises direct- ly upward from the burning mass, until it reaches the top of the jar, and then descends in circular wreaths to the bottom. On the principle of the difference of the conductibility of bodies, we direct all our operations for the communi- cation of heat with different degrees of rapidity. When we desire to abstract the heat rapidly from bodies, we surround them with good conductors ; if we wish to re- tard it, we select such as are bad. And, indeed, it is in this way that we regulate our changes of clothing. Thick woollen articles, which are very bad conductors, are adapted to the colc^ winter weather, when we desire to cut off the escape of heat from our bodies as much as is in our pow- er. Nature also resorts to the same principles — the.tbick coat of wool or of hair which serves for the covering of animals protects them from the cold by its non-condjuct- ing power. In these instances, in reality, the action of atmospheric air is brought into play, and that under the Why do such currents depend on the point of application of the h?at? Do the same laws hold in the case of gases ? How may this te proved ty experiment ? What applications are made of the principle of different conductibility ? In the for of animals how is the non-condu6tirig power of air called into use ? POINT OP MAXIMUM DENSITY. 257 most favorable circumstances ; for any motion of its par tides among the thickly matteH fibres is impossible, and its non-conducting power, undisturbed by circulation, i« rendered available. It has been stated that all bodies expand under the in fluence of heat — gases being the most expansible, liquid) next, and solids least. But the expansion of the two lat ter classes of bodies. is, far ffora being proportional t« their temperatnre ; for solids, and liquids expand increas ingly as their temperature rises — one degree of heat, it applied at 400°, produces a great-er dilatation than if ap plied at">100°. From this irregularity it is believed that gases arc free — they seem to expand uniformly at all tem- peratures. Besides this general irregularity which applies to all solids and liquids, there are other special irregularities, often of great interest. Water may afford an example. If some of this liquid be taken at 32° and warmed, in- stead of expanding it contracts, and continues to do so until it has reached about 39^°, after which it expands. It therefore follows, that if we take water at 39^°, whether we warm it or coolit, it expands-. At that temperature it is, therefore, ii;i the smallest space into which it can be brought by cooling — it has, therefore, the greatest densi- ty, and 39^° is spoken of as the point of maximum density of water. In, the same manner several other liquids, and even solids, have points of maximum detisity. ,, This fact is of considerable interest, when taken in con- nection with the circulatory movements we have been de- scribing. When a mass of water cools on a winter's night, the colder particles. do not contract and descend to the bottom, but aftei; 39J° is reached, they, being the lighter, float on the top, and hence freezing begins at the surface. Were it otherwise, and the liquid solidified from the bot- tom upward, all masses of water during the winter would be converted into solid blocks of ice, instead of being merely covered as they are with a screen of that sub- stance, which protects them from further action. Po solids and liquids expand with regularity ! Are there other irregu- larities besides this,? What is meant by the maximum density of water 7 At what temperature does it take place ? How does tliis effect the freez- ing of masses of water ? 258 CAPACITY FOE HEAT. LECTURE LII. Capacity for Heat and Latent Heat. — Illustration of the Different Capacities of Bodies for ^eat. — Stand- ards employed. — Process hy Melting. — Process of Mix- tures. — Effects of Compression. — Effect of Dilatation. — Latent Heat. — Caloric of Fluidity. — Caloric of Elasti- city^. — Artificial Cold. By the phrase capacity of bodies for heat we allude to the fact that different bodies require different degrees of heat to warm them equally. An experiment will serve to illustrate this important fact. If we take two bottles as precisely alike as we can obtain them, and, having filled one with water and the other with quicksilver, set them before the same fire, so as to receive equal quantities of heat in equal times, it will be found that the water requires a very much longer expos ure, and therefore a larger quantity of heat than the quick- silver to raise its temperature up to the same point. Or if we do the converse of this, and take the two bot- tles filled with their respective liquids, which, by having been immersed in a pan of boiling water, have both been brought to the same degree, and let them cool freely in the air, it will be found that the water requires much more time than the quicksilver to come down to the com- mon temperatures. It contained more heat at the high temperature than did the quicksilver, and required more time to cool ; it has, therefore, a greater capacity for heat ; or, to use a loose expression, at the same temperature holds more of it. There are several difierent ways by which the capacity of bodies for heat may be determined. Thus, we may notice the times they require for warming, or those ex- pended in cooling in a vacuum. Of course, we cannot What is meant by the capacity of bodies for heat ? Illustrate this by experiment. Can it be proved conversely? In what vf ays may the ca- pacity of bodies be determined ? Can the absolute amount of heat in bodies be determined ? METHOD OF MELTING. 259 tell the absolute amount of heat which is contained in any substance whatever, and these determinations are hence relative — different bodies being compared with a given one which is talcen as a standard. For these pur- poses water is the substance selected for solids and liquids and atmospheric air for gases and vapors. An illustration will show the methods by which the ca- pacity of bodies is determined by the process of melting. Let there be pi'ovided a mass of ice, jy. 281. a a, Fig. 281, in which a cavity, h d, has been previously made, and a slab of ice, c c, so as to cover the cavity j completely. In a small flask, d, place an ounce of water, raised to a temper- ature of 200°. Set this in the cavity, ] as shown in the figure, and put on the slab. The ice now begins to melt ; ' and, as the water forms, it collects in the bottom of the cavity. When the temperature of the flask has reached 32° it only remains to pour out the water and measure it. Next, let there be put in the flask an ounce of quick- silver, the temperature of which is raised, as before, to 200° ; measure the water which it can give rise to by melt- ing the ice, precisely as in the former experiment, and it will be found that the water melted twenty-three times as much as the quicksilver. Under these circumstances, therefore, a given weight of water gives twenty-three times as much heat as the same quantity of quicksilver. There are still other means of obtaining the same re- sults. Such, for instance, as by the method of mixtures. If a pint of water at 50° be mixed with a pint at 100° the temperature of the mixture is 75° ; but if a pint of mer- cury, at 100°, is mixed with a pint of water, at 40°, the temperature of the mixture will be 60°, so that the 40° lost by mercury only raised the water 20°. That this result may correspond with the foregoing, it should be recollected that, in this instance, we are using equal vol- umes, in that equal weights. Why is capacitjr a relative thing? What is the standard for solids and liquids ? What is it for gases and Tapora ? Describe the process for deter- ininin^ capacities by melting. How do water and quicksilver compare 1 Describe the process by mixtures. In this, how do water and quicksilver sompare ? 860 CHANGES OF SPECIFIC HEAT. In this way the capacities of a great number of bodies have been determined, and. tables constructed in which tfiey are recorded. . Such tables are given in the boolja of chemistry. The different capacities of bodies are also designated by the term specific heat, since it requires a specific quantity of heat to heat bodies equally. When a body is compressed, its specific heat or capaci ty for heat diminishes, and a portion makes it appearance as sensible heat. This may be proved by rapidly com- pressing air, which will give out enough heat to set tin- der on fire, or by beating a piece of iron vigorously, when it may be made red hot. On the other hand, when a jodyis dilated its capacity for heat increases. It is partly for this reason that the upper regions of the atmosphere are so cold the specific heat is great by reason of the rar- ity. It therefore requires a large amount of heat to bring the temperature up to a given point. It has also been found that the specific heat changes with the temperature, increasing therewith, so that it is not constant for the same body. There is reason to believe that the atoms of all simple substances have an equal capacity for heat; and that all compound bodies, composed of an equal number of single atoms combined in one and the same manner have a capacityfor heat which is inversely as their specific gravity. When a solid substance passes into the liquid form 3 large quantity of heat is rendered latent — that is to say undiscoverable to the thermometer. Thus, we may have ice at 32° and water at 32°, the one a solid and the other a liquid, and the precise reason of the physical difference between them is, that the water contains about 140°, which the ice does not — a quantity which is occupied in giving it the liquid state, and is insensible to the ther mometer. For this reason the transformation of a solid into a liquid is not an instantaneous phenomenon, but one requir- What is meant by specific heat ? How does specific heat change undei :onipression ! Does this take place in solids as well as gases ? What reason is there for the cold in the upper regions of the air ? Does spe- cific heat vary with the temperature ? What is observed respecting the atoms of simple bodies ? What respecting compound X What is latent neat? What is the latent heat of water? Why does the transformatioc of water into ice or ice into water require time? LATENT HEAT. 261 nff time. Ice must have its 140° degrees of latent heat before it can tum into water. And,' conversely, the solid- ification of a liquid is not instantaneous. It must have time to give oit the latent heat to which its liquid state is due. When a liquid passes into the form of a vapor it is the presence of a large quantity of latent heat which gives to it all its peculiarities. Thus, water in turning into steam absorbs nearly 1000° of latent heat, and when that steam reverts into the liquid state the heat reappears. To ^he caloric which is ' absorbed during fusion, the designation of caloric of fluidity is given, to that which gives their constitution to vapors the name of caloric of elasticity. And as different bodies require during these changes different quantities of heat, there are furnished in 'the works on chemistry tables of the caloric of fluidity, and caloric of elasticity of all the more common or im- portant bodies. Of all known bodies water has the greatest capacity for heat ; and, in consequence of the great amount of latent heat it contains, it is one of the great reservoirs of caloric, both for natural and artificial purposes. Hence, whenever a substance melts it absorbs heat and when it solidifies it gives out h6at. When a sub stance vaporizes it absorbs heat, and when a vapor lique fies it evolves heat. On these principles depend some of the processes re sorted to for the production of cold. If we take two solid'bodies, as salt and snow, which have such chemical relations to one another that, when mixed, they produce a forced fusion and enter on the liquid state ; before that change of form can take place, caloric of fluidity must be supplied, for snow cannot turn into water unless heat is giv- en it. The mixture, therefore, abstracting heat from any bodies around or in contact with it, brings down their temperature and thus produces cold. The same result attends the vaporization of a liquid; thus, ether poured on the hand or on the thermometer produces a great What is the physical diiFerence between water and steam 1 What ia the caloric of fluidity? What is the caloric of elasticity? What sub- stance has the greatest capacity for heat ? Why is cold produced by a mixture of salt aid snow? Why is it produced by the vaporization of ether ? 263 PHENOMENA OF BOILING. cold, because the vapor wbich rises must have caloric of elasticity in order to assume its peculiar form, and it takes heat from the body from which it is evaporating for that purpose. LECTURE LIII. On Evaporation and Boiling. — Phenomena of Boiling. — Effect of the Nature of the Vessel and the Tresswre. — Height of Mountains 'Determined,. — Effect of Increased Pressure. — Evaporation. — Vaporization in Vacuo. — Effect of Temperature on a Liquid iti Vacuo. — Expla- nation of Boiling, — Nature of Vapors. As the vaporization of liquids is connected with some of the most important mechanical applications, we shall proceed to consider it more minutely. When water is placed in an open vessel on the fire the temperature of the whole mass siscends on account of the currents described in Lecture LI. After a time minute bubbles make their appearance on the sides of the vessel; these rise a little distance and then disappear, but others soon take their places, and the water, being thrown into a rapid vibratory motion, emits a singing sound. Imme- diately after this the little bubbles make their way ta the surface of the liquid, and are followed by others which are larger, and the phenomenon of boiling takes place. The heat has now reached 212°, and it matters not how hot the fire may be, it never rises higher. DiflFerent liquids have different boiling points, but for the same body, under similar circumstances, the point is nearly fixed. It is, indeed, in consequence of this that the boiling of water is taken as the upper fixed point of the thermometer. Of the circumstances which can conti'ol the boiling point, two may be mentioned : the nature of the vessel and the pressure of the air. In a polished vessel, for instance, water does not boil Describe the different phenomena exhibited during the warming of water. At what temperature does ebullition set in ? What circumstancet •ontrol the boiling point? In a polished vessel what is the temperature 1 EFFECT OF PRESSURE. 263 until 214° ; but if a few grains of sand or other angular Dody is thrown in the temperature sinks to 212°. The absolute control which pressure exerts over the boiling point may be shown in many different Fig- 282. striking ways. Thus, if a glass of warm water be put under the receiver of an air-pump and exhaustion made, the water enters into rapid ebullition, and continues boiling until its tem- perature goes down to 67°. Water placed in a vacuum will therefore boil with the warmth of the hand. Advantage has been taken of this fact to determine the height of accessible eminences. For, as we ascend in the air, the pressure necessarily becomes less ; the superin- , cumbent column of the atmosphere being shortened, the boiling point therefore declines. It has been ascertained that if we ascend from the ground through 530 feet, the boiling point is lowered one degree ; and formulas are given by which, from a knowledge of that point, in any instance the altitude may be calculated. On the other hand, when the pressure on a liquid is increased, its boiling point ascends. This may be proved by taking a spherical boiler, a, properly supported over a spirit lamp, there being in its top three openings ; through d let a thermometer dip into some water which half fills the boiler, sxh let there be a stop- cock which can be opened and shut at pleasure, and through a third opening be- tween these let a tube, c, pass, dipping down nearly to the bottom of the boiler into some quicksilver which is beneath the water. Now let the water boil freely and the steam escape through h, the thermometer will mark 212°. Close the stop-cock so that the steam cannot get out, but, being con- fined in the boiler, exerts a pressure on the surface of the water, which is indicated by the rise of the mercury in the tube. As the column rises the boiling point rises, and if the instrument were Fig 283 Prove that it is affected by pressure. At what temperature will water boil ji an air-pump vacuum? How has this been applied for the determina tion of heights ? How does the boiling point vary when the pressure feather is instantly attracted, and, therefore, this remark- able experiment proves that the electric virtue which ema- nates from excited bodies is not always the same, and that a body which is repelled by excited glass is attracted by excited wax. Extensive inquiry has shown, that in reality there are two species of electricity, to which names have therefore What results may be shown by the instrument, Fig. 307 ? How may it be shown that metals conduct electricity 1 How may it be proved that other bodies are non-conductors ? What is meant by insulation? Prove that there are two different sorts of electricity ' What roniiis hiive been given to them ? N 290 TWO KINDS OF ELECTRICITY. been given. To one — because it arises from the frictioc of glass — vitreous electricity; and to the other, which arises under similar circumstances from vra.x, resinous electricity. The relations of these electrical forces to one another as respects attraction and repulsion, constitute the funda- mental law of this department of science. That general law, briefly expressed, is — " Like electricities repel and unlike ones attract." That is to say, two bodies which are both vitreously or both resinously electrified, will re- pel each other ; but if one is vitreous and the other res- inous, attraction takes place. To the two different species of electricity synpnymous designations are sometimes ap- plied. The vitreous is called positive, and the resinous negative electricity. For the sake of observing electrical phenomena more Fig. 309. readily, instruments have been in- vented, called electrical machines. They are of two kinds : the plate machine and the cylinder ; they derive their names from the shape , of the glass employed to yield the electricity. The plate machine, Fig. 309, consists of a circular plate of glass, a a, which can he turned upon an axis, b, by means of a winch, c; at 2 ELECTRICAL EXPERIMENTS. passes down the whole length of the exhausted tube as a pale milky flame, but giving now and then brilliant flashes, especially when the tube is touched. The phenomenon has some resemblance to that of the Northern lights. Fig. 312. Between two metallic plates, a b, Fig. 312, of which a is hung by a chain to the prime con- ductor, and h supported on a conducting stand, let some figures, made of paper, pith, or other I light body, be placed. The plates maybe three or four inches apart. On throwing the machine into activity the figures are alternately attracted and repelled, and move about with a dancing motion. From a brass rod, a c b, Fig. 313, which may be hung jv^.313. by an arch, g, to the prime conductor, three bells are suspended — two from a and b by chains, and the middle one, c, by a silk thread — ^between the bells two little metallic clappers, d e, are hung , by silk, and from the inside of the mid- dle bell a chain, _^ hangs down upon the table. On setting the electrical machine in activity, the clappers commence moving and ring the bells. This in- strument has been employed in connection with insulated • lightning-rods, to give warning of the approach of a thun der-cloud. To account for the various phenomena of electricity, tvvo theories have been invented. They pass under the names of Franklin's theory, or the theory of one fluid, and Dufay's theory, or the theory of two fluids. Franklin's theory is, that there exists throughout all space an ethereal and elastic fluid, which is characterized by being self-repulsive — that is, each of its particles repels the others; but it is attractive of the particles of all othei matter. To this the name of electric fluid has been given Different bodies are disposed to assume particular or spe cific quantities of this fluid, and when they have the amount that naturally belongs to them, they are said to be in a natural state or condition of equilibrium. But if more than Describe the experiment of the dancing figures. Describe the electrical bells. For what purpose have they been used? How many theories of electricity are there ? What is Franklin's theory? In what consists the natural, the positive, and negative state of bodies according to it ? ELECTRICAL THEOKIES. 293 the natural quantity is communicated to them, they be- come positively electrified,; and if they have less than their natural quantity, they are negatively electrified. The theory of two fluids is,. that there exists an ethere- al medium, the immediate properties of which are not known. It is composed of two species of electricity — the positive and the negative— each of these being self-" repellent, but attractive of the other kind. Bodies are in a ■neutral or natural state or cmdition of equilibrium, when they contain equal quantities of the two electrici- ties ; and they are positively electrified when the positive is in excess, and negative when the negative is in excess. Of these two theories, it appears that the latter will ac- count for the greater number of phenomena. LECTURE LIX. Induction, Distkibution, and Measurement op Elec- tricity. — Electrical Induction. — The Leyden, Jar. — Its Effects.-~Dr. Franklin's Discovery. — The Light- ning-Rod. — Distribution of Electricity. — Pointed Bodies. — Velocity of Electricity. — Modes of Developing Elec- tricity. — Zdmboni's Piles. — Perpetual Motion. — Elec- troscopes. — Electrometers. By electrical induction is meant that a body in an electrified state is able to induce an analogous condition in others in its neighborhood without being in immediate contact with them. This effect arises from the general law of attraction and lepulsion ; for the natural condition of bodies is such that they contain equal quantities of positive and negative elec- tricity ; and, when this is the case, they are said to be in the neutral state, or in a condition of equilibrium. When, therefore, an electrified body is brought into the neighborhood of a neutral one, both being insulated, disturbance immediately ensues. The electrified body separates the two electricities of the neutral body from What is Dufay's theorjr ? How does it account for the corresponding states of bodies 1 What is meant by electrical induction ? What is-the natural condition of bodies ? How does an electrified body disturb a "eu tralone? S94 THE LETDEN JAR. each other, repelling that of the same kind, and attract ing that of the opposite. Thus, if a body electrified po3< itively be brought near one that is neutral, the positive electricity of this last is repelled to the remoter part, but the negative is attracted to that part which is nearest the disturbing body. The Leyden jar. Fig. 314, is a glass jar, coated on the Fig. 314. inside and outside with tin foil to within an inch or two of the edge. Through the cork which closes the mouth a brass wire reaches down, BO as to be in contact with the inside coating, and terminates at its upper end in a ball. On connecting the outside coating with the ground, and presenting the ball to the prime conductor, a large amount of electricity is received by the machine ; and if it be touched on the outside by one hand, and communication be made with the ball by the other, a very bright spark passes, and the electric shock is felt. The mechanical eifects of lightning may be represented in a small way by this instrument. On passing a strong shock through a piece of wood it may be torn open, and other resisting media may be burst to pieces. The shock passed through a card perforates it. Dr. Franklin discovered the identity of lightning and electricity. He established this important fact by raising a kite in the air during a thunder-storm. The string of the kite, which was of hemp, terminated in a silken cord, and at the point where the two were attached a key was hung. The electricity, therefore, descended down the hempen string, but was insulated by the silk, and on pre- senting a finger to the key, sparks in rapid succession were drawn. It is on this fact that the lightning-rod for the protection of buildings depends. A metallic rod pro jects above the top of the building, and descends down to a certain depth in the ground, ofiering, therefore, a free passage for the electric fluid into the earth. When electricity is communicated to a conducting Describe the Leyden jar. How is it charged and discharged? Whatef fecta may be produced by it ? How and by whom was the identity of lightning and electricity proved ? What is the principle of the Ughtnin; rod ? DISTRIBUTION OP ELECTRICITY. 295 body it resides merely upon the surface, and does not penetrate to any depth within. In the case of spherical bodies, this superficial distribution is equal all over; but when the body to which the electricity is communicated is longer in oro, direction than the other, the electricity is chiefly found at its longer extremities; the quantity at any point being proportional to its distance from the center. - These principles may be very well illustrated by taking a long strip of tin foil, so arranged as to be rolled and un- rolled upon a glass axis, and connected with a pair of cork balls, the divergence of which shows its electrical condition. If, now, to this, when coiled up, a sufficient amount of electricity is communicated to make the balls diverge, on pulling out the tin foil, so as to have a larger surface, they will collapse ; but on vnnding the foil up again they will again diverge, showing that the distribu- tion of electricity is wholly superficial, and that when a given quantity is spread over a large surface it necessa- rily becomes weaker in effect. In the case of pointed bodies, the length of which is very great compared with their other dimensions, the chief accumulation of electricity takes place upon the point. When a needle is fastened upon a prime con- ductor, this accumulation becomes so great that the fluid escapes into the air, and may be seen in the dark in the form of a luminous brush. Or if, on the other hand, a needle be presented to a prime conductor it withdraws its electricity from it, and the point becomes gilded with a little star. The electric fluid moves with prodigious rapidity. It has a velocity greatly exceeding that of light. In a cop- per wire its velocity is 288,000 miles in one second. There are many diflerent ways in which electricity may be developed. In the processes we have hitherto described it originates in friction. And, as one kind of electricity can never make its appearance alone, but is always accompanied with an equal quantity of the other, Does electricity reside on the surface or in the interior of bodies ? How is its distribution dependent on their figure ? How may it be proved that electricityiff-distributed-superficiaUy? What is the effect of pointed bodies? How may a brush and a star of light be exhibited? What is the velocity of the electric fluid ? By what processes may electricity be devel- ODed ' Can one kind of electricity be obtained without the other 1 i'Jo ZAMBONI'S PILES. we uniformly find that the rubber and the surface rubbed are always in opposite states — if the one is positive the other is negative. It is on this principle that many ma- chines are furnished with means of collecting the fluid from the prime conductor or the rubber, and, therefore, of obtaining the positive or negative electricity at pleas- ure. Electricity may also be developed by heat. The tour- maline, a crystalized gem, when warmed, becomes posi- tive at one end and negative at the other. Changes of form and chemical changes of all kinds give rise to elec- tric development. Zamboni's electrical piles are made by pasting goW leaf on one side of a sheet of paper and thin sheet zinc on the other, and then punching out of it a number of circular pieces half an inch in diameter. If several thou- sands of these be packed together in a glass tube, so that their similar metallic faces shall all look the same way. Fig. 315. and be pressed tightly together at each end by metallic plates, it will be found that one extremity of the pile is positive and the other negative ; and that the ef- fect continues for a great length of time. Fig. 315 represents a pair of these piles, arranged so as to produce what was, at one time, regarded as a perpetual motion. Two piles, a h, are placed in such a po- sition that their poles are reversed, and between them a ring or light ball, c, vi- brates like a pendulum on an axis, d. It is alternately attracted to the one and then to the other, and will continue its movements for years. A glass shade is placed over it to protect it from external disturbance. The purposes of philosophy require means for the detection and measurement of electricity. The instil- ments for these uses are called electroscopes and elec- trometers ; they are of different kinds. A pair of cork balls, a a, Fig. 316, suspended by cot- ton threads so as to hang parallel to one another, and be in metallic communication with the ball, b, furnish a sim- What are the phenomena of the tourmaline 7 What are Zamboni's electrical piles ? How may these be made to furnish an apparent perpet- ual motion ? ^ rr r r ELECTROMETERS. 291 pie instrument of the kind. If any electricity is commu nicated to h, the balls participate in it, and as J^^-3i6. bodies electrified alike repel, these recede from each other. The amount of their diverg- ence gives a rough estimate of the relative quantity of electricity. All delicate electrome- ters should be protected from currents in the air by means of a glass cylinder or shade, as c c. ' ' ' The gold leaf electroscope differs from the foregoing only in the circumstance that, instead of a pair of threads and cork balls, it has a pair of gold leaves, the good con- ducting power and extreme flexibility of which adapt them well for this purpose. ^^e- 3iT- The quadrant electrometer, Fig. 317, is formed of an upright stem, a h, on which is fastened a graduated semicircle of ivory, "c, from the center of which hangs a cork ball, d. As this is repelled by the stem the graduation serves to show the number of degrees. But no quantity of electricity can ever drive it beyond 90°,; and, indeed, its degrees are not proportional to the quantities of electricity. '. The best electrometer is Coulomb's torsion trometer. Fig. 318, of which a de- scription has been given in Lecture XXIII. The best electroscope is Bohnen- berger^s. It consists of a small dry pile, a h. Fig. 319, supported hori- zontally beneath a glass shade, and from its extremities, a b, curved wires pass, which terminate in parallel plates, p m. One of these is, therefore, the posi- tive, and the other the negative pole of the pile. Between them there hangs a Describe the cork-ball electroscope. Describe the gold-leaf electroscopei What is the quadrant electrometer? Which is the best electrometer T Which is the best electroscope ? Describe it. N* Tig. 318. Tig. 319. 298 THE VOLTATC BATTERY. gold leaf, d g, which is in metallic communication with the plate, o n,\ry means of the rod, c. If the leaf hangs equally between the two plates, it is equally attracted by each, and remains motionless ; but on communicating the slightest trace of electricity to the plate, o n, the gold leaf instantly moves toward the plate which has the opposite polarity. LECTURE LX The Voltaic Batterv. — The Voltaic Pile. — The Trough. — Grove's Battery. — Phenomena of the Battery. — Sparks. — Incandescence. — Decomposition of Water. — Electromotive Force. — Resistanceto Conduction. — Power of the Battery. — Phenomena of a Simple Circle. The voltaic pile has a very close analogy in its con- struction with the dry piles just described. It consists of a series of zinc and copper plates, so arranged that the Fig. 320. same order is continually preserved, and be- tween them pieces of cloth, moistened with acidulated water — thus, copper, cloth, zinc copper, cloth, zinc, &c. There should be from thirty to fifty such pairs to form a pile of sufficient power. 3 When the opposite poles or ends of this in strument are touched, a shock is at once felt. It is not unlike the shock of a Leyden jar ; but the pile differs from the electrical machine in the circumstance that it can at onee recharge itself, and gives a shock of the same strength as often as it is touched. As the voltaic battery is now employed for numerous purposes in science, many forms more convenient than that described, have been introduced. In the voltaic Fig.asi. trough the zinc and copper plates being soldered together, are let into grooves in a box, as shown in Fig. 321, the cells between each pair of plates Describe the voltaic pile. Under what circumstances does it give a shock ? What is the form given to this instrument in the voltaic trough I G 299 serving to hold the mixture of water and sulphuric acid. Such an instrument is easily brought into activity, and its exciting fluid easily removed. Of late other more powerful forms of voltaic battery have been invented ; such, for instance, as Grove's arid Bunsen's. Grove's battery consists of a cylinder of zinc, Z, Z, Fig. 322, the surface of which is amalgamated with quicksilver. Jt is placed in a glass jar, G G. Fig.asz. Within this there is a cylinder of porous earth- i enware, p p, in which stands a sheet of pla- z| tinum, PP. In Bunsen's battery P is a cylin- der of carbon, into which, at r, a polar wire can be fastened. The glass cup, G G, is filled with dilute sulphuric acid (a mixture of one of acid to six of water), the porous cylinder is fill- ed with strong nitric acid, and the' amalgamated zinc is therefore in contact with dilute sulphuric acid, and the pla- tinum or carbon with nitric acid. By means of the bind- ing screws' polar wires may be fastened to the plates, and a number of jars may be connected together so as to form a compound battery. In this case, the wire coming fi-om the zinc of one cup is to be connected with the platinum or carbon of the next, the same aiTangement being con- tinued throughout. When several such cups are connected together, and the polar wdres of the terminal pairs brought in contact, a bright spark, or rather flame, instantly passes, and when these connecting wires are of capper the color of the light is of a brilliant green. By fastening on one of the polar wires conducting substances of different kinds, they bum or deflagrate with different phenomena, each metal yield- ing a colored light. If a fine iron or steel wire, in con- tact with one of the poles, be lowered down on some quicksilver into which the other is immersed, a brilliant combustion ensues — the iron, as it burns, throwing out in- numerable sparks ; and on pointing the polar wires with pieces of hard-burnt charcoal, on approaching them to each other a spark passes, and the points may now be drawn apart several inches, if the iiattery is powerful, the Describe Grove's battery. In this battery how many metals and liqtids are employed ? What effect ensues when the connecting wires are brought In contact 1 What phenomena do the different metals exhibit during iiombustion ? What ensues when charcoal-points are employed? 300 DECOMPOSITION OP WATER. flame still continuing to play between them. This flame which is arched upward, afTords the most brilliant ligh, that can be obtained Ijy any artificial process. If, between the polar wires of a voltaic battery, a piec» of platinum — a metal of extreme infusibility — intervenes and the metal withstands fusion and is not too thick, it be comes incandescent, and continues so while the curreu' passes. , But by far the most valuable effects to which these in struments give rise are decompositions. If the poles of a battery are terminated with pieces of platinum, and these are dipped in some water, bubbles of gas rapidly escape from each — they arise from the decomposition of the water. The apparatus Fig. 323, enables us to perform this experiment in a very satisfactory manner. It consists of two tubes, o Ji, which have lateral open- ings, p p, through which, by means of tight corks, platinum wires, terminat- ed by a little bunch of platinum, may be passed. The tubes, o h, are sus- pended vertically, in a small reser- voir of water, g, by an upright, V. They are also graduated into parts of equal capacity. By means of the binding screws at a and b the plati- num wires may be connected with the poles of an active battery. If, now, the two tubes are filled with water and im- mersed in the trough, and the communications with the battery established, gas rapidly rises in each, and collects in its upper part. In that tube which is in connection with the positive pole of the battery oxygen accumulates, in the other hydrogen. And it is to be observed that the quantity of the latter is equal to twice the quantity of the former gas. Water contains by volume twice as much hydrogen as it does oxygen. In any voltaic combination, the exciting cause of the electricity, whatever it may be, goes under the name of Can platinum be made continuously incandescent ? Describe the pw cess for the decomposition of water. What are the relative quantities of ixygen and hydrogen gases produced in this experiment 7 SIMPLE CIRCLE. 301 the electromotive force, and the resistances, which ob- struct the motion of the electricity,, are termed resis^ ances to conduction. The electromotive force determines the amount of elec- tricity which is set in motion ; and in a voltaic battery the resistances which arise are chiefly due to the imper feet conducting power of the liquid and metalline parts. ■The resistance of the metalline parts is directly as theij lengths and inversely as their sections. A wire two feej long resists twice asjmuch as a wire one foot, if their sec- tions are equal ; an5 of two wires that are of an equal length that which has a double thickness or section vvill conduct twice as well. The resistance of the liquid parts depends^ on the dis- tance of the plates from one another — ^it is inversely as their sections of those parts. The total force of any voltaic battery may be ascertain- ed by dividing the sum of all the electromotive forces by the sum of all the resistances The origin of the electrical action of voltaic combina- tions is, in all probability, due to chemical . changes going on in them. The study of a simple voltaic cir- cle throws much light on these facts. If we jp^. 354. take a plate of amalgamated zinc, z, an inch wide and six long, and a copper plate, c, of equal size, and dip them in some acidulated water contained in a glass jar,yj they form a simple voltaic circle. It is to be understood that common sheet zinc is easily covered over with quicksilver, or amalgamated, by washing it with sulphuric acid and water in a dish in which some quicksilver is placed. Now, so long as the two plates remain side by side without touching, no action whatever takes place ; but if we establish a metallic communication between them by' means of the wire d, innumerable bubbles of gas escape from the copper, c, and the zinc in the mean time slowly corrodes away. On lifting up d the action instantly ceases, What is meant by the term electromotive force ? What by resistances to conduction ? From what do the resistances chiefly arise? What is the law for the resistance of the metallic parts ? What for the liquid ? How is the total force of the' voltaic battery determined T Describe the apparatus. Fig. 324. 802 ELECTROTYPE. I on bringing it into contact again the action is re-establiBh- lished. And if the apparatus is in a dark place whenev- er i is lifted from either plate, z or c, a small but brilliant electric spark is seen, showing therefore that electricity la the agent at work. If the gas which rises from the copper plate be exam- ined, it turns out to be hydrogen, and the corrosion of the zinc is due to the combination of that metal with oxygen. Water, therefore, must have been decomposed to furnish these elements. The electric action of the common voltaic circle arises from the decomposition of water. If the vvire (i be a slender piece of platinum it contin- ues in an ignited condition as long as the apparatus is in activity. The electricity must, therefore, flow in a contin- uous current; and, as the most powerful voltaic batteries are nothing but combinations of these simple ones, the same reasoning applies to both, and we attribute their ac- tion to the same cause — chemical decompositions going on in them, and giving rise to an evolution of electri- city which flows in a continuous current from end to end of the instrument and back through its polar wires. A very beautiful process for working in metals, called the electrotype, and founded upon the principles explain- ed in this lecture, has been lately introduced into the arts. When water is submitted to the influence of a voltaic current we have seen that it is resolved into its constitu- ent elements, oxygen and hydrogen, a total separation ensuing, and each of these going to its own polar vrire. In the same manner, when a metalline salt transmits the voltaic current, decomposition ensues, the acid part of the salt being evolved at the positive and the metalline part at the negative pole. When the salt has been properly selected the metal is deposited as a coherent mass, and faithfully copies the form of any surface in which the negative pole is made to teiTninate. Thus, to the polar wire Z, Fig. 325, qf a simple voltaic battery let there be attached a coin or other object, N, one surface of which has been varnished or covered with some non- What ensues when a metallic communication is made between the metals ? How can it be proved that electricity is concerned in these re- sults ? Why do we know that water must have been decomposed ? Why do we know that there is a continuous current of electricity passing? On what principles is the electrotype process founded ? ELECTROTYPE. 303 conducting material ; to the other wire, S, let there be affixed a mass of copper, ,C, Fig.aas. and let the trough, N C, in which these are placed be filled with a solution of sulphate of copper. Now, when the bat-_ tery is charged, the sulphate of copper in the trough undergoes decomposition, metallic copper being deposited on the face of the coin, N ; and as this with- drawal of the metal from the so- lution goes on, the mass, C, undergoes corrosion, and, dis- solving in the liquid, replaces that which is continually accumulating on the face of the coin. "When the experi- menter judges that the deposit on N is Sufficiently thick, he removes it from the trough, and with the point of a knife splits it from the surface of the coin. The cast thus ob- tained is admirably exact. In the same manner that copper may thus be obtained from the sulphate, so other metals may be used. Casts in gold and silver, and even alloys, such as brass, may be obtained. There is no difficulty in gilding, silvering, or platinizing surfaces, and from a single cast, by using it in turn as a mould, innumerable copies may be taken. Describe one of the methods for taking casts. Can other metals be- ■ides copper be used ? Is this orocess adapted for gilding and sihering f 304 ELECTRO-MAGNETISM. Fig. 326. A LECTURE LXI. Electro-Magnetism. — Action of a Conducting Wire on the Needle. — Transverse Position assumed. — Effects of a Bent Wire. — The Multiplier. — Astatic Galvanometer. Electro-Magnet. — RotatoryMovements. — Attraction and Repulsion of Currents. — Electro-Dynamic Helix. — Elec- tro-Magnetic Theory. When a magnetic needle, having freedom of motion upon its center, .is brought near a wire through which an electric current is passing, the needle is deflected and tends to move into such a position as to set itself at right angles to the wire. Thus, let there be an electric cur rent moving in the wire A B, Fig. 326 ; in the direction of the arrow, and directly over the wire and par- allel to it, let there be placed, a sus- pended needle ; as soon as the cur- rent passes in the wire, the needle is deflected from its north and south position, and turns round transverse- ly, and if the current is strong enough the needle comes at right angles to the wire. Now, every thing remaining as before, let the current pass in the opposite direction, the deflection takes place as before, only now it is also in the opposite direction. If the needle be placed by the side of the wire the same effect is observed. On one side it dips down and on the other it rises up. % What effect ensues when a magnetic needle is brought near a conduct ing wire ? How may it be proved that the direction of the motion de pends on the direction of the current ? What takes place when the nee die is at the side of the wire ? GAI.VANIC MULTIPLIERS. 305 Ke- 327. X Fig- 338. 3i In whatever position the needle is placed as respects the conducting wire it tends to set itself at right anglea thereto. This discovery was made by Oersted in 1819. From the foregoing experiments it will appear that if a wire be bent into the form of a rectangle, as represented in Fig. 327, and an electrip current be made to flow round it in the direction of the arrows, all the parts of the current tend to move a needle in the interior of such a rectangle in the same direction, and, therefore, it will be much rnore energetically disturbed than by a single straight wire. If the wire, instead of making one convolution or turn, is bent many times on itself, so that the same current may apt again and again up- on the needle, the effect of a very feeble force may be rendered perceptible. On tjiis principle the galvanometer is constructed, copper wire, wrapped with silk, is bent on itself many times, forming a rectangle, d d, Fig. 328 ; the two projecting ends, a a, dip into mer- cury-cups, by which they may be connected with the apparatus, the electric current of which is to be measured. In the interior of the rectangle, supported on a pivot, is a magnetic needle, n s, the deflec- tions of which measure the current. A still more delicate instrument is made by placing two needles, with their poles reversed, on the same axis, N S, 4 re, suspending them by a fine thread in such a way that one ^ By whom were these facts discovered 1 What efiFect is there on a nee- dle in the interior of a rectangle? What is the effect when the wire makes many convolutions 7 Describe the deflecting galvanometer. fine 306 fiLEOTRO-MAGNETS. of the needles is in the inside of the rectangle and the other above. If the needles are of equal power the com- bination is astatic — that is, not under the magnetic influ- ence of- the earth ; but both of them are moved in the . same direction by the passage of the current. Such an instrument is called an astatic galvanometer. . When an electric current, moving in a wire, is made to pass round a piece of soft iron, so long as the current continues the iron is magnetic ; but the moment the cur- rent ceases the iron loses its magnetism. If, thei'efore, a bar of soft iron be bent into the form N S, Fig. 330, and Fig. 330. fe -v there be wound round it a copper wire in a continuously spiral course, the strands of the wire being kept irom touching one another, and also from contact with the iron, by being covered with silk, whenever a current is passed through the wires by the aid of the binding-screws, j? »», the iron becomes intensely magnetic. The amount of its magnetism may be measured by attaching the keeper. A, to the arm of a lever, a h, which works on a fulcrum, c ; A is a hook by which weights may be suspended. In this way magnets have been made which would support more than a ton. Mr. Faraday discovered that rotatory movements could be produced by magnets round conducting wires ; and, conversely, that conducting wires would rotate round magnets. Both these facts may be proved at once by the instrument Fig. 331. On the top of a pillar, gc, a strong copper wire, bent as in the figure, at d J] ia fastened. Describe the astatic galvanometer. How may transient magnetism be communicated to an iron bfr' Describe the instrument, J%. 330. ELECTRO-MAGNETIC ROTATIONS. SOT To the crook aty a fine platina wire, h, hangs -by a loop on which it has perfect free- Fig. 331. ^ dom of motion. Its lower end, «j on which is a small glass Dead, dips under some mer- cury in a reservoir, h, in the center of which a magnetiz- ed sewing-needle, n, is fasten- ed by means of a slip of cop- per, which communicates with the binding-screw, z. On the arm, i, there is soldered inflexibly another platinum wire, e, which dips into a mercury reservoir, a, which is in metallic connection with the binding-screw c by means of a slip of copper. From the center and bottom of this reservoir a magnet- ized sewing-needle is fixed by means of thin platinum wire, so as to have freedom of motion round e. Under these circumstances, if an electric current is passed &om c along i, in the direction of the arrow, to z, the magnet, m, rotates round the fixed wire in one direction, and the wire, Ti, round the fixed magnet n in the other. On re- versing the course of the current these motions are re- versed. On similar principles all kinds of rotatoi-y, reciprbca- tory, and other movements may be accomplished, magnets made to revolve on their own axes, and entire galvanic batteries round the poles of magnets. In frictional electricity we have seen that the funda- mental law of action is, that like electricities repel and unlike ones attract. In the same way attractive and repulsive motions have been discovered in the case of currents. If electric currents flow in two wares which are parallel to each other, and have freedom of motion, the wires are immediately disturbed. If the currents run in the same direction the wires move toward each other, if in the opposite the wires move apart. Or, briefly, " like currents attract, and, unlike ones repel." If a wire be coiled into a spiral form, and its ends car- ried back through its axis, as shown in Fig. 332, it forms How may movements of rotation of wires and magnets round one another be shown ? Describe the instrument, Fig. 331. What ensues on reversing the current 1 What is the action of currents on each other t What is the general law af this action ? 308 THEORY OF MAGNETISM. mg . 332. an electro-dynamic helix. If it be sus- pended with freedom of motion in a horizontal plane, it points as a magnetic needle would no, north and south ; or if suspended, so as to move in a vertical plane, it dips like a dipping-needle. All the properties of a needle may be simulated by such a helix; and if two he- lices, carrying currents, are presented to /^jOfVfflMpnnnnnp each other, they attract and repel, under UOUOOUOUOOUUO the same laws that two magnetic bars would do. If, therefore, we imagine an electric current to circu- late round a magnet transversely to its axis, such a sup- position will account for all its singular properties. Anticipating what will have to be said presently as re- spects thermo-electricity, it may be observed, that if we take a metal ring, and warm it in one point only, by a spirit-lamp, no effect ensues; but if the lamp is moved an electric current runs round the wire in the course the lamp has taken. As with this metal, wire, and lamp, so with the earth. The sun, by his apparent motion, warms the parts of the earth in succession, and electric currents are generated, which fbllow his course. We must now call to mind all that has been said respecting the influence of the sun's heat on the magnet, in Lecture LVII. This elucidates the cause of the needle pointing north and south. It comes into that position because it is the position in which the electric currents in it are parallel to those in the earth. This is the position, as has just been explained, that cur- rents will always assume. We see why, at the polar re- gions, it dips vertically down. It is again that its currents may be parallel with those of the earth ; for in those re- gions the sun performs his daily motion in circles parallel to the horizon. We see, also, that it is for the same cause, in intermediate latitudes, that the needle points north and also dips. What is an electro-dynamic helix ? When two such helices act on each other what phenomena arise 1 What ensues when a metal ring is warm- ed at one point by a lamp, and what when the lamp is moved ? I^siw do these facts bear on the polarity and dip of the needle ? Why does mag- netic needle point north and south ? Why does it dip ? MAGNETO-ELECTRICITY. 309 This prolific theory likewise includes all the phenom- ena of Oersted, such as the transverse position a needle takes when under the influence of a conducting-wire ; for this is again the position in which the currents of the needle are parallel to that in the wire. LECTURE LXII. Magneto-Electricitt. — Thermo-Electricity. — Pro- duction of Electric Currents by Magnets. — Momentary Nature of these Currents. — They give rise to Sparhs, Decompositions, ifc. — Magneto- Electric Machines. — In- duction of Currents by Currents. — Electro-Magnetic Tel- egraph. — Production of Cold and Heat by Electric Cur- rents. — Thermo-dectricity. — Melloni's Multiplier. If an electric current passing round the exterior of a bar of soft iron can convert it into a magnet, we should expect that the converse would hold good, and a magnet ought to be able to generate an electric current in a con- ducting-wire. Let there be a helix of copper wire, a, Fig. 333, the successive strands of which are kept from touching, and let its ends at b be brought in con- tact. If a bar magnet, N S, is introduced in the axis, so long as it is in actual movement an electric current will run through the wire, but as soon as the bar comes to rest the current ceases. On withdrawing the bar the current again flows, but now it flows in the opposite direction. If, therefore, we alternately introduce and remove with rapidity a steel magnet, opposite currents will inces- santly run round the helix. If we open the wire at the point b, every time the current passes a bright spark is How does this theory include Oersted's phenomena T Can a magnet detelop electric currents in a wire 7 Under what circumstances does this take place ? How long does the current continue 1 Describe the instru- ment, Fig. 333. 310 , MAGNETO-ELECTRIC MACHINE. seen ; or if the two separated ends dip into water it un- dergoes decomposition. Fig. 334. The same results would, of course, occur, if, instead of introducing and removing a permanent steel magnet, we continually changed the polarity of a stationary soft iron bar. Thus if a b, Fig. 334, be a rod of soft iron, surrounded by a helix, and there be taken a semicircular steel magnet, N c S, which can be made to revolve on a pivot at c — things being so ar- ranged that its poles, N and S, in their revolutions, just pass by the terminations of the bar, a b — the polarity of this bar will be reversed every half revolution the magnet makes, and this reversal of polari ty will generate electric currents in the wire. To instru- ments constructed on these principles the name of mag- neto-electric machines is given. The peculiarity of these currents is their momentary duration. Hence they have been called momentary cur- rents, and from the name of their discoverer, Faradian currents. There are a great many different forms of magneto- electric machines. In some, permanent steel magnets are employed ; in others, temporary soft iron ones, brought into activity by a voltaic battery. Fig. 335 represents Saxton's magneto-electric machine. It consists of a horse-shoe magnet, A B, laid horizontally. The keeper, G D, is wound round with many coils of wire, covered with silk. It rotates on an axis, E F, on which it is fixed, by means of a pulley and multiplying- wheel, E G. The terminations of the wire, h i, dip into mercury cups at K. When the wheel is set in motion the keeper rotates, its polarity being reversed every half turn it makes before the magnet, and momentary currents run through its wires. If it is- desirable to give the current of a magneto-elec- tric machine great intensity, so as to furnish powerful shocks, or effect decompositions, the wire which is wound What are magneto-electric machines ? What names have their cur- «nts received ? Describe Saxton's magneto-electric machine. What is the effect of using a long thin and short thick wire ? INDUCTION OF CURRENTS BY CURRENTS. 311 lound the keeper should be thin and long ; but for pro- ducing incandescence in metals, or for sparks or magnet ic operations, the wire should be short and thick. Fig. 335. Admitting the theory that all magnetic action arises from the passage of electrical currents, it follows, from the facts just detailed, that an electrical current must have the power of inducing others in conducting bodies in its neighborhood. Experiment proves that this conclusion is correct, and currents so arising are called induced or secondary currents. Thus, when two wires are extended parallel to one an- other, and through one of them an electric current is passed, a secondary current is instantly induced in the other; but its duration is only momentary. It flows in the opposite direction to the primary one. On stopping the primary current, induction again takes place in the secondary wire ; but the current now arising has the same direction as the primary one. The passage of an electri- cal current, therefore, develops other currents in its neighborhood, which flow in the opposite direction as the How may it be proved.that electric currents induce others in their neigh- borhood 1. What direction does the induced current take at first, and what at last? 312 MAGNETIC TELEGRAPH. primary one first acts, but in the same direction as it ceases. Morse's electro-magnetic telegraph is essentially a horse- shoe of soft iron, made temporarily magnetic by the pass- age of a voltaic current. In Fig. 336, m m represent tig. 336. the poles of the magnet, wound round with wire ; at « is a keeper, which is fastened to a lever, a I, which works on a fulcrum, at d ; the other end of the lever bears a steel point, s, which serves as a pen. At c is a clock ar- rangement for the purpose of drawing a narrow strip of paper, p p, in the direction of the arrows. W W are the wires which communicate with the distant station. As soon as a voltaic current is made to pass through these wires, the soft iron becomes magnetic, and draws the keeper, a, to its poles ; and the other end of the lever, I, rising up, the point s is pressed against the moving paper and makes a mark. When the lever first moves it sets the clock machinery in motion, and the bell, h, rings to give notice to the observer. When the distant operator stops the current, the magnetism oi m m ceases, and the keeper, a, rising, s is depressed from the paper. By let- ting the current flow round the magnet for a short or a longer time a dot or a line is made upon the paper — and Describe Morse's telegraph. How are the dots and lines which com- Dose the telegraphic alphabet made by the machine ? THERMO-ELECTRICITY. 313 the telegraphic alphabet consists of such a series of marks It is not necessary to use two wires to the instrument ; one alone is cotoiilonly ■employed to carry the current to the magnet;' it'is b'rought back through the earth. If a bslr of TjisriiutK, b. Fig. 337, and one of antimony, a, be sdldere'd tbgether at the point c, and by Fig. 337. means of wires attached to the other ends, a feeble' voltaic current is passed from the an- timony to the bismuth, heat will be genera- ted at the junction, c; but if the cun-ent is made to pass from the bismuth to the anti- mony, cold is produced, so that if an excava- tion be made at c, and a little water intro- duced in it it may be frozen. The converse of this also holds good. If we connect the free terminations of a and b, by means of a wire, and raise the temperature of the junction c, an electric cur- rent sets from the bismuth to the antimony ; but if we cool the junction the current sets in the- opposite way. To these currents the name of thermo-electric currents is g^ven. Thermo-electric currents, from the circumstance that they originate in good conductors, possess but very little intensity. They are unable to pass through the thinnest film of water, and, therefore, in operating with the^ it is necessary that all the parts of the apparatus through which they are to flow should be in perfect metallic contact. The slightest film of oxide upon a wire is sufficient to prevent their entrance into it. As the eflFects of the voltaic circle can be increased by increasing the number of pairs forming it, the'same is also true for thermo-electric currents. Thus, if we take a se- ries of bars of bismuth and antimony, and solder their alternate ends to one another, as shown pig, 339. in Fig. 338, oh warming one set of the j j j 6 6 o junctions, the current passes, and is \ A A A Ay^ greater in force according as the num- \'\'\f\fv her of alternations warmed is greater. a a a a a From their feeble intensity, these currents, when passed through the wire of a multiplying g^anotSbter, Fig. 329, What effects arise from passing feeble electric currents through a pair of bars of bismuth and antimony ? What are thermoielectric currents ? Why have they so little intensity ? How may that intensity be increased f J14 THERMO-MULTIPLIER. do not give rise to the same effects that are observed in ordinary voltaic currents — they lose as much of their force by the resistance to conduction of the slender wire as they gain by the effect which each coil impresses on the nee- dle. A multiplier, suited for thermo-electric currents, should be made of stout wire, and make but few turns round the needle. Melloni's thermo-electric pile is represented in Fig. 339. It consists of thirty or forty pairs of small bars of Fig. 339. bismuth and antimony, with their alternate ends soldered together, forming a bundle, F F. The polar wires, C C, projecting, are put in communication with the multiplier. To each end of the pile brass caps, as seen in the figure, fit. These serve to cut off the disturbing influence of currents of air ; and now if the hand or any other source of heat be presented^ to one side of the pile, the needle of the galvanometer immediately moves, and the amount of its deflection increases with the temperature of the radiant source. It is not necessary to use many alternations, as in the instrument of Melloni. Let a pair of heavy bars pig. 340. of bismuth and antimony, of the shape repre- sented in Fig. 340, be soldered by the edges, a h, to a, circular plate of thin copper, and at the others at a' b', to semicircular plates, e f, having projecting pieces to communicate with the wire of a galvanometer of few convolutions, ^ and the needle of which is nearly astatic. It will be fijund that extremely minute changes of temperature may be indicated — -the combination answering very well instead of Melloni's more costly instrument. Why does not the common galvanometer increase the effect of these currents ? What ought to be the construction of a thermo-electric multi- plier ? Describe UTblloni'B instrument. Is it necessary to use so mar y al- ternations y mg. 340. n ASTRONOMY. 315 ' ASTRONOMY. LECTURE LXIII. Astronomy. — The Figure of the Earth. — The Earth Ro- tates on her Axis. — Illustrations of Diurnal Rotation. — Annual Translation round the Sun. — The Year. — Mo- tions of the Moon. — Planets and Comets. — Astronomical Definitions. In the infancy of knowledge the first impreBsion which men entertained respecting the form of the earth we in- habit, was that it is an indefinitely-extended plane, the more central portions being the land, surrounded on all sides by an unknown expanse of sea. Many natural phe- nomena soon corrected these primitive ideas, and almost as far back as historic records reach, philosophers had come to the conclusion that our earth in reality is of a round or globular form. To this conclusion a consideration of the daily phenom- ena of the starry firmament would naturally lead. Every evening we see the stars rising in the east, and as the night goes on, passing over the vault of the sky, and at last setting in the west. During the day the same is also observed as respects the sun. And as these are events which are taking place day after day, in succession, and no man can doubt that the objects which we see to-day are those which we saw yesterday, it necessarily follows, that after they have sunk under the western horizon, they pursue their paths continuously, and that the earth neither extends indefinitely in the horizontal direction, nor verti cally downward, but that she is of limited dimensions or all sides. What was probably the primitive idea respecting the figure of the earth. How may it be proved thatthe earth is limited on all sides? 316 FIGURE OF THE EARTH. Where the prospect is uninterrupted, as at sea, we are further able not only to verify the foregoing conclusion, but also to obtain a clearer notion of the figure of the earth. Thus, as is seen in Fig. 341, let an observer be Fig. 341. watching a ship sailing toward him at sea. When she is at a great distance, as at a, he first perceives her topmast, but as she approaches from a toward S, more and more of her masts come into view, and finally her hull appears. When she arrives at h she is entirely visible. Now, as this takes place in whatever direction she may approach, whether from the north, south, east, or west, it obviously psints out the globular figure of the earth. In the distant position, more or less of the ship is obscured by the in- tervening convexity — a phenomenon which never could take place were the earth an extended plane. This great truth, though admitted by philosophers in ancient times, fell gradually into disrepute during the middle ages ; it was re-established at the restoration of learning only after a severe struggle. It is now the basif of modern astronomy. The spheroidal figure being therefore received as a demonstrated fact, it is next to be obseiTed that the ea'-tn is not motionless in space, but in every twenty-four hours turns Bound once upon her axis. That such a motion ac- tually occurs is clear from the fact of the rising and set' ting of the celestial bodies. To an observer at the equator, the stars rise jn the eastern horizon and set in the western, continuing in view for twelve hours, and being invisible for twelve. At the What facts prove that she is of a round or globular form ? When was the globular form of the earth denied, and when finally established ? Has the earth a motion on her axis ? In what time is it performed ? "What are the phenomena of the rising and setting of the star» at the equatoi and the poles? MOTION OF THE SUN AND MOON. 317 pole the rising or setting of a star is a phenomenon never seen ; but these heavenly bodies seem to pursue paths which are parallel to the horizon. In intermediate lati- tudes a certain number of stars never rise or set, while others exhibit that appearance. In any of these posi tions in our hemisphere >he motion of the heavens seems to be round one, or, rather, two points, situated in opposite directions ; to one of them the name of the north, and to the other of the south pole is given. These are the points to which the poles of the earth are directed. When observations are made for some days or months in succession, we find that there are motions among the celestial bodies themselves which require to be account- ed for. First, we observe that the sun does not remain stationary in a fixed position among the stars, but that he has an apparent motion ; and that after the lapse of a little more than three hundred and sixty-five days he comes round again to his original place. As with the diurnal motion so with this annual. Consideration soon satisfies us that it is not the sun which is in movement round the earth, but the earth which is in movement round the sun. To the period which she occupies in completing this rev- olution the name of the year is given. Its true length is three hundred and sixty-five days, five hours, forty-eight minutes, forty-nine seconds. The sun seems, in his daily motion, to accompany the stars; but if we mark the point upon the horizon at which he rises or sets we find that it differs very much for different times of the year. The same observation may be made by observing the length of the shadow of an upright pole or gnomon at midday. Such observa- tions show that there is a difference in his meridian alti- tude in winter and summer of forty-seven degrees. The observation of a single night satisfies us that the moon has a motion of her own round the earth. It is ac- complished in twenty-seven days, seven hours, and forty three minutes, and is called her periodical revolution; but, during this time, the earth has moved a certain dis- tance in the same direction — or, what is the same thing, the sun has advanced in the ecliptic, and before the moon overtakes him, twenty-nine days, twelve hours, and forty- What other motion besides this may be discovered? What is the year? What is the month? 318 DEFINITIONS. four minutes elapse. This, therefore, is termed her synod- ical revolution, or one month. There are a^so certain stars, some of which are re- markable for their brilliancy, which exhibit proper mo- tions. To these the name at planets is given. And at irregular intervals, and moving in different directions through the sky, there appear from time to time comets. Multitudes of these are telescopic, though some have ap peared of enormous magnitude. There a.re several technical terms used in astronomy which require explanation. ' By the celestial sphere we mean a sky or imaginary sphere, the center of which is occupied by the earth. On it, for the purposes of astronomy, we imagine certain points and fixed lines to exist. Those circles whose planes ^ass through the cevnter of the sphere are called great circles. The circumference of each is divided into three hundred and sixty parts, called degrees, and marked (°), each degree into sixty minutes, marked ('), and each minute into sixty seconds, marked (") All great circles bisect each other. Less circles are those whose planes do not pass through the center of the sphere. The axis of the earth is an imaginary line, drawn through her center, on which she turns. The extremities of this line are the poles. A line on the earth's surface every where equidistant from the poles is the equator. Circles drawn on the sur- face parallel to the equator are called simply parallels, and sometimes parallels of latitude. At sea, or where the prospect is unobstructed, the sky seems to meet the earth in a continuous circle all round. To this the name of sensible horizon is given. The ra- tional horizon is parallel to the sensible, and in a plane which passes through the center of the earth. That point of the celestial sphere immediately overhead is the zenith, the opposite point is the nadir. A circle drawn through the two poles and passing through the north and south points of the horizon is a What are the planets? What are comets? What is the celestial sphere ? What are great and less circles ? What is the axis of the earth ? What are the poles, the equator, and parallels of latitude ? What is tht •ensible and what the rational horizon ? What is the zenith and the nadir \ DEFINITIONS. 319 meridiaii. Hour circles are other great circles which pass through the poles. A circle drawn through the zenith and the east and west points of the horizon is the prime vertical. Other great circles passing through the zenith are vertical circles or circles of azimvth. The altitude of a body above the horizon is measured in degrees upon a vertical circle. As the zenith is 90° from the horizon, the altitude deducted from 90° gives the zenith distance. The azimuth of a body is its distance from the north or south estimated on the horizon, or by the arc of the horizon intercepted between a vertical circle passing through the body and the meridian. The latitude of a place is the altitude at that place of the pole above the horizon, or, what is the same thing, the arc of the meridian between the zenith of the place and the equator. At the earth's equator the pole is, therefore, in the horizon ; at the pole it is in the zenith. The longitude of a place on the earth is the arc of the equator intercepted between the meridian of that place and that of another place taken as a standard. The observatory of Greenwich is the standard position very commonly assumed. The longitude of a star is the arc of the ecliptic intercepted between that star and the first point of Aries. The latitude of a star is its distance from the ecliptic, measured on a great circle passing through the pole- of the ecliptic and the star. The declination of a heavenly body is the arc of an hour circle intercepted between it and the equator. The ecliptic is the apparent path which the surr de- scribes among the stars. It is a great circle which cuts the equator in two points, called the equinoxial points, because when the sun is in those points> the nights and days are equal ; one is the vernal, the other the autumnal equinox. From this circumstance the equator itself is sometimes called the equinoxial line. What is a meridian 7 What are hoar circles ? What is the prime ver- tical ? What are circles of azimuth ? What are altitude and zenith distance ? WKat azimuth, the latitude of a place, and the declination of a heavenlv body ? What is the longitude of a place and that of a star f Wh:t is tiiL'Hciiutic? 320 DEFINITIONH. Two points on the ecliptic, 90° distant from the equi- noxial points, are the solstitial points. When the sun is in one of these it is midsummer, in the other midwinter. Motions in the direction from west to east are direct. Retrograde motions are those from east to west. The ecliptic is divided into twelve equal parts called signs. They bear the following names and have the f<>llowing signs. Aries f Libra === Taurus a Scorpio m Gemini n Sagittarius / Cancer s Capricornus V? Leo iL Aquarius ~ Virgo n Pisces X Formerly these signs coincided with the constellations of the same name, but owing to the precession of the equinoxes, to be described hereafter, this has ceased to be the case. Two parallels to the equator — one for each hemisphere — which touch the ecliptic, are called tropics. That for the northern hemisphere is the tropic of Cancer ; that'for the south the tropic of Capricorn. Two other parallels — one for each hemisphere — as far from the poles as the tropics are from the equator, are the polar circles, the northern one is the arctic, the southern one ih& antarctic. The right ascension of a heavenly body is the distance intercepted on the equator between an hour circle passing through it and the vernal equinoxial point. The astronomical day begins at noon, the civil day at midnight. Both are divided into twenty-four hours, each hour into sixty minutes, each minute into sixty seconds. By the orbit of a body is meant the path it describes. This, in most cases, is an ellipse. The nodes are those points where the orbit of a planet intersects the ecliptic. The ascending node is that from which the planet rises toward the north, the descending that from which it descends to the south ; a line joining the two io the line of the nodes. What are the equinoxial and solstitial points? What are direct and retrograde motions ? How is the ecliptic divided ? What are the tropics and polar circles? What is right ascension? What is the difference between the astronomical and civil day ? What is an orbit ? What are he ascending? and descending nodes? MOTION OF THE SUN. 321 LECTURE LXIV. Translation op the Earth round the Sun, and its Phenomena. — Apparent Motion and, Diameter of the Sun. — Elliptical Motion of the Earth. — Sidereal Year, — Determination of the Sun's Distance. — Parallax. — Dimensions of the Sun. — Center of Gravity of the Two Bodies. — Phenomena of the Seasons. In the last lecture it has been observed that the sun has an apparent motion among the stars in a path called the ecliptic. A line joining that body with the earth, and following his motions, would always be found in the same plane, or, at all events, not deviating from that position by more .than a single second. Observation soon assures us that if we carefully ex- amine the rate of the sun's motion in right ascensioff, it is far from being the same each day. This want of uni- formity might, to some extent, be accounted for by the obliquity of the ecliptic; but even if we examine the motion in the ecliptic itself, the same holds good. The sun moves fastest at the end of the month of December, and most slowly in the end of June. Further, if we measure the apparent diameter of the sun at different periods of the year, we find that it is not always the same. At the time when the motion just spoken of is greatest, that is during the month of December, the diameter is also greatest ; and when in June the motion is slowest, the diameter is smallest. These facts, there- fore, suggest to us at once that the distance between the earth and the sun is not constant ; but in December it is least, and in June greatest, for the difference in size can plainly be attributable to nothing else but difference of distance. The annual motion of the sun in the heavens, like his diurnal motion, is, however, only a deception. It is not Does the sun move with apparently equal velocity each day ? When ia his motion fastest and when slowest? Is the sun always of the same size ? When is he largest and when smallest 1 How can we be certain that the earth does not move in a circle round the sun ? 322 MOTION OP THE EARTH. the sun which moves round the earth, but the earth which has a movement of translation round the sun, as well aa one upon her own axis. The path which she thus de- scribes is not a circle, for in that case, being always at the same distance, the sun would always be of the same apparent magnitude, and his motion always uniform ; but it is an ellipse, having the sun in one of its foci. Thus, in Fig. 342, let F be the sun, A D B E the elliptrc orbit of the earth ; it is obvious that as she moves in this path Yig. 342. she will be much nearer the focus F occupied by the sun when she arrives at A than when she is at B. To the former point, therefore, the name of 'perihelion, and to the latter of aphelion is given ; the line A B joining them is called the line of the apsides. The periodic time occupied in one complete revolution is called the sidereal year. Its length is 365 days, 6 hours, 9 minutes, 11^ seconds. The law which regulates the velocity of motion of the earth round the sun was discovered by Kepler. Tt has already been explained, in speaking of central forces, in Lecture XXI. It is " the radius vector (that is, the line How do we know it is in an ellipse ? What are the perihelion and aphe- lion points ? What is the line of the apsides ? What is the sidereal year? What is Keplo-'s law respecting the radius vector? PARALLAX. 323 joining the centers of the sun and earth) sweeps over equal areas in equal times." With these general ideas respecting the nature of the orbit described by the earth, we proceed, in the next place, to the determination of the actual size of that orbit: itt other words, to ascertain the distance between the earth and the sun. Let C, Fig. 343, be the center of the earth, B the po- sition of an observer upon it, ^ig- 343 and M the sun ; the observer, B, will see the sun in the direc- tion B M, and refer him in the heavens to the position, n. An observer at C, the center of the earth, would see him in the po- sition C M, and refer him to the point m. His apparent place in the sky, will, therefore, be different in the two instances. This difference is called fwr^ E dllax ; and a little consideration shows that the amount of parallax differs with the place of observation and posi- tion of the body observed, being greatest under the cir- cumstances just supposed, when the body is seen in the horizon, and becoming when the body is in the zenith. This diminution of the parallax is exemplified by sup- posing the sun at M' ; the observer at B refers him to n, the observer at C to m', but the angle B M' C is less than the angle B M C. Again, if the sun be at M" — that is, in the zenith — ^both observers, at B and C, refer him to m", and the parallax is 0. The horizontal parallax being measured by the angle, B M C is evidently the angle un- der which the semidiameter of the earth appears, as seen in this instance from the sun. Althoilgh we cannot have access to the center of the earth, there are many ways by which the parallax may be ascertained, the result of the most exact of which has fixed for the angle BMC the value of about eight sec- onds and a half. Now it is a very simple trigonometrical problem, knowing the value of this angle, and the length Wliat is parallax ? Why aues the parallax become in the zenith ? What is the horizontal parallax in reality ? What is the exact value of the parallax ? 324 DISTANCE AND SIZE OF THE SUN. of the line B C m miles, to determine the line C M. When the calculation is made, it gives about 95,000,000 miles. This, therefore, is the mean distance of the earth from the sun. Knowing the apparent diameter of an object, and its distance from us, we can easily determine its actual mag- nitude. Seen from the earth, the sun's apparent diame- ter subtends an angle of 32' 3"- The true diameter, there fore, must be 882,000 miles. But the diameter of th« earth is short of 8000 miles. Such, therefore, are the dimensions of the orbit of the earth, and of the bodies concerned in it. We are now in a position to verify all that has been said in respect of the relations of these bodies ; for, calling to mind what was proved in Lecture XXI, respecting. bodies situated as these are, we see that in strictness the one cannot revolve round the other, but both revolve round their common cen- ter of gravity. Recollecting also that the center of grav- ity of two bodies is at a distance inversely proportional to their weights, and that the sun is 354,936 times heavier than the earth, it follows that this point is only 267 miles from his center. So, therefore, with scarce an error, the center of the sun may be assumed as the center of the earth's orbit, and with truth she may be spoken of as re- volving arouild him. Occupying such a central position, this enormous globe is discovered to rotate on an axis inclined 82° 40' to the plane of the ecliptic, making one rotation in twenty-five days and ten hours, in a direction from west to east. This is proved by spots which appear from time to time on his surface, and follow his movements. He is the great source of light and heat to us, and determines the order of the seasons. His weight is five hundred times greater than that of all the planets and satellites of the solar system, though he is not of greater density than water. In Fig. 344 we have a general representation of the appearance of the solar spots. They consist of a dark nucleus, surrounded by a penumbra, and are very varia- What is the distance of the earth from the sun ? What is the actual diameter of the sun 1 At what distance is the center of gravity of the two bodies from the sun's center ? How is it known that the sun rotates on his axis ? What is the period of that rotation ? Describe the phenomena of his spots. SPOTS ON THE SUN. 325 ble, both in number and size. Sometimes for a consider- able period scarce any are seen, and then they occur in great numbers in irregular clusters. Their size varies Fig. 344. .'» =.?, ^ from -^ to -jJ-g- part of the sun's diameter. They aie, therefore, of enormous dimensions, often greatly exceed- ing the surface of the earth. Their duration is also very variable. Some have lasted for ten weeks, but more com- monly they disappear in the course of a month or less. They seem to be the seats of violent action, undergoing great changes of form, not only in appearance, but also in reality. On their first appearance on the sun's eastern edge, they move slowly — they move rapidly as they ap- proach the middle of his disc, and move slowly again aa they pass to the western edge. This is, however, an op- tical illusion, due to the globular figure of the sun. They . rarely appear at a greater distance than from 30° to 60° from the sun's equator, and cross his disc in thirteen days and sixteen hours. Their apparent revolution is, there- fore, twenty-seven days and eight hours ; and, making al- lowance for the simultaneous movement of the earth, this Sx!0 ^, =- -V.M- -r-'y e(j THE SEASONS. 3^1 gives for the sun's rotation on his axis twenty-five days and ten hours. To explain the occurrence of the seasons — spring, sum- mer, autumn, and winter — it is to be understood that the earth's axis of rotation, for the reasons explained in Lec- ture XXI, always points to the same direction in space, and, therefore, as the earth is translated roun^ the sun, is always parallel to itself Let, therefore, S, Fig. 345, be the sun, and EEE, &c., the positions the earth respectively occupies in the months marked in the figure. Her position is, therefore, in Libra at the vernal equinox, in Aries the autumnal, in Capricorn at the summer, and in Cancer at the winter solstice. In these different positions, P m represents the axis of the earth always parallel to itself, as has been said. Now, from the globular form of the earth, the sun can only shine on one half at a time. Let, therefore, the shaded portions represent the dark, and the light portions the illuminated halves. Further, in all the different positions, let E G represent the ecliptic, P e the arctic circle, and d m the antarctic. Now, when the earth is in the position marked Aries, both poles, P m, fall just with the illuminated half. It is, therefore, day over half the northern and half the south- em hemispheres at once. And as the earth turns round on her axis, the day and night must each be of equal length — that is to say, twelve hours long — all over the globe. Of course, precisely the same holds for the posi- tion at Libra. The former corresponds to September, the latter to March. But when the earth reaches Capricorn in June, one of her poles, P, will be in the illuminated half, the other, m, in the dark ; and for a space reaching from P to e, and m to d, a certain portion of her surface will also be illumin- ated, or also in shadow. The illuminated space, P e, as the earth makes her daily rotation, will be exposed to the sun all the time ; the dark space, m d, will be all the time in shadow. At this period of the year the sun never sets at the north polar circle, and never rises at the south. And the converse of all this happens when the earth moves round to Cancer, in December. Why does the earth's axis always point in the same direction T Ex- plain the phenomena of the seasons. 32S THE SOLAR SYSTEM. The temperature of any place depends on the amount of heat it receives from the sun. During the day the earth is continually warming; during the night cooling. When the sun is more than twelve hours above the horizon, and less than twelve below, the temperature rises, and con- versely. When the earth moves from Libra to Capri- corn, in the northern hemisphere, the days grow longer and the nights shorter, and the rise of temperature we call the approach of spring. As she passes from Capricorn to Aries, summer comes on. From Aries to Cancer, the night becomes longer than the day, and it is autumn — the reverse taking place from Cancer to Libra. It is also to be remarked, that similar but reverse phenomena are oc- curring for the southern hemisphere. This, therefore, ac- counts for the seasons, and accounts for all their attendant phenomena, that the sun never sets- in the polar circles during summer, nor rises during winter. LECTURE LXV. The Solar System. — The Planetary Bodies. — Inferior and Superior Planets. — Mercury. — Venus, her motions and phases^ — Transits of Venus over the Sun. — Their importance. — Mars, his physical appearance. Having established the general relations of the earth and sun, and shown how the former revolves round the latter in an elliptic orbit, we proceed, in the next place, to a description of the solar system. It has already been stated that among the stars there are some which plainly possess proper motions, some- times being found in one part of the heavens and some- times in another. To these, from their wandering mo- tion, the name of planets has been given. Like the earth, they revolve in elliptic orbits round the sun. Their names, commencing wdth the nearest to the sun, are — Mercury, Juno, Jupiter, Venus, Ceres, Saturn, Earth, Pallas, Uranus, Mars, Astrea, Neptune. Vesta, On what does the temperature of any place depend ? How is this con QBcted with the seasons ? What are the planets ? Mention their namei MERCURY. 329 There are, tlieiefore, two whose orbits are included in that of the earth, the others are on the outside of it. Mercury always appears in the close neighborhood of the sun, and hence is ordinarily difficult to be seen. In the evening, after sunset, he may, at the proper time, be discovered, but, soon retracing his path, is lost among the solar rays. After a time he reappears in the morning and proceeding farther and farther from the sun, with a velocity continually decreasing, he finally becomes station- ary, and then returns, to reappear again in the evening. The distance of this planet from the sun is more than. 37,000,000 of miles, his diameter 3200, he turns on his axis in 24h. 5' 3", and moves in his orbit with a velocity of" 111,000 miles in an hour. , Venus, which is the next of the planets, and, like Mer- cury, is inferior — that is, has her orbit interior to that of :he earth — ^from her magnitude and position, enables ua to trace the phenomena of such a planet in a clear and Fif.34S. Under what circumstances may M jrcury be seen 7 What is his dit tance from the sun, his diameter, and the time of his rotation ? 330 VENUS. perfect manner. She, too, is seen alternatoly as an even- ing and morning star, being first discovered, as at A, Fig. 346, emerging from the rays of the sun, and movino- with considerable rapidity from A toward B. Let K £e the position of the observer on the earth, vyhich, for the pres- ent, we will suppose to be stationary. To such an ob- server the motion of Venus, as she recedes from the sun, appears to become slower and slower, then to cease. And now the planet, passing from C to E, appears'to have a retrograde motion, the velocity of which contin- ually increases, then again lessens as she moves toward G-, then ceases ; and, lastly, the planet moves toward A with a continually accelerated motion. All this is evidently the effect which must ensue with a body pursuing an interior orbit. The stationary appear ance arises from the circumstance that at one point, C, she is coming toward the earth, at the opposite, G, re- treating from it ; while at A and at E she is crossing the field of view. But the planets shine only by the light of the sun. Ve- nus, moving thus in an interior orbit, ought, therefore, to exhibit phases. Thus, in Fig. 347, when she first emerges from the rays of the sun on the opposite side, as respects the earth, a position which is called her superior con- junction, A, she must exhibit to us the whole of her il- luminated disc ; but, as she passes from A to B, a portion of her unilluminated hemisphere is gradually exposed to view. This increases at D ; and at E we see half of the illuminated and half of the dark hemisphere. She looks, therefore, like a little half moon. As she comes into the position F G H we see more and more of her dark side. She becomes a thinner and thinner crescent, and at I is extinguished ; and, passing from this toward L M N 0, and from that to A, we gradually recover sight of more and more of her illuminated disc. These phenomena must necessarily hold for a planet moving in an interior orbit, and were predicted before the invention of the telescope. That instrument estab- lished the accuracy of the prediction. The points E and O are the points of greatest elonga- tion, A is the superior conjunction, and I the inferioT'. Vv^'r - 1 iyon 'r>i •in -'n* , '. 'ri« ' vlii'iii"? Hfiw Hn we arrffnt for her PHASKS OP VENU3. Fig.dn. 331 Common observation shows that this planet differs very much at different times in brilliancy. Two causes affect her in this respect :— ^-Ist, the different amount of illumi- nated surface which we perceive ; 2d, the difference of apparent magnitude of the planet as she changes position in her orbit. On her approach toward the earth from E to H the illuminated portion visible lessens , but then her dimensions increase by reason of her proximity. The What are the points of her greatest elongation and the superior and in 'erior coniunction? What causes affect the brilliancy of this planet 332 TRANSITS OF VENUS. maximum of brilliancy takes place when she is about 40'' from the sun. Moreover, it is obvious that at certain intervals, at the time of the inferior conjunction, both this and the preceding planet must appear to cross the face of the sun. To this phenomenon the name of a transit is given. The planet then appears as a round black spot or disc projected on the sun. In the case of Venus, these transits take place at in- tervals of about eight and one hundred and thirteen years. They furnish the most exact means of determining the sun's parallax. Let A B, Fig. 348, be the earth, V Ve 1^.348. nus, S the sun. Let a transit of the planet be observ- ed by two spectators, A B, at the opposite points of that diameter of the earth, perpendicular to the ecliptic. Then the spectator at A will see Venus projected on the sun's disc at C, and B at D ; but the angle A V B ia equal to the angle C V D ; and since the distance of the earth from the sun is to that of Venus from the same body, as about 2i to 1, C D will occupy on the sun's disc a space 2| times that under which the earth's diameter is Been — that is to say, five times as much as the horizontal parallax. The sun's parallax, as determined from the transit of 1769, is 8"-6 nearly. The period occupied by this planet in performing her revolution round the sun is 224 days, 16 hours, 42 min- utes, 25.5 seconds. The orbit is inclined to the ecliptic 3° 23' 25"- She revolves on her axis in 23h 21' 19' Her diameter is about 7800 miles. She is, therefore, very nearly the size of the earth. When is she most brilliant? What is a transit? At what intervall do these take place in the case of Venus? How are these used t» determine parallax T What is the period of revolution of this planet i What is her diameter? MARS. 333 Mars is the next planet, the earth intervening between him and Venus, his orbit is, therefore, an exterior one, and in common with the others that follow, he is desig- nated as a superior planet. He is of a reddish color, and sometimes appears gibbous, and both when in conjunction and opposition exhibits a full disc. The diameter differs very greatly according to his position, and with it, of course, his brilliancy varies. The distance from the sun is about 146 millions of miles, he revolves on his axis in 24h 31' 32", the inclination of his orbit to the ecliptic is 1° 51' 1". As with the earth his polar diameter is shorter than his equatorial. The physical appearance of Mars is somewhat remark- able. His polar regions, when seen through a telescope, have a brilliancy so much greater than the rest of his disc that there can be little doubt that, as with the earth so with this planet, accumulations of ice or snow take place during the winters of those regions. In 1781 the south polar spot was extremely bright; for a year it had not been exposed to the solar rays. The color of the planet most probably arises from a dense atmosphere which sun'ounds him, of the existence of which there is other proof depending on the appearance of stars as they ap proach him ; they grow dim and are sometimes wholly extinguished as their rays pass through that medium. ng. 349. Fig. 349 represents the telescopic appearance of Mars, according to Herschel ; a is the polar spot. Why is Mars called a superior jilanet 1 Does he exhibit phases ? What Is there remarkable respecting his pbysisal appearance 1 What reason* ate Ihcie fur supposint; he has a dense atmosphere 1 334 THE ASTEEOIDS. LECTURE LXVI. Thk Solar System. — The Five Asteroids.- -Jupiter and his Satellites. — Saturn,, his Rings and Satellites. — TJravMs. — Neptune. — The Comets. — Returns of Halley's Comet. — Comets of Enche and Biela. Outside of the orbit of Mara there occur five telescopic planets closely grouped together — they are Vesta, Juno, Ceres, Pallas, and Astrea. They have all been dis- covered within the present century, the last of them in 1846. From their smallness and distance they are far from being well known. The following table contains the chief facts in relation to them. Period of Revolu- Inclination of Distance in Diameter tion. Orbit to Ecliptic. miles. .in miles. Vesta 3 yrs. 66 d. 4h. 70 8' 225.000.000 ^ Juno 4 yrs.l28d. 13° 4i' 256.000.000 ■ 1320 Ceres i\ yrs. 10= 37' 25" 264.000.000 1320 Pallas 4 yrs. 7 m. 11 d. 34° 37' 30" 267.000.000 1920 Astrea 4 yrs. 2 m. 4 d. 5° 20' 250.000.000 It has been thought that these small planets are merely the fragments of a much larger one which has been burst asunder by some catastrophe. There seems to be some foundation for this opinion. It has been asserted that they are not round, but present angular faces. They are also enveloped in dense atmospheres, and in the case of Juno and Pallas, their orbits are greatly inclined to the ecliptic. These planets are sometimes called asteroids. Jupiter, the largest and perhaps the most interesting of the planets, has his orbit immediately beyondthat of the asteroids. He always presents his full disc to the earth, and performs his revolution round the sun in 11 years 318 days, at a distance of 495 millions of miles. He is nearly 1500 times the size of the earth, being 89,000 miles in diameter. What planets come next in order to Mars '! What is there remarkable respecting the size and orbits of these planets ? Under what name do they also go ? What is the position and size of Jupiter ? JUPITER. 335 Immediately aftei the invention of the telescope, it was discovered by Galileo that Jupiter is attended by four satellites or nsoons, which revolve round him in orbits almost in the plane of his equator. !Each of these satel- lites revolves on its own axis in the same time that it goes round its primai'y, so that, like our own moon, they always turn the same face to the planet. Like our moon, also, they exhibit the phenomena of lunar and solar "eclipses. Advantage has been taken of these Fig.ssa. eclipses to determine terrestrial longitudes, and we have already seen it was from them that the progressive mo- tion of light was first established. Jupiter revolves on his axis in 9h. 56'. This rapid ro- tation, therefore, causes him to assume a flattened form — his polar axis being j\ shorter than his equatorial, and as his axis is nearly perpendicular to the plane of his orbit, his days and nights must be equal, and there can be but little variation in his seasons. His disc is crossed by belts or zones, which are variable in number and parallel to his equator. Saturn, which is the next planet, performs his revolu- tion round the sun in about twenty-nine years and a half, at a distance of 915 millions of miles. The inclination of his orbit to the ecliptic is 2° 30'. He is about 900 times larger than the earth, being 79,000 miles in diameter. How many satellites has he ? What advantage has been taken of their eclipses 1 What is the time of rotation of this planet on his axis ? What is the relation of his equatorial to his polar diameter ? What is the dis- tance and size of Saturn ? 336 SATURN AND UKANUS. He turns on his axis in lOJ hours, and the flattening of his polar diameter is yL. Seen through the telescope, Saturn presents a most ex- traordinary, aspect. His disc is crossed with belts, like those of Jupiter ; a broad thin ring, or rather combina- tion of rings, sun-ounds him, and beyond this seven satel- lites revolve. The ring is plainly divided into two con- centric portions, a b, as seen in Fig. 351, and other sub- Fig. 351. division's have been suspected. The larger ring is nearly 205,000 miles in exterior diameter, and the space between the two 2G80 miles. The rings revolve on thfeir own cen- ter — which does not exactly coincide with the center of Saturn — in about 10 hours and 20 minutes. Theexcen- tricity of the rings is essential to their stability. UtiANUs, discovered in 1781, by Herschel, revolves in an orbit exterior to Saturn, in a period of about 84 years, and at a distance of 1840 millions of miles. The incli- nation of its orbit to the etliptic is 46^'. It can only be seen by the telescope. Its diameter is 35,000 miles. Six satellites have been discovered. By what extraordinary appendage is he attended ? How many satellitei has he ? What is the distance of Uranus ? By whom was ho discoreiod! NEPTUNE. 337 Neptune. — This planet was discovered in 1846, in con- sequence of mathematical investigations made by Adams and Leverrier, with a view of explaining the perturba- tions of Uranus. It was also seen in 1795 by*Lalande, and regarded by him as a fixed star. Its period is about 166 years — very nearly double that of Uranus. The in- clination of its orbit is 1° 45'. The excentricity is only 0.005. The orbit is, therefore, more nearly a perfect circle than that of any other planet. There is reason to believe that Neptune is surrounded by a ring analogous to the ring of Saturn. The planetary bodies now described, with their attend- ant satellites and the sun, taken collectively, constitute the solar system, a representation of which, as respects the order in which the bodies revolve, is given in Fig. 352. In the center is the sun, and in close proximity to him revolves Mercury, outside of whose orbit comes Ve nus. Then follows the earth, attended by her satellite Whi^ is the posilion of Neptune ? Of what is the solar system com posed ? P 338 ~ COMETS. the moon. Beyond the earth's orbit comes Mars ; then come the asteroids, followed by Jupiter, with his four moons. Still more distant is Saturn, surrounded by his rings and seven satellites ; then Uranus, with six ; and lastly, so far as our present knowledge extends, comes the recently-discovered planet Neptune. Such a representation as that given in Fig. 352, caii merely illustrate the order in which the members of the solar system occur, but can afford no suitable idea of their relative magnitudes and distances. Thus, in that figure, the apparent diameter of the sun is about the tenth of an inch, and were the proportions maintained, the diameter of the orbit of the planet Neptune should be about fifty feet. A similar observation might- be made as respects the planetary masses. But besides these bodies, there are others now to be described, which are members of our solar system.^ They are the comets. They move in very excentric orbits, and are only visible to us when near their perihelion. In ap- pearance they differ very greatly from one another, but Kg. 353. most commonly consist of a small brilliant point, from which there extends what is designated the tail. Some- In what respects are such representations of the solar system as that in /j%. 352 imperfect ? What are comets 7 What is rernarkable as lespeclj their physical constitution ^ RETURN OF COMETS. 339 times they are seen without this remarkable appendage. In other instances it is of the most extraordinary length, and in former ages, when the nature of these bodies waa ill understood, occasioned the utmost terrfir, for cometa were looked upon as omens of pestilence and disaster. The comet of 1811 had a tail nearly 95 millions of miles in length — that of 1744 had several, spreading forth in the form of a fan. The history of the discovery of the nature of comets is very interesting. Dr. Halley, a friend of Sir I. Newton, had his attention first fixed on the probability that several bodies, recorded as distinct, might be the periodic returns of the same identical comet, and closely examining one which was seen in 1682, came to the conclusion that it regularly appeared at intervals of seventy-five or seventy- six years. He therefore predicted that it ought to reapi- pear about the beginning of the year 1759. The comet actually came to its perihelion on March the 13th of that year, and again, after an interval of seventy-six years, in 1835. Besides the comet of Halley, there are two others, the periodic returns of which have been repeatedly observed. These are the comet of Encke and that of Biela. The former is a small body which revolves in an elliptical or- bit, with an inclination of 13^° in about 1200 days. Its nearest approach to the sun is about to the distance of the planet Mercury; its greatest departure somewhat less than the distance of Jupiter. Its motion is in the same direction as that of the planets. The comet of Biela has a period of 2460 days. It moves in an elliptical orbit, the length of which is to the breadth as about three to two. Its nearest approach to the sun is about equal to the distance of the earth; its greatest re- moval somewhat beyond that of Jupiter, It reappears with great regularity, b.ut in the month of January, 1846, it exhibited the wonderful phenomenon of a sudden division, two comets springing out of one. This fact was first seen oy Lieutenant Maury, at the National Observatory at Washington. Nothing is known vnth precision respecting the nature When was the periodic return of comets first detected ? What other two.comets have been frequently re-observed? What remarkable esult haa been noticed respecting Biela's comet ? 340 THE SECONDARY PLANETS. of these bodies. They are apparently only attenuated masses of gas, for it is said that through them stars of the sixth or seventh magnitude have been seen. In the case of some there appears to have been a solid nucleus of small dimensions. LECTURE LXVII. The Secondary Planets or Satellites. — The Moon, her Phases, her Period of Revolution, her Physical ap- pearance — always presents the same face. — Eclipses of the Moon. — Eclipses of the Sun. — Recurrence of Eclipses. — Occultations. The motions of the secondary bodies of the solar sys- tem, the satellites, and more especially the phenomena of our own moon, deserve, from their importance, a more detailed investigation. To these, therefore, I proceed in this lecture. That the moon has a proper motion in the heavens the observations of a single night completely proves. She is translated from west to east, so that she comes to the meridian about forty-five minutes later each day, and performs her revolution round the earth in about thirty days, exhibiting to us each night 'appearances that are continually changing, and known under the name of First when seen in the west, in the evening, she is a crescent, the convexity of which is turned to the sun. From night to night the illuminated portion increases, and about the seventh day she is half-moon. At this time she is said to be in her quadrature or dichotomy. The enlightened portion still increasing, she becomes gibbous, and about the fifteenth day is full. She now rises at sun- set. From this period she continually declines, becomes gib- bous, and at the end of a week half-moon. Still further she is crescentic ; and at last, after twenty-nine or thirty days, disappears in the rays of the sun. What is supposed to bo the physic*! constitution of these bodies ? What is the direction of the moon's motion ? In what time is a complete revo- lution completed 1 What are her phases ? Describe their order. PHASES OP THE MOON. 341 At new-moon, she is said to be in conjunction with the sun, at full-moon in opposition ; and these positions are called syzygies; the intermediate points between the syzygies and quadratures are octants. Fig. 354. >S The cause of the moon's phases admits of a ready ex- planation on the principle that she is a dark body, re- flecting the light of the sun, and moving in an orbit round the earth. Thus, let S, Fig. 354, be the sun, E the earth,, and a b c, &c., the moon seen in different positions of her orbit. From her globular figure, the rays of the sun can only illuminate one half of her at a time, and necessarily that half which looks toward him. Commencing, there- fore, at the position a, where both these bodies are on the same side of the earth, or in conjunction, the dark side of the moon js turned toward us, and she is invisi- ble ; but as she passes to the position b, which is the oc- tant, the illuminated portion comes into view. And when she has reached the position c, her quadrature, we see half the shining and half the dark hemisphere. Here, therefore, she is half-moon. From this point she now becomes gibbous ; and at e, being in opposition, exposes her illuminated hemisphere to us, and is, therefore, full- mcon. From this point, as she returns throughyj" A, she runs through the reverse changes, being in succes- sion gibbous, half-moon, crescentic, and finally disappear* '"g- What are the syzygies, and quadratures, and octants ? What i* *he ex planatioQ of the phases? 342 THE MOON. Viewed through a telescope, the surface of the moon is very irregular,^ there being high mountains and deep pits upon it. These, in the various positions she assumes as respects the sun,' cast their shadows, which are the dark marks we can discover by the eye, on her disc, and which are popularly supposed to be water. Fig. 355. The moon's diameter, measured at different times, va- ries considerably. This, therefore, proves that she is not always at the same distance from the earth ; and, in fact, she moves in an ellipsis, the earth being in one of the foci. Her distance is about 230,000 miles. She accom- panies the earth round the sun, and turns on her axis in piecisely the same length of time which it takes her to perform her monthly revolution. Consequently, she al- ways presents to us the same face. Her orbit is inclined to that of the ecliptic, at an angle of little more than five What is the appearance of the moon seen through a telescope ? Is her apparent diameter always the same ? What is her distance ? What is her period of rotation on her axis ? Does she always present exactly the same face to the earth ? ECLIPSE OF THE MOON. 343 degrees. Its ]»ointB of intersection with the ecliptic are the nodes. Her gi'eatest apparent diameter is 33| min- utes. The nodes move slowly round the ecliptic, in a di- rection contrary to that of the sun, completing an entira revolution in about eighteen years and a half. Although for the most part, she presents the same face to the earthi as has been said, yet this, in a small degree, is departed from in consequence of her libration. This takes place both in longitude and latitude, and brings small portions of her surface, otherwise unseen, into view. The relations of the sun, the earth, and the moon to one another afford an explanation of the interesting phe- nomenon of eclipses. These are of two kinds — eclipses of the moon and those of the sun. The earth and moon being dark bodies, which only shine by reflecting the light of the sun, project shadows into space. Let, therefore, A B, Fig. 356, be the sun, C D the earth, and M th6 moon, in such a position, as respects each other, that the moon, on arriving in oppo- sition, passes through the shadow of the earth. The light is, therefore, cut off, and a lunar eclipse takes place. Fig. 356. M The shadow cast by the earth is of a conical form, a figure necessarily arising from the great size of the sun when compared with that of the earth. The semi-diame- ter of the shadow at the points where the moon may cross it varies from about 37' to 46' — that is, it may be as much as three times the semidiameter of the moon. A lunar eclipse may, therefore, last about two hours. Thp time of the occurrence of an eclipse of the moon is the same at all places at which it is visible. It is, of oourse visible at all places where the moon is then to be How many kinds of eclipses are there ? Under what circumstance does s lunar eclipse take place ? How long may a lunar eclipse last 7 How is Its magnitude estimated ? 344 ECLIPSE OF THE SUN. seen. The magnitude of the eclipse is estimated in digits, the diameter of the moon being supposed to be divided into twelve digits. Whatever may be the circumstances under which a lunar eclipse takes place, the shadow of the earth is al- ways circular. Advantage has already been taken of thii fact in giving proof of the spherical figure of the earth. If the plane of the moon's orbit were not inclined to the ecliptic there would be a lunar eclipse every full moon. It is necessary, therefore, for this to occur, that the moon should be either in or near to the node, so that the sun, the earth, and the moon may be in the same line. It was explained in Lecture XXXV., that a body situated under the same circumstances as those under which the earth is now considered forms a penumbra as well as a true shadow. There is, therefore a gradual obscuration of light as the moon approaches the conical shadow, aris- ing from its gradual passage through the penumbra. An eclipse of the sun takes place under the following circumstances. Let A B, Fig. 357, be the sun, M the moon, and C D the earth. Whenever the moon passes Fig.ZSI. D B directly between the earth and the sun, she hides his disc from us, and a solar eclipse takes place. It is partial when only a portion of the sun is obscured, annular when a ring of light surrounds the moon at the middle of the eclipse, and total when the whole sun is covered. As the moon is so much smaller than the earth, the conical shadow which she casts can only cover a portion of the earth at a time. Solar eclipses occur at different times to different observers, and in this i-espect, therefore, eclipses of the moon are more frequently observed than What is to be observed respecting the figure of the earth's shadow ? Why is there not a lunar eclipse every month ? Under what circum- stance does an eclipse of the sun take place? Why is there a difference between solar and lunar eclipses as respects the time at which they art seen, and also as respects their relative frequency? ECLIPSES. 345 those of the sun. Like lunar eclipses, solar ones can only occur in or near one of the nodes. Solar eclipses can only occur at new moon, and lunar at lull moon. ^ Like the earth, the moon casts a penumbra ; it is a cone, the axis of which is a line joining the centers of the moon and sun, and the vertex of which is a point where tho tangents to the opposite sides of the bodies intersect. Eclipses recur again after a period of about 18J- years. In each year there cannot be less than two nor more than seven eclipses ; in the former case they are both solar, in the latter there must be five of the sun and two of the moon. There must, therefore, be at least two eclipses of the sun each year, and cannot be more than three of the moon. The satellites which move round Jupiter, Saturn, and Uranus, exhibit the same phenomena of phases and eclipses to the inhabitants of those bodies as are exhibited to us by our moon. Advantage has been taken of the eclipses of Jupiter's satellites for the purpose of deter- mining longitudes upon the earth, and from them the progressive motion of light was first established. An occultation is the intervention of the moon between the observer and a fixed star. Occultations may be used for the determination of longitudes. After what period do eclipses recur? How may they occur as to num- ber each year? What use is made of the eclipses of Jupiter's satellites ! What is an occultation ? 346 THE FIXED STARS. LECTURE LXVIII. The Fixed Stars. — Apparent Magnitudes. — Constella- tions. — The Zodiac. — Nomenclature of the Sfa7-s.— Double Stars. — Parallax. — Distance of the Stars. — Groups of Stars. — Nehulce. — Constitution of the Uni- verse. — Nebular Hypothesis. With the exception of the sun and moon, the heavenly bodies hitherto described form but an insignificant por- tion of the display which the skies present to us. For, besides them there are numberless other bodies of va- rious sizes which, for very great periods of time, maintain stationary positions, and for this reason are designated as fixed stars. The" fixed stars are classed according to their apparent dimensions ; those of the first magnitude are the largest, and the others follow in succession ; the number increases very greatly as the magnitudes are less. Of stars of the first magnitude there are about eighteen, of those of tho second sixty, and the telescope brings into view tens of thousands otherwise wholly invisible to the human eye. From very early times, with a view of the more ready designation of the stars, they have been divided into con- stellations ; that is, grouped together under some imag- inary form. The number of these for both hemispheres exceeds one hundred. They are commonly depicted upon celestial globes. The ecliptic passes through twelve of the constella- tions, occupying a zone of sixteen degrees in breadth, through the middle of which the line passes. This zone is called the zodiac, and its constellations with their signs are as follows : Aries T Libra ^ Taurus B Scorpio HI Gemini n Sagittarius t Gancer 25 Capricornus V? Leo SI Aquarius = Virgo n Pisces K What are the fixed stars ? How are they divided ? How many of the first and second magnitudes are there V What are constellations ? What is the zodiac ? Mention thp^ccinvtpllaMonF of it. DOUBLE STARS. 347 The order in which they are here set down is the >rder which they occupy in the heavens, commencing with the west and going east. Motions of the sun and planets in that direction are, therefore, said to be direct, and in the opposite retrograde. To many of the larger stars proper names have been given. These, in many instances, are oriental, such as Aldebaran, but they are chiefly designated by the aid of the Greek letters, the largest star in any constellation being called a, the second /3, &c., to these letters the name of the constellation is annexed. The position of any star is determined by its declina- tion and right ascension, and though these positions are commonly regarded as fixed, yet the great perfection to which modern astronomy has arrived has shown that the stars are affected by a variety of small motions, although, in some instances, these may arise in extrinsic causes, such, for example, as in the case of aberration, yet there can now be no doubt that the stars have proper motions of their own. This is most satisfactorily seen in the case of double stars, of which there are several thousands. These are bodies commonly arranged in pairs close to- gether, the physical connection between them is established by the circumstance that they revolve round one another j thus, y, Virginia, has a period of 629 years, and e, Bootis, one of 1600 years. From the planets the stars differ in a most striking particular : they shine by their own light. It this rfespect they resemble our sun, who must himself, at a suitable distance, exhibit all the aspect of a fixed star. We there- fore infer that the stars are suns like our own, each, probably like ours, surrounded by its attendant but in- visible planets ; and, therefore, though the number of the stars as seen by telescopes may be countless, the number of heavenly bodies actually existing, but not apparent because they do not shine by their own light, must be vastly greater. In our solar system there are between thirty and forty opaque globes to one central sun. It is immaterial from what part of the earth the fixed What are direct and what retrograde motions ? How are stars designa- ted 1. How is their position determined ? How is it known that some of them have proper motions ? What are double stars ' In what respect do stars differ from planets ? 348 DISTANCE OP THE STARS. Btars are seen ; they exhibit no change of position, and have no horizontal parallax : an object 8000 miles in di- ameter, at that distance is wholly invisible from them. But more, when viewed at intervals of six months, when the earth is on opposite sides of her orbit — a distance of 190 millions of miles intervening — the same result holds good. To the nearest of them, therefore, our sun must appear as a'mere mathematical lucid point— that is to say, a star. In Lecture LXV., the method of determining the dis tance of the sun has been given. The same principles apply in the determination of the distance of a fixed star. The horizontal parallax may be found without difficulty for the bodies of our solar system : it is, in reality, the angle under which the earth's semi-diameter is seen from them. But when this method is applied to the fixed stars, it is discovered that they have no such sensible parallax; and, therefore, that the earth is, as has been observed, wholly in- visible from them. This. is illustrated in Fig. 358, in which 'et S be the sun, ABC D.the earth, moving in her orbit, and the lines A a, B 5, C c, D d the axis of the earth, continued to the starry heavens. This axis, we have seen in Lecture XXI., is always parallel to itself; it would therefore trace in the starry heavens a circle, a b c d, oi equal magnitude with the earth's orbit, ABC D — that is, 190 millions of miles in diameter. If H be a star, when the earth is at the point A of her orbit the star will be distant from the pole of the heavens by the distance aH, and when she is at the point C, by the distance c H. It takes the earth six months to pass from A to C, 190 mil- lions of miles. But the most delicate means have hith- erto failed to detect any displacement of a star, such aa H, as respects the pole, when thus examined semi-annu- ally. It follows, thereibre, that the diameter of the earth's orbit is wholly invisible at those distances. Again, let E F I G, Fig. 359, represent the orbit of the CEirth, and K any fixed star, it is obvious that when the earth is at G the star would be seen by G K, and refer- red to the point, i/ when the earth is at F it would be seen by F K, and referred to h, and the angle i K A, which Have the stars any diurnal parallax ? What must be the appearance ol our sun to them 1 £7plajn llie illustrations given in Figs. 358 and 359 le specting parallax. ANNUAL FAEALIiAX. FSg. 358. Fig- 3S9- 349 IB equal to F K Gr, would be the annual parallax, or the angle under which the earth's orbit would be seen from the star. But though this is 190 millions of miles, so im- mense is the distance at which the fixed stars are placed that it is wholly imperceptible. In a few instances, however, an annual parallax has been discovered. Thus, in the star 61 Cygni, amounts to about one third of a secopd. The'distahee of the near- est fixed star is, therefore, enonUously great. The stars are not scattered uniformly over the vault of Have any stars an annual parallax 7 350 THE MILKY WAY. heaven, but appear arranged in collections or groups. Fig.sm. Just as the planets and their satellites make up, with our sun, one little system, so- too do suns grouped together form coloni'e's of stars. The milky wSy, Fig. 360, which is the group to which' we belong, qonsists of myriads of such suns, bound together by mutual attraictive influences. In this S may represent the position- of the solar sys- tem, ^nd the stars will ap- pear more densely scat- tered when viewed along S p, than along S m, S n, S c. But in other por- tions of the heavens are discovered small shining spaces — nehulee, as ' they are call ed— which, i und er powerful telescopes, are resolved into myriads of stars, Fig. 361, so far off that the human eye, when unassisted, is wholly una- ble to individualize them, and catches only the faint gleam of their collected lights.' Of these great numbers are now known. Such, therefore, is the system of the world. A planet, like Jupiter, with his attendant moons, is, as It were, the point of commencement ; a collection of such opaque bodies playing round a central sun is a fur- ther advance — a system of suns, such as form the more What are nehuliE? What is the milky way? 352 THE UNIVERSE. brilliant objects of our staiTy heavens — and thousands of such nebulae which cover the skies in whatever direction we look. These, taken altogether, constitute the Uni- verse — a magnificent monument of the greatness of God, and an enduring memento of the absolute insignificance of man. But though the universe is the type of Immensity and Eternity, we are not to suppose that it is wholly un changeable. From time to time new stars have sudden- ly blazed forth in the sky, and after obtaining v^onderful brilliancy have died away — and also old stars have disap- peared. Recent discoveries have shown that the light of very many is periodic — that it passes through a cycle of change and becomes alternately more and less bright in a fixed period of days. These intervals differ in differ- ent cases, and probably all are affected in the same way. There is abundant geological evidence to show that the light and heat of our sun were once far greater than now — the luxuriant vegetation of the secondary period could only have arisen in a greater brilliancy of that orb. The sun, then, is one of these periodic stars. The alternate appearance and disappearance of some of the new stars may arise from their orbitual motion. Thus, suppose E the earth, and A B C D the orbit of such Fig 362. E 3 a star. If the major axis of this orbit be nearly in the direction of the eye, as the star approaches to A, it will rapidly increase in brilliancy, and perhaps become wholly invisible at the distant point C. Such a star should, there- What is the structure of the Universe ? What changes have been ob- served in the light of some stars ? Is there reason to believe that the suu is a periodic star 7 Explain the probable cause of the phenomena ofnpw stars NEBULAR HYPOTHESIS. 353 fore, be periodical ; and that this is the case there is rea- son to believe as respects one which appeared in the years 945, 1264, 1572, in the constellation of Cassiopeia. Its period seems to be 319 years. Among the nebulae there are some which powerful tel- escopes feil to resolve into stars — a circumstance which has caused some astronomers to suppose that they are in reality diffused masses of matter which have not as yet taken on the definite form of globes, but are in the act of doing so. And, extending these views to all systems, they have supposed that all the planetary and stellar bodies are condensations of nebular matter. To this hypothesis, although if admitted it will account for a great many phenomena not otherwise readily explained, there are many objections : and it is also to be observed that every improvement which has been made in the tel- escope has succeeded in resolving into stars nebulae until then supposed to be unresolvable. The inference, there- fore, is, that were our instruments sufficiently powerful all would display the same constitution. LECTURE LXIX. Causes OF the Phenomena op the Solar System.- Definitions of the Parts of an J^lliptic Orbit. — Laws oj 'Kepler. — Conjoint Effects of a Centripetal and 'Projectile Force. — 'Newton's Theory of the Planetari/^Motions. — His Deductions from Kepler's Laws. — Causes ofPertur- Having, in the preceding Lectures, described the con- stitution of the solar system, and of the Universe gener- ally, we proceed, in the next place, to a determination of the causes which give rise to the planetary movements. We have to call to mind that observation proves that the figure of the orbits of these bodies is an ellipse, the sun What 13 meant by the nebular hypothesis ? What are the objections 'a it 1. Describe the parts of an elliptic, orbit. 354 ELLIPTIC ORBIT. Deing in one of the foci. Thus, in Fig. 363, let F be the M^.ABDEm elliptic orbit, A is the perihelion, B the Fig. 383. aphelion, F D the mean distance, and F C, which is tne distance of the focus from the center, the excentricity ; a line joining the sun and the planet is called the radius "ectoi. There are three anomalies — the true, the mean, and the excentric. They indicate the angular distance of aplanet from its perihelion, as seen from the sun. Let A ^ B be the orbit of a planet, S the sun, A B the transverse diameter of the orbit, p the place of tha planet, C the cen- " ter of the oi'bit, with which center let there be described a circle, A a; B ; through p draw x^ Q,, and suppose that while the real planet moves from A to p, with a velocity which varies with its distance, an imagin- ai-y one moves in the same orbit with an equable motion, »:> that when the real planet is at p, the imaginary one is at P, both performing their entire revolution in the same time. Then A S ji? is the true anomaly, ASP the mean anomaly, A C a; the excentric anomaly. From an attentive study of the phenomena of planetary What is the radius vector ? What are the true, the mean, and the ex rentric anomaly T kbplee's laws. 355 motijns, Kepler deduced their laws. These pass under she designation of the three laws of Kepler. _They are—. 1st. The planets all move in ellipses, of which the sun Mjcupies one of the foci. 2d. The motion is more rapid the nearer the planet is .0 the sun, so that th6 radius vector always sweeps over equal areas in equal times. 3d. The squares of the times of revolution are to each other as the cubes of the major axes of the orbits. It is one of the fundamental propositions of mechanical philosophy that a body must forever pursue its motion in a straight line unless acted upon by disturbing causes, and aiiy deflection ftom a rectilinear course is the evi- dence of the presence of a disturbing force. Thus, when a stone is thrown upward in>the air, it ought, upon these principles, to pursue a straight course, its velocity never changing ;• but universal observation assures us that from the very first moment its velocity continually diminishes, and after a time wholly ceases — -that then motion takes place in the opposite direction, and the stone falls to the surface of the earth. Informer Lectures, we have already traced the circumstances of these motions, and referred them to an attractive force common to all matter, and to which we give, in these cases, the name of universal at- traction, or attraction of gravitation. In speaking of the motions of projectiles, Lecture XX, it has been shown that, under the action of a force of impulse and a continuous force acting together, not only may a moving body be made to ascend and de- scend in a vertical line, but also in curvilinear orbits, such as the parabolic, the concavity of the curve looking toward the earth's center, which js the center of attraction. It should not, therefore, surprise us that the moon, which may be regarded in the light of a projectile, situated at a great distance from the earth, should pursue a cum- linear path, constantly returning upon itself, since such must be the inevitable consequence of a due apportion-' ment of the intensity of the projectile and central forces to one another. It is the force of gravity which, at each instant, makes What are the three laws of Kepler ? How may it be proved that an at tractive force exists in all the planetary masses? What is the result ol the action of a momentary and a continuous force 7 356 Newton's theory. a cannon-ball descend a little way from its rectilineal path. And it is the same force which also brings down the moon from the rectilinear path she would otherwise pursue, and makes her fall a little way to the earth. In Lecture XXI, Fig. 107, we have shown how, under this double influence, a circle, an ellipse, or other conic sec- tion, must be described ; and it was the discovery of these things that has given so great an eminence to Sir Isaac Newton, he having first proved that it is the same force which compels a projectile to return to the earth and re- tains the moon in her orbit. But more than this, extending this conclusion to the solar system generally, he showed that, as the moon is retained in her orbit by the attractive influence of the earth, so is the earth retained in hers by the attractive influence of the sun. 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