THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA GIFT OF Estate of Ernst and Eleanor van Lt5ben Sels (/' / M- NATURAL PHILOSOPHY FOR GENERAL READERS AND YOUNG PERSONS. TRANSLATED AND EDITED FROM GANOT'S COUKS ELEMENTAIRE DE PHYSIQUE (with the Author's sanction} BY E. ATKINSON, PH.D. F.C.S. PROFESSOR OF EXPERIMENTAL SCIENCE IN THE STAFF COLLEGE. SECOND EDITION. D. APPLETON AND CO. NEW YORK. 1876. LOAN STACK GIFT J?76 PREFACE. ^ I ^HE present work has its origin in an attempt to comply with a suggestion which has frequently been made to me, that I should prepare an abridged edition of my translation of Ganot's Elements de Physique, which could be used for purposes of more elementary instruction than that work, and in which the use of mathematical formulae would be dispensed with. But I soon found that to do anything of the kind which would be more than a mere series of extracts would be very difficult, and hence I turned my attention to another book by the same author, which has had a very extensive circulation in France, his Cours elementaire de Phy- sique, and this I have taken as the basis of the present book. It is not a mere translation, but such additions and altera- tions have been made as I thought fitted to render the book 318 vi Preface. useful to the classes for which it was more especially de- signed namely, as a text-book of physics for the middle and upper classes of boys' and of girls' schools, and as a familiar account of physical phenomena and laws for the general reader. In range it may perhaps be nearly taken to represent the amount of knowledge required for the matriculation examination of the London University. Although English scientific literature is not wanting in works in which the main physical phenomena are explained in familiar language, they are for the most part whether from too much conciseness in some parts or from too minute details in others, or again as being too costly not suited for direct teaching purposes. To facilitate reference, the articles of the present work have been numbered, and a copious index has been drawn up in accordance with this arrangement. E. ATKINSON. STAFF COLLEGE: 1872. ADVERTISEMENT TO THE SECOND EDITION. T N a work which only proposes to serve as an introduction to the study of a science, no great additions can be made without exceeding the range within which it is limited. Hence in the present edition I have not thought it desir- able to add more than about twenty pages of new matter, together with twenty-four new woodcuts and a coloured plate. E. A. STAFF COLLEGE: June 1875. PLATES. ELECTRICAL DISCHARGE IN HIGHLY RAREFIED GASES . Frontispiece SPECTRA OF METALS &c page 355 CONTENTS. BOOK I. GENERAL PROPERTIES OF MATTER, AND UNIVERSAL ATTRACTION. CHA1-. PAGE I. PRELIMINARY NOTIONS . . . . . ^._,i II. GENERAL PROPERTIES OF BODIES > - 4 III. MOTION AND FORCE . . . V * .12 IV. MOTION AND FORCE (continued) . . ... 29 V. LAWS OF FALLING BODIES. INCLINED PLANE. THE PENDULUM . . . .' ' -44 VI. MOLECULAR ATTRACTION ... . . 56 VII. PROPERTIES SPECIAL TO SOLIDS . . . .62 x Contents. BOOK II. HYDROSTATICS. CHAP. PAGH I. PRESSURES TRANSMITTED AND EXERTED BY LIQUIDS . . 65 II. EQUILIBRIUM OF LIQUIDS . * . -74 III. PRESSURES SUPPORTED BY BODIES IMMERSED IN LIQUIDS. SPECIFIC GRAVITIES. AREOMETERS . . 83 BOOK III. ON GASES. I. PROPERTIES OF GASES. ATMOSPHERE. BAROMETERS II. MEASUREMENT OF THE ELASTIC FORCE OF GASES III. APPARATUS FOUNDED ON THE PROPERTIES OF AIR IV. PRESSURE ON BODIES IN AIR. BALLOONS BOOK IV. ACOUSTICS. I. PRODUCTION, PROPAGATION, AND REFLECTION OF SOUND 150 II. MUSICAL SOUND. PHYSICAL THEORY OF Music . . 163 III. TRANSVERSE VIBRATIONS OF STRINGS. STRINGED INSTRU- MENTS . . ' "''*,? '' ''"*"* . . 175 IV. SOUND PIPES AND WIND INSTRUMENTS . 179 Contents. xi BOOK V. HEAT. CHAP. PAGE I. .GENERAL EFFECTS OF HEAT. THERMOMETERS , >',, . 189 II. RADIATION OF HEAT . . fo'irtj * ' 2O2 III. REFLECTION OF HEAT. REFLECTING, ABSORBING, AND EMISSIVE POWERS . . r 204 IV. CONDUCTING POWER OF BODIES . . . .213 V. MEASUREMENT OF THE EXPANSION O*F SOLIDS, LIQUIDS, AND GASES . . .'' . . . 217 VI. CHANGES OF STATE OF BODIES BY THE ACTION OF HEAT . . . . . , . 225 VII. FORMATION OF VAPOURS. MEASUREMENT OF THEIR ELASTIC FORCE . . ," . . 231 VIII. LIQUEFACTION OF VAPOURS AND GASES . . 246 IX.' SPECIFIC HEAT. CALORIMETRY . / . . 252 X. STEAM ENGINES . . . . ' . . 256 XI. HYGROMETRY . . . . . . 270 XII. METEOROLOGICAL PHENOMENA WHICH DEPEND UPON HEAT . 274 XIII. SOURCES OF HEAT AND COLD . . . 287 xii Contents. BOOK VI. ON LIGHT. CHAP. PAGi I. TRANSMISSION, VELOCITY, AND INTENSITY OF LIGHT . 294 II. REFLECTION OF LIGHT. MIRRORS . ; . . 302 III. REFRACTION OF LIGHT ; . . ; . i~ . 322 IV. EFFECTS OF REFRACTION THROUGH PRISMS AND THROUGH LENSES . . , . ':, j* ' .^'"^ . 320 V. DECOMPOSITION OF LIGHT BY PRISMS ; -.--<> - 34^ VI. INJURIOUS EFFECTS OF COLOUR IN LENSES. ACHRO- MATISM . . ., : -:v '. . <', f'^-.. . 361 VII. OPTICAL INSTRUMENTS . ".*' / 7 . VIII. OPTICAL RECREATIONS BOOK VII. ON MAGNETISM. I. PROPERTIES OF MAGNETS . . . . .400 II. TERRESTRIAL MAGNETISM. COMPASSES . ..40^ III. METHODS OF MAGNETISATION . ^ ^ ., . 411 Contents, xiii BOOK VIII. FRICTIONAL ELECTRICITY. CHAP. PAGE I. FUNDAMENTAL PRINCIPLES . , . 415 II. ACTIG&T OF ELECTRIFIED BODIES ON BODIES IN THE NATURAL STATE. INDUCED ELECTRICITY. ELEC- TRICAL MACHINES . . . / . 427 III. ELECTRICAL EXPERIMENTS . . .' . 437 IV. CONDENSATION OF ELECTRICITY . . . . 445 V. VARIOUS EFFECTS OF ACCUMULATED ELECTRICITY . 454 VI. ATMOSPHERIC ELECTRICITY. THUNDER AND LIGHTNING 461 VII. ELECTRICITY DUE TO CHEMICAL ACTION. VOLTAIC BATTERY . . . . . . 470 VIII. EFFECTS OF THE BATTERY . . . . 483 IX. ELECTROMAGNETISM ..... 493 X. ELECTRODYNAMICS . . . . . 499 XL ELECTROMAGNETS. TELEGRAPHS AND ELECTROMAG- NETIC MOTORS ...... 504 XII. INDUCTION BY CURRENTS . . . . . 519 XIII. THERMO-ELECTRIC CURRENTS .... 528 INDEX 532 ELEMENTARY COURSE OF PHYSICS. BOOK I. GENERAL PROPERTIES OF MATTER, AND UNIVERSAL ATTRACTION. CHAPTER I. PRELIMINARY NOTIONS. i. Definition of physics. The word physics is derived from the Greek (/.vote, nature ; for the ancients understood by the term physics the study of the whole of nature. They comprised within the domain of this science mechanics, astronomy, chemistry, botany, zoology, medicine, and even astrology and divination, whether by the stars or by the observation of physiognomy. The province of physics is at present much more restricted. Its object may be considered to be the study of those phenomena which do not depend on changes in the composition of bodies ; for these belong to chemistry. Thus, when water by cooling is changed into ice, and by heat this ice is again changed into water, the liquid is exactly the same as before ; not merely are all its properties the same, but its substance is identical with what it originally was. The passage of water to the state of ice, and the return of the latter to the liquid state, are physical phenomena. In like manner, when a brittle object, of porcelain or glass, for instance, falls to the ground and breaks, each piece retains exactly the same chemical composition. The fall of the vessel and its fracture against the ground are then physical phenomena. On the other hand, when wood burns, its substance is profoundly B 2 Properties of Matter and Universal Attraction. [1- modified. It consists of several different forms of matter, and is decomposed ; one part of its elements passes into the atmosphere as smoke, while another is left as a residue consisting of ash and charcoal. In short, the substance we know as wood has disappeared, and is replaced by others which are entirely different. The com- bustion of wood is then a chemical phenomenon. 2. Matter, mass, density. We understand by the term matter whatever can affect one or more of our senses ; that is to say, any- thing whose existence can be recognised by the sight, touch, taste, smell, or hearing. The mass of a body is the quantity of matter contained in this body. Different substances may contain very different quantities of matter in the same volume. It will subsequently be shown, for instance, that, for equal volumes, lead contains nearly eleven times as much matter as water, and gold nineteen times as much. This is expressed by saying that the masses of lead and of gold, are respectively eleven and nineteen times as dense as water. When one body has, for the same volume, twice or thrice the mass of another, it is said to be twice or thrice as dense ; and the density of one sub- stance in reference to another is the number which expresses how much matter the first body contains as compared with the second. 3. Simple and compound substances. It has been ascertained that all the various forms of matter with which we are acquainted may be resolved into about sixty-five different kinds, which are called simple substances or elements, to express that each only contains one kind of matter. Many of these are very rare, and are found in very minute quantities ; others are more widely diffused, and have important uses, but are not abundant ; and the great mass of the universe is made up of about fourteen ; the non-metallic bodies, or metalloids, oxygen, hydrogen, nitrogen, silicon, carbon, sulphur, phosphorus, and chlorine ; and the metals aluminium, potassium, sodium, calcium, magnesium, and iron. Very few of these elements occur in nature in the free state ; by far the greater number of the substances we know are compound ; that is, formed by the union of two, three, or four of these elements. Thus water consists of hydrogen and oxygen ; marble, of carbon, oxygen, and calcium ; muscular tissue, of carbon, hydrogen, oxygen, and nitrogen. The number of substances containing more than four elements is very small. The force in virtue of which different substances unite to form compounds, and which opposes the resolution of compounds into their elements, is called the force of chemical attraction or affinity. -5] Different States of Matter. 3 4. Internal constitution of bodies. Atoms, molecules, mole- cular forces. The properties of bodies prove that they are not formed of continuous and compact matter as they seem to be, but that they are agglomerations of excessively small material particles, which are called atoms. The elementary atoms can unite with each other to form compounds, but cannot be destroyed by any known process. The term molecule is given to the smallest cluster of atoms of any substance which is conceived capable of existing by itself ; every pure substance consists of similar molecules. The same properties which have led physicists to assume the ex- istence of atoms and molecules have also led to the assumption that these small particles do not touch, but are simply juxtaposed, retain- ing between them excessively small intervals, which we shall after- wards become acquainted with under the name of pores (9). But it maybe asked, How is it that bodies do not spontaneously fall into powder ? What gives them solidity and hardness ? What is the invisible force that unites atoms and molecules ? This force is the reciprocal attraction which the molecules of bodies exert upon each other and which is continually drawing them together. The force which holds together particles of the same kind of matter is called molecular attraction ; the force which holds together particles of different kinds of matter is called chemical attraction or affinity. When hydrogen and oxygen unite to form water, they do so by reason of the exercise of the latter force, while the particles of water are held together by molecular attraction. If molecular attraction were the only force acting upon the small particles of which bodies are composed, they would come into com- plete'contact, which is never the case. They are also under the influence of a repulsive force, in virtue of which their particles con- tinually tend to separate themselves ; this is the force of heat. Experiment shows, in fact, that whenever a body is heated, its volume increases because its molecules are driven apart ; while on the contrary its volume diminishes when it is cooled, because the molecules then become closer. The particular form which matter assumes whether solid, liquid, or gaseous- depends on the extent to which it is influenced by these antagonistic forces. 5. Different states of matter. All different substances present characters in virtue of which they may be divided into three distinct classes, solids , liquids, and gases. Solids, such as wood, stones, metals, &c., are substances which B 2 4 Properties of Matter and Universal Attraction. [5- are more or less hard, and retain the form which they possess naturally, or which has been given them by art. It is assumed that in solids molecular attraction preponderates over repulsion. Liquids, such as water, oil, meicury, are bodies which have no hardness, and present but little resistance when a body is immersed in them ; they have no shape of their own, but at once take that of the vessels in which they are contained ; they are virtually incom- pressible. It is assumed that in them molecular attraction is balanced by the repulsive force of heat, and, that while the mole- cules can freely glide over each other, they keep an invariable dis- tance apart if the temperature be not altered. Gases, such as hydrogen, oxygen, carbonic acid, are also called aeriform fluids, from their analogy with our air, which is a mixture of oxygen and nitrogen. They are very light bodies ; excepting a small number, which are coloured, they are invisible ; and hence a vessel filled with air, hydrogen, or any colourless gas, appears quite empty. Like liquids, they have no shape of their own, but, unlike liquids, they are eminently compressible and expansible. In them the repulsive force of heat preponderates over molecular attraction (4) ; whence it follows that they are continually tending to occupy a larger space. This property will be described as the expansibility of gases (i TO). There are many bodies which can exist in these three different forms ; thus water, exposed to great cold, becomes solid in the form of ice; at ordinary temperatures it is liquid, while at higher tem- peratures it becomes a gas. Sulphur, iodine, and several metals present the same phenomena. CHAPTER II. GENERAL PROPERTIES OF BODIES. 6. Extension. By general propertiesvtz understand thosewhich are common to all bodies, whether solids, liquids, or gases ; such for instance are extension, impenetrability, divisibility, porosity, com- pressibility , elasticity, inertia, and gravity. Specific properties are such as we -observe only in certain bodies, or in certain states of those bodies ; solidity, fluidity, tenacity, malle- ability, colour, hardness, etc. are -properties of this class. The first general property of bodies with which we are concerned -8] Divisibility. 5 is their extension or magnitude ; that is, the extent of space they occupy. All bodies, even the smallest atoms, have a certain ex- tension. Extension considered in only one direction, that of length, gives a line ; in two directions, length and breadth, a surface ; and, in the , three directions, length, breadth, and thickness, a volume. With respect to the above general properties, it may be re- marked that impenetrability and extension might be more aptly termed essential attributes of matter, since they suffice to define it ; and that divisibility, porosity, compressibility, and elasticity do not apply to atoms, but only to bodies or aggregates of atoms. 7. Impenetrability. This is the property in virtue of which two portions of matter cannot simultaneously occupy the same por- tion of space. Strictly speaking, this property only applies to the atoms of bodies. In many phenomena bodies appear to penetrate each other. Thus, if a pint of water and a pint of alcohol be mixed, the volume of the mixture is less than two pints. A similar contraction occurs in the formation of certain alloys ; thus brass, which is an alloy of copper and zinc, occupies a less volume than the united volumes of its constituents. This penetration is, however, only apparent, and is due to an alteration in the position of the molecules ; they come nearer each other, and the space occupied by the pores is diminished. A nail driven into wood is not a case of penetration. The mole- cules of the latter are driven apart by the nail, but wherever it has penetrated there is no wood. When water has been poured upon a heap of sand it at once disappears ; the water, however, does not penetrate the substance of the sand itself, but merely fills the in- terstices between the grains. 8. Divisibility- This is the property which all bodies have of being divided into distinct parts. Numerous examples may be cited of the extreme divisibility of matter. The tenth part of a grain of musk will continue for years to fill a room with its odoriferous particles, and at the end of that time will scarcely be diminished in weight. A piece of carmine not larger than a grain of corn, gives a dis- tinct colour to two gallons of water, from which it can be deduced that this small quantity of colouring matter cannot contain less than ten million particles. Blood is composed of red, flattened globules floating in a colour- 6 Properties of Matter and Universal Attraction. [8- less liquid called serum. In man the diameter of one of these globules is less than the 3,5ooth part of an inch, and the drop of blood which might be suspended from the point of a needle would contain about a million of globules. Again, the microscope has disclosed to us the existence of in- sects smaller even than these particles of blood ; the struggle for existence reaches even to these little creatures, for they devour still smaller ones. If blood runs in the veins of these devoured ones, how infinitesimal must be the magnitude of its component -globules ? Has then the divisibility of matter no limit? Although experi- ment fails to determine such limit, many facts in chemistry, such as the invariability in the relative weights of the elements which combine with each other, would lead us to believe that a limit does exist. It is on this account that bodies are conceived to be com- posed of extremely minute and in- divisible parts called atoms (4). 9. Porosity. Pores are the extremely small intervals which exist between the molecules of bodies, and porosity is the property which bodies possess of having pores. Two kinds of pores may be distinguished : physical or inter- molecular pores, where the inter- stices are so small that the mole- cules remain within the sphere of each other's attracting or repelling' forces ; and sensible pores, or actual cavities, across which these mole- cular forces cannot act. The contractions and expan- sions resulting from variations of temperature are due to the exis- tence of physical pores ; whilst in the organic world the sensible pores are the seat of the phenomena of exhalation and absorption. In wood, sponge, pumice stone, and in animal and vegetable -10] Porosity. 7 tissues, the sensible pores are apparent : physical pores never are seen. Yet since the volume of every body may be diminished, we conclude that all possess physical pores. The existence of sensible pores may be shown by the following experiment : A long glass tube, A (fig. i) is provided with a brass cup, ;, at the top, and a brass foot made to screw on to the plate of an air-pump. The bottom of the cup consists of a thick piece of leather. After pouring mercury into the cup so as entirely to cover the leather, the air-pump is worked, and a partial vacuum produced in the tube. By so doing, a shower of mercury is at once produced within the tube, for the atmospheric pressure on the mercury forces that liquid through the pores of the leather. In the same manner water or mercury may be forced through the pores of wood, by replacing the leather in the above experiment by a disc of wood cut perpendicular to the fibres. When a piece of chalk is thrown into water, air-bubbles at once rise to the surface, in consequence of the air in the pores of the chalk being expelled by the water. The chalk will be found to be heavier after immersion than it was before, and from the increase of its weight the volume of its pores may be easily determined. The porosity of gold was demonstrated by the celebrated Floren- tine experiment made in i66r. Some academicians at Florence, wishing to try whether water was compressible, filled a thin globe of gold with that liquid, and, after carefully closing the orifice hermetically, they exposed the globe to pressure with a view of altering its form, well knowing that any alteration in form must be accompanied by a diminution in volume. The consequence was, that the water forced its way through the pores of the gold, and stood on the outside of the globe like dew. This experiment has since been repeated with globes of other metals, and like results obtained. The Florentine academicians had concluded from their experi- ments that liquids were incompressible ; that is, could not be reduced in volume by pressure. This, however, is not the case ; liquids are compressible, though to a very small extent (74). By cooling, a far greater diminution in volume can be produced. From these facts we conclude that the molecules of liquids may be brought nearer each other, and therefore that there are pores between them. The facility, moreover, with which liquids mix is a proof of their porosity. 10. Applications of porosity. The property of porosity is 8 Properties of Matter and Universal A ttr action. [10- frequently utilised, more especially in the process of filtration. This consists in clarifying liquids by freeing them from particles ot matter which they hold in suspension ; as is done, for instance, with river water, which is turbid, owing to the earthy matter it carries along with it. The apparatus used for this purpose are called filters, and are usually constructed of unsized paper, felt, charcoal, etc. The pores of these substances are sufficiently large to allow liquids to pass, but small enough to arrest the particles held in suspension. Figure 2 represents a filtering fountain, one side of which is sup- Fig. 2. Fig. 3- posed to have been removed, so that its construction can be seen. It consists of a box about a yard high divided in the inside into two compartments by a porous slab, A. The water to be filtered is placed in the upper compartment, whence it slowly percolates through the pores of the stone into the lower one, leaving behind it the foreign substances. In one of the sides of the box is a tube a, which terminates in the lower compartment, and allows the air to escape in proportion as water enters. Figure 3 represents a filter known as the strainer of Hippocrates. It is a conical felt bag suspended by three cords, into which is poured the turbid liquor ; it slowly traverses the pores, while all -11] Compressibility. the solid particles to which the turbidity is due, remain behind on the filter. This method is well-adapted for clarifying syrups, jel- lies, and liqueurs. Layers of powdered wood charcoal are also used for filtration. A layer of sand or of broken glass produces the same effect. The limpidity of well-water is due to the filtration through strata of earth. 1 1 . Compressibility. This is the property which bodies possess of being diminished in volume by pressure without undergoing any loss of weight. Being due to the approach of the molecules, it is both a consequence and a proof of porosity. Compressibility is very marked in sponge, caoutchouc, cork, pith, paper, cloth, etc. Their volume is considerably diminished by mere pressure between the fingers. The compres- sibility of metals is proved by the impression which they receive from the die, in the process of coining. There is, in most cases, a. limit beyond which, when the pressure is increased, solids are fractured or reduced to powcjer. The compressibility of liquids is so small as to have remained for a long time un- detected : it may, however, be proved by experiment, as will be seen in the chapter on HYDROSTATICS (74). The most compressible bodies are gases, which by pressure may be made to occupy ten, twenty, or a hundred times less space than under ordinary circum- stances. The great com- pressibility of gases may be Fig. 4. demonstrated by means of a glass tube with very thick sides, closed at one end and provided with a tight-fitting solid piston (fig. 4). The enclosed air cannot escape, and yet when the handle io Properties of Matter and Universal Attraction. [11- of the piston is pressed it can be moved down to one-half to three-quarters the length of the tube ; proving that the volume of the air is reduced necessarily to half or a quarter what it was origi- nally. Most gases, when thus compressed, exhibit a remarkable property, to which we shall afterwards return, that, namely, of liquefying or passing from the gaseous to the liquid state. 12. Elasticity. Elasticity is the property which bodies possess of resuming their original form or volume, when, after having been compressed, bent, twisted, or pulled, the force which altered them has ceased to act. Four kinds of elasticity may be distinguished : the elasticity by pressure, as in the case of gases ; the elasticity by flexure or bending, observed in springs ; the elasticity of torsion or twisting, which is produced in linen or cotton threads when they are untwisted ; and, finally, the elasticity of tension or stretching, which is that of piano or violin strings when they are stretched. Whatever be the kind of elasticity, it is always due to a displace- ment of molecules. If the molecules have been brought nearer by- pressure, the repulsive force of heat tends to separate them ; if, on the contrary, they have been separated, molecular attraction tends to bring them near each other again. If a piece of whalebone be bent, the molecules in the concave part being compressed repel each other ; in the convex part, where they are separated, they tend to approach each other ; both these actions tend, therefore, to straighten it as soon as it is free. Gases and liquids are perfectly elastic; in other words, they regain exactly the same volume when the pressure becomes the same. Solid bodies present different degrees of elasticity, though none present the property in the same perfection as liquids and gases, and in all it varies according to the time during which the body has been exposed to pressure. Caoutchouc, ivory, glass, and marble possess considerable elasticity; lead, clay, and fats scarcely any. There is a limit to the elasticity of solids, beyond which they either break or are incapable of regaining their original form and volume. In sprains, for instance, the elasticity of the tendons has been exceeded, so also when glass breaks. In gases and liquids, on the contrary, no such limit can be reached ; they always regain their original volume. The elasticity of solids may be demonstrated by the following experiment : On a slab of polished black marble thinly smeared -13] Applications of Elasticity. II with oil, an ivory ball is allowed to drop from gradually increasing heights. Each time it will rebound and rise to a height a little less than that from which it fell, after having formed on the layer of oil a circular impression which is larger the greater the height of the fall (fig. 5). From this we conclude that the ball was flattened each time, and that it rebounded in conse- quence of the reaction of its compressed molecules. 13. Applications of elas- ticity. Numerous applications of the property of elasticity may be mentioned. It is owing to their elasticity that corks Fig. 5- are used for closing bottles. Pushed into the neck by the exercise of a certain force, they become compressed, and then their elasticity causing them to press against the sides, they completely close the neck. Children's balls depend upon the elasticity of gas : they are made of caoutchouc, and are inflated by air ; when they strike against the ground, or against a wall, their volume diminishes, and the air which they contain being suddenly compressed, expands, and, acting like a spring, makes the ball rebound. A similar application is met with in air-cushions. They are made of an air-tight niaterial, and being inflated by air, are both compressible and elastic, and thus form a very soft seat. Ah -guns are a further application. The breech in these is made of steel, and is hollow ; air is compressed in it by means of an in- strument called the compression-pump, and being suddenly liberated its expansive force is sufficient to expel the projectile. The use of carriage, and of watch and clock, springs depends upon the elasticity of steel. In like manner the elasticity of wool, hair, feathers, is made use of in mattresses, pillows, and seats. Lastly, it is owing to their elasticity that piano, guitar, or violin strings are capable of being put into a vibratory motion, which, as we shall prove, is the origin of the sounds which stringed instru- ments yield. 1 2 Properties of Matter and Universal A ttr action. [14- CHAPTER III. MOTION AND FORCE. 14. Rest and motion. To understand what we have to say about inertia, weight, universal gravitation, and the motion of liquids and gases, it is first of all necessary to give some very elementary notions about motion and force. A body is said to be at rest, when it remains in the same place ; to be in motion when it passes from one place to another. Both rest and motion are either absolute or relative. Absolute rest would be the entire absence of motion. No such condition, however, is known in the universe ; for the earth and the other planets rotate both about the sun and about their own axes ; and therefore, all the parts composing them share this double motion. Even the sun itself has a motion of rotation which ex- cludes the idea of absolute rest. Relative or apparent rest is the condition of a body which appears fixed in reference to surrounding objects, but which really shares with them a double motion. For instance, a passenger in a railway carriage may be in a slate of relative rest with respect to the train in which he travels, but he is in a state of relative motion with respect to the objects (fields, houses, etc.) past which the train rushes. These houses again enjoy merely a state of relative rest, for the earth itself which bears them is in a state of incessant rela- tive motion with respect to the celestial bodies of our solar system. The absolute motion of this passenger would be that measured in regard to a fixed point in space, which cannot be realised, for we know no such point. In short, absolute motion and rest are un- known to us ; in nature, relative motion and rest are alone presented to our observation. 15. Different kinds of motion. Motion is either rectilinear or curvilinear : rectilinear when the moving body travels along a straight line, as when a body falls to the ground ; curvilinear when it goes along a curved line, as in the case of a horse turning in a mill. Each kind of motion is either uniform or varied. -18] Inertia. i 3 1 6. uniform motion. Motion is said to be uniform when the moving body passes over equal spaces in equal intervals of time ; such, for instance, as the motion of a water-wheel when it makes exactly the same number of turns in a minute. Such, again, is the motion of the hands of a watch. A regiment of soldiers marching in step affords a further example of uniform motion. The velocity of motion is the space traversed in a given time, a second or an hour, for example. A train which moves thirty miles in each successive hour is said to have a velocity of thirty miles an hour. 17. Varied motion. Varied motion is that in which unequal spaces are traversed in equal times. If the spaces traversed in the same time go on increasing, the motion is said to be accelerated ; such is the motion of a train starting from a station ; if the spaces decrease, as is the case when a train comes into a station, the motion is retarded. If the distances, traversed in equal times, always increase by the same amount, the motion is said to be uniformly accelerated ; if, on the other hand, they constantly decrease by the same amount, the motion is uniformly retarded. We shall soon see examples of these kinds of motion in the case of falling bodies. 1 8. Inertia. Inertia is a purely negative property of matter ; it is the incapability of matter to change its own state of motion or of rest. Daily observation shows that a body never spontaneously passes from a state of rest into one of motion. Bodies in falling to the ground seem to set themselves in motion. This is, however, not in consequence of any inherent property ; but, as we shall afterwards see, because they are acted upon by the force of gravity. Not merely do bodies at rest persist in a state of rest, but bodies in motion continue to move. This principle may seem less obvious than the former, because we are accustomed to see many bodies gradually move more slowly, and ultimately stop, as is the case with a billiard-ball, for example. But this is not due to any inhe- rent preference for a state of rest on the part of the billiard-ball, but because its motion is impeded by the friction of the cloth on which it rolls, and by the resistance of the air. The smaller these resist- ances, the more prolonged is its motion ; as is observed, for instance, if a ball be set rolling on a smooth sheet of ice. If all im- p'eding causes were removed, a body once in motion would con- tinue to move for ever. 14 Properties of Matter and Universal Attraction. [19- 19. Effects due to inertia. Innumerable phenomena may be explained by the inertia of matter. For instance, before leaping a ditch we run towards it, in order that the motion of our bodies at the time of leaping may add itself to the muscular effort then made. On descending carelessly from a carriage in motion, the upper part of the body retains its motion, whilst the feet are prevented from doing so by friction against the ground ; the consequence is we fall towards the moving carriage. If a man in running strikes his foot against an obstacle he is apt to fall down in front, because the rest of his body tends to retain the motion it has acquired. When a horse at full gallop suddenly stops, if the rider does not hold fast with his knees, he is thrown over the horse's head in virtue of his inertia. A grindstone only gradually acquires its full speed, but then continues its movement even after the force has ceased to act. The terrible accidents on our railways are chiefly due to inertia. When the motion of the engine is suddenly arrested the carriages strive to continue the motion they had acquired, and in doing so are shattered against each other. The action of projectiles is another case. W 7 hen a bullet traverses a wall, or cuts a tree in two, it is owing to its tendency to/ retain the velocity which the explosion of the powder had imparted to it. In the action of hammers, and of pile driving, we have analogous cases. The actions of beating a coating with a stick to expel dust ; of shaking the snow from our shoes by kicking against the door-post ; of cleaning a dusty book by striking it against another, all depend upon the property of inertia. The hoop, the top, and other toys are further illustrations. 20. Forces, powers, resistances. Bodies being of themselves inert, and having no tendency to change either their state of rest or that of motion, any cause capable of making them pass from a state of rest to one of motion, or conversely from a state of motion to one of rest, is called a force. The attractions and repulsions exerted between the rnolecules are forces ; the muscular action which men and animals bring into play is a force, as is also the elasticity of gases and vapours which we shall subsequently discuss. The forces which tend to produce motion are called powers; these which tend to destroy motion are called resistances. Thus, -22] Friction. 1 5 when a man drags a burden along the ground his muscular force is a power, while the friction of the burden against the ground is a resistance. Forces of the kind called powers are always tending to accelerate motion, and are called accelerating forces. Resistances, on the contrary, always tending to retard it, are called retarding forces. 21. Friction. The surfaces of bodies are never perfectly smooth ; even the smoothest possess roughnesses which cannot be detected by the touch nor by ordinary sight ; and friction consists in the fact that the body must be raised over these obstacles or must break them down. They fit in each other like toothed wheels. Friction is of two kinds : sliding, in which one body slides over another, as when a box is dragged along a floor ; it is least when the two surfaces are always in contact, as in the motion of an axle in its bearing ; and rolling friction, as when a cylindrical body moves over a horizontal surface like an ordinary wheel. Friction is lessened by rubbing on the surfaces in contact fatty materials which are not absorbed by them. Moisture and oil in- crease the friction of wood, for they are absorbed by it, while tallow, soap, and black lead lessen it. Oil and lard lessen the friction of metallic surfaces. Rolling friction is less than sliding friction, hence the use of castors on pianos and other heavy furni- ture. On the other hand, rolling is sometimes changed into sliding friction, in order to increase it, as when a drag is applied to awheel. The friction of carriage-wheels is less, the greater the diameter of the wheel and the less that of the axle. Without friction on the ground neither man nor animals, neither ordinary carriages nor railway ones, could move ; without it no book would remain on a desk, and without it we could hold nothing in the hands. 22. Distinctive characters of forces. Three things are to be distinguished in each force ; the point of application, the direction, and the intensity. T\*& Point of application of a force is the point at which it exerts its action. Having attached a cord to a sledge, as shown in fig. 6, the point of application is the point A, at which the cord is actually attached. The direction of a force is the right line along which it urges" or tends to urge the point of application. In rig. 6 the cord A B re- presents the direction of the force. 1 6 Properties of Matter and Universal A ttraction. [22- The intensity of a force is its energy, its magnitude, or value, in reference to a certain standard. In fig. 6, which represents a horse drawing a cask on a sledge, a certain exertion of force is Fig. 6. required on the part of the horse ; if the sledge were loaded twice or thrice as much, the force required must be twice or thrice as great. 23. Measurement of forces. Dynamometer. The force which a motor (32) developes in pushing or drawing a body, is measured by the number of pounds necessary to produce the same pressure or the same pull ; so that a force is said to be a force of 40 or 50 pounds, when it can be replaced by the action of a weight of 4.0 or 50 pounds. The weight which thus represents the intensity of a force is determined by means of the dynamometer. There are several forms of this instrument, one of the simplest being that represented in fig. 7. It consists of a V-shaped plate of tempered steel, AB. At one end of the arm B is fixed an iron arc, ;/, which passes freely through an aperture at the end of the arm A. To this latter is fixed an arc, ;, fitting in the same manner in the arm B. The arc m is provided at the end with a crook, and n with a ring, and on the latter n there is a graduation obtained in the following manner : The apparatus being fixed to a resisting support, weights of i, 2, 3, 4, or more pounds are successively suspended to the crook. The arm B, supported by the arc , remains fixed, while the arm A, being moved by the weight attached to the arc ;;/, is lowered to an extent dependent on the weight. The load, is gradually increased until it has readied the utmost limit possible without breaking, care -24] Resultant and Component Forces. being taken at each load to mark a line on the arc n at the point at which the arm A stops. Fig- 7 . Fig. In order to apply it to the measurement of forces, to estimate, for instance, the effort necessary to drag a load (fig. 8), the crook of the arc m is fixed to the load, then holding in the hand the ring of the arc n it is pulled until the load is moved. The flexure of the arm A marks on the arc n the value in pounds of the effort of traction. The apparatus described is also used as a balance to determine the weight of bodies, and is known as the steelyard. When forces are once measured or expressed in weight, they may be represented as to their intensity by means of the line which indicates their direction. For this purpose a length is measured off on this line, starting from the point of application, which contains the unit of length as many times as the intensity of the force con- tains pounds. Thus, if in fig. 6 the effort of traction is 1 5 pounds, a length, AB, would be measured from A equal to 1 5 times the unit of length, which may be an inch for distance. Thus the work of the horse in drawing the sledge would be represented both in direction and intensity by the line AB. 24. Resultant and component forces. When a body is acted upon by only a single force, it is clear that, if it is not hindered by any obstacle, it will move in the direction of this force ; but if it is simultaneously acted upon by several forces in different directions, its direction will not, speaking generally, coincide with that of any C 1 8 Properties of Matter and Universal Attraction. [24- one of these forces. If two men, for example, on the banks of a river, tow a boat by means of ropes, as shown in fig. 9, the boat follows Fig. 9. neither the direction AB, nor the direction AC, in which these men are respectively pulling, but takes an intermediate direction, AE ; that is, it moves as if it were acted upon by a single force in the direction AE. As the single force, which we conceive as having the direction AE, produces the same effect as the forces of traction of these two men, is called the resultant of these two forces ; and conversely these, in reference to their resultant, are spoken of as the components. 2$. Value of the resultant of two concurring: forces. Paral- lelogram of forces. When two forces having different directions are applied to the same point A^ .B of a body, as represented in fig. 9, there is a very simple ratio between their intensities and the intensity of their resultant, which is of great importance from the number of its applications. It will first of all be necessary to define the word parallelogram, of which we shall make use. The parallelogram is a geometrical figure, formed of four right lines, each pair of which is parallel (fig. 10), that is, the two lines AB and CD are parallel, and also the lines AD and BC These lines form the sides of the parallelogram, and the po nts A, B, C, D, the angles. The diagonal is the line, like AC, joining two opposite angles A and C. In treatises on mechanics, proofs are given of the following im- Fig. 10. -26] Parallelogram of Forces. 19 portant theorem, which is known as the principle of the parallelo- gram of forces : When two forces applied at the same point A (fig. 1 1) are repre- sented in direction, and in intensity by the sides AB and AD of the Fig. IT. parallelogram ABCD, their resultant is represented both as to its intensity and direction by the diagonal AC of this parallelogram. That is, that the point A being simultaneously acted upon by two forces, whose directions and intensities are respectively represented by AB and AD ; this point moves in the direction AC exactly as if it were acted upon by a single force, the direction and intensity of which are represented by the line AC. Frequent applications are met with of the principle of the paral- lelogram of forces. Thus, in the flight of a bird, when the wings strike against the air, a resistance is offered which is equal to an impulsive force from back to front in the directions AH and AK (fig. 12) ; hence, representing by AB and AD, the intensities and di- rections of these impulsive forces, if the parallelogram be completed, we shall find that the resultant, or the single force which makes the bird advance, is represented in direction and magnitude by the diagonal AC. The same reasoning applies to the swimming both of men and fishes. 26. Another effect of tbe parallelogram of forces. We have seen that, in accordance with the principle of the parallelogram of 2O Properties of Matter and Universal Attraction. [26- forces, two forces applied at the same point of a body may be re- duced to a single one. By the aid of the same principle a single Fig. 12 force applied to a body may be replaced by two other forces pro- ducing together the same effect as the first. This force is then said to be decomposed into two others. It is but seldom indeed that the action of a force is entirely utilised ; it may almost always be decomposed into two others, only one of which produces a useful effect. Thus when the wind blows Fig. 13. against the sails ot a vessel, not quite directly, but a little on one side, as shewn in fig. 13, the effect of the wind in the direction va -28] Equilibrium of Forces. . 21 may be considered to be resolved into two others, one in the direc- tion ca, and the other in a lateral direction ba, of which the first moves the vessel. The second only guides it. 27. Case in which the forces are parallel. Value of the resultant. In the case of the boat drawn by a rope (fig. 9), the forces were concurrent, that is, their directions if produced would meet in one point ; but it may happen that the forces applied to the same body are parallel, and then two cases present themselves ; that is, they either act in the same direction as in the case of two horses drawing a carriage ; or they may act in opposite directions ; when a steamer for instance ascends a river, the current acts in .opposition to the force which urges the steamer. It can be proved that, in the first case, the resultant of the forces is equal to their sum ; and that in the second it is equal to their difference. 28. Equilibrium of forces. When several forces act upon a body at the same time, they do not always put it in motion; it may happen that while some of these forces tend to produce motion in a certain direction, the others tend to produce an equal and contrary motion in the opposite direction. It is clear that in this case, since the forces just neutralise each other, no effect can be produced. Whenever several forces applied to the same body thus mutually destroy each other, we have what is called equilibrium. The simplest case of equilibrium is that of two equal and oppo- site forces applied at the same point of a body. For instance, if two men pull at a cord with the same intensity, one in one direc- tion, and the other in the opposite One, equilibrium will be produced (fig. 14). In like manner if, in a well, two buckets of the same size Fig. 14. each full of water, are suspended at the end of a rope which passes round a pulley, the weight of one holds the other in equilibrium. The bodies which we consider ordinarily to be in a state of rest, are really in a state of equilibrium. For instance, when a body rests on a table, there is equilibrium between the force of gravity which tends to make the body fall, and the resistance which the table offers to the fall. If the weight of the body exceeds this re- 22 Properties of Matter and Universal Attraction. [28- sistance, equilibrium is destroyed, the table is broken, and the body falls. 29. Centrifugal force. We shall conclude these notions about forces by mentioning a force to which curvilinear motion is due, namely centrifugal Jorce. This may be explained as follows. Whenever a body has been put in motion in a particular direction, in virtue of its inertia, it tends always to move in this direction. Hence whenever a line is seen to move in a circle, this can only be due to some obstacle, or some new force which deviates it. b fact, since a curved line may be considered to consist of a series of infinitely small straight lines, the moving body, owing to its inertia, always tends to follow the prolongation of the small straight line which it traverses. It tends then to retain its motion in a straight line, and to fly from the curve which it is compelled to describe. This action is called the centrifugal force, from two Latin words which signify to fly from the centre. The production of centrifugal force in circular motion may be de- monstrated by means of the apparatus represented in fig. 15. On -31] Flattening of the Earth at the Poles. 23 a brass frame AB is stretched a stout brass wire, and on which are slid two ivory balls which can move freely along the wire : the balls being arranged as shown in the figure, the frame is rapidly rotated by means of the turning table. The balls, projected by the centri- fugal force, glide along the wire ; and strike the ends with the greater force, the greater the velocity of rotation. 30. Effects of centrifugal force. The centrifugal force is greater the greater the velocity, and the more marked the curvature of the line along which the movable body passes. Hence railways should be as straight as possible, for as the trains have a great velocity, when they move along a curve the centrifugal force is con- tinually tending to throw them off, and the more so the sharper the curve. It is owing to centrifugal force that the wheels of a carriage moving along a muddy road throw off the mud that adheres to the rim. In a circus, the horses and their riders always incline their bodies towards the centre, and the greater their speed the greater their in- clination. The object of this is to allow their weight to counteract the influence of the centrifugal force, which would throw them off if they stood upright. In sugar refineries centrifugal force is applied in removing syrup from crystallised sugar. The sugar is placed in a cylindrical ves- sel, whose sides are made of wire gauze, and which is put in rapid rotation. The centrifugal force scatters the coloured syrup through the meshes of the sieve, while the solid crystals are left behind colourless and pure. The same principle is applied in drying clothes in large washing establishments. A wet mop made to turn quickly about its own handle as an axis throws the water off on all sides, and quickly dries itself. A hoop trundled along the ground may move for a long time be- fore falling, but if we attempt to keep it upright while in a state of rest, it at once falls. The reason of this is that, while in motion, if it inclines to one side, the inclination causes it to describe a curved line, whence arises a centrifugal force which opposes the fall of the hoop at any rate so long as it retains a sufficient velocity. 31. Flattening: of the earth at the poles. One of the most remarkable effects of centrifugal force is the flattening of the earth at the two poles. To explain this phenomenon we must premise that the earth, which is nearly spherical in form, rotates about an imaginary axis passing through its two poles, and that, in this ro- tation, all points on the surface have not the same velocity, for they 24 Properties of Matter and Universal Attraction. [31 do not describe the same paths. For, at the equator, they describe every twenty-four hours a circumference equal to that of the earth, while points taken at increasing distances from the equator gradu- ally describe smaller and smaller circles to the poles where they have no motion. Hence, owing to the daily rotation about the earth's axis, a centrifugal force is produced which is greatest at the equator, and gradually diminishes up to the poles, where there is none at all. Hence, owing to this inequality in the intensity of the centrifugal force, there must arise an accumulation of matter about the equator, especially if, as geologists assume, the earth was origi- nally in a state of fusion. It has in fact been ascertained by di- rect measurement, that the radius of the earth at the poles is less than that at the equator by about 9 the latter, or 13^ miles. A similar flattening has been ob- served in other planets. To demonstrate this bulging at the equator and flattening at the poles, use is made of the apparatus represented in fig. 1 6. It consists of an iron rod, which may be fixed upon the turning-table, in- stead of the piece A B (fig. 1 5). At the bottom of the rod are fixed four thin elastic metal plates, which are joined at the top to a ring which can slide up and down the rod. The apparatus being then put in rapid rotation, the rings slide down the rod as represented in the figure to an extent depending on the rapidity of the rotation. LEVERS. +> 32. Mechanics. Machines. Mechanics is the science which treats of forces and of motion. Several forces being applied to the same body, it indicates the relation which must exist between them in order to produce equilibrium, or in order to produce a given effect. Any apparatus which serves to transmit the action of a force is a machine ; and any force which moves a machine is a motor. In cutting an apple with a knife, the hand is the motor, and the knife which transmits its action is a machine. A horse drawing a cart is -33] Levers. 25. a motor, and the cart which utilises the force of the horse in con- veying loads is a machine. The watercourse which works a wheel, the wind which turns a mill, and the steam which moves a locomo- tive, are all motors ; and the water-wheel, the wind-mill, and the locomotive are all machines. Machines do not increase the force of a motor: whatever is gained in force by a machine is lost in distance or in time ; but, by modifying its action, they render it capable of performing work which it alone could not do. For instance, by the aid of a lever, a man can raise burdens, which, without such help, would be impos- sible. We shall only describe here the lever, the simplest of all machines, and shall afterwards see its action in the case of balances. 33. levers. A lever is a rigid bar of wood or of metal mov- able about a fixed point or edge called \b.e fulcrum ; and subject to the action of two forces which tend to move it in opposite direc- tions. The force which acts as motor is called the power, and the other the resistance. Levers are divided into three classes, accord- ing to the different positions of the power, and resistance in reference to the fulcrum. A lever of the first kind'vs, one in which the fulcrum is between the power and the resistance. Fig. 17 represents one of this kind, in which the hand is the power, the weight P the resistance, while C is the fulcrum. Fig. 17. A lever of the second kind\a& the resistance between the power and the fulcrum, as in fig. 18. A lever of the third kind is one in which the power is applied between the resistance and the fulcrum as represented in fig. 19. In these different kinds of levers, the distances from the fulcrum 26 Properties of Matter and Universal Attraction. [33- to the power and to the resistance are called the arms of the lever. In fig. 19, for instance, the arm of the power is the distance from C to B, and that from C to A is the arm of the resistance. Fig. Fig. 19- 34. Effect of levers. Condition of equilibrium. It may be shown that the effect produced by a force by means of a lever in- creases with the length of the arm upon which it acts, that is, if the 35] Applications of Levers. 27 arm is twice, thrice, or four times as long, the useful effect is two, three, or four times as great. This is what led Archimedes to say, that, give him a fulcrum, and he would lift the world. Since a force produces a greater effect the longer the arm of the lever, it follows that in order to produce equilibrium between the power and the resistance, acting at the same time on a lever, if the arms are equal, the two forces themselves must be equal, and that if the arms of the lever are unequal, the two forces must b inversely as the arms of the lever \ thus, if the power is one-third that of the resistance, the arm of the power should be three times as long as that of the resistance. In a lever of the third kind the power must be always greater than the resistance, for the distance of the resistance from the ful- crum (AC, fig. 19) is always greater than the distance BC from the power B to the fulcrum.' In a lever of the second kind the power is always smaller than the resistance, for the arm BC is longer than the arm AC (fig. 18). These properties are expressed by saying that, in a lever of the third kind there is a loss of power, and in one of the second kind a gain. In a lever of the first kind there may be either gain, or loss, or they may just balance each other, for the arm BC of the power (fig. 17) may be either greater, or less than, or equal to, the arm AC. 35. Various applications of levers. Numerous applications of the different kinds of levers are met with in articles of every-day use. The ordinary balance (fig. ,34) is a lever of the first kind, as is also a Fl - 20 - pump handle. Scissors are another instance ; each handle is a lever, the fulcrum of which is the pivot C, the power is the hand and the resistance is the material to be cut (fig. 20). As levers of the second class may be enumerated the oars of a boat. The resistance of the water to the motion of the feather of the oar represents the ful- crum, the hand of the oars- man is the power, and the boat, or rather the water it displaces, is the resistance. The knife fixed at one end Fi e- and used in slicing roots, or cutting bread, is a lever of the second 28 Properties of Matter and Universal Attraction. [35- kind. Nutcrackers (fig. 21) afford a third illustration, as also does the common wheelbarrow. When two porters carry on a pole a load placed midway be- tween them, they share it equally, that is, each bears half, for the pole becomes a lever, of which each porter is a fulcrum as regards the other ; but if the load be nearer one than the other, he to whom it is nearer bears proportionally more of its weight. The consideration of this kind of lever explains why a finger, caught near the hinge of a shutting door, is so severely crushed. The third kind of lever is less frequently met with. The pedals used in pianos and in grindstones are instances. In the latter case the pedal consists of a wooden board AC (fig. 22) forming a lever. Fig. 22. The fulcrum is at C on a bolt fixed to the frame ; the power is the foot of the man turning, and the resistance, which is the motion to be transmitted to the wheel, is applied at A by means of a rod joined to a crank in the centre of the mill. In the common fire-tongs each leg is a lever of the third kind. The hand of a man pushing open a gate while standing near the .-37] -Gravitation. 29 hinges moves through much less space than the end of the gate, and must exert, therefore, a proportionally greater force. The most beautiful and numerous instances are met with in the muscular system of men and animals, almost all motions of which are effected by this mechanism. CHAPTER IV. 36. Universal attraction. It is stated that Newton, sitting one day in his garden and seeing an apple fall from a tree, was led by this circumstance to reflect upon the cause why bodies fell to the ground, and ultimately to the discovery of the important laws which govern the motion of the earth and of the stars. They may be thus stated : - i. All bodies in nature exert a mutual attraction upon each other at all distances, in 'virtue of which they are continually tending towards each other. 2. For the same distance the attractions between bodies are pro- portional to their masses. 3. The masses being equal, the attraction varies with the distance, being inversely proportional to the square of the distances asunder. To illustrate this, we may take the case of two spheres which, owing to their symmetry, attract each other just as if their masses were concentrated in their centres. If without other alteration the mass of one sphere were doubled, trebled, etc., the attraction be- tween them would be doubled, trebled, etc. If, however, the mass of one sphere being doubled, that of the other were increased three times, the distance between their centres remaining the same, the attraction would be increased six times. Lastly, if, without altering their masses, the distance between their centres were increased from i to 2, 3, 4, . . . units, the attraction would be diminished the 4th, 9th, 1 6th . . . part of its former intensity. 37. Gravitation. The term gravitation is applied more es- pecially to the attraction exerted between the heavenly bodies. The sun, being that member of our planetary system which has the largest mass, exerts also the greatest attraction, from which it might seem that the earth and the other planets ought to fall into the sun in virtue of this attraction. This would indeed be the case 3O Properties of Matter and Universal Attraction. [37- if they were only acted upon by the force of gravitation ; but owing to their inertia, the original impulse which they once received, con- stantly tends to carry them away from the sun in a straight line. This acquired velocity, combined with gravitation, makes the planets describe curves about the sun which are almost circular, and are called their orbits. 38. Gravity. This is the force in virtue of which bodies fall when they are no longer supported, that is, tend towards the centre of the earth. It is a particular case of universal attraction ; and is due to the reciprocal attraction exerted between the earth and bodies placed on its surface : it acts equally upon all bodies, whether they are at rest or in motion ; whether they are solids, liquids, or gases. Some bodies, such as clouds and smoke, appear not to be influenced by this force, for they rise in the atmo- sphere instead of sinking ; yet this, as will afterwards be seen, is no exception to the action of gravity. Gravity, being a particular case of universal attraction, acts upon bodies proportionally to their mass and inversely as the square of their distance ; that is, a body which contains twice or thrice as much matter as another, is attracted by the earth with a twofold or threefold force ; or, in other words, weighs twice or thrice as much. In like manner if one and the same body could be moved to twice or thrice its present distance from the centre of the earth, it would have one-fourth or one-ninth of its present weight ; we say the centre and not the surface of the earth, for it is demonstrated in treatises on mechanics that the attractive force of the earth which causes bodies to fall must be calculated from its centre. From the magnitude of the earth's radius, which is about 4,000 miles, all bodies on its surface may be considered to be virtually at the same distance from the centre, and we may therefore conclude that their difference in weight is merely due to their difference in mass. 39. The weight of a body increases from the equator to the poles. The force which makes bodies fall is not exactly the same at all points of the earth's surface. Two causes make it increase from the equator to the poles : the daily rotation of the earth about its axis, and the flattening at the poles. For the rotation of the earth gives rise to a centrifugal force acting from the centre to the surface, that is, in the opposite direction to the force of gravity. Hence bodies are continually acted upon by two forces in opposite directions ; the force of gravity which draws them towards the centre, and the centrifugal force which tends to drive them away -40] Weight of a Body. from it. So that it is really the excess of the first force over the second which makes bodies fall. But as the centrifugal force de- creases from the equator to the poles (30), the excess of gravity over this force becomes greater, and thus the weights of bodies increase as they come nearer the poles. The flattening of the earth concurs in producing the same effect ; for, in consequence of it, bodies placed on the surface of the earth are nearer the centre at the poles than they are at the equator, and are therefore more attracted. It must be added, that the increase in weight due to these two causes is very small, and is inappreciable by ordinary balances. 40. Vertical and horizontal lines. At any point of the earth's surface, the direction of gravity, that is, the line which a falling body describes, is called the vertical line. The vertical lines drawn at different points of the earth's surface converge very nearly to the earth's centre. Hence, owing to the great distance from the surface of the earth, to its centre, for points on the surface a and Fig. 23. &/(fig. 23), not far apart, these verticals may be assumed to be parallel ; but they are less parallel the further apart the points, as shown by the verticals a and d. For points situated on the same meridian the angle contained between the vertical lines equals the difference between the latitudes of those points. At each point on the surface of the earth a man standing up- right is in the direction of the vertical. But, as we have just seen, this direction changes from one place to another, and the same is the case with the position of the inhabitants of the various countries on the earth. As the earth is spherical, it follows that at two points, exactly opposite, two men will be in inverted positions in reference 32 Properties of Matter and Universal Attraction. [40- to each other ; from which is derived the term antipodes (opposite as regards the feet), given to the inhabitants of two diametrically opposite places. A plane or a line is said to be horizontal when it is perpendicular to the direction of the vertical. The surface of water in a state of equilibrium is always horizontal. In speaking of the level we shall learn how the horizontally of any surface or line is determined. 41. Plumb-line. The vertical line at any point of the globe is generally determined by the plumb-line (fig. 24), which consists of a cylindrical weight attached to the end of a string. In obedience to the action of gravity this weight draws the string in the direction of this force, and when it is at rest the string is in the vertical direc- tion. To ascertain by aid of the plumb-line whether a given surface, a wall for example, is vertical, a small metal plate is used., the side of which is equal to the diameter ot the weight. In the centre of this plate is a small hole, through which passes the string : holding in one hand the plate, and in the other the string, the edge of the plate is placed against the wall (fig. 24) ; if the weight just touches it the wall is vertical ; if the cylinder does not touch the wall, it shows that the wall is inclined outwards ; it is inclined inwards if the weight touches the wall when the plate is a little removed from it. -44] Determination of the Centre of Gravity. 3 3 42. Weight of a body. The weight of a body is the sum of the partial attractions which the earth exerts upon each of its mole- cules. Hence the weight of a body must increase as its mass does ; that is, if it contains twice or thrice as much matter, its weight must be twice or thrice as great. The weight of a body is not to be confounded with gravity ; this is the cause which produces the fall of bodies ; the weight is only the effect. We shall presently see how weight is determined by means of the balance ; gravita- tion is measured by the aid of the pendulum. 43. Centre of gravity. We have seen that all the partial attrac- tions which the earth exerts upon each of the molecules of a body are equivalent to a single force which is the weight of the body. Now it may be shown in mechanics, that whatever be the shape of any body, there is always a certain point through which this single force, the weight acts, in whatever position the body be placed in respect to the earth ; this point is called the centre of gravity of the body. To find the centre of gravity of a body is a purely geometrical problem ; in many cases, however, it can be at once determined. For instance, the centre of gravity of a right line of uniform density is the point which bisects its length ; in the circle and sphere it coincides with the geometrical centre ; in cylindrical bars it is the middle point of the axis ; in a square or a parallelogram it is at the point of intersection of the two diagonals. These rules, it must be remembered, presuppose that the several bodies are of uniform density. 44. Experimental determination of the centre of gravity. The centre of gravity of a body may also be found by experiment. Fig. 25. When its weight is not too great it is suspended by a string in two different positions ; the centre of gravity of the body is neces- sarily below the point of suspension, and therefore in the prolonga- I) 34 Properties of Matter and Universal Attraction. [44- tion of the vertical cord which sustains it. If then, in two dif- ferent positions, the vertical lines of suspension be prolonged, they cut one another, and the point of intersection is the centre of gravity sought. In the case of thin flat substances, like a piece of cardboard or a sheet of tin plate, the centre of gravity may be found by balancing the body in two different positions on a horizontal edge ; for in- stance sliding them near the edge of a table until they are ready to turn in either direction (fig. 25). The centre of gravity is then on the line ab. Seeking, in a similar manner, a second position of .equilibrium in which the line of contact is cd for instance, the centre of gravity must necessarily be on both these lines ; that is, must be at the point of their intersection^ ; or, more accurately, a little below this point, in the interior of the body, and at an equal distance from its two faces. If the body be thicker, three positions of equilibrium must be found ; the centre of gravity is then at the point of intersection of the three planes passing vertically through the lines of contact when the body is in equilibrium. 45. Equilibrium of heavy bodies. As the centre of gravity is the point where the whole action of gravity is concentrated, it follows that whenever this point rests upon any support, the action of gravity is destroyed, and therefore the body remains in equilibrium. There are, however, several cases, ac- cording as the body has one or more points of support. Where the body has only one point of support equi- librium is only possible when * lg - 26- the centre of gravity either coincides with this point, or is exactly above or below it in the same vertical line ; for then the action of gravity is destroyed by the resistance of the fixed point through which this force passes. -46] Different States of Equilibrium. 35 Fig. 27. The plumb-line (fig. 24) is a case of this kind, the centre ot gravity being below the point of support. Another example Js the case of a stick balanced on the ringer, as seen in fig. 26, in which the letter g indicates the position of equilibrium exactly over the point of support. If the body has two points ot support, it is not necessary for equi- librium that its centre of gravity coin- cide with either of these points, or be exactly above or below : it is sufficient if it be exactly below or above the right line which joins these two points, for the action of gravity may then be decomposed into two forces ap- plied at the points of support, and destroyed by the resistance of these points. A man on stilts (fig. 27) is an example of this case of equi- librium. Lastly if a body rests on the ground by three or more points ot support (fig. 28), equilibrium is produced whenever the centre of gravity is above the base formed by these points of support, that is, whenever the vertical let fall from the centre of gravity to the earth is within the points of support ; for gravity cannot then overturn the body beyond its points of support, and its only effect is to settle it more firmly on the ground. 46. Different states of equi- librium. Although a body supported by a fixed point is in equilibrium whenever its ^ =Ssa centre of gravity is in the vertical Fi s- 28 - line through that point, the fact that the centre of gravity tends incessantly to occupy the lowest possible position leads us to distin- guish between three states of equilibrium stable, unstable, neutral. D 2 36 Properties of Matter and Universal Attraction. [46- A body is said to be in stable equilibrium if it tends to return to its first position after the equilibrium has been slightly disturbed. Every body is in this state when its position is such that the slightest alteration of the same elevates its centre of gravity ; for the centre of gravity will descend again when permitted, and after a few oscillations the body will return to its original position. The pendulum of a clock continually oscillates about its position of stable equilibrium, and an egg on a level table is in this state when its long axis is horizontal. We have another illustration in the toy represented in fig. 29. These little figures, which are hollow and light, are loaded at the base with a small mass of lead, so that the centre of gravity is very Fig. 29. low. Hence when the figure is inclined, the centre of gravity is raised, and gravity tending to make it descend, the figure reverts to its original position after a number of oscillations on the right and left of its final position of eo 1 uilibrium. A body is said to be in imstable equilibrium, when, after the * slightest disturbance, it tends to depart still more from its original position. A body is in this state when its centre of gravity is vertically above the point of support, or higher than it would be in any adjacent position of the body. An egg standing on its end, or a stick balanced upright on the finger, is in this state (fig. 26). As soon as the stick is out of the vertical its centre of gravity de- scends, and gravity acting with increasing force, the stick falls, if care be not taken to bring the point of support below the centre ,-. of gravity, by which equilibrium is restored. Neutral equilibrium. A body is in a state of neutral equilibrium -47] Examples of Stable Equilibrium. 37 when it remains at rest in any position which can be given to it. This can only be the case when an alteration in the position of the body neither raises nor lowers its centre of gravity. A perfect sphere resting on a horizontal plane is in this state. Fig. 30 represents three cones A, B, C, placed respectively in stable, unstable, and neutral equilibrium upon a horizontal plane. The letter - in each shows the position of the centre of gravity. Fig. 30. 47. Examples of stable equilibrium. From what has been said it follows, that the wider the base on which a body rests the greater is its stability ; for then, even with a considerable inclination, its centre of gravity is above its base. The well-known leaning towers of Pisa and Bologna, are so much out of the vertical that they seem ready to fall at any moment ; and yet they have remained for centuries in their present position, be- cause their centres of gravity are above the base. Fig. 31 repre- sents the tower of Bologna, built in the year 1112, and known as the Garisenda. Its height is 165 feet, and it is 7 or 8 feet out of the vertical. The leaning is due to the foundations having given way. The tower on the side is that of Asarelli, the highest in Italy. In the cases we have hitherto considered, the position of the centre of gravity is fixed : this is not the case with men and animals, whose centre of gravity is continually varying with their attitudes, and with the loads they support. When a man, not carrying anything, stands upright, his centre of gravity is about the middle of the lower part of the pelvis, that is, between the two thigh bones. This, however, is not the case with a man carrying a load, for his own weight being added to that of the load, the common centre of gravity is neither that of the man nor of his burden. In this case, in order to retain his stability, the man must so modify his attitude as to keep his centre of gravity above the base 38 Properties of Matter and Universal Attraction. [47- formed by his two feet. Thus a porter with a load on his back is obliged to lean forward (fig. 32), while a man carrying a load in one hand is obliged to lean his body on the opposite side (fig. 33)- Again, it is impossible to stand on one leg if we keep one side Fig. 31. of the foot and head close to a vertical wall, because the latter pre- vents us from throwing the body's centre of gravity vertically above the supporting base. In the art of rope-dancing the difficulty consists in maintaining the centre of gravity exactly above the rope. In order more easily to accomplish this the performer holds in his hands a long pole, which, as soon as he feels himself leaning on one side, he inclines towards the opposite one ; and thus contrives to keep the centre of -48] The Balance. 39 gravity common to himself and to the pole, in a vertical line above the rope, and so preserves his equilibrium. Fig. 32. Fig. 33. 48. The balance. The balance is an instrument for deter- mining the relative weights or masses of bodies. There are many varieties. The ordinary balance (fig. 34) consists of a lever of the first kind, called the beam, with its fulcrum in the middle ; at the extremities of the beam are suspended two scale-pans, D and C ; one intended to receive the object to be weighed, and the other the counterpoise. The fulcrum consists of a steel prism, n, commonly called a knife- edge, which passes through the beam, and rests with its sharp edge, or axis of suspension, upon two supports ; these are formed of agate or polished steel, in order to diminish the friction. A needle or pointer is fixed to the beam, and oscillates with it in front of a graduated arc, a ; when the beam is perfectly horizontal, the needle points to the zero of the graduated arc. Since (34) two equal forces in a lever of the first kind cannot be in equilibrium unless their leverages are equal, the length of the arms ;/A and ?zB ought to remain equal during the process of weighing. To secure this the scales are suspended from hooks, whose curved parts have sharp edges, and rest on similar edges at the ends of the beam. In this manner the scales are supported on mere points, which remain unmoved during the oscillations of the beam. This mode of suspension is represented in the follow- ing figure. 4O Properties of Matter and Universal Attraction. [48- The weight of any body is determined by placing it in one of the pans of the balance D, for instance, and adding weights to the other until equilibrium is established, which is the case when the beam is quite horizontal. Fig. 34- 49. Conditions to be satisfied by a good balance. A good balance should be accurate, that is, it should give exactly the weight of a body : it should also be delicate, that is, the beam should be inclined by a very small difference between the weights in the two scales. Conditions of accuracy, i. The two arms of the beam ought to 50] Method of Double Weighing.' 41 be precisely equal, otherwise, according to the principle of the lever (34), unequal weights will be required to produce equilibrium. To test whether the arms of the beam are equal, weights are placed in the two scales until the beam becomes horizontal ; the contents of the scales being then interchanged, the beam will remain horizontal if its arms are equal, but if not it will descend on the side of the longer arm. ii. The balance ought to be in equilibrium when the scales are empty \ for otherwise, unequal weights must be placed in the scales in order to produce equilibrium. It must be borne in mind, how- ever, that the arms are not necessarily equal, even if the beam re- mains horizontal when the scales are empty ; for this result might also be produced by giving to the longer arm the lighter scale. iii. The beam being horizontal, its centre of gravity ought to be in the same vertical line with the edge of the fulcrum, and a little below the latter. For if the centre of gravity coincided with this line, the action of gravity on the beam would be null, and it would not oscillate. If the centre of gravity were above the edge of the fulcrum, the beam would be in unstable equilibrium ; while, if it is below the fulcrum, the weight of the beam is continually tending to bring it back to the horizontal position as soon as it diverges from it, and the balance oscillates with regularity. Conditions of delicacy. I. The centre of gravity of the beam should be very near the knife edge ; for then, when the beam is inclined, its weight only acting upon a short arm of the lever, offers but little resistance to the excess of weight in one of the pans. 2. The beam should be light ; for then the friction of the knife edge upon the supports is smaller the less the pressure. In order more effectually to diminish friction, the edges from which the beam and scales are suspended are made as sharp as possible, and the supports on which they rest are very hard. 3. Lastly, the longer the beam the more delicate is the balance ; because the difference in the weights in the pans then acts upon a longer arm of the lever. 50. Method of double weighing:. Notwithstanding the inac- curacy of a balance, the true weight of a body may always be determined by jt. To do so, the body to be weighed is placed in one scale, and shot or sand poured into the other until equilibrium is produced ; the body is then replaced by known weights until equilibrium is re-established. The sum of these weights will necessarily be equal to the weight of the body, for, acting under 42 Properties of Matter and Universal Attraction. [50- precisely the same circumstances, both have produced precisely the same effect. 51. Weighing machines. One of the forms of these instru- ments, which are of frequent use in railway stations, coal yards, etc., for weighing heavy loads, is represented in fig. 35. It con- sists of a platform, A, on which the body to be weighed is placed, and to which an upright B is fixed ; the whole rests on a frame, HE, by the following mode of suspension. Fi S- 35- To the upright, E, are adapted two pieces of iron, which support a beam, LR, by the aid of a knife edge, which traverses it at O. The two arms of the beam are unequal in length ; one of them supports a scale, D, in which are placed the weights ; the other arm of the beam has two rods, by which is suspended the movable part, AB. In order to relieve the knife edge which supports the platform, and to avoid a shock when it is unloaded, after a weighing has been made, the arm, OR, is lifted by raising a sup- port, r, which is below the beam, by means of the handle, M. The horizontality of the beam is ascertained by means of two indicators, m and ;z, the first fixed to the frame and the second to the beam. To understand the working of the mechanism reference must -51] Weighing Machines. 43 be made to fig. 36, in which the principal pieces only are repre- sented. A lever, th, which bifurcates underneath the platform, rests at one end on a double knife edge, z', and at the other, on the lower end of the rod, L//, which is fixed to the beam. A second lever, eg, rests at s on the lever z'/z, attached at g to the rod ag, which is also supported by the beam. Lastly, the distance is being the fifth of///, aO is also a fifth of OL. From this division of the two levers, ih and OL into propor- tional parts two important consequences follow. First, that when- the beam oscillates, the points a and g being lowered by a certain amount, the points L and h are lowered five times as much. But 1,1. Fig. 36. for a similar reason, since the lever ih oscillates upon the knife edge /, the knife edge s is lowered one fifth as much as the point, //, and therefore just as much as g. The lever ^therefore descends parallel to itself, and therefore also the platform A. Secondly : it follows moreover, from the proportional division of the levers OL and ///, that the pressure at the points of sus- pension, exercised by the load g on the platform, is independent of the place which it occupies on the latter, so that it just acts as if it were applied along the rod ag. This may be deduced from the properties of the lever by a simple calculation, which cannot how- ever be given here. Lastly, since the weight is applied at a, the longer the arm of the lever OC as compared with Qa, the smaller need be the weight in the scale D, in order to produce equilibrium. In most weighing machines Oa is the tenth of OC. Hence the weights in the scale D represent one-tenth the weight of the body on the platform. 44 Properties of Matter and Universal A ttraction, [52- CHAPTRR V LAWS OF FALLING BODIES. INCLINED PLANE. THE PENDULUM. 52. Laws of falling bodies. When bodies fall in a vacuum- that is, when they experience no resistance their fall is subject to the following laws : I. In a vaciium all bodies fall with equal rapidity. II. The space which a falling body traverses is proportional to the square of the time during which it has fallen ; that is, that if the space traversed in a second is 16 feet, in two seconds it will be 64 feet ; that is, 4 times as much, and in 3 seconds 9 times as much, or 144 feet, and so on. III. The velocity acquired by a fall- ing body is proportional to the duration of its fall ; that is, that if the velocity at the end of a second is 16 feet, at the end of two seconds it is twice 16, or 32 feet, at the end of 3 seconds 48 feet, and so forth. To demonstrate the first law by experiment a glass tube about two yards long (fig. 37) may be taken, having one of its extremities com- pletely closed, and a brass cock fixed to the other. After having introduced bodies of different weights and densi- ties (pieces of lead, paper, feather, &c.) into the tube, the air is withdrawn from it by an air-pump, and the cock closed. If the tube be now suddenly reversed, all the bodies will fall equally Fig. 37- quickly. On introducing a little air and again inverting the tube the lighter bodies become slightly retarded, and this retardation increases with the quantity of air introduced. -53] Inclined Plane. 45 It is, therefore, concluded that terrestrial attraction which is the cause to which the fall of bodies is due, is equally exerted on all substances, and that the difference in the velocity with which bodies fall is occasioned by the resistance of the air which is more per- ceptible the smaller the mass of bodies and the greater the surface they present. The resistance opposed by the air to falling bodies is especially remarkable in the case of liquids. The Staubbach in Switzerland is a good illustration ; an immense mass of water -is seen falling over a high precipice, but before reaching the bottom it is shattered by the air into the finest mist. In a vacuum, however, liquids fall like solids, without separation of their molecules. The water ha/nmer illustrates this ; the instrument consists of a thick glass tube about a foot long, half filled with water, the air having been expelled by ebullition previous to closing one extremity with the blow-pipe. When such a tube is suddenly inverted the water falls in one undivided mass against the other extremity of the tube, and produces a sharp dry sound, resembling that which accompanies the shock of two solid bodies. The two other laws are verified by the aid of the inclined plane, and of Atwood's machine (iig. 40). 53. Inclined plane. Any plane surface more or less oblique in reference to the horizon is an inclined plane. Such is the surface (fig. 38), and such also that of an ordinary desk and of most roads. When a body rests on a horizontal plane, the action of gravity is entirely counteracted by the resistance of this plane. This, however, is not the case when it is placed upon an inclined plane : 46 Properties of Matter and Universal Attraction. [53- the action of gravity is then decomposed into two forces (26), one perpendicular to the inclined plane, that is, acting along its sur- face, and the other parallel to the plane. The only effect of the first force is to press the first on the plane without imparting to it any motion ; while the second makes the body descend along the plane. This latter, however, is only one component of gravity : it is only a fraction, a third, or a quarter, according to the degree of inclination of the plane. Hence a body will roll down an inclined plane, but more slowly than if it fell vertically ; and the velocity is indeed less the smaller the angle which the plane makes with the horizon. A horse drawing a carriage on a road where there is a rise of one in twenty is really lifting one-twentieth of the load, besides overcoming the friction of the carriage. Hence the importance of making roads as level as possible ; it is for this reason that a road up a very steep hill is made to wind or zig-zag all the way, and an intelligent driver in ascending a steep hill on which is a broad road usually winds from side to side. The principle of the inclined plane is made use of in rolling heavy casks into or out of a waggon by means of two combined beams. 54. Demonstration of the second law of falling- bodies by the inclined plane. The above property which the inclined plane possesses, of slackening the fall of bodies, has been used to demon- strate the second law of their fall (52), that the space traversed by a falling body is proportional to the square of the time during which it has been falling. To make this experiment, an inclined plane is taken, along which is traced a scale graduated in inches ; then taking a well-polished ivory ball, a position is found by trial, at which it just takes a second to reach the bottom of the inclined plane A. Let us suppose that this is at the eleventh division. The experiment is then repeated by making the ball traverse four times the distance, that is, placing it at the forty-fourth division, and it will then be found to take two seconds in so doing. In like manner it will be found that in passing through nine times the distance, or through ninety-nine divisions, three seconds are required. Hence it is concluded, that the spaces traversed increase as the squares of the times. 55. Atwood's machine. Mr. Atwood invented a machine by which the velocity of falling bodies is slackened, and the laws of motion may be demonstrated. It consists of a wooden pillar -55] Atwood's Mac/tine. 47 about 2\ yards high (fig. 40). On the front of the pillar is a clockwork motion, H, regulated in the usual way by a seconds' pendulum, P. On the right of the column is a graduated scale which measures the spaces traversed by the falling bodies. Along this scale two sliders move, which can be fixed by a screw in any position ; one of these has a disc, A, and the other a ring, B (fig. 44). At the top of the column is a brass pulley whose axis instead of resting on pivots, turns on four other wheels, r, r, r f , r', called friction wheels, since they serve to diminish fric- tion (fig. 39). Two exactly equal weights, K and K', are attached to the end of a fine silk thread, which passes round the pulley. At the top of the column is a plate, , on which is placed the falling body (fig. 41). This plate is fixed to a horizontal axis which carries a small catch /, supported, Flg< 39> when the plate is horizontal, by a lever, ab, movable in the middle. A spring placed behind the dial tends to keep this lever in the position represented in fig. 41, while an excentric, e, moved by the clockwork, tends to incline towards the right the upper arm of the lever ad. The parts are so arranged, that when the needle is at zero of the graduation, the lever ab is moved by the excentric ; the plate n then lets fall the body which it sustained (fig. 42). These details being premised, we may add that the slackening which it produces in the fall of a body depends on the mechanical principle that when a moving body meets another at rest it imparts to this latter a part of its velocity, which is greater the greater the mass of the second body compared with the first. For instance if a body with the mass i, strikes against another at rest with the mass 19, the total mass being now 20, the common velocity after the impact is only a twentieth of the original velocity of the first. First experiment. To demonstrate the second law, that the spaces traversed are proportional to the squares of the times , a weight K is placed upon the ledge n (fig. 41), and it is loaded with an over- weight, which consists of a brass disc, m (fig. 47,) open at the side, so as to let pass a rod fixed to the weight K. Then below the ledge n the slider A is placed at such a distance that Km requires a second to traverse the space n A, which is easily obtained after a 48 Properties of Matter and Universal Attraction. [55 Fig. 41. Fig. 42- Fig. 43 Fig. 46. Fig. 47- Fig. 40. -55] Atwood's Machine. 49 few trials. If the mass ;;/ fell alone it would traverse in a second about 32 feet ; but from the principle stated above, it can only fall by imparting to the masses K and K' what it carries with it, and hence its fall is the more diminished the smaller the mass ;;z, as compared with the sum of the masses K and K'. The experiment being prepared as indicated in fig. 41 the pendu- lum is made to oscillate ; the clockwork then begins to move, and as soon as the needle arrives at zero the plate n drops (fig. 42), the weights K and m fall too, and the space A is traversed in a second by a uniformly accelerated motion. The experiment is recom- menced, the slider A being placed at four times its original distance, that is, that if the distance A were 8 inches (fig. 41) it is now 32 inches (fig. 43). But here when the plate n drops it is found that the weight Km requires exactly two seconds to traverse the space A;;. Increasing the space traversed to 72 inches the time required for the purpose is found to be three seconds. That is, that when the times are twice or thrice as great, the spaces traversed are four or nine times as great. Second experiment. To prove the law that the velocities are pro- portional to the times, the experiment is arranged as shown in figs. 44, 45, and 46, that is the weights K and m being arranged as in the first experiment on the ledge n, at a distance of 8 inches below this the sliding ring B is placed, and at 16 inches below the disc A. When the ledge n has dropped, the weights K and m still require a second to fall from n to B. But then the over-weight m being arrested by the ring B (fig. 45), the weight K only falls in virtue of its'acquired velocity. The motion which was uniformly accelerated from o to B (IQ) is kept uniform from B to A ; for the weight m was the cause of the acceleration, and this having ceased to act, the acceleration ceases. It is then found that the space 0B, equal to 8 having been traversed in one second, the space BA, equal to 16, is also traversed in a second. That is, 16 represents the velocity of the uniform motion, which, starting from the point B, has succeeded to the uniformly accelerated motion. The experiment is finally recommenced by placing the sliding- ring B at the distance 32 (fig. 46), and sliding-disc below B, also at the distance 32. The space 0B being then four times as great as in fig. 44, the weights K and m require, in accordance with the second law, twice the time. But the mass m being again arrested by the slider B, it is found that the weight K falls alone and uni- formly from B to A in one second. The number 32 from B to A E 50 Properties of Matter and Universal Attraction. [55- represents then the velocity acquired, starting from the point B after two seconds of fall. In the first part of the experiment it was ascertained that the velocity acquired after one second was 16 ; hence, in double the time, the velocity acquired is double. It may be shown, in like manner, that after three times the time, the velocity is trebled, and so on ; thus proving the third law. 56. Pendulum. This is the name given to any heavy mass sus- pended by a thread to a fixed point, or to any metallic rod movable about a horizontal axis. The ball, ;, suspended by the thread cm, which is fixed at the top at c (fig. 48), is a pendulum. So long as the thread is vertical, which is the case when the centre of gravity of the ball is exactly below the point of suspension, f, the pendulum remains at rest, for the action of gravity is de- Fig. 48. Fig. 49. Fig. 50. stroyed by the resistance at this point. This is no longer the case when the pendulum is removed from its vertical position ; when it is placed, for instance, in the direction en (fig. 49). The ball being raised, gravity tends to make it fall ; it returns from n to m, and reaches the latter point with exactly the velocity it would have ac- quired by falling vertically through the height, om. The ball, accordingly, does not stop at m t but, in virtue of its inertia, and of its acquired velocity, it continues to move in the direction mp ; as -57] Pendulum. the ball rises, however, gravity, which had acted from n to m as an accelerating force, n6w exerts a retarding action, for it acts in a di- rection contrary to that of the motion ; the motion, accordingly, becomes slower, and the ball stops at a distance, mp, which would be exactly equal to mn, were it not for the resistance of the air, and also the rigidity of the thread, cm, which, as it is, offers a certain resistance to being bent about the point c, in passing from the position en to cp, and vice versa. This being premised, the moment the ball stops at /, gravity acting so as to make it fall again, brings it from p to m, when, owing to its inherent velocity, it rises in effect as far as n, and so on ; a backward and forward motion is thus produced from n to- wards p, and from p towards n, which may last several hours. This motion is described as an oscillating motion. The path ot the ball from n to p, or from p to n, is known as a semi-oscillation, a complete oscillation being the mo- tion from n to p, and from p to ;/. In France the former is known as a single oscillation, and the back- ward and forward motion as a double oscillation. The extent or amplitude of the oscillation is the distance between the extreme positions, en and cp, and is measured by the arc, pn. 57. Simple and compound pendulum. A distinction is made in physics between the simple and the compound pendulum. A simple pendulum would be that formed by a single material point, suspended by a thread without weight. Such a pendulum has only a theoretical existence ; and it has only been assumed in order to arrive at the laws of oscillations of the pendulum which we shall presently describe. A compound or physical pendulum may be denned to be any body which can oscillate about a pointer an axis. The pendulum 2 Fig. 51. 5 2 Properties of Matter and Universal A t traction. [57 described above (fig. 48) is of this kind. The form may be greatly varied, but the most ordinary one is a glass or steel rod (fig. 52) fixed at the top to a thin flexible steel plate, or to a knife edge like that of the balance (fig. 34). At the bottom of the rod is a heavy lens-shaped mass of metal, usually of brass, and known as the bob. The lenticular is preferred to the spherical form, for it presents less resistan.ce to the air during each oscillation. 58. Xiaws of the pendulum. Galileo. Whatever be the form of the pendulum, ics oscillations always fall under the following laws. The first of these, that one and the same pendulum makes its oscillations in equal times, was discovered by Galileo, the celebrated physicist and astronomer, at the end of the sixteenth century. It is related that he was led to this discovery, while still young, by observing the regular motion of a lamp suspended to the vault of the cathedral at Pisa. This property of the pendulum has received the name of isochronism, from two Greek words which mean equal times, and such oscillations are said to be isochronous. First law; or, law of isochronism. The oscillations of one and tJie same pendulum are isochronous, that is, are effected in equal times. This law is only perfectly exact when the oscillations are of small amplitude, four or five degrees at most j for a greater ampli- tude the oscillation is longer. Second law ; or, law of lengths. With pendulums of different lengths the durations of the oscillations are proportional to the square roots of the lengths of the penduhims, that is to say, that if the lengths of the pendulums are as 1,4, 9, 16, the times of oscilla- tions will be as i, 2, 3, 4; these being the square roots of the former set of numbers. Third law. If the length of the pendulum remains the same, but the substances are different, the duration of the oscillations is independent of the substance of which the pendulums are formed ; that is, that whether of wood, or of ivory, or of metal, they all oscillate in the same length of time. Fourth law. The duration of the oscillations of a given pen- dulum is inversely as the square root of the force of gravity in the -blace in which the observation is made. 59. Verification of the laws of the pendulum. In order to verify the laws of the simple pendulum we are compelled to em- ploy a compound one, the construction of which differs as little as possible from that of the simple one (57). For this purpose a small sphere of a very dense substance, such as lead or platinum, -60] Measurement of tJie Force of Gravity. 53 is suspended from a fixed point by means of a very fine thread. A pendulum thus formed oscillates almost like a simple pendulum, the length of which is equal to the distance of the centre of the sphere from the point of suspension. In order to verify the isochronism of small oscillations, it is merely necessary to count the number of oscillations made in equal times, as the amplitudes of these oscillations diminish from pn to rq (fig. 50) say from three degrees to a fraction of a degree ; this number is found to be constant. That the times of vibration are proportional to the square roots of the lengths is verified by causing pendulums, whose lengths are as the numbers i, 4, 9, .... to oscillate simultaneously. (A B, fig. 51). The corresponding numbers of oscilla- tions in a given time are then found to be proportional to the fractions I, , ^, etc. . . . . , which shows that the times of os- cillation increase as the numbers I, 2, 3, .... etc. By taking several pendulums of exactly equal lengths B,C,D (fig. 51) but with spheres of different substances, lead, copper, ivory ; it is found that, neglecting the resistance of the air, these pendulums oscillate in equal times, thereby showing that the accelerating effect of gravity on all bodies is the same at the same place. 60. Measurement of tbe force of gravity. The relation which the fourth law of the pendulum establishes between the number of oscillations in a given time, and the force of gravity, is used to determine the magnitude of this force at different places on the globe. By counting the number of oscil- lations which one and the same pendulum makes in a given time, a minute, for example, in proceeding from the equator towards the poles, it has been found that this number continually increases, proving, therefore, that the force of gravity increases from the equator towards the poles. By means of the pendulum the velocity has been calculated which a body acquires in falling, in a second of time, in vacuo, that Fig. 52. 54 Properties of Matter and Universal Attraction. [60- is to say, when it experiences no resistance from the air. At London this is 32-19 feet. Since the velocity which a force imparts to a movable body in a given time is greater in proportion as this force is more intense, the force of gravity in different places is measured by the velocity which it imparts to a body falling freely in a vacuum : in London, for instance, its intensity is 32-19 feet, at the equator, 32-09, and at Spitzbergen 32*25 feet. 61. Application of the pendulum to clocks. The regulation of the motion of clocks is effected by means of pendulums, that of watches by balance-springs. Pendulums were first applied to this purpose by Huyghens in 1658, and in the same year Hooke applied a spiral spring to the balance of a watch. The manner of employ- ing the pendulum is shown in fig. 52. The pendulum rod passing between the prongs of a fork, a, communicates its motion to a rod, b, which oscillates on a horizontal axis, o. To this axis is fixed a piece, inn, called an escapement or crutch, terminated by two projections or pallets, which work alternately with the teeth of the escapement wheel, R. This wheel being acted on by the weight tends to move continuously, let us say, in the direction indicated by the arrow- head. Now if the pendulum is at rest, the wheel is held at rest by the pallet, M, and with it the whole of the clockwork and the weight. If, however, the pendulum moves and takes the position shown by the dotted line, m is raised, the wheel escapes from the confinement in which it was held by the pallet, the weight descends, and causes the wheel to turn until its motion is arrested by the other pallet, ;/ ; which in consequence of the motion of the pendulum will be brought into contact with another tooth of the escapement wheel. In this manner the descent of the weight is alternately permitted and arrested or, in a word, regulated by the pendulum. By means of a proper train of wheelwork the motion of the escapement is communicated to the hands of the clock ; and consequently their motion, too, is regulated by the pendulum. Hence, to regulate a clock when it goes too slow or too fast, the length of the pendulum must be altered. If the clock goes too slow, it is because the pendulum oscillates too slowly, and it must therefore be shortened ; if, on the contrary, it goes too fast, it must be lengthened. This shortening or lengthening is usually effected at the top of the pendulum by varying the length of the oscillating portion of the plate to which it is suspended. Clocks are provided 62] Metronome. 55 with a simple arrangement for this purpose, which, however, is not represented in the figure. A pendulum which makes one oscillation in a second is called a seconds pendulum. Its length is not the same in different parts of the earth ; it is somewhat less at the equator than at the poles. In London it amounts in round numbers to 39*14 inches, and in New York to 39-10 inches. Seeing that heat expands bodies, the length of the pendulum will be greater in summer, and less in winter. Hence a clock which has been once regulated for the mean temperature, will lose in summer and will gain in winter. How this effect of temperature is counteracted by a self-acting arrangement, will be seen in the chapter on Heat. Fig. 53- 62. Metronome. This is another application of the isochronism of the oscillations of the pendulum, and is used to mark the time in 56 Properties of Matter and Universal Attraction. [62- practising music. As this time varies in different compositions, it is important to be able to vary the duration of the oscillations, which is effected as follows. The bob of the pendulum, B (fig. 53). is of lead, and it oscillates about an axis, o ; the rod which is pro- longed above this axis is provided with a weight, A, which slides on this rod and can be fixed in any position. This weight obviously acts in opposition to the oscillations of the bob, B, for when this tends to oscillate, for instance, from right to left, the weight tends to move the rod in the opposite direction, and this resistance which it affords to the motion is greater the longer the arm of the lever, A 0, on which it acts. Hence the higher the weight, A, is raised the slower are the oscillations. At the base of the instrument there is a clockwork motion, which works an escapement with such force that, at each oscillation of the pendulum, a tooth strikes strongly against a pallet fixed to the axis, o, thus producing a regular beat which gives the time. In front of the box which contains the mechanism is a scale with numbers, indicating the height at which the weight must be placed to obtain a given number of oscillations in a minute. In the drawing this weight is at the number 92, which indicates that the pendulum makes 92 oscillations in a minute. CHAPTER VI. MOLECULAR ATTRACTION. 63. Cohesion and chemical affinity. After having described, under the name of universal gravitation, the attraction which exists between the stars and planetary bodies ; and under that of gravity, the attraction which the earth exerts upon all bodies in making them fall towards it, we have to investigate the attractions which hold together the ultimate particles or molecules of a body. These are cohesion, affinity, and adhesion. Cohesion is the force which unites two molecules of the same nature ; for example, two molecules of water, or two molecules of iron. Cohesion is strongly exerted in solids, less strongly in liquids, and scarcely at all in gases. Its intensity decreases as the tem- perature increases, because then the repulsive force due to heat increases. Hence it is, that when solid bodies are heated, they first -63] Molecular Attraction. 57 expand, then liquefy, and are ultimately converted into the gaseous state, provided that heat produces in them no chemical change. Cohesion varies not only with the nature of bodies, but also with the arrangement of their molecules ; for example, the difference between tempered and untempered steel is due to a difference in the molecular arrangement produced by tempering. Many of the properties of bodies, such as tenacity, hardness, and ductility, are due to the modifications which this force undergoes. In large masses of liquids, the force of gravity overcomes that of cohesion. Hence liquids acted upon by the former force have no special shape ; they take that of the vessel in which they are con- tained. But in smaller masses cohesion gets the upper hand, and liquids present then the spheroidal form. This is seen in the drops of dew on the leaves of plants ; it is also seen when a liquid is placed on a solid which it does not moisten ; as, for example, mercury upon wood. The experiment may also be made with water, by sprinkling upon the surface of the wood some light powder such as lycopodium or lampblack, and then dropping some water on it. Chemical affinity is the force which is exerted between molecules not of the same kind. Thus, in water,, which is composed of oxygen and hydrogen, it is affinity which unites these elements, but it is cohesion which binds together two molecules of water. In compound bodies cohesion and affinity operate simultaneously, while in simple bodies cohesion has alone to be considered. To affinity are due all the phenomena of combustion ; when carbon burns it is affinity which causes this body to combine with the oxygen of the air to form the gas known as carbonic acid. Affinity determines the combination of the elements, so that with a small number of them are formed the immense number of organic and mineral substances which serve for our daily uses. The causes which tend to weaken cohesion are most favourable to affinity ; for instance, the action of affinity between substances is facilitated by their division, and still more by converting them to u liquid or gaseous state. It is most powenully exerted by a body in its nascent state, that is, the state in which the body exists at the moment it is disengaged from a compound ; the body is then free, and ready to obey the feeblest affinity. An increase of temperature modifies affinity differently under different circumstances. In some cases, by diminishing cohesion, and increasing the distance between the molecules, heat promotes combination. Sulphur and oxygen, 58 Properties of Matter and Universal Attraction. [63- which at the ordinary temperature are without action on each other, combine to form sulphurous acid when the temperature is raised. In other cases heat tends to decompose compounds ; thus many metallic oxides, as for example those of silver and mercury, are decomposed, by the action of heat, into gas and metal. 64. Adhesion. Adhesion is the name given to the attraction manifested by two bodies when their surfaces are placed in con- tact. If two leaden bullets are cut with a penknife so as to form two equal and brightly polished surfaces, and the two faces are turned against each other until they are in the closest contact, they adhere so strongly as to require a force of more than 3 or 4 ounces to separate them. The same experiment may be made with two equal pieces of glass, which are polished and made perfectly plane. When they are pressed one against the other, the adhesion is so powerful that they cannot be separated without breaking. As the experiment succeeds in vacuo, it cannot be due to atmospheric pressure, but must be attributed to a reciprocal action between the two surfaces. The attraction also increases as the contact is pro- longed, and is greater in proportion as the contact is closer. To adhesion is due the resistance experienced in raising a plank placed on water ; and to the same force is ascribed the difficulty met with in walking through thick mud. If we dip a glass rod into water, on withdrawing it a drop will be found to collect at the bottom, and remain suspended there. As the weight of the drop tends to detach it, there must necessarily be some force superior to this weight which maintains it there ; this force is the force of adhesion. On the property of adhesion, depends the operations of gluing and soldering, of cementing, and coating mirrors. The force of adhesion operates also between solids and gases. If a metal plate be immersed in water bubbles will be found, to appear on the surface. As air cannot penetrate into the pores of the plate, the bubbles could not arise from air which had been expelled, but must be due to a layer of air which covered the plate and moistened it like a liquid. CAPILLARITY. ABSORPTION. 65. Capillary phenomena. When solid bodies are placed in contact with liquids, molecular attraction gives rise to a class of phenomena called capillary phenomena, because they are best seen in tubes whose diameters are comparable with the diameter of a hais. These phenomena are treated of in physics under the head -66] Capillarity. A bsorption. 59 of capillarity or capillary attraction : the latter expression is also applied to the force which produces the phenomena. The phenomena of capillarity are very various, but may all be referred to the mutual attraction of the liquid molecules for each other, and to the attraction between these molecules and solid bodies. The following are some of these phenomena : i. When a glass rod is placed in a liquid which wets it, water for instance, the liquid, as if not subject to the laws of gravity, is raised upwards against the sides of the solid, and its surface, instead of being horizontal, becomes slightly concave (fig. 54). Fig- 54- Fig 55- Fig. 56. ii. If instead of a solid rod, a hollow tube be immersed in water (fig- 55)> n t merely is the liquid raised around the tube, but it rises in the inside to a height which is greater, the narrower the tube ; and at the same time the surface of the liquid inside the tube assumes a concave form. iii. If the tube is not moistened by the liquid, as is the case with mercury, the liquid is depressed instead of being raised, and the more so the narrower the tubes (fig. 56) ; and the surface, which was previously concave, now becomes convex. The surface of a liquid exhibits the same concavity or convexity against the sides of a vessel in which it is contained, according as the sides are or are not moistened by the liquid. 66. Xiaws of capillarity. Gay-Lussac has shown experimentally that the elevation and depression of liquids in capillary tubes, the internal diameter of which does not exceed two millimetres, are governed by the following laws : I. When a capillary tube is placed in a liquid, the liquid is raised or depressed according as it does or does not moisten the 60 Properties of Matter and Universal .A t tract ion. [66 - tube, and the elevation -varies inversely as the diameter of the tube, that is, it is two or three times as great when this diameter is two or three times as small. II. The elevation varies -with the nature of the liquid, and ivith the temperature, but is independent of the nature and thickness oj the tube. 67. Effects due to capillarity. It is from capillarity that sap rises in plants, that oil rises in the wicks of lamps, and melted tallow in the wicks of candles. The interstices which exist between the fibres of the cotton of which the wicks are formed, act as capillary tubes in which the ascent takes place. In very porous bodies, the pores being in communication with each other form a series of capillary tubes, which produces the same effect. If a lump of sugar be placed in a cup in which a little coffee is left, the liquid is seen to rise rapidly and fill the entire piece ; and it is even to be remarked that the sugar then dissolves more quickly than if it had been directly immersed in the coffee. This is due to the fact that in the latter case the air which fills the pores not being able to escape so rapidly, as if the piece of sugar is only partially immersed, prevents the liquid from penetrating into the mass of the sugar, and thus retards the solution. Insects can often move on the surface of water without sinking. This is a capillary phenomenon caused by the fact, that as their feet are not wetted by the water, a depression is produced which keeps them up in spite of their weight. Similarly a sewing needle gently placed on water does not sink, because its surface, being covered with an oily layer, does not become wetted. But if previously washed in alcohol, or in potash, it at once sinks to the bottom. 68. Absorption and imbibition. The words absorption and imbibition are used almost promiscuously in physics ; they indicate the penetration of a liquid or a gas into a porous body. Absorp- tion is used both for liquids and gases, while imbibition is restricted to liquids. Charcoal has a great absorbing power for gases. If a piece of recently heated charcoal be passed into a bell jar full of carbonic acid placed over a mercury trough, the volume of gas is seen to diminish rapidly, and it is found that the gas which has disap- peared, in penetrating the charcoal represents a volume thirty-five times that of the solid. There are even gases, such as ammonia, of which charcoal can absorb ninety times its own volume. -69] Effects due to Imbibition. 61 Absorption takes place in all parts of plants, but more especially in the rootlets and by the leaves. These organs absorb, in the form of water, carbonic acid, and ammonia, the oxygen, hydrogen, carbon, and nitrogen necessary for the growth of the plants. Absorption also plays an important part both in the nutrition and respiration of animals. Animal tissues can even absorb solid substances. For instance, in those processes of the arts where the workmen have to handle salts of mercury or of lead, these metals are gradually absorbed into the system and produce serious evils. 69. effects due to imbibition. Imbibition has been defined as being the penetration of a liquid into the pores of a solid body. It is a capillary effect, for the pores being in intercommunication act like small tubes ; thus it is that water rises in wood, sponge, bibulous paper, sugar, sand, and in all bodies which possess pores of a perceptible size. Owing to imbibition, tobacco soon dries if kept in a wooden box, while it remains fresh if kept in a metal one, for then its moisture is not absorbed by the metal as it is by the wood. When water is absorbed by animal or vegetable matters their volume increases. Thus if a tolerably large sheet of dry paper be measured and be then moistened, it will be found to have appreciably increased by this process. This property is made use of in stretching paper on drawing boards ; the paper is moistened and is then glued or fastened with pins round the edge of the board. In drying, the paper contracts, and is tightly stretched. For the same reason, too, wall papers which have been fastened on cloth along the walls, are frequently liable to be torn. In bending wood, the side to be bent is heated, and the other side moistened. This being lengthened owing to the water it absorbs, while the other is contracted in consequence of the dry- ness, a curvature ensues on the heated side. It is often observed that, owing to the changes of volume which they undergo under the influence of moisture and dryness, the furniture of our rooms is frequently heard to crack when the weather changes. By the absorption of moisture ropes become shorter ; and lengthen when they dry. This may seem opposed to what has been stated about moistened paper, but the explanation is not difficult. Ropes are formed of fibres twisted together, and as these fibres swell owing to the water they absorb, the rope becomes larger, and hence each fibre should make in coiling a longer 62 Properties of Matter and Universal Attraction. [69- circuit ; and the rope will become more shortened the more it is moistened. For this reason, too, new cloths shrink considerably when they are moistened for the first time. It is related that Pope Sixtus, wishing to raise in a place in Rome, an obelisk brought from Heliopolis to Rome under Caligula, for fear of disturbing the operation, ordered the spectators to preserve profound silence under pain of death. The obelisk was on the point of being placed on its pedestal, when the ropes began to stretch, owing to the great traction to which they were exposed, and the operation was in great danger. A voice from the crowd that of the architect Zapaglia cried out, ' Wet the ropes/ which was done, and the operation successfully performed. CHAPTER VII. PROPERTIES SPECIAL TO SOLIDS. 70. Tenacity. Besides the general properties which we have hitherto been considering, and which are met with in solids, liquids, and gases, there are some special to solids which deserve mention, on account of the numerous applications which they present. They are tenacity, hardness, ductility, and malleability. Tenacity is the resistance which bodies oppose to being broken, when subjected to a greater or less traction. The tenacity of any particular body is determined by giving to it the form of a cylin- drical or prismatic rod, one end of which is then firmly fixed in a vertical position to a support. To the lower end is fixed a scale- pan, in which weights are successively added until the rod breaks. The breaking weight represents the limit of the tenacity of a rod for a given section. Of all substances iron has the greatest tenacity. A cylindrical iron rod with a section of a square centimetre, only breaks with a weight of 13,200 pounds. A rod of boxwood of the same dimensions, breaks with a weight of 2,640, and one of oak with 1,540 pounds ; a steel wire supports a load of 39,000 times its own length ; laths constructed of fine iron wire, the ^tn to ^th of an inch in diameter, can support a load of 60 tons for each square inch of section. Tenacity is directly proportional to the breaking weight, and inversely proportional to the area of a transverse section of the wire. Tenacity diminishes with the duration of the traction. A small -72] Tenacity. 63 force continuously applied for a long time will often break a wire, which would not at once be broken by a larger weight. Not only does tenacity vary with different substances, but it also varies with the form of the body. Thus, with the same sectional area, a cylinder has greater tenacity than a prism. The quantity of matter being the same, a hollow cylinder has greater tenacity than a solid one. The shape has also the same influence on the resistance to crushing, as it has on the resistance to traction. A hollow cylinder with the same mass, and the same weight, offers a greater resistance than the solid cylinder. It is for this reason that the bones of animals, the feathers of birds, the stems of corn and other plants, offer greater resistance than if they were solid, the mass remaining the same. 71. Hardness. Hardness is the resistance which bodies offer to being scratched or worn by others. It is only a relative property, for a body which is hard in reference to one body, may be soft in reference to others. The relative hardness of two bodies is ascer- tained by trying which of them will scratch the other. Diamond is jjfl the hardest of all bodies, for it scratches all, and is not scratched by any. The hardness of a body is expressed by referring it to a scale * of hardness : that usually adopted is 1. Talc 5. Apatite 8. Topaz 2. Rock salt 6. Felspar 9. Corundum 3. Calcspar 7. Quartz 10. Diamond 4. Flourspar Thus the hardness of a body which would scratch felspar, but would be scratched by quartz, would be expressed by the number 6-5. The pure metals are softer than their alloys. Hence, for jewellery and coinage, gold and silver, which are soft metals, are alloyed with copper to increase their hardness. The hardness of a body has no relation to its resistance to com- pression. Glass and diamond are much harder than wood, but the latter offers far greater resistance to the blow of a hammer. Hard bodies are often used for polishing powders ; for example, emery, pumice, and tripoli. Diamond, being the hardest of all bodies, can only be ground by means of its own powder. 72. Ductility. Ductility is the property in virtue of which a great number of bodies change their forms by the action of traction or pressure. 64 Properties of Matter and Universal A ttraction. [72- Certain bodies, such as clay, wax, etc., are so ductile that they can be drawn out, flattened, modelled, between the fingers ; others, such as the resins and glass, require the aid of heat. Glass is then so ductile that it can be drawn out into fine threads, which are flexible enough to be woven into cloth. Several metals, such as gold, silver, copper, are ductile, even at ordinary temperatures, but require the use of powerful machines, such as the draw-plate or the rolling-mill. 73. Malleability. Malleability is that modification of ductility which is exhibited when metals are hammered. This property greatly increases with the temperature ; everyone knows, for in- stance, that iron is easily forged when hot, and not when cold. Gold is very malleable even at the ordinary temperature. To make the extremely thin plates of gold, known as gold leaf, the gold is first pressed, by means of the rolling mill into long plates from two to three centimetres in breadth, and about a millimetre, the ^th of an inch in thickness. These plates are then beaten into small squares by means of a hammer ; these are then cut and beaten again, and so on. By beating them directly, the operation could not long be continued, for the metal would be torn : hence the plates to be beaten must be placed between plates of a substance which, while thin, affords great resistance. Sheets of vellum and parchment are first used for this purpose, and afterwards gold beater's skin. Leaves of gold are thus obtained, which are so thin, that 20,000 superposed are only an inch thick. Silver and copper may also be worked in the same manner. These leaves are used in the arts for gilding on wood, paper, and other materials. The following is the usual order of the metals under the draw- plate, the rolling mill, and the hammer, arranged in reference to their decreasing ductility. Draw-plate Rolling mill Hammer Platinum Gold Lead Silver Silver Tin Iron Copper Gold Copper Tin Zinc Gold Lead Silver Zinc Zinc Copper Tin Platinum i Platinum Lead Iron Iron The metals must be pure, if they are alloyed with other metals they are fragile, and have but little ductility. -75] Special Characteristics of Liquids. 6$ BOOK II. HYDROSTATICS. CHAPTER I. PRESSURES TRANSMITTED AND EXERTED BY LIQUIDS. 74. Province of Hydrostatics. The science of hydrostatics, from two Greek words, signifying equilibrium of water, treats of the conditions of the equilibrium of liquids, and of the pressure they exert, whether within their own mass, or on the sides of the vessels in which they are contained. 75. Special characteristics of liquids. One essential charac- ter of a liquid is the extreme mobility of its molecules, which are displaced by the slightest force. The fluidity of liquids is due to this property ; it, however, is not perfect, there is always a sufficient adherence between the molecules to produce a greater or less viscosity. Another essential property of liquids, and one by which they are distinguished from gases, is their almost entire incompressibility. We have already seen (5) that their compressibility is so small, that for a long time they were regarded as being quite incompressible. It was not before 1823 that Oersted, a Swedish physicist, first proved in an exact manner that liquids are compressible. The apparatus he used for this purpose is called the piezometer (7rifw, I compress, /itrpor, measure). By its means it has been found that a pressure of one atmosphere compresses distilled water by about the ^~ part of its volume ; mercury by the same pressure only undergoes about a tenth as great a diminution, and ether about 2^ times as much. Liquids are also porous, elastic, and impenetrable, like all other F 66 Hydrostatics. [75- bodies. The proofs of their porosity have been already given, their elasticity is a necessary consequence of their compressibility. Their impenetrability is manifested whenever a solid is immersed in water. For if a vessel be quite filled with water, and any solid body be placed in it which does not absorb the liquid, it will be observed that a volume of water flows over, which is exactly equal to that of the solid immersed. 76. Equality of pressures. Pascal's law. Liquids have the following remarkable property, which is not possessed by solids. It is often called 'Pascal's law/ for it was first enunciated by that dis- tinguished geometrician. Pressure exerted anywhere iipon a mass of liquid is transmitted undiminished in all directions, and acts with the same force on all equal surfaces, and in 'a direction at right angles to those sur- faces. To get a clearer idea of the truth of this principle, let us conceive a cylindrical vessel, in the sides of which are placed various cylin- drical tubulures, all of the same size, and closed by movable pistons (fig. 57). The vessel being filled with water, or any other liquid, the moment any pressure is applied to the piston A, all the other pistons are pressed outwards, showing that the pressure is not merely trans- mitted downwards upon the piston D, but laterally upon the pistons E and F, and upwards upon the pistons B and C. If, instead of pressing on the piston A, the pressure be exerted upon B, the same effects are produced ; the piston A is then forced upwards. In these different cases, not only is the pressure transmitted in all directions, but for the same surface it is transmitted with the same intensity. For instance, if the pressure on the piston A is twenty pounds, and its surface is equal to that of the piston B, the upward pressure on the latter is also twenty pounds ; but if the surface of the piston B is only a twentieth that of A, the pressure upon B is only one pound. This is the principle of the eqiiality of pressure. Fig. 57- -78] Pressures resulting from Weight of Liquids. 67 Fig. 58. 77. Consequence and verification of Pascal's principle. It follows from what has been said, that the pressure transmitted by a liquid is proportional to the extent of surface ; this is in- deed only another enuncia- tion of Pascal's principle. . To verify this, two cylin- ders are taken of unequal di- mensions, joined by a tube (fig. 58). These cylinders contain water, and are pro- vided with pistons which move in them with gentle friction. Now if the surface of the larger one, P, for instance, is twenty times that of the smaller one, /, it will be found that a weight of a pound placed upon p will balance a weight of twenty pounds placed upon P ; if these weights are in any other ratio, equilibrium is destroyed. The principle of the equality of pressures forms the basis of the whole science of hydrostatics, and we shall presently find a very important application of it in the hydraulic press (83). 78. Pressures resulting: from the weight of liquids. In what has been said, we have considered the pressures transmitted towards the sides of the vessel, when some external force is applied. It is not, however, necessary to exert an external pressure on the surface of a liquid in order to produce internal pressures in its mass, and on the sides of the vessel. The mere weight of the liquid itself is sufficient to produce pressures which vary with the depth and with the density of the liquid. For suppose any vessel filled with liquid ; if we conceive the liquid divided into horizontal layers of equal thickness, it is clear that the second layer supports a pressure equal to the weight of the first ; that the third supports the weight of the first and second, and so on ; so that the pressure increases with the number of layers, which is expressed by saying that gravity produces in liquids pres- sures proportional to the depth. It is obvious, moreover, that these pressures are proportional to the density of the liquids ; that is, that for the same depth, a liquid which has two or three times the density of another, will exert twice or thrice as much pressure. It follows from the principle of the equality of pressure in all directions, that the pressure produced by gravity in liquids is exerted F 2 68 Hydrostatics [78- not merely in the direction of this force, but horizontally, and also upwards, as will now be demonstrated. 79. lateral pressures. Hydraulic tourniquet. The existence of lateral pressures which liquids exert upon the sides of the vessel in which they are contained, may be demonstrated by means of the hydraulic tourniquet or Barker's mill (fig. 59). This consists essen- tially of a long glass tube, C, with a funnel, D, at the top. The bottom of the tube fits into a hollow brass box, which rests on a pivot ; in the sides of the box are fitted four brass tubes, ar- ranged crosswise, and all bent in the same direction at the ends. Waterdescendingthe long tube emerges by the aper- tures of the bent tubes, which are soon seen to rotate rapidly in the direction indicated by the arrow. This rotation is due to the lateral pressure exerted by the column of water in the long tube . For let us consider one of the bent tubes, A, B, repre- ____ sented in section on the left (fig. 59), and suppose first that the orifices, a and b, are closed. The column of water which then fills the tube C exerts upon the portions of the opposite sides, A and a, equal and contrary pressures which hold each other in equilibrium ; this is also the case at B and b, and thus no rotation can be produced in either direction. But if the orifices a and b are open, as is the case when the appa- ratus is at work, as the water issues by these orifices, the pressures at a and b no longer exist ; while those transmitted to A and B continuing to act, produce the rotation. -81] Pressure is Independent of Form of Vessel. 69 Rotating fireworks also act on the same principle as Barker's mill ; that is, an unbalanced reaction from the heated gases which issue from openings in them gives them motion in the opposite directions. It is in consequence of the lateral pressure of water that dykes and banks which retain rivers or reservoirs, sometimes give way, by becoming too weak for the pressure they have to support. 80. vertical upward pressure. The pressure which the upper layers of a liquid exert on the lower layers causes them to exert an equal reaction in an upward direction, a necessary consequence qf the principle of transmission of pressure in all directions. The following experiment (fig. 60) serves to exhibit the upward pressure of liquids. A large open glass tube, one end of which is ground, is fitted with a ground glass disc, a, or still better, with a thin card or piece of mica, the weight of which may be neglected. To the disc is fitted a -string, b, by which it can be held against the bottom of the tube. The whole is then immersed in water, and the disc does not fall, although no longer held by the string ; it is consequently kept in its position by the upward pressure of the water. If water be now slowly poured into the tube, the disc will Fi s- 6o - only sink when the height of the water inside the tube is equal to the height outside. It follows thence that the upward pressure on the disc is equal to the pressure of a column of .water, the base of which is the internal section of the tube , and the height the dis- tance from the disc to the outer surface of the liquid. Hence the iipward pressure of liquids at any point is governed by the same laws as the downward pressure. This upward pressure is termed the buoyancy of liquids ; it is perceived when the hand is plunged into water, and still more dis- tinctly if it is immersed in mercury, which being of greater density produces greater pressure. It is owing to this buoyancy that, if a hole be made in the bottom of a ship, water enters with force. 8 1. Pressure is independent of the shape of the vessel. The Hydrostatics. [81- pressure exerted by a liquid, in virtue of its weight, on any portion of the liquid, or on the sides of the vessel in which it is contained, depends on the depth and density of the liquid, but is independent of the shape of vessel and of the quantity of the liquid. This principle, which follows from the law of the equality of pressure, may be experimentally demonstrated by many forms of apparatus. The following is one frequently used, and is due to Masson. It consists of' a large conical vessel, M, screwed to a brass tubulure, r, fixed to a wooden support (fig. 61). This tubulure is closed by a disc, a, which does not adhere to it, but is Fig. 61. simply applied against the edge, and is kept there by a string attached to one end of an ordinary balance, to the other end of which is a scale-pan. Weights are placed in the latter, so as just to counterbalance the pressure of the water on the disc, when the vessel M is almost full ; water is then gradually added until the disc just begins to give way and allows some to escape. A rod, o, is then lowered until its point just grazes the surface of the liquid. If the vessel M be unscrewed and replaced by the cy- lindrical tube, P, the capacity of which is far less, on gradually pouring water in, the moment the level of the liquid just touches the point of the rod, o, the disc, a, begins to allow some water to -83] Hydraulic Press. escape. The same result ensues if for the straight tube, P, the inclined one Q, be substituted. In these three cases, therefore, pro- vided the height of the liquid is the same, the pressure on the disc, a, is the same, whatever be the shape and capacity of the vessels. Moreover, the weight which has to be put on the scale-pan to establish equilibrium, shows that the pressure exerted by the liquid is equal to the weight of a column of water, the base of which is the internal section of the ttibulure, c, and the height the vertical distance from the disc to the surface of the liquid. This principle is sometimes called the hydrostatical paradox, for at first sight it seems quite impossible. 82. Pascal's experiment. Pascal made the following experiment, which proves what great pressures may be pro- duced by even small quantities of liquid when contained in vessels of great height. He fixed firmly, in a stout cask, as represented in fig. 62, a very narrow tube about 30 feet in height, and then filled the cask and the tube with water. The effect of this was to burst the cask : for there was a pressure on the bottom of the cask equal to the weight of a column of water whose base was the bottom itself, and whose height was equal to that of the water in the tube (81). 83. Hydraulic press. The law of the equality of pressure has received a most important application in the hydraulic press, a machine by which enormous pressures may be produced. Its principle is due to Pascal, but it was first con- structed by Bramah in 1796. Fig. 63 represents an elevation, and fig. 64 a section of the instrument ; it consists of two iron cylinders or barrels, A and B, of unequal diameters. In the barrel A, which is of very small diameter, is a cylindrical rod, a, which acts as piston, and can be moved up and down by the lever, O. In the cylinder, B, the internal diameter of which Hydrostatics. [83- is 12 to 15 times that of the barrel, A, is a long cylindrical iron ram, C, which also forms a piston, and works water-tight in the barrel B. On the top of the ram, C, is an iron slab, K, which rises and falls with it. Four wrought-iron columns support a second plate, MN, which is fixed. The objects to be pressed are placed between K and MN. When the piston is raised by means of the level, a vacuum is produced in the barrel A, and a valve, S, at the bottom opens and allows water to pass from a reservoir, P, into the barrel. When a re-descends, the valve, S, closes ; but another valve, ;;z, placed at the bottom of the tube d, opens ; the water is thus forced by this tube into the large cylinder, B. At the next stroke of the piston, #, a fresh quantity of water is drawn from the reservoir, P, and forced into the barrel B, and so forth. -83] Hydraulic Press. 73 In consequence of the principle of the equality of pressure, the downward pressure exerted by the small piston, a, is transmitted upwards upon the piston C. The pressure which can be obtained depends on the relation of the piston C to that of the piston a. If the former has a transverse section fifty or a hundred times as large as the latter, the upward pressure on the large piston will be fifty or a hundred times that exerted upon the small one. By means of the lever, O, an additional advantage is obtained. If the distance from the fulcrum to the point where the power is applied is five times the distance from the fulcrum to the piston, a 7 the pressure on a will be five times the power. Thus, if a man acts on O with a force of sixty pounds, the force transmitted by the piston a will be 300 pounds, and the force which tends to raise the piston C will be 30,00x3 pounds, supposing the section of C is a hundred times that of a. The hydraulic press is used in all cases in which great pressures are required. It is used in pressing cloth, in extracting the juice of beet root, in expressing oil from seeds, and in pressing apples in making cider ; it also serves to test the strength of cannon, of steam boilers, and of chain cables. The parts composing the tubular bridge which spans the Menai Straits were raised by means of an hydraulic press. The cylinder of this machine, the largest which has ever been constructed, was nine feet long and twenty-two inches in internal diameter ; it was capable of raising a weight of two thousand tons. 74 Hydrostatics. [84 - CHAPTER II. EQUILIBRIUM OF LIQUIDS. 84. Conditions of the equilibrium of liquids. We have seen that the conditions of the equilibrium of a solid are that its centre of gravity be supported by a fixed point ; all the other parts of the body then retain the same state of equilibrium in consequence of cohesion, which unite the particles to each other, and to the centre of gravity. This is by no means the case with liquids ; owing to the greater mobility of their molecules, and the facility with which they obey the force of gravity, they would flow away and spread out in a horizontal position, if they were not retained by some obstacle. Hence a liquid cannot be at rest in any vessel, unless it satisfies the following conditions : I. The free surface of the liquid must be horizontal, that z's, perpendicular everywhere to the direction of gravity. II. Every molecule of the mass of the liquid must be subject in every direction to equal and contrary pressures. The second condition is self-evident ; for if, in two opposite directions, the pressures exerted on any given molecule were not equal and contrary, the molecule would be moved in the direction of the greater pressure, and there would be no equilibrium. Thus the second condition follows from the principle of the equality of pressures, and from the reaction which all pressure causes on the mass of liquids. To account for the first condition relative to the free surface of the liquid, let us observe that in a liquid whose F j 6s surface is horizontal, all the molecules supporting each other, the action of gravity is destroyed, and the liquid is at rest. But if the surface is not horizontal, if some parts are higher than others (fig. 65), the higher part, ad, exerts upon any horizontal layer, bd t a greater pressure than the part cd, and therefore as a given molecule, o, of the horizontal layer is exposed to a greater pressure in the direction bo than in the direction do, equilibrium is impossible. -85] L cvcl of L iqitids. 75 In saying that in order that a liquid be at rest its surface must be horizontal, we must remark that that presumes the liquid only to be acted upon by gravity, which is usually the case ; if it is under the action of other forces, as is the case with the capillary phenomena, where it is attracted by the sides of the vessel, its surface is then inclined so as to be perpendicular to the resultant of the forces which act upon it. 85. Level of liquids. A liquid is said to be level when all the points of its surface are in the same horizontal plane. This, how- ever, only applies to surfaces of small extent. For as the direction of the vertical constantly changes from one place to another on the Fig. 66. surface of the globe, the direction of the horizontal surfaces changes too ; that is to say, that a plane which is horizontal at one part of the earth's surface, is not parallel to a horizontal plane at a small distance ; they form an angle with each other. Hence a liquid surface of some extent in a state of equilibrium, being necessarily horizontal in each of its parts, does not form one single perfectly plane surface, but a series of plane surfaces inclined to each other ; which of course produces a curved surface. This curvature cannot, however, be perceived on surfaces of small extent, as in water contained in a vessel ; for the surface of such a liquid is so per- fectly levelled, that it reflects the rays of light like the most per- 7 6 Hydrostatics. [85- fectly polished plane mirror. The curvature is, however, easily observed on large surfaces like those of the sea. For if this surface were perfectly level, a ship in sailing away from the shore would only cease to be visible in consequence of increasing distance, and the less apparent parts, the masts and the cordage, would disappear first. This, however, is not the case ; the hull first sinks below the horizon, then the lower part of the masts, and ultimately the top, as seen in fig. 66, thus proving the curvature of the surface of the sea. 86. True and apparent level. When we consider a great surface of water the Mediterranean sea, for instance its surface is said to be level when all points of the surface are equidistant from the centre of the earth. This is the true level ; while that level which is defined as having all the points of its surface in the same horizontal plane, is the apparent level, the level for the eye. The true level only coincides with the apparent level when the liquid surfaces are very small. If the earth did not rotate about its own axis, the surface of all seas would form a true level ; but owing to the centrifugal force which results from its daily motion, the surface is heaped up at the equator, and the level is higher than at the poles. 87. Equilibrium of the same liquid in several communi- cating vessels. Not merely do liquids tend to become level Fig. 67. when they are placed in the same vessel, but also when they are placed in vessels which communicate with each other. Whatever -88] Equilibrium of L iquids. 77 the shape and the dimensions of these vessels, equilibrium will exist, when the surfaces of the liqidds in all the vessels are in the same horizontal plane. This principle may be demonstrated by means of the apparatus represented in fig. 67. It consists of a series of vessels of different shapes and capacities connected together by a common horizontal tubulure. When water or any other liquid is poured into the vessel, the level is seen to rise at the same time, and stop at exactly the same height in each. Equilibrium is then established. For as we have seen that the pressures exerted by a liquid do not depend upon its quantity but upon its height (81), when this is the same for all the vessels above the tube of communication abc, the pressure is necessarily everywhere equal, and therefore, as the liquid has no more tendency to flow from b towards a than from b to c, equilibrium continues. 88. Equilibrium of different liquids in communicating- vessels. In what has been said the communicating vessels all Fig. 68. contained the same liquid. It may, however, happen that the vessels contain liquids of different densities, which do not mix. Hydrostatics. [88- The level is then no longer the same ; the lighter liquids are higher, and equilibrium is only possible when the heights of the liquid columns in communication are inversely as their densities ; that is, that if one of the liquids is twice or thrice as dense as another, its height will be half or one-third as much. This principle is demonstrated experimentally by means of the apparatus represented in fig. 68. It consists of two glass tubes connected at the bottom by a narrow tube. The tubes are sup- ported by two vertical columns, and on each of them is a scale graduated on the glass itself. If then mercury is poured into one of the tubes, it quickly assumes the same level in each. On now pouring water into the tube A, the level of the mercury is seen to sink in this tube in virtue of the pressure of the water, and it rises in the other tube. Then, when equilibrium' is established the' mercury in B is higher than in the tube A by a quantity, cd. It is clear, then, that the pressure of the column of mercury, cd, counter- balances the pressure of the column of water, ab. If now the heights of ab and cd be measured by means of the graduated scales on the two tubes, it will be found that the height cd is 13-6 as small as that of ab ; which demonstrates the above principle, for we shall presently see that mercury is 13-6 times as heavy as water. 89. Equilibrium of superposed liquids. In order that there should be equilibrium when several heterogeneous liquids which do not mix are superposed in the same vessel, each of them must satisfy the conditions necessary for a single liquid ; and further, there will be a stable equilibrium only when the liquids are arranged in the order of their decreasing densities from the bottom upwards. The last condition is experimentally demonstrated by means of the phial of four elements (fig. 69). It consists of a long narrow bottle containing mercury, water saturated with carbonate of potass, alcohol coloured red, and petroleum. When- the phial is shaken the liquids mix, but when it is allowed to rest they separate ; the mercury sinks to the bottom, then comes the water, Fig. 69. -90] Water Level. 79 then the alcohol, and then the petroleum. This is the order of the decreasing densities of the bodies. The water is saturated with carbonate of potass to prevent its mixing with the alcohol. This separation of the liquids is due to the same causes as that which enables solid bodies to float on the surface of a liquid of greater density than their own. It is also from this principle that fresh water, at the mouths of rivers, floats for a long time on the denser salt water of the sea ; and for the same reason cream, which is lighter than milk, rises to the surface. APPLICATIONS OF THE PRINCIPLE OF THE EQUILIBRIUM OF LIQUIDS. 90. "Water level. In a great number of operations, such as the construction of canals, railways, roads, etc., it is continually neces- sary to determine the difference in level of two more or less distant places. The simplest apparatus for this purpose is the water level Fig. 70. which is an application of the conditions of equilibrium in commu- nicating vessels. It consists of a metal tube bent at both ends, in which are fitted glass tubes (fig. 70). It is placed on a tripod, and water poured in the tube until it rises in both limbs. When the liquid is at rest, the level of the water in both tubes is the same that is, they are both in the same horizontal plane. This instrument is used in levelling, or ascertaining how much one point is higher than another. If, for example, it is desired to m m So Hydrostatics. [90- find the difference between the heights of two places, a levelling- stafl"\s fixed on the latter place. This staff consists of a rule formed of two sliding pieces of wood, one of which supports a piece of tin plate, in the centre of which there is a mark. This staff being held vertically, an observer looks at it through the level along the surfaces in the two tubes, and directs the holder to raise or lower the slide until the mark is in the prolongation of the level in the two tubes. The assistant then reads off on the graduated rod the height of the mark upon the ground. If this height exceeds that of the level, the height of the latter is subtracted from that of the former, and the difference gives the difference in the heights of the two places. 91. Spirit level. The spirit level is both more delicate and more accurate than the water level. It consists of a glass tujpe (fig. 71), very slightly curved ; it is filled with spirit with the ex- Fig. 7 i. ception of a bubble of air, which tends to occupy the highest part. The tube is placed in a brass case, which is so arranged that when it is in a perfectly horizontal position the bubble of air is exactly between the two points marked in the case. But if the plane on which the instrument rests is ever so little inclined, the air bubble tends to move towards the higher part. This thus furnishes a ready means of ascertaining whether any article a table, a stand, or a bookshelf is quite horizontal. To take levels with this apparatus, it is fixed on a telescope, which can consequently be placed in a horizontal position. 92. Jets of water. The jets which ornament our gardens and public places, depend on the tendency of liquids always to become level. For the water which jets out always comes from a reservoir placed in a higher position than that where the jet is; and its jetting is a consequence of its tendency to form a level. Fig. 72 gives an idea of this phenomenon. On the eminence on the left of the figure is a reservoir containing water, from the bottom of which passes a -93] Streams, Springs, Wells. 81 tube which terminates in the centre of the basin. The water then jets out, forced by the pressure of a column of water, the height of Fig. 72. which is equal to the difference in level between the reservoir and the basin. Theory proves that in such a case the water always tends to rise to the level of the reservoir from which it is supplied. It never attains this freight, for the jet experiences three kinds of resistances : ist, the friction of the water in the conduit pipe ; 2nd, the resist- ance of the air ; and 3rd the hindrance offered by the particles falling from the height of the jet upon those ascending. 93. Streams, springs, wells. The formation of springs upon the surface of the earth, and in its interior, is also due to the tendency of water to seek its level. For gravity causes water to flow from higher to lower places. Hence it is that the rain which falls upon the earth, and the water arising from the melting of snow, pass down to the valleys, where they form brooks, streams, and rivers, which flow along their beds as along an inclined plane, until they emerge into the seas. A very small fall can give rise to a current. Thus the mean height of the Seine at Paris is not more than 35 yards above the sea-level. The extent of its course between these two points is about 224 miles, which scarcely amounts to a fall of G 82 Hydrostatics. [93- the 3 f gth part of an inch in a yard ; and water requires several days to traverse this distance. All the rain which falls does not flow upon the surface ; part of it penetrates into the earth, and gives rise to small subterranean watercourses which are called springs. It is in order to procure water from these that wells are sunk. 94. Artesian wells. When the spring which feeds a well comes from a place much higher than that where the well is sunk, it may happen that water tends to rise higher than the ground. This is what happens in what are called Artesian wells. These wells derive their name from the province of Artois, where it has long been cus- tomary to dig them, and from whence their use in other parts of Fig. 73- France and Europe was derived. It seems however, that at a very remote period, wells of the same kind were dug in China and Egypt. To understand the theory of these wells, it must be premised that the strata composing the earth's crust are of two kinds : the one permeable to water, such as sand, gravel, etc. ; the other impermeable, such as clay. Let us suppose, then, a basin of greater or less extent, in which the two impermeable layers AB, CD (fig. 73), enclose between them a permeable layer KK. The rain-water falling on the part of this layer which comes to the surface, which is called the outcrop, -will filter through it, and, following the natural fall of the ground, will collect in the hollow of the basin, whence it cannot escape, owing to the impermeable strata above and below it. If now a vertical hole, I, be sunk down to the water-bearing stratum, the water striving to regain its level will spout -95] Bodies immersed in Liquids. out to a height which depends on the difference between the levels of the outcrop and of the point at which the perforation is made. The waters which feed Artesian wells often come from a distance of sixty or seventy miles, The depth varies in different places. The well at Crenelle is 1,800 feet deep ; it gives 656 gallons of water in a minute, and is one of the deepest and most abundant which has been made. The temperature of the water is 27 C. It follows from the law of the increase of temperature with the in- creasing depth below the surface of the ground (297), that, if this well were 210 feet deeper, the water would have all the year round a temperature of 32 C v that is, the ordinary temperature of warm baths. CHAPTER III. PRESSURES SUPPORTED BY BODIES IMMERSED IN LIQUIDS. SPECIFIC GRAVITIES. AREOMETERS. 95. Pressure supported by a body immersed in a liquid. When a solid is immersed in a liquid, it is obvious that the pressures which the sides of the vessel support are also exerted against the surface of the body immersed, since liquids transmit pressure in all directions (76), But it is readily seen that the pressures which the immersed body supports do not neutral- ise themselves, but have a resultant, the tendency of which is to move the body upwards. Let us imagine a cube immersed in a mass of water (fig, 74), and that four of its edges are vertical. The horizontal pressures upon the two opposite faces, a and <, are clearly of the same inten- sity, for they are exerted at the same depth (78) ; and as they are in opposite ( directions they will balance one an- other, and the only effect will be to com- press the body without displacing it. But the vertical pressures on the faces *fand c are obviously un- equal. The first is pressed downwards by a column of water whose o 2 Fig. 74. Hydrostatics. [95- base is the face d, and whose height is dn, the lower face c is pressed upwards by the weight of a column of water whose base is the face itself, and whose height is en. The cube, therefore, is urged up- wards by a force equal to the difference between these two pressures, which latter is manifestly equal to the weight of a column of water having the same base and the same height as this cube. By this reasoning, therefore, we arrive at the remarkable principle, that any body immersed in a liquid is pressed upwards by a pressure equal to the weight of the volume of liquid which it displaces. We shall see how this principle can be experimentally verified. 96. Principle of Archimedes. Hydrostatic balance. We have thus seen that any body immersed in a liquid is submitted to the action of two forces gravity which tends to make it sink, and . Fig, 75- the buoyancy of the liquid which tends to raise it with a force equal to the weight of the liquid displaced. The body weighs less there- fore than in air, and the diminution of its weight is exactly equal to the weight of the displaced liquid. The above principle may be -96] Hydrostatic Balance. 85 thus enunciated : that a body immersed in a liquid loses a part of its weight equal to the weight of the displaced liquid. For instance, suppose that a body which in air weighs 1,000 grains, when im- mersed in water displaces a cubic inch of water ; it will now only weigh 1,000-252 = 748 grains (a cubic inch of water = 252 grains). This principle, which is remarkable for its numerous applications, is called the l principle of Archimedes,' after the discoverer. It is shown experimentally by means of the hydrostatic balance (fig. 75). This is an ordinary balance, each pan of which is provided with a hook ; the rod, c, slides in the hollow cylinder d. The beam is sup- ported on the rod, c, which can be fixed in any position by means of a screw, n. The beam being raised, a hollow brass cylinder, , is suspended to one of the pans, and below this a solid cylinder, a, whose volume is exactly equal to the capacity of the first cylinder ; lastly an equipoise is placed in the other pan. If now the hollow cylinder, a, be filled with water, the equilibrium is disturbed, but if at the same time the beam is lowered so that the solid cylinder becomes immersed in a vessel of water placed beneath it, the equi- librium will be restored. By being immersed in water, the cylinder a loses a part of its weight equal to that of the water in the cylinder b. Now as the capacity of the cylinder a is exactly the same as that of the cylinder , the principle which has been laid down is proved. It is stated that Archimedes discovered this principle on the occasion of a problem which had been propounded to him by Hiero, tyrant of Syracuse. This prince, desiring to offer to Jupiter a gold crown, had furnished a goldsmith with ten pounds of gold as the material for this purpose. The crown when finished was found to weigh ten pounds, but Hiero, suspecting that some of the gold had been replaced by silver, owing to the beauty of its workmanship, demanded from Archimedes a means of detecting the supposed fraud without destroying the crown. Archimedes pondering over the solution of the problem, was in the bath, when he observed that he could raise his limbs in water more easily than in air. This simple observation was a gleam of light for him ; he discovered the above principle, and this led him to a simple means of calculating the quantity of gold and silver in the crown. It is said that Archimedes was so transported with joy, at his discovery that he ran home from the bath, crying in the streets, EvprjKn, iviifKa (I have found it). We have all had occasion to make the observation of Archimedes, 86 Hydrostatics. [96- on observing how much lighter our limbs appear in water, and on the contrary, how much heavier they seem when lifted out. In like manner, if the body is almost entirely immersed in water, we can walk barefoot on the stones without injuring the feet ; but this is not possible when we are out of the water. For in the former case part of the weight of the body is raised by the liquid, while in the latter the whole weight of the body presses the feet against the sharp projections. 97. Equilibrium of immersed and floating: bodies. When a body is placed in a liquid, three cases are possible : the body may have the same specific gravity as the liquid, in which case it weighs as much as the liquid for an equal volume ; or it may be denser, in which case it weighs more ; or it is lighter, and in this case it weighs less. I. If the body immersed is of the same density as the liquid, the weight of the liquid displaced being the same as that of the body, it follows from Archimedes' principle that the buoyancy which tends to raise it, is exactly equal to the force with which gravity tends to sink it. The two forces are thus in equilibrium, and the body remains in suspension in any position in the liquid. II. If the body immersed is denser than the liquid, it sinks, for then its weight preponderates over the buoyancy. This is the case when a stone or a mass of metal is thrown into water. III. Lastly, if the immersed body is lighter than the liquid, the buoyancy prevails, and the body rises until it only displaces a weight of liquid equal to its own. It is then said to float. Cork, wax, wood, and all substances lighter than water, float on its surface. A body which floats on one liquid may sink in another; the body for this purpose must be lighter than the one liquid, but heavier than the other. An egg sinks at once if placed in ordinary water, since it is heavier than an equal volume of water ; but' it swims if placed in strong brine, which is denser than water. A piece of oak floats on water, but sinks in ether, which is lighter than water. Iron floats on mercury, but sinks at once in water. Yet a body, though denser than a liquid may float on its surface. For this purpose it must have such a shape as to displace a volume of liquid, the weight of which is greater than its own. Porcelain is much heavier than water, yet a porcelain saucer placed on water floats on the surface ; this arises from its concave shape, owing to which it displaces a weight of water equal to its own, though it is -100] Swimming. only partially immersed. For the same reason iron ships, even with very thick sides, float freely on water. 98. Cartesian diver. The different effects of suspension, im- mersion, and floating are reproduced by means of a well-known hydrostatic toy, the Cartesian diver (fig. 76). It consists of a glass cylinder, nearly full of water, on the top of which a brass cap, A, provided with a piston, is hermetically fitted. In the liquid there is a little porcelain figure, a fish, 0, for example, attached to a hollow- glass ball, m, which contains air and water, and floats on the sur- face. In the lower part of this figure there is a little hole by which water can enter or escape, according as the air in the interior is more or less compressed. The quantity of water in the globe is such, that very little more is required to make it sink. If the piston be slightly lowered the air is compressed, and this pressure is transmitted to the water of the vessel and to the air in the bulb. The con- sequence is, that a small quantity of water penetrates into the bulb, which therefore becomes heavier and sinks. If the pressure is relieved, the air in the bulb expands, expels the excess of water which had entered it, and the apparatus being now lighter, rises to the surface. The experiment may also be made, by replacing the brass cap and piston by a cover of sheet india rubber, which is tightly tied over the mouth. When this is pressed by the hand the same effects are produced. 99. Swimming bladder of fishes. Most fishes have an air-bladder below the spine, which is called the swimming bladder. The fish can compress or dilate this at pleasure by means of a muscular effort, and pro- duce the same effects as those just described that is, it can either rise or sink in water. 100. Swimming. The human body is lighter, on the whole, than an equal volume of water ; it conse- quently floats on the surface and still better in sea water, which is 88 Hydrostatics. [100- heavier than fresh water. The difficulty in swimming consists, not so much in floating, as in keeping the head above water, so as to breathe freely. In man the head is heavier than the lower parts, and consequently tends to sink, and hence swimming is not natural to him, but is an art which requires to be learned. With quadrupeds on the contrary, the head being less heavy than the posterior part of the body, remains above water without any effort, and these animals therefore swim naturally. If a person who cannot swim, and who falls into the water, retains Fig. 77. coolness enough to turn on his back, so that his face is out of water, he can breathe freely, and wait until help arrives. Instead of this, however, he generally attempts to raise his arms out of water, as if grasping at some fixed support. This is very dangerous, for as the arms no longer displace a quantity of liquid equal to their own bulk, their weight is not diminished to that extent, but concurs with that of the head in making them sink. Weight for weight, fat persons swim more easily than lean ones, for they displace more water. For the same reason air bladders, or cork girdles, are fastened to persons who are learning to swim (fig. 77), for then, without any considerable increase of weight, they displace more water, which increases the buoyancy and keeps them up. Several kinds of birds, such as ducks, geese, and swans, swim easily on water. They owe this property to a thick coating of a light impervious down which covers the lower part of the body, so that they displace, even with a small immersion, a weight equal to their own. -101] Specific Gravity. SPECIFIC GRAVITY. HYDROMETERS. 101. Specific gravity. Daily experience shows us that different substances have very unequal weights for one and the same volume. For instance, we all know that gold weighs more than silver, lead than iron, stone than wood. In order to compare equal volumes of various substances as to their weights, the weight of water has been taken as a standard of comparison as unity. For water is everywhere met with, and can always be had pure ; this latter condition is necessary, for the weight of a given quantity of water differs with the substances it holds in solution. As, more- over, the weight varies with the temperature, a constant temperature must be adopted. Hence the unit of weight is distilled water at a temperature of 4 degrees, for at this point, as we shall afterwards see (228), water has its greatest density. Fig. 78- Thus having agreed to represent by I the weight of a certain volume of distilled water at 4 degrees, the specific gravity of a body 90 Hydrostatics. [101- is the weight of the same 'volume of it as compared with that of water, or what is the same, the number which expresses how much it weighs as compared with water. Thus, when we say that the specific gravity of gold is 19, and that of lead n, we mean that the former metal is 19 times, and the latter n times as heavy as water. 102. Determination of the specific gravity of solids. Three methods are commonly used in determining the specific gravities of solids and liquids. These are the method of the hydrostatic balance, that of the hydrometer, and that of the specific gravity flask. All three, however, depend on the same principle, that of first ascertaining the weight of a body, and then that of an equal volume of water. We shall first apply these methods to determin- ing the specific gravity of solids, and then to the specific gravity of liquids. i. Hydrostatic balance. To obtain the specific gravity of a solid, a piece of iron for instance, by the hydrostatic balance (fig. 78), it is first weighed in air by suspending it to the hook of one of the plates. Let us suppose that its weight is 585 grains. It is then weighed while immersed in distilled water, as shown in fig. 78. It will now weigh less ; suppose the weight to be 510 grains, this is in accordance with Archimedes' principle, for it now loses a weight equal to that of the water which it displaces. Hence, subtracting 5 10 from 585. the difference 75 represents the weight of the displaced water, that is, the weight of a volume of water equal to that of the iron : we need now only calculate how often the weight 75, that of the water, is contained in 585, that of the iron, and the quotient 7-8 is the specific gravity of iron ; it says that, for equal volumes, this substance weighs 7-8 times as much as water. Nicholson's hydrometer. This apparatus consists of a hollow metallic cylinder (fig. 79), to which is fixed a cone, d, loaded with lead. The object of the latter is to depress the centre of gravity so that the cylinder does not upset when in the water. At the top is a stem, c, terminated by a pan, a, in which is placed the substance whose specific gravity is to be determined. On the stem a standard point, c, is marked. The apparatus stands partly out of the water, and the first step is to ascertain the weight which must be placed in the pan in order to make the hydrometer sink to the standard point c (fig. 80). Let this weight be 125 grains, and let sulphur be the substance whose specific gravity is to be determined. The weights are then removed from the pan, and replaced by a piece of sulphur which weighs less -102] Specific Gravity of Solids. than 125 grains, and weights added until the hydrometer is again depressed to the standard, c. If, for instance, it has been necessary Fig. 79. Fig. 80. to add 55 grains, the weight of the sulphur is evidently the difference between 125 and 55 grains, that is, 70 grains. Having thus determined the weight of the sulphur in air, it is now only necessary to ascertain the weight of an equal volume in water. To do this, the piece of sulphur is placed in the lower pan at d, as represented in fig. 81. The whole weight is not changed, nevertheless the hydrometer no longer sinks to the standard ; the sulphur, by immersion, has lost part of its weight equal to that of the water displaced. Weights are added to the upper pan until the hydrometer sinks again to the standard. This weight, 34-4 grains for example, represents the weight of the volume of water displaced ; that is, of the volume of water equal to the volume of the sulphur. It is only necessary, therefore, to divide 70 grains, the weight in air, by 34-4 grains, and the quotient 2-03 is the specific gravity. Specific gravity flask. In this method, which is advantageously used for the determination of the specific gravity of bodies in a state of powder, a wide-necked flask is used which can be care- fully closed by a ground glass disc (fig. 82). Having filled it with water it is closed with the disc, great care being taken that not a bubble of air is left. After being carefully wiped dry, it is placed in the pan of a balance, and by its side is the substance, a, whose Hydrostatics. [102- Fig. 82. specific gravity is to be determined. The whole is then equi- poised by placing weights in the other pan of the balance. The substance, a, is then removed, and weights added in its place, until equilibrium is again established. The weight necessary for this purpose gives the weight of the substance in air. To obtain its weight in water it is placed in the flask, the disc adjusted, and the whole again carefully wiped. In order now to equipoise the tare in the second pan, weights must be added on the side of the flask to make up for the water displaced. The weights necessary for this purpose represent then the weight of a volume of water equal to that of the body. Dividing, then, the weight of the body in air by the weight of an equal volume of water, we have the specific gravity sought. 103. Specific gravity of liquids. These are determined by the same methods as those of solids. Hydrostatic balance. In determining the specific gravity of a liquid by this means, a body is suspended to one of the pans of the balance, which is neither dissolved by the liquid whose specific gravity is to be determined, nor by water ; for instance, a ball of platinum, which is insoluble in all ordinary liquids. This ball is first weighed in air, then in water, and finally in the liquid in question,, which we will suppose is alcohol. Let us assume that in air the ball weighs 5 10 grains, in water 486 grains, and in alcohol 489 grains. The loss of weight in water has thus been 510 less 486, or 24 grains, and in alcohol 510 less 499, or 21 grains ; which tells us that if a volume of water equal to that of the ball weighs 24 grains, the same volume of alcohol weighs 21 grains. Hence, to obtain the specific weight of alcohol we must ascertain how many times the number 21 con- tains 24, which of course is obtained by division. The quotient thus obtained is cr866, which represents the specific gravity of alco- hol as compared with water. ,, ii. Fahrenheit's hydrometer. This instrument (fig. 83) resembles Nicholson's hydrometer, but is made of glass, so as to be used in all liquids. At its lower extremity, instead of a pan, it is loaded with a small bulb containing mercury. There is a standard mark on the stem, at the top of which is a pan. 103] Specific Gravity of Liquids. 93 The weight of the instrument is first accurately determined in air by means of an ordinary balance. Let us suppose that its Fig. 83. weight is 618 grains, and that the liquid whose specific gravity is to be determined, is olive oil. The hydrometer is placed in water, and the pan loaded with weights, until the liquid is level with the mark on the stem. Suppose it has 'been necessary to add 93 grains for this purpose ; these 93 grains, together with the 61 8 which the instru- ment weighs, make 711 grains, which represents the weight of water displaced by the instrument (97). The hydrometer is then removed, wiped dry, and immersed in the olive oil. Let us suppose that now only 3 1 grains need be added to sink the hydrometer to the mark. These together with the 618 grains which the instru- ment weighs, in all 649, represent the weight of the displaced oil We thus learn that equal volumes of oil and water weigh respec- tively 649 and 711. Hence we obtain the specific gravity of the latter as compared with the former by dividing 649 by 7 11 - The quotient is 0-91, which teaches us that if a certain volume of water weighs 100 grammes, the same volume of oil weighs 91 grammes. Neither Fahrenheit's nor Nicholson's hydrometers, give such accurate results as the hydrostatic balance. Specific gravity flask. This has been already described. In 94 Hydrostatics. [103- determining the specific gravity of a liquid, the flask is first weighed, empty, and then, successively, full of water and of the given liquid. If the weight of the flask be subtracted from the two weights thus obtained, the result represents the weights of equal volumes of the liquid, and of water, from which the specific gravity is obtained by division. Specific gravities of solids. Platinum .' ,' . . 22-069 Aluminum . . . 2*68 Gold . . , \ 19-36 Glass .... 2-48 Lead . . . .11-35 Anthracite , . . i'8o Silver .... 10-47 Coal . . . . 132 Copper . . . 8-87 Amber. , . ^. 1-07 Iron . . , . 778 Oak .... 0-84 Zinc .... 6-86 Yellow pine . . . 0-65 Diamonds . . . 3-53 Common poplar . . 0-38 Statuary marble . . 2-83 Cork . . . . 0-24 Specific gravities of liquids. Mercury . . . 13-60 Distilled water at o C. 0-99 Bromine . . . 2-96 Claret . . " ; . 0-99 Sulphuric acid . . 1*84 Olive oil . " . 0^91 Milk i . . . 1*03 Oil of turpentine . . 0-87 Sea water , . . 1*02 Absolute alcohol J . 0-80 Distilled water at 4 C. i-oo Ether /.*''.-, . 072 104. Use of table* of specific gravities. Tables of specific gravity admit of numerous applications. In mineralogy the specific gravity of a mineral is often a highly distinctive character. Jewellers also use them. By means of tables of specific gravities the weight of a body may be calculated when its volume is known, and con- versely the volume when its weight is known. With a view to explaining the last-mentioned use of these tables, it will be well to explain the connection existing between the British units of length, capacity, and weight. It will be sufficient for this purpose to define that which exists between the yard, gallon, and pound avoirdtipois, since other measures stand to these in well- known relations. The yard, consisting of 36 inches, may be regarded as the primary unit. Though it is essentially an arbitrary standard, it is determined by this that the simple pendulum which makes one oscillation in a second, at London on the sea level, is 39' 1 3 75 inches long (61). The gallon contains 277-274 cubic 106] Beaumfs Hydrometer. 95 inches. A gallon of distilled water at the standard temperature weighs 10 Ibs. avoirdupois or 70,000 grains troy ; or, which comes to the same thing, one cubic inch of water weighs 252-5 grains. On the French system the metre is the primary unit, and is so chosen that 10,000,000 metres are the length of a quadrant of the meridian from either pole to the equator. The metre contains 10 decimetres, or 100 centimetres, or 1,000 millimetres, its length equals 1-0936 yard. The unit of the measure of capacity^ is the litre or cubic decimetre. The unit of weight is the gramme, which is the weight of a cubic centimetre of distilled water at 4 C. The kilogramme contains 1,000 grammes, or is the weight of a decimetre of distilled water at 4 C. The gramme equals 15-443 grains. Suppose it is required to calculate the weight of a cubic foot of coal. A cubic foot contains 1,728 cubic inches ; the weight of a cubic foot of water would therefore be 1,728 times 252-5 grains, this being the weight of one cubic inch of water. The product of this multiplication divided by 7,000 grains (the number contained in a pound avoirdupois) gives 62-3 pounds as the weight of a cubic foot of water ; and as we learn, from the tables, that coal is 1-32 times as heavy as water, the weight of a cubic foot of coal will be 1-32 times 62-3 or 83-16 pounds. 105. Hydrometers with variable volume. The hydrometers of Nicholson and Fahrenheit are called hydrometers of constant volume, but variable weight, because they are always immersed to the same extent, but carry different weights. There are also hydro- meters of variable volume but of constant weight. These instru- ments known under the different names of acidometer, alcoholometer, lactometer, and saccharometer, are not used to determine the specific gravity of the liquids, but to show whether the acids, alcohols, solutions of sugar, etc., are more or less concentrated. 1 06. Beaume's hydrometer. This, which was the first of these instruments, may serve as a type of them. It consists of a glass tube, AB (fig. 84), loaded at its lower end with mercury, and with a bulb blown in the middle. The stem, the external diameter of which is as regular as possible, is hollow, and the scale is marked upon it. The graduation of the instrument differs according as the liquid, for which it is to be used, is heavier or lighter than water. In the first case it is so constructed, that it sinks in water nearly to the Hydrostatics. [106- Fig. 84. top of the stem, to a point A, which is marked zero. A solution of fifteen parts of salt in eighty-five parts of water is made, and the instrument immersed in it. It sinks to a certain point on the stem, B, which is marked 15 ; the distance between A and B is divided into 15 equal parts, and the graduation continued to the bottom of the stem. Sometimes the graduation is on a piece of paper in the interior of the stem. The hydrometer thus graduated only serves for liquids of a greater specific gravity than water, such as acids and saline solutions. For liquids lighter than water a different plan must be adopted. Beaume took for zero the point to which the apparatus sank in a solution of 10 parts of salt in 90 of water, and for 10 he took the level in distilled water. This distance he divided into 10, and continued the division to the top of the scale. The graduation of these hydrometers is entirely arbitrary, and they give neither the densities of the liquids, nor the quantities dissolved. But they are very useful in making mixtures or solu- tions in given proportions ; the results they give being sufficiently near in the majority of cases. For instance, it is found that a well-made syrup marks 35 on Beaume"'s hydrometer, from which a manufacturer can readily judge whether a syrup which is being evaporated has reached the proper degree of concentration. 107. Gay-Xiussac's alcoholometer The spirits of wine and brandy, in daily use, are a mixture of pure alcohol and water. The more alcohol they contain the stronger they are ; the more water they contain so much the weaker are they. Hence it is important to have a simple means of exactly determining the quantity of water contained in spirituous liquors. This is effected by means of Gay- Lussac's alcoholometer, which has the same shape as Beaume's, and only differs in the graduation. This is effected as follows : Mixtures of absolute alcohol and distilled water are made, con- taining 5, 10, 20, 30, etc., per cent, of the former. The alcoholo- meter is so constructed that when placed in pure distilled water, the bottom of its stem is level with the water, and this point is zero. It is next placed in absolute alcohol, which marks 100, and then successively in mixtures of different strengths, containing 10, 20, -108] Lactometer. 97 30, etc.,, per cent. Ths divisions thus obtained are not exactly equal, but their difference is not great, and they are subdivided into ten divisions, each of which marks one per cent. of absolute alcohol in a liquid. Thus a brandy in which the alcoholometer stood at 48, would contain 48 per cent, of absolute alcohol, and the rest would be water. All these determinations are made at 15 C., and for that temperature only are the indications correct. For, other things being the same, if the temperature rises the liquid expands, and the alcoholometer will sink, and the contrary, if the temperature falls. To obviate this error Gay- Lussac constructed a table which for each percentage of alcohol gives the reading of the instrument for each degree of temperature from o up to 30. When the exact analysis of an alcoholic mixture is to be made, the temperature of the liquid is first determined, and then the point to which the alcoholometer sinks in it. The number in the table corresponding to these data indicates the percentage of alcohol. From its giving the percentage of alcohol, this is often called the centesimal alcoholometer. 1 08. lactometer. The lactometer is a hydrometer like Beaume's, specially graduated for the purpose of ascertaining the quality of milk (fig. 86). This is accom- plished in the following manner : The instrument is immersed in a vessel containing pure milk, and the point to which it sinks is marked zero on a paper strip affixed to the stem. Mix- tures are then made of ^ of milk and ^ of water ; of ^ and T 2 5 , and so on to Fig. 85. of milk and ~ of water. The lac- Fig. 86. tometer is successively immersed in these, and sinks to different depths ; the point at which it stops in each case is marked by a number on the stem, and thus indicates a milk of a particular strength, that is, one containing a certain quantity of admixed water. The lactometer is, however, no infallible test for the adulteration of milk ; for the density of natural milk is subject to variation, and an apparent fraud may really be due to a bad natural quality of milk. 98 On Gases. [109- B O O K III. ON GASES. CHAPTER I. PROPERTIES OF GASES. ATMOSPHERE. BAROMETERS. 109. Physical properties of gases. Gases, as we have already seen, are bodies whose molecules are in a constant state of repul- sion in virtue of which they possess the most perfect mobility, and are continually tending to occupy a greater space. This property of gases is known by the names expansibility, tension, or elastic force, from which they are often called elastic fluids. The number of gases with which chemistry makes us acquainted is very considerable ; but only four are elementary ; these are oxygen, hydrogen, nitrogen, and chlorine. Some gases are coloured, but most of them are colourless. Some have a disagreeable odour, others are quite inodorous. Some are noxious, acting as poison to men and animals which breathe them ; such are carbonic oxide, which is produced by the combustion of charcoal ; sulphuretted hydrogen, which is given off from drains. Others are inoffensive, such as nitrogen and hydrogen ; yet an animal cannot live in them. They are not deleterious, in the sense of being poisonous ; but they do not support life. The only gas which has this property is oxy- gen; an animal deprived of this gas, even for a few seconds, soon dies. Gases and liquids have several properties in common, and some in which they seem to differ are in reality only different degrees of the same property. Thus, in both, the particles are capable ot moving ; in gases quite freely ; in liquids not quite freely, owing to a certain degree of viscosity. Both are compressible, though in very different degrees ; if a liquid and a gas both exist under a pressure of one atmosphere, and then the pressure be doubled, the water is compressed by about the 200*600^ P art (75)? while the gas is compressed by one-half. In density there is a great difference ; water, which is the type of liquids, is about 770 times as heavy as -110] Atmospheric Air. 99 air, the type of gaseous bodies, while under a pressure ot one atmosphere. The property by which gases are distinguished from liquids is their tendency to indefinite expansion. Matter assumes the solid, liquid, or gaseous form according to the relative strength of the cohesive and repulsive forces exerted between their particles. In liquids these forces balance ; in gases repulsion preponderates. By the aid of pressure and of very low temperatures, the force of cohesion may be so far increased in many gases that they are converted into liquids ; and there is reason for believing that, with a sufficient degree of pressure and cold, they might all be liquefied. On the other hand, heat, which increases the force of repulsion, converts liquids, such as water, alcohol, and ether, into the aSriform state in which they obey all the laws of gases. This ae'riform state of liquids is known by the name of vapour, while gases are bodies which under ordinary temperature and pressure, remain in the aeriform state. In describing the properties of gases we shall for obvious reasons, have exclusive reference to atmospheric air as their type. no. Atmospheric air. Air is the gaseous fluid in which we v live. It was regarded by the ancients as one of the four elements. Modern chemistry, however, has shown that it is a mixture of oxygen and nitrogen gases in the proportion of 2O'8 volumes of the former to 79^2 volumes of the latter. By weight it consists of 23 parts of oxygen to 77 parts of nitrogen. The oxygen feeds all the combustions, which are produced round about us ; and it also supports animal life. If it alone were present, or even if it were present in a larger proportion, the combustions would be too brisk, and life too active. The coal of our fireplaces would burn almost instantaneously, and even the grates in which it is contained would take fire. Life would be promptly destroyed by so active an agent. The function of the nitrogen is to attenuate the too powerful effects of the oxygen. Air is inodorous, transparent, and colourless, at any rate in small masses. In larger masses it is blue ; thus arises the blue colour of the sky. Without air the celestial vault would appear black ; it appears almost so when viewed from the tops of very high mountains, and from balloons ; for then the air above is very highly rarefied. Air too, in virtue of its elasticity, is the medium for transmitting sounds ; so that, if we were without it, the use of speech and of music would be lost. H 2 100 On Gases. [Ill- Fig. 87. ill. Expansibility of gases. This property of gases, their tendency to assume continually a greater volume, is exhibited by means of the following experiment. A bladder closed by a stop- cock, moistened so as to render it more flexible, and about half full of air, is placed under the receiver of the air pump (rig. 87), and a partial vacuum is produced, on which the bladder immediately distends. This arises from the fact that the molecules of air repel each other, and press against the sides of the bladder. Under ordinary con- ditions this internal pressure is counter- balanced by the air in the receiver, which exerts an equal and contrary pressure. But when this pressure is removed by exhausting the receiver, the internal pressure becomes evident. When air is again admitted into the receiver the bladder resumes its original form. The same effects would be produced what- ever gases were contained in the bladder, thus showing that all are expansible. 112. "Weight of gases. From their extreme fluidity and expansibility, gases seem to be unin- fluenced by the force of gravity ; they nevertheless possess weight, like solids and liquids. To show this, a glass globe of 3 or 4 quarts capacity is taken (fig. 88), the neck of which is provided with a stop-cock, which hermetically closes it, and by which it can be screwed to the plate of the air pump. The globe is then completely exhausted, and its weight determined by means of a delicate balance. Air is now allowed to enter, and the globe again weighed. The weight in the second case will be found to be greater than before, and if the capa- city of the vessel is known, the increase will ob- viously be the weight of that volume of air. By a modification of this method, and with the adoption of certain precautions, the weight of air and of other gases has been determined : 100 cubic inches of dry air under the ordinary atmospheric pressure of 30 in. and at the temperature of 16 C., weigh 31 grains ; the same volume of carbonic acid gas under the same circumstances weighs Fig. 88. - 114] A tmospheric Pressure. i o I 47-25 grains ; 100 cubic inches of hydrogen, the lightest of all gases, weigh 2-14 grains; and 100 cubic inches of hydriodic acid gas weigh 146 grains. The ratio of the destiny of air at o C. and 30 inches pressure to that of water at o C. is found to be O'ooi296. In other words, the latter is about 770 times as heavy as the former. 113. The atmosphere. Experiments proving its weight. The atmosphere is the name given to the layer of air which, like a light coating, surrounds our globe in every part. It shares the rotatory motion of the globe, and would remain fixed relatively to terrestrial objects, but for local circumstances, which produce winds, and are constantly disturbing its equilibrium. The existence of this gaseous mass is proved by the winds, which incessantly blow on the surface of the earth ; by the flight of birds, and the suspension of clouds. Besides the oxygen and nitrogen of which the air is composed, it also contains a quantity of aqueous vapour, which varies with the temperature, the season, the locality, and the direction of the winds. The mean amount of this in London is from 5 to 6 grains in a cubic foot of air. It further contains from 3 to 6 parts in 10,000 of carbonic acid. This arises from the respiration of man and animals, from the decay of organic matter, and from the combustion of wood and coal. ' This latter cause of the production of carbonic acid increases every year. It has been calculated that in Europe alone about ioj. mil- liards of cubic yards of carbonic acid are every year sent into the atmosphere from this source. This mass of gas is equal to what would be produced by 509 millions of individuals, each by the act of respiration converting 1 54 grains of carbon in the system into carbonic acid every hour. Notwithstanding this enormous continual production of carbonic acid on the surface of the globe, the composition of the atmosphere does not vary ; for plants in the process of vegetation decompose the carbonic acid, assimilating the carbon, and restoring to the atmosphere the oxygen which is being continually, consumed in the processes of respiration and combustion. Thus, by a natural harmony, the atmosphere retains an almost uniform quantity of this gas, so that there is no fear of its accu- mulating to such an extent as to be injurious to the human species. 1 14. Atmospheric pressure. Having seen that air has weight, it is easy to conceive that the great mass of air which constitutes 1O2 On Gases. [114- the atmosphere must exert a great pressure on the surface of the earth, arid on all bodies found there. This pressure is called the atmospheric pressure. It necessarily decreases as we ascend in the atmosphere ; for if we conceive the atmosphere resolved into horizontal layers superposed on each other, it is clear that the lower layers which support the weight of the whole atmosphere are the most compressed, and the most dense ; while the higher layers are less and less compressed, and therefore less and less dense. This is expressed by saying that they are more rarefied or more rare. In saying that 100 cubic inches of air weighed 31 grains, it was understood that air at the sea level was referred to ; at any greater height this volume of air' would weigh less. The pressure of the atmosphere may be demonstrated by a number of experiments, among which are the following : 115. Crushing force of the atmosphere. On one end of a stout glass cylinder, about 5 inches high, and open at both ends, a Fig. 90- piece of bladder is tied quite air-tight. The other end, the edge of which is ground and well greased, is pressed on the plate of the air- pump (fig. 89). The bladder is pressed downwards by the weight of the atmosphere, and is pressed upwards by the expansive force of the air in the cylinder. These two pressures at first counterbalance each other ; the bladder is not pressed in either direction, but as soon as ; the internal air is removed from the vessel, by working the air-pump, the bladder is depressed by the weight of the atmo- 116] Magdeburg HcmispJieres. 103 sphere above it, and finally bursts with a loud report caused by the sudden entrance of the air. 116. Magdeburg; hemispheres. The preceding experiment only serves to illustrate the downward pressure of the atmosphere. By means of the Magdeburg hemispheres (fig. 90), the invention of which is due to Otto von Guericke, burgomaster of Magdeburg, it can be shown that the pressure acts in all directions. This ap- paratus consists of two hollow brass hemispheres of 4 to 4^ inches Fig. 91. diameter, the edges of which are made to fit tightly, and are well greased. One of the hemispheres is provided with a stopcock, by which it can be screwed on the air-pump, and on the other there is a handle. As long as the hemispheres contain air they can be separated without any difficulty, for the external pressure of the atmosphere is counterbalanced by the elastic force of the air in the interior. But when the air in the interior is pumped out by means of the air-pump, the hemispheres cannot be separated with- out a powerful effort, fig. 91 ; and as this is the case in whatever position they are held, it follows that the atmospheric pressure is transmitted in all directions. We shall presently see (119) that the pressure of the atmosphere 104 On Gases. [116 on a square inch is about 15 Ibs. Hence if in the above experiment, the area, not of each of the hemispheres, but of the circle along which they are pressed, is 10 square inches, the force by which they are pressed together is 150 Ibs. and this force would be required to separate them. It is related that Otto von Guericke, the inventor of this appa- ratus, constructed hemispheres the internal diameter of which was about 2 feet ; when applied against each other and exhausted, twelve horses, six pulling at each hemisphere, were required to separate them. DETERMINATION OF THE ATMOSPHERIC PRESSURE. BAROMETERS. 117. Torricelli's experi- ment. The above experiments demonstrate the existence of the atmospheric pressure, but they give no indications as to its amount. The following experi- ment, which was first made in 1643 by Torricelli, a pupil of Galileo, not merely proves the pressure of the atmosphere, but also gives an exact measure of its weight. A glass tube is taken, about a yard long, and a quarter of an inch internal diameter (fig. 92). It is sealed at one end, and is quite filled with mercury. The aperture C being closed by the thumb, the tube is inverted, the open end placed in a small mercury trough, and the thumb removed. The tube being in a vertical position, the column of mercury sinks, and after oscil- lating some time, it finally comes to rest at a height A, which at Fig. 92. the level of the sea is about thirty inches above the mercury in the trough. The mercury is raised in the tube by the pressure of -119] A mount of the A tmospheric Pressure 105 the atmosphere on the mercury in the trough. There is no contrary pressure on the mercury in the tube, because it is closed. But if the end of the tube be opened, the atmosphere will press equally inside and outside the tube, and the mercury will sink to the level of that in the trough. It has been shown in hydrostatics (88) that the heights of two columns of liquid in communication with each other are inversely as their densities ; and hence it follows, that the pressure of the atmosphere is equal to that of a column of mer- cury, the. height of which is thirty inches. That the mercury sank in the first case was due to its weight being greater than the pressure of the atmosphere. If, however, the weight of the atmosphere diminishes, the height of the column which it can sustain must also diminish. 1 1 8. Pascal's experiments. Pascal, who wished to prove that the force which sustained the mercury in the tube was really the pressure of the atmosphere, made the following experiments : i. If it were the case, the column of mercury ought to descend in propor- tion as we ascend in the atmosphere (i 14). He accordingly requested one of his relations to repeat Torricelli's experiment on the summit of the Puy de Dome in Auvergne. This was done, and it was found that the mercurial column was about three inches lower, thus proving that it is really the weight of the atmosphere which supports the mercury, since, when this weight diminishes, the height of the column also diminishes, ii. Pascal repeated Torricelli's experiment at Rouen, in 1646, with other liquids. He took a tube closed at one end, nearly 40 feet long, and having filled it with water, placed it vertically in a vessel of water, and found that the water stood in the tube at a height of 34 feet ; that is, 1 3-6 times as high as mercury. But since mercury is 13-6 times as heavy as water, the weight of the column of water was exactly equal to that of the column of mercury in Torricelli's experiment, and it was con- sequently the same force, the pressure of the atmosphere, which successively supported the two liquids. Pascal's other experiments with oil and with wine gave similar results. He found, for in- stance that a column of oil stood at a height of about 37 feet. 119. Amount of the atmospheric pressure. Let us assume that the tube in the above experiment is a cylinder, the cross-section of which is equal to a square inch, then, since the height of the mercurial column in round numbers is 30 inches, the column will contain 30 cubic inches, and as a cubic inch of mercury weighs 3433-5 grains = 0-49 of a pound, the pressure of such a column on a io6 On Gases. [119- square inch of surface is equal to 14*7 pounds. In round numbers the pressure of the atmosphere is taken at 15 pounds on the square inch. A surface of a foot square contains 144 square inches, and therefore the pressure upon it is equal to 2,160 pounds, or nearly a ton. A gas or a liquid which acts in such a manner that a square inch of surface is exposed to a pressure, 1 5 pounds, is said to exert a pressure of one atmospliere. If, for instance, the elastic force of the steam of a boiler is so great that each square inch of the internal surface is ex- posed to a pressure of 90 pounds ( = 6x 15), we say it was under a pressure of six atmospheres. 120. Different kinds of baro- meters. The instruments used for measuring the atmospheric pressure are called barometers, from two Greek words which signify measure of weight (air, of course, being understood). In ordinary ba- rometers, the pressure* is measured by the height of a column of mer- cury, as in Torricelli's experiment ; the barometers which we are about to describe are of this kind. But there are barometers without mercury, one of which, the aneroid (135) is remarkable for its simplicity and portability. 121. Cistern barometer. Or- dinary barometers are classed as syphon and cistern barometers. Fig. 93 represents the usual form of the cistern barometer. It consists of a glass tube ai, closed at one end, about thirty-three inches long, Fig. 93. and about half an inch in diameter. The tube is filled with mercury, and then its open end is inverted -122] Fortiris Barometer. 107 in mercury contained in a glass vessel, A, of a peculiar shape ; only the front half of this is visible, the other being fixed in a mahogany board which supports the whole barometer. The bottom of the cistern forms a spherical well, which is filled with mercury, and in which the tube ai is immersed. The tube is not fixed tightly in the neck, so that the atmospheric pressure can be freely trans- mitted to the mercury of the bath, and thus supports the column of mercury ai. If the pressure increases the mercury rises, if it de- creases the mercury sinks. At the top of the tube on the right is a scale divided in inches to measure the height of the mercury in the tube. The graduation starts from the zero which is level with the mercury in the bath. Hence, if the top of the mercury at a stands at thirty inches, for instance, this signifies that the height of the column of mercury is thirty inches. Only a portion of the scale is given, since, for ordi- nary purposes, the variations of the atmospheric pressure are within a few inches. Where greater variations occur, as in the use of the barometer for measuring heights, the graduated part must be longer. It will be observed that the starting-point of the graduation, the zero, is at the level of the mercury in the cistern. But the zero of the scale does not always correspond to the level of the mercury in the cistern. For as the atmospheric pressure is not always the same, the height of the mercurial column varies ; sometimes mercury is forced from the cistern into the tube, and sometimes from the tube into the cistern, so that, in the majority of cases, the graduation of the barometer does not indicate the true height. To diminish this source of error, the cistern has the form represented in fig. 93. Its upper part, that corresponding to the level of the mercury, is about four inches in diameter ; so that, whether the mercury passes from the cistern into the tube, or from the tube into the cistern, as it is spread over a large surface the variations in the level are very small and may be neglected. To complete this description it may be added, that on the scale is a small index, c, sliding along a vertical rod. When made level with the mercury this index points on the one side to the divisions on the graduated scale, and, on the other side, to certain inscriptions, the use of which will be afterwards stated (127). Lastly, in the middle of the tube are two thermometers, one with a Fahrenheit and the other with a Centigrade graduation. 122. Fox-tin's barometer. Forties barometer (fig. 94) differs io8 On Gases. [122- from that just described, in the shape of the cistern. The base of the cistern is made of leather, and can be raised or lowered by means of a screw ; this has the advantage, that a constant level can be obtained, and also that the instrument is made more portable. For, in travelling, it is only necessary to raise the leather until the mercury, which rises with it, quite fills the cistern ; the ba- rometer may then be inclined, and even inverted, without any fear that a bubble of air may enter, or that the shock of the mercury may crack the tube. Fig. 95 shows the construction of the cistern. It consists of a glass cylinder, &, which allows the mer- cury to'be seen ; the bottom of the cylinder is cemented to a box-wood cylinder, zz, on which is firmly fixed at ii the chamois leather, inn, which is the base of the cistern. At the bottom of this leather is a small wooden button, r, against which the screw C works, by which it is raised or lowered. This screw works in the bottom of a brass cylinder, G, which is fastened on the glass cylinder. At the top of the cistern there is a small ivory pointer, a, the point of which exactly cor- responds to the zero on the scale. The upper part of the cistern is closed by buckskin, ce, which is fastened to the barometer tube, E, and to a tubulure in the wooden disc, which Fig. 94. covers the cistern. The barometer tube is drawn out at the open end, which is immersed in the mercury. The atmo- spheric pressure is transmitted through the pores of the leather. In using this barometer, the mercury is first made level with the point a, which is effected by turning the screw C either in one direction or the other. In this manner the distance of the top, B, of the column of mercury from the ivory point a, gives Fig. 95- -123] Gay-Lussacs Syphon Barometer. 109 , exactly the height of the barometer. For the graduation is measured from the point a. Lastly, the lower part of the cistern is enclosed in a brass case, which is connected with the lid by three screws k, k, k. To the cistern is screwed a long brass case, which encloses the whole of the tube, as seen in figure. At the top of this case there are two longitudinal slits, on opposite sides, so that the level of the mercury, B, is seen. The scale on the case is graduated in millimetres or in inches. An index, A, moved by the hand, gives, by means of a vernier, the height j of the mercury to ~ of a milli- metre. At the bottom of the case is affixed a thermometer to indicate the temperature. 123. Gay-Xrtissac's syphon barometer. The syphon baro- meter has no cistern, but con- sists of a bent glass tube (fig. 96), one of the branches of which is much longer than the other. The longer branch, which is closed at the top, is filled with mercury as in the cistern baro- meter, while the shorter branch, which is open, serves as a cistern. The difference between the two levels is the height of the barometer. Fig. 96 represents the syphon barometer as modified by Gay- Lussac. In order to render it more available for travelling, -by preventing the entrance of air, I . . , & , ' he joined the two branches by a capillary tube ; when the instrument is inverted (fig. 97), the tube always remains full in virtue of its capillarity, and air cannot pene- trate into the longer branch, which, of course, is absolutely necessary. A sudden shock, however, might separate the mercury and admit some air. To avoid this M. Bunten has introduced an ingenious modification into the apparatus. The longer branch, A, is drawn out to a fine point, and is joined to a tube, B, of the form repre- . 96. Fig. 97 . Fig. 9 8. IIO On Gases. [123- sented in fig. 98. By this arrangement, if air passes through the capillary tube, it cannot penetrate the drawn-out extremity of the longer branch, but lodges in the upper part of the enlargement B. Jn this position it does not affect the observations, since the vacuum is always at the upper part of the tube ; it is, moreover, easily removed. In Gay-Lussac's barometer the shorter branch is closed, but there is a lateral capillary aperture *, through which the at- mospheric pressure is transmitted. The barometric height is determined by means of two scales, which have a common zero at the middle of the longer branch, and are graduated in contrary directions, the one from the middle to a, and the other from the middle to b, either on the tube itself, or on brass rules fixed parallel to the tube. Two sliding indexes are moved until they correspond to the level of the mercury in a and b. The total height of the barometer ab is the sum of the distances from the middle to a and b respectively. 124. Precautions in reference to barometers. In constructing barometers, mercury is chosen in preference to any other liquid. For being the densest of all liquids it stands at the least height When the mercurial barometer stands at thirty inches, the water barometer would stand at about thirty-four feet. It also deserves preference because it does not moisten the glass. It is necessary that the mercury be pure and free from oxide ; otherwise it adheres to the glass and tarnishes it. Moreover, if it is impure its density is changed, and the height of the barometer is too great or too small. Mercury is purified, before being used for barometers, by treatment with dilute nitric acid, and by distillation. The space at the top of the tube (figs. 96 and 99), which is called the Torricellian vacuum, must be quite free from air and from Fig. 99- -125] Variations in the Height of the Barometer. 1 1 1 aqueous vapour, for otherwise either would depress the mercurial column. Now, glass tubes always condense aqueous vapour on their surface. Under the ordinary pressure of the atmosphere this layer of moisture adheres to the glass ; but in a vacuum where there is no pressure it escapes, and there is formed a mix- ture of air and aqueous vapour which depresses the mercurial column. The air and moisture ran only be got rid of by boiling the mercury in the tube. To obtain this result, a small quantity of pure mercury is placed in the tube and boiled for some time, fig. 100. Fig. too. It is then allowed to cool, and a further quantity, previously warmed added, which is boiled, and so on, until the tube is quite full ; in this manner the moisture and the air which adhere to the sides of the tube pass off with the mercurial vapour. The bulb at the end is placed there to collect the mercury which may distil over. It is afterwards removed. A barometer is free from air and moisture if, when it is inclined, the mercury strikes with a sharp metallic sound against the top of the tube. If there is air or moisture in it, the sound is deadened, 125. Variations in the height of the barometer. When the barometer is observed for several days, its height is found to vary in the same place, not only from one day to another, but also during the same day. The extent of these variations, that is, the difference between the greatest and the least height, is different in different places. It in- creases from the equator towards the poles. The greatest variations are observed in winter. 112 On Gases. [125- The mean daily height is the height obtained by dividing the sum of 24 successive hourly observations by 24. In our latitudes, the barometric height at noon corresponds to the mean daily height. The mean monthly height is obtained by adding together the mean daily heights for a month, and dividing by 30. The mean yearly height is similarly obtained. Under the equator, the mean annual height at the level of the sea is o m "758, or 29-14 inches. It increases from the equator, and between the latitudes 30 and 40, it attains a maximum of o m 763, or 30-04 inches. In lower latitudes it decreases, and in Paris it does not exceed o m 7568. The general mean at the level of the sea is o m 76i or 29-96 inches. The mean monthly height is greater in winter than in summer, in consequence of the cooler atmosphere. Two kinds of variations are observed in the barometer : ist, the accidental variations, which present no regularity ; they depend on the seasons, the direction of the winds, and the geographical position, and are common in our climates : 2nd, the daily varia- tions, which are produced periodically at certain hours of the day. At the equator, and between the tropics, no accidental variations are observed ; but the daily variations take place with such regu- larity that a barometer may serve to a certain extent as a clock. The barometer sinks from midday till towards four o'clock ; it then rises, and reaches its maximum at about ten o'clock in the evening. It then again sinks, and reaches a second minimum towards four o'clock in the morning, and a second maximum at ten o'clock. In the temperate zones there are also daily variations, but they are detected with difficulty, since they occur in conjunction with ac- cidental variations. The hours of the maxima and minima appear to be the same in all climates, whatever be the latitude ; they merely vary a little with the seasons. 126. Causes of barometric variations. It is observed that the course of the barometer is generally in the opposite direction to that of the thermometer; that is. that when the temperature rises the barometer falls, and vice versa ; which indicates that the barometric variations at any given place are produced by the ex- pansion or contraction of the air, and therefore by its change in density. If the temperature were the same throughout the whole extent of the atmosphere, no currents would be produced, and at -127] Barometric Variations. 1 1 3 the same height^ the atmospheric pressure would be everywhere the same. But when any portion of the atmosphere becomes warmer than the neighbouring parts, its specific gravity is dimin- ished, and it rises and passes away through the upper regions of the atmosphere ; whence it follows that the pressure is diminished, and the barometer falls. If any portion of the atmosphere retains its temperature, while the neighbouring parts become cooler, the same effect is produced ; for in this case, too, the density of the first-mentioned portion is less than that of the others. Hence, also, it usually happens, that an extraordinary fall of the barometer at one place is counterbalanced by an extraordinary rise at another place. The daily variations appear to result from the expansions' and contractions which are periodically produced in the atmosphere by the heat of the sun during the rotation of the earth. 127. Relation of barometric variations to the state of the V weather. It has been observed that, in our climate, the baro- meter in fine weather is generally above 30 inches, and is below this point when there is rain, snow, wind, or storm, and also, that for any given number of days on which the barometer stands at 30 inches, there are as many fine as rainy days. From this coinci- dence between the height of the barometer and the state of the weather, the following indications have been marked on the barometer, counting by thirds of an inch above and below 30 inches : Height State of the weather 3 1 inches . . . . . . Very dry. 3of . . . , . Settled weather. 30^ . . . . . . Fine weather. 30 Variable. 29! Rain or wind. 29^ .,.... Much rain. 29 ... . . . Tempest. In using the barometer as an indicator of the state of the weather, we must not forget that it really only serves to measure the weight of. the atmosphere and that it only rises or falls as this weight in- creases or diminishes ; and although a change of weather fre- quently coincides with a change in the pressure, they are not necessarily connected. This coincidence arises from meteorolo- gical conditions peculiar to our climate, and does not always occur. That a fall in the barometer usually precedes rain in our latitudes, is caused by the position of Europe. The south-west winds, which I 114 On Gases. [127- are hot, and consequently light, make the barometer sink ; but at the same time as they become charged with aqueous vapour in crossing the ocean, they bring us rain. The winds of the north and north-east, on the contrary, being colder and denser, make the Fig, 101. Fig. 102. barometer rise ; and, as they only reach us after having passed over vast continents, they are generally dry. When the barometer rises or sinks slowly, that is,- for two or Determination of the Heights of Places. 115 three days, towards fine weather or towards rain, it has been found, from a great number of observations, that the indications are then extremely probable. Sudden variations in either direction indicate bad weather or wind. 1 23. Wheel barometer. The wheel barometer, which was in- vented by Hooke, is a syphon barometer, and is especially intended to indicate good and bad weather (fig. 101). In the shorter leg of the syphon there is a float a, which rises and falls with the mercury (fig. 102), A string attached to this float passes round a pulley, and at the other end there is another and somewhat lighter weight. A needle fixed to the pulley moves round a graduated circle, on which is marked variable, rain, fiiu weather, etc. When the pressure varies the float sinks or rises, and moves the needle round to the corresponding points on the scale. The barometers ordinarily met with in houses, and which are called weather glasses, are of this kind. They are, however, of little use, for two reasons. The first is, that they are neither very delicate nor precise in their indications. The second, which applies equally to all barometers, is, that those commonly in use in this country are made in London, and the indications, if they are of any value, are only so for a place at the same level and of the same climatic conditions as London. Thus a barometer standing at a certain height in London would indicate a certain state of weather, but if removed to Shooter's Hill it would stand half an inch lower, and would indicate a different state of weather. As the pressure differs with the level and with geographical conditions, it is neces- sary to take these into account if exact data are wanted. 129, Determination of the heights of places by the baro- meter. One of the most important of the uses of the barometer has been its application to the measurement of the heights of places above the sea level. For, if we suppose the atmosphere divided into horizontal layers of equal thickness, a hundred for instance, a barometer at the sea level would support the weight of a hundred of these layers ; and, as we have seen (117), would be at rest when its height was thirty inches. If it were raised in the atmo- sphere to the height of ten such layers, it would now only support the weight of ninety such layers, and the mercury would therefore necessarily sink. It would sink still further if it were raised to the twentieth layer, and so on to the limit of the atmosphere if that were possible. There it would be under no pressure, and the level of the mercury in the tube and in the cistern would be the same. I 2 Ii6 On Gases. [129- As the mercury sinks in proportion as we rise in the atmosphere, we might, from the amount by which it is lower, deduce the height above the sea level. If air had everywhere the same density up to the extreme limit of the atmosphere, the calculation would be very simple ; for as mercury is about 10,500 times as heavy as air, an inch of the barometer would correspond to a column of air about 875 feet ; hence, in ascending a mountain, a diminution of an inch in the height of the barometer would correspond to an ascent of about 875 feet. But the density of the air decreases as we ascend, for the layers of air necessarily support a less weight ; hence, the measurement of the heights by the barometer is not so simple as we have supposed. Very complete tables have, however, been constructed, by which the difference in height between any two places may be readily ascertained, if we know the corresponding heights of the barometer. For small elevations we may assume that an ascent of 900 feet produces a depression of an inch in the height of the barometer. For measuring heights by the barometer the aneroid (135) is extremely convenient. 130. Height of the atmosphere. In virtue of the expansive force of the air, it might be supposed that the molecules would expand indefinitely into the planetary spaces. But, in proportion as the air expands, its expansive force decreases, and is further weakened by the low temperature of the upper regions of the atmosphere, so that, at a certain height, an equilibrium is estab- lished between the expansive force which separates the molecules, and the action of gravity which draws them towards the centre of the earth. It is therefore concluded that the atmosphere is limited. From the weight of the atmosphere, and its decrease in density, and from the observation of certain phenomena of twilight, its height has been estimated at from 30 to 40 miles. Above that height the air is extremely rarefied, and at a height of 60 miles it is assumed that there is a perfect vacuum. From certain observa- tions recently made in the tropical zone, and particularly at Rio Janeiro, on the twilight arc, M. Liais estimates the height of the atmosphere at between 198 and 212 miles, considerably higher, therefore, than what has hitherto been believed. ILLUSTRATIONS OF ATMOSPHERIC PRESSURE. 131. The pressure of the atmosphere is transmitted in all directions. The atmosphere, like any other mass of fluid (76), -132] Pressure supported by the Hitman Body. 1 1 7 must necessarily transmit its pressure in all directions, upwards and laterally as well as downwards. We have already seen a striking instance of this in the Magdeburg hemispheres (116), and the following experiment furnishes another illustration of this point. A tumbler full of water is carefully covered with a sheet of paper, which is kept in position by one hand, while with the other the tumbler is inverted. Removing then the hand which held the paper, the water does not fall out, both water and paper being kept in position by the upward pressure (fig. 103). The object of the paper is to present a flat surface of water, for otherwise the water would divide and would allow air to enter, and then the. experiment would fail. The use of the wine-tester also depends on the pressure of the Fig. 103. Fig. 104. atmosphere. It consists of a tin tube (fig. 104), terminating at the bottom in a small cone, the end of which, o, is open ; at the top there .is a small aperture, which is closed by the thumb. The two ends being open, the tube is immersed in the liquid to be tested ; closing then the upper end .by the thumb, as shown in the figure, the tube is withdrawn, and remains filled in consequence of the pressure at o. But if the thumb be withdrawn the pressure is transmitted both upwards and downwards, and the liquid flows out in obedience to the action of gravity. 132. Pressure supported by tne human body. The surface of the body of a man of middle size is about 16 square feet ; the pressure, therefore, which a man supports on the surface of his body is 37,560 pounds, or upwards of 16 tons. Such an enormous pressure might seem impossible to be borne ; but it must be re- membered that in all directions there are equal and contrary pres- sures which counterbalance one another. It might also be supposed On Gases. [132- that the effect of this force, acting in all directions, would be to press the body together and crush it. But the solid parts of the skeleton could resist a far greater pressure ; and as to the liquids contained in the organs and vessels, from what has been said about liquids (75), it is clear that they are virtually incompressible. The gases, too, are compressed by the weight of the atmosphere, but they resist it in virtue of their elasticity. They are, in short, like a bottle full of air. The sides of the latter are pressed in by the weight of the atmosphere; but they can stand this. however thin their walls, for the pressure of the gas from within quite counter- balances that which presses on the out- side. The following experiment (fig. 105) illustrates the effect of atmospheric pressure on the human body. A glass vessel open at both ends, being placed on the plate of the air-pump, the upper Fig. 105. end of the cylinder is closed by the hand and a vacuum is made. The hand then becomes pressed by the weight of the atmosphere, and can only be taken away by a great effort. And as the elasticity of the gas contained in the organs is not counterbalanced by the weight of the atmosphere, the palm of the hand swells, and blood tends to escape from the pores. The operation of cupping in medicine is an application of the effect of removing the atmospheric pressure from the human body. The human mouth applied upon any part, in the action of sucking, is a kind of cupping apparatus. The mouth of the leech is such an apparatus with one lancet. CHAPTER II. MEASUREMENT OF THE ELASTIC FORCE OF GASES. 133. Boyle's law. The law of the compressibility of gases was discovered by Boyle, and subsequently, though independently, by Mariotte. In consequence it is in England commonly called Boyle's law, and on the Continent Mariotte's law. It is as follows : -133] Boyle's Law. 119 ' The temperature remaining the same, the volume of a given quantity of gas is inversely as the pressure which it bears. This law is verified by means of an apparatus called Mariotte's tube (fig. 1 06). It consists of a long glass tube fixed to a vertical Fig. 106. Fig. 107. support : it is open at the top ; and the other end, which is bent into a short vertical leg, is closed. On the shorter leg there is a scale, which indicates equal capacities ; the scale against the long leg gives the heights. The zero in both scales is in the same hori- zontal line. A small quantity ot mercury is poured into the tube, so that its level in both branches is at zero, which is effected without much 120 On Gases. [133- difficulty. The air in the short leg is thus under the ordinary atmo- spheric pressure. If mercury is then poured into the longer tube the volume of the air in the smaller tube is gradually reduced. If this be continued until it is only one-half, that is, until it is reduced from 10 to 5, as shown in figure 107, and if the height of the mer- curial column , C A, be no w measured, it will be found exactly equal to the height of the barometer at the time of the . experiment. The pressure of the column CA is therefore equal to an atmosphere, which, with the atmospheric pressure acting on the surface of the column at C, makes two atmospheres. Accordingly, by doubling the pressure, the volume of the gas has been diminished to one-half. If mercury be poured into the longer branch until the volume of the air is reduced to one-third its original volume, it will be found that the distance between the level of the two tubes is equal to two barometric columns. The pressure is now three atmospheres, while the volume is reduced to one-third. Dulong and Petit have verified the law for air up to 27 atmospheres, by means of an apparatus analogous to that which has been described. The law also holds good in the case of pressures of less than one atmosphere. To demonstrate this, Fig. 109. mercury is poured into a graduated tube, until it is about two-thirds full, the rest being air. It is then inverted in a deep trough containing mercury (fig. 108), and lowered until the levels of the mercury inside and outside the tube are the same, and the volume AB, which is then under a pressure of one atmosphere, is noted. The tube is then raised, as represented in fig. 109, until the volume of the air, AC, is doubled. The height of the mercury in the tube, above the mercury in the trough, is then Fig. 108. -134] Manometers. 1 2 1 found to be exactly half the height of the barometer at the time of the experiment. Accordingly, for half the pressure the volume has been doubled. In the experiment with Mariotte's tube, as the quantity of air remains the same, its density must obviously increase as its volume diminishes, and vice versa. The law may thus be enunciated : ' For the same temperature the density of a gas is proportional to' its pressure' Hence, as water is 773 times as heavy as air, under a pressure of 773 atmospheres air would be as dense as water. Until within the last few years Boyle's law was supposed to be absolutely true for all gases at all pressures ; but several physicists have since observed that the gas is not rigorously exact, especially in the case of those gases which can be liquefied. They are more compressed than is required by the law. For air, Dulong and Arago investigated the pressure up to 27 atmospheres, and observed that the volume of air always diminished a little more than is re- quired by Boyle's law. But, as these differences were very small, they attributed them to errors of observation, and concluded that the law was perfectly exact, at any rate up to 27 atmospheres. For ordinary pressures Boyle's law may be assumed to be exact for all gases. 134. Manometers. Manometers are instruments for measuring the elastic force of gases or vapours. In all manometers the unit chosen is the pressure of one atmosphere, or 30 inches of mercury at the standard temperature, which, as we have seen, is nearly 1 5 Ibs. to the square inch. The open air manometer is represented in fig. 1 10 fixed against a board fastened to a wall, and connected with a steam boiler. It consists of a glass tube about 20 feet in height open at the top, and fixed at the other end to a glass bath C, con- taining mercury. A long tube connects this with the boiler. When the elastic force of the vapour in the boiler is equal to the pressure of the atmosphere, it will counterpoise the weight ot the atmosphere which is transmitted through the tube, and the level of the mercury is then the same in the tube and in the bath. At this level the number i is marked on the board. Then since a column of mercury 30 inches in height represents a pressure of an atmosphere, the number 2 is marked at this height above i ; at a height of 30 inches above this the number 3 is marked, and so on, each interval of 30 inches representing an atmosphere. Thus, for instance, if the mercury had been forced up to 3^, as represented in the drawing that would indicate that the tension of the vapour in 22 On Gases. [134 the boiler is 3^ atmospheres ; so that, on each square inch of the internal surface of the boiler, there is a pressure of 3^+15. pounds, or 52 j pounds. The manometer with compressed air is founded on Mariotte's law : it consists of a glass tube closed at the top (fig. in), and filled with dry air. It is firmly cemented in a small bath containing mercury. By a tubulure, this bath is connected with the closed vessel containing all the gas or vapour whose elastic force is to be measured. -135] Aneroid Barometer. 123 In the graduation of this manometer, the quantity of air con- tained in the tube is such, that when the aperture communicates freely with the atmosphere, the level of the mercury is the same in the tube and in the bath. Consequently, at this level, the number i is marked on the scale to which the tube is affixed. As the pressure acting through the tubulure A increases, the mercury rises in the tube, until its weight added to the elastic force of the com- pressed air, is equal to the external pressure. It would consequently be incorrect to mark two atmospheres in the middle of the tube ; Fig. 112. for since the volume of the air is reduced to one-half, its elastic force is equal to two atmospheres, and, together with the weight of the mercury raised in the tube, is therefore more than two atmo- spheres. The position of the number is a little below the middle, at such a height that the elastic force of the compressed air, together with the weight of the mercury in the tube, is equal to two atmospheres. The exact position of the numbers 2, 3, 4, etc., on the manometer scale can only be determined by calcula- tion. 135. Aneroid barometer. This instrument derives its name 124 On Gases. [135- from the circumstance that no liquid is used in its construction (a, without, vnpbc, moist). Fig. 112 represents one of the forms of these instruments constructed by Mr. Casella ; it consists of a cylindrical metal box, exhausted of air, the top of which is made of thin cor- rugated metal, so elastic that it readily yields to alterations in the pressure of the atmosphere. When the pressure increases, the top is pressed inwards ; when on the contrary it decreases, the elasticity of the lid, aided by a spring, tends to move it in the opposite direction. These motions are transmitted by delicate multiplying levers to an index which moves on a scale. The instrument is graduated empirically by comparing its indications under different pressures with those of an ordinary mercurial barometer. The aneroid has the advantage of being portable, and can be constructed of such delicacy as to indicate the difference in pressure between the height of an ordinary table and the ground. It is hence much used in surveying and in determining heights in mountain ascents. But it is somewhat liable to get out of repair, especially when it has been subjected to great variations of pres- sure : and its indications must from time to time be compared by means of a standard barometer. MIXTURE AND SOLUTION OF CASES. 1 36. Laws of the mixture of gases. We have seen that liquids, when they do not act chemically on each other, tend continually to separate, and to become superposed in the order of their densities. This is not the case with gases ; being under a continual tendency to expand, when they mix, their mixture is found to be subject to the following laws : I. Whatever their densities, gases mix in equal proportions in all parts of the vzssel in which they are contained. II. The elastic force of the mixture is equal to the sum of the elastic forces of the constituents. The first law was shown experimentally by Berthollet, by means of an apparatus represented in fig. 113. It consisted of two glass globes provided with stopcocks, which could be screwed one on the other. The upper globe was filled with hydrogen, and the lower one with carbonic acid, which has 22 times the density of hydrogen. The globes having been fixed together were placed in the cellars of the Paris Observatory, and the stopcocks then opened, the globe -137] Mixture of Gases and Liquids. 12=; containing hydrogen being uppermost. Bertholiet found, after some time, that the pressure had not changed, and that, in spite of the difference in density, the two gases had becorne uniformly mixed in the two globes. Experiments made in the same manner with other gases gave the same results, and it was found that the diffusion was more rapid in proportion as the difference between the densities was greater. In accordance with this law, air being a mixture of nitrogen and oxy- gen, which are different in density, its composition should be the same in all parts of the atmosphere, which in fact is what has been ob- served. Gaseous mixtures follow Boyle's law, like simple gases, as has been proved for air (133), which is a mix- ture of nitrogen and oxygen. 137. Mixture of gases and liquids. many liquids possess the property of absorbing gases. Under the same conditions of pressure and temperature a liquid does not absorb equal quantities of different gases. At the ordinary tem- perature and pressure water dissolves j 2 ^~ its volume of nitrogen, Y*5o i ts volume of oxygen, its own volume of carbonic acid, and 430 times its volume of ammoniacal gas. The general laws of gas-absorption are the following : I . For the same gas, the same liquid, and the same temperature ', the weight of gas absorbed is proportional to the pressure. This may also be expressed by saying that at all pressures the volume dissolved is the same ; or that the density of the gas absorbed is in a constant relation with that of the external gas which is not ab- sorbed. Accordingly, when the pressure diminishes, the quantity of dis- solved gas decreases. If a solution of a gas be placed under the air-pump and a vacuum created, the gas obeys its expansive force and escapes with effervescence. The manufacture of aerated water is a practical application of this law. By means of force-pumps an excess of carbonic acid is Fig. 113. Absorption. Water and 126 On Gases. [137- dissolved in the water, and the solution is then preserved in care- fully closed vessels. It is the carbonic acid dissolved in beer, in champagne, and in all effervescing liquids, which, rapidly escaping when the bottles are uncorked, produces the well-known report, and carries with it a greater or less quantity of the liquid. I 1. The quantity of gas absorbed is greater when the temperature is lower; that is to say, when the elastic force of the gas is less. III. The quantity of gas which a liquid can dissolve is indepen- dent of the nature and of the quantity of other gases which it may already hold in solution. CHAPTER III. APPARATUS FOUNDED ON THE PROPERTIES OF AIR. 138. Air-pump. The air-pump is an instrument by which a vacuum can be produced in a given space, or rather by which air can be greatly rarefied, for an absolute vacuum cannot be pro- duced by its means. It was invented by Otto von Guericke in 1650, a few years after the invention of the barometer. Fig. 114 gives a perspective view of the pump, fig. 115 gives a detailed longitudinal section, and fig. 116 gives a cross section. The pump consists of two stout glass barrels in which twD pis- tons, P and Q, made of leather well soaked with oil, move up and down, and close the barrels air-tight. The pistons are fixed to two racks, A and B, working with a pinion (K, fig. 1 16), which is moved by a handle MN, so that, when one piston rises, the other de- scends. The two barrels are firmly cemented on the base, H, which is of brass ; on this plate is a column, I, terminated by a plate G. On this plate is a glass bell jar which is called the receiver. In the interior of the column is a conduit, which is prolonged below the base to between the two barrels. It there branches in the shape of a T, terminating in two apertures, a and b, in the bottom of the cylinders. These apertures are conical, and are closed by two small conical valves ; these latter are fixed to metal rods which work air-tight, but with gentle friction in the pistons. In the pistons is a cylindrical cavity communicating with the lower part of the pump by two apertures, s and t (fig. 1 16). These apertures are closed -138] A ir-pnmp. 127 by small clack valves, kept in position by springs v/hich surround the rods themselves. The four valves, a, b, s, /, it may be remarked, open upwards. These details being known, the working of the machine is readily Fig. 114. understood. It is sufficient to consider what takes place in a single piston (fig. 114). The piston P being first at the bottom of its stroke, on rising it raises the rod which traverses it, and therewith the valve a, which remains open during the ascent. The valve, /, which is in the piston, remains closed by the action of the spring 128 On Gases. [138- and the pressure of the atmosphere, which acts in the barrel through an aperture, r, in the cover. From this position of the two valves, it will be seen that, as the piston rises, the external pressure of the atmosphere cannot act in the bottom of the barrel, but the air of the receiver, in virtue of its elasticity, expands and passes by the conduit, I and H, into the barrel. The receiver is still full of air, but it is more rarefied ; it is less dense. When the piston descends, the rod which bears the valve, rt, Fig. 115. descending with it, communication between the receiver and the barrel is cut ofY. The air in the barrel becomes more and more compressed, its elastic force increases, and finally overcomes the atmospheric pressure ; so that the valve t> being pressed upwards by the elastic force of the air in the interior more strongly than it is pressed downwards by the atmosphere, is raised, and allows the air of the barrel to escape into the upper part of the barrel, and thence into the atmosphere. Thus a certain quantity of air has -139] A ir-pump. 129 been removed. A fresh quantity is removed at a second stroke of the piston, another at the third, and so on. The air in the receiver is thus gradually more and more rarefied ; yet all the air cannot be entirely extracted, for it ultimately becomes so rarefied both in the receiver and in the barrel, that when the piston P is at the bottom of its stroke, the compressed gas below the piston has no longer sufficient force to overcome the resistance of the atmosphere and force open the valve, /. The limit of rarefaction has then been attained, and it is useless to work the pump any longer. What has been said in refer- ence to one barrel applies also to the other. The machine works with one ; and the first air-pumps had but one. The advantage of having two is that the vacuum is more rapidly produced. The use of double- action air-pumps was first intro- duced by Hawksbee. 139. Measurement of the degree of rarefaction in the receiver. Since a perfect vacuum cannot be obtained in the receiver, it is useful to have a means of ascertaining the de- gree of rarefaction at any par- ticular time. This is effected by means of a glass cylinder, E, connected by a brass cap with the conduit in the column I Fig> Il6- (fig. 114). In this cylinder is placed a bent glass tube, closed at one end and open at the other. This is called the air-pump gauge. It is fixed against a plate, on which is a graduated scale. The closed branch being at first full of mercury, so long as the air in the receiver P and in the cylinder E has sufficient tension, it sustains the mercury in the tube ; the height of which is from six to eight inches. But as the pump is worked the air becomes more and more rarefied, and has no longer the elastic force suffi- cient for retaining the column of mercury in the closed limb. It accordingly sinks in this limb and rises in the other. The greater K 130 On Gases. [139- the rarefaction, the smaller the difference of the level in the two limbs. They are, however, never exactly equal ; that would correspond to a perfect vacuum. The mercury is always at least the ^ tn f an inch higher in the closed branch. This is expressed by saying that a vacuum has been created within -5 th of an inch. 140. Uses of tne air-pump. A great many experiments with the air-pump have been already described. Such are the mercurial rain (fig. i), the fall of bodies in vacuo (fig. 37), the bladder (fig. 87), the bursting of a bladder (fig. 89), the Magdeburg hemispheres (fig. 90), and the baroscope (fig. 1 34). The fountain in vacuo (fig. 117) is an experiment made with the air- pump, and shows well the elastic force of the air. It is a flask con- taining water and air ; the neck is closed by a cork, through which passes a tube dipping in the liquid. The flask being placed under the receiver, a jet of water issues from the top of the tube as soon as the air is sufficiently rarefied. This is due to the elastic force of the air enclosed in the flask. By means of the air-pump it may be shown that air, by reason of the oxygen it contains, is necessary for the support of combustion and of life. For if we place a lighted taper under the receiver and begin to exhaust the air, the flame becomes weaker as rare- faction proceeds, and is finally extin- guished. Similarly an animal faints and dies, if a vacuum is formed in a receiver under which it is placed. Mammalia and birds soon die in vacuo. Fishes and reptiles support the loss of air for a much longer time. Insects can live several days in vacuo. 141. Application of the vacuum to the preservation of food. An important application has been made of the vacuum in preserving food. In air, under the influence of heat, moisture, and oxygen, animal and vegetable matters rapidly ferment and putrefy ; Fig. 117. -142] Condensing Pump. but if the oxygen be removed, either by exhausting or by other means, they may be kept fresh for many years. Appert of Paris was the first in 1 809 to devise a means of pre- serving food in vacuo, or rather in a space deprived of oxygen, which practically amounts to the same. This method consists in placing the substances to be preserved in tin vessels, which are closed hermetically, and then heated in boiling water for some time ; under the influence of heat the small quantity of oxygen left in the vessel is absorbed by the substance placed there, so that only nitrogen is present in the free state, a gas which cannot induce fermentation. Substances properly prepared in this manner may be kept for years without alteration. Appert's method is modified in England in the following manner. Instead of boiling the food while Contained in the closed vessel, a small hole is left in the lid, through which escape the air and vapours produced during ebulli- tion. When it is supposed that all the air has been expelled, a drop of melted lead is allowed to fall on the small hole in the cover which completely closes it. This method is practised on the large scale in preserving food and vegetables for the use of sailors, and also in preserving Australian meat, which is now consumed in large quantities. 142. Condensing- pump. The condensing pump is an ap- paratus for compressing air or any other gas. The form usually adopted is the following : In a cylinder, A, of small diameter (fig. 1 1 8), there is a solid piston, the rod of which is worked by the hand. The cylinder is pro- vided with a screw which fits into the receiver, K. Fig. 119 shows the arrangement of the valves, which are so constructed K 2 132 On Gases. [142- that the lateral valve, o, opens from the outside, and the lower valve, j, from the inside. When the piston descends, the valve o closes, and the elastic force of the compressed air opens the valve s, which thus allows the compressed air to pass into the receiver. When the piston ascends, s closes and o opens, and permits the entrance of fresh air, which in turn becomes compressed by the descent of the piston, and so on. This apparatus is chiefly used for charging liquids with gases. For this purpose the stopcock B is connected with a reservoir of the gas, by means of the tube D. The pump exhausts this gas, and forces it into the vessel K, in which the liquid is contained. This can be drawn off by the stopcock E. The artificial aerated waters are made by means of analogous apparatus. 143. Hero's fountain. Hero's fountain is an arrangement by which a jet may be obtained, which lasts for some time. It derives its name from its inventor, Hero, who lived at Alexandria. 120 B.C., and depends on the elasticity of the air. It consists of a brass dish (fig. 120), and of two glass globes. The dish com- municates with the lower part of the globe by a long tube ; and another tube connects the two globes. A third tube passes through the dish to the lower part of the upper globe. This tube having been taken out, the upper globe is partially filled with water, the tube is then replaced, and water is poured into the dish. The water flows through the long tube into the lower globe, and expels the air, which is forced into the upper globe ; the air thus com- pressed, acts upon the water, and makes it jet out as represented in the figure. If it were not for the resistance of the atmosphere, and friction, the liquid would rise to a height above the water in the dish equal to the difference of the level in the two globes. 144. Intermittent fountain. The intermittent fountain de- pends partly on the elastic force of the air and partly on the atmospheric pressure. It consists of a stoppered glass globe a (fig. 121), provided with two or three capillary tubulures. A glass tube, d, open at both ends, reaches at one end to the upper part of the globe, a ; the other end is fitted in a support, c, placed in the middle of the dish, m, which supports the whole appa- ratus. The support, c, is perforated with small holes, which allow air to pass into the tube just above a little aperture in the dish, m. The water, with which the globe, a, is nearly two-thirds filled, -144] Intermittent Fountain. 133 runs out by the tubes, as shown in the figure ; the internal pres- sure being equal to the atmospheric pressure, together with the weight of the column of water, while the external pressure at that point is only that of the atmosphere. These conditions prevail so long as the lower end of the glass tube is open, that is, so long as Fig. 120. air can enter and keep the air in a at the same density as the ex- ternal air ; but the apparatus is arranged so that the orifice in the dish does not allow so much water to flow out as it receives from the upper tubes, in consequence of which the level gradually rises in 134 On Gases. [144- the dish, and then closes the lower end of the glass tube. As the external air cannot now enter the globe, a, the air becomes rarefied in proportion as the flow continues, until the pressure of the column of water, together with the elastic force of the air contained in the globe, is equal to this external pressure ; the flow consequently Fig. 121. stops. But as water continues to flow out of the dish at m, the tube opens again, air enters, and the flow recommences, and so on, as long as there is water in the globe a. 145. Syphon inkstand. This instrument, the object of which is to protect ink from too rapid evaporation is an interesting illus- tration of the pressure of the atmosphere, and of the elasticity of -146] Suction Pump. 135 Fig. 122. air. It consists of a glass vessel of the shape of a truncated pyra- mid (fig. 122), closed everywhere except at the bottom, where there is a tubulure, which is always open. The inkstand is partially full of ink, while there is air at the top. The level of the ink inside being higher than in the tubulure, the elastic force of the air inside is a little less than the pressure of the atmosphere on the ink in the tubulure. As the ink there is used, its level sinks, and is finally lower than the point o. At this moment a bubble of air passes into the interior, and the elastic force being thereby increased, the level of the ink descends in the inside and rises in the tubulure. This goes on until the internal level is at the point o. More ink must then be added, which is effected by pouring it into the tubulure, care being taken to incline the inkstand in the opposite direction. The fountains in birdcages are on a similar principle. PUMPS. 146. Suction-pump. Pumps are machines for raising liquids. Their invention, which is of great antiquity, is attributed to Ctesibius. a celebrated mechanician, who flourished at Alexandria, 130 B.C. There are many modifications of pumps, but they may all be referred to three types, the suction or lift-pump, the forcing pump, and the suction arid forcing pump. The suction or lifting pump, represented in fig. 123. consists of a cast-iron cylinder called the barrel, at the bottom of which is a pipe of a smaller diameter, which dips in the well. At the top of this pipe is a clack valve, which is represented in the drawing as being open. It moves easily up and down, and it establishes a communication between the cylinder and the body of the pump when it is open, and breaks it when closed. The piston in the barrel consists of a thick disc of metal or of leather, coated with tow or with leather. The piston is perforated by a small hole, which is closed by a valve ; the valve is like that in the barrel, and, like it, opens upwards. The pistoh is worked by means of 136 On Gases. [146- a long lever, which is the handle. This is joined at one end to a forked' rod, a, which is connected with the piston rod, b. As it is important that the piston move in a straight line, it is guided by passing through a hole in a fixed piece, o. Fig. 123. The manner in which the water is raised will be understood from an inspection of figs. 124, 125, and 126, which represent the piston and the valves in three different positions. When the pump has not been worked, the barrel and the pipe are full of air under the ordinary atmospheric pressure, which counterbalances the external atmospheric pressure on the well. Hence it follows -146] Sziction Pump. 137 that the level of the water inside and outside is the same. When the piston rises (fig. 124), as it is pressed down by its own weight and by that of the atmosphere, a vacuum is created below the piston ; but, in virtue of its elastic force, the air which fills the pipe B quickly opens the valve, against one of the series of holes in the rotating disc. A tone is now heard, which is tolerably pure when the rotations are sufficiently rapid, and the number of vibrations of which can be readily deter- mined. Suppose, for instance, that there are 48 in the inner series of holes. Then each time a hole passes in front of the glass tube a condensed wave is produced which reaches the ear in the ordinary manner. If, for example, the disc makes 16 turns in a second, in each second 16 times 48 or 768 holes, pass in front of the tube, and there are produced 768 waves, which fall upon the ear within a second, at equal intervals of time. If in like manner the tube were held over the second series of holes, while the rotation goes on at the same rate, we should hear the tones corresponding to 16 times 60, or 960 vibrations in a second. Thus proceeding in like manner, and moving the tube successively from, the central to the circum- ferential series of holes we hear successively, the fundamental note, the major third, the fifth, and the octave (173). 172. Limit of perceptible sounds. Savart, a French physicist, was the first to determine the limit of the number of vibrations which the ear could perceive. He invented an apparatus for this purpose which is known as . Savarfs toothed wheel. It consists essentially of a metal wheel with a series of equidistant sharp teeth on its periphery. This is made to rotate at a uniform rate, and a card, or still better, a thin elastic steel plate is held so that in the rotation of the wheel each of the teeth strikes against the plate, and each time produces a sound. If, for instance, the rim of the wheel 1 66 Acoustics. [172- has 6co teeth, and it is made to rotate 4 times in a second, 2400 impulses are given in a second. The number of impulses depends thus on the velocity of rotation and the sounds produced are pure and continuous. Thus to determine the number of vibrations corresponding to any particular note, it is simply necessary to turn the wheel at a uniform rate until it produces a note in unison (173) with the one in question. Knowing then the number of teeth on the wheel and the rate of rotation, the number of vibrations can be at once calculated. By means of this apparatus Savart ascertained that the deepest sounds are produced by 16 vibrations in a second. If the number of vibrations is less, no sound is heard. The same physicist found that the highest sound which the ear can perceive cor- responds to 48,000 vibrations in a second. Between these two limits it will be seen what an enormous quantity of sounds may be produced and perceived. Yet the sounds used in music, and more especially in singing, are comprised within much narrower limits. Thus the number of vibrations produced by the human voice has been ascertained ; and it has been found that the lowest notes of a man's voice are made by 190 vibrations in a second, and the highest notes by 678. The lowest note of a woman's voice corresponds to 572 vibrations, and the highest to 1,606. 173. Musical scale. Gamut. The human ear can distin- guish among several sounds not merely which is the highest, or the lowest, but it can also estimate the relations which exist between the numbers of vibrations corresponding to each of these sounds. Not, indeed, that we can say whether one sound produces two or three times as many vibrations as another ; but whenever the number of vibrations of two successive or simultaneous sounds are in a simple ratio, these sounds excite in us an agreeable sensation, which varies with the ratio of the vibrations of the two sounds, and which the ear can readily estimate. Hence results a series of sounds characterised by relations which have their origin in the nature of our organisation, and which constitute what is called the musical scale. In this series the sounds are reproduced in the same order, in periods of seven, each period constituting a gamut ; and the seven sounds or notes of each gamut are designated by the names C, D, E, F, G, A, B, or by nt or do, re, mi, fa, sol, la, si. The first six of these letters are the first syllables of the lines of a hymn which -174] Musical Scale. 167 was sung by the chorister children to St. John, their patron saint, when they prayed to be freed from hoarseness ; and the word si is formed of the first letters of St. John's name. "Ut queant laxis resonare fibris Ittira gestorum famuli tuorum Solve polluti labii reatum S ancte I oannes The word gamut is derived from gamma, the third letter of the Greek alphabet, because Guido d'Arezzo, who first (in the eleventh century) represented notes by points placed on parallel lines, denoted these lines by letters, and chose the letter gamma to desig- nate the first line. If we agree to represent by I the number of vibrations of the fundamental note C or do of the gamut, that is to say, of the deepest note, experiment shows that the numbers of vibrations of the other notes of the scale are those given in this table : C DEFGAB^r do re mi fa sol la si do T 9 5 4 3 5. 15 ~ 1 8 4 3 2 3 8 2 This table does not give the absolute numbers of the vibrations of the various notes, but only their relative numbers. Knowing the absolute number of vibrations of the fundamental C, we may deduce those of the other notes by multiplying them by |, Jj, *, . . . or 2 respectively ; and we thus find that at the octave (174), the number of vibrations is double that of the fundamental note. The scale may be continued by taking the octaves of these notes namely, c, d, e,f,g, a, b, and again the octaves of these last, and so forth. 1 74. Intervals. An interval is the ratio of one sound to another, that is, the relation between the numbers of vibrations which pro- duce these sounds. The interval between two consecutive notes of the gamut is called a second \ such as the interval from do to re, from re to mi, from mi to/, and so on. If between any two notes which are compared, there are one, two, three, four, five, or six intermediate notes, these intervals are called respectively, a third, a. fourth, fifth, sixth, seventh, and octave. Thus the interval from C to E is a third, that from C to F a fourth, from C to G a fifth, from C to A a sixth, and from C to B a seventh, and from C to c an octave. 1 68 Acoustics. [174- Although two or more notes may be separately musical, it does not follow that, when sounded together, they produce a pleasant sensation. When the ear can distinguish without fatigue the ratio between two sounds, which is the case when the ratio is simple, the accord or co-existence of these two sounds forms a consonance ; but if the number of vibrations is in a complicated ratio the ear is un- pleasantly affected and we have dissonance. The simplest concord is unison, in which the numbers of vibra- tions are equal ; then cornes the octave, in which the number of vibrations of one sound is double that of the other ; then the fifth, where the ratio of the sounds is as 3 to 2 ; the fourth, of which the ratio is 4 to 3 ; and lastly, the third, where the ratio is 5 to 4. If three notes are sounded together they are concordant, when the number of their vibrations are as 4 : 5 : 6. Three such notes form a harmonic triad, and if sounded with a fourth note, which is the octave of the lowest, they constitute what is called a major chord. Thus C, E, G, form a major triad, G, B, d form a major triad, and F, A, c form a major triad. C, G, and F have, for this reason, special names, being called respectively, the tonic, domi- nant, and sub-dominant, and the three triads the tonic, dominant, and sub-dominant triads or chords respectively. If, however, the ratio of any three notes is as 10 : 12 : 15, the three sounds are slightly dissonant, but not so much as to dis- qualify them from producing a pleasant sensation, at least under certain circumstances. When these three notes and the octave to the lower are sounded together they constitute what in music is called a minor chord. The intervals between the notes in the scale are C to D f. G to A \. D to E \. A to B f . E to F i-;. B to C f. F to G f. It will be seen that there are here three kinds of intervals ; the interval f is called a major tone, and that of ^~ a minor tone ; the relation between the major and the minor tone is f : = f, and is called a comma. The interval ^f is called a major semitone. The major scale is formed of the following succession of intervals : a major tone, a minor tone, a major semitone, a major tone, a minor and a major semitone. It is this succession -176] Musical Temperament. 169 which constitutes the scale ; the key note, or the tonic, may have any number of vibrations ; but once its height is fixed, that of the other notes are always in the above ratio. 175. On semitones and on scales with different key notes. It is found convenient for the purpose of music to introduce notes intermediate to the seven notes of the gamut ; this is done by in- creasing or diminishing those notes by an interval of ff, which is called a minor semitone. When a note (say C) is increased by this interval, it is said to be sharpened, and is denoted by the symbol Ctf , called < C sharp ; ' that is Ctt -*-C = ff. When it is de- creased by the same interval, it is said to be flattened, and is represented thus B b , called ' B flat ; ' that is, B + B b = f f . If the effect of this be examined, it will be found that the number of notes in the scale from C up to c has been increased from seven to twenty-one notes, all of which can be easily distinguished by the ear. Thus, reckoning C to equal i, we have C C8 Db D Dtf Eb E etc. 2f. 27 9 75 6 5 <- 24 25 8 64 5 4 CtC - Hitherto we have made the note C the tonic or key note. Any other of the twenty-one distinct notes above-mentioned, for instance, G, or F, or Ctf , etc, may be made the key note, and a scale of notes constructed with reference to it. This will be found to give rise in each case to a series of notes, some of which are identical with those contained in the series of which C is the key note, but most of them different. And of course the same would be true for the minor scale as well as for the major scale, and indeed for other scales, which may be constructed by means of the fundamental triad. 176. On musical temperament. The number of notes that arise from the construction of the scales described in the last article is enormous ; so much so as to prove quite unmanageable in the practice of music ; and particularly for music designed for instruments with fixed notes such as the pianoforte. Accordingly it becomes practically important to reduce the number of notes, which is done by slightly altering their just proportions. This process is called temperament. By tempering the notes, however more or less dissonance is introduced, and accordingly several dif- ferent systems of temperament have been devised for rendering this dissonance as slight as possible. The system usually adopted is called the system of equal temperament. It consists in the sub- 1 70 Acoustics. [176- stitution between C and c of eleven notes at equal intervals, each interval being the twelfth root of 2, or 1-05946. By this means the distinction between the semitones is abolished, so that, for example, Cff and Db become the same note. The scale of twelve notes thus formed is called the chromatic scale. It of course follows that the major triad becomes slightly dissonant. Thus in the diatonic scale, if we reckon C to be i, E is denoted by 1*25000, and G by i '50000. On the system of equal temperament if C is denoted by i, E is denoted by 1-25992 and G by 1-49831. 1/7. The number of vibrations producing- each note. The tuning fork. Hitherto we have not assigned any numerical value to that symbol the note C. In the theory of music it is common to assign 256 double vibrations to the middle C. This, however, is arbitrary ; its justification is the facility with which this number may be subdivided. An instrument is in tune provided the in- tervals between the notes are correct, when C is yielded by any number of vibrations per second not differing much from 256. Moreover, two instruments are in tune with one another if, being separately in tune, they have any one note, for instance, C, yielded by the same number of vibrations. Consequently, if two instru- ments have one note (say C) in common, they can then be brought into tune jointly, by having their remaining notes separately ad- justed with reference to that fundamental note. A tuning fork or diapason is an instrument yielding a constant sound, and is used as a'Standard for tuning musical instruments. It consists of an elastic steel rod, bent as represented in fig. 149. It is made to vibrate either by drawing a bow across the ends, as shown in the figure, or by striking one of the legs against a hard body, or by rapidly separating the two legs by means of a steel rod. The vibration pro- duces a note which is always the same for the same tuning fork. The note is strengthened by fixing the tuning fork on a box open at one end called a resonance box (178)." It has been remarked for some years that not only has the pitch of the tuning fork, that is, concert pitch, been getting higher in the larger theatres of Europe, but also that it is not the same in London, Paris, Vienna, Milan, etc. This is a source of great inconvenience both to composers and singers, and a commission was appointed to establish in France a tuning fork of uniform pitch, and to prepare a standard which would serve as an invariable type. In accord- ance with the recommendations of that body, a normal timing fork -177] Tuning Fork. . 171 has been established, which is compulsory on all musical esta- blishments in France, and a standard has been deposited in the Conservatory of Music in Paris. It makes 870 single or 435 double vibrations in a second and yields the note la of the treble stave ; the do or C of the same stave makes thus 261 double vibrations in a second. The standard tuning fork adopted by the Society of Art in Lon- don, on the recommendation of a committee of eminent musicians, makes 264 double vibrations in a second, and gives the middle C Fig. 149. of the treble stave. The corresponding a or la gives therefore 440 vibrations in a second. The middle C is the note sounded by the white key immediately on the left of the two black keys which are near the middle of the keyboard of a pianoforte. It is designated in musical notation as For purposes of comparison it is convenient to call this note c /9 and the next lower octave c ; the octave lower than this C, and the still lower one C,, and so on. The lowest note of grand pianos is A,, which gives 27-2 vibrations in a second. In like manner the higher octaves are distinguished by affixes, Acoustics. [177- thus c" c'" r iv and so forth. In height the pianoforte reaches to a ir with 3,520, or c v with 4,224 vibrations in a second. The practical range of musical sounds is comprised within 40 and about 4,000 vibrations in a second ; or a range or 7 octaves. 178. Resonance of air. The action of the resonance-box in strengthening sound (fig. 149) may be illustrated by the follow ing experiment (fig. 1 50). AB is a glass cylinder about 8 inches in height, and I to i^ in diameter. If now an ordinary tuning fork be made to vibrate, its sound is very faint, and if it is held Fig. 150. over the empty cylinder probably no alteration will be experienced. When, however, water is slowly and noiselessly poured into the cylinder, on reaching a certain height, the previously faint sound is far louder. Any other tuning fork, which yields a different note, if held over the cylinder will not have its note strengthened. Revert- ing now to the original tuning fork, if while it is still sounding and its sound is being strengthened by its nearness to the cylinder, we continue to pour in water, the sound becomes as faint as it was originally. If now the excess of water be agaki removed until the tone of the fork is once more strengthened, and if, removing the -179] Harmonics. 173 fork, we sound the column again by blowing into it, we find that the column of air emits the same note as the tuning fork. Hence then the tuning fork could set a column of air of a particular length in vibration so as to produce the same note ; and this adding itself to the original note strengthened it. 179. Compound musical tones. Harmonics. Overtones. We have already seen that there is a peculiar quality or timbre, as it is called, by which the notes of different instruments are cha- racterised. Thus we readily distinguish between the note C when sounded on a pianoforte and the same note sounded on an organ or a trumpet. This peculiarity of the tone is due to the fact that only in very few cases does an instrument give a pure note but that in most cases it is accompanied by a series of upper notes or harmonics. To understand what these are we may refer to 191, in which it is stated that by successively intensifying the current of air, we get in a stopped pipe a succession of notes the numbers of whose vibrations are as the series of odd numbers, i, 3, 5, 7, etc. So too if we similarly sound an open pipe we get the series of notes whose numbers of vibrations are represented by the series of even numbers, i, 2, 3, 4, 5, etc. These are called* respectively the odd and even harmonics of the primary note. Now if we sound a particular note on the piano, by a little at- tention a practised ear can discover that the primary note is ac- companied by a series of higher notes each of which gradually gets fainter. These upper notes may be detected, and the com- pound nature of the primary sound analysed even by an unpractised ear by the use of resonance 'globes which Helmholtz devised for this purpose. These instruments, one of which is represented in fig. 151, are an application of the principle explained in the fore- going paragraph. They are small hollow spheres, the pro- jection ^, which has a small hole, is placed in the ear while the wider aperture a is directed towards the source of sound. Each of these resonators is constructed or tuned for a par- ticular note ; so that if having sounded the string of a piano- Flg> ISI> forte, we hold near it a resonator tuned for a particular note, this note if present will be intensified. Thus, if we depress the key c. Acoustics. [179- we hear no particular strengthening if a resonator sounded for g be held near the ear ; but when the resonators sounded for c /t g lt c //y are used we hear them powerfully respond when held to the ear. Hence the notes c fl g n c,,, are contained in the mass of sound which is produced when the key c t is depressed. Helmholtz's researches show that the different timbre or quality of the sounds yielded by different instruments is due to the fact that they are accompanied in each case by special har- monics or overtones in varying intensity. Helmholtz's principal results are as follows : Simple tones those, that is to say, without any admixture of overtones are most easily produced when a tuning fork is held near a resonance-box of suitable length. These notes are soft and are free from all sharpness and roughness. Fhite notes are also nearly pure, for their overtones are very feeble. Wide-stopped organ pipes give the fundamental note almost perfectly pure, narrower ones give along with it the fifth of the octave. Wide open pipes give the octave along with the fundamental note ; and narrow ones give a series of overtones. The overtones present in the sound of stretched strings depend on their substance and on the manner in which they are made to sound. In good pianos the overtones are powerful up to the sixth. In stringed instalments the fundamental note is comparatively stronger than in pianos ; the first overtones are feebler, the higher, from the sixth to the tenth, on the contrary, are far more distinct, and produce the penetrating character of the sound of stringed instruments. Metallic rods and plates produce, along with the fundamental note, a series of very high overtones which are discordant with each other, but are continuous and of equal strength with the primary note. Thus is produced that peculiarity known as a metallic sound. ., By the occurrence of the lower harmonics along with the primary note the tone is more sonorous, richer and deeper than the primary note ; by the occurrence of the higher overtones, the clang acquires its penetrating character. -181] Transverse Vibrations of Strings. 175 CHAPTER III. TRANSVERSE VIBRATIONS OF STRINGS. STRINGED INSTRUMENTS. 1 80. Transverse vibrations of strings. We have already seen (156), that when an elastic string, stretched at the ends, is removed from its position of equilibrium, it reverts to it as soon as it is let go, making a- series of vibrations which produce a sound. The strings used in music are commonly of catgut or metallic wire. The vibrations which strings experience may be either transversal or longitudinal, but practically the former are alone important. Tansversal vibrations may be produced by drawing a bow across, the string, as in the case of the violin ; or by striking the string, as in the case of the pianoforte ; or by pulling them transversely and then letting them go suddenly, as in the case of the guitar^ and the harp. 181. Laws of the transverse vibrations of strings. The number of transverse vibrations which a string can give in a certain time, that is, the sound it yields, vary with its length, its diameter, its tension, and with its specific gravity in the following manner : The tension being constant, the number of vibrations in a second is inversely as the length ; that is, that if a string makes 18 vibra- tions in a second for instance, it will make 36 if its length is halved, 54 if its length is one-third, and so on. On this property depends the violin, the centre basso, etc., for in these instruments by pressing the string with a finger, the length is reduced or increased at pleasure, and the number of vibrations, and therewith the note is regulated. With strings of the same length and tension the number of vibrations in a second is inversely as the diameter of the string ; that is, the thinner a string, the greater its number of vibrations, and the higher its pitch. In the violin, the treble string, which is the thinnest, makes double the number of vibrations of that which would be made by a string twice its size, that is to say, the dia- meter of which is twice as great. ij6 A coustics. [181- The number of vibrations in a second is directly as the square root of the stretching weight or tension ; that is, that when the tension of a string is four times as great, the number of vibrations is doubled ; when the tension is nine times as great, the number is trebled, and so on. This, then, furnishes a means of altering the character of a note by stretching, as is done in stringed instru- ments. Other things being equal, the number of vibrations in a second of a string is inversely as the square root of its density. Hence, the greater the density of the materials of which strings are made, the less easily they vibrate, and the deeper are the sounds they yield. From the preceding laws it will be seen how easy it is to vary the number of the vibrations of strings and make them yield an extreme variety of sounds, from the deepest, to the highest used in music. 182. Verification of the laws of the vibrations of strings. Sonometer. This may be effected by means of an instrument called the sonometer or monochord. It consists of a thin wooden box to strengthen the sound. On this there are two fixed bridges A and B (fig. 152), over which pass the strings AB, CD, which Fig. 152. are commonly metal wires. These are fastened at one end, and stretched at the other by a weight P, which can be increased at will. By means of a third movable bridge D, the length of that portion of the wire which is to be put in vibration can be altered at pleasure If two strings are taken, which are identical in all respects, and are stretched by equal weights, they will be found, on being struck, to yield the same sound. If now one of them be divided by the -183] Stringed Instruments. 177 movable bridge D into two equal parts, the sound yielded by CD will be the higher octave of that yielded by the entire string AB, which shows that the number of vibrations is doubled, and thus verifies the law. To verify the second law, the bridge D is removed. If the string AB is taken so that it has double the diameter of the other, but both stretched by the same weight, it will be found that the sound which the thinnest string yields is the next higher octave of that yielded by AB ; proving thus that the number of vibrations is doubled. The two strings being of the same diameter, and the same length, if the weight which stretches the one be four times that which stretches the other, the sound yielded by the first is the higher octave of that of the second, which shows that, the number of vibrations is doubled ; when the weight is nine times as great, the sound is the higher octave of the fifth of the former. The fourth law is established by using strings of different den- sities, but of the same dimensions, and stretched to the same extent. 183. Stringed instruments. Stringed musical instruments depend on the production of transverse vibrations. In some, such as the piano, the sounds are constant, and each note requires a separate string : in others, such as the violin and guitar, the sounds are varied by the fingering, and can be produced by fewer strings. In the piano the vibrations of the strings are produced by the stroke of the hammer, which is moved by a series of bent levers communicating with the keys. The sound is strengthened by the vibrations of the air in the soimding board 'on which the strings are stretched. Whenever a key is struck, a damper is raised, which falls when the finger is removed from the key and stops the vibra- tions of the corresponding string. By means of a pedal all the dampers can be simultaneously raised, and the vibrations then last for some time. The harp is a sort of transition from the instruments with con- stant to those with variable sounds. Its strings correspond to the* natural notes of the scale ; by means of the pedals the lengths of the vibrating parts can be changed, so as to produce sharps and flats. The sound is strengthened by the sounding box, and by the vibrations of all the strings harmonic with those played. In the violin and guitar each string can give a great number of sounds according to the length of the vibrating part, which is de- N Acoustics. [183- termined by the pressure of the fingers of the left hand while the right hand plays the bow, or the strings themselves. In both these instruments the vibrations are communicated to the upper face of the sounding box, by means of the bridge over which the strings pass. These vibrations are communicated from the upper to the lower face of the box, either by the sides, or by an intermediate piece called the sound post. The air in the interior is set in vibra- tion by both faces, and the strengthening of the sound is produced -by all these simultaneous vibrations. The value of the instrument consists in the perfection with which all possible sounds are in- tensified, which depends essentially on the quality of the wood, and the relative arrangement of the parts. Instruments of the class of the violin are very difficult to play, and require a very delicate ear ; but in the hands of skilful artists, they produce marvellous effects. They are the very soul of an orchestra, and the most beautiful pieces of music have been composed for them. 184. Longitudinal vibra- tions of string's and rods. When a violin bow is passed over the string of the mono- chord at a very acute angle, an unpleasant but powerful tone is heard. If the tension of the string be altered, there is no change in the note. If the string be touched in the middle it yields the octave when the bow is passed over it. These tones are pro- duced by longitudinal vibra- tions, their pitch varies in- versely as the length of the string, but is independent of the thickness and tension. In like manner if a glass tube be grasped in the middle, and rubbed lengthwise with a wet cloth, a Fig. 153- - 185] Production of Sound in Pipes. 1 79 penetrating but not unpleasant tone is produced. If grasped at a quarter of its length and if the shorter part be made to, vibrate, the octave of the former tone is obtained. Marloye's harp y tig. 153, is an arrangement which illustrates the sounds produced by the longitudinal vibration of rods. It consists of a series of deal rods of different lengths and thicknesses. They are sounded by rubbing the rods lengthwise with resined fingers. A series of notes of varying pitch is thus produced, which by a skilful artist is far from unpleasing. The tuning-fork, the triangle, and musical boxes are examples of the transverse vibration of rods. In musical boxes small plates of steel of different dimensions are fixed on a rod, like the teeth of a comb. A cylinder whose axis is parallel to this rod, and whose surface is studded with steel teeth, arranged in a certain order, is placed near the plates. By means of a clockwork motion the cylinder rotates, and the teeth striking the steel plates set them in vibration, producing a tune, which depends on the arrangement of the teeth on the cylinder. CHAPTER IV. SOUND PIPES AND WIND INSTRUMENTS. 185. Production of sound in pipes. Sound pipes are hollow pipes or tubes in which sounds are produced by making the. en- closed column of air vibrate. In the cases hitherto considered the sound results from the vibrations of solid bodies, and the air only serves as a vehicle for transmitting them. In wind instru- ments, on the contrary, when the sides of the tube are of adequate thickness, the enclosed column of air is the sounding body. In fact, the substance of the tubes is without influence on the primary tone ; with equal dimensions it is the same whether the tubes are of glass, of wood, or of metal. These different materials simply do no more than give rise to different harmonics, and impart a dif- ferent timbre to the compound tone produced. If tubes were simply blown into, there could be no sound ; there would merely be a continuous progressive motion of the air. To produce a sound, by some means or other a rapid succession of N 2 i8o Acoustics. [185- condensations and rarefactions must be produced, which are then transmitted to the whole column of air in the tube. Hence the ne- cessity of having a mouthpiece, that is, the end by which air enters, so shaped that the air enters in an intermittent, and not a contin- uous manner. From the arrangement made use of to set the enclosed air in vibration, wind instruments are divided into mouth instruments and reed instruments. 1 86. Mouth instruments. In mouth instruments all parts of the mouthpiece are fixed. The pipes are either of wood or metal, N Fig. 154. Fig. 155. Fig. 156. Fig. 157. Fig. 158. rectangular or cylindrical, and are always long as compared with the diameter. Fig. 154 represents a wooden rectangular organ pipe; fig. 155 gives a longitudinal section by which the internal details are seen. The lower part P, by which air enters, is called the_/>0/; it emerges through a narrow slit i, and, on the opposite -187] Reed Instruments. 181 side, is a transverse aperture called the mouth ; a and b are the lips, the upper one of which is bevelled. The current of air arriving by the mouth, strikes against the upper lip, is compressed, and by its elasticity reacts upon the current and stops it. This, however, only lasts for an instant, for, as the air escapes at ab, the current from the foot continues, and so on for the whole time. In this way, pulsations are produced, which, transmitted to the air in the pipe, make it vibrate, and a sound is the result. In order that a pure note may be produced, there must be a certain relation between the form of the lips and the magnitude of the mouth ; the tube also ought to have a great length in comparison with its diameter. The number of vibrations depends in general on the dimensions of the pipe and the velocity of the current of air. The mouthpiece we have described is used in organs. Fig. 156 represents another modification much in use in organ playing, and fig. 1 57 gives a longitudinal section. The letters indicate the same parts as in fig. 155. Fig. 158 shows the mouthpiece of a flageolet and whistle. In the German flute the mouthpiece consists of a small lateral circular aperture in the pipe. By means of his lips the player causes the current of air to graze against the edge of this aperture. 187. Reed instruments. In reed instruments the air is set in vibration by means of elastic tongues or plates, which are called reeds, and which are divided into free reeds and beating reeds. Beating reed. This consists of a piece of wood or metal, a (fig. 1 60), which is grooved like a spoon. It is fixed to a kind of stopper, K, perforated by a hole, which connects the cavity with a long pipe, T. The groove is covered by a brass plate, /, which is called the tongue. In its ordinary position this is slightly away from the edges of the groove, but being very flexible, readily ap- proaches, and closes it. Lastly, a cuived wire br } presses against the tongue, and can be moved up and down. The vibrating part of the tongue can thereby be shortened or lengthened at will, and the number of vibrations thus regulated. By means of this wire, reed pipes are tuned. The reed is fitted to the top of a rectangular pipe KN, called the wind channel. This is closed everywhere, except at the bottom, where it can be fitted on a bellows. In models of reed pipes used in illustrating lectures, the sides of the upper part of 182 Acoustics. [187- the tube are made of glass, so as to show the construction of the reed. This arrangement is represented in fig, 159. When air arrives in the wind channel, it first passes between the tongue and the groove, and escapes by the pipe T ; but as the velocity increases, the tongue strikes against the edge of the groove, and closing it completely, the current is stopped. But, in virtue of its elasticity, the tongue reverts to its original position, Fig. 159- Fig. 1 60. Fig. 161. and thus by a series of alternate openings and closings, the same series of pulsations are produced as in mouth instruments ; hence is formed a sound which is higher the more rapid the current of air. Free reed. Grenie invented in 1810 a kind of reed called a. free reed, because the tongue, instead of striking against the edges of the groove, like the reed described above, grazes them so as to os- cillate backwards and forwards. The groove consists, in this case, -189] Nodes and Loops. 183 of a small wooden box, ac, fig. 161, the front of which is of brass plate. In the middle of this is a longitudinal slit, in which is ap- plied the tongue, which can oscillate freely backwards and forwards so as to allow air to pass, which it closes each time it grazes the edges of the slit. In this case also a wire, r, regulates the length of the vibrating part of the tongue. A reed can be very simply made from a piece of straw. About an inch from a knot an incision is made at r, (fig. 162), with a Fig. 162. sharp penknife, which is about a quarter as deep as the diameter of the straw ; and then by laying the knife flat the straw- is slit as far as the knot ; the strip r r, thus produced forms a reed joined with the pipe .y r. The note of this pipe depends on the length of the tube s r and is higher the shorter the tube is made. In order to sound the pipe, the whole length of the reed is placed in the mouth and the lips firmly closed. 1 88. Bellows. In acoustics a bellows is an apparatus by which wind instruments, such as the syren and organ pipes, are worked. Between the four legs of a table there is a pair of bellows, S (fig. 163), which is worked by means of a pedal, P. D is a reservoir of flexible leather, in which is stored the air forced in by the bellows. If this reservoir is pressed by means of weights on a rod, T, moved by the hand, the air is driven through a pipe, A, into a wind chest, mn, fixed on the table. ' In this chest there are small holes closed by leather valves s (fig. 164). These can be opened by pressing on keys, a, in front of the box. Below the valve is a spring, r, which raises the valve when the key is not depressed. The sound pipe is placed in one of these holes. 189. Nodes and loops. Experiment shows, that when a pipe is sounded, the column of air is subdivided into equal parts, vibrat- ing in unison, and separated by surfaces where the velocity of air is null. These fixed parts are called nodes : and the parts between the nodes where the column of air is in a state of vibration is called a loop, or a ventral segment. It will be seen afterwards, that one and the same pipe may be made to yield several sounds, and that the nodes and ventral seg- ments then alter their position. When a pipe closed at one end, a 1 8 4 Acoustics. [189- stopped pipe, is made to yield its fundamental sound, that is, the deepest one, the bottom is always a node, and the mouthpieces a ventral segment. An open pipe when sounded has a ventral segment at each end ; and if it yields the fundamental sound, there is a single node in the middle. Fig. 163. When an aperture is opened in the side of a sounding pipe, the sound does not change if the aperture corresponds to a loop ; but if it corresponds to a node, the sound .is altered, for this node then becomes a loop. This property is used in wind instruments like the flute, the clarionet, along which holes are made which can be closed by the fingers, or by the aid of keys. The formation of nodes and loops is far from being restricted to sounding tubes. Strings, plates and membranes, when they vibrate, exhibit parts which are fixed, and parts which are very mobile, that is to say, nodes and loops. , -191] Pitch Pipes. 185 190. Laws of the v4bration of air in pipes. The vibrations of air in pipes present two cases -according as they are open or stopped. Laws of stopped pipes. When having placed a stopped pipe on the bellows, air is slowly passed, the deepest note, the fundamental, sound, is produced. If, then, we denote by I the corresponding number of vibrations, when the current of air is forced, we suddenly get the sound corresponding to 3 ; and if the wind be still more forced, we have successively the sounds 5, 7, etc. ; that is to say, sounds which by their pitch correspond to vibrations 3, 5, 7, etc. times as numerous as those of the fundamental sound. Hence closed pipes, when the air is forced, give successively sounds re- presented by the series of odd numbers. The sounds 3, 5, 7, etc., are called the harmonics of the fundamental note I. 2. With pipes of different lengths, the number of vibrations corresponding to the fundamental note are in- / versely as the lengths ; that is to say, that a pipe, which all is half as long as another, will yield a sound which is the octave of that yielded by this pipe. Laws of open pipes. The fundamental note being still represented by unity, the harmonics obtained by forcing the wind are successively represented by 2, 3, 4, 5, 6, etc., that is, by the natural series of numbers. The fundamental note of an open pipe is always an octave higher than the fundamental note of a closed pipe of the same length. These laws are known as Bernoulli's laws from the name of their discoverer, Daniel Bernoulli. 191. Pitch pipe. Instead of organ pipes of various lengths and bellows, these laws may be conveniently demonstrated by means of a pitch pipe, hg. 165,. which is a small sound pipe with a movable graduated stopper. If having closed the pipe at its full length, we blow into it, we get the fundamental note of the stopped pipe, say c ; if now we blow into it more strongly we get the note Fig. 165. g t , which is the major fifth of the higher octave of c, and more strongly still the note e /n which is the major third of its second octave, and so on for the others. In like manner having just closed the pipe, if we push in the stopper until its length is one half and sound it, we get the higher 1 86 A caustics. [191 octave of the fundamental note, by making it ^ its original length we get the major third of c, and so for any other aliquot part. By removing the stopper altogether we have an open pipe, and the note c which it yields is the octave of the stopped one, and .this sounded by increasingly powerful currents of air gives the following series of notes, c, c^ g tl c iu e tjl and so forth. 192. Wind Instruments. Wind instruments are straight or curved tubes, which are sounded by means of a current of air forced into them. They have all an aperture by which air is forced into them, and, according to the form of this aperture, they are divided into mouth instruments and reed instruments ; in some, such as the organ, the notes are fixed, and require a separate pipe for each note ; in others the notes are variable, and are produced by only one tube ; the flute, horn, etc., are of this class. Fig. 1 66. The Pandaean pipe, the flageolet, and the German flute are mouth instruments. The principal reed instruments are the clarionet, the oboe, the cornopean, and the bassoon. The Pandtzan pipe, fig. 166, consists of tubes of different sizes corresponding to the different notes of the gamut. In the organ the pipes are of various kinds, namely, mouth pipes, open and stopped, and reed pipes with apertures of various shapes. The air is furnished by means of bellows, from which it passes into the wind chest, and thence into any pipe which is desired ; this is effected by means of valves which are opened by depressing keys like those of the piano. In the larger and richer organs there are several rows of key-boards arranged at different heights. In thejtfttte, the mouthpiece consists of a simple lateral circular aperture ; the current of air is directed by means of the lips, so that it grazes the edge of the aperture. The holes at different distances are closed either by the fingers or by keys ; when one of -193] Human Voice. 8 7 the holes is opened, a loop is produced in the corresponding layer of air, which modifies the distribution of nodes and loops in the interior, and thus alters the note. The whistling of a key is similarly produced. Mouth instruments. In the trumpet, the horn, the trombone, cornet-a-piston, and ophicleide, the lips form the reed, and vibrate in the mouthpiece (fig. 167), which terminates in a smaller tube by which it can be affixed to the instrument. In the horn, different tones are pro- duced by altering the distance of the lips. In the trombone, one part of the tube slides within the other, and the performer can alter at will the length of the tube, and thus produce higher or lower notes. In the cornet-a-piston, the tube forms several convo- lutions ; pistons placed at different distances can, when played, cut off communications w r ith other parts of the tube, and thus alter the length of the vibrating column of air. 193. The Human Voice. If we bevel off the- Fig. 167. ends of a piece of gutta-percha or of wooden tubing, so that two summits are left, and if now two pieces of thin vulcanised india- rubber or leather be stretched and tied between them so as to leave a narrow slit, we have then a sort of membranous reed pipe (fig. 1 68). For if we blow into the tube we get a note which is higher the tighter the lips are stretched; and the vibrations of the lips which form the slit can be distinctly seen. This simple experiment well illus- trates the manner in which the sound of the human voice is produced in the glottis at the top of the windpipe. The windpipe becomes narrow towards the top, ends in a slit, formed by elastic bands, the vocal chords. These are joined back and front to the material of the windpipe, and can be more or less tightly stretched by means of various muscles. The human voice may thus be regarded as a reed pipe formed by two elastic bands. The essential sonorous part of the human voice is formed by the vowels. They acquire their special sound by the fact that to pro- Fig. 168. 1 88 Acoustics. [193- duce them in each case, the cavity of the mouth spontaneously alters its shape and thus acts as a special resonator to each sound. The consonants are noises which formed by the lips, tongue, and teeth accompany the vowels at their commencement and cessation. The sounds by which the consonants are produced are much less intense than the vowel sounds. Hence they are inaudible at distances at which the vowel sounds can be distinctly heard. Therefore, in speaking with 'people hard of hearing, it is by no means necessary to speak louder, but it is sufficient to intensify the consonants. Indeed, distinctness of speech does not depend on loud screaming, but is produced by careful articulation. -194] Heat. 189 BOOK V. HEAT. CHAPTER I. GENERAL EFFECTS OF HEAT. THERMOMETERS. 194. Keat. Hypothesis as to its nature. The sensations of heat and cold are familiar to all of us. In ordinary language the term heat is not only used to express a particular sensation, but also to describe that particular state or condition of matter which produces this sensation. Besides this effect, heat acts variously upon bodies ; it melts ice, boils water, makes metals red-hot, and so forth. Two theories as to the cause of heat are current at the present time ; these are the theory of emission, and the theory of undula- tion, On the first theory, heat is caused by a subtle imponderable fluid, which surrounds the molecules of bodies, and which can pass from one body to another. These heat atmospheres, which thus surround the molecules, exert a repelling influence on each other, in conse- quence of which heat acts in opposition to the force of cohesion. The entrance of this substance into our bodies produces the sensa- tion of warmth, its egress the sensation of cold. On the second hypothesis the heat of a body is caused by an oscillating or vibratory motion of its material particles, and the hottest bodies are those in which the vibrations have the greatest velocity and the greatest amplitude. Hence, on this view, heat is not a substance, but a condition of matter, and a condition which can be transferred from one body to another. It is also assumed that there is an imponderable elastic ether, which pervades all bodies and infinite space, and is capable of transmitting a vibratory motion with great velocity. A rapid vibratory motion of this ether produces heat, just as sound is produced by a vibratory motion ot 1 90 On Heat. [194- atmospheric air, and the transference of heat from one body to another is effected by the intervention of this ether. This hypothesis is now admitted by the most distinguished physicists ; it affords a better explanation of the phenomena of heat than any other theory, and it reveals an intimate connection between heat and light. In accordance with it, heat is a form of motion ; and it will hereafter be shown that heat may be con- verted into motion, and, conversely, motion may be converted into heat. Although the undulatory theory of heat is the correct one, the one, that is, which best^ explains and accounts for the greatest number of facts, yet it may be sometimes convenient to use language which is based on the older hypothesis. Thus, in speaking, of a body becoming heated or cooled, we say that it gains or loses heat : in reality, the motion of the particles is increased or diminished. In what follows, however, the phenomena of heat will be con- sidered, as far as possible, independently of either hypothesis. 195. General effects of heat. The general action of heat upon bodies is to develope a repulsive force between their molecules which is continually struggling with molecular attraction. Under its influence, therefore, bodies tend to expand that is, to assume a greater volume. All bodies expand by the action of heat. As a general rule gases are the most expansible, then liquids, and, lastly, solids. The expansion of bodies by heat is thus a new general property to be added to those already studied. The action of heat upon bodies is not merely to expand them ; when accumulated in sufficient quantity, bodies first lose their solidity and become somewhat softer ; then, as the heat still in- creases, the force of repulsion balances molecular attraction, and then bodies liquefy. Wax, resin, sulphur thus pass readily from the solid to the liquid state ; heat thus produces in solids a change of state of aggregation. But in liquids it also produces a similar change. When bodies are heated they first expand ; heated still more their molecular attraction is again overcome by the force of repulsion, and bodies are then changed into aeriform liquids called vapours. If, instead of becoming accumulated in bodies, heat is given out, that is, if bodies are cooled instead of being heated, the opposite phenomena are produced : the molecules come nearer each other, -196] Expansion. 191 the volume of the pores diminishes, and hence that of the body, which is expressed by saying that the body contracts. By cooling, vapours, losing their elastic force, revert to the liquid state ; and liquids themselves, by the same process, gradually return to the solid state. Thus water changes into ice, and mercury becomes as hard as lead. Thus, according as heat accumulates in, or is dissipated by, bodies, two physical effects may be produced : i, Changes in volume, consisting in expansions and contractions. 2. Changes of condi- tion, that is, the change of solids into liquids, of liquids into vapours, and conversely. We shall first discuss the expansion of bodies, and afterwards their changes of state. 196. Expansion. All bodies are expanded by heat, but to very different extents. Gases are most expansible, then liquids, and after them solids. In solids which have definite figures, we can either consider the expansion in one dimension, or the linear expansion ; in two dimen- sions, the superficial expansion, or in three dimensions, the cubical expansion or the expansion of volume, although one of these never takes place without the other. As liquids and gases have no definite shapes, we can only consider the alterations of volume, which they undergo. Fig. 169. To show the linear expansion of solids, the apparatus represented in fig. 169 may be used.. A metal rod, A, is fixed at one end by 192 On Heat. [196- a screw, B, while the other end presses against the short arm, C, of an index, D, which moves on a scale. Below the rod, A, there is a sort of cylindrical lamp in which spirit is burned. The needle, D, is at first at the zero point, but, as the rod becomes heated, the needle moves along the scale, which shows that the short arm, C, of the lever is slightly displaced, pushed by the rod, A, as it expands. It will be observed that if rods of different metals are used, the index will be moved to different extents, showing that their expan- sibility differs. Thus it will be found that brass is more expansible than iron, or steel. The cubical expansion of solids is 'shown by a Gravcsande's ring. It consists of a brass ball a (fig. 170), which at .the ordin- ary temperature passes freely through a ring, ;/z, almost of the same diameter. But when the ball has been heated, it expands and no longer passes through the ring. It does so, however, on reverting to its original tem- perature. The expansibility of liquids and gases, which is far greater than that of solids, is easily shown. For a liquid a glass tube with a bulb at one end may be u.sed (fig. 171), Fig. 170. which is filled with some liquid, coloured alcohol or mercury, for instance. When the bulb is gently heated, by placing it in tepid water, for example, the column of liquid is seen to rise consider- ably in the tube ; thus from a to b. The experiment may be made in a similar manner with gases ; yet as they are far more expansible than liquids, a long tube bent twice maybe fused to the bulb tube, as represented in fig. 172. An index of mercury, m, is introduced in the tube, which is effected by gently heating the bulb so as to expel some of the air ; a drop of mercury being then placed in the funnel, a, on cooling the air in the bulb and the tube contracts, and the pressure of the atmo- sphere forces the droplet to ;;/ for instance. The apparatus being thus arranged, if the bulb is held in the hand for a few moments, -198] Thermometers. 193 the enclosed air expands sufficiently to force the index from m to , an expansion which is far greater than in the case of liquids. It will thus be seen that the general effect of heat upon bodies is to expand them. Yet this only applies to bodies which, like the metals, glass, etc. do not absorb moisture. Bodies which absorb moisture, such as wood, paper, clay, undergo a contraction when heated, owing to the increase of temperature ex- pelling moisture from their pores. Thus a moist sheet of paper placed before the fire coils up on the heated side. Coopers, too, to curve the staves of barrels, heat them on one side, by lighting a fire in the inside of the barrel when the staves are placed close together. The part turned towards the fire contracts in dry- ing, and curves on the side exposed to the action of heat. MEASUREMENT OF TEMPERATURES. THERMOMETRY. 197. Temperature. The tempe- rature or hotness of a body may be de- fined as being the greater or less extent to which it tends to impart sensible heat to other bodies. The temperature of any particular body is varied, by adding to it or withdrawing from it a certain amount of sensible heat. The temperature of a body must not be confounded with the quantity of heat it possesses ; a body may have a high tempe- rature and yet have a very small quantity of heat, and conversely a low temperature may yet possess a large amount of heat. If a cup of water be taken from a bucketful, both will indicate the same temperature, yet the quantities of heat they possess will be different. The subject of the quantity of heat will be afterwards more fully explained in the chapter on SPECIFIC HEAT. 198. Thermometers. Thermometers are instruments for mea- suring temperatures. Owing to the imperfections of our senses we are unable to measure temperatures by the sensations of heat or O 194 On Heat. [198- cold which they produce in us, and for this purpose recourse must l>e had to the physical effects of heat upon bodies. The most accurate and the most convenient are the expansive effects. Solids, having but little expansibility, can only be used to examine large intervals of temperature ; gases, on the other hand, are very ex- pansible, and only serve to measure small alterations of temperature. They are, moreover, affected by changes of atmospheric pressure. For these reasons, liquids are best suited for the construction of thermometers. Mercury and alcohol are the only ones used the former because its expansion is regular, and it only boils at a very high temperature, and the latter because it does not solidify at the greatest known cold. The mercurial thermometer is the most extensively used. It consists of a capillary glass tube, at the end of which is blown the bulb, a cylindrical or spherical reservoir (fig. 173). Both the bulb and a part of the stem are filled with mercury, and the expansion is measured by a scale graduated either on the stem itself (fig. 178), or on a frame to which it is attached (fig. 177). The filling of the tube with mercury is effected by fusing to the tube a small funnel as shown in fig. 173. In this is placed a small quantity of mercury, and the bulb is then gently heated by a spirit lamp. The expanded air par- tially escapes by the funnel, and on cooling, the air which remains con- tracts, and a portion of the mercury passes into the bulb. The bulb is then again warmed, and allowed to cool, a Fig. 173- fresh quan Fig. 174. tity of mercury enters, and so on, until the bulb and part of the tube are full of mercury. The mercury is then heated to boiling ; the mercurial vapours in escaping carry with them the air and moisture which remain in the tube. The tube being full of the expanded mercury and of mercurial vapour, is hermetically sealed -199] Graduation of tJie Thermo? faeter. 195 at one end. When the thermometer is cold the mercury ought to fill the bulb and a portion of the stem. 199. Graduation of the thermometer. The thermometer having been filled, as has just been described, whenever the tem- perature rises or sinks, the mercury rises or sinks in the stem, and these variations furnish a means of measuring temperatures. For this purpose a graduated scale must be constructed along the stem. In graduating the scale two points must be fixed, which represent identical temperatures and which can always be easily produced. Experiment has shown that ice always melts at the same point whatever be the degree of heat, and that distilled water under the same pressure, and in a vessel of the same kind, always boils at the same temperature. Consequently, for the first fixed point, or zero, the temperature of melting ice has been taken ; and, for a second fixed point, the temperature of boiling water in a metallic vessel under the normal atmospheric pressure of 30 inches. This interval of temperature, that is, the range from zero to the boiling point, is taken as the unit for comparing tempera- tures ; just as a certain length, a foot or a yard for instance, is used as a basis for comparing lengths. Flg> I75- To obtain zero, snow or pounded ice is placed in a vessel, in the bottom of which is an aperture by which water escapes (fig. 175). The bulb and a part of the stem of the thermometer are immersed in ihis for about a quarter of an hour ; the mercury sinks, and the level at which it finally rests, t for instance, is marked by tying a piece of thread round the stem. O 2 196 On Heat. [199- The second fixed point is determined by means of the apparatus represented in fig. 176. It consists of a tin-plate vessel containing Fig. 176. Fig. 177- distilled water, in the lid of which is a long tube. The thermo- meter is placed in this by means of a cork, and the water heated -200] Construction of the Thermometer Scale. 197 to boiling. The thermometer is thus surrounded by steam, which, liberated from the liquid escapes by the lateral apertures. This steam is at the same temperature as the water from which it is liberated, and, when the mercury is stationary, a second mark is made upon the stem. 200. Construction of the scale. Just as the foot-rule which is adopted as the unit of comparison for length is divided into a number of equal divisions called inches, for the purpose of having a smaller unit of comparison, so likewise the unit of comparison of temperatures, the range from zero to the boiling point, must be divided into a number of parts of equal capacity called degrees. There are three modes in which this is done. On the Continent, and more especially in France, this space is divided into 100 parts, and this division is called the Centigrade or Celsius scale ; the latter being the name of the inventor. The Centigrade thermometer is almost exclusively adopted in foreign scientific works, and as its use is gradually extending in this country, it has been and will be adopted in this book. The degrees are designated by a small cipher placed a little above on the right of the number which marks the temperature, and to indicate temperatures below zero the minus sign is placed before them. Thus - 15 signifies 15 degrees below zero. In accurate thermometers the scale is marked on the stem itself (fig. 178). It cannot be displaced, and its length remains fixed, as glass has very little expansi- bility. This is effected by covering the stem with a thin layer of wax, and then marking the divisions of the scale, as well as the corresponding numbers, with a steel point. The thermometer is then exposed for about ten minutes to the vapours of a substance called hydrofluoric acid, which attacks the glass where the wax has been removed. The rest of the wax is then removed, and the stem is found to be permanently etched. Scales are also constructed on plates of ivory, wood, Fig7i 7 8. or metal, against which the stem is placed. Fig. 177, represents a mercury thermometer mounted on ivory; its scale extends from 20 degrees below zero to 1 10 degrees above. Besides the Centigrade scale two others are frequently used Fahrenheit's scale and Reaumur's scale. 198 0// #htf. [200- In Reaumur's scale the fixed points are the same as on the Centigrade scale, but the distance between them is divided into So degrees instead of into icn. That is to say, 80 degrees Reaumur are equal to ico degrees Centigrade ; one degree Reaumur is equal to ^ or f of a degree Centigrade, and one degree Centigrade equals T 8 ~ or * degree Reaumur. Consequently to convert any number of Reaumur degrees into Centigrade degrees (20 for ex- ample), it is merely necessary to multiply them by f (which gives 25). Similarly, Centigrade degrees are converted into Reaumur's by multiplying them by f. The thermometric scale invented by Fahrenheit in 1714 is still much used in England, and also in Holland and North America. The higher fixed point is like that of the other scales, the tempera*- ture of boiling water, but the null-point or zero is the temperature obtained by mixing equal weights of sal-ammoniac and snow, and the interval between the two points is divided into 212 degrees. The zero was selected because the temperature was the lowest then known, and was erroneously thought to represent absolute cold. When Fahrenheit's thermometer is placed in melting ice it stands at 32 degrees, and, therefore, 100 degrees on the Centigrade scale are equal to 180 degrees on the Fahrenheit scale, and thus i degree Centigrade is equal to f degree Fahrenheit, and conversely I degree Fahrenheit is equal to f of a degree Centigrade. If it be required to convert a certain number of Fahrenheit de- grees (95 for example) into Centigrade degrees, the number 32 must be first substracted, in order that the degrees may count from the same point of the scale. The remainder in the example is thus 63, and as i degree Fahrenheit is equal to f of a degree Centigrade, 63 degrees are equal 10.63 x f or 35 degrees Centigrade. If F be the given temperature in Fahrenheit's degrees and C the corresponding temperature in Centigrade degrees, the former may be converted into the latter by means of the formula (F-32) and conversely, Centigrade degrees may be converted into Fahren- heit by means of the formula These formulae are applicable to all temperatures of the two scales, provided the signs are taken into account. Thus, to convert the -202] A Icohol Thermometer. 199 temperature of 5 degrees Fahrenheit into Centigrade degrees we have In like manner we have for converting Reaumur's into Fahren- heit's degrees the formula and conversely, for changing Fahrenheit's into Reaumur's degrees the formula (F- 3 2)| = R. 201. Alcohol thermometer. The alcohol thermometer differs from the mercurial thermometer in being filled with coloured alcohol. But as the expansion of liquids is less regular in propor- tion as they are near the boiling point, alcohol, which boils at 78 C, expands very irregularly. Hence, alcohol thermometers are usually graduated by placing them in baths at different temperatures to- gether with a standard mercurial thermometer. The filling is effected by gently heating the bulb, so as to expel a certain quantity of air, then in- verting it and plunging the open end into alcohol (fig. 179). The interior air contracts on cooling, and the atmospheric pressure raises the alcohol in the tube and in the bulb. It does not at first fill it completely, for some air remains ; but the alcohol is then boiled, and its vapours expel all the air ; the tube is then again inverted and placed in alcohol, and now the instrument fills completely. The further construction resembles that of a mercurial thermometer. 202. Limits to the employment of mercurial thermometers. Of all thermometers in which liquids are used, the one with mercury is the most useful, because this liquid expands most re- gularly, and is easily obtained pure, and because its expansion be- tween 36 and 100 is regular, that is, proportional to the degree Fig. 179. 2OO On Heat. [202- of heat. It also has the advantage of having a very low specific heat. But for temperatures below - 36 C. the alcohol thermometer must be used, for mercury solidifies at 40 C. to a mass like lead. Above 100 degrees the coefficient of expansion increases 'and the indications of the mercurial thermometers are only approximate, the error amounting sometimes to several degrees. Mercurial thermometers also cannot be used for temperatures above 350, for this is the boiling point of mercury. \ Observations by means of the thermometer. In taking the tem- perature of a room, the thermometer is usually suspended against the wall. This may, however, give rise to an error of several de- grees ; for if the wall communicates with the outside, and especially if it has a northern aspect, it will, generally speaking, be colder than the air in the room, and will communicate to the thermometer too low a temperature. On the other hand it may happen that the wall becomes too much heated by the sun's rays, or by chimney flues, and then the thermometer will be too high. The only way to obtain with accuracy the temperature of the air in a room is to suspend the thermometer by a string in the centre at a distance from any object which might raise or lower its tempera- ture. The same remark applies to the determination of the temperature of the atmosphere ; the thermometer must be suspended in the open air, in the shade, and not against a wall. 203. Leslie's differential thermo- meter. Sir John Leslie constructed a thermometer for showing the difference in temperature of two neighbouring places, from which it has received the name differential thermometer. It consists of two glass bulbs containing air, and joined by a bent glass tube of small diameter fixed on a frame (fig. 180). Before the apparatus is sealed, a coloured liquid is introduced in sufficient quantity to fill the horizontal part of the tube and about half the vertical legs. It is im- portant to use a liquid which does not give off vapours at ordinary temperatures, and dilute sulphuric acid coloured with litmus is generally preferred. The apparatus being closed, the air is passed Fig. i 204] Maximum and Minimum Tliermometers. 201 from one bulb into the other, by heating them unequally, until the level of the liquid is the same in both branches. A zero is marked at each end of the liquid column. To graduate the apparatus, one of the bulbs is raised to a temperature 10 higher than the other. The air of the first is expanded and causes the column of liquid, ba, to rise in the other leg. When the column is stationary the number 10 is marked on each side at the level of the liquid, the distance between zero and 10 being divided into 10 equal parts, both above and below zero, on each leg. 204. Rutherford's maximum and minimum thermometers. It is necessary, in meteorological observations, to know the highest temperature of the day, and the lowest temperature of the night. Ordinary thermometers could only give these indications by a con- tinuous observation, which would be impracticable. Several in- struments have accordingly been invented for this purpose, the simplest of which is Rutherford's. On a rectangular piece of plate glass (fig. 181) two thermometers are fixed, whose stems are bent iK Iwte 40 00 20 Fig. 181. horizontally. The one, A, is a mercurial, and the other, B, an alcohol thermometer. In A there is a small piece of iron wire, A, moving freely in' the tube, which serves as an index. The ther- mometer being placed horizontally, when the temperature rises the mercury pushes the index before it. But as soon as the mercury contracts, the index remains in that part of the tube to which it has been moved, for there is no adhesion between the iron and the mercury. In this way the index registers the highest temperature which has been obtained ; in the figure this is 31. In the minimum thermometer there is a small hollow glass tube which serves as index. When it is at the end of the column of liquid, and the tem- perature falls, the column contracts and carries the index with it, 202 On Heat. [204- in consequence of adhesion, until it has reached the greatest con- traction. When the temperature rises, the alcohol expands, and passing between the sides of the tube and the index does not dis- place B. The position of the index gives therefore the lowest tem- perature which has been reached : in the figure this was 9^ degrees frelow zero. 205. Pyrometers. The name pyrometers is given to instru- ments for measuring temperatures so high that mercurial ther- mometers could not be used. The older contrivances for this purpose, Wedgwood's, Daniell's (which in principle resembled the apparatus in fig. 170), Brongniart's, etc., are gone entirely out of use. None of them gives an exact measure of temperature. CHAPTER II. RADIATION OF HEAT. 206. Radiant heat. If we stand in front of a fire, or expose ourselves to the sun's heat, we experience a sensation of warmth which is not due to the temperature of the air, for if a screen be interposed, the sensation immediately disappears, which would not be the case if the surrounding air had a high temperature. Hence bodies can send out rays which excite heat, and which penetrate through the air without heating it, as rays of light through trans- parent bodies. Heat thus propagated is said to be radiated ; and we shall use the term ray of heat, or thermal, or calorific ray, in a similar sense to that in which we use the term ray of light, or luminous ray. We shall find that the property of radiating heat is not confined to incandescent substances, such as a fire, or a lamp, or a red-hot ball, but that bodies of all temperatures radiate heat. Thus a bottle full of hot water and a bottle full of cold water both emit heat ; the first emits more as compared with the second, the greater the difference of temperature between the two. 207. Laws of radiation. The radiation of heat is governed by three laws. I. Radiation takes place in all directions round a body. If a thermometer be placed in different positions round a heated body, it indicates everywhere a rise in temperature ; at equal distances from the source of heat it indicates the same rise in temperature. -208] Radiant Heat. 203 II. Heat is propagated in a right line. For, if a screen be placed in the right line which joins the source of heat and the thermometer, so as to stop the rays, the latter is not affected. But in passing obliquely from one medium into another, as from air into a glass, calorific like luminous rays become deviated, an effect known as refraction. The laws of this phenomenon are the same for heat as for light, and they will be more fully discussed under the latter subject. III. Radiant heat is propagated in vacua as -well as in air. This is demonstrated by the following ex- periment. In the bottom .of a glass flask a thermometer is fixed in such a manner that its bulb occupies the centre of the flask (fig. 182). The neck of the flask is then carefully narrowed by means of the blow-pipe, F ; g . l82 . and then the apparatus having been suitably attached to an air-pump a vacuum is produced in the interior. This having been done, the tube is sealed at the narrow part. On immersing this apparatus in hot water, or on bringing near it some hot char- coal, the thermometer is at once seen to rise. This could only be due to radiation through the vacuum in the interior, for glass is so bad a conductor, that the heat could not travel with this rapidity through the sides of the flask, and the stem of the thermometer. 208. Causes which modify the intensity of radiant heat. The intensity of radiant heat transmitted to us by heated bodies depends on the temperature of the source of heat, and on its distance. The corresponding laws may be thus stated : I. The intensity of radiant heat is proportional to the temperature of the source. I 1. The intensity of radiant heat is inversely as the square of the distance. The first law is demonstrated by placing a metal box containing water at 10, 20, or 30, successively at equal distances from the bulb of a differential thermometer. The temperatures indicated by the latter are then found to be in the same ratio as those of the box : for instance, if the temperature of that corresponding to the box at 10 be 2, those of the others will be 4 and 6 respectively. The second law is demonstrated experimentally by placing the differential thermometer at a certain distance from the source of heat, a yard for distance, and then removing it to double the 204 On Heat. [208- distance. In the latter case, the amount of heat received is not one-half but one-quarter. If the distance be three yards the quan- tity of heat is one-ninth, and so forth. 209. Interchange of heat among all bodies. Owing to the radiation which is continually taking place in all directions round a body, there is a continual interchange of heat. If the bodies are all at the same temperature, each one sends to the surrounding ones a quantity equal to that which it receives, and their temperatures remain stationary. But if their temperatures are unequal, as the hot bodies emit more heat than they receive, they therefore sink in temperature ; while, as the bodies of lower temperatures receive more heat than they emit, their temperature rises ; thus the tempera- tures are all ultimately equal. The radiation does not stop ; it goes on, but without loss or gain from each body, and this condition is accordingly known as the mobile equilibrium of temperature. From what has been said it will be understood that bodies placed in our rooms all tend to assume a uniform temperature ; generally speaking this is not the case, for many causes concur in cooling one set, and in heating the others. Thus bodies placed near a wall cooled by the outer air find a cause for cooling. Those, on the contrary, which are at the top of the room, tend to acquire a higher temperature ; for as heated air rises as being less dense, the layers nearest the ceiling are always hotter than the lower ones. From this continual interchange of heat, there is necessarily a limit to the cooling of bodies, for they always tend to resume, on the one hand, what they lose on the other. To have an indefinite cooling, a body should be suspended in space, not receiving heat from any body. As it would then lose heat without acquiring any, there is no telling to what extent its. temperature would sink. CHAPTER III. REFLECTION OF HEAT. REFLECTING, ABSORBING, AND EMISSIVE POWERS. 210. Iiaw of the reflection of heat. When the heat rays emitted by a source of heat fall upon the surface of a body, they are divided generally into two parts ; one, which passes into the mass of a body and raises the temperature ; the other, which darts -211] Reflection of Heat. 205 off from the surface like an elastic ball striking against a hard body ; this is expressed by saying that these rays are reflected. Thus let A be the source of heat, a cubical box rilled with hot water (fig. 183), and near it a screen which does not allow heat to pass, but near the bottom of which is an aperture. If behind this screen a polished surface be placed on which the rays emitted by the cube impinge, and beyond this again a differential thermometer, the latter indicates an increase of temperature when one of its bulbs is so placed that it receives the rays reflected by the polished body. In this experiment, rays like AB which fall on the reflecting surface ; ^^-.^^jt-^fs: Fig. 183. are called incident rays, from a Latin word which signifies to fall ; and the angle of incidence is not the angle which they make with the reflecting surface, but the angle, ABC, which they make with a straight line, BC, perpendicular to this surface. In like manner the angle, CBD, which the reflected rays make with the same straight line, is called the angle of reflection. The reflection of heat is always subject to the law, that the angle of reflection is equal to the angle of incidence. We shall subse- quently see that the reflection of light is governed by the same law. 211. Reflection of heat from concave mirrors. The effects of the reflection of heat may be very powerful when it takes place from the surface of concave mirrors, which are spherical surfaces of glass or of metal. These mirrors may be regarded as being made up of an infinite number of extremely small planes inclined towards each other in such a manner as to determine the curvature. From the symmetrical grouping of these small facets, it follows that when a group of rays fall upon a concave mirror, these rays, in obedience 2O6 On Heat. [211- to the laws of reflection coincide in a single point, to which the name focus is applied, to express the great quantity of heat which is concentrated there. (321). In treating of light we shall discuss in detail the properties of the focus in concave mirrors ; for the present it will be suffick nt to de- scribe experiments which demonstrate the great intensity which radiant heat may acquire when concentrated in these points. Fig. 184 represents an experiment which is frequently made in physical lectures. Two reflectors, A and B (fig. 185), are arranged at a dis- tance of 4 to 5 yards, and so that their axes coincide. In the focus of one of them, A, is placed a small basket, ;/, containing a red-hot Fig. 184. iron ball. In the focus of the other, B, is placed an imflammable body, such as gun-cotton or phosphorus. The rays emitted from the focus, 71, are first reflected from the mirror, A, in a direction parallel to the axis ; and impinging on the other mirror, B, are reflected so that they coincide in the focus ;//. That this is so, is proved by the fact that the inflammable substance placed in this point takes fire, which is not the case if it is above or below it. The same effect may be produced by the sun's rays. For this purpose a concave reflector is so placed that the sun's rays strike directly against it (fig. 185) ; if then a combustible substance, such as paper, vyood, cork, etc., be held by means of a pincette in the focus, these bodies are seen to take fire. The effect produced -212] Reflecting Power of Substances. 207 depends on the magnitude of the mirrors. With a mirror having an aperture of 6 feet, that is, the distance from one edge to the other, copper and silver are melted in a few minutes ; and silicious stones and flints are softened and even melted. In consequence of the high temperatures produced in the foci of concave mirrors and of the facility with which combustible bodies may be ignited there, they have been called burning mirrors. It is stated that Archimedes burnt the Roman vessels before Syra- cuse by means of such mirrors. Buffon constructed burning Fig. 185. mirrors of such power as to prove that the feat attributed to Archi- medes was possible. The mirrors were made of a number of silvered plane mirrors about 8 inches long by 5 broad. They could be turned independently of each other in such a manner that the rays reflected from each coincided in the same point. With 128 mirrors and a hot summer's sun Buftbn ignited a plank of tarred wood at a distance of 70 yards. 212. Reflecting: power of various substances. It has been seen that heat which falls upon a body is always divided into two 208 On Heat. [212- parts, one which is reflected on the surface, and the other which passes into the mass of the body, and raises its temperature. The quantities of heat thus absorbed, or reflected, vary in different sub- stances ; one set reflects much and absorbs little, which is ex- pressed by saying that they have a great reflecting power ; others, on the contrary, reflect very little heat, but absorb a great deal, and are therefore spoken of as havirg great absorbing power. It is clear that these properties are the inverse of each other, for every body which absorbs much heat can reflect but little, and conversely. In order to compare the reflecting powers of various substances, Leslie took as a source of heat a tin plate cube full of boiling water, which he placed in front of a concave mirror (fig. 186). The rays Fig. 186. emitted from this towards the reflector tended after reflection to become concentrated on the focus F. In front of this were placed successively small square plates of paper, glass, metal, in short, ot all the substances whose reflecting power was to be examined. As shown in the drawing, these rays after a first reflection from the mirror, were reflected a second time from these plates, and finally impringed against the bulb of a differential thermometer. Now, as in this experiment the source of heat was the same, as was also the distance from the reflector ; yet the thermometer indicated very various degrees of heat according to the material of which the small plates were formed. The temperature was highest when the -213] A bsorbing Power. 209 plate was made of polished brass, which metal is therefore the best re- flector. The reflecting power of silver is only T 9 5 that of brass ; that of tin i ; of glass 5 . Water and lampblack were found to be des- titute of reflecting power, for when the plates were coated with lampblack, or moistened with water, the thermometer indicated no increase in temperature, showing that it received no heat. 213. Absorbing- power. In order to compare the absorbent powers of various substances, Leslie arranged the experiment as shown in fig. 187. The source of heat and the reflector being the Fig. 187. same as in the preceding experiment, the differential thermometer was placed in the focus, where it received directly all the heat re- flected by the mirror. The surface of the focal bulb was altered for each experiment by coating it successively with various ma- terials, paper, tinfoil, gold, silver, copper, and leadfoil ; it was also coated with a thin layer of lampblack ; it was moistened, and so on. It was thus found that when the focal bulb was coated with lampblack, or with water, the thermometer indicated the highest temperatures ; whence it was concluded that lampblack and water have the greatest absorbing power. The lowest temperature was exhibited when the bulb was coated with thin metal foil, more especially with silver ; thus indicating that these substances absorb the least proportion of the heat which is of the temperature of boiling water (216). The result was arrived at which could indeed be fore- p 210 On Heat. [213- seen, that those bodies which best reflect heat absorb it least ; and that, conversely the best absorbents are the worst reflectors. 214. Emissive power. The emissive or radiating power is the property bodies have of emitting more or less easily the heat they contain ; it is the inverse of the absorbing power. Leslie compared the emissive powers of various bodies by means of the apparatus represented in fig. 187. The focal bulb of the thermometer was left uncoated, and the various substances were applied successively to the sides of the tin cube. One of them, for instance, was left in its ordinary condition ; the second was coated with lampblack ; to the third a sheet of white paper was fixed, and to the fourth a glass plate. Turning first of all the blackened face towards the reflector, the thermometer indicated a considerable increase of temperature, thus showing that the cube sent much heat towards the reflector. Turning then successively the other faces towards the reflector, it was found that the paper side emitted less heat than the blackened face, but more than the glass side, which in turn emitted more than the tin side. Working in this manner, Leslie found that lampblack has the greatest emissive power, then paper, then ordinary glass, then the metals. * The order of their emissive powers is thus the same as that of their absorbing powers. It is thus concluded that bodies which best absorb heat, also radiate best ; and Dulong and Petit have proved that for each substance the emissive power is in all cases proportional to the absorbing powen 215. Causes which modify the reflecting 1 , absorbing-, and radiating- powers. As the radiating and absorbing powers are equal, any cause which affects the one affects the other also. And as the reflecting power varies in an inverse manner, whatever in- creases it diminishes the radiating and absorbing powers, and-z/zV^ versa. It has been already stated that these different powers vary with different bodies, and that metals have the greatest reflecting power, and lampblack the feeblest. In the same body these powers are modified by the degree of polish, the density, the thickness of the radiating substance, the obliquity of the incident or emitted rays, and, lastly, by the nature of the source of heat. It has been assumed usually that the reflecting power increases with the polish of the surface, and that the other powers diminish therewith. But Melloni showed, that by scratching a polished metallic surface its reflecting power was sometimes diminished and sometimes increased. This phenomenon he attributed to the -216] Different Kinds of Heat. 211 greater or less density of the reflecting surface. If the plate had been originally hammered, its homogeneity would be destroyed by this process, the molecules would be closer together on the surface than in the interior, and the reflecting power would be increased. But if the surface is scratched the internal and less dense mass becomes exposed, and the reflecting power diminished. On the contrary, in a plate which has not been hammered and which is homogeneous, the reflecting power is increased wrfen the plate is scratched, because the density at the surface is increased by the scratches. The absorbing power varies with the inclination of the incident rays. It is greatest at right angles ; and it diminishes in propor- tion as the incident rays 'deviate from the perpendicular direction. This is one of the reasons why the sun is hotter in summer than in winter, because, in the former case, the solar rays are less oblique. The radiating power of gaseous bodies in a state of combustion is very weak, as is seen by bringing the bulb of a thermometer near a hydrogen flame, the temperature of which is very high. But if a platinum spiral be placed in this flame, it assumes the temperature of the flame, and radiates a considerable quantity of heat, as is in- dicated by the thermometer. It is for an analogous reason, that the flames of oil and of gas lamps radiate more than a hydrogen flame, in consequence of the excess of carbon which they contain, and which, not being entirely burned, becomes incandescent in the flame. The absorbing power of a body is also influenced by the nature of the source of heat. Thus, for the same quantity of heat emitted, a surface coated with white lead absorbs twice as much, if the heat comes from a cube filled with hot water, as it does if the heat is that of a lamp. Lampblack, on the contrary, absorbs the same amount of heat whatever be the source. 216. Different kinds of beat. Diathermaneity. Just as different substances possess the power of allowing the rays of light to pass through them to different extents, and are said to be more or less transparent (305), so also modern investigation has shown that all bodies do not allow the rays of heat to traverse them with equal facility, and are therefore said to be more or less diathermanous. Thus the metals are just as adiathermanous for heat rays as they are opaque for the rays of light. On the other hand rock salt stands in the same relation to heat rays that a perfectly colourless and transparent body, such as glass, does to luminous rays. It is perfectly diathermanous. p 2 212 On Heat. [216- One and the same substance may be diathermanous to varying extents for heat from different sources. Thus colourless glass allows the sun's rays to pass through it with facility, but less so the heat emitted by a flame, or by an incandescent body, and far less again the heat of a cube filled with boiling water, which is known as a Leslie's cube (212). Water allows the solar heat to traverse it partially, but stops the obscure heat of a Leslie's cube. Again, alum is colourless and transparent for light, but almost entirely dia- thermanous for obscure rays. A body which is opaque for light may be diathermanous for certain kinds of heat. Thus, a solution of iodine in bisulphide of carbon is perfectly opaque for the rays of light, but is traversed by obscure heat rays with facility. In investigating the diathermaneity of bodies, Melloni used the thermo-multiplier, for a description of which we must refer to Book VIII. Chapter xiii. He first of all placed the thermo-multiplier at a certain distance from a source of heat, and having observed the deflection, he determined to what extent this was enfeebled by the interposition of various bodies, such as plates of glass, alum, and rock salt. In like manner he used various sources of heat, for instance the sun, an oil or spirit lamp, an ignited spiral of platinum wire, a heated blackened metal plate, or a cube filled with hot water, and he concluded that there are different kinds of heat rays, or different colours of heat, with regard to which various diather- manous substances behave just as coloured transparent substances do in regard to different kinds of light. Thus when white light traverses red glass, only the red rays are transmitted, all other kinds being absorbed. If this red light falls on another red glass it traverses it without enfeeblement ; but is completely absorbed by blue glass. Similar results are met with in regard to the rays of heat. 217. Applications. The property which bodies possess of ab- sorbing, emitting, and reflecting heat, meets with numerous appli- cations in domestic economy and in the arts. Leslie stated that white bodies reflect heat very well, and absorb very little, and that the contrary is the case with black substances. This principle is not universally true, as Leslie supposed ; for example, white lead has as great an absorbing power for non-luminous rays as lamp- black. But it holds good in regard to absorbents like cloth, cotton, wool, and other organic substances when exposed to luminous heat, such as that of the sun's rays. Accordingly, the most suitable -218] Conductivity of Solids. 213 coloured clothing for summer is just that which experience has taught us to use, namely, white, for it absorbs less of the sun's rays than black clothing, and hence feels cooler. The polished fire-irons before a fire are cold, whilst the black fender is often unbearably hot. If a liquid is to be kept hot as long as possible, it must be placed in a brightly polished metallic vessel, for then, the emissive power being less, the cooling is slower. It is for this reason advantageous that the steam pipes, etc., of locomotives should be kept brightly polished. Snow is a powerful reflector, and, therefore, neither absorbs nor emits much heat ; owing to its small emissive power it protects from cold the ground and the plants which it covers ; and owing to its small absorbing power it melts but slowly during a thaw. A branch of a tree, a bar of metal, a stone in the midst of a mass of snow, accelerate the fusion by the heat they absorb, and which they radiate about them. In the Alps the mountaineers accelerate the fusion of the snow by covering it with earth, which increases the absorbing power. Metal cooking vessels should be black and rough on the outside, for then their absorbing power is greater and they become heated more rapidly. Their bright and polished surface is purchased at the expense of combustible. This is what is seen in vessels of silver and of white procelain. In common unglazed earthenware liquids are more rapidly heated, but also more rapidly cooled. It is observed that the ripening of grapes and other fruits is ac- celerated when they are placed in contact with a black wall (mortar mixed with lampblack). This arises from the fact, that from the great emissive power of the wall, as well as from its great absorbing power, it becomes more highly heated under the influence of the sun, and gives up more to the fruit. Glass is used for fire-screens, for while it allows the cheerful light of the fire to pass, it stops most of the heat. CHAPTER IV. CONDUCTING POWER OF BODIES. 2 1 8. Conductivity of solids, In the phenomena of radiation which have been considered, heat is transmitted from one body to another through space, without raising the temperature of the 214 On Heat. [218- medium through which it passes. It may also be propagated through the mass of a body by an internal radiation from molecule to' molecule. This internal propagation in the mass of a body is called conductivity ; and good conductors are those bodies which readily transmit heat in their mass, while those through which it passes with difficulty are called bad conductors. Organic substances conduct heat badly. De la Rive and De Candolle have shown that woods conduct better in the direction of their fibres than in a transverse direction ; and have remarked upon the influence which this feeble conducting power, in a transverse direction, exerts in preserving a tree from sudden changes of tem- perature, enabling it to resist alike a sudden abstraction of heat from within, and the sudden accession of heat from without. Tyndall Fig. xE has also shown that this tendency is aided by the low conducting power of the bark, which is in all cases less than that of the wood. Cotton, wool, straw, bran, powdered gypsum, etc., are all bad conductors. In order to compare the conducting power or conductivity of dif- ferent solids, Ingenhousz constructed the apparatus which bears his rame, and which is represented in fig 188. It is a metal trough, in which, by means of tubulures and corks, are fixed rods of the same dimensions, but of different materials ; for instance, iron, copper, wood, glass. These rods extend to a slight distance in the trough, and the parts outside are coated with wax, which melts at 61. The box being filled with boiling water, it is observed that the wax melts to a certain distance on the metal rods, while on. the -219] Conducting Power of Liqidds. 21$ others there is no trace of fusion. The conducting power is evidently greater in proportion as the wax has fused to a greater distance. The experiment is sometimes modified by attaching glass balls or marbles to the ends of the rods by means of wax. As the wax melts, the balls drop off, and this in the order of their respective con- ductivities. By these and other experiments it has been ascer- tained that metals are the best conductors, then marble, porcelain, brick, wood, glass, etc. 219. Conducting power of liquids. Manner in which they are heated. Liquids, with the exception of mercury, which is a metal, are all bad conductors of heat. They conduct so imperfectly that Rumford assumed water to be entirely destitute of conducting power. But its conductivity, though small, has been established beyond doubt, as well as that of other liquids, by the most accurate experiments. From their small conducting power, liquids are not heated in the same manner as solids. If heat be applied to a solid, whether on the top, the bottom, or the sides, it is transmitted from layer to layer, and the whole mass becomes heated. This is not the case with a liquid ; if it is heated at the top, the heat is only pro- pagated with extreme slowness, and it cannot be completely heated. But if it be heated at the bottom, the temperature of the liquid rapidly rises. This however, is not owing to its conductivity, but to ascending and descending currents, which in virtue of the mobility of the molecules, are produced through- out the whole mass of liquid. The existence of these cur- rents may be demonstrated by placing in the water a powder of near the same density, for instance, oak sawdust, and then gently heating the vessel at the bottom. As the lower layers of the liquid become heated they expand, while the upper layers, which are colder and therefore denser, sink and take the place of the first ; these in their turn become heated, rise, and so on, until the entire Fig. 216 On Heat. [219- mass is heated. These currents are evident from the sawdust which is seen to rise slowly in the centre, and to redescend near the edges. 220. Conductivity of gases. Gases are extremely bad con- ductors of heat ; but this cannot be easily demonstrated by ex- periment, owing to the extreme mobility of their particles. For so soon as they are heated in any part of their mass, expan- sions and currents are produced, in virtue of which the heated parts mingle with the cold ones ; hence a general elevation of tempera- ture, which we might be tempted to consider as due to conduc- tivity. When, however, gases are hindered in their motion, their conductivity seems extremely small, as the following examples show. 221. Applications. The greater or less conductivity of bodies meet with numerous applications. If a liquid is to be kept warm for a long time, it is placed in a vessel and packed round with non- conducting substances, such as shavings, straw, bruised charcoal. For this purpose water pipes and pumps are wrapped in straw at the approach of frost. The same means are used to hinder a body from becoming heated. Ice is transported in summer by packing it in bran, or folding it in flannel. Double walls constructed of thick planks having between them any finely divided materials such as shavings, sawdust, dry leaves, etc., retain heat extremely well ; they are likewise advantageous in hot countries, for they prevent its access. If a layer of asbestos, a very fibrous substance, is placed on the hand, a red-hot iron ball can be held without inconvenience. Red-hot cannon balls can be wheeled to the gun's mouth in wooden barrows partially filled with sand. Lava has been known to flow over a layer of ashes under- neath which was a bed of ice, and the non-conducting power of the ashes has prevented the ice from fusion. A covering of snow pro- tects seed and young grain from frost. In fireproof safes the hollow walls are filled with wood ashes, or powdered gypsum, or ignited alum. The clothes which we wear are not warm in themselves ; they only hinder the body from losing heat, in consequence of their spongy texture and the air they enclose. The warmth of bed-covers and of counterpanes is explained in a similar manner. Double windows are frequently used in cold climates to keep a room warm they do this by the non-conducting layer of air interposed between them. It is for the same reason that two shirts are warmer than one of the same material, but of double the thickness. Hence too the warmth of furs, eider down, etc. -222] Expansion of Solids. 2 1 7 That water boils more rapidly in a metallic vessel than in one of porcelain of the same thickness ; that a burning piece of wood can be held close to the burning part with the naked hand, while a piece of iron heated at one end can only be held at a great distance, are easily explained by reference to their various conductivities. The sensation of heat or cold which we feel when in contact with certain bodies is materially influenced by their conductivity. If their temperature is lower than ours, they appear colder than they really are, because, from their conductivity, heat passes away from us. If, on the contrary, their temperature is higher than that of our body, they appear warmer from the heat which they give up at dif- ferent parts of their mass. Hence it is clear why carpets, for ex- ample, are warmer than wooden floors, and why the latter are warmer than stone floors. CHAPTER V. MEASUREMENT OF THE EXPANSION OF SOLIDS, LIQUIDS, AND GASES. 222. Expansion of solids. The expansion of bodies by heat being a general effect which exerts its influence on all bodies, and is continually changing their volume, it will be readily understood that the determination of the amount of this expansion is a problem of great importance, both in its purely scientific, as well as in its prac- tical, aspects. We shall first describe the method of determining the expansion of solids. We have already seen that the expansion of solids may be either as regards the length or the volume. Hence the investigation of the expansion of solids may be divided into two parts, the first relating to linear, and the second to cubical expansion. Linear expansion. In order to compare with each other the ex- pansion of bodies, the elongation is taken which the unit of length undergoes when he is heated from zero to i degree, and this elonga- tion is called the coefficient of linear expansion. The coefficients ot a great number of substances were accurately determined towards the end of the last century by Lavoisier and Laplace. They took a bar of the substance to be determined, placed it in melting ice, and then accurately .determined its length. Having placed it then in a bath of boiling water, they again measured its length. They 218 On Heat. [222- then observed an elongation, which represented the total expansion for an increase of temperature of 100 degrees. This, divided by 100, gave the coefficient of linear expansion for one degree. In this manner the following numbers may be obtained : Coefficients of linear expansion for i between o and 100 C. White glass. . 0-00000861 Bronze . . 0-000018167 Platinum . . 0*00000884 Brass . . . 0*000018782 Steel . . . 0-00001079 Silver . . . 0-000019097 Iron -. . . 0*00001220 Tin . .' . 0-000021730 Gold . 0-00001466 Lead . . 0-000028575 Copper . . 0*00001718 Zinc . . . 0-000029417 It will be seen from this table, that the coefficients of expansion are in all cases very small. Thus, when we say that the coefficient of expansion of copper is about o-c 00017, w e mean that a rod of this metal when heated through i degree, will expand by 17 millionths of its length ; that is to say, a rod of copper a million feet in length would be longer by 17 feet under these circumstances. Cubical expansion. The coefficient of cubical expansion is the in- crease in volume for a temperature of one degree. Calculation shows that the coefficient of cubical expansion is three times its coefficient of linear expansion ; and these coefficients may therefore be obtained by multiplying the above numbers by three. 223. Applications of the expansion of solids. In the arts we meet with numerous examples of the influence of expansion, (i.) The bars of furnaces must not be fitted tightly at their extrem- ities, but must, at least, be free at one end, otherwise, in expanding, they would exert sufficient force to split the masonry, (ii.) In making railways a small space is left between the successive rails, for, if they touched, the force of expansion would cause them to curve or would break the chairs, (iii.) Water pipes are fitted to one another by means of telescopic joints, which allow room for expansion, (iv.) If a glass is heated or cooled too rapidly it cracks ; this arises from the fact that glass being a bad conductor of heat, the sides become unequally heated, and consequently un- equally expanded, and the strain thereby produced is sufficient to cause a fracture. When bodies have been heated to a high temperature, the force produced by their contraction on cooling is very considerable ; it is equal to the force which is needed to compress or expand the material to the same extent by mechanical means. According to 224] Compensation Pendulum. 219 Barlow a bar of malleable iron a square inch in section is stretched I6 -- of its length by a weight of a ton ; the same increase is ex- perienced by about 9 C. A difference of 45 C. between the cold of winter and the heat of summer is not unfrequently experienced in this country. In that range a wrought iron bar, ten inches long will vary in length by ~o of an inch, and will exert a strain, if its ends are securely fastened, of fifty tons. An application of this contractile force is seen in the mode of securing the tires on wheels. The tire being made red hot, and thus considerably expanded, is placed on the circumference of the wheel, and then cooled. The tire, when cold, clasps the wheel with such force as not only to secure itself on the rim, but also to press home the joints of the spokes into the felloes and nave. Another interesting application was made in the case of a gallery at the Conservatoire des Arts et Metiers in Paris, the walls of which had begun to bulge outwards. Iron bars were passed across the building, and screwed into plates on the outside of the walls. Each alternate bar was then heated by means of lamps, and when the bar had expanded, it was screwed up. The bars being then allowed to cool contracted, and in so doing drew the walls together. The same operation was performed on the other bars. 224. Compensation pendulum. An important application of the expansion of metals has been made in the compensation pendu- lum. To understand the utility of such an arrangement, we must call to mind what has been said about pendulums ; namely, that their oscillations are isochronous, that is, are made in equal times, and that their application to the regulation of clocks depends upon this property. But we have also seen that the duration of an oscil- lation depends on the length of the pendulum ; the longer the pen- dulum the more slowly it oscillates, and, therefore, the shorter it is, the more rapidly does it oscillate. Hence a pendulum formed of a single rod terminated by a metal bob, c, as represented in fig. 52, could not be an exact regulator ; for, as the temperature rises, it would elongate, and the clock would go slower : the exact opposite would take place when it contracted by cooling. These inconve- niences have been remedied by taking the remedy from the cause of the evil. For this purpose the pendulum rod consists of several metal bars arranged as represented in fig. 190. The rods, a,b, c, d, are of steel, and all expand in a downward direction when the tempera- ture rises, thus making the bob sink. The rod, d, supporting the 220 On Heat. [224- bob is fixed to a cross-piece mn, which in turn is fastened to two rods, k and /i, which are connected to the piece or, and therefore cannot expand downwards, but only in an upward direction ; they raise the piece ;//, and with it the bob. In order, therefore, that this latter shall neither raise nor sink, it is necessary that the upward expansion of the rods, k and h, shall exactly com- pensate the downward expansion of the rods,tf,, c,d. Brass being more expansible than steel, com- pensation is effected by taking the first metal for the rods h and k, and the second for the rods, a, b, r, and d. The only condition necessary for com- pensation is that the lengths of the two metals must be inversely as their coefficients of expansion. That is to say, that if brass is two or three times as ex- pansible as steel, its length must be one- half or one- third as much. In fig. 190 the pendulum has been represented with a single frame of steel and one of brass ; but in order to reduce the length, there are always at least two rows of steel and brass. EXPANSION OF LIQUIDS. 225. Absolute and apparent expansions. We have already seen that liquids are more expan- sible than solids (200), which is a consequence of their feeble cohesion ; but their expansibility is far less regular, and the less so the nearer their tempera- ture approaches that of their boiling point. In solids two kinds of expansion have to be con- sidered, the longitudinal and the cubical. Now it is clear that the latter is the only kind of expansion Fig. 190. which can be observed in the case of liquids. The expansion may be either real or apparent. The former is the real increase in volume which a liquid assumes when it is heated ; while the latter is that which the eye actually observes, that produced in the vessel containing the liquid. Thus in thermometers, when the liquid expands and rises in the stem, the apparent expansion is observed, which is less than the real or abso- lute expansion. For, while the mercury expands, the bulb of the thermometer does so too ; its volume is greater, and hence the -226] Maximum Density of Water. 22\ liquid does not rise so high in the stem as it would if the volume of the bulb were unaltered. If a flask of thin glass, provided with a capillary stem, the flask and part of the stem being filled with some coloured liquid, be immersed in hot water, the column of liquid in the stem at first sinks, but then immediately after rises, and continues to do so until the liquid inside has the same temperature as the hot water. The first sinking of the liquid is not due to its contraction ; it arises from the expansion of the glass, which becomes heated before the heat can reach the liquid ; but the expansion of the liquid soon exceeds that of the glass, and the liquid then ascends. Hence, since, whatever be the nature of the material in which a liquid is contained, it has some expansibility, and always expands with, the liquid, the apparent expansion is the only one directly ob- served in liquids. The coefficient of expansion of a liquid is the increase which the unit of volume experiences for a rise in temperature of one degree. These coefficients greatly vary. In a glass vessel the apparent expansion of mercury is 1-5 parts in ten thousands ; that of water is 4-6 parts, that is, three times as great ; alcohol is still more expansible, for its coefficient is ir6 parts in ten thousands. 226. Maximum density of water. Water presents the re- markable phenomenon that when its temperature sinks it contracts up to 4 ; but from that point, although the cooling continues, it expands up to the freezing point, so that 4 represent the point of greatest contraction of water, or, what is called, its point of maximum density, These phenomenon may be observed by comparing a water thermometer, one, that is to say. filled with water, with one of mercury ; both being exposed to gradually diminishing tempe- rature. Hope used the following method to determine the maximum density of water. He took 222 On Heat. [226- a deep vessel perforated by two lateral apertures, in which he fixed thermometers (fig. 190), and having filled the vessel with water at o, he placed it in a room at a temperature of 1 5. As the layers of liquid at the sides of the vessel became heated they sank to the bottom, and the lower thermometer marked 4, while that of the upper one was still at zero. Hope then made the inverse experi- ment ; having filled the vessel with water at 15, he placed it in a room at zero. The lower thermometer having sunk to 4, remained stationary for some time, while the upper one cooled down until it reached zero. Both these experiments prove that water is heavier at 4 than at o, for in both cases it sinks to the lower part of the vessel. This phenomenon is of great importance in the economy of nature. In winter the temperature of lakes and rivers falls, from being in contact with the cold air, and from other causes, such as radiation. The colder water sinks to the bottom, and a continual series of currents goes on until the whole has a temperature of 4. The cooling on the surface still continues, but the cooled layers being lighter remain on the surface, and ultimately freeze. The ice formed thus protects the water below, which remains at a tempera- ture of 4, even in the most severe winters, a temperature at which fish and other inhabitants of the waters are not destroyed. EXPANSION OF GASES. 227. Value of the coefficient of expansion of gases. Net merely are gases the most expansible of all bodies, but their expan- sion is the most regular. It was originally assumed, on the basis of Gay Lussac's experiments, that all gases expanded to the same extent for the same increase of temperature, that is, that they had all the same coefficient of expansion. It has, however, been established that the coefficients of various gases do present slight differences. They are, however, so slight, that for all practical purposes they may be assumed to be the same ; that is to say, 367 parts in a hundred thousand, or, in other words, that 100,000 volumes of air, or any other gas, when heated through i degree Centigrade, would become 100,367 volumes or i volume in 273. This expansibility is about 13 times as great as that of water. 228. Effects of the expansion of gases. The expansion of gases affords us numerous important applications, not merely in -228] Effects of the Expansion of Gases. 223 domestic economy, but also in atmospheric phenomena. Thus in our dwellings, when the air is heated and vitiated by the presence of a great number of persons, it expands and rises in virtue of its diminished density to the highest parts of rooms ; and to allow this to escape, apertures are made in the cornice, while fresh and pure air enters by the joints of the doors and of the windows. When in winter the door of a warm room is put ajar, and a lighted candle held near the top, fig. 192, the direction of the flame proves the existence of a current of warm air from the inside to the outside. If we lower the flame, it will be found that at about the middle it is not affected by any air current, but that lower down near the ground, the flame is driven inwards. In theatres the spectators in the gal- leries are exposed to the highest tempera- ture and the most impure air, while those near the orchestra respire in a purer air. Draughts in chimneys are due to the expansion of air. Heated by the fire in the grate, the air rises in the chimney with a velocity which is greater the more it is expanded. Hence results a rapid current of air, which supports and quickens the combustion by constantly renewing the oxygen absorbed. The expansion and contraction of air have a fortunate influence on the temperature of that part of the atmosphere in which we live. For when the ground is strongly heated by the sun's burning rays, the layers of air in immediate contact with it tend to acquire the same temperature and to form a stifling atmosphere ; but these layers, gradually expanding, rise in virtue of their diminished den- sity ; while the higher layers, which are colder and denser, gradually replace them. Thus the high temperature whidi would otherwise be produced in the lower regions is moderated, and never exceeds the limits which plants and animals can support. The expansion and contraction produced in the atmosphere over a large tract of country are the cause of all winds, from the lightest zephyr to the most violent hurricane. These winds, which at times are so destructive, so capricious in the direction, and so variable in their intensity, not merely have the effect of mixing the heated and the cooler part of the atmosphere, and of thus modera- ting extremes of temperature, but by driving away the vitiated at- 224 On Heat. [228- mosphere of our towns, and replacing it by pure air, they are one of the principal causes of salubrity ; without them our cities would be the centres of infection, where epidemic diseases of all kinds would be permanent. Without winds, clouds would remain motion- less over the country where they were formed, the greater part of the globe would be condemned to absolute aridity, and neither rivers nor brooks would moisten the soil. But, carried by the winds, the clouds formed above the seas are transported to the centres of continents, where they fall as rain ; and this having fertilised the soil, gives rise to the numerous rivers which fall into the ocean, thus establishing a continuous circulation from the seas towards the continents and from continents towards seas. 229. Density of gases. The densities of solids and of liquids have been determined in reference to water (101) ; those of gases by comparison with air ; that is, having taken: as a term of com- parison, or unity, the weight of a certain volume .of air, the weight of the same volume of other gases is determined. But as gases are very compressible and very expansible, and'as therefore their densities may greatly vary, they must be reduced to a definite pres- sure and temperature. This is why the temperature of zero and the pressure of 30 inches have been chosen. ; ;.'.; i. Hence the relative density of a gas, ,or its specific gravity, is the relation of the weight of a certain volume of the gas to that of the same volume of air ; both the gas and the air being at zero and at a pressure of 30 inches. In order therefore, to find the specific gravity of a gas, oxygen for instance, it is necessary to determine the weight of a certain volume of this gas, at a pressure of 30 inches, and a temperature of zero, and then the weight of the same volume of air under the same conditions. For this purpose a large globe of about two gallons capacity is used, like that represented in fig. 88, the neck of which is provided with a stop cock, which can be screwed to the air-pump. The globe is first weighed empty, and then full of air, and after- wards full of the gas in question. The weights of the gas and of the air are obtained by substracting the weight of the exhausted globe from the weight of the globes filled, respectively, with air and gas. The quotient, obtained by dividing the latter by the former, gives the specific gravity of the gas. It is difficult to make these determinations at the same temperature and pressure, and therefore all the weights are reduced by calculation to zero, and the standard pressure of 30 inches. -230] Fusion. 22$ In this manner the following densities have been found : Air .... I'oooo Oxygen V ; . . 1*1056 Hydrogen . . . 0-0692 Carbonic acid . _ .'"''' 1-5290 Nitrogen . . . 0*9714 Chlorine .. ^ ...... . 3-4400 From these numbers the lightest of gases, and therefore of a bodies, is hydrogen, whose density is less than T \th of air. CHAPTER VI. CHANGES OF STATE OF BODIES BY THE ACTION OF HEAT. 230. Fusion. In treating of the general effects of heat, we have seen that its action is not only to expand them, but to cause them to pass from the solid to the liquid state, or from the latter state to the former, according as the temperature rises or falls ; then from the liquid to the aeriform state, or conversely. These vari- ous changes of slate we shall now investigate under the name of fusion, solidification, vaporisation, and liquefaction. Fusion is the .passage of a solid body to the liquid state by the action of heat. This phenomenon is produced when the force of cohesion which unites the molecules is balanced by the force of re- pulsion (4) ; but as the cohesive force varies in different substances, the temperature at which bodies melt does so likewise. For some substances this temperature is very low, and for others very high, as the following table shows : Fusing points of certain substances. Mercury. .-38-8 Sulphur Bromine . Uv . 12-5 Tin ' . Ice. Bismuth Butter . + 33 Lead . Phosphorus . 44 Zinc Potassium 55 Antimony Stearine . . 60 Silver . White wax . . 65 Gold . Sodium . 90 Iron Q 228 264 335 422 450 looo 1250 1 500 226 On Heat. [230- Some substances, however, such as paper, wood, wool, and certain salts, do not fuse at a high temperature, but are decomposed. Many bodies have long been considered refractory ; that is, in- capable of fusion ; but, in the degree in which it has been possible to produce higher temperatures, their number has diminished. Gaudin has succeeded in fusing rock crystal by means of a lamp fed by a jet of oxygen ; and more recently Despretz, by combining the effects of the sun, the voltaic battery, and the oxy-hydrogen blow- pipe, has melted alumina and magnesia, and has softened carbon, so that it was flexible, which is a condition near that of fusion. Some substances pass from the solid to the liquid state without showing any definite melting point ; for example, glass and iron be- come gradually softer and softer when heated, and pass by imper- ceptible stages from the solid to the liquid condition. This inter- mediate condition is spoken of as the state of vitreous ftision. Such substances may be said to melt at the lowest temperature at which perceptible softening occurs, and to be fully melted when the further elevation of temperature does not make them more fluid ; but no precise temperatures can be given as their melting points. 231. Xiaws of fusion. It has been experimentally found, that the fusion of bodies is governed by the two following laws : I. Every substance begins to fuse at a certain temperature, which is invariable for one and the same substance if the pressure be constant. II. Whatever be the intensity of the source of heat, from the mo~ ment fusion commences, the temperature of the body ceases to rise, and remains constant until the fusion is complete. For instance, the melting point of ice is zero, and a piece of this substance exposed to the sun's rays, placed in front of a fire or over a lamp, could never be heated beyond this temperature. Ex- posure to a more intense heat would only accelerate the fusion, the temperature would remain at zero until the whole of the ice was melted. 232. latent heat. Since, during the passage of a body from the solid to the liquid state, the temperature remains constant until the fusion is complete, whatever be the intensity of the source of heat, it must be concluded that, in changing their condition, bodies absorb a considerable amount of heat, the only effect of which is to maintain them in the liquid state. This heat, which is not indicated by the thermometer, is called latent heat, or latent heat of fusion -233] Solidification. 227 an expression which, though not in strict accordance with modern ideas, is convenient from the fact of its universal recognition and employment. An idea of what is meant by latent heat may be obtained from the following experiment. If a pound of water at 80' is mixed with a pound of water at zero, the temperature of the mixture is 40. But if a pound of pounded ice at zero is mixed with a pound of water at 80, the ice melts, and two pounds of water at zero are obtained. The pound of ice at zero is changed into a pound of water also at zero, but as the hot water is. also lowered to this tem- perature, what has become of the 80 of heat it possessed ? They exist in the water which results from the ice ; their effect has neither been to increase its temperature nor its volume, but simply to impart fluidity to it. Consequently, the mere change of a pound of ice to a pound of water at the same temperature requires as much heat as will raise a pound of water through 80. This quantity of heat represents the latent heat of the fusion of ice, or the latent heat of water. Every substance in melting absorbs a certain amount of heat, which, however, varies materially with different substances. The enormous quantity of heat absorbed by ice in melting, ex- plains how it is that so long a time is required for thaw. And conversely, it is owing to the latent heat of water, that even when its temperature has been reduced to zero, so long a time is required before it is entirely frozen. Before it can be so it must give out the heat which had been consumed in its liquefaction : it thus be- comes a source of heat which retards the solidification. Faraday has calculated that the heat given out by a cubic yard of water in freezing is equal to that which would be produced by the complete combustion of a bushel of coals. Were it not for the great amount of heat which must be absor- bed by snow or ice in melting, we should, on a change from frost to mild weather, be liable to the most destructive floods, from the sud- den melting of the accumulated snow and ice. 233. Solidification. Those substances which are liquefied by heat revert to the solid state on cooling, and this passage from the liquid to the solid state is called solidification. If this solidification takes place at a low temperature it is frequently spoken of as con- gelation. In all cases the phenomenon is subject to the following laws : Q 2 223 On Heat. [233- I. Every body, under the same pressure, solidifies at a fixed tem- perature, which is the same as that of fusion. II. From the commencement to the end of the solidification, the temperature of a liquid remains constant. Thus if lead begins to melt at 335, melted lead in like manner when cooled down begins to solidify at 335. Moreover, until it is completely solidified, the temperature remains constant at 335. This arises from the fact, that the liquid metal in proportion as it solidifies restores the heat it had absorbed in being melted. The same phenomenon is observed whenever a liquid solidifies (^32). Many liquids, such as alcohol, ether, and bisulphide of carbon, do not solidify even at the lowest known temperature. Pure water solidifies at zero; salt water at 2-5, olive and rape oils at 6 ; linseed and nut oils at 27. Water presents the remarkable phenomenon, that when it solidi- fies and forms ice its volume undergoes a material increase. In speaking of the maximum density of water we have already seen that, on cooling, it expands from 4 degrees to zero ; it further ex- pands on the moment of solidifying, or contracts on melting by about 10 per cent. One volume of ice at o gives 0-908 of water at o, or i volume of water at o gives 1-102 of ice at the same tem- perature. The increase of volume in the formation of ice is accompanied by an expansive force which sometimes produces powerful mecha- nical effects, of which the bursting of water pipes and the breaking of jugs containing water are familiar examples. The splitting ot stones, rocks, and the swelling up of moist ground during frost, are caused by the fact that water penetrates into the pores and there becomes frozen. The expansive force of ice was strikingly shown by some experi- ments of Major Williams in Canada. Having quite filled a 1 3-inch iron bomb-shell with water, he firmly closed the touch-hole with an iron plug weighing 3 pounds, and exposed it in this state to the frost. After some time the iron plug was forced out with a loud ex- Fig- 193- plosion, and thrown to a distance of 415 feet, the shell was cracked, and a mass of ice projected from the crack as shown in fig. 193. From the expansion which water undergoes in freezing, it is clear that ice must be less dense than water ; and this in fact is the -235] Solution. 229 case, for ice floats on the surface of the water. In the polar seas, where the temperature is always very low, masses of floating ice are met with which are called ice-fields. They rise out of the sea to a height of 4 or 5 yards, and are immersed to a depth of 7 or 8 yards, and they frequently extend over 40 miles. True mountains of ice, or icebergs, are found floating on those seas ; they have not the same area, but attain very great heights. Cast-iron, bismuth, and antimony expand, on solidifying like water, and can thus be used for casting ; but gold, silver, and cop- per contract, and hence coins of these metals cannot be cast, but must be stamped with a die. 234. Crystallisation. When bodies pass slowly from the liquid to the solid state, their molecules, instead of becoming grouped in a confused manner, generally acquire a regular order and arrange- ment, in virtue of which these bodies assume the geometrical shapes of cubes, pyramids, and prisms, etc., which are perfectly definite, and are known as crystals. Flakes of snow, when looked at under the microscope, ice in the process of formation, sugar candy, rock crystal, alum, common salt, and many other substances afford well- known instances of crystallisation. Two methods are in use for crystallising substances ; the dry way and the moist way. By the first method bodies are melted by heat, and then allowed to cool slowly. The vessel in which the operation is performed becomes lined with crystals, which are made apparent by inverting the vessel and pouring out the excess of liquid befoVe the whole of" it is melted. Sulphur, bismuth, and many other metals are thus easily crystallised. The second method consists in dissolving in hot water the substance to be crystallised, and then allowing it to cool slowly. The body is then deposited on the sides of vessels in crystals which are larger and better shaped the more slowly the crystallisation is effected. In this manner sugar candy and salts are crystallised. 235. Solution. A body is said to dissolve when it becomes liquid in consequence of an affinity between its molecules and those of a liquid. Gum arabic, sugar, and most salts dissolve in water. During solution, as well as during fusion, a certain quantity of heat always becomes latent, and hence it is that the solution of a substance usually produces a diminution of temperature. In cer- tain cases, however, instead of the temperature being lowered, it actually rises, as when caustic potass is dissolved in water, This 230 On Heat. [235- depends upon the fact that during the solution ofa solid in a liquid, two simultaneous and contrary phenomena are produced. The first is the passage from the solid to the liquid condition, which always lowers the temperature. The second is the chemical combination of the body dissolved with the liquid, and which, as in the case of all chemical combinations, produces an increase of temperature. Consequently, as the one or the other of these effects predominates, or as they are equal, the temperature either rises, or sinks, or re- mains constant. 236. Freezing- mixtures. The absorption of heat in the pas- sage of bodies from the solid to the liquid state has been used to produce artificial cold. This is effected by mixing together bodies which have an affinity for each other, and of which one at least is solid, such as water and a salt, ice and a salt, or an acid and a salt. Chemical affinity accelerates the fusion, the portion which melts robs the rest of the mixture of a large quantity of sensible heat, which thus becomes latent. In many cases a very considerable diminution of temperature is produced. If the substances taken be themselves first previously cooled down, a still more considerable diminution of temperature is occa- sioned. Freezing mixtures are frequently used in chemistry, in physics, and in domestic economy. The portable ice-making machines which have come into use during the last few years, consist of a cylindrical metallic vessel divided into four concentric compart- ments. In the central one is placed the water to be fro'zen ; in the next there is the freezing mixture, which usually consists of sul- phate of sodium and hydrochloric acid ; 6 pounds of the former and 5 of the latter will make 5 to 6 pounds of ice in an hour. The third compartment also contains water, and the outside one con- tains some badly conducting substance, such as cotton, to prevent the influence of the external temperature. The best effect is obtained when pretty large quantities, 2 or 3 pounds, of the mix- ture are used, and when they are intimately mixed. It is also advantageous to use the machines for a series of successive opera- tions. -238] Elastic Force of Vapours. 231 CHAPTER VII. FORMATION OF VAPOURS. MEASUREMENT OF THEIR ELASTIC FORCE. 237. Vapours. We have already seen (109) that vapours are the aeriform fluids into which substances, such as ether, alcohol, water, and mercury, are changed by the absorption of heat. In respect to the property of disengaging vapours, liquids are divided into two classes, volatile liquids, and fixed liquids. The first are those which have a tendency to pass into the state of vapour at the ordinary or even at lower temperatures ; such, for instance, are water, ether, chloroform, alcohol, which disappear more or less rapidly when exposed to the air in open vessels. To this class belongs a numerous family of liquids met with in nature, such as essence of turpentine, oil of lemons, of lavender, of thyme, of roses, etc., which are known as the essential oils. Fixed liquids, on the contrary, are those which emit no vapour at any temperature ; such, for instance, are the fatty oils, as olive, rape, etc. When strongly heated these oils are decomposed, and give rise to gaseous products ; but they do not emit vapours of the same nature as their own. There are some of them which are known as drying oils^ that become thicker in the air ; but this is in consequence of their having absorbed oxygen, and not in con- sequence of evaporation. Some substances give vapours even in the solid state. Ice gives an instance of this, as is seen in dry cold winters, where the snow and ice quite disappear from the ground, without there having been any fusion. Camphor and odoriferous bodies, in general present the same phenomenon. 238. Elastic force of vapours. Vapours formed on the surface of a liquid are disengaged in virtue of their elasticity ; but this force is generally far lower than the pressure of the atmosphere, and hence liquids exposed to the air only evaporate slowly. The following experiment renders evident the elastic force of vapours. A bent glass tube has the shorter limb closed (fig. 194) ; this branch and part of the longer are filled with mercury. A drop of ether is then passed into the closed leg, which in virtue 232 On Heat. [238- of its lower density rises to the top of the tube at B. The tube thus arranged is immersed in a water bath at a temperature of about 45. The mercury then sinks slowly in the short branch, and the space AB is filled with a gas which has all the appearance of air. This gas or aeriform fluid is nothing but the vapour of ether, whose elastic force counterbalances not only the pressure of the column of mercury CA, but also the atmo- spheric pressure exerted at C. If the water in the vessel be cooled, or if the tube be withdrawn, the mercury gradually rises in the short leg, and the drop of liquid which seemed almost to have dis- appeared is re-formed. If, on the contrary, the water in which the tube is immersed be still more heated, the drop diminishes and the mercury descends further in the short leg ; thus showing that fresh vapours are formed, and that the elastic force increases. This increase of tension with the tempe- rature continues as long as any liquid remains to be vaporised. The crackling of wood in fires is due to the increased tension of the vapours and gases formed in the pores of the wood during combustion. In roasting chesnuts it is usual to slit the outer skin ; the object of this is to allow the vapour formed to escape, for otherwise it would be liable to acquire such a tension as to burst the chesnut and scatter the particles far and wide. 239. Formation of vapours in a vacuum. In the previous experiment the liquid changed very slowly into the state of vapour ; the same is the case when a liquid is freely exposed to the air. In both cases the atmosphere is an obstacle to the vaporisa- tion. In a vacuum there is no resistance, and the formation of vapours is instantaneous, as is seen in the following experiment. Four barometer tubes, filled with mercury, are immersed side by -240] Formation of Vapours in a Vacuum. 233 side in the same trough (fig. 195). One of them, A, serves as a barometer, that is, only contains dry mercury, and a few drops ot water, alcohol, and ether are respectively introduced into the tubes, B, C, D. When the liquids reach the vacuum a depression of the mercury is at once pro- duced. But this depres- sion cannot be produced by the weight of the liquid, for it is but an infinitely small fraction of the weight of the displaced mercury. Hence in the case of each liquid, some vapour must have been formed whose elastic force has depressed the mer- curial column, and as the depression is greater in the tube D than in the tube C, and greater in this than in the tube B, it is concluded that, for the same temperature, the elastic force of ether is greater than that of alco- hol vapour, and that this in turn has a greater elastic force than that of water. If the depression Fig. 195- be measured by means of a graduated scale, it will be found that at a temperature of 20 the elastic force of ether is twenty-five times as great as that of water, and that of alcohol almost four times as great. From these experiments we obtain trie two follow- ing laws for the formation of vapours : I. In a vacuum all volatile liquids are instantaneously converted into vapour. II. At the same temperature the vapours of different liquids have different elastic forces. 240. Iiimit to the formation and to the tension of vapours. Saturated space. The quantity of vapour which can be formed in a given space, whether at the ordinary or at higher temperatures, 234 On Heat. [240- is always limited. For instance, in the above experiment, the de- pression of mercury in each tube, B, C, D, is not stopped for want of liquid which might form fresh vapours, for care is taken always to add so much that a slight excess remains unvaporised. Thus, in the tube D, enough ether is left ; yet we might wait weeks and years, and if the temperature did not increase, we should always see a portion of liquid in the tube, and the level of the mercury remain stationary. This shows that no new vapours can be formed in the tube, and at the same time that the elastic force of the vapour which is there cannot increase, which is expressed by saying that it has attained its maximum tension. When a given space has acquired all the vapour which it can contain, it is said to be saturated. For instance, if in a bottle full of dry air a little water be placed, and the vessel be hermetically closed, part of the water will evaporate slowly, until the elastic force of the vapour formed holds in equilibrium the expansive force of that which still tends to form ; the formation of vapour then ceases, and the space is saturated. 241. The quantity of vapour which saturates a given space is the same whether this is vacuous or contains air. For the same temperature the quantity of vapour necessary to saturate a given space is the same, whether the space is quite vacuous, or contains air or any other gas. In the above bottle, whether it be full of air, or has been exhausted, the total quantity which evapo- rates is exactly the same ; the difference being that, in the first case, the evaporation only takes place slowly, while in the second case it is instantaneous. Yet, for the same space, whether it be vacuous or full of air, the quantity of vapour formed which corre- sponds to the state of saturation, varies with the temperature. The higher the temperature, the greater is the quantity of vapour contained in a given space, the denser it is therefore ; on the other hand, the lower the temperature, the less is the quantity required to saturate a given space. The quantity of vapour present in air is very variable ; but, spite of the abundant vaporisation produced on the surface of seas, lakes, and rivers, the air in the lower regions of the atmosphere is never quite saturated, even when it rains. This arises from the fact, that aqueous vapour being less dense than air, in proportion as it is formed, rises into the higher regions of the atmosphere, where, condensed by cooling, it falls as rain. -242] Evaporation. 235 242. Evaporation. Causes which accelerate it. We have hitherto designated, under the general term of vaporisation, all production of vapour under whatever circumstances it takes place, whether slow or rapid, whether in air or in a vacuum ; while the term evaporation is especially assigned to the slow formation of a vapour on the surface of a volatile liquid when it is exposed in the open air. It is in consequence of evaporation that the level gradually diminishes in a pond full of water, and ultimately dries up if it is not fed by a spring. Owing to the same cause the earth moistened by rain dries up and ultimately hardens ; that moist linen exposed in the air soon dries up. Several causes influence the rapidity of the evaporation of a liquid : the temperature ; the quantity of the same vapour in the surrounding atmosphere ; the renewal of this atmosphere ; the extent of the surface of evapora- tion. Influence of temperature. Heat being the agent of all evapora- tion, the higher the temperature the more abundant is the forma- tion of vapour. This property is utilised in the arts to hasten and complete the drying of a large number of products which are exposed in stoves ; that is to say, in chambers, the temperature of which is kept at 30, 40, 50, and even 60 degrees, and the air of which is continually renewed to allow the vapour formed to escape. Influence of pressure. We have already seen that the pressure of the atmosphere is an obstacle to the disengagement of vapours, and it will thus be understood that when this pressure is diminished they ought to be formed more abundantly. This, in point of fact, is what takes place whenever liquids are removed from the pressure of the atmosphere. In sugar refineries, in order to concentrate the syrups (that is, to reduce the volume by removing part of the water they contain), they are placed in large spherical vessels ; and then, by the aid of large air-pumps of special construction, and worked by steam engines, the air in the boilers is rarefied, which considerably accelerates the evaporation of water, and quickly brings the syrups to the wished-for degree of concentration. Influence of the renewal of air. In order to understand the in- fluence of the third cause, it is to be observed that no evaporation could take place in a space already saturated with vapour of the same liquid, and that it would reach its maximum in air com- pletely freed from this vapour. It therefore follows that, between On Heat. [242- these two extremes, the rapidity of evaporation varies according as the surrounding atmosphere is already more or less charged with the same vapour. The effect of the renewal of this atmosphere is similarly ex- plained ; for if the air or gas, which surrounds the liquid, is not renewed, it soon becomes saturated, and evaporation ceases. Thus it is that the wind, removing the layers of air which are in contact with the earth, soon dries up the roads and streets. Hence, too, it is that linen hung out to dry, does so far more rapidly on a windy than on a dry day. The greater the extent of surface which a liquid presents to the air, the more numerous are the points from which vapour is dis- engaged. Hence the evaporation of a liquid should be effected in vessels which are wide and shallow. This is what is done in the process of extracting salt from sea water in salt gardens. The sea water is admitted into broad and shallow pits excavated in the ground. Under the influence of the sun's heat the water evapo- rates slowly, and when its concentration has reached the point at which the liquid is saturated, the salt then begins to form on the surface and is raked off. 243. Ebullition. Ebullition, or boiling, is the rapid production of elastic bubbles of vapour in the mass of a liquid itself. When a liquid, water for example, is heated at the lower part of a vessel, the first bubbles are due to the disengagement of air which had previously been absorbed. Small bubbles of vapour Fig. 196. -245] Causes which Influence the Boiling Point. 237 then begin to rise from the heated parts of the sides, but as they pass through the upper layers, the temperature of which is lower, they condense before reaching the surface. The formation and successive condensation of these first bubbles occasion the singing noticed in liquids before they begin to boil. Lastly, large bubbles rise and burst on the surface, and this constitutes the phenomenon of ebullition (fig. 196). 244. liaws of ebullition. The laws of ebullition have been determined experimentally, and are as follows : I. The temperature of ebullition, or the boiling point, increases ivith the pressure. II. For a given pressure ebullition commences at a certain tem- perature, which varies in different liquids, but which, for equal pressures, is always the same in the same liquid. III. Whatever be the intensity of the source of heat, as soon as ebullition commences, the temperature of the liquid remains sta- tionary. % Thus, the boiling point of water under the ordinary atmospheric pressure being 100, it could not be heated beyond that point, whatever the intensity of the source of heat ; hence all the heat which passes from the source into the liquid is absorbed by the vapour disengaged. But, as this vapour is itself at 100, we must conclude that this heat is not absorbed to raise the temperature of the vapour, but simply to produce it ; that is, to change the sub- stance from the liquid into the gaseous state, a phenomenon analo- gous to that which fusion presents (232). This disappearance of heat during ebullition will be subsequently investigated under the name of latent heat of vaporisation (250). Boiling points under the pressure of an atmosphere. Sulphurous acid . . . 10 Turpentine 160 Ether 37 Strong sulphuric acid . . 325 Bisulphide of carbon . . 48 Mercury 350 Bromine 63 Sulphur 447 Alcohol 78 Cadmium. . . . 'V '."860 Distilled water .... 100 Zinc 1040 245. Causes which influence the boiling- point. The boiling point of a liquid is affected by the substances in solution, by the degree of pressure to which it is subjected, and by the nature of the vessels in which the boiling takes place. 238 On Heat. [245- The ebullition of a liquid is the more retarded, the greater the quantity of any substance it may contain in solution, provided that the substance be not volatile, or, at all events, be less volatile than the liquid itself. Water which boils at 100 when pure, boils at 109 when it is saturated with common salt ; that is, when it has taken up as much of this salt as it can dissolve. Fatty matters combined with water also raise its boiling point ; hence it is that fat soup burns more severely than water. Fig. 197. Pressure. The degree of pressure to which a liquid is subjected has a most important influence on its boiling point The greater the pressure the greater must be the tension, in order that the vapour may be disengaged, and therefore the higher the temperature On the contrary, the less the pressure, the lower the temperature at which ebullition takes place. If the pressure of the atmosphere be removed, water may be made to boil, even at the ordinary tern- 245] Influence of P res stir e on the Boiling Point. 239 perature. The experiment may be arranged in the manner repre- sented in fig. 197. A glass cup containing water is placed under the bell-jar of an air-pump, or, in order that the experiment may be seen by a number of spectators, the bell is placed on a movable plate connected with the pump by a tube. When a vacuum is pro- duced, or when the air is very rarefied, the water is seen to boil, evidently indicating a considerable disengagement of vapour. Yet the temperature of the liquid is not raised ; the boiling is, on the contrary, a source of cold, owing to the heat, which becomes latent in the formation of vapours. The influence of pressure on ebullition may further be illustrated by means of an experiment of Franklin's. The apparatus consists of a bulb and a tube, joined by a tube of smaller dimensions (fig. 198). The tube is drawn out, and the apparatus filled with water, which is then in great part boiled away by means of a spirit-lamp. Fig. 198. When it has been boiled sufficiently long to expel all the air, the tube is sealed. There is then a vacuum in the apparatus, or rather, there is only a pressure due to the tension of aqueous vapour, which at ordinary temperatures is very small. Consequently, if the bulb be placed in the hand, as shown in the figure, the heat is sufficient to produce a pressure, which drives the water into the tube and causes a brisk ebullition. A paradoxical but very simple experiment also well illustrates the dependence of the boiling point on the pressure. In a glass flask water is boiled for some time, and when all air has been ex- pelled by the steam, the flask is closed by a cork and inverted, as shown in fig. 199. If the bottom is then cooled by a stream of 240 On Heat. [245- cold water from a* sponge, the water begins to boil again. This arises from the condensation of the steam above the surface of the water, by which a partial vacuum is produced. As the pressure of air diminishes in proportion as we rise in the atmosphere, it will be seen from what has been said, that on high mountains water must boil at lower temperatures than on the sea level. This, in fact, is the case ; on Mont Blanc, at a height of 15,800 feet, water boils at 84 ; at Quito, at a height of 11,000 feet, at 90 ; and at Madrid, the height of which is 3,000 feet, it boils at 97. This diminution in the tempera- ture of ebullition at great heights is a material obstacle to the preparation of food, for, at the temperature of 90, the extraction of the nourish- ment and of the flavour is far more imperfect than under the usual conditions. In deep mines, on the contrary, such as those of Fig- X 99- Cornwall and Lancashire, the reverse is the case : the pressure increases with the depth, and the boiling point is higher than at 100. Influence of the nature of the vessel on the boiling point. Gay- Lussac observed that water in a glass vessel required a higher temperature for ebullition than in a metal one. Taking the tem- perature of boiling water in a copper vessel at 100, its boiling point in a glass vessel was found to be 101 ; and if the glass vessel had been previously cleaned by means of sulphuric acid and of potass, the temperature would rise to 105 or even to 106 before ebullition commenced. Whatever be the boiling point of water, the temperature of its vapour is uninfluenced by the substance of the vessels. 246. Papin's digester. What has hitherto been said in re- ference to the formation of vapour has applied to the case of liquids heated in open vessels. Only under these conditions can ebulli- -246] Papiiis Digester. 241 tion take place ; for, in a closed vessel, since the vapours cannot escape into the atmosphere, their elastic force and their density continually increase, but that peculiarly rapid disengagement which constitutes boiling is impossible. There is, moreover, this differ- ence between heating in an open and in a closed vessel ; that, in the former case, the temperature can never exceed that of ebullition, while in a closed vessel it may be raised so to speak, to an in- definite extent. Thus we have seen (246) that, in an open vessel, water cannot be heated beyond 100 C., all the heat im- parted to it being absorbed by the vapours disengaged. But as this disengagement of vapour cannot take place in a closed vessel, water and the vapour may be raised to a far higher temperature than 100. Yet this is not unattended with danger, from the very high tension which the vapour then assumes. Figure 200 represents the apparatus used in physical lectures for the purpose of heating water in a closed vessel beyond 100 degrees. It is known as Papin's Di- gester. It consists of a cylindrical bronze vessel, M (fig. 200), provided with a cover, which is firmly fastened down by a screw. In order to close the vessel hermetically, sheet lead is Fig- 2 - placed between the edges of the cover and the vessel. At the bottom of a cylindrical cavity, which traverses a cylinder and tubulure, the cover is perforated by a small orifice in which there is a rod, u. This rod presses against a lever, ab, movable at a, and the pressure may be regulated by means of a weight, /, movable on this lever. The lever is so weighted, that when the tension in the interior is equal to six atmospheres, for example, the valve rises and the vapour escapes; The destruction of the apparatus is thus avoided, and the mecha- R 242 On Heat. [246- nism, which will be described in speaking of the steam engine (269) has hence received the name (A safety valve. The digester is filled about two-thirds with water, and is heated on a furnace. The water may thus be raised to a temperature far above 100, and the tension of the vapour increased to several atmospheres, accord- ing to the weight on the lever. The apparatus has received the name digester, from a Latin word signifying to dissolve, for the high temperature which water can acquire greatly increases its solvent power. Thus it is used to extract from bones the substance known as glue, which could not be accomplished at 100. From the enormous elastic force which vapour may acquire in a closed vessel, it will be understood how important it is not to close tightly the ves- sel in which water is contained for domestic purposes. Thus a hot water-bottle for heating the feet of invalids should be un- corked before being placed near the fire ; for it might burst, or at any rate the cork might be driven out, and a more or less serious accident be caused. In like manner, when a locomotive stops, the steam must be allowed to escape ; for otherwise, as it is continually being formed in the boiler without any being con- sumed in working the engine, it would ultimately acquire such an elastic force that an explosion would ensue. 247. Measurement of the elastic force of aqueous va- pour. The important applica- Fig. 201, tions which have been made of the elastic force of aqueous vapour, have led philosophers to measure with care the intensity of this force at various temperatures. Dalton first measured the elastic force of aqueous vapour for -247] Elastic Force of Aqueous Vapour. 243 temperatures between o and 100, by means of the apparatus re- presented in fig. 201. Two barometer tubes, A and B, are filled with mercury, and inverted in an iron bath full of mercury, and placed on a furnace. The tube, A, is an ordinary barometer tube, freed from air and moisture ; but into the tube, B, is introduced a small quantity of water. The tubes are supported in a cylindrical vessel full of water, the temperature of which is indicated by the thermometer /. The bath being gradually heated, the water in the cylinder becomes heated too : the water which is in the tube B vaporises, and in proportion as the elastic force of its vapour in- creases, the mercury sinks. The depressions of the mercury cor- responding to each degree of the thermometer, are indicated on the scale. Thus, if, when the thermometer is at 70, the mercury is 233 millimetres lower in the tubs B than in the tube A, this shows that at 70 the tension of aqueous vapour is 233 millimetres ; which amounts to saying that it exercises on the sides of the vessel which contains it a pressure equal to the weight of a column of mercury 233 millimetres in height. By noting in the above manner the depression in the baro- meter, B, as compared with A, Dalton determined the elastic force of aqueous vapour from o to 100. He found it to be 760 milli- metres, or 29-92 inches ; that is to say, an atmosphere (118). Dulong and Arago determined the elastic force of aqueous vapour above 100 up to pressures of 24 atmospheres. More recently Regnault measured the elastic force of aqueous vapour both above and below 100 ; and from the researches of this experimenter the following table has been taken, in which the elas- tic forces at various temperatures are respectively measured by the height in millimetres of the column of mercury which they can balance. Elastic force of aqueous vapour. Temperatures Tensions in millimetres Temperatures Tensions in millimetres 4'6o 60 14879 5 6'53 70 233-09 10 9*i7 80 354^4 15 1270 90 525^5 20 1 7 '39 JOO 760-00 30 3i'5S 101 787-63 40 54'9 J 1 20 I520-OO 50 91-98 160 458O-OO R 2 244 On Heat. [247- This table shows that the elastic force of aqueous vapour in- creases far more rapidly than the temperature. Thus at 50 the tension is only 91-9 millimetres; while at 100 degrees, that is to say, double the temperature, the tension is eight times as great. 248. Latent beat of vapour. In speaking of ebullition we have seen that, from the moment a liquid begins to boil, its tempera- ture ceases to rise whatever be the intensity of the source of heat. It follows that a considerable quantity of heat becomes absorbed in ebullition, the only effect of which is to transform the body from the liquid to the gaseous condition. And conversely, when a saturated vapour passes into the state of liquid, it gives out an amount of heat. These phenomena were first observed by Black, and he des- cribed them by saying that, during vaporisation, a quantity of sen- sible heat became latent, and that the latent heat again became free during condensation. The quantity of heat which a liquid must absorb in passing from the liquid to the gaseous state, and which it gives out in passing from the state of vapour to that of liquid, is spoken of as the latent heat of evaporation. The analogy of these phenomena to those of fusion will be at once seen. The modes of determining them need not be described ; but the following results which have been obtained for the latent heats of evaporation of a few liquids may be here given : Water . . . ' / . 540 Bisulphide of carbon . . 87 Alcohol .... 208 Turpentine ",'"' . . 74 Ether . . . .90 Bromine . . . .46 The meaning of these numbers is, in the case of water, for in- stance, that it requires as much heat to convert a pound of water from the state of liquid at the boiling point to that of vapour at the same temperature, as would raise a pound of water through 540 degrees, or 540 pounds of water through one degree ; or that the conversion of one pound of vapour of alcohol at 78 into liquid alcohol of the same temperature would heat 208 pounds of water through one degree. 249. Cold due to evaporation. Whatever be the temperature at which a vapour is produced, an absorption of heat always takes place. If, therefore, a liquid evaporates, and does not receive from without a quantity of heat equal to that which is expended in pro- ducing the vapour, its temperature sinks, and the cooling is greater in proportion as the evaporation is more rapid. '" -250] Water Frozen in a Vacuum. 245 This may become a source of very great cooling. Thus if a few drops of ether be placed on the hand, and this be agitated to accelerate the evaporation, great cold is experienced. With liquids which are less volatile than ether, like alcohol and water, the same phenomenon is produced, but the cooling is less marked. On coming out of a bath, and more especially in the open air and with some wind, a very sharp cold is experienced, due to the vapour formed on the surface of the body. Moist linen is cold and injurious, because it withdraws from the body the heat which the moisture requires for evaporation. The cooling effect produced by a wind or draught does not necessarily arise from the wind being cooler, for it may, as shown by the thermometer, be actually warmer ; but arises from the rapid evaporation it causes from the surface of the skin. We have the feeling of oppression, even at moderate temperatures, when we are in an atmosphere saturated by moisture in which no evaporation takes place. The cooling produced by the use of fans is due to the increased evaporation they produce. The freshness occasioned by watering the streets is also an effect of evaporation. The cold produced by evaporation is used in hot climates to cool water by means of alcarrazas. These are porous earthen vessels, through which water percolates, so that on the outside there is a continual evapo- ration, which is accelerated when the vessels are placed in a current of air. For the same reason wine is cooled by wrap- ping the bottles in wet cloths and placing them in a draught. 250. Water and mercury frozen in a vacuum. From the great quantity of heat which disappears when a liquid is converted into vapour it will be seen that by accelerating the evaporation we have a means of producing intense cold. We have seen that liquids vaporise more rapidly the lower the pressure. Hence, if a vessel containing water be placed in a Fig. 202. space from which the air is exhausted, it should cool very rapidly. Leslie succeeded in freezing water by means of rapid evapora- tion. Under the receiver of the air-pump is placed a vessel con- 246 On Heat. [250- taining strong sulphuric acid, a substance which has a great affi- nity for water, and above it a thin, shallow, porous capsule (fig. 202) containing a small quantity of water. By exhausting the receiver the water begins to boil, and since the vapours are absorbed by the sulphuric acid as fast as they are formed, a rapid evaporisa- tion is produced, which quickly effects the freezing of the water. By using liquids more volatile than water, more particularly liquid sulphurous acid, which boils at 10, a degree of cold is obtained sufficiently intense to freeze mercury. The experiment may be made by covering the bulb of a thermometer with cotton wool, and after having moistened it with liquid sulphurous acid, placing it under the receiver of the air pump. When a vacuum is produced the mercury is quickly frozen. Thilorier, by directing a jet of liquid carbonic acid on the bulb of an alcohol thermometer, obtained a cold of 100 without freez- ing the alcohol. With a mixture of solid carbonic acid, liquid pro- toxide of nitrogen and ether, M. Despretz obtained a sufficient degree of cold to reduce alcohol to the viscous state. By means of the evaporation of bisulphide of carbon the forma- tion of ice may be illustrated without the aid of an air-pump. A little water is dropped on a small piece of wood, and a capsule of thin copper foil, containing bisulphide of carbon, is placed on the water. The evaporation of the bisulphide is accelerated by means of a pair of bellows, and after a few minutes the water freezes round the capsule, so that the latter adheres to the wood. CHAPTER VIII. LIQUEFACTION OF VAPOURS AND GASES. 251. liquefaction of vapours. The liquefaction or condensa- tion of vapours is their passage from the aeriform to the liquid state. Condensation may be due to three causes cooling, com- pression, or chemical affinity. When vapours are condensed, their latent heat becomes free, that is, it affects the thermometer. This is readily seen when a current of steam at 100 is passed into a vessel of water at the ordi- nary temperature. The liquid becomes rapidly heated, and soon reaches 100. The quantity of heat given up in liquefaction is equal to the quantity absorbed in producing the vapour. -251] Liquefaction of Gases. 247 Liquefaction by chemical affinity. The affinity of certain sub- stances for water is so great as to condense the vapours in the atmosphere, even when they are far from their point of saturation. Thus, when highly hygroscopic substances, such as quicklime, potass, sulphuric acid, are exposed in the air, they always absorb aqueous vapour. Certain varieties of common salt exposed to the air absorb and condense so much aqueous vapour as to become liquid. Many other salts have the same property, and are hence called deliquescent salts. Liquefaction by pressure. Let us suppose a vessel containing aqueous vapour, a cylinder for instance, and in this cylinder a piston which can be depressed at will, like that represented in fig. 4 page 9. As the vapour is not at first in a state of saturation, when the piston is depressed, it behaves like a true gas, the pressure increasing its elastic force and density without liquefying it. But the more the piston is depressed the smaller does the volume of the vapour become, and a point is ultimately reached at which the vapour present is just sufficient to saturate the space. From this point the slightest increase of pressure causes a portion of vapour to pass into the liquid state, and the liquefaction continues as long as the excess of pressure lasts ; so that if the piston descends to the bottom of the cylinder all the vapour is condensed. In this ex- periment it is to be observed, that when once saturation is attained, provided there is no air in the cylinder, the resistance to the de- pression of the piston does not increase in proportion as it descends, which arises from the condensation of the vapour, and confirms what was previously said (240), as to the maximum tension of vapour in a state of saturation. Liquefaction by cooling. Cooling, as well as pressure, only causes vapours to liquefy when they are in a state of saturation. But when once a given space is saturated, the slightest lowering of temperature takes from the vapours the heat which gives them their fluidity, the attraction between the molecules preponderates, they agglomerate, forming extremely small droplets, which float in the air and are deposited on the surrounding bodies. Vapours are ordinarily condensed by cooling. Thus, the vapours exhnled from the nose and mouth of animals first saturate the colder air in which they are disengaged, and they condense with a cloud-like appearance. It is owing to the same phenomenon that the vapours become visible which are disengaged from boiling water, those which rise from chimneys, the fogs formed above 248 On Heat. [251- rivers, and so forth. All these vapours are more apparent in winter than in summer, for then the air is colder, and the condensation more complete. In cold weather, the windows in heated rooms are seen to become covered with dew on the inside. The air of these rooms is in general far from being saturated with vapour, but the layers of air in immediate contact with the windows become colder ; and as the quantity of vapour necessary to saturate a given space is less, the colder this space, a moment is reached at which the air in contact with the windows is saturated, and then the vapours they contain are quickly deposited. In a time of thaw, when the air is hotter on the outside than on the inside, the deposit is formed on the outside. To the same cause is due the deposit of moisture formed on walls, which is expressed by saying that \hzysweat ; an unsuitable expres- sion, for the moisture does not come from the walls but from the atmosphere. The walls are colder than the air, and they lower the temperature of the layers in contact with them, and condense the vapours. A similar effect is produced when in summer a bottle of wine is brought from the cellar, or when a glass is filled with cold water ; a deposit of dew is formed on the surface of these vessels. The same phenomenon does not occur in winter, for then the tem- perature of the atmosphere being the same as that of the bottle, or even lower, the layers of air in immediate contact with it are not cooled. 252. Heat disengaged during: condensation. It has been seen that any liquid in vaporising absorbs a quantity of heat. This heat is not destroyed, for, in the converse change, it reappears in the sensible state ; that is to say, it is capable of acting on our sense of feeling and on the thermometer. For instance, we know that a pound of water absorbs in vaporising 540 units of heat (248) ; that is to say, a quantity of heat necessary to raise 540 pounds of water from o to i; conversely, a pound of steam at 100, which is liquefied and gives a pound of water at 100, causes 540 units to pass from the latent to the sensible state, an amount of heat which is utilised in heating by steam. 253. Application to beating- by steam. The quantity of heat which becomes free when aqueous vapour is condensed is utilised in the arts for heating private houses, hot-houses, and public buildings. Steam is produced in boilers like those used in steam engines, and passes from thence into metal tubes concealed behind the wain- .scot, or into columns which serve at the same time as ornaments -254] Stills. 249 for rooms. The steam condensing in these tubes gives up a con- siderable quantity of heat, which they impart to the surrounding air. 254. Distillation, stills. Distillation is an operation by which volatile liquid may be separated from substances which it holds in solution, or by which two liquids of different volatilities may be sepa- rated. The operation depends on the transformation of liquids into vapours by the action of heat, and on the condensation of these vapours by cooling. The apparatus used in distillation is called a still. Its form may vary greatly, but consists essentially of three parts; ist, the body. Fig. 203. A (fig. 203), a copper vessel containing the liquid, the lower part of which fits in the furnace ; 2nd, the head, B, which fits on the body, and from which a lateral tube, C, leads to, 3rd, the worm, S, a long spiral tin or copper tube, placed in a cistern kept con- stantly full of cold water. The object of the worm is to condense the vapour, by exposing a greater extent of cold surface. To free ordinary well water from the many impurities which it contains, it is placed in a still and heated. The vapours disen- gaged are condensed in the worm, and the distilled water arising from the condensation is collected in the receiver, D. The vapours in condensing rapidly heat the water in the cistern, which must, 250 On Heat. [254- therefore, be constantly renewed. For this purpose a continual supply of cold water passes into the bottom of the cistern, while the lighter heated water rises to the surface, and escapes by a tube in the top of the cistern. Brandy is obtained from wine by means of distillation. Wine, consists essentially of water, alcohol, and colouring matter ; when heated in a still to a temperature between 78 and 100, the alcohol, which boils at 78, vaporises, while water, which only boils at 100, remains behind, or at all events only passes over in small quantity. The liquid resulting from this distillation, is brandy, which is es- sentially a mixture of alcohol and water. 255. Liquefaction of gases. We have already seen that a saturated vapour, the temperature of which is constant, is lique- fied by increasing the pressure, and that, the pressure remaining constant, it is brought into the liquid state by diminishing the tem- perature. Unsaturated vapours behave in all respects like gases. And it is natural to suppose, that what are ordinarily called permanent gases are really unsaturated vapours. For the gaseous form is accidental, and is not inherent in the nature of the substance. At ordinary temperatures sulphurous acid is a gas, while in countries near the poles it is a liquid ; in temperate climates ether is a liquid, at a tropical heat it is a gas. And just as unsaturated vapours may be brought to the state of saturation and then liquefied by suitably diminishing the temperature or increasing the pressure, so, by the same means, gases may be liquefied. But as they are mostly very far removed from this state of saturation great cold and pressure are required. Some of them may indeed be liquefied either by cold or by pressure ; for the majority, however, both processes must be simultaneously employed. Few gases can resist these combined actions, and probably those which have not yet been liquefied, hydrogen, oxygen, nitrogen, binoxide of nitrogen, and carbonic oxide, would become so if submitted to a sufficient degree of cold and pressure. One of the most remarkable experiments on the liquefaction of gases is that made by Thilorier to liquefy and solidify carbonic acid. The principle of the method was first devised and applied by Faraday. The apparatus consists of two cast iron cylinders with very thick sides, of 5 to 6 quarts capacity. They are her- metically closed, and are connected by means of a leaden tube. In one of these cylinders, A, called the generator, are placed the -255] Liquefaction of Gases. 251 substances by whose chemical action carbonic acid is evolved. These are ordinarily bicarbonate of soda, D, and sulphuric acid in the tube, C. The second cylinder, called the receiver, B, is empty ; and the gas disengaged by the chemical action in the generator distils over, and as the receiver is colder, it condenses in virtue of its increasing pressure. As much as two quarts of liquid carbonic acid have thus been prepared. Fig. 204. At a temperature of 1 5 degrees the tension of the compressed gas in the cylinders is not less than 50 atmospheres ; a pressure which would burst the vessels if they were riot solidly constructed. An accident of this kind happened some years ago, and caused the death of Thilorier's assistant. To obtain solid carbonic acid, the receiver is provided with a stopcock attached to a tube, which dips in the liquid acid. On opening this stopcock the liquid acid driven by pressure jets out ; passing then from a tension of 50 atmospheres down to a single one, a part of the liquid volatilised ; and in consequence of the heat absorbed by this evaporation, the rest is so much cooled as to solidify in white flakes like snow, or anhydrous phosphoric acid. 252 On Heat. [255- Solid carbonic acid evaporates very slowly. By means of an alcohol thermometer its temperature has been found to be about 90. A small quantity placed on the hand does not produce the sensation of such great cold as might be expected. This arises from the imperfect contact. But if the solid be mixed with ether the cold produced is so intense, that when a little is placed on the skin all the effects of a severe burn are produced. A mixture of these two substances solidifies four times its weight of mercury in a few minutes. When a tube containing liquid carbonic acid is placed in this mixture the liquid becomes solid, and looks like a transparent piece of ice. CHAPTER IX. SPECIFIC HEAT. CALORIMETRY. 256. Calorimetry. Thermal unit. The object of calorimetry is to measure the quantity of heat which a body parts with or absorbs when its temperature sinks or rises through a certain number of degrees, or when it changes its condition. Quantities of heat may be expressed by any of its directly mea- surable effects, but the most convenient is the alteration of tem- perature ; and quantities of heat are usually defined by stating the extent to which they are capable of raising the temperature of a known weight of a known substance, such as water. The unit chosen by comparison, and called the thermal unit, is not everywhere the same. In France it is the quantity of heat necessary to raise the temperature of one kilogramme of water through one degree Centigrade ; this is called a calorie. In this book we shall adopt, as a thermal unit, the quantity of heat neces- sary to raise one pound of water through one degree Centigrade : i calorie = 2*2 thermal units, and i thermal unit = 0^45 calorie. 257. Specific heat. When equal weights of two different sub- stances at the same temperature placed in similar vessels are sub- jected for the same length of time to the heat of the same lamp, or are placed at the same distance in front of the same fire, it is found that their temperature will vary considerably ; the mercury will be much hotter than the water. But as from the conditions of the -258] Determination of Specific Heats. 253 experiment, they have each been receiving the same amount of heat, it is clear that the quantity of heat which is sufficient to raise the temperature of mercury through a certain number of de- grees will only raise the temperature of the same quantity of water through a less number of degrees ; in other words, that it requires more heat to raise the temperature of water through one degree than it does to raise the temperature of mercury by the same extent. Conversely, if the same quantities of water and of mercury at 100 C. be allowed to cool down to the temperature of the atmosphere, the water will require a much longer time for the purpose than the mercury ; hence, in cooling through the same number of degrees, water gives out more heat than does mercury. It is readily seen that ail bodies have not the same specific heat. If a pound of mercury at 100 is mixed with a pound of water at zero, the temperature of the mixture will only be about 3. That is to say, that while the mercury has cooled through 97, the tempe- rature of the water has only been raised 3. Consequently, the same weight of water requires about 32 times as much heat as mercury does to produce the same elevation of temperature. If similar experiments are made with other substances it will be found that the quantity of heat required to effect a certain change of temperature is different for almost every substance, and we speak of the specific heat or calorific capacity of a body as the quantity of heat which it absorbs when its temperature rises through a given range of temperature, from zero to i for example, compared with the quantity of heat which would be absorbed under the same cir- cumstances, by the same weight of water. In other words, water is taken as the standard for the comparison of specific heats. Thus, to say that the specific heat of lead is 0-0314, means that the quan- tity of heat which would raise the temperature of any given quantity of lead through i C. would only raise the temperature for the same quantity of water through 0-0314. 258. Determination of the specific beats of solids and of liquids. Three methods have been employed for determining the specific heats of bodies ; (i.) the method of melting ice, (ii.) the method of mixtures, and (iii.) that of cooling. In the latter, the specific heat of a body is determined by the time which it takes to cool through a certain temperature. Method of the fusion of ice. This method of determining specific heats is based on the fact that to melt a pound of ice, 80 thermal units are necessary, or more exactly 79*25. The substance to be 254 On Heat. [258- determined is raised to a known temperature, 100 for instance, and is then rapidly placed in ice. In cooling from 100 to zero, the body melts a certain quantity of ice, which is collected in the form of water. From the weight of this water, from that of the body, and from the number of degrees through which it is cooled, the specific heat may be readily calculated. To facilitate the execution of this method Lavoisier and Laplace devised an apparatus which is called the ice calorimeter. Fig. 205 gives a perspective view of it, and fig. 206 represents a section. It consists of three concentric tin vessels, M, A, B, each with covers of the same material ; in the central one is placed the body M, whose Fig. 205. Fig. 2 o5. specific heat is to be determined, while the two others, A and B, are filled with pounded ice. The ice in the compartment A is melted by the heated body, and the water resulting from the lique- faction runs off by the stopcock D, and is collected in a vessel; the ice in the compartment B cuts off the heating influence of the sur- rounding atmosphere. The stopcock E gives issue to the water which arises from the liquefaction of the ice in B. Method of mixtures. In determining the specific heat of a solid body by this method, it is weighed and raised to a known tempera- ture, by keeping it, for instance, for some time in a closed space heated by steam ; it is then immersed in a mass of cold water, the weight and temperature of which are known. The water becomes -258] Determination of Specific Heats. 255 heated by the heat given up by the body in cooling, and both are ultimately at the same temperature. From this common tempera- ture, from the respective weights of the water and of the substance, and lastly from their temperatures at the time of mixture, the spe- cific heat of the body is deduced by a simple calculation. Specific Specific Substances. heats. Substances. heats. Water . . I -0000 Zinc v . . 0-0955 Turpentine . . 0-4259 Copper . . 0-0951 Wood charcoal . 0-24II Silver . '", . 0-0570 Sulphur . , . 0'2025 Tin r . . . . 0-0562 Graphite . . 0'20l8 Antimony . . . . 0-0507 Thermometer glass . 0-1976 Mercury 0-0333 Phosphorus . . 0-1895 Gold . . :; . 0-0324 Diamond . 0-1469 Platinum . '".' . 0-0324 Iron . 0-1138 Lead . . v . 0*0314 Nickel . . 0-1086 Bismuth . . . . 0-0308 It will be seen from the above table that water and oil of tur- pentine have a much greater specific heat than that of other sub- stances, and more especially than the metals. It is from its great specific heat that water requires a long time in being heated or cooled ; and that, for the same weight and temperature, it absorbs or gives out far more heat than other substances. This double property is applied in heating by hot water, and it plays a most im- portant part in the economy of nature. Those bodies which have great specific heat, and therefore which require a great quantity of heat to raise them through a given tempera- ture, also in cooling through the same range give out a great quantity. This difference between bodies as to the quantities of heat they contain may be illustrated by a simple ex- periment. A number of small bullets of various metals, iron, tin, lead, bismuth, and copper are heated to a temperature of about 200 C by immersing them in hot oil ; they are then placed on a Fig. 207. 256 On Heat. [258- cake of bees-wax, c D, about half an inch in thickness (fig. 207). It will then be found that the iron and copper melt themselves through first, then follows the tin, while the lead and bismuth make but little way, being unable to sink much more than half their way through the wax. CHAPTER X. STEAM ENGINES. 259. Invention of the steam engine. Steam engines are un- doubtedly the most important of the applications of the physical sciences to the arts. Based on the very great elastic force which aqueous vapour assumes at a high temperature (247), and on the condensation of this vapour by cooling (251), steam engines have created, in a small volume and at small expense, very considerable motive powers. Their importance has caused much discussion and investigation as to their inventor, or rather inventors ; for it is only by the suc- cessive efforts of several men of genius that these machines have at- tained their present simplicity and precision. The history of the steam engine commences with Hero, the in- ventor of the fountain which bears his name, who invented, nearly two thousand years ago, a steam tourniquet, known as the eolipyle, analogous to the hydraulic tourniquet. The names of Salomon of Caux, and then of the Marquis of Worcester, are mentioned in the history of the steam engine. Denis Papin, a French physicist, to whom is due the apparatus already described (246), was the first who caused a piston to ascend in a vertical cylinder closed at the bottom and open at the top by means of the elastic force of steam, and to descend by con- densing this vapour by cooling ; so that the piston which descended in virtue of atmospheric pressure had an up and down motion in the cylinder, which is still the principle of all steam engines. Papin, who was a Protestant, was obliged to fly from France in consequence of the revocation of the Edict of Nantes, and the description and plan of his machine was published in Germany in 1690. He even made a model large enough to move a boat by means of paddle-wheels. In this model there was water under- -259] Steam Engines. 257 neath the piston at the bottom of the cylinder. When a furnace was placed under this, the water vaporised, and the elastic force raised the piston ; when it was at the top of its course the furnace was withdrawn ; the cylinder cooling, the vapour was condensed, and the piston sank. In 1705 Newcomen and Cawley constructed a steam engine, or ' fire-pump,' as it was then called, the object of which was to drain mines. In this engine the steam was produced separately in a boiler m below the cylinder c containing the piston^. The conden- Fig. 208. sation also was effected by cold water from a cistern, n, being in- jected into the cylinder through a cock, b. This was opened when the piston was to descend, and was closed after the descent ; a second one, a, was opened through which steam entered, and so on. But the sides of the cylinder being cooled by this injection of cold water, the steam which filled it was partially condensed, until the sides were again heated : there was- thus a considerable loss of steam, and therefore of fuel. The condensed water flowed out by a pipe, at the end of which was the valve v, which opened as the piston^ descended, w w is the beam by which the motion is transmitted to the pump rod, d. s 258 On Heat. [260- 260. Watt's improvements in the steam engine. James Watt, a mathematical instrument maker in Glasgow, had to repair the model of a Newcomen's engine belonging to the physical cabinet of the University. Struck by the enormous quantity of steam and of condensing water used by this engine, he entered upon a long series of researches and improvements, which he pursued with ad- mirable perseverance for fifty years, without ever being content with the success he obtained. Thus it was that Newcomen's machine, successively metamorphosed in all its parts, at last really became Watt's machine. Condenser. Watt's first and principal invention was the condenser. This name is given to a closed vessel quite distinct from the cylin- der in which the piston moves, and only connected with it by a tube provided with a stopcock. In this vessel cold water is injected, and the vapour is condensed by opening the connecting stopcock. Thus as the sides of the cylinder are not cooled, all the steam which enters there is utilised. Thus there was effected so great an economy of steam, and therefore of fuel, that Watt and Boulton his partner, having taken a patent, realised great profits by only requiring, for a certain number of years, a third of the saving in the consumption of coal as compared with Newcomen's engine. Single-acting engine. In Newcomen's engine the cylinder of which was open at the top, the steam only lifted the piston ; and then, when steam was condensed, the pressure of the atmosphere brought it down again ; whence the name atmospheric engine, by which it was designated. As the piston descended, air penetrated into the cylinder and cooled the sides, in consequence of which a portion of the vapour which penetrated into the cylinder was con- densed until the sides were again heated. To remove this source of loss, Watt closed the cylinder altogether, and caused the vapour to act above the piston, so as to make it descend ; then by an arrange- ment of stopcocks, alternately opened and closed by the action of the engine itself, the steam passed simultaneously above and below the piston. This being pressed equally in opposite directions, re- mained in equilibrium ; so that a simple counterpoise acting by means of a lever at the end of the piston rod raised the piston again, and so on. This machine, into which air did not enter, and where the atmospheric pressure did not act, was called the single- acting engine, to express that the steam had a useful action on only one side of the piston. The single-acting engine had the great disadvantage that it had -260] Double-acting Engine. 2. 59 no real force except when the piston was descending. It could transmit motion to pumps for emptying mines, because, for that, effort in only one direction was required ; but it would not furnish a sufficiently regular motion for many industries, for cotton manu- factures for instance. Hence Watt's task was not completed ; and he was not long in finding another plan. Double-acting engine. In this engine, one form of which we shall presently describe, and which is represented in fig. 209, the cylinder is closed both at top and at the bottom, but the steam acts alternately on the two faces of the piston ; that is to say, that by a system of stopcocks, opened and closed by the engine itself, when the lower part of the cylinder communicates with the condenser, the upper part, on the contrary, is connected with the boiler, and the steam acting in all its force on the piston causes it to descend. Then when this is at the bottom of its stroke the parts change ; the top of the cylinder is in connection with the condenser, and the bottom with the boiler ; the piston rises again and so forth, whence results an alternating rectilinear motion which is changed into a continuous circular motion, as will be presently described (262). Air-pump. Watt completed his engine by the addition of three pumps, which are worked by the engine, and play an important part. For the cold water of the condenser becomes rapidly heated by the heat which the steam gives up to it (253), and this water, soon reaching 100 degrees, would no longer condense the steam. Moreover the air, which is always dissolved in cold water, is libe- rated in the boiler, owing to the increase in temperature. Now this air, passing both above and below the piston, would soon stop its motion. To prevent these two injurious effects, Watt applied to the engine a suction-pump, which continually withdrew from the condenser the air and water which tended to accumulate there. Feed-pump and cold-water-piimp. The two other pumps which Watt added are the feed-pump and the cold-water-pump. The first is a force-pump which sends into the boiler the hot water with- drawn from the condenser by the air-pump., thnas producing a con- siderable saving in fuel. The other is a suction-pump, which raises either from a well or a river, or some other source, the cold water intended to replace that heated in the condenser, and withdrawn by the air-pump. Besides the important parts which have thus been described, we owe to Watt the arrangement for distributing the steam alternately above and below the piston : the regulator, whose function, when S 2 26o On Heat. [260- the machine works too slowly, is to admit more steam into the cy- linder, and, on the other hand, to diminish the quantity when the velocity is too great. Lastly, the parallelogram, which imparts to the piston rod a rectilinear motion. We may add that Watt, who had begun life as a philosophical instrument maker, carried into the execution of these great mechanisms the same perfection as is required for the best scientific instruments. 261. Description of tbe double-acting- engine. We have already seen that the double-action engine is that in which the steam acts alternately above and below the piston (260). Fig. 209 represents an engine of this kind, and fig. 213 gives a section of the cylinder, of the piston, and of the distribution of steam. The entire engine is of iron. To the piston T is fixed a rod A, which slides with gentle friction in a tubulure U placed at the centre of the plate which closes the cylinder (fig. 213). As it is very important that no steam shall escape between the piston rod and this tubulure, the latter is formed of two pieces, one attached to the plate, while the other, which fits in the first, can be pressed as tightly as is desired, so as to compress the material soaked with fat which is between the two tubulures. This arrangement is called a stuffing box ; it prevents the escape of steam without interfering with the motion of the piston. On the two sides of the cylinder are two columns h k, which guide the piston rod in its upward and downward motion. The end of the piston rod is connected with a long piece B, called the con- necting rod, which in turn is jointed with a shorter piece M, called the crank, the length of which is just half that of the stroke of the piston. This is rigidly fixed to a horizontal shaft, D, so that it can- not move without transmitting its motion. By means of this connecting rod and crank, the alternating rec- tilinear motion of the piston and of the rod is changed into a con- tinuous circular motion. For the.rod during the ascent of the piston, acts upwards upon the crank, making it turn in the direction of the arrow. When the piston is at the top of its stroke, the motion rod and the crank are one in front of the other. As the piston descends the motion rod again acts, so as always to turn it in the same direc- tion ; and when the piston is at the bottom of the stroke, they are again vertical, but one in the prolongation of the other. Hence it follows that the axle which has made half a turn during the ascent, makes a second one during the descent, and thus a complete revo- lution during each double oscillation of the piston. -261] Double-acting Engine, 261 To transmit the motion to machinery, on the axle D is fixed a sheave on which works an endless band XY of leather, or of gutta- " K *W Fig. 209. 262 On Heat. [261- percha, which works on another sheave fixed to the machinery to be turned. Moved by the first sheave, this band communicates its motion to the second ; in this manner the motion is transmitted to all the workshops of a large factory. On the right of the fixed sheave, G, there is a second, which is not fixed to the horizontal shaft ; this is the movable sheave. Its object is to suspend all the motion in the machine without stopping the steam engine. By means of an iron fork not seen in the figure, which encloses the band, the latter may be slid from the fixed to the movable sheave. As this latter is not connected with the horizontal shaft, it does not turn with it, and does not transmit its motion to the band. On the horizontal shaft is a very large iron wheel V, called the fly-wheel, which is necessary for keeping up the motion. For each time that the piston is at the top or bottom of its stroke, there is a momentary arrest, during which the motion of the whole machine tends to stop. These are called the dead points. It is then that the fly-wheel, in virtue of its inertia and of its acquired velocity, moves the horizontal shaft, and thus keeps up a regular motion. 262. Excentric. Valve-chest. The excentric is an arrange- ment by which a continuous circular motion is changed into an alternating rectilinear motion. It is very frequently used in machinery. One of these is fitted to the horizontal shaft at E, and the other at e. The former works the feed-pump, and the latter the valve- chest. The action of both is the same. Figures 210 and 211 repre- sent it on a larger scale, in two diametrically opposite positions. It consists of a circular piece KE, fixed to the horizontal shaft, but in such a manner that the centre of rotation does not coincide with the centre of the piece ; the latter being at C, the former at O. It follows from this construction that the point C constantly describes a circumference about O, which is represented in the drawing by a dotted line. Hence in 'each half turn it passes from the position represented in fig. 210 to that represented in fig. 211, and vice versa. So that the point C, in turning about the point O, does really per- form an up and down motion. To use this motion, the excentric is surrounded by a collar run, in which it can turn freely like an axle in its box : hence, during the rotation of the horizontal shaft, the collar shares the ascend- ing and descending motion of the point C, but not its rotatory motion. The excentric alone turns, the collar only rises a.nd -262] Valve-chest. 263 sinks. By thus transmitting its motion to a rod /, it works the valve-^ehest. Fig. 210. Fig. 2ii. Valve-chest. We have still to describe the valve-chest, the ar- rangement by which steam passes alternately above and below the piston. Fig. 213 presents a vertical section of this valve-chest, and of the cylinder. The steam enters the valve-chest from the boiler by the brass tube x. From the valve-chest two conduits, a and ^, are connected with the cylinder, one above and the other below. If they were both open at once, the steam acting equally on the two faces of the piston would keep it at rest. But one of these is always closed by a slide valve, y, fixed to a rod, /. This moves alternately, up and down, by means of an excentric, e, placed on the horizontal shaft. In fig. 213 the slide-valve closes the con- duit , and allowing the steam to enter at b, below the piston, the latter rises. But when it reaches the top of the stroke the excentric has passed from the position represented in fig. 210 to that in fig. 21 1 ; hence the rod, /, sinks, and with it the slide-valve, which then closes the conduit b, and allows the vapour to enter at a (fig. 212). The piston then sinks, and so forth at each displacement of the slide valve. In completing this account of the manner in which steam is dis- 264 On Heat. [262- tributed, it remains to explain what happens when the steam presses below the piston (fig. 213). It must not remain above, otherwise the piston could not move. But while the steam enters below by the conduit b, the top of the cylinder, by means of a conduit a, is connected with a cavity O, from which passes a tube L. Through this tube the steam which has already acted upon the piston passes into the atmosphere, or else is condensed in a vessel filled with Fig. Fig. 213. cold water, which has been already mentioned, the condenser (262). If, on the other hand, the piston sinks, the slide-valve being in the position of fig. 212, the vapour below the piston passes by the conduit &, to the cavity O, and to the tube L. 263. Regulator. The object of this arrangement is to regulate the quantity of steam which reaches the valve-chest, increasing it when the machine works too slowly and diminishing it when it works too rapidly. It consists of a parallelogram kr, each apex of -265] Various Kinds of Steam Engines. 26$ which is jointed. A toothed wheel, a, connected with the horizontal shaft, transmits its motion to a similar wheel, b, fixed to the rod c, which supports the parallelogram. This turns then with the rod the more rapidly the greater the velocity of the machine. But the two upper arms are provided with two solid balls, m and n ; moreover, a socket, r, to which are attached the two lower arms, is not fixed to the rod c, but can glide along it. Hence the centri- fugal force (29) acting on the balls m and n makes them diverge, the parallelogram opens, and the socket rises. It transmits its motion to a lever, s, the short arm of which being lowered presses upon a long rod, /. This inclining the lever, O, effects a small rota- tion in a valve, v, placed in the tube .r, by which steam comes (fig. 213). This valve, either by stopping the tube x, or leaving it open, admits more or less steam. 264. Feed-pump. The object of this, as its name implies, is to renew the water in the boiler in the degree in which it evaporates. In fig. 209 this pump, placed at Q, on the left of the drawing, re- ceives its motion from an excentric by means of a long rod, and it works both as cold-water-pump and as feed-pump ; as cold-water- pump, inasmuch as it withdraws water from a well by a suction-pipe placed below the engine ; and as feed-pump by its then forcing water into the boiler by the pipe R. 265. Various kinds of steam engines. A low pressure engine is one in which the pressure of the vapour does not much exceed an atmosphere ; and a high pressure engine is one in which the pressure of the steam usually exceeds this amount considerably. Low pressure engines are mostly condensing engines : in other words, they generally have a condenser where the steam becomes condensed after having acted on the piston ; on the other hand, high pressure engines are frequently without a condenser ; the loco- motive is an example. If the communication between the cylinder and the boiler remains open during the whole motion of the piston, the steam retains es- sentially the same elastic force, and is said to act without expansion : but if, by a suitable arrangement of the slide-valve, the steam ceases to pass into the cylinder when the piston is at | or f of its course, then the vapour expands ; that is to say, in virtue of its elastic force which is due to the high temperature, it still acts on the piston and causes it to finish its course. Hence a distinction is made between expanding and non-expanding engines. The principle of expansion is not applicable to low pressure 266 On Heat. [265- engines, for the elastic force of the steam is inconsiderable. But for high or mean pressure engines it not only effects a great saving in steam, and therefore in fuel, but it regulates the motion by diminishing the pressure the moment the acquired velocity of the piston tends to increase. 266. Work of an engine. Horse-power. The work of an engine is measured by the mean pressure on the piston multiplied by the area of the piston multiplied by the length of the stroke. In Fig. 214. England the unit of work is the foot-pound ; that is, the work per- formed in raising a weight of one pound through a height of a foot. Thus, to raise a weight of 14 pounds through a height of 20 feet would require 280 foot-pounds. In France the kilogrammetre is used ; that is, the work performed in raising a kilogramme through a metre. This unit corresponds to 7*233 foot-pounds. The rate of work in machines is the amount of work performed -267] Steam Boiler. in a given time ; a second or an hour, for example. In England the rates of work are compared by means of horse-power, which is a conventional unit, and represents 550 foot-pounds in a second. In France a similar unit is used, called the cheval vapeur, which represents the work performed in raising 75 kilogrammes through one metre in a second. It is equal to about 542 foot-pounds per second. 267. Steam boiler. We have still to describe the steam boiler or arrangement by which the steam is generated, and its various accessories. Fig. 214 gives a longi- tudinal and fig. 215 a trans- verse section of the steam boiler and its furnace. The generator consists of two wrought iron cylinders with hemispherical ends. Below are two cylinders, BB, of smaller diameter, which are called heaters, and which are connected with the generators by two strong tubes. The object of these heaters is to expose a greater surface to be heated. They are full of water, as also are the tubes which connect them with the boiler, which is only half full. The feed-water sent by the pump, Q, reaches the boiler by a tubu- lure, 11, which is immersed to the bottom to prevent cold water from condensing steam ; a second tubulure, m, leads, the vapour to the valve-chest. In the middle of the boiler is an oval hole, called a manhole, the object of which is to allow workmen to enter the boiler when it needs repair. This hole, as well as two front ones, B B, of the heaters are closed by what are called autoclaves. Here the cover instead of being on the outside is on the inside. A screw T fixed to this cover makes it press against the sides ; and as the pressure of the steam acts in the same direction, the greater the pressure the more tightly is the vessel closed. The furnace in which the boiler is placed, is so constructed as to multiply the surface heated, and to render the combustion as Fig. 215. 268 On Heat. [267- complete as possible. The products of combustion pass into tall chimneys, which from their great height increase the draught and thereby promote the combustion. 268. Float. This is a small apparatus, the object of which is to show the level of water in the boiler. It consists of a lever, at one end of which is a piece of stone,- F, and at the other a counter- poise, a. The mass F weighs more than the counterpoise a ; but as it is immersed in water, and thus loses part of its weight (96), it is in equilibrium, and the lever is horizontal so long as the level of water is at the desired height. But it sinks when there is too little water, and rises in the contrary direction when there is too much. Guided by these indications, the stoker can regulate the supply of water. 269. Safety-valve. The pressure of steam in the boiler is measured by means of the manometer (134). But this instrument would not prevent explosions if its indications were neglected. Hence on boilers two safety- valves, are placed, similar to that which Papin adopted in his di- gester (248). Fig. 216 rep resents on a larger scale one of these valves. It consists of a metal stopper c closing a tubulure A, fixed on the boiler. To prevent Flg - 2l6< this from sticking to the sides, the metal stopper is hollowed on three sides, as shown at S. It thus more resembles a clack-valve than an ordinary cork. On the piece rests a movable lever, ab, loaded with a weight,/. By moving this along the lever the load on the valve can be modified at will. For this purpose marks are placed which indicate the position of the load which corresponds to a given pressure. Thus, suppose it is desired that the pressure shall not exceed 5 atmospheres, the weight is placed at the division 5 on the lever. Then, as long as the pressure is less than 5, the safety-valve remains closed : but, if the pressure exceeds this amount, the valve opens and gives exit to the steam, thus preventing an explosion. 270. Safety-whistle. This is another safety apparatus, which indicates at a distance when the level of water in the boiler is too low. It consists of a float, F (fig. 217), supported by a lever, ih, -270] Safety Whistle. 269 which moves about the joint c ; a counterpoise, ^, balances the float, and a small conical stopper, a, fixed to the lever, closes a tubulure on the boiler. This tubulure is closed at the top by two hollow hemispheres. In the centre of the lower arc is a disc, which does not quite reach the edges. Between the two hemispheres is a circular interval through which vapour escapes when the cone a does not close the tubulure. As long as the water is at the right height the float F is raised, Fig. 217. and presses the cone against the tubulure ; but if the level sinks the float sinks, and with it the cone. The steam escapes round the disc e, and gives a very acute sound in striking against the edges of the upper hemisphere which are bevelled. The system con- stitutes, in fact, an organ pipe with a very short mouthpiece, and yielding, therefore, a very acute sound. On locomotives a similar whistle enables the driver to signal at a great distance by opening a stopcock, which allows the steam to escape. 270 On Heat. [271- CHAPTER XI. HYGROMETRY. 271. Object of hygrometry. The object of hygrometry is to determine the quantity of aqueous vapour contained in a given volume of air. This quantity is very variable ; but the atmosphere is never completely saturated with vapour, at any rate, in our climates. Nor is it ever completely dry ; for if hygrometric sub- stances, that is to say, substances with a great affinity for water, such as chloride of calcium, sulphuric acid, etc., be at any time exposed to the air, they absorb more or less aqueous vapour. The degree of moisture does not depend on the absolute quantity of aqueous vapour present in the air, but on the greater or less distance of the air from its point of saturation. When the air is cold, it may be moist with very little vapour, and, on the contrary, when it is warm, it may be very dry, even with a large quantity of vapour. In summer the air usually contains more aqueous vapour than in winter, notwithstanding which it is less moist, because, the temperature being higher, the vapour is farther from its point of saturation. When a room is warmed, the quantity of moisture is not diminished, but the moisture of the air is lessened, because its point of saturation is raised. The air may thus become so dry as to be injurious to the health, and it is hence usual to place vessels of water on the stoves used for heating. The quantity of vapour contained in the air varies greatly with the seasons, the climates, the temperature, and various local causes. A mean degree of moisture is best suited to the animal economy. In a state of great dry ness, as is the case, for instance, during the prevalence of north-east winds, the cutaneous transpiration is too abundant, the skin dries up and chaps, and general discomfort ensues. In an atmosphere which is too moist, perspiration stops, a feeling of depression and heaviness is felt. Hence it is necessary to regulate in a suitable manner the moisture of dwelling rooms, so as to avoid these two extremes. 272. Hygroscopes and hygrometers. There are two classes of instruments by which the hygrometric state of the air may be -273] Hygrometric State of the A ir. 271 known. One class, called hygroscopes, simply tell whether the air is more or less moist, but give no indications as to the quantity of moisture it contains ; others, called hygrometers, enable us to mea- sure it with some accuracy. All substances which absorb aqueous vapour, like common salt and many others known as deliquescent salts, may serve as hygro- scopes. This is also the case with a great number of animal and vegetable substances, such as paper, parchment, hair, cat- gut, etc., which, elongating as the air becomes moist, and contracting as it becomes dry, give an indication of the greater or less quantity of vapour in the air. A great number of instru- ments have been constructed which serve as hygroscopes. One of the commonest is that repre- sented in fig. 218. It consists of a small figure representing a monk fixed on a support ; the head is provided with a cowl of thin cardboard, movable about the point a, where it is attached to the end of a small piece of Fig - 2l8 - twisted catgut. The other end of this is fixed in a tubulure, o, as seen in the section. The catgut twisting as it becomes dry, and untwisting as it is moist, moves the cowl which is carefully arranged, so that the head is -covered when the atmosphere is moist, and un- covered when it is dry. This instrument, and all others of the same class, only change slowly, and their indications are always behindhand with the state of the weather ; nor are they, moreover, very exact. 273. Hygrometric state of the air. By this term we do not understand the actual quantity of vapour present, but the ratio of the quantity of vapour which the air actually contains to that which it would contain if it were saturated. Thus, if we say that the air is three-fifths saturated, we mean that it contains three-fifths of the vapour which it would contain in a state of saturation. 2/2 On Heat. [273- The most exact of all hygrometers are the chemical hygrometers. They consist essentially of an arrangement by which a given measured volume of air is passed through a series of drying tubes that is, tubes containing some hygroscopic substance, such as chloride of calcium, or pumice saturated with sulphuric acid. These tubes, being previously weighed, are weighed again after the operation ; an increase of weight is observed, which is due to the moisture absorbed by the hygroscopic substance, and this increase represents the weight of the moisture in the volume of air taken. This method is very exact, but it is both difficult and tedious of execution. More convenient than the above are what are called condensation hygrometers, in which the vapour of the atmosphere is made to con- dense on a body artificially cooled. When a body gradually cools in a moist atmosphere, the layer of air in immediate contact with it cools also, and a point is ulti- mately reached at which the va- pour present is just sufficient to saturate the air : the least dimi- nution of temperature then cau- ses a precipitation of moisture on the body in the form of dew. When the temperature rises again, the dew disappears, and the mean of these two tempera- tures is taken as the dew point. A good example of an instru- ment of this class is met with in DanielPs hygrometer. This consists of two glass bulbs at the extremities of a glass tube bent twice (fig. 219). The bulb A is two-thirds full of ether, Fig 2I9 and a very delicate thermo- meter dips in it ; the rest of the space contains nothing but the vapour of ether, the ether having been boiled before the bulb B was sealed The bulb B is covered with muslin, and ether is dropped upon it. The ether in evaporating cools the bulb, and the vapour contained in it is con- densed. The internal tension being thus diminished, the ether in -273] Wet Bulb Hygrometer. 273 A forms vapours which condense in the other bulb, B. In propor- tion as ether distils from the lower to the upper bulb, the ether in A becomes colder, and ultimately the temperature of the air in imme- diate contact with A sinks to that point at which its vapour is just more than sufficient to saturate it, and the excess is accordingly deposited on the outside as a ring of dew corresponding to the sur- face of the ether. The temperature of this point is noted by means of the thermometer in the inside. The addition of ether to the bulb B is then discontinued, the temperature of A rises, and the temperature at which the dew disappears is noted. In order to render the deposition of dew more perceptible, the bulb A is made of black glass. These two points having been determined, their mean is taken as that of the dew-point. The tem- perature of air at the time of the experiment is indicated by the thermometer on the stem. The tension f, corresponding to the temperature of the dew point, is then found in the table of tensions (249). This tension is exactly that of the vapour present in the air at the time of the experiment. The tension, F of vapour saturated at the temperature of the at- mosphere is found by means of the same table ; the quotient obtained by dividing / by F, represents the hygrometric state of the air. For instance, the temperature of the air being 15, suppose the dew point is 5. From this table the corresponding ten- sions are /= 6-5 3 millimetres, and F = i27o milli- metres, which gives 0-514 for the ratio of /to F, or the hygrometric state. A very convenient form of hygrometer, and one whose use is gradually extending, is that known as the Pyschrometer or wet bulb hygrometer, which is based on the principle that a moistened body evaporates in the air more rapidly in proportion as the air is drier (242) ; and, in consequence of this evaporation, the temperature of the body sinks. The application of the prin- ciple to this purpose was first suggested by Leslie. The form of the apparatus usually adopted in this country is due to Mason. It consists of two delicate thermometers placed on a wooden stand (fig. 220). One of the bulbs is covered with muslin, and is kept continually moist by being connected with a reservoir of water by T Fig. 220. 2/4 On Heat. [273- means of a string. Unless the air is saturated with moisture, the wet bulb thermometer always indicates a lower temperature than the other, and the difference between the indications of the two thermo- meters is greater in proportion as the air can take up more moisture. According to Glashier the temperature of the dew point may be obtained by multiplying the difference between the temperatures of the wet and dry bulb by a number which depends on the temperature of the air at the time of observation, and subtracting the product thus obtained from this last-named temperature. The following are the numbers : Dry bulb temperature F. Factor Dry bulb temperature F. Factor Below 24 8-5 34 to 35 2-6 24t025 7'3 3540 2'5 25 26 6-4 4045 2-3 26 27 6-1 4550 2'I 2728 5'9 5055 2'0 2829 57 5560 r8 2930 5-0 6065 1-8 30-31 4-6 6570 17 3132 3-6 70-75 1-5 3233 3'i 7580 1-3 3334 2-8 8085 fO These are often known as Glashier 's factors. The temperatures are expressed on the Fahrenheit scale. CHAPTER XII. METEOROLOGICAL PHENOMENA WHICH DEPEND UPON HEAT. 274. Meteorology. Meteorology is that part of physics which is concerned with the phenomena which occur in the atmosphere ; such, for instance, as variations in the temperature of the air, wind, rain, storms, electrical phenomena, etc. Though of quite recent origin, this science is an important application of the physical sciences, and furnishes useful indications to navigation, to agricul- ture, and to hygiene. -276] Mean Temperature. 275 275. Mean temperature. The mean daily temperature, or simply temperature, is that obtained by adding together 24 hourly observations, and dividing by 24. A very close approximation to the mean temperature is obtained by taking the mean of the maxima and minima temperatures of the day and of the night, which are determined by means of the maximum and minimum thermometers (204). These ought to be protected from the solar rays, raised above the ground, and be far from all objects which might influence them by their radiation. The lowest daily tem- perature is at 4 A.M., and the highest at 2 P.M. The temperature of a month is the mean of those of 30 days, and the temperature of the year is the mean of those of 12 months. The highest mean monthly temperature is in July, and the lowest in January. Finally, the temperature of a place is the mean of its annual temperature, for a great series of years. The mean tem- perature of London is 8*28 C., or 46*9 F. The temperatures in all cases are those of the air and not those of the ground. 276. Causes which modify the temperature of the air. The principal causes which modify the temperature of the air are the latitude of a place, its height that is, its distance above the sea the direction of the winds, and the proximity of seas. Influence of the latitude. The temperature of the air and of the ground diminishes from the equator towards the poles. This is due to the fact, that the sun's rays, which are perpendicular at the equator, are more and more inclined as we come near the poles. Now we have seen (215) that the greater the obliquity under which the rays of heat fall upon a body, the less is the body heated ; hence the heat absorbed decreases from the equator to the poles, for the rays are then more oblique. Yet, as in summer, the days are longer as we get nearer the north, the loss due to the increasing obliquity of the sun is partially compensated by the sun remaining longer above the horizon. Under the equator, where the length of the days is constant, the temperature is almost invariable ; in the latitude of London, and the more northerly countries, where the days are very unequal, the temperature varies greatly ; but in summer it sometimes rises almost as high as under the equator. The^lowering of the temperature produced by the latitude is small ; thus in a latitude of 115 miles north of ours, the temperature is only i C. lower. Influence of altitude. The height of a place has a much more considerable influence on the temperature than its latitude. In T 2 2;6 On Heat. [276- the temperate zone a diminution of i C. corresponds in the mean to an ascent of 180 yards. The cooling on ascending in the atmosphere has been observed in balloon ascents, and a proof of it is seen in the perpetual snows which cover the highest mountains, even under the torrid zones. The height at which snow remains unmelted through the year, or the line of perpetual snow met with, differs in different places. On the Andes it commences at a height of 14,760 feet, and on the Alps at 8,880 feet. Direction of winds. As winds share the temperature of the coun- tries which they have traversed, their direction exercises great influence on the air in any place. In our climate the hottest winds are the south, then come the south-east, the south-west, the west, the east, the north-west, notfh, and lastly, the north-east, which is the coldest. The character of the wind changes with the seasons ; the east-wind, which is cold in winter, is hot in summer. Proximity of the seas. The neighbourhood of the sea tends to render the temperature of the air uniform, by heating it in winter, and cooling it in summer. The average temperature of the sea in equatorial and polar countries is always higher than that of the atmosphere. With reference to the uniformity of the temperature, it has been found that in temperate regions, that is, from 25 to 50 of latitude, the difference between the maximum and minimum temperature of a day does not exceed, on the sea, 2 to 3 ; while on land it amounts to 12 to 15. In islands the uniformity of temperature is very perceptible, even during the greatest heats. In continents, on the contrary, the winters for the same latitudes become colder, and the difference between the temperature of summer and winter becomes greater. 277. Gulf stream. A similar influence to that of the winds is exerted by currents of warm water. To one of these, the Gulf stream, the mildness of the climate in the north-west of Europe is usually assigned. This great body of water, taking its origin in equatorial regions, flows through the Gulf of Mexico, from whence it derives its name ; passing by the southern shores of North America it makes its way -in a north-westerly direction across the Atlantic, and finally washes the coast of Ireland and the north-west of Europe generally. Its temperature in the Gulf is about 28 C. ; and generally is a little more than 5 C. higher than the rest of the ocean on which it floats, owing to its lower specific gravity. To -279] Climate. 277 its influence is due the milder climate of western Europe, as com- pared with that of the opposite coast of America ; thus the river Hudson, which is in the same latitude as Rome, is frozen over three months in the year. It also causes the polar regions to be separa- ted from the coasts of Europe by a girdle of open sea ; and hence the harbour of Hammerfest is open the year round. Besides its in- fluence in thus moderating climate, the Gulf stream is an important help to navigators. 278. isothermal lines. When on a map all the points whose temperature is known to be the same are joined, curves are obtained which Humboldt first noticed, and which he called isothermal lines. If the temperature of a place only varied with the obliquity of the sun's rays, that is, with the latitude, isothermal lines would all be parallel to the equator ; but as the temperature is influenced by many local causes, especially by the height, the isothermal lines, are always more or less curved. On the sea, however, they are almost parallel. A distinction is made between isothermal lines, tsotheral lines, and isochimenal lines, where the mean general, the mean summer, and the mean winter temperatures are respectively constant. An isothermal zone is the space comprised between two isothermal lines. Kupffer also distinguishes isogeothermal lines, where the mean temperature of the soil is constant. 279. Climate. By the climate of a place is understood the whole of the meteorological conditions to which a place is sub- jected ; its mean annual temperature, summer and winter tempera- tures, and by the extremes within which these are comprised. Some writers distinguish seven classes of climates, according to their mean annual temperature, a hot climate from 30 to 25 C. ; a warm climate from 25 to 20 C. ; a mild climate from 20 to 15 C. ; a temperate climate from 15 to 10 C. ; a cold climate from 10 to 5 C. ; a very cold climate from 5 to zero ; and an arctic climate where the temperature is below zero. Those climates again, are classed as constant climates, where the difference between the mean and summer and winter tempera- ture does not exceed 6 to 8 ; variable climates, where the differ- ence amounts to from 16 to 20 ; and extreme climates, where the difference is greater than 30. The climates of Paris and London are variable ; those of Pekin and New York are extreme. Island climates are generally little variable, as the temperature of the sea is constant ; and hence the distinction between land and sea cli- mates. Marine climates are characterised by the fact, that the 278 On Heat. [279- difference between the temperature of summer and winter is always less than in the case of continental climates. But the temperature is by no means the only character which influences climates ; there are, in addition, the moisture of the air, the quantity and frequency of the rains, the number of storms, the direction and in- tensity of the winds, and the nature of the soil. FOG. RAIN. DEW. 280. Fog-s and mists. When aqueous vapours, rising from a vessel of boiling water, diffuse in the colder air, they are condensed ; a sort of cloud is formed which consists of a number of small hollow vesicles of water, which remain suspended in the air. These are usually spoken of as vapours, yet they are not so, at any rate not in the physical sense of the word ; for they are partially con- densed vapours. When this condensation of aqueous vapours is not occasioned by contact with cold solid bodies, but takes place throughout large spaces of the atmosphere, the effect is to form, fogs or mists, which, in fact, are nothing more than the appearance seen over a vessel of hot water. A chief cause of fogs consists in the moist soil being at a higher temperature than the air. The vapours which then ascend con- dense and become visible. In all cases, however, the air must have reached its point of saturation before condensation takes place. Fogs may also be produced when a current of hot and moist air passes over a river at a lower temperature than its own, for then the air being cooled, as soon as it is saturated the excess of vapour present is condensed. The distinction between mists and fogs is one of degree rather than of kind. A fog is a very thick mist. 281. Clouds. Clouds are masses of vapour, cqndensed into little drops or vesicles of extreme minuteness, like fogs ; from which they only differ in occupying the higher regions of the atmosphere ; they always result from the condensation of vapours which rise from the earth or the sea. According to their appearance, they have been 'divided by Howard into four principal kinds : the nim- bus, the stratus, the cumulus, and the cirrus. These four kinds are represented in fig. 221, and are designated respectively by one, two, three, and four birds on the wing. The cirrus consist of small whitish clouds, which have a fibrous -281] Clouds. 279 or wispy appearance, and occupy the highest regions of the atmo- sphere. The name of mare's tails, by which they are generally known, well describes their appearance. From the low tempera- ture of the spaces which they occupy, it is more than probable that cirrus clouds consist of frozen particles ; and hence it is that haloes, coronas, and other optical appearances, produced by refraction and reflection from ice crystals, appear almost always in these clouds and their derivatives. Their appearance often precedes a change of weather. The cumulus are rounded spherical forms which look like moun- Fig. 221. tains piled one on the other. They are more frequent in summer than in winter, and, after being formed in the morning, they gene- rally disappear towards evening. If, on the contrary, they become more numerous, and especially if surmounted by cirrus clouds, rain or storms may be expected. Stratus clouds consist of very large and continuous horizontal sheets, which chiefly form at sunset, and disappear at sunrise; 28o On Heat. [281- They are frequent in autumn and unusual in spring time, and are lower than the proceeding. The nimbus, or rain clouds, which are sometimes classed as one of the fundamental varieties, are properly a combination of the three preceding kinds. They affect no particular form, and are solely distinguished by a uniform grey tint, and by fringed edges. They are indicated on the right of the figure by the presence of one bird. The fundamental forms pass into one another in the most varied manner ; Howard has classed these traditional forms as cirro- cumulus, firro-stratus, and cumulo-stratus, and it is often very difficult to tell, from the appearance of a cloud, which type it most resembles. The cirro-cumulus is most characteristically known as a ' mackerel sky ; ' it consists of small roundish masses, disposed with more or less irregularity and Connection. It is frequent in summer, and attendant on warm and dry weather. Cirro-stratus appears to result from the subsidence of the fibres of cirrus to a horizontal position, at the same time that they approach each other laterally. The form and relative position when seen in the distance frequently give the idea of shoals of fish. The tendency of cumulo- stratus is to spread, settle down into the nimbus, and finally fall as rain. The height of clouds varies greatly ; in the mean it is from 1,300 to 1,500 yards in winter, and from 3,300 to 4,400 yards in summer. But they often exist at greater heights ; Gay-Lussac, in his balloon ascent, at a height of 7,650 yards, observed cirrus- clouds above him, which appeared still to be at a considerable height. In Ethiopia M. d'Abbadie observed storm-clouds whose height was only 230 yards above the ground. In order to explain the suspension of clouds in the atmosphere, H alley first proposed the hypothesis of vesicular vapours. He sup- posed that clouds are formed of an infinity of extremely minute vesicles, hollow, like soap bubbles filled with air, which is hotter than the surrounding air ; so that these vesicles float in the air like so many small balloons. This theory has at present many opponents, who assume that clouds and fogs consist of extremely minute droplets of water, which are retained in the atmosphere by the ascensional force of currents of hot air, just as light powders are raised by the wind. Ordinarily, clouds do not appear to descend, but this absence of downward motion is only apparent. In fact, clouds do usually fall slowly, but then the lower part is continually -283] Rain. 28 [ dissipated on coming in contact with the lower and more heated layers ; at the same time the upper part is always increasing from the condensation of new vapours, so that from these two actions clouds appear to retain the same height. 282. Formation of clouds. Many causes may concur in the formation of clouds. I. The low temperature of the higher regions of the atmosphere. For owing to the solar radiation, vapours are constantly disengaged from the earth and from the waters, which from their elastic force and lower density rise in the atmosphere ; meeting there continually colder and colder layers of air, they sink to the point of saturation, and then condensing in infinitely small droplets, they give rise to clouds. II. The hot and moist currents of air rising during the day undergo a gradually feebler pressure, and thus is produced an expansion, which is a source of intense cold, and produces a con- densation of vapour. Hence it is that high mountains, stopping the aerial currents, and forcing them to rise, are an abundant source of rain. III. A hot, moist current of air mixing with a colder current, undergoes a cooling, which brings about a condensation of the vapour. Thus the hot and moist winds of* the south and south-west, mixing with the colder air of our latitudes, give rain. The winds, of the north and north-east tend also, in mixing with our atmosphere, to condense the vapours ; but as these winds, owing to their low temperature, are very dry, the mixture rarely attains saturation, and generally gives no rain. 283. Rain. When, by the constant condensation of aqueous vapour, the individual vapour vesicles become larger and heavier, and when finally individual vesicles unite, they form regular drops, which fall as rain. The quantity of rain which falls annually in any given place, or the annual rainfall, is measured by means of a rain gaitge or pluviometer. Many local circumstances may effect the quantity of rain which falls in different countries ; but, other things being equal, most rain falls in hot climates, for there the vaporisation is most abundant. The rain-fall decreases, in fact from the equator to the poles. At London it is 23-5 inches ; at Bordeaux it is 25*8 ; at Madeira it is 277 ; at Havannah it is 91-2 ; and at St. Domingo it is 107-6. The quantity varies with the seasons ; in Paris, in winter it is 4'2 inches ; in spring 6-9 ; in summer 6-3 ; and in autumn 4-8 inches. 282 On Heat. [283- An inch of rain on a square yard of surface expresses a fall of 4674 pounds, or 4-67 gallons. On an acre it corresponds to 22,622 gallons, or 100-9935 tons. 100 tons per inch per acre is a ready way of remembering this. 284. Dew. Hoarfrost. Dew is merely aqueous vapour which has condensed on bodies during the night in the form of minute, globules. It is occasioned by the chilling which bodies near the surface of the earth experience in consequence of nocturnal radia- tion. Their temperature having then sank several degrees below that of the air, it frequently happens, especially in hot seasons, that this temperature is below that at which the atmosphere is saturated. The layer of air which is immediately in contact with the chilled bodies, and which virtually has the same temperature, then deposits a portion of the vapour which it contains : just as when a bottle of cold water is brought into a warm room, it be- comes covered with moisture, owing to the condensation of aqueous vapour upon it. According to this theory, which was first propounded by Dr. Wells, all causes which promote the cooling of bodies increase the quantity of dew. These causes are the emissive power of bodies, the state of the sky, and the agitation of the air. Bodies which have a great radiating power more readily become cool, and there- fore ought to condense more vapour. In fact there is generally no deposit of dew on metals, whose radiating power is very small, especially when they are polished ; while the ground, sand, glass, and plants, which have a great radiating power, become abundantly covered with dew. On some plants, for instance, not merely are droplets of dew formed, but regular layers of water. The state of the sky also exercises a great influence on the for- mation of dew. If the sky is cloudless, the planetary spaces send to the earth an inappreciable quantity of heat, while the earth radiates very considerably, and therefore becoming very much chilled, there is an abundant deposit of dew. But if there are clouds, as their temperature is far higher than that of the planetary spaces, they radiate in turn towards the earth, and as bodies on the surface of the earth only experience a feeble chilling, no deposit of dew takes place Wind also influences the quantity of vapour deposited. If it is feeble, it increases it, inasmuch as it renews the air ; if it is strong, it diminishes it, as it heats the bodies by contact, and thus does not the air time to become cooled. Finally, the deposit of dew is -285] Snow. Sleet. 28 3 more abundant according as the air is moister, for then it is nearer its point of saturation. Hoar frost and rime are nothing more than dew which has been deposited on bodies cooled below zero, and has therefore become frozen. The flocculent form which the small crystals pre- sent, of which rime is formed, shows that the vapours solidify directly, without passing through the liquid state. Hoar frost, like dew, is formed on bodies which radiate most, such as the stalks and leaves of vegetables, and is chiefly deposited on the parts turned towards the sky. 285. Snow. Sleet. Snow is water solidified in stellate crystals, variously modified, and floating in the atmosphere. These crystals arise from the congelation of the minute vesicles which constitute the clouds, when the temperature of the latter is below zero. They Fig. 222. are more regular when formed in a calm atmosphere. Their form may be investigated by collecting them on a black surface, and viewing them through a strong lens. The regularity, and at the same time variety, of their forms are truly beautiful. Fig. 222 shows some of the forms as seen through a microscope. It snows most in countries near the poles, or which are high above the sea level. Towards the poles, the earth is constantly covered with snow ; the same is the case on high mountains, where there are perpetual snows even in equatorial countries. 284 On Heat. [285- Sleet is also solidified water, and consists of small icy needles pressed together in a confused manner. Its formation is ascribed to the sudden congelation of the minute globules of the clouds in an agitated atmosphere. 286. Bail. Hail is a mass of compact. globules of ice of different sizes, which fall in the atmosphere. In our climates hail falls principally during spring and summer, and at the hottest times of the day : it rarely falls at night. The fall of hail is always pre- ceded by a peculiar noise. Hail is generally the precursor of storms,, it rarely accompanies them, and follows them more rarely still. A hailstone consists of a core of snow, which is surrounded by con- centric layers of ice. Hail falls from the size of small peas to that of an egg or an orange. The formation of hailstones, and more especially their great size, have never been altogether satisfactorily accounted for. While snow sometimes falls for days together, hail- storms seldom last longer than a quarter of an hour, and they are also far less frequent. ON WINDS IN GENERAL. 287. Direction and velocity of winds. Winds are currents moving in the atmosphere with variable directions and velocities. There are eight principal directions in which they blow : north, north-east, east, south-east, south, south-west, west, and north-west. Mariners further divide each of the distances between these eight directions into four others, making in all 32 directions, which are called points or rhumbs. A figure of these 32 rhumbs on a circle in the form of a star, is known as the mariner's card. The direction of the wind is determined by means of vanes, and its velocity by means of the anemometer. There are several forms of this instrument ; the most usual consists of a small vane with fans, which the wind turns ; the velocity is deduced from the number of turns made in a given time, which is measured by means of an endless screw and wheel-work. In our climate the mean velocity is from 1 8 to 20 feet in a second. With a . velocity of 6 or 7 feet, the wind is moderate ; with 30 or 35 feet, it is fresh ; with 60 or 70 feet, it is strong ; with a velocity of 85 to 90 feet, it is a tempest, and from 90 to 120 it is a hurricane. 288. Causes of winds. Winds are produced by the disturbance of the equilibrium in some part of the atmosphere, a disturbance -289] Winds. 285 always resulting from a difference in temperature between adjacent countries. Thus, if the temperature of a certain extent of ground becomes higher, the air in contact with it becomes heated, it ex- pands, and rises towards the higher regions of the atmosphere ; whence it flows, producing winds which blow from hot to cold countries. But at the same time the equilibrium is destroyed at the surface of the earth, for the barometric pressure on the colder adjacent parts is greater than on that which has been heated, and hence a current will be produced with a velocity dependent on the difference between these pressures ; thus two distinct winds will be produced, an upper one setting outwards from the heated region, and a lower one setting inwards towards it. 289. Regular, periodical, and variable winds. According to the more or less constant directions in which winds blow, they may be classed as regular, periodical, and variable winds. i. Regular winds are those which blow all the year through in a virtually constant direction. These winds, which are also known as the trade winds, are uninterruptedly observed far from the land in equatorial regions, blowing from the north-east to the south-west in the northern hemisphere, and from the south-east to the north- west in the southern hemisphere. They prevail on the two sides of the equator as far as 30 of latitude, and they blow m the same direction as the apparent motion of the sun, that is, from east to west. The air above the equator being gradually heated, rises as the sun passes round from east to west, and its place is supplied by the colder air from the north or south. The direction of the wind, however, is modified by this fact ; that the velocity which this colder air has derived from the rotation of the earth, namely, the velocity of the surface of the earth at that point from which it started, is less than the velocity of the surface of the earth at the point at which it has now arrived ; hence the currents acquire, in reference to the equator, the constant direction which constitutes the trade winds. ii. Periodical winds are those which blow regularly in the same direction at the same seasons, and at the same hours of the day ; the monsoon, simoom, and the land and sea breeze are examples of this class. The name monsoon is given to winds which blow for six months in one direction, and for six months in another. They are principally observed in the Red Sea and in the Arabian Gulf, in the Bay of Bengal and in the Chinese Sea. These winds 286 On Heat. [289- blow towards the continents in summer, and in a contrary direc- tion in winter. The simoom is a hot wind which blows over the deserts of Asia and Africa, and which is characterised by its high temperature and by the sands which it raises in the atmosphere and carries with it. During the prevalence of this wind the air is darkened, the skin feels dry, the respiration is accelerated, and a burning thirst is experienced. This wind is known under the name of sirocco in Italy and Algiers, where it blows from the great desert of Sahara. During its prevalence people remain at home, the windows and doors being carefully closed. In Egypt, where it prevails from the end of April to June, it is called kamsin, from a word signifying fifty ; for it lasts ordinarily 50 days ; 25 before the spring equinox, and 25 after. When caravans are surprised by this wind, men cover their faces with thick clothes, and camels turn their backs to the torment. The natives of Africa, in order to protect themselves from the effects of the too rapid perspiration occasioned by this wind, cover themselves with fatty substances. The land and sea breeze is a wind which blows on the sea coast during the day from the sea towards the land, and during the night from the land to the sea. For during the day the land becomes more heated than the sea, in consequence of its lower specific heat (257) and greater conductivity, and hence as the superincum- bent air becomes more heated than that upon the sea, it ascends and is replaced by a current of colder and denser air flowing from the sea towards the land. During the night the land cools more rapidly than the sea, and hence the same phenomenon is produced in a contrary direction. The sea breeze commences after sunrise, increases to three o'clock in the afternoon, decreases towards evening, and is changed into the land breeze after sunset. These winds are only perceived at a slight distance from the shores. They are regular in the tropics, but less so in our climates ; and traces of them are seen as far as the coasts of Greenland. The proximity of mountains also gives rise to periodical daily breezes. iii. Variable winds are those which blow sometimes in one direction and sometimes .in another, alternately, without being subject to any law. In mean latitudes the direction of the winds is very variable ; towards the poles this irregularity increases, and under the arctic zone the winds frequently blow from several points of the horizon at once. On the other hand, in approaching the torrid zone, they become more regular. The south-west wind -292] Sources of Heat and Cold. 287 prevails in the north of France, in England, and in Germany; in the south of France the direction inclines towards the north, and in Spain and Italy the north wind predominates. 290. law of the rotation of winds. Spite of the great irregu- larity which characterises the direction of the winds in our latitude, it has been ascertained that the wind has a preponderating ten- dency to veer round according to the sun's motion ; that is, to pass from north, through north-east, east, south-east to south, and so on round in the same direction from west to north ; that it often makes a complete circuit in that direction, or more than one in succes- sion, occupying many days in doing so, but that it rarely veers, and very rarely or never makes a complete circuit in the opposite direc- tion. For a station in south latitude a contrary law of rotation pre- vails. This law, though more or less suspected for a long time, was first formally enunciated and explained by Dove, and is known as Dove's law of rotation of winds. CHAPTER XIII. SOURCES OF HEAT AND COLD. 291. Different sources of heat. The following different sources of heat may be distinguished : i. the mechanical sources, comprising friction, percussion, and pressure ; ii. the physical sources that is, solar radiation, terrestrial heat, the molecular actions, the changes of condition and electricity ; iii. the chemical sources, or molecular combinations, and more especially combustion. MECHANICAL SOURCES. 292. Beat due to friction. The friction of two bodies, one against the other, produces heat, which is greater the greater the pressure and the more rapid the motion. For example, the axles of carriage wheels, by their friction against the boxes, often become so strongly heated as to take fire. By rubbing together two pieces of ice in a vacuum below zero, Sir H. Davy partially melted them. 288 On Heat. [292- In boring a brass cannon Rumford found that the heat developed in the course of 2^ hours was sufficient to raise 26^ pounds of water from zero to the boiling point. This may be well illustrated by an experiment, fig. 223, devised by Prof. Tyndal. A brass tube, b, closed at the bottom, about 4 inches long and less than an inch in diameter, fits on the whirling table, having been three-quarters filled with cold water and corked. Fig. 223. If now it be clasped by a sort of wooden squeezer in which there are two semicircular grooves, and then be made to rotate, the heat developed by the friction is sufficient to boil the water and expel the cork by which it is closed. 293. Heat due to pressure and percussion. If a body be SO compressed that its density is increased, its temperature rises ac- cording as the volume diminishes. In solids and liquids, which are but little compressible, ihe disengagement of heat is not great ; though Joule has verified it in the case of water and of oil, which were exposed to pressures of 15 to 25 atmospheres. Similarly, when weights are laid on metallic pillars, heat is evolved, and ab- sorbed when they are removed. The production of heat by the compression of gases is easily shown by means of the pneumatic syringe, (fig. 224). This consists of a glass tube with thick sides, closed hermetically by a leathern piston. At the bottom of this, there is a cavity in which a small piece of tinder is placed. The tube being full of air the piston is suddenly plunged downwards, the air thus compressed disengages as much heat as to ignite the tinder, which is seen to burn when the piston is rapidly withdrawn. The inflammation of the tinder in this experiment indicates a temperature of at least 300. At the moment of compression a bright flash is observed, which was -294] PJiysical Sources of Heat. 289 originally attributed to the high temperature of the air ; but it is simply due to the combustion of the oil which greases the piston. Fig. 224. Percussion is also a source of heat, as is observed in the sparks which are thrown off by horses in trotting over a hard pavement. In firing a shot at an iron target, a sheet of flame is frequently seen at the moment of impact ; and Mr. Whitworth has used iron shells which are exploded by the concussion on striking an iron target. A small piece of iron hammered on the anvil becomes very hot. The heat is not simply due to an approximation of the molecules, that is, to an increase in density, but arises from a vibratory motion imparted to them ; for lead, which does not become denser by being hammered, nevertheless becomes heated. PHYSICAL SOURCES. 294. Solar radiation. The most intense of all sources of heat is the sun. The cause of its heat is unknown ; some have con- sidered it to be an ignited mass experiencing immense eruptions, while others have regarded it as composed of layers acting chemically on each other like the couples of a voltaic battery, and giving rise to electrical currents, which produce light and solar heat. On both hypotheses the incandescence of the sun would have a limit. Different attempts have been made to determine the quantity of heat annually emitted by the sun. M. Pouillet, by means of an apparatus, which he calls a pyrheliometer, has calculated that if the total quantity of heat which the earth receives from the sun in the course of a year were employed to melt rce, it would be capable of melting a layer of ice all round the earth of 35 yards in thickness. U 290 On Heat. [294- But from the surface which the air exposes to the solar radiation, and from the distance which separates the earth from the sun, the quantity of heat which the earth receives can only be o^ir.o'oo.ooo f the heat emitted by the sun. Faraday has calculated that the average amount of heat radiated in a day on each acre of ground in the latitude of London is equal to that which would be produced by the combustion of sixty sacks of coal. 295. Terrestrial beat. Our globe possesses a heat peculiar to it, which is called the terrestrial heat. The temperature of the earth gradually sinks from the surface to a certain depth, at which it remains constant in all seasons. It is hence concluded that the sun's heat does not penetrate below a certain internal layer, which is called the layer of constant temperature : its depth below the earth's external surface varies, of cour c e, in different parts of the globe ; at Paris it is about thirty yards, and the temperature is con- stant at i i -8 C. Below the layer of constant temperature, the temperature is ob- served to increase, on the average i C. for every 90 feet. This in- crease has been verified in mines and artesian wells. According to this, at a depth of 3,000 yards, the temperature of a corresponding layer would be 100, and at a depth of 20 to 30 miles there would be a temperature sufficient to melt all substances which exist on the surface. Hot springs and volcanoes confirm the existence of this central heat. The heat produced by the changes of condition has been already treated of in the articles solidification and liqtiefaclion ; the Heat produced by electrical action will be discussed under the head of ELECTRICITY. CHEMICAL SOURCES. 296. Chemical combinations. Combustion. Whenever two bodies unite in virtue of their reciprocal affinity this operation is known as the act of chemical combination. Chemical combinations are usually accompanied by a certain elevation of temperature. When these combinations take place slowly, as when iron oxidises in the air, and produces rust, the heat produced is imperceptible ; but if they take place rapidly, the disengagement of heat is very intense. The same quantity of heat is produced in both cases, but when evolved slowly it is dissipated as fast as formed. -297] RumforcTs Calorimeter. 291 Combustion is chemical combination attended with the evolution, of light and heat. In the ordinary combustion in lamps, fires, candles, the carbon and hydrogen of the coal or of the oil, etc., combine with the oxygen of the air, giving rise to aqueous vapour, gases, and other volatile products which are given off as smoke. The old expression that fire destroys everything is incorrect. It destroys nothing, it simply puts certain elements at liberty to unite with others ; it decomposes but at the same time produces. A body in being burned is transformed, but its substance is not destroyed. Many combustibles burn with flame. A flame is a gas or vapour raised to a high temperature by combustion. Its illuminating power varies with the nature of the products formed. The presence of a solid body in the flame increases the illuminating power. The flames of hydrogen, carbonic oxide, and alcohol are pale, because they only contain gaseous products of combustion. But the flames of candles, lamps, coal gas, have a high illuminating power. They owe this to the fact that the high temperature produced decomposes certain of the gases with the production of carbon, which, not being perfectly burned, becomes incandescent in the flame. Coal gas, when burnt in an arrangement by which it obtains an adequate supply of air, is almost entirely devoid of luminosity. A non-lumi- nous flame may be made luminous by placing in it platinum wire, or asbestos. The temperature of a flame does not depend on its illuminating power. A hydrogen flame, which is the palest of all flames^ gives the greatest heat. 297. i. umford's ca- lorimeter. In order to determine the amount of heat which is produced by combustion, Rumford used the calorimeter de- picted in fig. 225. A metal box contains a pj g< 225 known weight of water at a known temperature ; through it passes a copper worm tube, ss, which is open at one end s', and at the other ends in a funnel c. The U 2 292 On Heat. [297- substance whose heating effect is to be determined, is placed under- neath the funnel, and having been previously weighed, is ignited. The gaseous products of combustion pass then through the worm, and imparting their heat to the water, raise the temperature. From the weight of the water and its increase in temperature, which is measured by the thermometer, and from the weight of the body burned, its heating effect may be determined. By experiments with more perfect arrangements, based however, on the same principle, the heating effect of the following substances has been determined. The numbers represent the number of pounds of water which are raised i C. by the combustion of a pound of the substance. Hydrogen .... 34000 Dry turf 4800 Petroleum .... 12300 Wood 2900 Coal 6500 Carbonic oxide . . . 2400 Phosphorus . . . 5700 Sulphur 2200 SOURCES OF COLD. 298. Various sources of cold. Besides the cold caused by the passage of a body from the solid to the liquid state, of which we have already spoken, cold is produced by the expansion of gases, by radiation in general, and more especially by nocturnal radiation. 299. Cold produced toy the expansion of gases. We have seen, that when a gas is compressed, its temperature rises. The reverse of this is also the case : when a gas is rarefied a reduction of temperature ensues, because a quantity of sensible heat disappears when the gas becomes increased to a larger volume. This may be shown by placing a delicate Breguet's thermometer under the re- ceiver of an air-pump, and exhausting ; at each stroke of the piston the needle moves in the direction of zero, and regains its original temperature when air is admitted. Kirk has invented a machine for the manufacture of ice, which depends on this property. The heat developed by the compression of air is removed by a current of cold water ; the vessel containing the compressed air being placed in brine, the air is allowed to expand ; in so doing it cools the brine so considerably as to freeze water contained in vessels placed in the brine. It is stated that by this means a ton of coals (used in working a steam engine by which the compression is ef- fected) can produce a ton of ice. -300] Cold Produced by Radiation. 293 300. Cold produced by nocturnal radiation. During the day, the ground receives from the sun more heat than radiates into space, and the temperature rises. The reverse is the case during night. The heat which the earth loses by radiation is no longer compen- sated for, and consequently a fall of temperature takes place, which is greater according as the sky is clearer, for clouds send towards the earth rays of greater intensity than those which come from the celestial spaces. In some winters it has been found that rivers have not frozen, the sky having been cloudy, although the thermo- meter has been for several days below - 4 ; while in other less severe winters the rivers freeze when the sky is clear. The emissive power exercises a great influence on the cold produced by radiation ; the greater it is the greater is the cold. In Bengal, the nocturnal cooling is used in manufacturing ice. Large flat vessels containing water are placed on non-conducting substances, such as straw or dry leaves. In consequence of the radiation th,e water freezes, even when the temperature of the air is 10 Cc The same method can be applied in all cases with a clear sky. It is said that the Peruvians in order to preserve the shoots of young plants from freezing, light great fires in their neighbourhood, the smoke of which producing an artificial cloud, hinders the cooling produced by radiation. Country people are in the habit of saying that it freezes more when the moon appears than when it is hidden by clouds. They are right in this ; but the freezing is not, as they think, due to the influence of the moon. It is owing to the absence of .clouds. 294 'On Light. [301 BOOK IV. ON LIGHT. CHAPTER I. TRANSMISSION, VELOCITY, AND INTENSITY OF LIGHT. 301. Theories of light. Light is the agent which, by its action on the retina, excites in us the sensation of vision. That part of phy- sics which deals with the properties of light is known as optics, In order to explain the origin of light, various hypotheses have been made, the most important of which are the emission or cor- puscular theory, and the nndulatory theory. On the emission theory it is assumed that luminous bodies emit, in all directions, an imponderable substance, which . consists of molecules of an extreme degree of tenuity : these are propagated in right lines with an almost infinite velocity. Penetrating into the eye they act on the retina, and determine the sensation which con- stitutes vision. On the undulatory theory, all bodies, as well as the celestial spaces, are filled by an extremely subtle elastic medium, which is called the luminiferous ether. The luminosity of a body is due to an infinitely rapid vibratory motion of its molecules, which, when communicated to the ether, is propagated in all directions in the form of spherical waves ; and this vibratory motion, being thus transmitted to the retina, calls forth the sensation of vision. The vibrations of the ether take place not in the direction of the wave, bu-t in a plane at right angles to it. The latter are called the trans- versal vibrations. An idea of these may be formed by shaking a rope at one end. The vibrations, or to and fro movements, of the particles of the rope, are at right angles to the length of the rope, but the onward motion of the wave's form is in the direction of the length of the rope. -302] Various Sources of L igJit. 295 On the emission theory the propagation of light is effected by a motion of translation of particles of light thrown out from the luminous body, as a bullet is discharged from a gun. On the un- dulatory theory there is no progressive motion of the particles themselves, but only of the state of disturbance which was com- municated by the luminous body ; it is a motion of oscillation, and, like the propagation of waves in water, takes place by a series of vibrations. The luminiferous ether penetrates all bodies, but, on account of its extreme tenuity, it is uninfluenced by gravitation ; it occupies space, and although it presents no appreciable resistance to the motion of the denser bodies, it is possible that it hinders the motion of the smaller comets. It has been found, for example, that Encke's comet, whose period of revolution is about 3^ years, has its period diminished by about 0*1 1 of a day at each successive rotation, and this diminution is ascribed by some to the resistance of the ether. The fundamental principles of the undulatory theory were enun- ciated by Huyghens, and subsequently by Euler. The emission theory, principally owing to Newton's powerful support, was for long the prevalent scientific creed. The undulatory theory was adopted and advocated by Young, who showed how a large number of optical phenomena, particularly those of diffraction, were to be explained by that theory. Subsequently to, though independently of, Young, Fresnel showed that the phenomena of diffraction, and also those of polarisation, are explicable on the same theory, which, since his time, has been generally accepted. The undulatory theory not only explains the phenomena of light, but it reveals an intimate connection between these phenomena and those of heat ; it shows, also, how completely analogous the phenomena of light are to those of sound, regard being had to the differences of the media in which these two classes of phenomena take place. 302. Various sources of light. The various sources of light are the sun, the stars, heat, chemical combination, phosphorescence, electricity, and meteoric phenomena. The origin of the light emitted by the sun and by the stars is unknown ; it is assumed by some that the ignited envelope by which the sun is surrounded is gaseous, and at a very high temperature. As regards the light developed by heat, Pouillet has observed that bodies begin to be luminous in the dark at a temperature of 296 On Light. [302- 500 to 600 ; above that the light is brighter in proportion as the temperature is higher. The luminous effects witnessed in many chemical combinations are due to the high temperatures produced. This is the case with the artificial lights used for illuminations ; for luminous flames are nothing more than gaseous matters containing solids heated to the point of incandescence. Phosphorescence is the property which a large number of sub- stances possess of emitting light when placed under certain condi- tions. Spontaneous phosphorescence is observed in certain vegetables and animals ; for instance, it is very intense in the glowworm and in the lampyre, and the brightness of their light appears to depend on their will. In tropical climates the sea is often covered with a bright phosphorescent light due to some extremely small zoophytes. These animalculas emit a luminous matter so subtle that MM. Quoy and Gaimard, during a voyage under the equator, having placed two in a tumbler of water, the liquid immediately became luminous throughout its entire mass. Decaying wood, and certain kinds of fish in a state of putrefac- tion, also exhibit this phenomenon. Certain substances, too, become phosphorescent by friction ; while others become luminous in the dark by having been previously exposed to the sun's rays. 303. Opaque, transparent, translucent bodies. Absorption of light. Bodies illuminated by a source of light present two dis- tinct effects ; one class, such as wood, metals, most stones, com- pletely stop it ; while others, such as air and glass, allow light to pass. The first class of bodies comprehends those which are called opaqiie, and the second the transparent and translucent bodies. The term transparent or diaphanous is applied to all bodies which at all transmit light ; while transhicency is usually restricted to the case of bodies through which objects cannot be distinctly seen. Polished glass may be called either transparent or diaphanous ; but ground glass, oiled paper, thin porcelain, are translucent ; for, while they transmit light, objects cannot be distinguished through them. Of all bodies which transmit light, none can be said to be per- fectly diaphanous ; all extinguish, or absorb, a portion of the light which impinges on them. The most transparent, such as air, water, glass, gradually extinguish the light which penetrates them ; and if their thickness be considerable, they may weaken it so much that no impression is produced on the eye. Thus, on the tops of high -304] Propagation of Light. 297 mountains the number of stars visible to the naked eye is greater than in the plain ; a phenomenon arising from the fact, that in the former case the layer of air traversed is not so thick as in the latter . case. In like manner too the sun appears less luminous when on the horizon, for then its rays traverse thicker layers of air. Just as there are no perfectly transparent substances, so too there are none which are quite opaque ; at any rate, when the thickness is inconsiderable. Gold, which is one of the densest metals, when beaten out in the 'form of fine leaf, allows an appreciable quantity of light to traverse it. Foucault has recently shown, that when the object glass of a telescope is thinly silvered, the layer is so transparent, that the sun can be viewed through it without danger to the eyes, since the me- tallic layer reflects the greater part of the heat and light ; the tint appears slightly bluish, while in the case of gold it is greenish. 304. Propagation of light. A medium is any space or sub- stance which light can traverse, such as a vacuum, air, water, glass, etc. A medium is said to be homogeneous when its chemical com- position and density are the same in all parts ; conditions which are independent of each other. The atmosphere, for instance, has every- where the same composition, but not the same density, owing to the variations in pressure and temperature, to which it is subject in various places. Experiment shows that in every homogeneous medium light is propagated in a right line. For, if an opaque body is placed in the right line which joins the eye and the luminous body, the light is intercepted. In like manner we cannot receive any impression of light through a series of holes in opaque plates, superposed in each other, excepting these holes are in a straight line. The light which passes into a dark room by a small aperture, leaves a luminous trace, which is visible from the light falling on the particles suspended in the atmosphere. Light emanates from luminous bodies in all directions, for we see them equally in all positions in which we are placed round them. Light changes its direction on meeting an object which it cannot penetrate, or when it passes from one medium to another. These phenomena will be described under the heads reflection and re- fraction. This emanation of light in all directions about a luminous body is called radiation, as in the case of heat ; a luminous ray, or ray of light * is the line in which light is propagated ; a luminous pencil, or 298 On Light. [304- pencil of light, is a collection of rays from the same source. It is said to be parallel, when it is composed of parallel rays ; divergent, when the rays separate from each other ; and convergent, when they tend towards the same point. Examples of these will occur in the study of mirrors and of lenses. 305. Shadow. Penumbra. When light falls upon an opaque body, it cannot penetrate into the space immediately behind it, and this space is called the shadow. In determining the extent and the shape of shadow projected by a body, two cases are to be distinguished : that in which the lumi- nous source is a single point, and that in which it is a body of any appreciable extent. Fig. 226. In the first case, let L (fig. 226) be the luminous point,.and M a spherical body, which causes the shadow. If an infinitely long straight line move round the sphere M, always passing through the point L, this line will produce a conical surface, which beyond the sphere, separates that portion of space which is in shadow from that which is illuminated. In the present case, on placing behind the opaque body a screen, the limit of the shadow will be sharply de- fined. This is not, however, usually the case, for luminous bodies have always a certain magnitude, and are not merely him: nous points ; the shadow formed by a luminous point is called the geo- metrical shadow.. In the second case let L (fig. 227) be a luminous sphere, and let a tangent bn, be drawn externally to this sphere and the sphere M. Assuming that this line moves tangentially round the two bodies, it will produce on the screen a circle, no, completely in darkness. If now a second straight line, bm, be drawn tangentially on the inside of the two spheres, it will produce a cone on the screen, the summit -306] Velocity of Light. 299 of which is at S, and the base on the screen is the circle r?n, which is greater than the circle no. The circular space between the two circumferences is neither entirely in the shadow, nor entirely in the light, for it is only illuminated by a part of the body L ; whence arises the name penumbra. Under ordinary conditions in which luminous bodies have a certain size, shadows are always sur- rounded by a penumbra. This decreases in intensity from the centre towards the edges, and has a greater extent the nearer the luminous body is to the body illuminated, and the more distant the screen. Fig. 227. 306. Velocity of light. Light moves with such a velocity that at the surface of the earth there is, to ordinary observation, no ap- preciable interval between the occurrence of any luminous pheno- menon and its perception by the eye. And, accordingly, this ve- locity was first determined by means of astronomical observations. Romer, a Danish astronomer, in 1675, first deduced the velocity of light from an observation of the eclipses of Jupiter's first satellite. Jupiter is a planet round which four satellites revolve, as the moon does round the earth. This first satellite, e (fig.. 228), suffers occupation that is, passes into Jupiter's shadow at equal inter- vals of time, which are 42 h. 28 m. 36 s. While the earth moves in that part of its orbit nearest Jupiter, its distance from that planet does not materially alter, and the intervals between two suc- cessive occultations of the satellite are approximately the same ; but in proportion as the earth moves away in its revolution round the sun, S, the interval between two occultations increases ; and when? at the end of six months, the earth has passed from the position T to the position /, a total retardation of 16 m. 36 s. is observed between the time at which the phenomenon is seen and that at 300 . On Light. [306 - which it is calculated to take place. But when the earth was in the position T, the sun's light reflected from the satellite e had to traverse the distance eT, while in the second position the light had to traverse the distance et. This distance exceeds the first by the quantity /T, for, from the great distance of the satellite , the rays et and el may be considered parallel. Consequently, light requires 16 m. 56 s. to travel the diameter /T of the terrestrial orbit, or twice the distance of the earth from the sun. To give some idea of this enormous velocity, it may be remarked that a cannon ball would require more than seventeen years to tra- verse the distance from the earth to the sun, while light would re- quire 8 minutes and 18 seconds. Spite of this enormous velocity of light, the stars nearest the earth are separated from it by at least 206,265 times the distance of the sun. Consequently, the light which they send requires 3^ years to reach us. Those stars which are only visible by means of the telescope, are possibly at such a distance that thousands of years would be required for their light to reach our planetary system. We may hence form an idea of the immensity of the heavens, and how small is our globe in comparison with this infinity. 307. Intensity of light. Law of its decrease. Photometer. The intensity of a source of light, that is, the energy of its illu- minating power, is measured by the quantity of light which it sends on a given surface ; for example, a screen a yard square. From the property which luminous rays have of diverging, this quantity of light, this intensity, decreases rapidly as the illuminated body is removed from the luminous body. It maybe shown by geometrical considerations, that the intensity of light is inversely as the square of the distance ; that is, that when the distance of an illuminated body from the source of light is doubled, it receives one-fourth the -307] Intensity of L ight. Photometer. 301 amount of light ; at three times the distance, one-ninth, and so forth. This law may be demonstrated by the aid of an apparatus called a pliotoineter, from, two Greek words which signify measure of light. It consists of a ground glass screen A, fixed vertically on a wooden base (fig. 229). In front of this screen is an opaque rod B, beyond which are the sources of light to be compared, in such a manner that the shadows of the rod form on the screen. Now it will be observed, that when the two sources have the same illuminating power, the depth of the shadows is the same : but if one of the sources of Fig. 229. light is more powerful than the other, the corresponding shadow is deeper ; and in order that the shadows be of equal intensity, the more powerful light must be removed further away. These details being premised, the law of the decrease of light may be demonstrated as follows : In a darkroom, a candle is placed at any distance from the photometer, a yard for instance ; and then, at double the distance, four of the same kind of candles are placed in the same line, in the direction of the opaque rod. The two shadows on the screen will then be found to have exactly the same depth ; which shows that, at two yard's distance, four candles have no more illuminating power than one candle at a distance of one yard ; 302 On Light. [307- from which it is concluded that each of them, at double the dis- tance, has one quarter the illuminating power. It may also be shown in the same manner, that nine candles, at three yards only, have the same illuminating power as one at a yard, and so forth, which proves the law. It is important to observe, that it is in consequence of the diver- gence of luminous rays that light decreases as the distance increases. This decrease does not obtain in the case of parallel rays : their lustre would be the same at all distances, where it not for the ab- sorption which takes place in even the most transparent media. CHAPTER II. REFLECTION OF LIGHT. MIRRORS. 308. Xiaws of the reflection of light. When a ray of light meets a polished surface, it is not destroyed by this obstacle : but Fig. 230. -3081 Reflection of Light. 303 bounds off from it, changing its direction, and this phenomenon is termed the reflection of light. Thus, if through a hole in the shutter of a dark room, a pencil of the sun's rays, CD, be allowed to enter, and it be received on a plane mirror, this pencil is reflected in the direction DB, and forms on the ceiling an image, the shape of which will be discussed in speaking of the camera obscura. As in speaking of the reflection of calorific rays (210) the ray CD is the incident ray, BD is the reflected ray, and the straight line AD at right angles to the mirror is the normal. Lastly, the angles CD A and ADB are called re- spectively the angles of in- cidence and the angles of reflection. The reflection of light is governed by the following two laws, which, as we have seen, also prevail for heat : I. The angle of reflection is equal to the angle of inci- dence. II. The incident and the reflected ray are both in the same plane, which is per- . pendicnlar to the reflecting surface. First proof. The two laws may be demonstrated by the apparatus represented in fig. 231. It consists of a graduated circle in a vertical plane, on three levelling screws. Two brass slides, I and K, move round the circumference. Fig. 231. They support two small tubes i and c, directed exactly towards the centre, and intended to give passage respectively to the incident and reflected rays. On the slide I there is, moreover, a small mirror M, which can be inclined at will. The zero of the graduation is at A, and extends to 90 degrees on each side. These details being known, the slide I having been more or less removed from zero, the mirror, M, is inclined so that a luminous ray, S, after having been reflected on this mirror, shall pass through 304 On Light. [308- the tube /, and fall upon a second mirror, m, arranged horizontally in the centre of the circle : there the luminous ray is reflected a second time, and takes the direction mE. The slide K is then removed to or from A, until the eye being placed at E, the reflected ray, mE, is received through the tube c. If, now, the number of degrees contained in the arcs AB and AC be read off, there will be found to be exactly equal. Hence the angles of incidence "and of reflection >ma and amC, measured by their arcs, are equal, which verifies the first law. The second law is also verified ; for, in the construction of the apparatus, care is taken that the axes of the tubes, i and c, are in one and the same plane parallel to that of the graduated circle, and therefore perpendicular to the surface of the small mirror ;/*, and containing the normal ma. In the above drawing the direction in which light is propagated is represented by arrows ; the same will be the case with all optical diagrams, which we shall have occasion to introduce. 309. The reflection in light is never complete. The light which falls upon a body is never completely reflected ; a certain portion is always extinguished, absorbed by the reflecting surface. If we represent by 100 the quantity of incident light, the reflected portion will be 80, 90, 95, according to the nature and degree of polish of the reflecting body ; but it will never amount to 100. The best reflectors are polished metals, especially if they are white like mercury, and silver. Black bodies reflect no light. Translucent substances reflect a small quantity, and absorb more or less according to their thickness, while they transmit the remainder. This is what takes place with air, water, glass, and all transparent media. For one and the same substance the quantity of reflected light increases not only with the degree of polish, but with the obliquity of the incident ray. For instance, if a sheet of white paper be placed before a candle, and be looked at very obliquely, an image of the flame is seen by reflection, which is not the case if the eye re- ceives less oblique rays. The intensity of the reflection varies with different bodies, even when the degree of polish and the angle of incidence are the same. It also varies with the nature of the medium which the light is traversing before and after reflection. Polished glass immersed in water loses a great part of its reflecting power. 310. Irregular reflection. Diffused or scattered light. The -310] Irregular Reflection. 305 reflection from the surfaces of polished bodies, the laws of which have just been stated, is called the regular or specular reflection : from a Latin word signifying mirror : but the quantity thus reflected is less than the incident light. The light incident on an opaque body is separated, in fact, into three parts ; one is reflected regularly, another irregularly, that is, in all directions ; while a third is ex- tinguished, or absorbed by the reflecting body. Thus, if in the experiment represented in fig. 230, the beam, CD, be caught on an unpolished surface instead of on a mirror, not only will it be seen in the direction DB, corresponding to regular reflec- tion, but it will be seen in all positions in the darkroom : whence it is concluded that light is reflected in all directions and under all obliquities ; which is apparently contrary to the laws of reflection. This irregularly reflected light is called scattered or diffused light : it is that which makes bodies visible ; it has its origin in the struc- ture of bodies themselves, which, from their roughness, present an infinity of small facettes variously inclined, and which reflect light in all directions. Diffused light plays an important part in the phenomena of vision. For while luminous bodies are visible of themselves, opaque bodies are only so in consequence of the diffused light which they send in all directions. Thus when we look at a piece of furniture, a table, or a flower, it is the diffused light reflected on all sides, and in all directions by the object, which enables us to see them in what- ever direction we may be placed in reference to the light which illuminates them. When luminous bodies only reflect light regu- larly, it is not them we see, but, acting like mirrors, they only give us the image of the luminous body whose light they send towards us. If, for example, a beam of the sun's light falls on a well- polished mirror in a dark room, the more perfectly the light is re- flected the less visible is the mirror in the different parts of the room. The eye does not perceive the image of the mirror, but that of the sun. If the reflecting power of the mirror be diminished by sprinkling on it a light powder, the sun's image becomes feebler, and the mirror is visible from all parts of the room. Perfectly smooth polished reflecting surfaces, if such there were, would be invisible, and absolutely non-reflecting surfaces would also appear all equally black, and would be confounded with each other. Two bodies, one white and the other black, placed in darkness, are quite invisible, for that which is white, not receiving any light, can re- flect none. 306 On Light. [310- It is the diffused light reflected by the air, by the clouds, by the ground which illuminates our rooms and all bodies not directly exposed to the sun's rays ; and the more diffused light a body sends towards us, the more precisely can we distinguish it. From the inside of our rooms we well see external objects, for they are power- fully illuminated ; but from the outside we only see confusedly in the interior of apartments the objects found there, for they receive but little light. 311. Direction in which we see bodies. Whenever a pencil of light passes in a straight line from a body to our eye, we see it exactly as it is ; but if in consequence of reflection, or any other cause, the pencil of light is deviated in its route, if it ceases to come to us in a straight line, we no longer see the body in its proper Fig. 232. place, but in the direction of tlie luminous pencil 'at the moment it enters the eye. Thus if the pencil AB is deflected at B (fig. 232), and takes the direction BC, the eye does not see the point A at A but at #, in the prolongation of CB. This principle is general, and, though very simple, well deserves the attention of the reader, for on it are based the numerous effects of vision which mirrors and lenses present. MIRRORS. 312. iviirrors. Images. Mirrors are bodies with polished surfaces, which show by reflection objects presented to them. The place at which objects appear is their image. According to their shape, they are divided into plane and curved mirrors. We have an example of a plane mirror in the looking glasses which adorn our apartments. In these mirrors it is not the glass which reflects light in sufficient quantity to give neat and well denned images ; it is a metallic layer on the back of the glass. This layer is an amalgam of tin, that is, an alloy of this metal with mercury. The glass only has the effect of giving the metal the necessary polish, and of preserving it from external agencies which tend to tarnish it. Metal mirrors are also constructed of gold, silver, steel, tin. -313] Formation of Images in Plane Mirrors. 307 They have all the defect of tarnishing on contact with the air ; yet they were in frequent use among the Romans. We cannot go back to the origin of mirrors. The first was doubtless the surface of clear water. Those of metal appear to be of high antiquity, for mention is made in Exodus of a bronze ewer, made by Moses with the mirrors offered him by the Israelitish women. 313. Formation of images in plane mirrors. Plane mirrors are those whose surface is plane ; such, for example, are the pier glasses which adorn the chimney-pieces of our rooms. To under- Fig. 233. stand the formation of images in these mirrors, let us first con- sider the case in which a small object is placed in front of such a mirror ; for instance, the flame of a candle (fig. 233). A divergent pencil of light emitted by this flame and falling on the mirror is reflected there, as shown, in fig. 233. But it follows from the laws of reflection, that each ray of this pencil retains, in reference to the mirror, the same obliquity as it had before ; whence it follows that the reflected rays have the same divergence in reference to 308 On Light. [313- each other as the incident rays. Hence if we imagine the reflected pencil prolonged behind the mirror, all the rays composing it will coincide in the same point. But as we always see objects in the direction the luminous rays have when they reach us (311), it follows that the eye which receives the reflected pencil should see the flame of the candle just in the place where the prolongation of these reflected rays coincide. There, in fact, is produced the image of this flame as seen in fig. 233. If how, instead of supposing a very small object placed in front of the mirror, we consider a body of any dimensions, in order to understand the formation of its image we need do no more than Fig. 234. apply to each of its parts w ; hat has been said in reference to a single luminous point ; for instance, in fig. 234, which represents a person in front of a mirror, the rays from the forehead, for instance, are reflected from the mirror and return to the eye, producing an image of the forehead. In like manner the rays from the chin being reflected from the mirror reach the eye as if they proceeded from the chin of the image, and so on with all parts of the face ; hence the illusion which makes us see our image on the other side of the mirror. < 314. Nature of the images in plane mirrors. Real and virtual images. If, while looking in a mirror, we raise the right -315] Multiple Images Formed by Glass Mirrors. 309 hand, it is the left which seems raised in the mirror ; and if we raise the left hand the right seems raised. We should falsely ex- press this transposition of the parts of the image in reference to the object if we merely say that the image was reversed ; if it were nothing else than the object reversed, in raising the right hand the image should also raise the right hand, while it really is the left which is raised. This special equality which exists between an object and its image is expressed by saying, that the image is symmetrical in reference to the object ; that is, that any point of the image is arranged behind the mirror in identically the same manner as the corresponding point of the object in front. For it may be shown by geometrical considerations, that these two points are equidistant from the mirror, and on the same right line, which is at right angles . to the surface. From the respective distance and position of the different parts of the object and of its image, it is concluded that the latter is of the same magnitude as it, and equidistant from the mirror. Lastly, images formed in plane mirrors are virtual, by which we mean, that they have no real existence, and are only an illusion of the eyes. For in fig. 233 as well as in fig. 234 the light, as it does not pass behind the mirror, cannot form any image there, and that which we see has no existence ; this is expressed by the word virtual as opposed to actual or real. Virtual images are only an optical illusion ; but we shall soon see that, in concave mirrors and in lenses, real images are produced which can be received on screens ; this is not the case with virtual images. We may thus sum up what we have said : images in plane mirrors are symmetrical in reference to the object, of the same magni- tude, at the same distance on the other side of the mirror, and are virtual. 315. Multiple images formed by glass mirrors. Metallic mirrors which have but one reflecting surface only give one image ; it is different with glass mirrors, the two surfaces of which reflect though to an unequal extent. For if we apply any object, the point of a pencil, for instance, against a thick piece of polished glass, at first when it is looked at obliquely a very feeble image is seen in contact with it ; then, beyond it, another and far more in- tense one. The first image is due to the light reflected from the anterior surface of the plate ; that is, on the glass itself, while the second is due to the light which penetrating into the glass, is re- 3io On Light. [315- fleeted from the layer of metal by which the posterior face is covered. The difference in intensity of the two images is readily explained ; glass being very transparent, only a small quantity of light is reflected from the rirst face of the mirror, which gives the least intense image ; while the greater part of the incident light passing into the mass is reflected from the surface of the metal, and gives the most luminous image. The above experiment furnishes a simple means of measuring the thickness of a glass mirror. For the more intense image should appear behind the layer of metal at the same distance as the point of the pencil in front ; and it follows thence, that the distance between the point of the pencil and the point of its image is double the thickness of the mirror. If this distance seems to be the eighth of an inch, it will be concluded that the real thickness is th of an inch. The double reflection from mirrors is prejudicial to the sharpness of the images, so that, in scientific observations, metallic mirrors are preferred to glass ones. Fig. 235. 316. Reflection from transparent bodies. We have seen that glass, spite of its transparency, reflects a sufficient amount of light to give images, which, though feeble, are distinct. The same is the case with water and other transparent liquids. Thus, on the borders 317] Multiple Images in Parallel Glass Mirrors. 3 1 1 of a pool, we see formed in the water the reversed image of objects on the opposite bank. We say reversed image, so as to express the appearance ; but more strictly we should say symmetrical, from what we have before said (314). Fig" 2 35 represents the phenomenon of reflection from the surface of water ; it shows how the reflected rays, reaching the eye in an upward direction, reproduce the image of objects situated above the water, just as they would if reflected from a horizontal mirror. 317. Multiple images in parallel or inclined glass mirrors. When a source of light is placed between two plane parallel mirrors, we observe a series of images the brightness of which gradually decreases. Fig. 236. These images are due to successive reflections on the two mirrors. Thus, let M and N fig. 236 be the sections of the two mirrors, A a luminous body, and o the eye of the observer. This latter receives the rays which come directly from the object A, and in addition the following pencils : i. the ray A&?, which after a single reflection gives the first image a ; ii. the ray Aufo, which after two reflections furnishes the second image a" ; iii. the ray kefgo, which is reflected three times, and produces a third image a' and so on for rays which 312 On Light. [317- undergo four, five, or six reflections. The number ot images is theoretically infinite, but in practice it is limited, for as light is never completely reflected at each incidence (309) the images successively lose their lustre and finish by disappearing entirely. In order not to complicate the figure, only those rays are given which fall at first on the mirror M; but the same, construction should be repeated for the mirror N, which would double the number of images. If the mirrors, instead of being parallel, make an angle with each other, the number of images is less. Fig. 237 represents the case in which they form a right angle ; three images, a, a', a", are then formed ; the first two after a single reflection ; the third after two reflections. If the angle is one of 60 degrees, there are five images. The Kaleidoscope, which consists of three glass mirrors enclosed in a pasteboard tube at an angle of 60, and the Debuscope of two mirrors at an angle of 60, are well known applications of this pro- perty of reflection from inclined mirrors. CURVED MIRRORS. 318. Concave mirrors. There are many kinds of curved mirrors ; those most in use are called spherical mirrors, from their curvature being that of a sphere. They may be either of metal or of glass, and are either concave or convex:, according as the reflection is from the internal or the external face of the mirror. -319] Focus of Concave Mirrors. 313 A curved watch-glass, seen from above, gives an idea of a convex mirror, especially if it is covered by a coating of metal on the in- side ; the same glass coated externally and seen from the inside becomes a concave mirror. We shall first investigate concave mirrors, and, to facilitate the investigation, will first consider what is called a section ; that is, the figure obtained by cutting it into two equal parts. Let MN be the section of a spherical mirror, and C the centre of the corre- sponding sphere. In reference to the sphere this point is called the centre of curvature ; the point A is the centre of the. figure. The infinite right line, ACX, which passes through A and C, is the principal axis of the mirror : any right line, /CW, which simply passes through the centre C, and not through the centre of figure A, is a secondary axis. The angle MCN, formed by joining the centre and extremities of the mirror, is the aperture. A principal or meridional section is any section made by a plane through its principal axis. In speaking of mirrors those lines alone will be considered which lie in the same principal section. There is only one principal axis, but the number of secondary axes is unlimited. The theory of the reflection of light from curved mirrors is easily deduced from the laws of reflection from plane mirrors, by considering the surface of the former as made up of an infinitude of extremely small plane surfaces, all equally inclined to each other so as to form a regular spherical surface. Thus, on this hypo- thesis, when a ray of light falls upon any point whatever of a curved mirror, it is really from a small plane mirror that it is reflected ; the reflection takes place then in accordance with the laws already laid down (308). 3 1 9. Focus of concave mirrors. The small facettes, of which we have assumed concave mirrors to be made up, being all inclined towards a common centre, which is the centre of curvature of the On Light. [319- mirror, it follows from this obliquity that the rays reflected by these mirrors tend to unite in a single point, which is called the focus, as we have already seen in the case of heat (211). To explain this property of curved mirrors, let SI be a ray fall- ing upon such a mirror parallel to the axis AX (fig. 238). From the hypothesis assumed above, the reflection takes place at I, on an infinitely small plane mirror. It can be shown by geometrical con- siderations that the perpendicular to this small mirror is represented by the right line CI from the centre C to the point I. Hence the Fig 239. angle SIC represents the angle of incidence ; and it we imagine on the other side of the perpendicular, a straight line IF, which makes with CI an angle FIC, equal to CIS, this straight line will be in the direction of the reflected ray. But when the incident rays are parallel to the axis of the mirror, as in the above example, it may be proved by geometrical con- siderations, that the point F, where the luminous ray cuts the axes, is the middle of AC ; that is, it is equidistant from the centre and the mirror. This property being common to all rays parallel to -320] Conjugate Focus. 315 the axis, it follows that, after reflection, these rays will all coincide in the same focus, F, as shown in the figure. The focus described above, namely, that formed at an equal distance from the centre and from the mirror, is called \^Q principal fociis ; it is produced whenever the rays falling on the mirror are parallel to its axis. An example of this is seen in fig. 239, which represents a pencil of solar light falling upon a concave mirror. If, where the reflected rays tend to concentrate themselves, a small ground glass screen be placed, a highly luminous point will appear, which is the principal focus. 320. Conjugate focus. In the preceding examples we have considered the case of pencils of parallel rays, which presupposes a luminous object at an infinite, or at all events a very great, distance. Let us now consider the case in which the source of light being at a small distance, the rays falling on the mirror are divergent, as shown in fig. 240. Here the reflected rays are con- Fig. 240. verged, but less so than in figs. 238 and 239, which results from the divergence of the light in arriving on the mirror. Hence the point where the reflected rays coincide is more distant ; instead of being at F, equidistant from the mirror and the centre, it is at b, between the points F and C. This point, b, where the rays coincide, is also a focus. To distinguish it from the principal focus F, it is called the conjugate focus, from a Latin word meaning connected ; for there is between the position of the luminous point B, and that of this focus, this connection, that when the luminous object is at B, the rays form their focus at b\ and that conversely, if the luminous object is removed to b, the reflected rays form their focus at B. 316 On Light. [320- We have seen that there is only a single position for the prin- cipal focus, which is at an equal distance from the centre and from the mirror : this is not the case with the conjugate focus, the position of which is very variable. For suppose that in fig. 240 the candle is removed away from the mirror, as the incident rays make then, with the perpendicular, cm, gradually increasing angles of incidence, the angles of reflection, cmb, increase too, and the focus b approaches the point F, with which it will ultimately coin- cide, when the candle is so far distant that the incident rays are virtually parallel. If, on the contrary, the candle is brought nearer the mirror, the rays falling upon it make with the perpendicular, cm, angles which are gradually smaller, the angles of reflection, cmb, decrease also. Hence the rays sent by the mirror coincide at gradually greater distances, the focus b advances towards the centres; and if the candle comes nearer the point, so as to coincide with it, the case will be the same as the focus b ; so that the candle and its image will coincide at c. Lastly ; if the candle always approaching the mirror passes between the centre and the principal focus F, the conjugate focus b, continually removing from the mirror, passes on the other side of the centre, is formed at a greater distance the nearer the luminous body is to the principal focus ; if the candle coincides with this latter point, the conjugate focus forms at an infinite distance, and the reflected rays become parallel. These different effects of reflection are a consequence of the constant equality between the angle of incidence and the angle of reflection. They are very simply verified by placing in a dark room a candle in front of a concave mirror successively in various positions, and then ascertaining by trial where the luminous focus is formed on a small screen of paper held in the hand, and which is approached to or receded from the mirror. 321. Virtual focus. After having described the different po- sitions of the point in which the rays reflected by a concave mirror coincide, when the luminous body is either beyond or in the prin- cipal focus, we have to inquire what becomes of these same rays when the source of light is in any point, P, which is nearer the mirror than the principal focus (fig. 241). In this case the reflec- ted rays form a diverging pencil, and cannot therefore produce any focus in front of the mirror ; but as regards the eye which receives them, they produce exactly the same effect as in plane mirrors -322] Formation of Images in Concave Mirrors. 3 1 7 (313); that is, the eye receives exactly the same impression from the reflected rays IM and im, as if the candle were placed behind the Fig. 241. mirror at the point/, where the prolongation of these rays coincide. Hence the image of the candle is seen at p, but as the light does not penetrate behind the mirror, this image does not really exist : hence the focus which seems to form at p is called the virtual focus, the expression being understood in the same sense as in plane mirrors. 322. Formation of images in concave mirrors. Concave mirrors give rise to two kinds of images, real and virtual. Their formation is readily understood after what has been said respecting the conjugate and the virtual focus. We may however remark, when a luminous or illuminated point is situate on the principal axis of a mirror, its focus, real or virtual, is always formed on this axis. This is the case in figs. 240 and 241, but if the luminous point is on a secondary axis, the focus is formed on this axis. Thus, if in fig. 238 a candle were placed at d, on the secondary axis, z'C infinitely small intervals of time that they may be considered continuous, the wire is said to be traversed by an electric or voltaic current. The direction of this current in the connecting wire is assumed to be from the copper to the zinc ; or, in other words, this is the direction in which the positive electricity is supposed to flow, the direction of the negative current in the wire being from the zinc to the copper. But the existence of this current is purely hypothetical, and must not be taken as more than a convenient mode of explaining the phenomena developed in the wire. 454. Voltaic couple. Electromotive series. The arrange- -454] . Electromotive Series. 475 ment just described, consisting of two metals in metallic contact, and a conducting liquid in which they are placed, constitutes a simple voltaic element or couple. So long as the metals are not in contact, the couple is said to be open, and when connected it is closed. For the production of a voltaic current it is not necessary that one of the metals be .unaffected by the liquid, but merely that the chemical action upon the one be greater than upon the other. The metal which is most attacked is called \^\&. positive or generating plate, and that which is leq.st attacked the negative or collecting plate. The positive metal determines the direction of the current, which proceeds in the liquid from the positive to the negative plate, and out of the liquid through the connecting wire from the negative to the positive plate. In speaking of the direction of the current, the positive current is always understood ; to avoid confusion, the existence of the current in the opposite direction, the negative current, is tacitly ignored. As a voltaic current is produced whenever two metals are placed in metallic contact in a liquid which acts more powerfully upon one than upon the other, there is great choice in the mode of producing such currents. In reference to their electrical deportment, the metals have been arranged in what is called an electromotive series^ in which the most electropositive are at one end, and the most electronegative at the other. Hence when any two of these are placed in contact in dilute acid, the current in the connecting wire proceeds from the one lower in the list to the one higher. The principal metals are as follows : Zinc Nickel Gold Lead Copper Platinum Iron Silver Graphite. Thus iron placed in dilute sulphuric acid is electronegative towards zinc, but is electropositive towards copper; copper in turn is electro-negative towards iron and zinc, but is electropositive towards silver, platinum, or graphite. The force produced by the difference in chemical action on two metals in a liquid is called the electromotive force ; it is greater in proportion to the distance of the two metals from one another in the series. That is to say, it is greater, the greater the difference between the chemical action upon the two metals immersed. Thus 476 Voltaic Electricity. [454- the electromotive force between zinc and platinum is greater than that between zinc and iron, or between zinc and copper. 455. Poles and electrodes. If the wire connecting the two terminal plates of a /oltaic couple be cut, it is clear, from what has been said about the origin and direction of the current, that positive electricity will tend to accumulate at the end of the wire attached to the copper or negative plate, and negative electricity on the wire attached to the zinc or positive plate. These terminals have been called the poles of the battery. For experimental purposes, more especially in the decomposition of salts, plates of platinum are attached to the ends of the wires. Instead of the term poles the word electrode (/jXwrpr/v and 6ody, a way) is now commonly used ; for these are the ways through which the respective electricities emerge. It is important not to confound the positive plate with the positive pole or electrode. The positive electrode is that connected with the negative plate, while the negative electrode is connected with the positive plate. 456. Voltaic battery. When a series of voltaic elements or pairs are arranged in such a manner that the zinc of one element is connected with the copper of another ; the zinc of this with the copper of another, and so on, such an arrangement is called a vol- taic battery ; and by its means the effects produced by a single element are capable of being very greatly increased. The earliest of these arrangements was the voltaic pile devised by Volta himself. It will be readily seen that it is merely a series of simple voltaic couples, the moistened disc acting as the liquid, and that the terminal zinc is the negative and the terminal copper the positive pole. From the mode of its arrangement, and from its discoverer, the apparatus is known as the voltaic pile, a term applied to all apparatus of this kind for accumulating the effects of dynamical electricity. The distribution of electricity in the pile varies according as it is in connection with the ground by one of its extremities, or as it is insulated by being placed on a non-conducting cake of resin or glass. In the former case, the end in contact with the ground is neutral, and the rest of the apparatus only contains one kind of electricity ; this is negative, if a copper disc is in contact with the ground, and positive if it is a zinc disc. In the insulated pile the electricity is not uniformly distributed. -456] - Voltaic Battery. 477 By means of the proof-plane and the electroscope it may be de- monstrated that the middle part is in a neutral state, and that' one- half is charged with positive and the other with negative electricity, the tension increasing from the middle to the ends. The half terminated by a zinc is charged with negative electricity, and that by a copper with positive electricity. The effects of the pile will be discussed in other places. The original form of the voltaic pile for it possesses now only an historical interest has a great many inconveniences ; among these is the fact, that the weight of the discs of zinc and copper is so great that it presses out the acidulated liquid from the discs, and the electrical action is soon weakened. It has received a great many improvements, the principal object of which has been to facilitate manipulation, and to produce greater electromotive force. One of the earliest of these modifications was the crown of cups, or couronne des tasses, invented by Volta himself : an improved form of this is known as Wollaston's battery (fig. 378). Fig. 376 gives a vertical section of two consecutive Wollaston's elements. The acidulated water is contained in glass vessels, B B Fig. 376. Fig. 377- in each of which is a couple. Fig. 377 represents the arrangement of one of these couples : it consists of a thick sheet of zinc, Z, and a strip of copper, 0, by which it can be connected with the next couple. A plate of copper, C C, is bent so as to sun ound the plate of zinc without touching, contact being prevented by small pieces of 47* Voltaic Electricity. [456- cork. The plate, C, is provided with a copper tongue, o', which is soldered to the zinc of the next couple and so forth. Fig. 378 represents a pile of sixteen couples united in two parallel series of eight each. All these couples are fixed to a cross Fig. 378- frame of wood, by which they can be raised or lowered at pleasure. When the battery is not wanted, the couples are lifted out of the liquid. The water in these vessels is usually acidulated with ^ sulphuric and ^ of nitric acid. 457. Enfeeblement of tne current in batteries. Secondary currents. The batteries already described, Volta's and Wollaston's, which consist essentially of two metals and one liquid, labour under the objection that the currents produced rapidly diminish in inten- sity. This is principally due to three causes ; the first is the decrease in the chemical action owing to the neutralisation of the sulphuric acid by its combination with the zinc. This is a necessary action, for upon it depends the current ; it therefore occurs in all batteries, and is without remedy, except by replacement of the acid and zinc. The second is due to what is called local action ; that is, the pro- duction of small closed currents in the active metal, from the im- purities it contains. These local currents rapidly wear away the active plate, without contributing anything to the general current. -459] Danieirs Battery. 479 They are remedied by amalgamating the zinc with mercury, by which chemical action is prevented until the circuit is closed. The third arises from secondary currents. These are currents which are produced in the battery in a contrary direction to the principal cur- rent, and which destroy it either totally or partially. In the funda- mental experiment (fig. 367), when the current is closed, sulphate of zinc is formed, which dissolves in the liquid, and at the same time a layer of hydrogen gas is gradually deposited on the surface of the copper plate. Now it has been found, that the hydrogen de- posited in this manner on metallic surfaces acts far more energeti- cally than ordinary hydrogen. In virtue of this increased activity it gradually reduces some of the sulphate of zinc formed, and a layer of metallic zinc, is formed upon the copper ; hence, instead of having two different metals unequally attacked, the two metals be- come gradually less different, and, consequently, in the wire there are two currents tending to become equal ; the total effect, and the current really observed, become weaker and weaker. 458. Constant batteries. Banieil's. The serious objections to the use of- what are called single fluid elements has led to their abandonment, and they are now replaced by two fluid elements, which are both more constant and more powerful. They have been replaced by batteries with two liquids, which are called constant batteries, because their action is without material alteration for a considerable period of time. The es- sential point to be attended to in securing a constant current is to pre- vent the polarisation of the inactive metal ; in other words, to hinder any permanent deposition of hydrogen on its surface. This is effected by plac- ing the inactive metal in a liquid upon which the deposited hydrogen can act chemically. 459. Daniell's battery. This was the first form of the constant battery, and was invented by Daniell in the year 1 836. As regards the constancy of its action, it is still the best of all constant batteries. Fig. 379 repre- sents a single element. A glass or porcelain vessel, V, contains a saturated solution of sulphate of copper, in which is immersed a 4^0 Voltaic Electricity. [459- copper cylinder, C, open at both ends, and perforated by holes. At the upper part of this cylinder there is an annular shelf, G, also perforated by small holes, and below the level of the solution : this is intended to support crystals of sulphate of copper to replace that decomposed as the electrical action proceeds. Inside the cylinder is a thin porous vessel, P, of unglazed earthenware. This contains either a solution of common salt or dilute sulphuric acid> in which is placed the cylinder of amalgamated zinc, Z. Two thin strips of copper, p and , fixed by binding screws to the copper and to the zinc, serve for connecting the elements in series. When a DanielPs element is closed, the hydrogen resulting from Fig. 380. the action of the dilute acid on the zinc is liberated on the surface of the copper plate, but meets there the sulphate of copper, which is reduced, forming sulphuric acid and metallic copper which is deposited on the surface of the copper plate. In this way the sul- phate of copper in the solution is taken up, and if it were all con- sumed, hydrogen would be deposited on the copper, and the current would lose its constancy. This is prevented by the crystals of sul- phate of copper which keep the solution saturated. The sulphuric acid produced by the decomposition of the sulphate permeates the porous cylinder, and tends to replace the acid used up by its action on the zinc ; and as the quantity of sulphuric acid formed in the solution of sulphate of copper is regular, and proportional to the acid used in dissolving the zinc, the action of this acid on the zinc is regular also, and thus a constant current is produced. -460] BunseiJs Battery. 481 Fig. 380 represents a series of three Daniell's elements of a somewhat different pattern. Here the zinc of one is connected with the copper of the next by a copper strip. Instead of placing the crystals of sulphate of copper on a shelf in the copper plate, they are contained in glass flasks, the necks of which are immersed in a solution of sulphate of copper. This form of element is exten- sively used in the French telegraphs. 460. Bunsen's battery. Bunsen's battery, also known as the sine carbon battery, was invented in 1 843 ; it is nothing more than Daniell's batteiy, in which nitric acid is substituted for solution of sulphate of copper, and in which copper is replaced by a cylinder Fig. 381. of carbon. This is made either of the graphitoidal carbon depo- sited in gas retorts, or by calcining in an iron mould an intimate mixture of coke and bituminous coal, finely powdered and strongly compressed. Both these modifications of carbon are good con- ductors. Each element consists of the following parts : i. a vessel, F (fig. 381), either of stoneware or of glass, containing, as in Daniell's, dilute sulphuric acid ; 2. a hollow cylinder, Z, of amalga- mated zinc ; 3. a porous vessel, V, in which is ordinary nitric acid ; 4. a cylinder of carbon, C, prepared in the above manner. In the vessel, F, the zinc is first placed, and in it the carbon as seen in P. To the carbon is fixed a binding screw, m (fig. 382), to which a copper wire is attached, forming the positive pole. The zinc is provided with a similar binding screw, #, and wire, which is thus the negative pole. In Bunsen's battery the hydrogen resulting from the action is I I 482 Voltaic Electricity. [460- liberated on the surface of the carbon. This being surrounded by nitric acid, the hydrogen decomposes this acid, forming water and hyponitrous acid, which dissolves, or is subsequently disengaged as nitrous fumes. And, though the hydrogen is most completely got rid of by the decomposition of the nitric acid, the production of these nitrous fumes is very noxious. The elements are arranged to form a battery (fig. 382) by con- necting each carbon to the zinc of the following one by means of the Fig. 382. clamps, mn, and a strip of copper, c, represented in the top of the figure. The copper is pressed at one end between the carbon and the clamp, and at the other it is soldered to the clamp, n, which is fitted on the zinc of the following element, and so forth. The clamp of the first carbon and that of the last zinc are alone provided with binding screws, to which are attached the wires. 461. Xieclan che's battery. Each element of this battery con- sists of a rod of carbon placed in a porous pot which is then tightly packed with a mixture of pyrolusite (peroxide of manganese) and coke. The porous pot is contained in an outer vessel in which is the electropositive metal zinc. The exciting liquid is a solution of sal-ammoniac. This battery, from its simplicity, its constancy, combined with considerable electromotive force is coming into use for telegraphs, and for alarums in private houses. -462] Effects of the Battery. 483 CHAPTER VIII. EFFECTS OF THE BATTERY. 462. Physiological effects. The remarkable phenomena of the voltaic battery may be classed under the heads physiological, chemical, mechanical, and physical effects ; and these latter may be again subdivided into the thermal, luminous, and magnetic Fig. 383- effects. All are due to the recombination of the opposite electri- cities like those of the electrical machine ; but they are far more remarkable and more energetic, owing to the continuity of their action. To produce them the body experimented upon must be connected on the one side with the positive and on the other with the negative pole. I I 2 484 Voltaic Electricity. [462- The physiological effects consist of shocks and violent contrac- tions which the current produces in the muscles, not only of living, but of dead animals, as has been seen in Galvani's experiment with the frog. When the electrodes of a strong battery are held in the two hands a violent shock is felt, resembling that of a Leyden jar, espe- cially if the hands are moistened with acidulated or saline water, which increases the conductivity. The shock is more violent in proportion to the number of elements used ; with a Bunsen's- battery of 50 to 60 couples the shock is very strong, with 150 or 200 couples it is unbearable, and even dangerous when continued. It is less perceptible in the fore part of the arms than the shock of the Leyden jar, and when transmitted through a chain of several per- sons, it is generally only felt by those nearest the poles. The shock, as in the case of the Leyden jar, is due to the recom- position of the two electricities ; with this difference, that with the Leyden jar the discharge being instantaneous, the resultant shock is so also ; while in the latter case, as the battery is immediately recharged after each discharge, the shocks succeed each other with rapidity. John Aldina, a nephew of Galvani, was the first to study the action of the battery on dead animals. He came to Paris at the beginning of the present century, and repeated on a large scale several of his experiments at the veterinary school of Alfort near Paris. 463. Thermal effects. When a voltaic current is passed through a metallic wire the same effects are produced as by the discharge of an electric battery ; the wire becomes heated and even incandescent if it is very short and thin. With a powerful battery all metals are melted, even iridium and platinum, the least fusible of metals. Carbon is the only body which hitherto has not been fused by it. M. Despretz, however, with a battery composed of 600 Bunsen's elements joined in six series, has raised rods of very pure carbon to such a temperature that they were softened and could be welded together, indicating an incipient fusion. A battery of thirty to forty Bunsen's elements is sufficient to melt and volatilise fine wires of lead, tin, zinc, copper, gold, silver, iron, and even platinum, with differently coloured sparks. Iron and platinum burn with a brilliant white light ; lead with a purple light ; the light of tin and of gold is bluish white ; the light of zinc is a mixture of white and gold ; finally, copper and silver give a -464] Luminous Effects. 485 green light. The heat tig effects of the voltaic current are used in firing mines for military purposes and for blasting operations. 464. Luminous effects. In closing a voltaic battery a spark is obtained at the point of contact, which is frequently of great bril- liance. A similar spark is also perceived on breaking contact. These luminous effects are obtained when the battery is sufficiently powerful, by bringing the two electrodes very nearly in contact ; a Fig. 384- succession of bright sparks springs across the interval, which follow each other with such rapidity as to produce a continuous light. With eight or ten of Grove's elements brilliant luminous 486 Voltaic Electricity. [464- sparks are obtained by connecting one terminal of the battery with a file, and moving its point along the teeth of another file connected with the other terminal. The most beautiful effect of the electric light is obtained when two pencils of charcoal are connected with the terminals of a powerful battery ih the manner represented in fig. 384. The two charcoals being placed in contact the current passes, and their ends soon become incandescent. If they are then removed to a distance of about the tenth of an inch, according to the intensity of the cur- rent, a luminous arc extends between the two points, which has an exceedingly brilliant lustre, and is called the voltaic arc. The length of this arc varies with the force of the current. In air it may exceed two inches with a battery of 600 elements. If the charcoal attached to the positive pole be examined, it will be found to have become hollowed, and worn away, while the negative charcoal has increased. It thus seems that the carbon is trans- ported from the positive to the negative pole, and that this is the manner in which the transmission of the electricity between the two poles is effected. The intensity of the electric light is very great. Bunsen, in ex- perimenting with forty-eight couples, and removing the charcoals to a distance of a quarter of an inch, found that the intensity of the electric light is equal to that of 572 candles. Too great precautions cannot be taken against the effect of the electric light when they attain a certain intensity. The light of 100 couples, he says, may produce very painful affections of the eyes. With 600, a single moment's exposure to the light is suffi- cient to produce very violet headaches and pains in the eye, and the whole frame is affected as by a powerful sunstroke. Attempts have been made to apply the electric light to the illu- mination of rooms and even of streets ; but partly the cost, and partly the difficulty of producing with it a uniform illumination, inasmuch as the shadows are thrown into too sharp relief, have hitherto been great obstacles to its use. Yet it is advantageously applied in special cases, such as the photo-electric microscope, illuminations in theatres, &c. Fig. 384 represents an arrange- ment for public illumination. On a convenient support, an electric lamp is placed ; this is a mechanism which is worked by the current from a powerful battery, and which keeps the carbon poles at a suitable distance, a condition necessary for the permanence and steadiness of the light. -465] Decomposition of Water. 487 DECOMPOSITION OF WATER. 465. Chemical effects. These are among the most important of all the actions, either of the simple or compound circuit. They consist of the separation and transport of the elements of the bodies traversed by the current. The first decomposition effected by the battery was that of water, obtained in 1800 by Carlisle and Nicholson by means of a voltaic pile. Water is rapidly decomposed by four or five Bunsen's cells ; the apparatus (fig. 385) is very con- Fig. 385- venient for the purpose. It consists of a glass vessel fixed on a wooden base. In the bottom of the vessel two platinum electrodes are fitted, communicating by means of copper wires with the binding screws, a and b. The vessel is filled with water to which some sulphuric acid has been added to increase its conductivity, for pure water is a very imperfect conductor ; two glass tubes filled with water are inverted over the electrodes, and, on interposing the apparatus in the circuit of a battery, decomposition is rapidly set up, and gas bubbles rise from the surface of each pole. The volume of gas liberated at the negative pole is about double that at the positive, and on examination the former gas is found to be hydrogen and the latter gas oxygen. This experiment accordingly gives at once the qualitative and quantitative analysis of water ; for it shows that its composition consists of two parts by volume of hydrogen to one part by volume of oxygen. 488 Voltaic Electricity. [466- 466. Electrolysis. To those substances which, like water, are resolved into their elements by the voltaic current, the term elec- trolyte has been applied by Faraday, to whom the principal dis- coveries in this subject, and the nomenclature are due ; electrolysis is the decomposition by the voltaic battery. By means of the battery, the compound nature of several sub- stances which had previously been considered as elements has been determined. By means of a battery of 250 couples, Davy, shortly after the discovery of the decomposition of water, succeeded in decomposing the alkalies potass and soda, and proved that they were the oxides of the hitherto unknown metals potassium and sodium. The decomposition of potass may be demonstrated with the aid of the battery of four to six elements in the following manner ; a small cavity is made in a piece of solid caustic potass, which is moistened, and a drop of mercury placed in it (fig. 386). The potass is placed on a piece of platinum con- Fig. 386. nected with the posi- tive pole of the battery. The mercury is then touched with the negative pole. When the current passes, the potass is decom- posed, oxygen is liberated at the positive pole, while the potassium liberated at the negative pole amalgamates with the mercury. On distilling this amalgam out of contact with air, the mercury passes off, leaving the potassium. The decomposition of binary compounds, that is, bodies contain- ing two elements, is quite analogous to that of water and of potass ; one of the elements goes to the positive, and the other to the nega- tive pole. The bodies separated at the positive pole are called electronegative elements, because at the moment of separation they are considered to be charged with negative electricity, while those separated at the negative pole are called electropositive elements. One and the same body may be electronegative or electropositive, according to the body with which it is associated. For instance, sulphur is electronegative towards hydrogen, but is electropositive towards oxygen. The various elements may be -467] Electrotype. 489 arranged in such a series that any one in combination is electro- negative to any following, but electropositive towards all preceding ones. This is called the electrochemical series, and begins with oxygen as the most electronegative element, ending with potas- sium as the most electropositive. APPLICATION OF THE DECOMPOSITION PRODUCED BY THE BATTERY. 467. Electrotype. In the ordinary methods of reproducing in metal statues, basreliefs, etc., moulds of dry earth are prepared, which are faithful hollow copies of these_ .objects ; then either melted iron or bronze are run into these ; when the metal is solid, an exact copy in relief is obtained of the object. In electrotypes, a mould of the object to be produced is required, but the repro- duction is effected without either fusion or fire. The current of a battery quietly deposits a layer of metal of any desired thickness on a faithful impression of the object. This is the meaning of the term ofgalvanoplastics, which is derived from the word galvanism, and from a Greek word which signifies ' to model.' The practice of electrometallurgy consists of two distirlet opera- tions ; firstly, the preparation of the mould or impression of the objects to be reproduced ; and, secondly, the deposit of the metal in this mould. The first process is the most delicate, and that on which mainly depends the success of the operation. Various substances are used for taking impressions, wax, stearine, fusible metal, gutta percha, etc. Of these the most useful, at any rate for small objects, is gutta percha. This substance, which is hard at ordinary temperatures, softens when placed in warm water. When it has acquired the proper degree of softness, a plate of this is placed on the object to be copied and pressed against it. When the object is of metal, a medal for instance, the gutta percha is easily detached as soon as it is cold ; but with a wood engraving or a plaster cast, the gutta percha adheres, and cannot be detached without danger of tearing. This may be remedied by previously brushing the mould over with black lead or graphite, as it ought to be called. Suppose the subject to be reproduced is a medal (fig. 388), when the mould is obtained we have this metal hollow and inverted. It is now necessary to make its surface a conductor, for gutta percha being an insulator could not transmit the current from the battery. 490 Voltaic Electricity. [467- n This is effected by brushing it over very carefully with graphite (which is a very good conductor) in all those places where the metal is to be deposited. Three copper wires are then fixed to it, one of which is merely a sup- port, while the two others con- duct the current to the metallic surface. The mould is then ready for the metal to be deposited upon it ; copper is ordinarily used, but silver and gold also deposit well. In order to take a copper cast, a bath is filled with satu- Fig. 387. Fig. 388. rated solution of sulphate of copper and two copper rods, B and A, stretched across (fig. 389) : one connected with the negative and the other with the positive pole of a Grove's, or preferably, from its greater constancy, a Daniell's element. From the rod connected with the negative pole, B, is suspended the mould, ;;z, and from the other A, a plate of copper, C. The current being thus closed, the sulphate of copper is decomposed, acid is liberated at the positive pole, while copper is deposited at the negative pole, on the mould suspended from the rod, B, to which indeed several moulds maybe attached. The copper plate suspended from the positive pole serves a double purpose ; it not only closes the current, but it keeps the -468] Electrogilding. 491 solution in a state of concentration, for the acid liberated at the positive pole dissolves the copper, and reproduces a quantity of sulphate of copper equal to that which has been decomposed. The Fig. 389- bath always remains, therefore, at the same degree ot concentration, that is to say, always contains the same amount of salt in solution, \\hich is a condition necessary for forming a uniform deposit. 468. Electrogilding-. The old method of gilding was by means of mercury. It was effected by an amalgam of gold and mercury, which was applied on the metal to be gilded. The objects thus covered were heated in a furnace, the mercury volatilised, and the gold remained in a very thin layer on the objects. The same process was used for silvering ; but they were expensive and un- healthy methods, and have now been entirely replaced by electro- gilding, and electrosilvering. Brugnatelli, a pupil of Volta, appears to have been the first, in 1803, to observe that a body could be gilt by means of the battery and an alkaline solution of gold ; but M. de la Rive was the first who really used the battery in gilding. The methods both of gilding and silvering owe their present high state of perfection principally to the improvements of Elkington, Ruolz, and others. The difference between electrogilding and electrosilvering and the processes described in the previous article is this, that, in the 492 Voltaic Electricity. [468- former, the metal is deposited on a mould in order to reproduce the objects given ; while, in the latter, the objects are permanently covered with a thin layer of gold or silver. The pieces to be coated have to undergo three preparatory pro- cesses. The first consists in heating them so as to remove the tatty matter which has adhered to thiem in previous processes. Fig. 390. As the objects to be gilt are usually of copper, and their surface during the operation of heating becomes covered with a layer of suboxide or protoxide of copper, this is removed by the second operation. For this purpose the objects, while still hot, are immersed in very dilute nitric acid, where they remain until the oxide is removed. They are then rubbed with a hard brush, washed in distilled water, and dried in gently heated sawdust. To remove all spots they must undergo the third process, which consists in rapidly immersing them in ordinary nitric acid, and then in a mixture of nitric acid, bay salt, and soot. They are then well washed in distilled water, and dried as before in sawdust. When thus prepared the objects are attached to the negative pole of a battery of three or four cells, and if they are to be silvered they must be immersed in a bath of silver kept at a temperature of sixty to eighty degrees. They remain in the bath for a time which depends on the thickness of the desired deposit. There is great -469] Electromagnetism. 493 difference in the composition of the bath. That most in use con-. sists of two parts of cyanide of silver and two parts of cyanide of potassium, dissolved in 250 parts of water. In order to keep the bath in a state of concentration, a piece of silver is suspended from the positive electrode, which dissolves in proportion as the silver dissolved in the bath is deposited on the objects attached to the negative pole. The processes of electrogilding are quite the same as those of electrosilvering, with the exception that a bath of gold is used in- stead of one of silver, and the positive plate terminates in a plate of gold. The bath used is a solution of cyanide of gold and potas- sium. The method which has just been described can not only be used for gilding copper, but also for silver, bronze, brass, German silver, etc. But other metals, such as iron, steel, zinc, tin, and lead, are very difficult to gild well. To obtain a good coating they must first be covered with a layer of copper by means of the battery and a bath of sulphate of copper ; the copper with which they are coated is then gilded, as in the previous case. CHAPTER IX. ELECTROMAGNETISM. 469. Relation between magnetism and electricity. Early in the history of the two sciences, the analogy was remarked which existed between the phenomena of electricity and magnetism. It was observed that, in both cases, like kinds of electricity repelled each other, as also did like kinds of magnetism, and that unlike kinds attracted. It had moreover been observed that lightning, in striking a ship, often reversed the polarity of compass needles, and even sometimes robbed them of all magnetic power. But though there were many points of resemblance between electricity and magnetism, the dissimilarities were numerous. For instance, magnetic properties cannot be transmitted to good conductors, as can electrical properties. A magnet placed in contact with the earth does not lose its magnetism as does an electrified body. Again, electricity can be produced in all bodies, while magnetism is only manifested by a very small number. Among these resem- 494 Voltaic Electricity. [469- blances and dissimilarities, nothing could be affirmed respecting the identity of the causes which produce electricity and magnetism, when, towards the end of 1819, Oersted, a professor of physics in Copenhagen, made a memorable discovery, which for ever inti- mately connected these two physical agents. Thus arose a new branch of science called electromagnetism, to express that the phenomena are at once magnetic and electrical. 470. Action of current upon magnets. The fact which Oersted discovered was the directive action of currents upon magnets. He found that electrical currents have a directive action upon the magnetic needle, and always tend to set it at right angles to their own direction. Fig. 39i- To verify this action of currents upon magnets, the experiment is arranged as shown in fig. 391. A magnetic needle, movable upon a pivot, being at rest in the direction of the magnetic meridian, a wire traversed by a current is brought near it, care being taken to bring it lengthways. The needle is then seen to deviate from its position of rest, to oscillate, and ultimately come to rest in a position which is nearly at right angles to that of the current ; and the more nearly, the more powerful the current. In this experiment the direction in which the north pole is de- flected varies with the direction of the current ; if it goes from south to north above the needle, the north pole is deflected to the -472] Action of Magnets on Currents. 495 west ; if, on the contrary, it goes from north to south but still above the needle the north pole is deflected to the east. When the cur- rent passes below the needle, the same phenomena are reproduced in exactly the reverse order. All these different cases have been reduced to a single one by Ampere. 471. Ampere's rule. Ampere has given the following memoria technica, by which all the various directions of the needle under the influence of a current may be remembered. If we imagine an observer placed in the connecting wire in such a manner that the current entering by his feet issues by his head, and that his face is always turned towards the needle, we shall see that in the above four positions, the north pole is always deflected towards the left of the observer. By thus personifying the current, the different cases may be comprised in this general principle : In the directive action of currents on magnets, the north pole is always deflected towards the left of the current. 47?. Action of magnets and of the earth on currents. Just as currents act on magnets, so also magnets act upon currents. To Fig. 392. prove this, a circle of copper wire provided at the ends with steel points dip in two mercury cups (fig. 392). These mercury cups are at the ends of two metal rods attached to two vertical columns, with which can be connected the poles of Bunsen's element. By this arrangement, which is known as Ampere's stand, we have a movable circuit continually traversed by a current. When this circuit is at rest, if a powerful magnet be placed beneath the circuit, 496 Voltaic Electricity. [472 but in its plane, the circuit will be seen to turn and set transversely to the bar, which is the converse of Oersted's experiment. The terrestrial globe, which acts like a magnet on magnetic needles, acts in the same manner on the movable circuits, that is, it directs them perpendicularly to the magnetic meridian. This action may be demonstrated by the above apparatus. With this view, before the current traverses the circuit, it is placed in the magnetic meridian, and then the two poles of the battery are con- nected with the two columns : the circuit is soon observed to set transversely to its first position, and so that, in the lower part of the circuit, the direction of the current is from east to west. 473. Galvanometer, or multiplier. The name galvanometer multiplier, or rheometer is given to a very delicate apparatus, by which the ex ; stence, direction, and intensity of currents may be de- termined. It was invented by Schweigger in Germany a short time after Oersted's discovery. In order to understand its principle, let us suppose a magnetic needle, ab, suspended by a filament of silk (fig. 393), and surrounded in the plane of the magnetic meridian by a copper wire forming a Fig. 393- complete circuit round the needle in the direction of its length. When this wire is traversed by a current, it follows, from what has been said in the previous paragraph, that in every part of the circuit an observer lying in the wire in the direction of the arrows, and looking at the needle, ab, would have his left always turned towards the same point of the horizon, and consequently, that the action of the current in every part would tend to turn the north pole in the. same direction : that is to say, that the actions of the four branches of the circuit .concur to give the north pole the same direction. By coiling the copper wire in the direction of the needle, as represented -473] Galvanometer. 497 in the figure, the action of the current has been multiplied. If instead of a single one, there are several circuits, provided they are insulated, the action becomes still more multiplied, and the deflec- tion of the needle increases ; or, what is the same thing, a much feebler current will produce deflection. As the directive action of the earth continually tends to keep the needle in the magnetic meridian, and thus opposes the action of the current, the effect of the latter is increased by using an astatic system of two needles as shown in fig. 394. The action of the earth on the needle is then very feeble, and, further, the actions of the current on the two needles become accumulated. In fact, the action of the circuit, from the direction of the current indicated by the arrows, tends to deflect the north pole of the lower needle ab towards the west. The upper needle, a' b f , is subjected to the action Fig. 395- ot two contrary currents, no and qp, but as the first is nearer, its action preponderates. Now this current, passing below the needle, evidently tends to turn the pole, of, towards the east, and conse- quently, the pole, b', towards the west ; that is to say, in the same direction as the pole, a, of the other needle. K K 498 Electromagnetism. [473 From these principles it will be easy to understand the theory of the multiplier. The apparatus, represented in fig. 395, consists of a thick brass plate resting on levelling screws ; on this is a copper frame on which is coiled a great number of turns of wire covered with silk. The two ends terminate in binding screws, n and m. Above the frame is a graduated circle, with a central slit parallel to the direction in which the^vire is coiled. By means of a very fine filament of silk, an astatic system is suspended ; it consists of two needles, ab and a! b' ', one above the scale, and the other within the circuit itself. In using the instrument it is so adjusted that the needles, and also the slit, are in the magnetic meridian. 474. Uses of the galvanometer. To show, by means of the multiplier, the electricity developed in chemical actions, for instance in the action of acids on metals, two platinum wires may be attached to the binding screws, m and n. Then one of them is plunged in very dilute sulphuric acid, and the other placed in contact with a piece of zinc held in the hand, which is dipped in the liquid. An immediate deflection is observed, which indicates the existence of a current : and from the direction which the north pole of each needle assumes, it is seen that the direction of the current is that indicated by the arrows. From which we may conclude, in accordance with the explanation given as to the origin of electricity in the simple voltaic circuit, that the acid is positively electrified and the zinc negatively. The length and diameter of the wire vary with the purpose for which the galvanometer is intended. For one which is to be used in observing the currents due to chemical actions, a wire about \ millimetre in diameter, and making about 800 turns, is well adapted. Those for thermo-electric currents, which have low inten- sity, require a thicker and shorter wire, for example, thirty turns of a wire f millimetre in diameter. For very delicate experiments, as in physiological investigations, galvanometers with as many as 30,000 turns have been used. 475. Magnetisation by electrical currents. From the in- fluence which currents exert upon magnets, turning the north pole co the left and the south pole to the right, it is natural to think, that by acting upon magnetic substances in the natural state the currents would tend to separate the two magnetisms. In fact, when a wire traversed by a current is immersed in iron filings, they adhere to it in large quantities, but become detached as soon as the -476] Magnetisation by Electrical Currents. ,499 current ceases, while there is no action on any other non-magnetic metal. The action of electrical currents on magnetic substances is well seen in an experiment due to Ampere, which consists in coiling an in- sulated copper wire round an unmagnetised steel bar. If a current Fig. 396. be passed through the wire, even for a short time, the bar becomes strongly magnetised. The same effect is produced with a bar of soft iron, but in this case the magnetisation is temporary ; when the current ceases, the iron, which is destitute of coercive force, re- verts instantaneously to the natural state ; and, if in this experi- ment, we imagine an observer floating in the direction of the current, the north pole is always on his left hand. If the charge of a Leyden jar be transmitted through the wire by connecting one end with the outer coating, and the other with the inner coating, the bar is also magnetised. Hence both voltaic and frictional electricity can be used for magnetising. CHAPTER X. ELECTRODYNAMICS. 476. Reciprocal action of currents on currents. Ampere did not restrict himself to trying the action of magnets and of the earth upon movable currents ; he went further, and was led to the important discovery, that electrical currents act on each other as do magnets ; and he thus created an entirely new branch of physics, to which the name electrodynamics has been given. The actions which currents exert on each other are different according as they are parallel or angular. I. Two currents which are parallel, but in contrary directions^ repel each other. KK 2 Electrodynamics. [476- II. Two currents ; parallel and in the same direction, attract e(ich other. To verify these laws use is made of the apparatus represented in fig. 397. On a wooden support are fixed two brass columns, A and B, joined at the top by a wooden cross-piece. In the centre of this is a brass binding screw, a, and below this a mercury cup, o. In this is placed an iron pivot which joins the end of a copper wire. This wire is coiled in the manner represented in the figure, terminating in a mercury cup, c, on the base of the apparatus. It thus forms a circuit Fig. 397- movable about the pivot. This being premised, the circuit is arranged in the plane of the two columns, as shown in fig. 397, and the current from a Bunsen's battery is passed through it to the foot of the column, A ; it passes thence by a copper wire to the binding screw, a ; thence into the cup, ao, traverses the entire movable circuit in the direction of the arrows, reaches the cup, C, whence, by a copper strip, it reaches the foot of the column, B, rises in this, and ultimately returns to the battery. When the current passes, the circuit moves away from the columns, and, after a few oscillations, comes to rest crosswise to its original position ; thus showing that the ascending current in the columns and the descending current in the circuit repel each other, thereby proving the first law. The second law may be established by means of the same ap- paratus, replacing the movable circuit depicted in fig. 397 by another so arranged that the current is ascending in both the columns and in the two branches of the circuit. When the mov- able circuit is displaced, and the current is passed, the latter returns briskly towards the columns. Law of angidar currents. In the case of two angular currents, -479] Solenoids. 501 one fixed and the other movable, Ampere found that there was attraction when both the currents moved towards, or both away from, the apex of the angle ; and that repulsion took place when, one current moving towards the apex, the other moved away from it. SOLENOIDS. 477. structure of a solenoid. A solenoid is a system of equal and parallel circular currents formed of the same pieces of covered copper wire, and coiled in the form of a helix or spiral, as re- presented in fig. 398. A sole- noid, however, is only complete when part of the wire, BC, passes in the direction of the axis in the interior of the helix. With this arrangement, when the circuit is suspended in the mer- Fig 398> cury cups, ab t of the apparatus (ng. 397), and a current is passed through, it is directed by the earth exactly as if it were a magnetic needle. If the solenoid be removed it will, after a few oscillations, return, so that its axis is in the magnetic meridian. Further, it will be found that, in the lower half of the coils of which the solenoid consists, the direction of the current is from east to west ; in other words, the current is descending on that side of the coil turned towards the east, and ascending on the west. In this experiment the solenoid is directed like a magnetic needle, and the north pole, as in mag- nets, is that end which points towards the north, and the south pole that which points towards the south. 478. Mutual actions of magnets and solenoids. Exactly the same phenomena of attraction and repulsion exist between solenoids and magnets as between magnets. For if to a movable solenoid traversed by a current, one of the poles of a magnet be presented, attraction or repulsion will take place, according as the poles of the magnet and of the solenoid are of contrary, or of the same name. The same phenomenon takes place when a solenoid, traversed by a current and held in the hand, is presented to a movable mag- netic needle. Hence the law of attractions and repulsions applies exactly to the case of the mutual action of solenoids and of magnets. 479. Mutual actions of solenoids. When two solenoids tra- 502 Electrodynamics. [479- versed by a powerful current are allowed to act on each other, one of them being held in the hand, and the other being movable about a vertical axis, as shown in fig. 399, attraction and repulsion Fig. 399- will take place, just as in the case of two magnets. These pheno- mena are readily explained by reference to what has been said about the mutual actions of the currents, bearing in mind the direc- tion of the currents in the ends presented to each other. 480. Ampere s theory of magnetism. Ampere has propounded a most ingenious theory, based on the analogy which exists be- tween solenoids and magnets, by which all magnetic phenomena may be referred to electrodynamical principles. Instead of attributing magnetic phenomena to the existence of two fluids, Ampere assumes that each individual molecule of a magnetic substance is traversed by a closed electric current. When the magnetic substance is not magnetised, these molecular currents, under the influence of their mutual attractions, occupy such positions that their total action on any external substance is null. Magnetisation consists in giving to these molecular currents a parallel direction, and the stronger the magnetising force the more perfect the parallelism. The limit of magnetisation is at- tained when the currents are completely parallel. The resultant of the actions of all the molecular currents is equivalent to that of a single current which traverses the outside of a magnet. For by inspection of fig. 400, in which the molecular currents are represented by a series of small internal circles in the two ends of a cylindrical bar, it will be seen that the adjacent -481] Ampere's Theory of Magnetism. 503 parts of the currents oppose one another, and cannot exercise any external electrodynamic action, which is not the case with those on the surface. The direction of these currents in mag- nets can be ascer- tained by considering the suspended sole- noid (fig. 398). If we suppose it traversed by a current, and in equi- librium in the magne- tic meridian, it will set in such a position that in the lower half of each coil the current flows from east to west. We may then esta- blish the following rule. At the north pole (English] of a magnet the direction of the Amptrian currents is opposite that of the hands of a watch) and at the south pole the direction is the same as that oj the hands. 481. Terrestrial current. In order to explain on this supposi- tion tenestrial magnetic effects, the existence of electrical currents is assumed which continually circulate round our globe from east to west, perpendicular to the magnetic meridian. . The resultant of their action is a single current traversing the magnetic equator from east to west. These currents are supposed to be thermo-electric currents due to the variations of temperature caused by the successive influence of the sun on the different parts of the globe from east to west. These currents direct magnetic needles ; for a suspended mag- netic needle comes to rest when the molecular currents on its under surface are parallel, and in the same direction as the earth currents. As the molecular currents are at right angles to the direction of its length, the needle places its greatest length at right angles to east and west, or north and south. Natural magnetisa- tion is probably imparted in the same way to iron minerals. 504 Electromagnets. [482- CHAPTER XI. ELECTROMAGNETS. TELEGRAPHS AND ELECTROMAGNETIC MOTORS. 482. Electromagnets Electromagnets are bars of soft iron which, under the influence of a voltaic current, become magnets ; but this magnetism is only tempo- rary, for the coercive force of per- fectly soft iron is null, and the magnetism ceases as soon as the current ceases to pass through the wire. If, however, the iron is not quite pure, it retains more or less traces of magnetism. The electro- magnets have the horse-shoe form, as shown in fig. 401, and a copper wire, covered with silk or cotton, is rolled several times round them on the two branches, so as to form two bobbins, A and B. In order that the two ends of the horse-shoe may be of opposite polarity the winding on the two limbs, A and B, must be such that, if the horse- shoe were straightened out, it would be in the same direction. Electromagnets, instead of being made in one piece, are fre- quently constructed of two cylinders, firmly screwed to a stout piece of the same metal. Such are the electromagnets in Morse's telegraph (487), the electromagnetic machine (502). The helices on them must He such that the current shall flow in the same direction as the hand of a watch as seen from the south pole, and against the hands of a watch as seen from the north pole. The force of such magnets depends on their dimensions, on the number of turns of wire, and on the strength of the current. An electromagnet need not be very powerful to support one person (fig. 402). Electromagnets have extended applications, in tele- graphs, in clocks, and in electromagnetic engines. Fig. 401. -483] Electric Telegraph. 505 ELECTRIC TELEGRAPH. 483. Electric telegraphs. These are apparatus by which signals can be transmitted to considerable distances, and with enormous velocity, by means of voltaic currents propagated in Fig. 402. metal wires. Towards the end of the last century, and at the beginning of the present, many philosophers proposed to corre- spond at a distance by means of the effects produced by electrical machines when propagated in insulated conducting wires. In 181 1, Scemmering invented a telegraph in which he used the de- composition of water for giving signals. In 1820, at a time when 506 Electric Telegraph. [483- the electromagnet was unknown, Ampere proposed to correspond by means of magnetic needles, above which a current was sent, as many wires and needles being used as letters were required. In 1 834, Gauss and Weber constructed an electromagnetic telegraph, in which a voltaic current transmitted by a wire acted on a magnet- ised bar ; the oscillations of which under its influence were ob- served by a telescope. They succeeded in thus sending signals from the Observatory to the Physical Cabinet in Gottingen, a dis- tance of a mile and a quarter, and to them belongs the honour of having first demonstrated experimentally the possibility of electrical communication at a considerable distance. In 1837, Steinheil in Munich, and Wheatstone in London, constructed telegraphs in which several wires each acted on a single needle : the current in the first case being produced by an electromagnetic machine, and in the second by a constant battery. Every electric telegraph consists essentially of three parts : I, a circuit, consisting of a metallic connection between two places, and an electromotor, for producing the current ; 2, a communicator, for sending the signals from one station ; and, 3, an indicator, for receiving them at the other station. The manner in which these objects, especially the last two, are effected can be greatly varied ; the three principal systems are the needle telegraph, the dial tele- graph, and the printing telegraph. The needle telegraph is essentially a vertical galvanometer ; that is to say, a magnetic needle suspended vertically in a coil of insu- lated wire. To the needle is attached an index, which is seen on the front of the apparatus. The signs are made by transmitting Fig. 403. the current in different directions through the multiplier, by which the needle is deflected either to the right or left, according to the --484] Principle of Morses Telegraph. 507 will of the operator. The instrument by which this is effected is called a key, or commutator. In the dial telegraph an electromagnet causes an idex to move over a dial provided with the twenty-six letters of the alphabet ; that letter in front of which the needle stops, being the letter sent. By this kind of telegraph messages are not sent with great rapid- ity ; yet, as the manipulation is very simple, it is frequently used on railways and in private offices. 484. Principle of Morse's telegraph. This telegraph is based on the temporary magnetisation of an electromagnet by the inter- mittent passage of currents. Thus let E (fig. 403) be a fixed electromagnet, the insulated wires of which are attached to the two binding screws, a and b. Above this magnet is a lever, mn, movable about an axis, i, and ending in an armature of soft iron, m, so that, whenever the magnet is traversed by a current, the armature is attracted, and the part of the lever on the right of the fulcrum is lowered ; then, when the current no longer passes, a spring, R, raises the lever to an extent regulated by a screw, O. Suppose, for example, the electromagnet is at Bristol, and that there is a battery, P, at London, and two metal wires, A and B, by one of which the binding screw, $, is permanently connected with the negative pole of the battery, while the experimenter holds the other wire in his hand. So long as the experimenter does not place the wire which he holds in his hand in contact with the posi- tive pole, the current does not pass ; and, as the electromagnet does .not act, the arm of the lever is raised (fig. 403). But the moment Fig. 404. contact is made, the current is closed, the electromagnet attracts, and the lever is lowered (fig. 404) ; but it resumes its original Electric Telegraph. [484- position as soon as contact is broken, and so on at the will of the operator. Thus one person at London can cause the lever, mn, to oscillate at Bristol as often and as rapidly as possible as he desires. This is, in its simplest form, the principle of the elementary mech- anism of electrical telegraphs based on electromagnetism. It only remains to give to these oscillations a definite meaning. 485. line wire. Of the various essentials for a telegraphic com- munication, the batteries or sources of power have been already described, and we shall therefore pass to the explanation of the circuit, or line wire. Line wires are either aerial, subterranean, or sub- marine. The aerial wire consists of a stout galvanised iron wire connecting two stations. At certain intervals are wooden posts, to which are attached insulating supports of por- celain, which sustain the wire (fig. 405). Subterranean wires are used for cases in which an aerial wire would not be sufficiently protected against accident, as in towns. They consist usually of copper wires covered with gutta percha ; this insulates them from the earth in which they are placed. Submarine wires or cables are such as are employed in deep seas where great strength is required. The ordinary form is represented in figs. 406 and 407. The core consists of seven fine wires of very pure Fig. 406. Fig. 407. copper, which are twisted together and surrounded by an insulating covering. This is surrounded by an insulating coating of four concentric layers of gutta percha alternating with the same number -486] The Earth as a Conductor. 509 of layers of a material known as Chattertorts compound, which is essentially a mixture of resin, pitch, and gutta percha applied hot. Round this is a layer of tarred hemp, and this again is surrounded by a protective coating of steel wire coated with tarred hemp, which preserves it from the corrosive action of the sea. Fig. 406 gives a longitudinal view of a submarine cable, and fig. 407 a cross section. The diameter of the cable is about an inch, and it weighs about a ton to the mile. 486. The ear tii as a conductor. In figs. 403 and 404 we have not merely a wire connecting the positive pole of the battery with the electromagnet, but there is a second one which acts on a return wire. In 1837 Steinheil made the very important discovery that the earth might be utilised for the return conductor. This has the twofold advantage of doing away with the expense of a second wire, and also of lessening the resistance. With this view, at the sending station, a long copper wire is attached to the negative pole, which is fixed at the other end to a copper plate, Q. This plate is placed in water if possible (fig. 408), or Fig. 408. at all events is sunk some depth in earth. In like manner, at the receiving station, a similar wire and plate s are connected with the binding screw, b. Thus while the negative electricity passes into the ground by the plate, Q, the positive electricity which reaches the electromagnet and the binding screw, enters the ground by the plate, S. Hence there is in the wire, A, and in the electromagnet, the same circulation, and therefore the same effects as when the binding screw, b, communicates directly with the negative pole of the battery by means of a metal wire. 5io Electric Telegraph. [487- 487. Morse's telegraph. Fig. 409 represents a station at which a despatch is being sent by the help of this apparatus, and fig. 410 represents the receiving station. At each station the apparatus is the same ; it is double, and consists of two distinct parts, the key, by which the signals are sent, and the receiving instrument which registers them. These two parts are represented on a larger scale in figs. 411 and 412. To understand how they work let us commence with fig. 409. Below the table is a box containing the battery, which furnishes the Fig. 409. current. This passes by the wire, P, into the key, which will be after- wards described (fig. 411). Thence it passes into a small galvano- meter, , which indicates by the deflection of its needle whether the -488] Morses Telegraph. current is passing or not. The current ultimately attains the piece, M, which acts as a lightning conductor, as we shall afterwards see, and thence it goes to the wire, L, which is the line wire. This wire is again seen at the top of fig. 410, whence the arriving current again passes into the lightning conductor, then into a gal- Fig. 410. vanometer, and next a key, whence it passes into the electromag- net, which makes part of the receiver. It then enters the wire, T, which leads it to earth. 488. Morse's key and receiving: instrument. The general arrangement of the apparatus being understood, the following are the details of its action. The key consists of a small mahogany base, which acts as support for a metallic lever, hk (fig. 411), mov- 512 Electric Telegraph. [488- able in its middle on a horizontal axis. The extremity, B, of this lever is always pressed upwards by a spring, r, beneath ; at the other end a screw passes through it, which rests on a small metal sup- port, in contact with the wire, A. Fig. 41 1 represents the key at the moment it re- Fig. 411. ceives the dispatch, as at work for instance in fig. 410. The current enters then by the wire, L, which is the line wire, rises into the lever, kh, and de- scends by the screw pin, a, into the wire, A, which leads to the indi- cator. If, on the other hand, the key is to be used for sending a message, as represented in fig. 409, it will be seen that the lever, kh, does not touch the metal pin in which the wire, P, terminates. But if the lever, h, is lowered by pressing the end, B, contact is set up, and the current, P, at once passes into the lever, hk, and thence into the wire, L, which leads it to the station signalled to ; for the same wire is used to send and to receive the message. The indicator consists of an electromagnet, E (fig. 412), which whenever the current is transmitted, acts attractively on an armature of soft iron, ;#, fixed at the end of a lever, mn, movable about an axis; when the current is open, the lever is raised by a spring, R. At Fig. 412. the other end of the lever there is a pencil x, which writes the signals. For this purpose a long band of strong paper, ab, rolled round a drum, S (figs. 409 and 410), passes between two copper rollers with a rough surface, turning in contrary directions. Drawn in the direction of the arrows, the band of paper becomes rolled on -488] Telegraph Alphabet. 513 a second drum, O, which is turned by hand. A clockwork motion placed in the box, V, works the rollers, between which the band of paper passes. The paper being thus set in motion, whenever the electromagnet works, the point, x 9 strikes the paper, and, without perforating it, produces an indentation, the shape of which depends on the time during which the point is in contact with the paper. If it only strikes it instantaneously, it makes a dot (.) ; but if the contact is of any greater duration a line or dash of corresponding length is pro- duced. Hence, by varying the length of contact of the transmitting key at one station, a combination of dots or dashes may be produced at another station, and it is only necessary to give a definite meaning to these combinations. This is effected as follows in Morse's alphabet : SINGLE SlNGnj PRINTING. NEEDLE. FEINTING. NEEDLE. A x / N A B AV I/I C -- AA P Jk D AN Q IIJ E - N R vA F \\A S SN< G /A T / H NNNN TJ \\/ I -- SN V NNN/ J N/// W Jl K IJ X As/ L J* Y A// M 11 Z /As Fig- 413- The other signals are those of the single needle instrument (483). The signal V denotes a deflection of the top of the vertical L L 514 Electric Telegraph [488- needle to the left, and the signal / to the right. They correspond respectively to the dot and dash of the Morse alphabet. Any one present while a message is being received at a telegraph station, is astonished at the promptitude and accuracy with which signals are read and transmitted by the operators. These acquire such skill that they can read a message by the sounds which the arma- ture makes in striking against the electromagnet of the indicator. Based on this fact a form of instrument invented in America has come into use for the purpose of reading by sound. The sounder, as it is called, is essentially a small electromagnet on an ebonite base, resembling the relay in fig. 416. The armature is attached to one end of a lever, and is kept at a certain distance from the electro- magnet by a spring. When the current passes the armature is at- tracted against the electromagnet, with a sharp click, and when the current ceases it is withdrawn by the spring. Hence the interval between the sounds is of longer or shorter duration according to the will of the sounder, and thus in effect a series of short and long sounds can be produced which correspond to the dots and dashes of the Morse alphabet. 489. Improvements in Morse's telegraph. In the apparatus just described, the indentations on the paper only give indistinct dots and dashes, unless the current transmitted be very powerful. To get rid of this inconvenience, and to expend less force, the apparatus has been modified so that the signals can be traced in ink. With this view, all the other parts being the same, the follow- ing arrangement is made : -491] Electrical A larnm. 5 1 5 A roller, a, fig. 414, covered with flannel, is moistened with a suitable ink. Above the roller, and in contact with it, is an endless band, p h, rolled on two pulleys, 0, 0', which are turned by the clock- work motion which moves the paper. This is kept by a roller, , very near the chain, but not touching it. That being premised, whenever the current passes in the electromagnet, the armature, A, is attracted, the arm of the lever k, is depressed, and a pin, 2, at its end rests on the band, and places it in contact with the paper. The band depositing the ink which it has taken from the roller, makes on the paper as it moves along, a dot or a dash, according to the length of time the current passes, and which dots and dashes have the same meaning as above. 490. XiigHtningr conductor. Besides the parts of the telegraph already described there are three of which mention must be made ; the lightning conductor, the alarum, and the relay. The influence of storm clouds in decomposing the natural elec- tricity of the wire, often produces sufficient tension, not merely to interfere with the transmission of the despatches, but also to pro- duce dangerous discharges. The lightning conductor is designed to remedy these inconveniences. Represented at M in figs. 409 and 410, it consists of a vertical stand on which are two copper plates, indented like a saw, and arranged so that the teeth are near each other but do not touch. One of these plates is connected with the earth, the other with the line wire. Hence, when, by the inductive action of a storm cloud, electricity accumulates in wires and in the apparatus, it escapes by the points to the plate which is connected with the ground, and thus all danger from a discharge is avoided. 491. Electrical alarum. The electrical alarum is intended to warn the receiving station that a despatch is about to be sent. Represented in fig. 415, it consists of a board on which is fixed an electromagnet by means of a piece of brass, E. The current from the line arriving by a binding screw, ;;/, passes to the wire of the electromagnet, thence into the armature, a, into a steel spring, c, which presses against the armature, and ultimately emerges by a second terminal, n. Thus, whenever the current of the line wire reaches the electro- magnet, the armature, a, is attracted, and a clapper, P, fixed to this armature, strikes against "a bell, T, and makes it sound. The moment the clapper strikes, as the armature is no longer in contact with the spring, C, the current is open, the electromagnet no longer LL 2 516 Electric Telegraph. [491- attracts, ^.nd the armature reverts to its original position by the action of a spring, e, to which it is fixed. The current being closed afresh, a second attraction takes place, a^d so on until the telegraph clerk, thus warned, lets the cur- rent pass directly into the indi- cator without passing through the alarum. This he accom- plishes by means of an instru- ment called the shunt. Relay. In describing the re- ceiver we have assumed that the current pf the line* coming by the wire, C (fig. 416), entered directly into the electromagnet, and worked the armature, A, producing a despatch ; but when the current has to traverse a dis- tance of a few miles, owing to the resistance of the wire and the losses of insulation, its in- tensity is diminished so greatly that it cannot act upon the elec- tromagnet with sufficient force to print a despatch. Hence it is necessary to have recourse to a relay, that is, to an auxiliary electromagnet, which is still traversed by the current of the line, but which serves to introduce into the communi- cator the current of a local battery of four or five elements placed at the station, and only used to print the signals transmitted by the wire. For this purpose the current from the line entering the relay by the binding screw, L (fig. 416), passes into an electromagnet, E, whence it passes into the earth by the binding screw, T. Now, each time that the current of the line passes into the relay, the electro- magnet attracts an armature, A, fixed at the bottom of a vertical lever, /, which oscillates about a horizontal axis. At each oscillation the top of the lever,/, strikes against a button, #, and at this moment the current of the local battery which enters by the binding screw, r, ascends the column, m, passes into the lever,/, descends by the rod, 0, which transmits it to the binding screw, T : thence it enters the electromagnet of the indicator, whence it emerges by the wire, Z, to return to the local battery from which it started. Then when the current of the line is open, the electro- -492] Electromagnetic Machines. 517 magnet of the relay does not act, and the lever, /, drawn by a spring, r, leaves the bottom, ;/, as shown in the drawing, and the local current no longer passes. Thus the relay transmits to the Fig. 416. indicator exactly the same phases of passage and intermittence as those effected by the key in the station which sends the despatch. 492. Electromagnetic machines. Many physicists have at- tempted to utilise the attractive force of electromagnets as a motive power. M. Jacobi, of St. Petersburg, appears to have been the first to construct a machine of this kind, with which, in 1838, he moved on the Neva a small boat containing twelve persons. Since that time the construction of these machines has been materially modi- fied ; but in all the expense of zinc and acids which they use far exceeds that of steam engines of the same force. Until some cheaper source of electricity shall have been discovered there is no expectation that they can be applied at all advantageously. Fig. 418 represents an electromagnetic machine constructed by Froment. It consists of four electromagnets acting in two couples, on two pieces of soft iron, P, only one of which is seen in the figure. This piece, attracted by the electromagnets, EF, transmits the motion by means of a connecting rod to a crank m fixed at the end of a horizontal axis. To this is fixed a fly-wheel like that of a steam engine, which is intended to regulate the rotatory 'mo- tion. On this axis also is a piece of metal, , of a greater diameter, the action of which will be described presently. The current of the battery, entering at A, passes into a cast-iron base, B, then by various metallic connections it reaches the metal piece, n. Thence the current ought to pass alternately to the first Electromagnetic Machines. [492- -493] Induction by Currents. 519 couple of electromagnets, EF, and then to the second, ef. In order to understand how this alteration in the path of the current is ef- fected, let us refer to fig. 417 on the right of the picture, which re- presents a section of the piece, n, and its accessories. On this piece is a projection, e, which is called a cam, and which, during a com- plete turn, successively touches two springs, a and b ; these are in- tended to transmit to the electromagnets the current, the direction of which is indicated by the unbarbed arrows ; the barbed arrows do not show the direction of the current but the direction of the motion of the various pieces of the machine. These details being known, it will be seen that the current passes alternately into two springs, #"and b, and from thence into, the two systems of electromagnets, EF and ef: the piece P is first of all attracted, then a similar one, which is placed at the other, end of the axis of the fly-wheel. There is thus produced a continuous cir- culating motion, which is transmitted by an endless band to a system 01 wheel work, which works two lifting pumps. CHAPTER XII. INDUCTION BY CURRENTS. 493. Induction by currents. We have already seen (398) that by the term induction is meant the action which electrified bodies exert at a distance on bodies in the natural state. Hitherto we have only had to deal with electrostatical induction ; we shall now see that dynamical electricity produces analogous effects. Faraday discovered this class of phenomena in 1832, and he gave the name of currents of induction, or induced currents, to instanta- neous currents developed in metallic conductors under the influ- ence of metallic conductors traversed by electric currents, or by the influence of powerful magnets, or even by the magnetic action of the earth ; and the currents which give rise to them he called inducing currents. The inductive action of currents at the moment of opening or closing may be shown by means of a coil with two wires. This consists (fig. 419) of a hollow cylinder of wood or of cardboard, on which a quantity of stout silk-covered copper wire is coiled ; on this 520 Induction. [493- is coiled a considerably greater length of fine copper wire, also in- sulated by being covered with silk. This latter coil, which is called the secondary coil, is connected by its ends with two binding screws, a, b, from which wires pass to a galvanometer G. while the thicker wire, the primary coil, is connected by its extremities with two binding screws, c and d. One of these, d, being connected with one pole of a battery, when a wire from the other pole is con- nected with c, the current passes in a primary coil, and in this alone. The following phenomena are then observed : i. At the moment at which the thick wire is traversed by the current, the galvanometer, by the deflection of the needle, indicates the existence in the secondary coil bf a current inverse to that in the primary coil, that is, in the contrary direction : this is only in- stantaneous, for the needle immediately reverts to zero, and remains so as long as the inducing current passes through cd. Fig. 419. ii. At the moment at which the current is opened, that is, when the wire, cd, ceases to be traversed by a current, there is again pro- duced in the wire, ab, an induced current instantaneous like the first, but direct, that is, in the same direction as the inducing current. 494. Induction by magnets and by the action of the earth. It has been seen that the influence of a current magnetises a steel bar ; in like manner a magnet can' produce induced electrical currents in metallic circuits. Faraday showed this by means of a coil with a single wire of 200 to 300 yards in length. The two extremities of the wire being connected with the galvanometer, as shown in fig. 420, a strongly magnetised bar is suddenly in- serted in the bobbin, and the following phenomena are observed : -494] Induction by Magnets. 521 i. At the moment at which the magnet is introduced, the galva- nometer indicates in the wire the existence of a current, the direc- tion of which is opposed to that which circulates round the magnet, considering the latter as a solenoid on Ampere's theory (480). ii. The needle soon returns to zero, and remains there as long as the magnet is in the coil ; when it is withdrawn, the needle of the galvanometer, which has returned to zero, indicates the existence of a direct current. The inductive action of magnets may also be illustrated by the following experiment : A bar of soft iron is placed in the above bobbin and a strong magnet suddenly brought in contact with it ; the needle of the galvanometer is reflected, but returns to zero when the magnet is stationary, and is deflected in the opposite direction when it is removed. The induction is here produced by Fig. 420. the magnetisation of the soft iron bar in the interior of the bobbin under the influence of the magnet. Faraday discovered that terrestrial magnetism can develope in- duced currents in metallic bodies in motion ; that it acts like a powerful magnet placed in the interior of the earth in the direction of the dipping needle, or according to the theory of Ampere, like a series of electrical currents directed from east to west parallel to the magnetic equator. He first proved this by placing a long 522 Induction. [494- helix of copper wire covered with silk in the plane of the magnetic meridian parallel to the dipping needle ; by turning this helix through a semicircle round an axis in its middle, perpendicular to its length, he observed that at each turn a galvanometer, connected with the two ends of the helix, was deflected. 495. Properties of induced currents. Notwithstanding their instantaneous character, it appears mainly from the experiments of Faraday their discoverer, that induced currents have all the pro- perties of ordinary currents. They produce violent physiological luminous, calorific, and chemical effects, and finally give rise to new induced currents. They also deflect the magnetic needle, and magnetise steel bars when they are passed through a copper wire coiled in a helix round the bars. The intensity of the shock produced by induced currents renders their effects comparable to those of electricity in a state of tension. But as they act on the galvanometer the electricity is present, both in a state of tension and in the dynamical condition. These phenomena of induction currents are well seen in Ruhm- korff's coil, which we shall now describe. 496. RuhmkorfPs coil. This is an arrangement for producing induced currents, in which a current is induced by the action of an electric current, whose circuit is alternately opened and closed in rapid succession. These instruments, known as inductoriums, or induction coils, present considerable variety in their construction, but all consist essentially of a hollow cylinder in which is a bar of Fig. 421. soft iron, or bundle of iron wires, with two helices coiled round it, one connected with the poles of a battery, the current of which is -496] Ruhmkorjf's Coil. 523 alternately opened and closed by a self-acting arrangement, and the other serving for the development of the induced current. By means of these apparatus, with a current of. three or four Grove's cells, physical, chemical, and physiological effects are produced equal to and superior to those obtainable with electrical machines and even the most powerful Leyden batteries. Of all the forms those constructed by Ruhmkorff in Paris, and by Ladd and Apps in this country, are the most powerful. Fig. 421 is a representation of one, the coil of which is about 14 inches in length. T\\e pi'imary or inducing wire is of copper, and is about 2 mm. in diameter, and 14 or 1 5 yards in length. It is coiled directly on a cylinder of cardboard, which forms the nucleus of the appa ratus, and is enclosed in an insulating cylinder of glass, or of ebonite. On these is coiled the secondary or induced wire, which is also of copper, and is about |mm. in diameter. A great point of these apparatus is the insulation. The wires are not merely insulated by being in the first case covered with silk, but each individual coil is separated from the rest by a layer of melted shellac. The length of the secondary wire varies greatly ; in some of the largest sizes it is as much as several miles. With these great lengths the wire is thinner, about |mm. The following is the working of the apparatus. The current arriving by the wire, P, at a binding screw, a, passes thence into the commutator, C (fig. 421) ; thence by the binding screw, b, it enters the primary wire, where it acts inductively on the secondary wire ; having traversed the primary wire it emerges by the wire, s (fig. 422). Following the direction of the arrows, it will be seen that the current ascends in the binding screw, z, reaches an oscillating piece of iron, o, called the hammer, descends by the anvil, /i, and passes into a copper plate, K, which takes it to the commutator, C. It goes from there to the binding screw, c, and finally to the negative pole of the battery by the wire, N. Fi The current in the primary wire only acts inductively on the secondary wire (493), when it 524 Induction. [496- opens or closes, and hence it must be constantly interrupted. This is effected by means of the oscillating hammer, o, omitted in figure 421, but represented on a larger scale in fig. 422. In the centre of the bobbin is a bundle of soft iron wires, forming together a cylin- der a little larger than the bobbin, and thus projecting at the end as seen at A. When the current passes in the primary wire, this hammer, 347 I effects of, 348 ; dark lines of, 349 Specular reflection, 310 Spherical aberration, 361 ; mirrors, 318 Spirit-level, 91 Springs, 93 ; intermittent, 150 Staubbach, 52 TON Steam boiler, 267 ; engine, 259, 265 Steel, 397 Steelyard, 23 Stereoscope, 386 Stethoscope, 166 Stills, 254 Stool, insulating, 417 Strata-permeable, 94 Stratification of the electric light, 497 Stratus clouds, 281 St. Elmo's fire, 448* Streams, 93 Stringed instruments, 183 Strings, transverse vibrations of, 180 Structure of the eye, 383 Sub-dominant chords, 174 Submarine wire, 485 Subterranean wire, 485 Suction pump, 146 Superficial expansion, 196 Surface, 6 ; atmospheric pressure on, 119 Suspension, axis of, 48 Swimming, 100 ; bladder of fishes, 99 Symmer's hypothesis, 403 Syphon, 149 ; barometer, 123 ; ink- stand, 145 Syren, 171 Syringe, pneumatic, 293 '"TANTALUS'S cup, 150 -* Telegraph dial, 483 ; electric, 483 ; line wire, 485 ; Morse's, 487 Telescopes, 362-377 Tempered steel, 387 Temperature, 197 ; of the air, 276 ; mobile equilibrium of, 210 Tenacity, 70 Tension, 12 ; of gases, 109 ; maximum, 240 ; of vapours, 240 ; of electricity, 409 Terrestrial current, 481 ; heat, 295 ; telescope, 366 Thallium, 352 Thermal unit, 256 Thermoelectric pile, 501 ; series, 500 Thermo-electricity, 499 Thermometers, 198 ; alcohol, 201 ; differential, 203 ; graduation of, 199 ; mercurial, 198 ; scale of, 199, 200 Thermo-multipliers, 501 Thunder and lightning, 439, 443 Timbre, 170 Time, 344 Tone, major and minor, 174 Tonic chords, 174 542 Index. TOR Torricelli's experiment, 117 ; vacuum, 124 Torsion, 12 Tourniquet, hydraulic, 79 Tower of Pisa, 47 ; of Bologna, 47 Traction, 23 Trade winds, 289 Translucent bodies, 303 Transparent bodies, 303 ; colours of, 355 ; reflection from, 317 Triangle, 184 Trombone, 192 True time, 344 Trumpet, speaking, 167 ; ear, 168 Tube, graduation of, 121 ; luminous, 423 ; Mariotte's, 133 ; speaking, 166 Tuning-fork, 177, 184; normal, 177 Turning-table, 29 Tympanum, 157 UNDULATION of heat, 194 Undulatory theory, 301 Unison, 174 Unit of length, 23 ; thermal, 256 Units, British, 104 ; French, 10 Universal discharger, 434 ~\ VACUUM, 124, 141 ; formation of * vapours in, 239 Valve chest, 262 ; slide, 262 ; safety, 269 Vane, electrical, 420 Vapour, 109; quantity which saturates a space, 241 ; latent heat of, 248 Vapours, 237 ; elastic force, 238 ; for- mation in a vacuum, 239, 240 ; li- quefaction of, 251 Variable winds, 289 Variations, barometric, 125 Velocity, 16 ; of falling bodies, 52 ; of sound, 161 ; of light, 306 Ventral segment, 189 Vertical lines, 40 ; pressure, 80 Vesicular vapours, 281 Vibration, 156 Vibrations of strings, 180 ; laws of, 181; in pipes, 190 ; rods, 183 Virtual focus, 321, 339, 343 ; images, 314, 322, 342 ZON Vision, mechanism of, 383 ; distance of distinct, 384 ; binocular, 385 Vital fluid, 449 Vitreous fusion, 230 ; humour, 383 Voice, human, 193 Volatile liquids, 237 Voltaic arc, 464 ; battery, 456, 462 ; couple, 451, 454 ; current, 456 ; pile, 451, 456 Volta s cannon, 424 ; condensing elec- troscope, 450 ; fundamental experi- ment, 450 Volume, 6, MOI Vowel sounds, 216 "\17ATER, decomposition of, 465 ; hammer, 52 ; jets of, 92 ; latent heat of, 232 ; level, 90 ; maximum density of, 226 ; and mercury frozen in a vacuum, 250 Watt's steam engine, 260 Wave, condensed, 157 ; rarefied, 157 Weather, 127 ; glasses, 128 Weighing machines, 51 ; method of double, 50 Weight of the air, 113; of a body, 39, 42 ; of gases, 112 ; of liquids, 78 Wells, 93 Wet-bulb, hygrometer, 273 Wheel barometer, 128 ; escapement, 61 ; fly, 261 ; friction, 55 Whirl, electrical, 420 Whistle, safety, 270 White light, 346 ; recomposition of, /L 53 Whitworth's shells, 293 Winds, 287, 288 ; law of rotation of, 290 ; variable, 289 Wind instruments, 192 ; channel, 187 ; chest, 188 Wine tester, 131 Wollaston's battery, 456 Y ARD, 104 ;INC carbon battery, 460 Zone, isothermal, 278