John Swett C^J 00 ELEMENTS OF NATURAL PHILOSOPHY FOR THE USE OF anti BY J. A. GILLET, PROFESSOR OF PHYSICS IX THE NORMAL COLLEGE OF THE CITY OF NEW YORK, AND W. J. ROLFE, FORMERLY HEAD MASTER OF THE HIGH SCHOOL, CAMBRIDGE, MASS. POTTER, AINSWORTH, & CO. NEW YORK AND CHICAGO. 1884. Copyright, 1881, BY J. A GtLLET AND W. J. ROLFE. SSUCAViiON SEPT, Press of Rand, Avery, 6 Co., Boston. PREFACE. THIS book is an abridgment of the " Natural Philos- ophy" by the same authors, with such changes as were required to adapt it to younger pupils. As the larger book is in no sense .a revision of the " Natural Philos- ophy " of the "Cambridge Course of Physics," but an entirely new work, differing from its predecessor both in matter and in method of presentation, so this book is equally independent of the earlier " Handbook of Natural Philosophy." Two kinds of type have been used, as in the larger book, with a view to adapting it to the wants of different schools. The matter in the larger type forms a brief and easy course, complete in itself and sufficient for classes that can spend only a single school term in the study. The portions in smaller type will enable teachers to extend this course more or less, according to their per- sonal tastes or the ability of their pupils. Those who have time for the whole book may find the division con- venient in reviews and examinations, and also in fixing the minimum to be required of pupils who have little taste or aptitude for physics. iv PREFACE. The authors have carefully avoided doing an tvie teacher's work for him by anticipating every familiar illustration which he Would either give his pupils orally or lead them to see and state for themselves. Teachers may be supposed to know something, and it is a very dull pupil that knows nothing at all, except what is " in the book." Both teacher and pupil become mere ma- chines when the one has only to hear the other repeat what he has learned by rote from the printed page. Such practical hints and suggestions as may be needed by the young and inexperienced instructor had better be fur- nished him outside of the text-book. It may be added that the hook of which this is an abridgment will be useful in various ways to the teacher of this ; and he will also get much help from any of the following works, to which the authors have already acknowledged their indebtedness in che preface to the larger book : Baseband's Natural Philosophy. D. Appleton & Co. : New York (reprint). Ganotfs Physics. Wm. Wood & Co. : New York (reprint). Tait's Recent Advances in Physical Science. Macmillan & Co. : New York. Maxwell's Matter and Motion. Macmillan & Co. : New York. Tyndall's Sound. D. Appleton & Co. : New York (reprint). Mayer's Sound. D. Appleton & Co. : New York. Helmholtz's Popular Lectures. 1st Series. D. Appleton Co. : New York (reprint). Taylor's Sound and Music. Macmillan Co. : New York. TyndalFs Heat a Mode of Motion. D. Appleton & Co. : New York (reprint). Maxwell's Theory of Heat. D. Appleton & Co. : New York (reprint). Mayer's Light. D. Appleton Co. : New York. PREFACE. V Tyndall's Lectures on Light. D. Appleton & Co. : New York. Rood's Modern Chromatics. D. Appleton & Co. : New York. Jeffries's Color Blindness. Houghton, Mifflin, & Co. : Boston. Gordon's Electricity and Magnetism. D. Appleton & Co. : New York (reprint). Jenkin's Electricity and Magnetism. D. Appleton & Co. ; New York (reprint). Tyndall's Lessons in Electricity. D. Appleton & Co.: New York (reprint). Prescott's Telegraph. D. Appleton & Co. : New York. Prescott's Telephone, etc. D. Appleton & Co.: New York. Sawyer's Electric Lighting. D. Van Nostrand : New York. Loomis's Meteorology. Harper & Brothers : New York. Stewart's Energy. D. Appleton & Co. : New York. CONTENTS. I. CONSTITUTION OF MATTER i II. MECHANICS 5 A. DEFINITIONS. UNITS. NEWTON'S LAWS OF MO- TION 5 B. WORK AND ENERGY 17 C. COMPOSITION AND RESOLUTION OF FORCES ... 20 D. GRAVITY AND EQUILIBRIUM 23 E. FALLING BODIES 30 F. THE PENDULUM 36 G. MACHINES 39 III. PHYSICS 53 I. STATES OF MATTER 53 A. THREE STATES OF MATTER 53 B. FLUIDS 55 C. GASES 63 D. LIQUIDS . 69 E. SOLIDS 90 II. SOUND . 93 A. ORIGIN OF SOUND 93 B. PROPAGATION OF SOUND 96 C. RESONANCE 104 D. MUSICAL INSTRUMENTS 106 E. THE HUMAN EAR 112 III. HEAT 114 I. EFFECTS OF HEAT 114 A. EXPANSION 114 B. MEASUREMENT OF TEMPERATURE 119 Vlll CONTENTS. PAGE C. CHANGE OF STATE 123 I. FUSION AND SOLIDIFICATION 123 II. EVAPORATION AND CONDENSATION .... 125 D. MEASUREMENT OF HEAT 131 II. RELATIONS BETWEEN HEAT AND WORK 134 III. DISTRIBUTION OK HEAT 139 A. CONDUCTION 139 B. CONVECTION 143 C. RADIATION AND ABSORPTION 143 IV. LIGHT 149 A. RADIATION 149 B. REFLECTION 156 C. REFRACTION 158 D. DISPERSION 161 E. LENSES 165 F. OPTICAL INSTRUMENTS 173 G. COLOR 185 V. MAGNETISM 192 VI. ELECTRICITY 201 I. FRICTIONAL ELECTRICITY 201 A. ELECTRICAL ATTRACTIONS AND REPULSIONS . . 201 B. ELECTRICAL CONDUCTION AND INSULATION . . 204 C. ELECTRICAL INDUCTION 205 D. ELECTRICAL POTENTIAL 209 E. ELECTRICAL CHARGE AND DISCHARGE .... 210 II. VOLTAIC ELECTRICITY 221 A. DEFLECTION OF THE NEEDLE 221 B. FLOW OF ELECTRICITY THROUGH CONDUCTORS . 224 C. ELECTRO-CHEMICAL ACTION 226 I. VOLTAIC BATTERIES 226 II. ELECTROLYSIS 232 D. ELECTRO-MAGNETIC INDUCTION 234 E. TELEGRAPHY 242 F. TRANSMISSION OF POWER BY MEANS OF ELECTRI- CITY 251 G. ELECTRO-THERMAL ACTION 252 VII. METEOROLOGY 257 I. CONSTITUTION OF THE ATMOSPHERE ..... 257 II. TEMPERATURE OF THE ATMOSPHERE 260 III. HUMIDITY OF THE ATMOSPHERE 268 IV. MOVEMENTS OF THE ATMOSPHERE 270 V. CONDENSATION IN THE ATMOSPHERE 277 A. DEW AND HOAR-FROST 277 CONTENTS. PAGE B. FOG AND MIST 2 79 C. CLOUDS AND RAIN 2Sl D. STORMS : VI. ELECTRICAL PHENOMENA OF THE ATMOSPHERE . . 292 A. ATMOSPHERIC ELECTRICITY 292 B. LIGHTNING 2 93 C. THE AURORA 2 9 6 VII. OPTICAL PHENOMENA OF THE ATMOSPHERE ... 298 A. REFRACTION 2 9 8 B. REFLECTION 33 C. CORONA AND HALOS 35 VIII. THE THREE GREAT CIRCULATIONS OF THE GLOBE 307 ELEMENTS OF NATURAL PHILOSOPHY. ELEMENTS OF NATURAL PHILOSOPHY. i. CONSTITUTION OF MATTER. 1. Molecules and Atoms. All bodies are supposed to be made up of very small particles, called molecules, which are in turn made up of still smaller particles, called atoms. These molecules are far too minute to be seen with the most powerful microscope, and are separated by spaces many times as large as the molecules themselves. It has been estimated that there are at least 300 quintillions of molecules in one cubic inch of air, a number which would be represented by 3 fol- lowed by twenty ciphers. At the same time it is believed that the material molecules themselves occupy only ^ of the space in the cubic inch. The atoms that make up the molecules are also believed to be very far apart compared with their size. We thus gain some notion of the extreme fineness of the atomic dust of which matter is composed. We can resolve bodies into molecules, and molecules into atoms ; but it has not been found possible to divide the atoms. 2. Substance. The substance of a body depends upon the internal structure of its molecules. All the molecules of the same substance are supposed to be exactly alike. A i ELEMENTS OF c t)6dy may^ t>e divided and subdivided at will, and the sub- stance of every portion will remain the same so long as the molecules are unchanged. If the molecules are divided, or their structure is altered by changing the kind, number, or grouping of their atoms, the substance of the body is changed. If a piece of iron is reduced to the finest powder, every parti- cle is iron still ; but if the iron rusts, its molecules unite with those of oxygen in the air, forming more complex molecules and a new substance. Ice may be changed to water, and water to steam, without change of substance, for the molecules remain the same ; but if we divide these molecules by chemical pro- cesses we obtain oxygen and hydrogen, two substances made up of less complex molecules. 3. The Ether. A highly rarefied fluid, called the ether, is supposed to fill all space and to permeate all bodies. It fills alike the spaces among the planets and stars and those among molecules and atoms. It is without weight, and offers no resistance to bodies, molecules, or atoms moving about in it. 4. The Structure of Bodies analogous to that of the Sidereal Universe. The Sidereal Universe is composed of stars, each of which is probably, like our own sun, the centre of a solar system composed of sun and planets. 1\\t planets and moons which compose a solar system correspond to the atoms which compose the molecules, and the solar systems correspond to the molecules which compose the body. The planets in the solar system are sometimes found singly, as in the case of Venus, and sometimes in groups, as in the case of Jupiter and his moons. The same is true of the atoms in the molecules. 5. All Matter is Porous. From what has been said, it wiU be evident that all matter is porous, that is, it contains spaces which are not occupied with material particles. When these pores are too small to be seen with the microscope, they are called physical pores. In wood and many other NATURAL PHILOSOPHY. 3 substances the pores are large enough to be seen ; they are then called sensible pores. 6. The Three Orders of Material Units. The three orders of material units are atoms, molecules, and bodies. 7. Atomic, Molecular, and Molar Motion. Every par- ticle of matter in the universe is in incessant motion. The atoms are all the time moving about in the molecules ; the molecules, in bodies ; and bodies, in space. The motion of the atoms within the molecules is called atomic motion ; that of the molecules in bodies, molecular motion ; and that of bodies in space, molar motion. Molar motion is often called mechanical motion. Sometimes the term molecular is applied to the motion of both atoms and molecules. 8. The Three Great Forces of Nature. There are three forces corresponding to the three orders of material units. These are affinity, cohesion, and gravity. Affinity is the force which binds together the atoms into molecules. It is therefore an atomic force. It is the strongest of the forces, but it acts only through infinites- imal distances. Cohesion is a molecular force. It binds together the molecules into bodies. It is a weaker force than affinity, but is capable of acting through greater, though still insen- sible distances. Gravity is a molar force. It binds together bodies. It is the weakest of the three forces, but is capable of acting through all known distances. 9. Elasticity. Elasticity is the tendency of a body to spring back to its original condition when it has been dis- torted in any way. Any distortion, whether produced by stretching, by bending, by twisting, by compression, or by rarefaction, is called a strain. The force which produces the strain is called a stress. Elas- ticity is always developed by some kind of strain. All bodies 4 ELEMENTS OF are elastic to some extent, but usually, when the distortion pro- ceeds beyond a certain point, the elasticity of the body breaks down. This point is called the limit of the elasticity of the body. 10. Chemical Properties of Matter. The properties of matter which grow out of the atomic structure of the molecules and the action of affinity are called chemical properties. 11. Physical Properties of Matter. The properties of matter which grow out of the molecular structure of bodies and the action of cohesion are called physical properties. 12. The Physical Sciences. The physical sciences deal with the action of forces on material units, irrespective of the phenomena of life. Mechanics deals with the action of forces and the laws of motion, irrespective of any order of material units. Astronomy deals with gravity and molar units. Physics deals with cohesion, molecules, and physical properties of matter. Chemistry deals with affinity, atoms, and chemical prop- erties of matter. Natural Philosophy includes both Mechanics and Phys- ics. NATURAL PHILOSOPHY. II. MECHANICS. A. DEFINITIONS. UNITS. NEWTON'S LAWS OF MOTION. 13. The Three Fundamental Units. The three funda- mental units of Mechanics, from which all the other me- chanical and physical units are derived, are the unit of time, the unit of length, and the unit of mass. In the English system these units are the second, the foot, and the pound (avoirdupois). In the French system they are the second, the centimetre, and the gramme. 14. English and French Units of Length. The English standard unit of length is the yard, which is divided into three equal parts, called feet. The foot is subdivided into twelve equal parts, called inches. The yard is simply the length marked on a certain rod preserved by the govern- ment. The French standard unit of length is the metre. This is, theoretically, the ten-millionth of the distance from the equator to the pole, or the forty-millionth of the distance round the earth. Practically, it is the length of a rod preserved by the French government, which differs appre- ciably from the theoretical length of the metre. The metre is about 3^ feet. It is divided into ten, one hundred, and one thousand equal parts, called decimetres, centimetres, and millimetres. Decametre, hectometre, and kilometre are, re- spectively, ten metres, one hundred metres, and one thou- sand metres. In the French or Metric system of units the prefixes deci, centi, and milli always indicate tenths, hun- 6 ELEMENTS OF dredths, and thousandths of the unit, while the prefixes deca, hecto, and kilo always indicate tens, hundreds, and thousands of the units. For readily comparing the French units of length with our familiar English units, it will be convenient to remember that a metre is about forty inches ; a decimetre, about four inches ; a centimetre about T 4 ff of an inch ; and a millimetre, about -fa of an inch. A kilometre is about five furlongs, or | of a mile. 15. Units of Surface and of Volume. The units of sur- face are squares, one of whose sides is the unit of length. Thus, the English units of surface are the square yard, the square foot, and the square inch. The French units of surface are the square metre, the square decimetre, and the square centimetre. The units of volume are cubes, one of whose edges is the unit of length. The English units of volume are the cubic yard, the cubic foot, and the cubic inch. The French units of volume are the cubic metre, the cubic decimetre, and the cubic centimetre. The French unit of capacity is the cubic decimetre. It is called the litre, and is equal to about if pints, or a little less than a quart. 1 6. Units of Mass. The mass of a body is the quantity of matter w r hich it contains. The English unit of mass is the mass of a certain piece of metal preserved by the gov- ernment and called the pound avoirdupois. It is divided into 7000 equal parts, called grains. The French unit of mass is the mass of a cubic centimetre of water at its maximum density. It is called a gramme, and is equal to about 15^ grains. A kilogramme is equal to about 2\ pounds. 17. Unit of Density. The density of a body is the quantity of matter in a unit of its volume. The density of water at a temperature of 39 F. is usually taken as the unit of density. 18. Units of Velocity. Velocity is rate of motion. The NATURAL PHILOSOPHY. 7 English unit of velocity is the velocity of one/00/ a second. The French unit is the velocity of a centimetre a second. When we speak of the velocity of a body as being five, ten, or twenty feet a second, we mean that, at the instant to which we refer, the body is moving fast enough to go five, ten, or twenty feet in a second, provided it were to keep on moving at the same rate. It does not, however, follow that it will actually go five, ten, or twenty feet in a second, for its rate may change. 19. The Action of Forces on Matter. Any push or pull, of whatever origin, upon any portion of matter is called a force. In the realm of matter these forces always act between two different portions of matter. Thus, affinity is a pull between two 'atoms; cohesion, a pull between two molecules; and gravity, a pull between two bodies. The action of a pulling, or attractive, force may be illustrated by fastening two balls to the ends of an india-rubber cord and then separating the balls so as to stretch the cord. The stretched cord will pull upon both balls. The action of a push- ing, or repulsive, force may be illustrated by placing a rod of india-rubber between two balls and then crowding the balls together. The compressed rubber will push upon both balls. This action of a force between two portions of matter takes different names according to the aspect under which it is viewed. When we take into account the whole phenomenon of the action, we call it a stress. This stress, according to the mode in which it acts, may be described as attraction, repulsion, ten- sion, pressure, torsion, etc. When we confine our attention to one of the portions of matter, we see only one aspect of the stress, namely, that which affects the portion of matter under consideration. This aspect of the phenomenon we call, with reference to its effect, an external force, acting upon that portion of matter, and, with reference to its cause, the action of the other portion of matter. The opposite aspect of the stress is called the reaction on the other portion of matter. 20. Newton's First Law of Motion. Every body perse- veres in its state of rest or of moving uniformly in a straight line, unless compelled to change this stale by external forces. 8 ELEMENTS OF This is Newton's first law of motion. No portion of matter in the universe, so far as known, is absolutely at rest. Were there such a portion of matter, it could be put in motion only by an external force. Bodies are commonly spoken of as at rest when they are not changing their positions with respect to other bodies around them. Thus, we say that a body is at rest on the deck of a steamer, though it is really moving forward with the steamer ; and that bodies are at rest on the surface of the earth, though they are moving along with the earth. In all such cases bodies are oifly relatively at rest. In common language bodies are said to be at rest with respect to each other when they are all moving along at the same rate and in the same direction. When, in common language, a body is said to be put in motion, what really takes place is that its motion is changed either in rate or direction. Unless acted upon by external forces, a moving body would always go on in a straight line and at a uniform rate. This seems to be contradicted by common experience. All moving bodies at the surface of the earth show a decided tendency to stop. But all such moving bodies are acted upon by some external force acting as a resistance. The chief resistances encountered by moving bodies 2ccz friction and resistance of the atmosphere. In proportion as these resistances are diminished, the longer is the time a body will continue to move. A smooth stone is soon brought to rest when sliding over the surface of the earth. The same stone will slide much longer over ice, where there is less friction. A top that will spin for ten minutes in the air will spin more than half an hour in a vacuum. Since the time a body will continue in motion increases in proportion as the resistance is diminished, we may reasonably infer that, were the resistance entirely removed, the body would continue in mo- tion forever. 21. Inertia. The tendency of a body to persevere in its state of rest or motion is called inertia. The inertia of a NATURAL PHILOSOPHY. body is directly proportional to its mass. This inertia must be overcome by some external force in order to put a body in motion, or to change the rate or direction of its motion. It takes time for a force to overcome the inertia of matter. Hence, when a body receives a sudden blow, the part of the body immediately receiving the blow yields before there is time to overcome the inertia of the surrounding parts. There are many striking illustrations of inertia. If a number of checkers are piled up in a column, one of them may be knocked out by a very rapid blow with a table knife without overturning the column. A feeble blow will fail. Stick two needles into the ends of a broomstick and rest the needles on Fig. i. two glass goblets, as shown in Figure I. Strike the middle of the stick a quick, sharp blow with a heavy poker. The stick will break without breaking the needles or the goblets. Here again a feeble or indecisive blow will fail. A soft body, fired fast enough, will hit as hard as lead. A tallow candle may be fired from a gun through a pine board. 22. Centrifugal Forfe. The so-called centrifugal force is an illustration of Newton's first law of motion. It is simply the tendency of the parts of a rotating body to keep moving in straight lines. This tendency increases with the speed of rotation, and sometimes to such a degree as to overcome the cohesion of the body. In this case the body will fly in pieces, as large grindstones and heavy fly-wheels have been known to do. If a stone is fastened to the end IO ELEMENTS OF of a string and twirled rapidly around the ringer, the ten- dency of the stone to fly off in a straight line may become sufficient to break the string. Iti this case the stone will start off in a line tangent to the circle it was describing. This tendency to move on in a straight line must be counteracted by the force acting towards the centre, in order to keep a body moving in a circle. The faster the body moves, the greater the pull needed to keep the body Fig. 2. in its circular path. The greater the pull upon the body towards the centre, the greater the pull of the body away from the centre. The pull upon the body towards the cen- tre is called the centripetal force, and the pull of the body aw ay from the centre is called the centrifugal force. These two forces are only the two aspects of the stress of attraction between the body and the centre about which it is revolving. The pull of a revolving body away from the centre may be illustrated by the pieces of apparatus shown in Figures 2 and 3- In the first, two balls M and M' are placed on the rod NATURAL PHILOSOPHY. I I Fig.*. A B, which passes through them. The rod is then put in rapid rotation by turning the crank, and the balls fly apart. If the flexible rings of Figure 3 are whirled in place of the rod, they will become more and more flattened as the speed of rotation increases. This change of form is due to the pull of each part of the rings away from the central axis. The pull will be greatest at the central point of the rings, because this part is moving fastest. It was in this way that the earth became flattened at the poles while in the fluid state. The centrifugal railway (Figure 4) shows a curious effect of this outward pull. A carriage starting from A descends the incline to B, passes up around the circle C, and then up the incline to D. The outward pull of the carriage due to its velocity is sufficient to keep it against the rails while passing around the circle, though it is part of the time travelling bottom up. Fig. 4. 23. Stability of a Rotating Body. The tendency of the particles of matter to keep moving in the same plane explains why a top will stand upright so long as it is spinning rapidly, though it topples over at once as soon as it comes to rest. For the same reason a bicycle is not easily overturned while its large wheel is in rapid rotation. 24. External Forces tend to put Bodies in Motion or to 12 ELEMENTS OF change their Velocities. Suppose a rubber cord fastened at one end to a body, not acted on by any other force than the tension of the cord, and suppose the cord to be kept stretched to the same extent all of the time, so as to exert a uniform pull upon the body. The body will begin to move in the direction of the pull, and will move faster and faster the longer the pull continues, gaining the same amount of velocity each second. If it were moving at the rate of two feet a second at the end of the first second, it will be moving at the rate of four feet a second at the end of the second second, at the rate of six feet a second at the end of the third second, and so on. 25. Units of Force. Forces may be measured either by the pressure which they would produce or by the rate at which they would increase the velocity of a mass of matter. In the former case the unit of force is the force of gravity on a unit of mass. In the English system it is the force of gravity on the mass of a pound or a grain, and is called a. pound or a grain. In the French system it is the force of gravity on a mass of a gramme, and is called a gramme. These units are called gravitation units ; and since they depend upon the intensity of gravity, they are variable, changing with the intensity of gravity at different places on the surface of the earth, and at different eleva- tions above the surface. In the latter case the unit of force is the force that will impart to a unit of mass a unit of velocity in a unit of time. In the English system it is the force that will impart to a mass of a pound a velocity of a foot in a second. It is called & poundal. At Greenwich it takes 32.2 poundals of force to hold up a pound. A system of absolute measurement has been devised in England, and adopted by the British Association. The units pf this system are all based upon the centimetre, gramme, and NATURAL PHILOSOPHY. 13 second as the three fundamental units of length, mass, and time. This system of measurement is called the centimetre- gramme-second system, or more briefly, the C. G. S. system. Its units are called the centimetre-gramme-second units, or more briefly, the C. G. S. units. In the C. G. S. system the unit of force is the force that will impart to a mass of a gramme a velocity of one centimetre a second. It is called a dyne. It takes 445,000 dynes of force to hold up a pound at Greenwich. These units are indepen- dent of gravity, and are invariable. They are called absolute units. 26. The Impulse of Force. The effect of a force in producing motion is directly proportional to its intensity and the time during which it acts. The product of the intensity and the time during which it acts is called the impulse of the force. 27. Momentum. The motion of a body is measured by the mass and the velocity of the body, and is directly propor- tional to the two. If two bodies have equal velocities, but one has five times the mass of the other, it is said to have five times the motion ; or if the two have equal masses, and one has five times the velocity of the other, it is said to have five times the motion of the other. The, product of the mass of a body and its velocity is called the momentum of the body. 28. Newton's Second Law of Motion. Change of motion is proportional to the impressed force, and takes place in the direction in which the force acts. This is Newton's second law of motion. By motion, as here used, Newton means what is now called momentum, in which the quantity of matter moved is taken into account as well as the rate at which it travels. For in- stance, there would be the same change of motion, whether the velocity of four pounds was changed one foot a second, or the velocity of one pound four feet a second- Jn either case the change of momentum would be four. 14 ELEMENTS OF By impressed force Newton means what is now called im- pulse, in which the time the force acts is taken into account as well as the intensity of the force. Thus, the impulse, or im- pressed force, would be the same whether a force of a poundal were acting five seconds or a force of five poundals were acting one second. In either case the impulse, or impressed force, would be five. Newton's second law, stated in terms of momentum, would be : The change of momentum of a body is numerically equal to the impulse which proditced it, and is in the same direction. An unbalanced external force acting upon a body always changes the velocity of the body in the direction in which it acts. This change of velocity is called acceleration. The acceleration produced in a given time by a force acting upon a body is precisely the same whether the body is at first at rest or in motion, or whether the force is acting alone or with other forces. When the acceleration is opposed to the original motion of a body, it is usually called a retardation. Newton's second law, stated in terms of acceleration, would be : When any number of forces act upon a body, the accelera- tion due to each force is the same in magnitude and direction as if the others had not been in action. The total acceleration produced by the action of a force is directly proportional to the impulse of the force, and inversely proportional to the mass acted upon. A force of 40 poundals acting for 20 seconds upon a mass of 50 pounds would produce an acceleration of 40 X 20 -f- 50 = 16 feet. A force of 300 dynes acting 80 seconds upon 200 grammes would produce an accel- eration of 300 X 80 -r- 200 := 1 2o centimetres. The total change of momentum produced by the action of a force is numerically equal to the impulse of the force. A force of 40 poundals acting 30 seconds would produce a change of momentum equal to 40 X 30= 1200 units (English). A force of 250 dynes acting 20 seconds would produce a change of mo- mentum equal to 250 X 20 = 5000 units (C. G. S.)- NATURAL PHILOSOPHY. 15 QUESTIONS ON NEWTON'S SECOND LAW. 1. What acceleration would be produced by a force of 30 poundals acting on a mass of 80 pounds for 70 seconds ? 2. What acceleration would be produced by a force of 240 dynes acting on amass of 3 kilogrammes for 3 minutes ? 3. What must be the intensity of a force that would give 90 pounds an acceleration of 1000 feet in 20 seconds ? 4. What must be the intensity of a force that would give a mass of 80 grammes an acceleration of 50 metres in 2 minutes ? 5. What must be the mass of a body to which a force of 60 poundals would give an acceleration of 500 feet in 30 seconds ? 6. What must be the mass of a body to which a force of 500 dynes would give an acceleration of 8 decimetres in 8 seconds ? 7. What momentum would IDC imparted to a body by a force of 70 poundals in 90 seconds ? 8 What momentum would be imparted to a body by a force of 350 dynes in 75 seconds ? 9. What force would be needed to change the momentum of a body 300 units (English) in 9 seconds ? 10. What force would be needed to change the momentum of a body 900 units (C. G. S-) in 60 seconds? 11. How long will it take a force of 120 poundals to impart a momentum of 700 units to a' body ? 12. How long would it take a force of 600 dynes to impart a momentum of 19,000 units to a body ? 13. How long would it take a force of 20 poundals, acting in the opposite direction to the motion of the body, to stop a body having a momentum of 300 units ? 14. How long will it take a force of 80 dynes, acting in the opposite direction to the motion of the body, to stop a body hav- ing 1000 units of momentum ? Fig. 5. 29. Parallelogram of Motion. To find "* the path of a body A (Figure 5) acted on by two forces at the same time, draw A B to represent the path the body would have taken had it been acted on by the first force alone, and A C to represent the path it would have taken had it been acted on c i6 ELEMENTS OF by the other force alone. Through B draw B D parallel to A C, and through C draw CD parallel to AB so as to complete the parallelogram A B D C. Draw the diago- nal AD. This diagonal will represent the path taken by the body when acted upon by both forces together. 30. Newton's Third Law of Motion. Newton's third law of motion is as follows : Reaction is always equal and opposite to action ; that is to say, the actions of two bodies upon each other are always equal and in opposite directions. This law simply states the fact that a force always acts upon two portions of matter (19), and that the stress, whether that of tension or pressure, is equal upon both portions. A stone raised from the earth attracts the earth just as much as the earth attracts the stone. Gravity really acts as a stress of ten- sion between the two, and pulls th'em equally but in oppo- site directions. When the stone falls the earth moves up to meet it. When the two meet they have each the same momen- tum, but the earth, owing to its great mass, has only a very small velocity. W T hen a cannon is fired, the igniting powder pushes back upon the cannon just as hard as it pushes forward on the ball. Were the cannon as free to move as the ball, it would start back, or recoil, with the same momentum that the ball starts forward with, but of course with a less velocity. 31. Collision of Elastic Bodies. We have an illustration of action and reaction in the collision of elastic bodies. Place two ivory balls of exactly Fig. 6. the same size at the centre of the curved railway in Figure 6. Move one of the balls up to one end of the track, and let it roll back against the ball at rest- There will be a slight strain of compression when NATURAL PHILOSOPHY. 1 7 the balls strike, and this will develop a stress of elasticity be- tween them which will act equally upon both and in opposite directions. This stress will stop the first ball and start the second off with the velocity the first had on striking it. Place several ivory balls of the same size on the centre of the track, and allow the first ball to roll against the end of "the line. All the balls will remain at rest except the last, which will be shot up the track. In this case the strain of compression and stress of elasticity have been propagated along the line from ball to ball. Each ball has been compressed a little in turn, and in recovering itself has pushed upon the ball behind it enough to stop it, and upon the one in front enough to flatten it a little. Each ball except the last was kept from moving forward by the reaction of the ball in front. B. WORK AND ENERGY. 32. Work. Work is said to be done when anything is moved against resistance. We may consider work either with reference to the force that moves the body, or with reference to the resistance overcome. When we think of the force as moving the body, we say that work is done by the force upon the body. When we think of the resistance as overcome by the body, we say that work is done by the body upon the resistance. When we think of the resist- ance as impeding the motion of the body, we say that work is done by the resistance upon the body. These terms apply to different aspects of the same work. Thus, when we raise a weight, in winding up a clock, we may say that work is done by the force used upon the weight, or by the weight upon or against gravity, or by gravity upon the weight. The amount of work done is the same in whatever aspect we view it. When the clock weight runs down again, we may say that work is done by gravity upon the weight, or by the weight upon the resistance of the wheels, or by the resistance of the wheels upon the weight, according to the aspect in which we view the work. When a weight is allowed to fall freely to the earth, the work done is that of increasing the l8 ELEMENTS OF velocity of the body. In this case work is done by gravity upon the body, and by the body upon its inertia. Work is done in every case in which the velocity of a body is changed, for the inertia of the body always resists this change. . 33. Units of Work. The unit of work is the work done in moving anything a unit of distance against a unit of re- sistance, or by a unit of force acting through a unit of distance. A resistance is, of course, merely the opposing action of some force, and is measured in poundals or dynes. The English unit of work is the work done in moving a mass against a poundal of resistance, or by the force of a poundal acting one foot. It is called &foot-poundal. The C. G. S. unit of work is the work done in moving a mass one centimetre against a dyne of resistance, or by the force of a dyne acting one centimetre. It is called an erg. There are 421,393.8 ergs in a foot-poundal. These are absolute units. The gravitation unit of work is the work done in raising a unit of mass a unit in height. The English gravitation unit is the work done in raising a pound one foot high. It is called a foot-pound. It varies with the force of gravity in different parts of the earth and at different elevations. At Greenwich there are 32.2 foot-poundals in a foot- pound. 34. Energy. Energy is the capacity for doing work. It is measured in the same units as work, a unit of energy being the capacity for doing a unit of work. Thus, we may speak of so many foot-poundals, or of so many ergs, of energy. The force that tends to stop a moving body acts upon it as a resistance, and every moving body has the power to overcome this resistance through a greater or less distance according to its momentum and velocity. Hence every moving body has a capacity for doing work, or energy. A body which is not in motion may have a capacity for doing NATURAL PHILOSOPHY. 19 work growing out of its condition with respect to some force. Thus, a raised weight has the ability to drive a clock, compressed steam the ability to drive a locomotive, and a coiled spring the ability to drive a watch. 35. Position of Advantage. A body is said to have a position of advantage with respect to a force when it is so situated that it is possible for that force to put it in motion. A weight raised from the earth has a position of advantage with respect to gravity, since it is possible for gravity to put it in motion by pulling it to the earth again. For a similar reason molecules when separated from each other have positions of advantage with respect to cohesion ; and atoms when separated from each other, with respect to affinity. A strained body has a position of advantage with respect to elasticity. 36. Kinetic Energy. The energy of motion is called kinetic energy. The kinetic energy of a body is equal to the product of the momentum of the body and % its velocity. Now we may regard this work either as work done by the force acting as a resistance upon the body or by the body upon the resistance. 37. Potential Energy. The energy of position is called potential energy. It is universally true that a body, in re- turning from a position of advantage to its original posi- tion, does exactly the same amount of work that was done upon it in putting it in its position of advantage. Thus, to raise a pound weight 12 feet high requires 12 foot-pounds of work. The same weight, in falling 12 feet, will do 12 foot-pounds of work. If it takes 300 ergs of work to coil a spring, the spring in uncoiling will do 300 ergs of work. Hence the potential energy of a body is equal to the work required to put the body in its position oj advantage. 20 ELEMENTS OF QUESTIONS ON ENERGY. 15. How many foot-poundals of energy has a mass of 2500 pounds with a velocity of 5000 feet a second ? 1 6. How many ergs of energy has a mass of 8965 grammes with a velocity of 8000 centimetres a second ? 17. How many foot-poundals of energy has a mass of 3 tons with a velocity of 500 feet a second ? 1 8. How many ergs of energy has a mass of 9 kilogrammes with a velocity of 8 metres a second ? C. COMPOSITION AND RESOLUTION OF FORCES. 38. Representation of Forces by Lines. A force may be completely represented by a line ; the length of the line representing the intensity of the force, the direction of the line the direction in which the force acts, and one end of the line \hz point of application of the force. 39. Resultant and Component Forces. There is usually some one force that would have the same effect upon a body, in producing pressure or motion, as that of the several forces that may be acting together upon it. This force is called the resultant of these forces, and they are called its components. 40. Composition and Resolution of Forces. The combin- ing of several forces into one resultant is called the composi- tion of forces ; and the decomposition of one force into two or more components, the resolution of forces. In the composition and resolution of forces it is necessary to find the intensity, the direction, and the point of application of the resultant or components. 41. The Parallelogram of Forces. Of the great vari- ety of cases that may occur in the composition of forces, the most important is that in which two forces act upon a point in different directions. For example, let the two forces A B and A C (Figure 7) be acting upon the point A in the directions indicated by the arrows. Through NATURAL PHILOSOPHY. 21 Fig. 7 . V B draw the line B D parallel to A C ; and through C, the line CE parallel to A B, so as to form the parallelogram ABRC. The diagonal A R of this parallelogram will be the resultant of these two for- ces. This method is called the parallelogram of forces. If a force A G (Figure 8), having the intensity of the result- ant A R, but the opposite direction, were applied to A, it would balance this resultant, and, there- Fig. 8. fore, its components A B an.d AC. The fact that the resultant of a- forces may be balanced by an equal force applied to the same point in the opposite direction en- ables us to find the resultant of forces experimentally, and so to verify the above method. The apparatus for this experimental Fig. 9. determination is shown in Figure 9. A B D C is a parallelogram jointed at its four corners. Cords pass from the corners B and Cover the pulleys M and N. Weights P and P' are attached ELEMENTS to the ends of these cords. The number of ounces in the weight P is equal to the number of inches in the side A B j and the number of ounces in P', to the number of inches in A C. Hang from A a weight P", less than the sum of P and P'. The parallelogram will take up a position of equilibrium such that the cords attached to B and C will be found to form pro- longations of the sides A B and A C, and the diagonal A D will be vertical. The number of inches in the diagonal will be found to be equal to the number of ounces in the weight hung from A. The two forces P and P' which are acting on the point A are represented by the lines A B and A C, and their resultant by the diagonal A D. This vertical resultant is bal- anced by the equal force P" acting in the opposite direction. 42. Composition of Several Forces acting in Different Direc- tions upon a Point. When more than two forces, A B, A C, A D, and A E (Figure 10) are acting in different directions upon a point A, their resultant may be Fig 1It found by the following method : First find the resultant A K*- of the two forces A B and A C ; then the resultant A R 1 of the first resultant A 7? 1 and of the third force AD; and, finally, the resultant A R z of the second resultant A R* and of the fourth force A E. This last result- ant will be the resultant of all the forces. 43. Resolution of a Force into two Oblique Forces. To resolve the force A R (Figure 11) into two forces having the directions A B and A C, draw R M parallel to A C, and R N parallel to A B. A A" and A J/will represent the forces required. The resolution of forces may be illustrated by the case of a vessel sailing in any other direction than that of the wind. NATURAL PHILOSOPHY. 23 Let the line A B (Figure 12) represent the direction of the keel of the vessel ; the line CD, the direction of the face of the sail ; and the line WE, the direction and intensity of the wind. To find the intensity of the force which would be effective in driving the vessel forward, first resolve the force of the wind IV E into two components, one D E tangent to the sail, and the other FE perpendicular to the Fig. 12. sail. This latter component will be the only part of the force of the wind that will have any effect upon the sail. This force must again be resolved into two com- ponents, one G E perpendicular to the length of the vessel, and the other HE in the direction of the vessel. This last component will be the only portion of the force of the wind that will be effective in moving the vessel forward. D. GRAVITY AND EQUILIBRIUM. 44. Law of Gravity. The law of gravity was discovered by Newton. It is as follows : Every portion of matter attracts every other portion of matter with a force directly proportional to the product of the masses acted Fig. 13. upon, and inversely proportional to the square of the distances be- tween them. 45. Centre of Gravity. The direction of gravity at the surface of the earth is that of a plumb- line. Gravity acts upon every particle of which a body is com- posed, but the parallel forces acting upon the various particles may be resolved into one, and the point of application of this resultant is called the centre of ELEMENTS OF gravity of the body. Thus, G is the centre of gravity in the stone in Figure 13. The whole of the force of gravity act- ing upon a body may be considered as applied at the centre of gravity. If a force equal to the resultant of the forces of gravity is applied to the centre of gravity in the opposite di- rection, the body will balance or be in equilibrium. The centre of gravity may therefore be defined as the point upon which the body will balance in every position. When a body is homogeneous throughout, the centre of grav- ity is at the centre of figure of the body. When the body is not homogeneous throughout, the centre of gravity is away from the centre of figure towards the denser side of the body. The centre of gravity often lies entirely outside of the material of the body, as in the case of a ring or a hollow sphere. When this is the case, the centre of gravity must be rigidly connected to the body in order to have the body balance on it. A system of bodies may have a common centre of gravity lying outside of all the bodies. The centre of gravity of two spheres will lie somewhere on a line between their centres of gravity. If the spheres have the same mass, this point will lie just midway between their centres of gravity. If one sphere has a greater mass than the other, the centre of gravity of the system will lie nearer the centre of gravity of the larger sphere. If there is sufficient difference between their masses, their common centre of gravity may lie within the larger sphere. 46. Experimental Method of finding the Ce?itre of Grav- Fig. 14 ity. Since the result- ant of the forces of grav- ity acting upon a body, and the force which bal- ances it, must act along the same line in opposite directions, the centre of gravity of a body sus- pended so as to turn freely must be in a ver- NATURAL PHILOSOPHY. 2$ tical line under the point of suspension. Hence, if we sus- pend any body from two points and mark the vertical lines from each point of suspension (Figure 14), the centre of gravity must be where these verticals cross. 47. Kinds of Equilibrium. When a body, on being tipped a little, tends to return to its old position, it is said to be in stable equilibrium ; when it tends to fall to a new position, in unstable equilibrium ; and when it rests equally well in every position, in indifferent equilibrium. When a body is in stable equilibrium, its centre of grav- ity rises on tipping the body ; when it is in unstable equi- librium, its centre of gravity falls on tipping the body ; and when it is in indifferent equilibrium, its centre of grav- ity neither rises nor falls on tipping the body. Fig. 15. Fig. 16. 48. Equilibrium of a Body resting on a Fixed Point or Axis. A body resting on a point or axis can be in equi- librium only when the centre of gravity and the point or axis of support lie in the same vertical line. This can be the case only when the centre of gravity is either directly above or below the point or axis of support. In the former case the body is in unstable equilibrium. This case is shown in Figure 15. O is the axis of support, and G the centre of gravity. It will be seen that gravity will tend to 26 ELEMENTS OF Fig. 17. topple the body over as soon as it is tipped. In the latter case the body is in stable equilibrium. This case is shown in Figure 16. As soon as the body is tipped gravity tends to right it. The toy called the balancer (Figure 17) is an illustration of stable equi- librium in a body resting on a point. The balls at the ends of the wires at each side of the figure bring the centre of gravity of the whole below the toe on which the figure is resting. In a similar way a Fig. is. cork may be balanced on the point of a needle by sticking two forks into it, as shown in Figure 18. When the centre of' gravity is at the point or axis of support, the body is in indifferent equilibrium. 49. Equilibrium of a Body resting on a Horizontal Plane at One Point only. Such a body can be in equilibrium only when its centre of gravity and the point where it Fig. 19. touches the plane are both in the same vertical. Figure 19 represents two positions of equilibrium of an oval body on a horizontal plane. In the first case the body is in unstable equilibrium, because its centre of gravity will NATURAL PHILOSOPHY. begin to fall as soon as it is tipped. In the second case the body is in stable equilibrium, because its centre of gravity is in its lowest possible position. Fig. 20. The toy call ler (Figure 20) is an illustration of stable equilibrium of a body touching a horizontal plane at one point. The centre of gravity is so low down that the body can- not be tipped without raising this point. 50. Equilibrium of a Body resting on a Horizontal Plane at Several Points. Such a body will be in stable equilib- rium when the vertical line Fig. 21. from its centre of gravity passes within the polygon formed by joining the several points on which the body rests, as in Figure 21. This poly- gon is called the base of the gi body. The lower the centre y of gravity, and the greater the distance of its vertical from the nearest side of the base, the greater the stability of the equilibrium of the body, because the farther the body would ha^e to be tipped, and the more its centre of gravity would have to be raised, to overturn it (Figure 22). In Figure 22, in order to overturn either of the bodies abed, we must tip it so as to carry its centre of gravity through the raise it through the distance he; and it is evident that he are greater in the case of the right-hand body. 28 ELEMENTS OF For this reason a high load on a wagon is more likely to tip over than a low one. A leaning body, like the famous Leaning Tower at Pisa, may be in stable equilibrium, because the verti- cal from the centre of gravity falls within the base. Fig. 22. 51. Weight. Weight is the downward pressure which gravity causes a body to exert. While a body will have the same mass wherever it may be, its weight will vary with the force of gravity acting upon it. As this force is in- versely proportional to the square of the distance (44), at twice the distance from the centre of the earth a body would have only one fourth the weight it has at the sur- face of the earth. On the sun, which has a much greater mass than the earth (44), the same body would have 28 times the weight it has on the earth. The English unit of weight is the pound avoirdupois ; the French unit is the gramme. The weight of a body is ascertained either by finding how much it will bend a spring, as in the spring balance, or by find- ing how many known weights at one end of a beam will coun- terpoise it when placed on the other end, as in the ordinary balance. By the last method the weight of the body would be found to be the same everywhere, for it is not the weight of the body which is found in this case, but its mass. This is found by comparing the weight of a body with that of a known mass. The weight of the mass to be weighed, and that of the mass used to counterpoise it, both change with the force of gravity. NATURAL PHILOSOPHY. 2 9 Fig. 23. 52. The Balance. The balance (Figure 23) consists of a rigid bar A B, called the beam, supported on an axis O at its centre. This axis is just above the centre of gravity of the beam, that the beam may be in stable equilibrium. When the beam is exactly horizontal, it is in equilibrium. Two scale pans are suspended from the ends of the beam at equal distances from the axis. The body to be weighed is placed in one pan, and is counterpoised by known weights in the other. 53. Specific Gravity. The specific gravity of a sub- stance is its weight compared with the weight of the same bulk of some standard substance. The substance commonly taken as the standard for solids and liquids is distilled water at a temperature of 39 F. A cubic foot of such water weighs 62.425 Ibs. avoirdupois. The weight of a gallon of water is 10 Ibs. The weight of a cubic centi- metre of water is a gramme, and the weight of a litre of water is a kilogramme. In the following table we give the specific gravities of some liquids and solids. Liquids, at Temperature of Freezing Water. Water, sea, .... 1.026 Alcohol, pure . . . .791 " proof spirit . .916 Ether 716 Mercury .... 13.596 Naphtha 848 Oil, linseed 940 " olive 915 " whale 923 " turpentine . . . .870 Blood, human . . . .1.055 Milk, of cow . . . .1.03 ELEMENTS OF Solids. Copper 8.95 Gold 19.26 Iron 7.79 Indium 22.4 Lead 11.4 Platinum . . . . 21.5 Silver 10.5 Tin 7.3 Zinc 6.9 Ice 92 Basalt 3.00 Clay 1.92 Glass, crown ... 2.5 " flint .... 3.0 Quartz (rock crystal) . 2.65 Fir, spruce 48 to .7 Oak, European . .69 to .99 Lignum-vitae . . 65 to 1.33 The weight of a cubic foot of any substance is equal to 62.425 Ibs. avoirdupois multiplied by its specific gravity. The weight of a cubic centimetre of any substance, in grammes, is equal to its specific gravity. The weight of a litre (or cubic decimetre) of any substance, in kilogrammes, is equal to its specific gravity. The weight of a gallon of any liquid, in Ibs. avoirdupois, is equal to its specific gravity multiplied by 10. QUESTIONS ON THE ABOVE TABLE. 19. What is the weight of a cubic foot of mercury ? 20. What is the weight of a gallon of milk ? 21. How many gallons in 50 Ibs. of pure alcohol ? 22. What is the weight of 15 litres of ether ? 23. How many litres in 8 kilogrammes of olive oil ? 24. What is the weight of a cubic yard of clay ? 25. What is the weight of a cubic foot of flint glass ? 26. What is the weight of a cubic inch of silver? 27. How many cubic feet in a ton of ice ? 28. How many cubic inches in a pound of quartz ? 29. What is the weight of a cubic decimetre of silver? 30. What is the weight of a cubic metre of lead ? E. FALLING BODIES. 54. All Bodies fall at the Same Rate in a Vacuum. ~ That light and heavy bodies fall at the same rate in a vacuum may be shown with the guinea and feather tube NATURAL PHILOSOPHY. (Figure 24). The tube contains a bit of metal and a feather. Exhaust the air from the tube, and invert the tube. The metal and the feather will Fig. 24. be seen to fall through the tube at the same rate. The reason that light and heavy bodies fall in a vacuum at the same rate is that the force of gravity acting upon a body varies directly as the mass of the body. The force of gravity on a mass of a pound is about 32 poundals ; on a mass of two pounds, 64 poundals ; on a mass of half a pound, 16 poundals ; on a mass of one ounce, 2 poundals ; etc. The force of gravity on a mass of one gramme is about 981 dynes; on a mass of a decagramme, 9810 dynes ; on a mass of a decigramme, 98.1 dynes; etc. Since the intensity of the gravity acting upon a body increases just as rapidly as the mass of the body, gravity, if left to itself, would cause all bodies to fall at the same rate ; for if the mass of one body is twice or thrice as great as that of another, gravity will act upon it with twice or thrice the intensity. 55. Bodies fall with Unequal Veloci- ties in the Air. A bullet will fall through the air much faster than a feather. The air offers resistance to every body falling through it. The denser a body and the less its surface, the less its motion is re- tarded by the air. Gold-leaf falls slowly in the air, while the same gold in the form of a solid sphere would fall almost as rapidly in the air as in a vacuum. The resistance of the air increases with the velocity, and after a while it becomes equal to the attraction of gravity upon a body. When this is the case, the body will gain no more 32 ELEMENTS OF velocity, but keep falling at a uniform rate. Were a body shot downward with a velocity greater than this, it would be retarded by the resistance of the air, which would then be greater than the pull of gravity, until its velocity were reduced to that at which the resistance of the air would be just equal to the pull of gravity. 56. Acceleration produced by Gravity. When bodies are falling near the earth, gravity increases their velocity at the uniform rate of about 32.2 feet a second, in a vacuum. This acceleration per second produced by gravity is usually represented by ", and is called the intensity of gravity. It is equal to about 981 centimetres, or 9.81 metres. When a body is rising, gravity retards its velocity at the rate of 32.2 feet, or 9.81 metres a second. Were a body thrown up in a vacuum, it would be just as many seconds in falling as it is in rising, and it would reach the point it started from with the velocity it had on starting. It gains just as much velocity in falling as it lost in rising. The velocity acquired by a body falling from a state of rest will be equal to the proditct of the intensity of gravity and the number of seconds the body has been falling. If we represent the velocity acquired by ?/, and the number of seconds the body has been falling by /, the formula for the velocity of a body falling from a state of rest will be v=.gt. If a body were falling from a state of rest, the number of feet of velocity it would acquire in 20 seconds would be 32.2 X 20 = 644 ; and the number of metres of velocity it would acquire would be 9.81 X 20 = 196.2. The distance passed over by a moving body is always equal to the product of its mean velocity and the time. Since falling bodies gain velocity at a uniform rate, the mean velocity of a body falling from a state of rest will be one half the velocity it has acquired. As the velocity is =gt, the mean velocity will be ]/2 gt. If we represent the space passed over by s, we shall have The distance passed over by a body falling 4 seconds from NATURAL PHILOSOPHY. 33 a state of rest would be equal to i6.h X 1 6 r= 257.6 feet, or to 4.9 x 16= 78.4 metres. From the formula we have V ~ Z Substituting this value of/ in the formula we have " */ QUESTIONS ON FALLING BODIES. 31. How long would it take a body falling from a state of rest to acquire a velocity of 193.2 feet ? If I Q3- 2 / - = ^= 6 seconds. g 32.2 32. How long would it take a body falling from a state of rest to acquire a velocity of 39.24 metres a second ? v 39.24 / = - = =~ = 4 seconds. 33. How far must a body fall from a state of rest to acquire a velocity of 1500 feet a second ? 7/ 2 2250000 J = 2^ r "644" = 34 93 8 feet - 34. How far must a body fall from a state of rest to acquire a velocity of 800 metres a second ? v 2 640000 s ~ 2g = ~ 19.62 = 3 26l 9-7 metres. 35. How many feet of velocity would a body acquire in falling 25 seconds from a state of rest ? 36. How many metres of velocity would a body acquire in falling 42 seconds from a state of rest ? 37. How long would a body have to fall from a state of rest to acquire a velocity of 986 feet ? 3 34 ELEMENTS OF 38. How long would a body have to fall from a state of rest to acquire a velocity of 25,000 centimetres a second ? 39. How many feet would a body fall from a state of rest in 32 seconds ? 40. How many metres would a body fall from a state of rest in 45 seconds ? 41. How far would a body have to fall from a state of rest to acquire a velocity of 1200 feet a second ? 42. How far would a body have to fall from a state of rest to acquire a velocity of 300 metres a second ? 57. The Height to which a Body can rise. A body moving upward will continue to rise till all of its velocity is exhausted. A rising body loses velocity just as fast as a falling body gains it. Hence the height to which a body can rise with a given velocity is just equal to the height from which it must fall to gain that "velocity. The height to which a body can rise will therefore be represented by the formula In this case s is' the distance a body can rise, and v the velocity with which it starts. The height to which a body can rise increases as the square of the velocity with which it starts. 58. Transformation of Energy in the Case of a Body pro- jected upward. When a body is projected upward, its energy on leaving the surface of the earth is entirely kinetic. As it rises, it moves slower and slower, and so loses kinetic energy, but as it is separated farther and farther from the earth, it gains potential energy. At the highest point the body reaches, its energy is entirely potential. As it falls again, it moves faster and faster, and so gains kinetic energy, but as it comes nearer and nearer the earth, it loses potential energy. While the body is rising its kinetic energy is gradually transformed into poten- tial energy; and when it falls again, its potential energy is changed back again into kinetic energy. The energy possessed by the body is precisely the same at every point in its path. When the body strikes the earth, its energy is apparently destroyed ; but when we come to the subject of Heat, we shall see that this is not really the case. NATURAL PHILOSOPHY. 35 59. The Path of a Body projected horizontally or ob- liquely. When a body is projected horizontally or obliquely, gravity draws it towards the earth faster and faster the longer it acts upon it, and so causes it to describe a curved path. The curve in this case would be a parabola were it not for the resistance of the air. The curved line in Figure 25 shows approximately the path of a cannon-ball through Fig. 25. the air, when fired in the direction of A B. The line A C represents the range of the ball, or the greatest horizontal A distance it is thrown. Were it not for the resistance of the air, the range would be greatest when the cannon was pointed 45 above the horizon. 60. Intensity of Gravity. The intensity of gravity varies as we pass from the equator to the poles. At the equator its intensity is sufficient to give a mass in a vacuum an acceleration of 32.088 feet per second, while at the poles it is sufficient to give a mass in a vacuum an acceleration of 32.253 feet per second. The value of g in centimetres varies from 978.10 at the equator to 983.11 at the poles. The intensity of gravity also varies u'iih the height (44). At twice the distance from the centre of the earth, the intensity of gravity is only one fourth as great ; at three times the distance, one ninth as great ; and so on. Since uponndal is a force that will give to a mass of a pound an acceleration of a foot in a second, and since gravity will give a mass of a pound an acceleration of 32.2 feet a second, it follows that there are about 32.2 poundals in a pound at Greenwich as has already been stated (33). A poundal is about half ar 4 ounce. The number of poundals in a pound at any place is equal to the value of g in feet at that place. Since gravity will give a mass of a gramme an acceleration of 981 centimetres, it follows that there are 981 dynes in a gramme of force at Greenwich. The number of dynes in a gramme at any place is equal to the value of g in centimetres at that place. 36 ELEMENTS OF The value of g at any place is ascertained by means of a pendulum. F. THE PENDULUM. 6 1. The Pendulum. Any body free to turn on a hori- zontal axis which does not pass through its centre of gravity can be in stable equilibrium only when its centre Fig. 26. of gravity is below the axis of support and in the same vertical plane with it. When pulled aside from this position o'f equilibrium and released, the body will vibrate to and fro across its position of stable equilibrium, until friction and the resistance of the air bring it to rest. A body suspended in this way, no matter what its shape, is called a pendulum. The usual form of the pendulum is that shown in Figure 26. It consists of a rod which can turn on an axis O at its upper end, and which carries a heavy piece of metal M, called the ball, at its lower end. The ball can be raised or lowered by means of the screw V. The arc described by the pendulum is called the amplitude of the vibration, and the time it takes to describe it is called the time of vibration. 62. The Laws of the Pendulum. It has been found, by mathematical investigation, that for small vibrations the time of vibration is independent of the amplitude , also, that the time of vibration increases as the square root of the length of the pendulum, and decreases as the square root of the intensity of gravity increases. In other words, when the amplitude does not exceed 3 or 4, the same pendulum will vibrate at the same rate, no matter what may be the amplitude of vibration; but if the pendulum is made four, nine, or sixteen times as long, it will vibrate one half, one third, or one fourth as fast ; while, if a pendulum were kept of the same length, and the NATURAL PHILOSOPHY. 37 intensity of gravity were to become four, nine, or sixteen times as great, the pendulum would vibrate two, three, or four times as fast. 63. Simple and Compound Pendulums. The simple pen- dulum is an ideal one, whose ball is a single heavy particle suspended by a line without weight. Every pendulum actually used is a compound one, consisting of a heavy weight hung from a fixed point by means of a rod of wood or metal. Each particle of such a pendulum may be regarded as a simple pen- dulum ; but as these particles are at different distances from the point of suspension, they tend to vibrate at different rates. The particles near the point of suspension are retarded by the tendency of the particles below them to vibrate at a slower rate, while the particles near the lower end of the pendulum are accelerated by the tendency of the' particles above them to vibrate more rapidly. At some point between these there must be a particle whose vibration is neither retarded nor accelerated. As this particle is vibrating at its normal rate, its distance from the point of suspension must be the length of a simple pendulum that would vibrate at the rate of the compound pendulum. The point where this particle is situated is called the centre of vibra- tion and its distance from the point of suspension, the virtual length of the pendulum. If a pendulum is inverted and suspended by its centre of vibration, the former point of suspension becomes its new centre of vibration. This remarkable property of a compound pen- dulum enables us readily to find the centre of vibration. We have only to reverse the pendulum, and find, by trial, the point at which it must be suspended to vibrate at the same rate as before. A pendulum constructed for this purpose is called a reversible pendulum. 64. Use of the Pendulum for measuring Time. The most important use of the pendulum is for measuring time. A common clock is an instrument for keeping a pendulum in vibration, and recording its beats. The essential parts of the arrangement by which this is accom- plished are shown in Figure 27. The 'scape-wheel R is turned ELEMENTS OF by a weight or spring, and its motion is regulated by means of the escapement m n. This turns on the axis o, and is connected Fig. 27. with the pendulum rod by means of the forked arm a b. When the pendulum is at rest, the hooks n and in of the escapement catch the teeth of the scape-wheel, and keep it from turning. As the pendulum vibrates, the hooks of the escapement alternately release and catch the teeth of the scape- wheel, and so compel it to turn slowly, and at a uniform rate. The hooks of the es- capement are of such shape that each tooth of the scape-wheel, as it slips off the hook, gives the escapement a little push so as to keep up the vibration of the pendulum. Each tooth of the scape-wheel is caught twice during the revolution of the wheel, once by each hook of the escapement. Hence, if the scape-wheel has thirty teeth, it will make one revolution for every sixty beats of the pendulum. The axis of the scape-wheel carries the second-hand of the clock, which registers the beats of the pen- dulum up to sixty. The scape-wheel is con- nected with another which turns g 1 ^ as fast. The axis of this wheel carries the minute- hand, which registers the revolution of the second-hand up to sixty. This second wheel is connected with a third which turns i 1 ^ as fast as itself. The axis of this last wheel carries the hour- hand, which registers the revolution of the minute-hand up to twelve, or half a day. 65. Transformations of Energy in the Vibrations of the Pendulum. When the pendulum reaches its farthest point to the right or left, its energy is entirely potential ; and when its ball is at its lowest point, its energy is entirely kinetic. As the ball rises, its kinetic energy is transformed into potential energy, and as it falls again, its potential energy is transformed into kinetic energy. The energy consumed in overcoming the friction of the axis NATURAL PHILOSOPHY. 39 of the pendulum and of the wheels of the clock and the resist- ance of the air is supplied by the falling weight or uncoiling spring ; and when the store of energy in the weight or spring is consumed, it must be renewed by again raising the weight or coiling the spring in winding up the clock. This new supply of energy is drawn from the hand and arm of the person who winds the clock. G. MACHINES. 66. Simple Machines. A machine is an instrument by which a force is applied to do work. Every machine, how- ever complicated, is made up of a very few elements, called simple machines, or mechanical powers. These are the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw. The force applied to work the machine is called the power ; and the resistance overcome by the machine, the work. A perfect machine would be one which offered no friction or other resistance of its own. Such a machine has only an ideal existence. In every machine in actual use the work done is partly useful in overcoming the resistance we desire to over- come, and partly useless in overcoming the resistance of the machine itself. In the theory of machines the resistance of the machine itself is left out of view. The magnitude of the resist- ance to be overcome is represented by a rising weight, and the magnitude of the power is usually represented by a falling weight. The resistance is often called the weight. 67. The General Law of Machines. The work done by the power upon a machine, and the work done by a machine upon the resistance, are simply different aspects of the same work (32), and hence they are equal in amount. Now the work done by a falling weight is equal to the product of the weight and the distance it falls, and the work done in raising a weight is the product of the weight and the distance it is raised. If, then, we represent the work done by the power upon the machine by a falling weight, and the work done 40 ELEMENTS OF by the machine upon the resistance by a rising weight, we arrive at the following general law of machines : The power multiplied by the distance through which it moves is always equal to the weight multiplied by the distance through which it moves. This law is often stated thus : In any machine, the power and weight will be in equilibrium when they are in the inverse ratio of their velocities. The following facts result from the general law of machines just stated : (i.) The faster the power moves, compared with the weight, the greater the weight it will balance. (2.) When the power moves faster than the weight, it will balance a weight greater than itself ; and when it moves slower than the weight, it will balance a weight less than itself ; and when it moves just as fast as the weight, it will balance a weight equal to itself. (3.) The power will balance a weight just as many times itself as its velocity is times that of the weight. 68. Gain and Loss of Power in a Machine. When, in any machine, the power balances a weight greater than itself, there is said to be a gain of power, or mechanical advantage ; and when the power balances a weight less than itself, a loss of power, or mechanical disadvantage. When there is a gain of power there is always a corre- sponding loss of speed, and when there is a loss of power there is a corresponding gain of speed. A machine might be described as an instrument by which we change the point at which the power acts, the direction in which it acts, or the rate at which it acts. The last change is the most important one effected by a machine. When the machine causes the power to act upon the resistance at a slower rate than it would were it applied directly to it, there is a gain of power ; and when it causes it to act upon it at a quicker rate, there is a loss of power. When the machine does not change the rate, there is neither gain nor loss of power. NATURAL PHILOSOPHY. 41 QUESTIONS ON THE GENERAL LA IV OF MACHINES. 43. In a machine, the power moves 25 inches while the weight is moving 35 inches. What weight would be balanced by 63 pounds of power ? If we denote the power by P, the weight by W, the velocity of the power by VP, the velocity of the weight by V W, and the distances passed over by the power and weight, respectively, by DP and D W, then we shall have, in the above example, VP V W W = 45 pounds. 44. In a machine, a power of 27 pounds balances a weight of 45 pounds. How far does the power move while the weight moves 60 inches? 1*=~\W VP = % VW DP = f X 60 = 100 inches. 45. In a machine, the power moves 56 inches while the weight moves 21 inches. What power will balance a weight of 600 pounds ? 46. In a machine, the power moves 35 inches while the weight is moving 63 inches. What weight will be balanced by 250 pounds of power ? 47. In a machine, the power moves 15 centimetres while the weight moves 40 centimetres. What power will balance a weight of 90 grammes ? 48. In a machine, the power moves 24 centimetres while the weight is moving 56 centimetres. What weight would be bal- anced by 1 30 grammes of power ? 49. In a machine, a power of 28 pounds balances a weight of 49 pounds. How far will the power move while the weight moves 20 inches ? 50. In a machine, a power of 40 pounds balances a weight of 32 pounds. How far will the weight move while the power is moving 30 inches ? 51. In a'machine, a power of 50 grammes balances a weight ELEMENTS OF of 80 grammes. How far will the power move while the weight is moving 15 centimetres ? 52. In a machine, a power of 81 grammes balances a weight of 63 grammes. How far will the weight move while the power is moving 25 centimetres ? 69. The Lever. The lever is a rigid bar, capable of turn- ing upon a fixed point or axis. The point on which the lever Fig. 28. turns is called \hefulcrum. Different forms of the lever are shown in Figure 28. F is the fulcrum, W the weight, and P the power. When the fulcrum is between the power and weight, the lever is said to be of \htfirst order ; when the weight is between the fulcrum and power, the lever is said to be of the second order ; and when the power is between the fulcrum and weight, the lever is said to be of the third order. Fig. 29. Fig. 30. W A bar used for raising a weight is a lever. When it is used as shown in Figure 29, it is a lever of the first order. When it Fig. 3 1. is used as shown in Figure 30, it is a lever of the second order. A fishing- rod (Figure 31) is a lever of the third order. The arms of a lever are the distances from the fulcrum to the points where the power and weight are applied, in case the lever is straight ; or the distances from the fulcrum to the lines which show the direction of the power and weight, in case the lever is bent. NATURAL PHILOSOPHY. 43 In Figure 28, FP is in each case the power arm, and F W the weight arm. In Figure 32 the dotted Fig. 32. lines, which are supposed to be drawn from the fulcrum perpendicularly to the directions in which the weight and a power act, are the arms of the bent lever, abfc. 70. The Special Law of the Lever. The special law of the lever is that the velocities of the power and weight are in the direct ratio of the lengths of the arms to which they are applied ; that is, if one arm of the lever is three times as long or one third as long as the other, the power or weight applied to this arm will move three times as fast or one third as fast as the one applied to the other arm. There will be a gain of power in the lever whenever the power arm is the longer ; for the power will then move the faster, and will balance a weight greater than itself. There will be a loss of power when the power arm is the shorter ; for the power will then move the slower, and will balance a weight less than itself. In a lever of the second order there will always be a gain of power, and in a lever of the third order a loss of power. In the lever of the first order there will be a gain or loss of power, or neither, according as the fulcrum is nearer the weight, or nearer the power, or midway between the two. 71. The Compound Lever. Sometimes two or more simple levers are combined, as shown in Figure 33. If P is five times as far from the fulcrum f Fig. 33. as A is, the point P will then move five times as fast as the point A, and a pull of one pound on P will exert a pull of five pounds on A. If B is five times as far from the fulcrum F as W is, the five pounds of pull on B will exert twenty-five pounds of pull at W. In this case one pound of pull exerted at P will balance twenty-five pounds at \V ; but it would be found on 44 ELEMENTS OF trial that by pulling P down one inch, W would be raised only one twenty-fifth of an inch. Such a combination of levers is called a compound lever. QUESTIONS ON THE LEVER. 53. In a lever, the power arm is 18 inches and the weight arm is 42 inches. What weight would be balanced by 60 pounds of power ? Denote the power arm by P A, and the weight arm by W A. =% W A = \ VW W W '= 25!" pounds. 54. In a lever, the power arm is 36 inches, and the weight arm 27 inches. What power will balance a weight of 75 pounds ? 55. In a lever, the power arm is 14 decimetres long, and the weight arm 21 decimetres. What weight would be balanced by 70 grammes of power ? 56. In a lever, the power arm is 49 decimetres long, and the weight arm 28 decimetres. What power would balance a weight of 17 kilogrammes ? 57. In a lever, a power of 30 pounds balances a weight of 50 pounds, and the power arm is 80 inches long. What is the length of the weight arm ? 58. In a lever, a power of 70 pounds balances a weight of 20 pounds, and the weight arm is 30 inches long. What is the length of the power arm ? 59. In a lever, a power of 150 grammes balances a weight of 250 grammes, and the power arm is 18 decimetres in length. What is the length of the weight arm ? 60. In a lever of the first order, a power of 30 pounds bal- ances a weight of 40 pounds, and the power arm is 27 inches long. What is the length of the lever ? 61. In a lever of the first order, a power of 55 grammes bal- ances a weight of 35 grammes, and the weight arm is 13 deci- metres long. What is the length of the lever ? NATURAL PHILOSOPHY. 45 62. In a lever of the second order, the length of the lever is 65 decimetres, and a power of 24 grammes will balance a weight of 64 grammes. What is the length of the weight arm ? 63. In a lever of the third order, the length of the lever is 28 decimetres, and the length of the power arm is 12 decime- tres. What power will balance 18 grammes of weight? 72. The Pulley. The pulley is a small Fig. 34 . grooved wheel turning freely in a frame called the block. It is a machine in which power is applied to do work by means of a cord instead of a bar, as in the case of the lever. The wheel of the pulley serves simply to diminish friction at the points over which the cord is drawn. In Figure 34 the block of the pulley D C is fastened to the beam above, so as to be stationary, while the block of Fig. 35- Fig. 36. Fig. 37- the pulley A B is free to move up and down. The former is called a fixed pulley ; and the latter, a movable pulley. A fixed pulley serves simply to change the direction in which the power acts. 73. Systems of Pulleys with one Cord. 46 ELEMENTS OF In Figures 35, 36, and 37, are shown systems of pulleys with a single cord, that is, in which one cord passes over all the pulleys. The power is applied to the end of the rope, and the weight is attached to the movable block. In the first case, on raising the movable block one inch, three inches of rope will be released, since the rope comes three times to that block. In this case the power will move three times as fast as the weight. In the second case, on raising the movable block one inch, four inches of rope will be released, since the rope comes four times to this block. In this case the power will move four times as fast as the weight. In the third case the power will move six times as fast as the weight. The special law of a system of pulleys with a single rope is that the velocities of the power and weight are in the inverse ratio of the number of times the cord comes to each. As the cord always comes once to the power, the power will balance a weight as many times itself as the cord comes times to the block bearing the weight. QUESTIONS ON PULLEYS WITH SINGLE ROPE. 64. In a system of pulleys with a single rope, the rope comes 13 times to the block bearing the weight. What weight would be balanced by 75 pounds of power ? 65. In a system of pulleys with a single cord, the cord comes 9 times to the block bearing the weight. What power would balance 19 grammes of weight ? 66. In a system of pulleys with a single rope, a power of 13 pounds balances a weight of 91 pounds. How many times does the rope come to the block bearing the weight ? 67. In a system of pulleys with a single rope, a power of 72 grammes balances a weight of 792 grammes. How many times does the rope come to the block bearing the weight ? 74. Systems of Pulleys with more than one Rope. The law of the pulley is sometimes stated as follows : A stretched rope must have the same tension throughout its whole length. NATURAL PHILOSOPHY. 47 Figure 38 represents a system of pulleys in which two ropes are used. Here a weight of four pounds is balanced by a power Fig. 38. of one pound. The parts of the rope Fig. 39. A D and A B must each have a ten- sion equal to the power. The rope A rebalances the two tensions, #/> and A, and must therefore have a 2 tension of twice the power. The three tensions supporting the pulley A |>) amount therefore to four times the i power. i In the system shown in Figure 39 p four ropes are used. The tensions of 8 the several ropes will be readily un- 4 Aw derstood from the numbers. It will be seen that in this case the power is doubled by each movable pulley which is added ; but, as in all the systems we have examined, what is gained in power is lost in speed. 75. Wheel and Axle. The wheel and axle (Figure 40) consists of a wheel, or drum, #, mounted on an axle b. The power and weight are applied Fig. 40. to ropes which pass, one over the wheel and the other over the axle, in opposite directions, so that one unwinds as the other winds up. The power and weight are really applied to the wheel and axle at the point where the rope touches each, that is, at the end of the radius of each. The one applied to the wheel moves the faster, and just as many times faster as the circumference or the radius of the wheel is times the circumference or the radius of the axle. The special law of the wheel and axle is that the veloci- ties of the power and weight are in the direct ratio of the radii to whicti they are applied. When the power is applied to V ELEMENTS OF the wheel, there is a gain of power ; and when it is applied to the axle, there is a loss of power. The chief use of the wheel and axle in machinery is in transmitting rotary motion from one piece to another, with or without a change of velocity. For an increase of velocity, a large wheel must act upon a small one; and for a diminution of velocity, a small wheel must act upon a large one. When there is to be no change of velocity, the wheels must both be of the same size. 76. Cog-Wheels. There are various ways in which the axle of one wheel is made to act on the circumference of another. Sometimes the one turns the other by rub- bing against it, or by friction. The most common way, however, is by means of teeth or cogs raised on the surfaces of the wheels and axles. The cogs on the wheel are usually called teeth, while those on the axle are called leaves, and the part of the axle from which they project is called tis\t pinion. 77. The Gain of Power by Wheel- Work, in the train of wheels in Figure 41, if the circumference of the wheel a is 36 inches, and that of the pinion b is 9 inches, or one fourth as great, a power of one pound at P will exert a force of four pounds on b. If the circumference of the wheel e is 30 inches, and that of the pinion C 10 inches, the four pounds acting on the former will exert a force of twelve pounds on the latter. If the circumference of the wheel f is 40 inches, and that of the axle d 8 inches, the twelve pounds acting on/" will exert a force of sixty pounds on d. One pound at P will then balance sixty pounds at W. But in this case, as in all others, what is gained in power is lost in speed ; since the one pound at P must move througli sixty inches in order to raise the sixty pounds at W one inch. NATURAL PHILOSOPHY. 49 78. Belted Wheels. Another way in which wheels and axles may be made to act upon one another is by means of a belt, or band, passing over them both. They may thus be at any dis- tance apart, and may turn either the same way or contrary ways, Fig. 42. Fig. 43- according as the belt does or does not cross between them (Fig- ures 42 and 43). A cog-wheel and its pinion must, of course, always turn in contrary directions. 79. The Windlass and Capstan. The windlass is a hori- zontal barrel turned by means of a Fi g . 44 crank or spokes (Figure 44). It may be regarded as a modification of the wheel and axle, the crank taking the place of the wheel. The capstan is an upright drum turned by means of levers, which may be removed at pleasure. QUESTIONS ON THE WHEEL AND AXLE. 68. The radius of a wheel is 40 inches, and that of its axle 15 inches. What weight on the axle would be balanced by 50 pounds of power on the wheel ? Denote the radius of the wheel by R W, and that of the axle by R A. RW=\ RA vp\ vw P = W 50-5- I = W=. 133^ pounds. 69. The radius of a wheel is 18 decimetres, and that of its axle 12 cl&ci metres. What weight on the wheel would be bal- anced by 32 grammes of power on the axle ? 4 50 ELEMENTS OF 70. In a wheel and axle, a power of 63 pounds on the axle balances a weight of 35 pounds on the wheel. The radius of the wheel is 16 decimetres. What is the radius of the axle ? 71. A power of 21 pounds on the wheel balances a weight of 77 pounds on the axle. The radius of the axle is 5 inches. What is the radius of the wheel ? 80. The Inclined Plane. An inclined plane is simply an inclined surface. It is easier to roll a body up an in- clined surface than to raise the body vertically to the same height. The reason is obvious. The body must be raised against the action of gravity ; and^by rolling the body up the inclined surface, the power is compelled to act through a distance equal to the length of the surface in raising the weight the height of it. The special law of the inclined plane is that the velocities of the power and weight are in the ratio of the length of the plane to its height. Since the power and weight are in the inverse ratio of their velocities, it follows that the power will be to the weight as the height of the plane is to its length. The law of the inclined plane may be demonstrated by means Fig. 45. of the apparatus represented in Figure 45. R S is a smooth piece of hard wood hinged at R ; by means of a screw it can be clamped at any angle x against the curved support ; a is a metal cylinder, to the axis of which is attached a string passing over a pulley to a scale-pan P. It is thus easy to ascertain by direct experiments what weight must be placed in the pan P in order to balance a roller of any given weight. The line R S represents the length, S T the height, and R T the base of the inclined plane. 8 1. The Wedge. Instead of lifting a weight by moving NATURAL PHILOSOPHY. it along an inclined plane, we may do the same thing by pushing the inclined plane under the weight. F; 6 When used in this way the inclined plane is called the wedge. A wedge which is used for splitting wood has usually the form of a double inclined plane, as in Figure 46. The law of the wedge is the same as that of the inclined plane ; but since a wedge is usually driven by a blow instead of a force acting continuously, it is difficult to illustrate this law by experiments. The wedge is especially useful when a large weight is to be raised through a very short distance. Thus, a tall chimney, the foundation of which has settled on one side, has been made up- right again by driving wedges under that side. So, too, ships are often raised in docks by driving wedges under their keels. Cutting and piercing instruments, such as razors, knives, chisels, awls, pins, needles, and the like, are different forms of wedges. 82. The Screw. In Figure 47 we have a machine called the screw. It is a movable inclined plane, in which the inclined surface winds round a cylinder. The cylinder is the body of the screw, and the inclined sur- face is its thread. The screw usually turns in a block N, called the ;////. Within the nut there are threads exactly corresponding to those on the screw. The threads of the screw move in the spaces between those of the nut. The power is usually applied to the screw by means of a lever P. Sometimes the screw is fixed and the nut is movable, and sometimes the nut is fixed and the screw movable. ELEMENTS OF 83. The Endless Screw. In Figure 48 the thread of the Fig. 48. screw works between the teeth of the wheel ; hence, if the screw is turned, the wheel must turn. Since as fast as the teeth at the left escape from the screw those on the right come up to it, the screw is act- ing upon the wheel continually ; hence this machine is called the endless screw. NATURAL PHILOSOPHY. 53 III. PHYSICS. I. STATES OF MATTER. A. THREE STATES OF MATTER. 84. The Three States. Matter exists in three different states, known as the solid, the liquid, and \hegaseous. Ice is a solid, water is a liquid, and steam and air are gases. While the substance of a body depends upon its atomic structure (2), the state of a body depends upon its mo- lecular structure. Hence the state of matter is a. physical condition, and changes of state are physical changes. 85. Cohesion in the Different States of Matter. The different states of matter depend upon the strength of the attraction of cohesion among the molecules. This is compara- tively strong in solids, very weak in liquids, and entirely wanting in gases. The molecules of some solids are bound together much more firmly than those of others by cohesion ; but even when this bond is weakest, the molecules manifest a disposition to main- tain their -relative positions in the body, and the body to preserve its form. In liquids the bond of cohesion is so slight that the molecules manifest no disposition to maintain their relative posi- tions in the body, nor does the body tend to preserve its form. Gases are not held together at all by cohesion, but only by gravity. 86. Molecular Motion in the Different States of Matter. 54 ELEMENTS OF The molecules are, undoubtedly, in incessant motion in every state of matter, but their freedom of motion is very different in the different states. In so/ids, the molecules, when left to them- selves, have fixed positions, within which they can move to a limited extent, but from which they can never escape. When left to themselves, the molecules of a solid never move around among themselves so as to change their relative positions. A molecule in the interior can never work its way to the surface, nor can one at the surface work its way into the interior. In liquids, the molecules are all the time moving about among themselves in the interior of the mass with the utmost freedom. No molecule is confined within particular limits within the mass, but every molecule is continually moving to and fro in every direc- tion throughout the entire mass. They, however, never escape from the influence of cohesion. So long as they are in the in- terior of the mass, the cohesion of the molecules on one side of them is exactly balanced by that of the molecules on the other side ; hence it does not interfere with the freedom of their motion. But as the molecules come to the surface, they experience only the pull of the molecules behind them, and this is usually suffi- cient to stop their outward motion and to cause them to return into the interior of the mass. In gases, the molecules are moving without the slightest restraint from cohesion ; hence they move in straight lines. They are continually striking together and rebounding again, but after each rebound they move in straight lines till they encounter other molecules. There is no force acting within the mass of a gas which tends to check the motion of the molecules at any point ; hence gases do not, like liquids, tend to assume a definite surface. 87. The Distances between the Molfcules in the Different States of Matter. As a rule, the molecules are nearer to- gether in solids than in liquids, and in liquids than in gases. The molecules of steam are about seventeen hundred times as far apart as those of water. 88. Behavior of the Different States of Matter when Small Portions of each are placed in Empty Vessels. If a small portion of a solid is placed in an empty vessel, it will either not conform to the shape of the vessel at all, or, in the case of a soft NATURAL PHILOSOPHY. 55 solid, only slowly and imperfectly. This is owing to the ten- dency of a solid to maintain its shape. If a small amount of a liquid is put into an empty vessel, it will conform at once and perfectly to the shape of the vessel, but it will not completely till it. The liquid will sink to the lowest part of the vessel, and will be separated by a definite surface from the space in the upper part of the vessel. This is because the cohesion of the liquid checks the outward motion of the molecules, and so keeps them from moving away from the mass. If any portion of a. gas, however small, is placed in an empty vessel, however large, the gas will completely fill the vessel. This is because there is nothing to check the outward motion of the molecules of the gas, save the walls of the vessel in which it is enclosed. B. FLUIDS. 89. Fluids. Owing to their freedom of molecular mo- tion, liquids and gases have several characteristics in common. They are, accordingly, often classed together as fluids. This appellation is derived from the readiness with which portions of each of these states of matter flow over or among each other. 90. Pascal's Law. One of the most remarkable char- acteristics of a fluid is the way in which it transmits any pressure that is brought to bear on it. If any pressure is brought to bear on any portion of the surface of a fluid which fills a closed vessel, a pressure just equal to it will be trans- mitted through the fluid to every equal portion of surface. This law was enunciated by Pascal, and is known, as Pascal's law. The following experiment shows that pressure is trans- mitted in all directions by a Fig. 49 . fluid. A tube (Figure 49) is provided with a piston and fit- ted with a hollow globe, which is pierced with a number of orifices, arranged in a circle around-it. Fill the globe and ELEMENTS OF tube with water. If the piston is pushed in, the water spouts out of all the orifices, and not merely those opposite the piston. Conceive a vessel of any form, in the sides of which are a number of cylindrical apertures, all of the same size, and closed Fig. 50. with movable pistons, as shown at A, B, C, D, and E (Figure 50). Suppose a pound of pressure brought to bear upon A. A pound of pressure will be transmitted to each of the other pistons in the direction of the arrows. If the piston B has only half the surface of A, it will receive only y a pound of pressure ; if it has twice the surface of A, it will re- ceive 2 pounds of pressure ; if it has three times the surface of A, it will receive 3 pounds of pressure ; etc. Hence, by means of a liquid, a small pressure upon a small surface may be made to exert a great pressure upon a large surface. 91. The Hydraulic Press. In Figure 51 we have two Fig. 51. cylinders, with a piston in each. Suppose that the surface of the larger pis- ton is fifty times that of the smaller ; if the latter is pressed downward by a weight of one pound, an upward pressure of one pound will be brought to bear upon each portion of the surface of the large piston equal to that of the small piston. The whole upward pressure on the large piston will then be fifty times the downward pressure on the small one. If the surface of the larger piston had been one hundred times that of the smaller, one pound on the latter would have balanced one hundred on the former ; and so on. The hydraulic press is constructed on the principle just illustrated. One form of this press is shown in Figures 52 and 53. The two cylinders A and B are connected by the NATURAL PHILOSOPHY. 57 pipe d. The piston #, in the cylinder A, is worked by the handle O, and forces water into the large cylinder B, where it presses up the piston C. If the end of the pis- ton Cis 1000 times as large as that of the piston a, a pres- sure of 2 pounds on a would exert a pressure of 2000 pounds, or one ton, upon C. If a man, in working the Fig. 52. handle O, forces down the piston a with a pressure of 50 pounds, he would bring to bear upon C a pressure of 25 tons. This press is used for pressing cotton, hay, cloth, etc., into bales ; for extracting oil from seeds ; for testing cannon, boilers, etc. ; and for raising ships out of the water. 58 ELEMENTS OF The hydraulic jack is a form of the hydraulic press, adapted to raising heavy weights. 92. The Principle of Archimedes. A body in a fluid is buoyed up by a force equal to the weight of tlie fluid it dis- places. This fact was discovered by Archimedes, and is therefore designated by his name. This principle may be verified by the following experiment. A brass cylinder is constructed so as just to fill a cup. The cup and cylinder are hung from one pan of a balance (Figure 54) and counterpoised in the air by weights in the other pan. Fig S3- The cylinder is then allowed to hang in a vessel of water. The weights overbalance the cup and cylinder, showing that the water lifts the cylinder up. Equilibrium is restored by filling the cup with water. When the cup is full, the beam of the bal- ance will be horizontal, and the cylinder will be completely in the water, showing that the cylinder is buoyed up by the water with a force equal to the weight of a cupful of water, or to the weight of the water displaced by the cylinder. 93. Forces acting upon a Body immersed in a Fluid. Every body immersed in a fluid is subjected to two forces : one equal to its own weight, which tends to make the body NATURAL PHILOSOPHY. 59 sink ; the other equal to the weight of the liquid displaced, which tends to make the body rise. When a body displaces more than its own weight of a Fig. 54. fluid, it will rise in that fluid ; when it displaces less than its own weight, it will sink ; and when it displaces just its own weight, it will remain suspended wherever it happens to be. Fig. 55- These three cases may be illustrated by putting an egg into salt and fresh water (Figure 55). When the egg is placed in salt water, it rises to the surface because it displaces more than its own weight of the brine. When it is put into the fresh 6o ELEMENTS OF water, it sinks to the bottom because it displaces less than its own weight of the water. When it is put into a proper mixture Fig. 5 6. of fresh water and brine, it will remain suspended in the fluid, because it displaces just its own weight of the mixture. 94. Floating Bodies. Every body floating in a fluid displaces just its own weight of the fluid. This is equally true of a ship floating in water, or a balloon floating in the air (Figure 56). The more heavily the ship is loaded, the deeper she sinks into the water. By throwing out the sand which is used as ballast, the balloon is made lighter, so as to displace more than its own weight of air. It '" then rises till it comes into more highly rarefied air, where it displaces just its own weight, when it again floats along at the same level. If F i g . 57 . some of the gas is allowed to escape, the balloon becomes less in bulk, and so displaces less than its own weight of air. It then sinks until it again displaces its own weight. The appendage at the side of the bal- loon (Figure 56) is called a parachute, and can be used in descending from the balloon. It consists of a large circular piece of cloth (Figure 57) about 16 feet in diameter, which, by the resistance of the air, spreads out like a gigantic um- brella. In the centre there is an aperture, through which the air, compressed by the rapidity of the descent, makes its escape ; NATURAL PHILOSOPHY. 61 for otherwise oscillations might be produced, which would be dangerous to the aeronaut. In Figure 56 the parachute is attached to the network of the balloon by means of a cord, which passes round a pulley, and is fixed at the other end to the boat. When the cord is cut the parachute sinks, at first very rapidly, but more slowly as it be- comes distended, as represented in the figure. 95. Method of finding the Specific Gravity of Solids and Liquids. To find the specific gravity (53) of a solid or liquid, it is necessary to find the weight of a volume of water Fig. 58. Fig. 59. equal to that of a portion of the solid or liquid whose specific gravity is to be found. By means of the principle of Ar- chimedes, the weight of this volume of water is easily found. Suppose we wish to find the specific gravity of copper. Fasten the piece of copper to one pan of the balance by a fine thread (Figure 58), and counterpoise it in the air with weights in the other pan. Suppose it to weigh 125.35 grains. Then suspend it in a vessel of water and restore the equilibrium by placing weights in the pan supporting the copper. Suppose it to require 14.24 grains. This, according to the principle of 62 ELEMENTS OF Archimedes, is the weight of the water displaced by the copper, or of a volume of water equal to that of the copper. The specific gravity of the copper is then ^f.^f = 8.8. When the body whose specific gravity we wish to find is lighter than water, we must fasten it to a heavy body to sink it. We then find, by the above method, the weight of the water displaced by the sinker alone, and by the sinker and light body together. The difference between the two will be the weight of the water displaced by the lighter body. The specific gravity of a liquid may be found by the follow- ing method. A glass ball, weighted with mercury inside, is first accurately weighed in air. It is then immersed in a vessel of alcohol or other liquid under examination (Figure 59), and equilibrium is restored by adding weights to the pan from which the ball is suspended. Suppose 35.43 grains are required. This will be the weight of the ball's volume of alcohol. Next immerse the ball in water, and restore the equilibrium as before. Suppose it requires 44.28 grains this time. This will be the weight of the ball's volume of water. The specific gravity of alcohol will be f f ;|f == .8. 96. The Hydrometer. A hydrometer is an instrument for finding the specific gravity of liquids. Common forms of it are shown in Figure 60. They are weighted at the lower end with mercury to keep them in an up- right position. The bulb above the mercury causes them to dis- place enough of a liquid to float in it. When put in a liquid they sink in it till they displace their own weight. The deeper they sink in a liquid, the less its spe- cific gravity. Their stems are graduated in such a way that the number on the stem at the sur- face of the liquid indicates the specific gravity of the liquid. This is a convenient, but not very accurate method of ascertain- ing the specific gravity of a liquid. Fig. 60. NATURAL PHILOSOPHY. Fig. 61. C. GASES. 97. Expansibility of Gases. One of the most marked characteristics of a gas is its capacity for indefinite expan- sion. The tendency of a gas to expand may be illustrated by means of an india-rubber bag partially filled with air, closed air-tight, and placed under the receiver of an air- pump. When the air is exhausted from the receiver, the bag fills out, as shown in Figure 6 1 . The tendency of a gas to expand is due to two facts, namely, that the molecules of a gas are not held together by cohesion (85), and that they are moving rapidly in straight lines (86). The condition of a gas in a closed vessel has been likened to that of a swarm of bees in a closed room, when all the bees are flying at random in straight lines. They would be constantly flying against one another and against the walls of the room. It has been calculated that the mole- cules of air are moving at the average rate of about 1600 feet a second. This velocity would be sufficient to carry a body in a vacuum some 40,000 feet, or about 7 miles high. Now the molecules of air in the rubber bag are all the time flying against one another and against the bag with this enormous velocity. They therefore tend to expand the bag. So long as there was air in the receiver outside the bag, the blows against the bag from within were met and balanced by an equal number ol blows from without ; but as the air was exhausted from the receiver, there were fewer and fewer blows upon the bag deliv- ered by the molecules on the outside, and hence the bag began to yield to the more numerous blows from within. 98. The Diffusion of Gases. When any two gases are brought into contact, they rapidly mix with each other. 64 ELEMENTS OF This mixture of gases when brought into contact is called dif- fusion. It is due to the fact that the molecules are far apart and in constant motion. The molecules of the one gas quickly move into the spaces among the molecules of the -other gas. 99. The Expansive Power of a Gas increased by Heat. A bulb with a tube projecting from it is placed in a vessel of water so that the open end of the tube is under water, as shown in Figure 62. If the bulb is heated, the air in it will expand so as to drive out a portion of it through the water. Heat always increases the expansive power of a gas. This is Fig. 62. because heat causes the molecules to fly about with greater velocity, and therefore with greater energy. 100. The Expansive Power of a Gas increased by an Increase of Pressure. An increase of pressure in a gas in- creases its expansive power. This is because the increased pressure crowds the molecules nearer together, so that there are more molecules in the same space to beat against the enclosure. In the cylinder of the steam-engine the steam is kept at a high temperature and under great pressure. 1 01. The Three Laws of Gases. Equal volumes of all gases, at the same temperature and under the same pressure, contain the same number of molecules. This is Avogadro's law. The volume of a confined mass of gas varies inversely as the pressure to which it is exposed. The less the pressure the greater the volume, and the greater the pressure the less the volume. This is Mariotte's law. This law might be stated thus : the number of molecules of a gas in a given space, and the expansive power of the gas, vary directly as the pressure to which the gas is exposed. NATURAL PHILOSOPHY. 65 The volume of a gas under constant pressure varies directly as the absolute temperature of the gas. This is Charles s law. By absolute temperature is meant temperature measured from a point 459 below the ordinary zero. The temperature indi- cated by an ordinary thermometer may be converted into abso- lute temperature by adding 459 to it. Thus, a temperature of 70 on our scale would be a temperature of 70 + 459 = 5 2 9 on the absolute scale. A temperature of 15 on our scale would be a temperature of 459 -[- ( 15) = 444 on the absolute scale. 102. The Air- Pump. The essential parts of an air- pump are shown in Figures 63 and 64. There is a flat plate for holding the receiver E, called the pump-plate. It is ground perfectly flat, so that an air-tight joint is formed between it and the receiver when the latter is placed upon it. A tube connects the pump-plate with the cylinder, in which a piston is moved up and down by means of the 5 66 ELEMENTS OF handle. There is a little valve 6* in the piston, pressed down by a spiral spring above it. There is also a valve S' at the bottom of the barrel, fastened to a rod which passes through the piston in such a way that the valve is opened when the piston rises, and closed when the piston is pushed down, by the friction of the rod against the pis ton. When the piston is drawn up the valve in the piston is closed, and no air can pass from above the piston into the space below it. At the same time S' at the bottom of the barrel is opened, and the expansive force of the air in the receiver E causes some of the air to pass out through the tube into the barrel below the piston. When the pis- Fig. 6 4 . ton is pushed down the valve S' is closed by the friction of the rod, and the valve ,5" is opened by the expansive force of the air below it as the air becomes compressed, and the air in the barrel below the piston passes above it again. In this way, every time the piston is moved up and down, a part of the air is removed from the receiver. F is a gauge for showing the extent of the exhaustion ; R is a cock, by means of which the receiver and the barrel may be put into communication with each other, or either may be shut off from the other, and be put into communication with the external air. There are many different forms of air-pumps ; but with none of the ordinary pumps is it possible to obtain perfect exhaustion. NATURAL PHILOSOPHY. The air becomes finally so attenuated as not to have sufficient expansive force to open the valve. 103. Pressure of the Air. The pressure of the air may be illustrated by the following experiments. Place a small bell-jar, open at both ends, on the plate of the air-pump, and cover the top of the jar with the palm of the hand. When the air is ex- hausted from the jar, the hand is pressed firmly down upon the mouth of the jar. This is an illustration of the downward pres- sure of the air. It was not perceived at first, because the down- ward pressure of the air upon the hand was balanced by the upward pressure of the air within the jar. The weight-lifter (Figure 65) serves to illustrate the upward pressure of the air. It consists of a cylinder of glass or metal, A B, with a piston moving up and down in it, air-tight. The cylinder is closed at the top by a plate C, to which may be screwed a tube to connect the cylinder with the air- pump. The cylinder is open at the bottom, and a heavy weight is fastened with a strap to the piston. If the air is exhausted from the cylinder above the piston, the pis- ton and weight are raised by the upward pressure of the air acting upon the bottom of the piston. Figures 66 and 67 represent two brass hemispheres, some four inches in diameter, the edges of which are made to fit tightly together. The whole can be screwed to the air-pump by means of the stop-cock at the bottom. While the hemispheres contain air they can be separated with ease, since the outward pressure is just balanced by the inward pressure ; but when the air within is pumped out, it is very hard to pull them apart. Since it is equally difficult to do this in whatever position the hemispheres are held, the experiment shows that the air presses in all directions. This piece of apparatus is called the Magdeburg hemispheres, from Otto von Guericke, of Magdeburg, by whom it was invented. 68 ELEMENTS OF Fig. 66. Fig. 67. The pressure of the air at the level of the sea is about impounds to a square inch, or a ton to the square foot. The surface of the body of a man of middle size is about 1 6 square feet ; the pressure, therefore, which a man supports on the surface of his bodyis 35,560 pounds, or nearly 16 tons. Such enormous pressure might seem impossible to be borne; but it must be remembered that, in all directions, there are equal and contrary pres- sures which counterbalance one another. It might also be supposed 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 the cavities of the body are filled with air or liquids which exert a pressure outward equal to that of the external air. When the external pressure is removed from any part of the body, either by means of a cupping vessel or by the air-pump, the pressure from within is seen by the distension of the surface. 104. The Pressure of the Air decreases as we ascend above the Level of the Sea. The pressure of the air at the level of the sea is due to the downward pressure of all the layers of air above, transmitted throughout the mass below ac- cording to Pascal's law (90). Each layer of molecules of air is pulled downward by gravity, and transmits this pressure to all the layers below. Hence the pressure of a gas increases with the depth. It, however, in- creases more rapidly than the depth. For, gases being compres- sible, as we descend in a gas the molecules are crowded more closely together, so that there are more molecules exerting pres- NATURAL PHILOSOPHY. sure in each layer, and there are more layers in any given differ- ence of depth. D. LIQUIDS. 105. Compressibility of Liquids. For a long time it was thought that liquids were entirely incompressible. In the year 1661 some academicians of Florence, wishing to find whether water was compressible, filled a thin globe of gold with that liquid, and, after closing the orifice perfectly tight, subjected the globe to great pressure, with a view of altering its form, knowing that any alteration of form would occasion a diminution of capacity. They failed to compress the water, but discovered the porosity of gold, for the water forced its way through the pores of the globe, and stood on the outside like dew. In more recent times it has been shown that liquids are slightly compres- sible. The apparatus for measuring the compressibility of a liquid is shown in Figure 68. It consists of a strong glass cylinder enclosing along glass bulb A, from which proceeds a fine bent tube, with its end dipping under the mercury in the bottom of the cylinder at O. The liquid to be tested is introduced into the bulb A so as to fill both it and the tube. The cylinder is then filled with water through the funnel R, and pressure applied by means of the thumb-screw P. which forces a piston down upon the water. The rise of the mercury in the fine tube shows the amount of the compression of the liquid in the bulb. For a pressure of one atmosphere, or 15 pounds to the square inch, the volume of water is diminished about 5 parts in 100,000. At the depth of a mile, the volume of sea-water is diminished i part in 130. 70 ELEMENTS OF In liquids, as in gases, elasticity is developed only by com- pression, but their elasticity is perfect. No matter to what pressure a liquid has been subjected, it will return to exactly its original volume as soon as the pressure is removed. 1 06. The Tendency of Liquids to assume a Globular Form. When left to itself, a liquid always assumes a globular form. This is because all the molecules, as they work their way through the mass, are stopped by the force of gravity and cohesion at the same distance from the cen- tre of the mass. The tendency of the molecules of liquids to collect into spheres -may be shown by the following experiment. Prepare a mixture of water and alcohol which shall be just as heavy as sweet oil, bulk for bulk, and introduce some of the oil carefully into the centre of this mixture by means of a dropping-tube ; the oil will neither rise nor sink, but gather into a beautiful sphere. Rain-drops, dew-drops, and the manufacture of shot illustrate this tendency of the molecules of liquids. In the manufacture of shot, melted lead is poured through a sieve at the top of a very high tower, and the drops in falling take the form of spheres, which become solid before they reach the bottom. 107. The Free Surface of a Liquid at Rest is a Level Surface. A level surface is one along which gravity does not tend to produce any motion. Gravity always acts perpen- dicularly to such a surface, and hence there can be no com- ponent of gravity which would tend to produce motion along that surface. The surface of a liquid at rest must be a level surface, else gravity would tend to move the liquid along the sar- face, and the liquid could not remain at rest. 1 08. The Downward Pressure of a Liquid due to Gravity is proportioned to the Depth. Since the downward pres- sure of a liquid due to gravity at any point is the pressure that has been transmitted to that point by the layers NATURAL PHILOSOPHY. 7 1 of molecules above, the pressure at that point will be proportional to the number of layers of molecules abore the point ; and since liquids are practically incompressible, the number of layers of molecules will be proportional to Ihe depth. The amount of pressure transmitted to the layers below by any layer of molecules is entirely independent of the extent of the layer. For if the upper layer consisted of a single molecule, it would exert the pressure of a molecule upon the surface of a molecule, and that pressure would be transmitted to every equal surface below. If the upper layer consisted of 5 molecules, they would exert a pressure of 5 molecules upon a surface of 5 mole- Fig. 6 9 . cules, which would be the pressure of one molecule to the sur- face of one molecule as before. Hencr ;he pressure at any point in a vessel containing a liquid does Kot depend at all upon the size and shape of the vessel, but simply upon the depth of the point below the surface. 109. Pascal's Vessels. The Jact that the pressure of a liquid upon a given surface depends upon the depth of the liquid only, and not upon the size or shape of the vessel which contains the liquid, may be illustrated by means of Pascal's vessels (Figure 69). The vessels M, />,and Q may in turn be screwed into the plate c. A disc a suspended from one end of the beam of a balance with a thread, and held up by weights at the other 72 ELEMENTS OF end of the beam, serves as the bottom of the vessel, which it closes water-tight. Water is poured carefully into the vessel M till its depth is just sufficient to displace the plate a, and the height of the water is marked by the point o. M is then re- moved, and P and Q are in turn put into its place. It will be found that each will have to be, filled to exactly the same height to displace the plate a. It follows from the above that a very small quantity of water can produce very great pressure. Let us imagine a cask, for example, filled with water, and having a long narrow tube tightly fitted into its top. If water is poured into the tube, there will be a pressure on the bottom of the cask equal to the weight of a column of water whose base is the bottom itself, and whose height is equal to that of the water in the tube. The pressure may be made as great as we please ; by means of a mere thread of water forty feet high, Pascal succeeded in burst- ing a very solidly constructed cask. 1 1 o. The Upward Pressure of a Liquid. The down- ward pressure of a liquid at any point must be balanced by an equal upward pressure, according to the law that action and reaction are always equal and opposite (30). The following experiment (Figure 70) serves to show the upward pressure of liquids. A large open glass tube A, one Fig. 70. en d of which is ground, is fitted with a ground-glass disc 6>, or still better with a thin card or piece of mica, the weight of which may be neglected. To this is attached a string C, by which it can be held against the bottom of the tube. If the whole is then immersed in water, 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 is now slowly poured into the tube, the disc will sink only when the height of the water inside the tube is equal to the height outside. in. The Pressures of different Liquids at the same Depth NATURAL PHILOSOPHY. 73 are proportional to their Densities. The pressure at the same depth would be about 12*4 times as great in mercury as in water, and about .8 as great in alcohol as in water. This is owing to the fact that, mercury being about 12^ times as dense as water, each layer of mercury would transmit downward 12% times as much pressure as a layer of the same thickness of water; and a layer of alcohol .8 times as much. 112. The Pressure is the same at every Point in a Hori- zontal Layer of a Liquid at Rest. Owing to the extreme mobility of liquids, it would be impossible for a liquid to remain at rest if at any point in it the pressures acting upon that point from all directions were not equal or balanced. If the upward or downward pressure at any point were not balanced, a particle at that point would tend to move up or down as the case might be. If the pressure were not the same throughout a horizontal layer, there would be some point in the horizontal layer where the horizontal pressures to the right and left would not be balanced, and a particle at that point would move in the direction in which it was urged by the greater pressure ; that is, the liquid would not be at rest. This is true of all fluids, both liquids and gases. Any disturbance of the equilibrium of pressure in horizontal layers gives rise to currents which will flow towards the region of low pressure till the equilibrium is restored. 113. Rise of Liquids in Communicating Vessels. When a liquid is contained in vessels which communicate with each other and is at rest, it will be found to stand at the same height in all the vessels, whatever may be their size or shape. Thus, in Figure 71, the water stands at the same height in all the tubes as in the large vessel. If one of the tubes is cut off below the level of the water in the other vessels, and drawn out to a narrow mouth, the liquid will spout out of this tube nearly to the height of the liquid in the others. The rise of a liquid 74 ELEMENTS OF Fig. 71. to the same height in a series of communicating vessels is due to the fact that when a liquid is at rest the pressure must be the same throughout each horizontal layer. Each horizontal layer of the water taken through all the vessels must be the same distance below the free surface of the liquid in each vessel. Hence these free surfaces must be in the same horizontal line, or at the same level. The tendency of liquids to find their own level is very important, and of continual appli- cation. When any system of pipes, however complicated, is connected with a reservoir, the water will rise in every pipe to the level of the water in the reservoir. 114. Springs and Artesian Wells. All natural collections of water illustrate the tendency of a liquid to find its level. Thus, the Great Lakes of North America may be regarded as a number of vessels connected together, and hence the waters tend to maintain the same level in all. The same is true of the source of a river and the sea, the bed of the river connecting the two like a pipe. Springs illustrate the same fact. The earth is composed of layers, or strata, of two kinds : those through which water can pass, as sand and gravel ; and those through which it cannot pass, as clay. The rain which falls on high ground sinks through the soil until it reaches a layer of this latter kind, and along this it runs until it finds some opening through which it flows as a spring. It is the same with Artesian wells. These wells derive their name from the province of Artois in France, the first part of Europe where they became common. It would seem, however, that wells of the same kind were made in China and Egypt, many centuries earlier. In Figure 72 suppose A B and CD to be two strata of clay, and K J\ to be a stratum of sand or gravel between them. The NATURAL PHILOSOPHY. 75 rain falling on the hills on either side will filter down through this sand or gravel, and collect in the hollow between the two strata of clay, which prevent its escape. If now a hole is bored clown to K K, the water, striving to regain its level, will rise to the surface at H, or spout out to a considerable height above it. Sometimes the water between two such impervious strata makes its way to the surface through some fissure in the upper stratum, constituting a deep-seated spring. 115. The Spirit- Level. The spirit-level consists of a closed glass tube, A B (Figure 73), with a slight upward curvature. It is filled with spirit, except Fig. 73 . a bubble of air which .- -^^a. - v ^ _^r-- j tends to rise to the high- c j B< ^ p> est part of the tube. It is set in a case CD, and when this is placed on a perfectly level surface the bubble is exactly in the middle of the tube, as in the figure. 1 1 6. Rise of two Different Liquids in Communicating Vessels. If into one of two communicating tubes (Figure 74) we pour any liquid, as mercury, it will rise to the same height in both branches. If now we pour water into one of the tubes, the mercury will rise somewhat in the other, but not nearly so high as the water. The height of the two liquids above the surface of separation will be in the inverse ratio of the densities of the liquids. This is because the pressures of the two liquids at the surface of separation must be equal, so as to balance each other. Now the downward pressure of the water at the surface of the 7 6 ELEMENTS OF mercury is due to the depth of the water above it, and the upward pressure of the mercury at the same point is due to the depth of the mer- cury above the level of this surface in the other tube ; and to have these pressures equal, the depths must be in the inverse ratio of the densities of the liquids. 117. Capillarity. The rise of liquids in communicating ves- sels is modified in a remarkable manner when any of the ves- sels are of small diam- eter. Such narrow vessels and fine tubes are called capillary, from the Latin capillus, a hair ; and their action upon the rise of liquids within them is known as capillary action. This action is not, however, confined to the cases of fine tubes ; but when the containing vessel is wide, the action extends only a short distance from the sides of the vessel. The free surface of a liquid in a wide vessel is not horizontal in the neighborhood of the sides of the vessel, but presents a decided curvature. When the liquid wets the vessel, as in the case of water in a glass vessel (Figure 75), the surface of the liquid near the sides is concave. When the liquid does not ivet the vessel, as in the case of mercury in a glass vessel (Figure 76). the surface near the sides is convex. When a narrow tube of glass is plunged into water or any other liquid that will wet it (Figure 77), the liquid rises higher within the tube than on the outside, and the column of liquid within the tube will be concave at the top. In this case there is a capillary ascension which varies in amount with the diameter of the tube and the NATURAL PHILOSOPHY. 77 nature of the liquid. The finer the tube, the higher the liquid will rise in it. If a glass tube is plunged in mer- cury, which does not wet it, the mercury \\\\\ fall within the tube below the lei 8s ' 127. Use of the Barometer in measuring the Height of Mountains. One of the chief uses of the barometer is to measure the height of mountains. It has already been stated that the atmospheric pressure is less as the height above the earth is greater. When we have found at what rate it diminishes, we can readily find the height of mountains by means of the barometer. We have to find the difference between the read- ings of the barometer at the level of the sea and at the top of the mountain. This shows how much the pressure has diminished, and from this we can find the height of the mountain. If the pressure of the atmosphere decreased uniformly as we ascend, it would be very easy to find the elevation of a place by means of a ba- rometer. But, owing to the variations in the density of the air as we ascend, the pressure changes according to a complicated law ; and this complicates the formula for finding the exact ele- vation of a place from the readings of the barome- ter. As a rough rule, it may be stated that the barometer falls one inch for every 900 feet of ascent. 128. The Suction-Pump. The suction- pump consists of a cylinder, or barrel, at the top of a pipe A (Figure 86), communicating with the water in the well or cistern. A pis- ton Pis moved up and down in the barrel by means of the handle B. There is a valve S at the top of the pipe A, and another valve O in the piston. Both valves open upwards. The pump first ex- hausts the air from the pipe. As the air is exhausted, the water is driven up through the pipe and finally into the pump-barrel by the pressure of the air on the surface of the water in the cistern. Every time the piston is pushed down the valve S closes, and keeps the water in the barrel NATURAL PHILOSOPHY. from passing back into the cistern : at the same time the valve in the piston opens, and allows the water below it to pass above it. When the piston is raised, the valve O closes, and keeps the water above it from passing below it ; at the same time the valve is forced open by the pressure from below, and the water rushes up through it to fill the barrel behind the piston. As the piston is raised, the water above the piston passes out by the discharge- Fig. 86. Fig. 87. pipe at the top of the barrel. With this pump the water is raised into the barrel by atmospheric pressure, and is then lifted out of the barrel by the piston. Hence with the suction-pump water can be raised only about 30 feet high. 129. The Force-Pump . The simple force-pump is sho\ v:-, ELEMENTS OF in Figure 87. The piston P is solid. The discharge-pipe D communicates with the bottom of the cylinder, and has a valve O in it opening upward. There is also a valve S in the bottom of the barrel, also opening upward. When the plunger is raised the valve O closes, and the water rushes into the cylinder through the valve S; when the plunger is pressed down, the valve 5 1 closes, and the water is forced out through the valve O into the discharge-pipe. The only limit to the height to which water may be raised by means of this pump is that of the power used and of the strength of the pump. Fig. 88. Fig. 89. Fig. 90. The force-pump and the stiction-pump may be combined, as shown in Figures 88 and 89 ; that is to say, the cylinder of the force-pump may be at the top of a pipe about 30 feet above the surface of the water to be raised. 130. The Air-Chamber . The air-chamber is a device by which the water from a force-pump may be made to escape in a continuous and forcible stream. It consists of an air-tight box C above the valve O in the discharge- pipe (Figures 87 and 90). The pipe D passes nearly to the bottom of the chamber. When the pump is working, NATURAL PHILOSOPHY. the water is forced into the air-chamber through the valve O. As soon as the end of the pipe D is covered, the air in the upper part of the chamber begins to be compressed. The compression i?icreases the elastic force of the air, and causes it to press steadily and powerfully on the surface of the water, forcing the liquid out through the pipe D in a steady stream. If D ends in a narrow nozzle, the water will be obliged to pass through it very rapidly to escape from the chamber as rapidly as it is pumped into it. In this way a stream may be obtained of sufficient force to be thrown a great distance, as in the fire-engine. 131. The Siphon. The siphon is used for transferring liquids from one vessel to another. It consists of a bent tube with arms of unequal length (Figure 91). The air must be removed from the tube in the first place, either by applying the mouth to the end B, after the other arm of the siphon has been introduced into the vessel of water, or by filling the siphon with water before it is placed in the vessel. The water will flow through the siphon from C to B until Fig. 9 i. the vessel is emptied, or until the level of the water falls below the mouth of the arm in the vessel. The flow of the liquid through the siphon seems op- posed to the well-known fact that water will not run up hill. But notwithstanding this seem- ing inconsistency, it will be seen that the water is flowing from a higher level C to a lower level B. If we consider a layer of water in the siphon at J/, we see that the force which acts upon it from left to right is equal to the pressure of the atmosphere minus the pressure of 86 ELEMENTS OF the water in the tube from M to C, whose depth is D C; and the pressure which acts upon it from right to left is equal to the pressure of the atmosphere minus the pressure of the water in the tube from M to B, whose depth is A B. Since A is greater than D C, the pressure at M towards the right will be greater than that towards the left. Consequently the water at M moves on towards B, and as it moves away more water is driven up into the arm C M to take its place by the pressure of the atmosphere on the surface of the water in the vessel. No liquid will flow through a siphon unless the atmospheric pressure is sufficient to raise it to the bend of the tube. 132. Tantalus's Cup. This is a glass cup, with a siphon tube passing through the bottom, as shown in Figure 92. If water is poured into the cup, it will rise both inside and outside the siphon until it has reached the top of the tube, when it will begin to flow out. If the water runs into the cup less rapidly Fig. 92. than the siphon carries it out, it will sink in the cup until the shorter arm no longer dips into the liquid, and the flow from the siphon ceases. The cup will then fill, as before ; and so on. In many places there are springs which flow at intervals, like the siphon in this experiment, and whose action may be explained in the same way. A cavity under ground (Fig- ure 93) may be gradually filled with water by springs, and then emptied through an opening which forms a natural siphon. In some cases of this kind the flow stops and begins again several times in an hour. 133. Water- Wheels. One of the most important sources of mechanical power is that of falling water. The falling or running water is made to turn a wheel called a water- wheel ; and this wheel, by means of bands or gearing, is made to work almost any kind of machinery. Water-wheels are of various forms. Some turn on an upright axis, and others on a horizontal axis. The latter NATURAL PHILOSOPHY. are called vertical water-wheels, and the former horizontal water-wheels. - 93- One of the most common of vertical water-wheels is rep- resented in Figure 94. It consists of a series of boxes, or buckets, arranged on Fig . 94 . the outside of a wheel or cylinder. Water is al- lowed to flow into these buckets on one side of the wheel, and by its weight causes the wheel to turn. The buckets are so con- structed that they hold water as long as possi- ble while they are going clown, but allow it all to run out before they begin to rise on the other side. A wheel like this is called a breast-wheel. The overshot wheel is similar to the breast-wheel in all respects, except that the water is led over the top of the wheel, and poured into the buckets on the other side. 88 ELEMENTS OF The tmdershot wheel has boards projecting from its cir- cumference, like the paddle-wheel of a steamboat. The water runs under the wheel, and turns it by the force of the current pressing against the boards. 134. The Hydraulic Tourniquet. If a vessel (Figure 95), having a spout and faucet on one side, is filled with water Fj and floated in a dish on water so as to move easily, and the faucet is then opened so as to allow the water to escape, the vessel will begin to move backward. This is due to the reaction of the water against the back of the ves- sel. While the faucet was closed, the pressure of the water against the front of the vessel at the orifice balanced the pressure of the water against the back of 9 the vessel at the same point. But when the faucet is open, there is no pressure against the front of the vessel to balance the reaction of the wa- ter against the back ; hence the backward motion of the vessel while the water is escaping. The hydraulic tourniquet (Figure 96) consists of a vessel Fig. 96. NATURAL PHILOSOPHY. 8 9 capable of turning on a vertical axis. Two tubes project from the bottom of the vessel in opposite directions. The ends of these tubes are open, and are bent round in opposite directions. As the water escapes from these tubes, its reaction against the parts of the tubes opposite the openings causes the apparatus to rotate rapidly. 135. Turbine Wheel. One form of the turbine -wheel is shown in Figure 97. This wheel turns in a horizontal plane. The buckets are placed in the outer part of the wheel, which is free to turn on a vertical axis. The curved partitions, or guides, within the wheel are stationary. These partitions are placed at the bottom of a long cylinder, into which the water is admitted by the pipe. The partitions are curved, so as to direct the water against the buckets at the most advantageous angle. The water is discharged at the rim of the wheel. Figure 98 is a section of a turbine wheel. The buckets are represented in the outer portion, and the guides in the inner circle. There are many kinds of turbines, and their effective power Fig. 97. Fig. 98. is from 75 to 88 per cent of that in the acting body of water. In the best form of overshot and breast wheels, it is from 65 to 75 per cent, and in undershot wheels from 25 to 33 per cent. ELEMENTS OF D. SOLIDS. 136. Tendency of Solids to assume a Crystalline Struc- ttire. Solids, as a rule, tend to assume a crystalline struc- ture. " This tendency is best shown by allowing a substance to pass gradually from a liquid to a solid state. Place a rather dilute solution of acetate of lead (sugar of lead) in a tank with parallel sides of glass (such as is often used for projection), and fix two platinum wires in the solution, about an inch apart. Place the* tank before the condenser of a magic lantern, and focus the wires on the screen. Connect the wires with the poles of a small voltaic battery. The lead will separate from the solution, and collect as a solid upon the wire connected with the negative pole of the battery. Beautiful fern-like forms will be seen to grow up on the screen. These forms are the crystals of lead. As the substance passes slowly from the liquid to the solid state, the molecules are free to arrange them- selves according to their tendencies. If alum is added to hot water as long as it will dissolve, and then the water is allowed to cool slowly, a part of the alum will be deposited on the bottom of the dish, not in a confused mass, but in beautiful crystals. If saltpetre, nitrate of baryta, or cor- rosive sublimate is treated in the same way, beautiful crystals will be formed, but in each case the crystals will have a different shape. Melt some sulphur in a crucible, and allow it to cool slowly Fig. 99. till a crust forms on the surface ; then carefully break the crust and pour off the remaining liquid, and the crucible will be found lined with delicate needle- shaped crystals (Figure 99). Large crystals of many solids can be obtained by dissolving as much of the solid as is possible in cold water, and then setting it away in a shallow dish where it will 'be free from dust and disturbance, and allowing the water to evaporate very slowly. The more NATURAL PHILOSOPHY. 91 gradual the formation, the larger arc the crystals. The larger crystals seen in cabinets of minerals were probably cen- turies in forming. The water in which the solid was dis- solved found its way into a cavity of a rock, and there slowly evaporated. The tendency of the cohesive force to form the molecules into crystals is strikingly shown in cannon which have been many times fired, and in shafts of machinery and axles of car-wheels which are continually jarred. Such bodies often become brit- tle, and on breaking show the smooth faces of the crystals which have been formed. The continued jarring gives the mole- cules a slight freedom of motion, and crystals are slowly built up. Many solids are crystalline in structure which do not appear to be so. Thus, a piece of ice is a mass of the most perfect crystals, but they are so closely packed together that we cannot readily distinguish them. 137. Properties of So/ids. A body is said to be tena- cious when it is difficult to pull it in two. All solids are more or less tenacious, but they differ greatly in the degree of their tenacity. A body is said to be hard when it is difficult to scratch or indent it, that is to say, when it is difficult to displace its molecules. All solids are elastic within certain limits, and this elasticity may be developed by stretching, by bending, by twisting, and by compres- sion, that is, by any kind of strain whatever. Different solids, however, differ greatly in the limit of their elas- ticity (9). When the strain is carried beyond the limit of elasticity, the body must either break or take up perma- nently a new form. A body which is apt to break when strained beyond the limit of elasticity is said to be brittle. A brittle substance is not always easily broken. Such a body will not break unless strained beyond the limit of its elasticity, and that is often a difficult thing to do. It is not easy to* break a glass rod an inch in diameter, yet glass 92 ELEMENTS OF is the most brittle substance known. Substances which can readily take permanently new forms are said to be mal- leable or ductile. A malleable substance is one that can be hammered or rolled into sheets, and a ductile substance one that can be drawn into wire. All malleable substances are to some extent ductile, but the most malleable are not the most ductile. Gold is one of the most malleable of the metals. In the manu- facture of gold-leaf, it is hammered out into sheets so thin that it takes from 300,000 to 350,000 of them to make the thickness of a single inch. The gold is first rolled out into sheets by passing it many times between steel rollers in what is called a rolling-machine. The rollers are so arranged that they can be brought nearer to each other, pressing the gold into a thinner and thinner sheet every time it is passed between them. After it has thus been rolled out to the. thickness of writing-paper, it is cut up into pieces about an inch square. These are piled into a stack with alternate pieces of tough paper, and beaten with wooden mal- lets. They are again cut up into small pieces, and arranged in a stack with alternate squares of gold-heater's skin, and again beaten with mallets. This last process is usually repeated three times. NATURAL PHILOSOPHY. 93 II. SOUND. A. ORIGIN OF SOUND. 138. Sound originates in Molar Vibrations. Fix a point on a stand so as to be nearly in contact with a glass bell (Figure 100), and also hang a pith ball in contact Fi" 100. with the bell on the opposite side. If we draw a rosined bow across the edge of the bell, this will be made to emit a musical sound, and will also be heard to tap against the point, showing that it is in vibration. The pith ball will also be kept swinging as long as the sound continues. On touching the bell lightly, we feel that it is vibrating. 94 ELEMENTS OF Fig. 101. By grasping it firmly, we stop both the vibration and the sound. Strike one prong of a tuning-fork, and hold it to the ear ; it is found to be emitting sound. Fill a glass brimful of water, and hold the edge of the prongs in contact with the water ; a shower of spray will fly off on each side, showing that the prong is in vibration. When a string or wire is emitting a sound, it may often be seen to be vibrating. It as- Fig. 102 sumes the form of an elongated spindle (Figure 101). If the front of an organ pipe is made of glass, and a little stretched membrane covered with sand is lowered into it (Figure 102), when the pipe is emitting a sound, the sand will be seen to be agitated, showing that the air within the pipe is in a state of vibration. By similar experiments it has been ascertained that every body which is emitting sound is in a state of molar vibra- tion. When the vibration stops, the sound ceases. The more intense the vibration, the louder the sound. Sound, therefore, origi- nates i?i molar vibrations of ordinary matter, solid, liquid, or gaseous. 139. Fundamental and Harmonic Vibra- tions. Strew sand upon a horizontal plate of brass, and then, holding it with the thumb and finger (Figure 103), draw a bow across the edge of the plate so as to throw it into vibration. The sand will be tossed up and clown at first, but will quickly come to rest in definite NATURAL PHILOSOPHY. 95 lines, called nodal lines. These are lines of rest which separate the vibrating segments of the plate. By touching the plates at different points with the thumb and fingers, a great variety of figures may be produced with the sand, Fig. 194- 96 ELEMENTS OF showing that it is possible for the plate to break up into vibrating segments in a great many different ways. A series of these nodal figures is shown in Figure 104. Strings and columns of air may be also made to vibrate in segments. Figure 105 shows a string vibrating as a whole, in two segments, in three segments, and in four segments. The vibration of a body as a whole is called ^fundamental vibration ; and the vibration of its segments, its harmonic vibra- tion. The harmonic vibrations are more rapid than the funda- Fig. 105. mental vibrations. In a complete series of harmonic vibrations, the rate of vibration in the first harmonic is twice the funda- mental rate ; in the second harmonic, three times the fundamen- tal rate ; in the third harmonic, four times the fundamental rate; and so on. It is not only possible to produce harmonic vibrations in a body, but it is almost impossible not to produce them when a body is thrown into vibration. Whenever the fundamental vibration of a body is started, some of the harmonic vibrations are almost certain to be started with it. Hence it follows that the molar vibrations of bodies which originate sound are more or less complicated. B. PROPAGATION OF SOUND. 140. Sound is not propagated in a Vacuum. In Figure 1 06 the bell B is suspended by silk threads under the receiver of the air-pump. The bell is struck by means of NATURAL PHILOSOPHY. 97 clock-work, which can be set in motion by the sliding-rod r. If the bell is struck before exhausting the air, it can be distinctly heard ; but as the air is exhausted, the sound becomes fainter and fainter, Fig. 106. until at last it can hardly be perceived, even with the ear close to the receiver. Sound, then, cannot pass through a vacuum. The slight sound which is heard is transmitted by the little air left in the receiver, and by the cords which hold up the bell. 141. Sound is propagated in Gases, Liquids, and Solids. If hydrogen or any other gas is now allowed to pass into the receiver, the sound of the bell is heard again. If a bell is put under water and struck, it can be heard. If a person puts his ear close to the rail of an iron fence, and the rail is struck at a considerable distance, he hears the blow twice. The first sound comes through the rail ; the second, which soon follows, comes through the air. These experiments show that sound passes through gases, liquids, and solids. Sounds are propagated chiefly by the air. 142. Sound is propagated by Waves. When any vibrat- ing body, as the prong of a tuning-fork, is moving forward, it crowds together the molecules of the air in front of it, and so produces a strain of compression in the air. As the body moves back again to its original position and beyond it on the other side, it allows the molecules of the air 7 98 ELEMENTS OF behind it to separate somewhat, and so produces a strain of rarefaction in the air. Each of these strains is propa- gated through the air from molecule to molecule in pre- cisely the same way that the strain of compression was propagated from ball to ball in Figure 8. The molecules of air in front of the vibrating body simply vibrate to and fro with the sounding body. This vibrating motion is also propagated from molecule to molecule through the air ; but while the strains of compression and rarefaction are continually moving forward, each molecule of air moves forward a short distance and then returns. The strains of compression and rarefaction constitute what is called a sound -wave, and each strain is called a phase of the wave. If the body continues in vibration, the phases of the waves will follow each other in regular succession. The distance occupied by the two strains or phases is called the length of the wave. As the strain of compression is formed while the vibrating surface is moving forward, and the strain of rarefaction while the surface is moving backward, the length of each of these phases will be the distance the strain propagates itself while the sounding body performs half a vibration, and the length of the sound-wave will be the distance the strain can propagate itself while the sounding body is making a complete vibration. Hence, the faster the sounding body vibrates the shorter the sound-waves, and the slower it vibrates the longer the waves. 143. The Intensity of Sound. The intensity of sound at any point depends upon the energy of the vibration of the molecules at that point. As the sound-waves spread in all directiens from the sounding body, a greater and greater number of particles of air must be set in motion, and the motion of each must be more feeble ; and since the surfaces of spheres increase as the squares of their radii, the number of particles to be set in motion increases as the square of the distance from NATURAL PHILOSOPHY. 99 the sounding body. Sound, then, diminishes in intensity as the square of the distance from the sounding body increases. If the sound-waves are prevented from spreading in all direc- tions, the particles of air lose little of their motion, and the sound little of its intensity. Thus, Biot found that through one of the water-pipes of Paris words spoken in a very low tone could be heard at the distance of about three quarters of a mile. The sides of the pipe kept the sound-waves from spreading. In the same way conversation can be carried on between distant parts of a large building by means of small tubes, called speaking- tubes. 144. The Velocity of Sound. The velocity of sound in air has been several times determined by experiment. In 1822 the French Board of Longitude chose two heights near Paris, and from the top of each fired a cannon at intervals of ten minutes during the night. The time be- tween seeing the flash and hearing the report was care- fully noted at both stations, and the average of the results showed that sound travels through the air at the rate of 1090 feet a second. In such experiments the time taken by the light to pass between the stations is too small to be per- ceived. The velocity of sound in air depends somewhat upon the state of the atmosphere. Sound-waves travel faster with the wind than against it, and the higher the temperature of the air, the greater the velocity of sound in it. 'The velocity given above is for the temperature of 32. The velocity of sound in water is about 4700 feet a second, and its velocity in solids is still greater. 145. The Reflection of Sound. When sound-waves meet the surface of a new medium, they are, in part, thrown back, or reflected. In this reflection, as in all cases of reflected motion, the angles of incidence and reflection are equal to each other. Echoes are produced by the reflection of sound. In order to get an echo, we must have a reflecting surface far enough away 100 ELEMENTS OF to give an appreciable interval between the direct and reflected sounds. When the surface is less than 100 feet distant, the reflected sound blends with the direct sound. The reflecting surface has often such a shape as to cause the different portions of the reflected wave to converge to a point, and so to intensify the reflected sound. Multiple echoes may be produced by successive reflections from surfaces at different distances on the same side, or by alternate reflections from two surfaces on opposite sides. In some localities a pistol-shot is repeated thirty or forty times. 146. The Speaking-Trumpet. The speaking-trumpet (Figure 107) consists of a long tube (sometimes six feet long), slightly tapering towards the speaker, furnished at this end with a hollow mouth-piece, which nearly fits the lips, and at the other with a funnel-shaped enlargement, Fig. 107. called the bell, opening out to a width of about a foot. It is much used at sea, and is found very effectual in making the voice heard at a distance. The explanation usually given of its action is, that the slightly conical form of the long tube produces a series of reflections in directions more and more nearly parallel to the axis ; but this explana- tion fails to account for the utility of the bell, which expe- rience has shown to be considerable. 147. The Ear-Trumpet. The ear-trumpet is used by persons who are hard of hearing. It is essentially an inverted speaking-trumpet, and consists of a conical metallic tube, one of whose extremities, terminating in a bell, re- ceives the sound, while the other end is introduced into the ear. This instrument is the reverse of the speaking- trumpet. The bell serves as a mouth-piece ; that is, it receives the sound coming from the mouth of the person NATURAL PHILOSOPHY. IOI who speaks. These sounds are transmitted by a series of reflections to the interior of the trumpet, so that the waves, which would become greatly developed, are concentrated on the auditory apparatus, and produce a far greater effect than divergent waves would have done. 148. Loud ness of Sound. The loudness, or intensity, of sound depends upon the energy of the molecular vibrations in the sound-waves. In a curve representing the form of the sound-wave, the loud ness would be represented by the height of the curve, or the amplitude of the wave. 149. Pitch of Sound. The pitch of sound depends upon the rate at which the pulsations of sound strike upon the drum of the ear, or upon the length of the sound-waves. The length of the sound-waves depends chiefly upon the rate of vibration of the sonorous body. Two sounds are said to be in unison when the rate of vibration is the same; to form an octave, when their rates of vibration are as 2 to i ; a fifth, when their rates of vibra- tion are as 3 to 2 ; a fourth, when their rates of vibration are as 4 to 3 ; and a major third, when their rates of vibra- tion are as 5 to 4. In the lowest note of the organ there are 16^ vibrations a second. In the lowest note of the piano there are 33 vibrations a second, and in the highest note 4224 : giving a range of 7 octaves. In the highest note ever heard in an orchestra there are 4752 vibrations a second. This note is given by the piccolo flute. In the shrillest sounds that are audible there are about 32.000 vibrations a second, the upper limit of audibility varying with different persons. The voice of ordinary chorus-singers ranges from TOO to 1000 vibrations a second, and the extreme limits of the human voice are 50 and 1500 vibrations a second. 150. Quality of Sound. The quality of sound depends upon the form of the sound-waves, that is, upon the har- monic vibrations which are present with the fundamental vibrations in the sonorous body. The pitch of sound is 102 ELEMENTS OF determined chiefly by the fundamental note. Two sounds of the same pitch may differ in quality, because of differ- ences in their harmonics, fundamental tones are those produced by the fundamental vibrations of a sonorous body ; and harmonic tones, those produced by the harmonic vibrations. No two instruments or voices give tones of the same quality, though they may be of the same loud- ness and pitch. The difference between a noise and a musical sound is that the latter is smooth and regular, and the former rough and irreg- ular. Musical sounds are produced by rapid periodic vibrations of a body, and noises by non-periodic vibrations. 151. Interference of Sound. When two equal water- waves meet in the same phase, namely, so that the crest of one coincides with the crest of the other, and the hollow of one with the hollow of the other, their combination produces at the point of meeting a wave of double the height. Were the two waves to meet in opposite phases, that is, so that the hollow of one coincides with the crest of the other, their combination would leave the surface of the water undisturbed ; there would be neither depression nor elevation. In a similar way, when two equal sound-waves meet in the same phase, their combination would produce at the point of meeting a wave of twice the degree of condensation and rarefaction of either of the component waves. Were the two waves to meet in opposite phases, the air would be undisturbed at the place of meeting; there would be neither condensation nor rarefaction. An ear at the point of meeting of the wave in the first case would hear a sound much louder than that conveyed by either sound-wave alone ; while in the second case it would hear no sound at all. The meeting of two sound-waves so as to neutralize each other is called the interference of sound. Strike a tuning-fork so as to throw its prongs into vibration, NATURAL PHILOSOPHY. 103 hold it vertically near the ear, and turn it slowly around so as to bring the sides, the edges, and the corners of the prongs successively towards the ear. Four positions of the fork will be found in which its sound will be in- Fig. 108. audible. Let a and b (Figure 108) be \ the ends of the prongs of a tuning-fork \ in vibration. The sound of the fork is inaudible when the ear is on any one of \ the dotted lines. As the prongs vibrate, each develops a series of waves, and along the dotted lines these two sets of waves will be of equal intensity and in opposite phases. Hence along these lines the two sets of waves neutralize each other, and silence results from the combination of two sounds. 152. Musical Beats. Suppose two tuning-forks, slightly different in pitch, to be started together, and suppose the prongs of both to be moving forward at the same time ; they will start waves of the same phase which will coincide with and intensify each other. The fork having the higher pitch will, however, immediately begin to gain on the other, and the coin- cidence of the waves will be less and less perfect until this fork has gained half a vibration on the other. The prongs of the two forks will now be moving in opposite directions at the same time, and the waves started by the two forks will be in opposi- tion, and will neutralize each other wholly or in part. After this there will again be partial coincidence of the waves, and the degree of coincidence will increase till the higher fork has gained a whole vibration on the lower one, when the coincidence will again be complete. When two such forks are started together, the sound gradually dies away till it becomes nearly -or altogether inaudible ; it then swells out loudly, and gradually dies away again at regular intervals. These gradual risings and fallings in the intensity of sound are called beats. These beats occur whenever two sounds of nearly the same pitch are produced together. The rate of beating will be equal to the difference of the rate of "vibration in the two sonorous bodies. If one of the bodies gains one vibration a second on the other," the sounds will beat once a second; if it gains two 104 ELEMENTS OF vibrations a second, the sounds will beat twice a second ; and so on. Even after the beats become too rapid to be distinguished by the ear, they give a disagreeable roughness to the sound. According to Helmholtz, dissonance is entirely due to the rough- ness produced by a rapid succession of beats, which take place between either the fundamental tones or the harmonics which are present in the two sounds. C. RESONANCE. 153. Sympathetic Vibrations of Tuning-Porks. Take two tuning-forks of exactly the same pitch, cause one of them to vibrate, and hold it near the other without touch- ing it. The second fork will soon begin to vibrate, and will emit a distinctly audible sound after the first has been stopped. The second fork will not be started by the first unless the two are of exactly the same pitch, as may be shown by sticking a little pellet of wax to the prong of one of the forks so as to diminish its rate of vibration. Vibra- tions started in one body by the vibrations of another are called sympathetic vibrations. The production of sound by sympathetic vibrations is called resonance. The vibrations are communicated from one fork to the other by means of the air. The vibrations of the first fork produce condensations and rarefactions in the air which succeed each other at the rate at which the fork is vibrating. The number of condensations which would pass any point in a second is exactly equal to the number of vibrations executed by the fork in a second. In the condensations the pressure of the air is in- creased, and in the rarefactions it is diminished. Each con- densation as it passes the prong of the second fork gives it a little push. As the second fork vibrates at exactly the same rate as the first, each condensation arrives in time to push the prong just as it is ready to move forward of itself; hence the prong is always pushed in the direction in which it is moving. The push of one condensation moves the prong but little, but NATURAL PHILOSOPHY. 105 the pushes are so timed that each moves it a little farther than the last, until the fork is made to vibrate strongly. When the second fork cannot vibrate at the same rate as the first, the condensation will sometimes push in the direction in which the prong is moving and sometimes in the opposite direction. Hence one push will neutralize the effect of another instead of augmenting it. 154. Sympathetic Vibrations of Strings. If a piano is opened and one of the keys gently depressed so as to raise the damper without striking the string with the hammer, and the note of the string is then sung over the piano, the string will begin to vibrate and will emit an audible sound for a little time after the voice ceases. It is only necessary to hit the pitch of a string accurately and to sustain the note sufficiently. Strings may be thrown into vibration by their harmonic notes as well as by their fundamental notes. 155. Sympathetic Vibrations of Masses of A ir. I f a vi brat- ing tuning-fork is held at the end of a tube an inch and a half or two inches in diameter, the* sound of the fork will be power- fully reinforced, provided the tube is of suitable length. The suitable length for a tube open at both ends is one half of the length of the wave produced by the fork. A tube closed at one end resounds most powerfully when its length is one quarter of the length of the wave produced by the fork. The column of air in the tube is thrown into powerful sympathetic vibrations by the fork, and these vibrations greatly augment the sound. The moment the fork is stopped the resonance ceases. Columns of air may also be thrown into sympathetic vibration by their harmonic vibrations. By altering the shape of the tube it may be made to reinforce certain harmonics more powerfully than others, and so change the quality of the exciting sound. 156. Sounding Boards and Boxes. The sound of a tuning-fork is feeble unless reinforced by a resonant case of suitable dimensions to which the fork is fixed. Such a resonant case is called a sounding-box. Thin pieces of dry straight-grained pine, such as are em- ployed for the faces of violins and the sounding-boards of pianos, are capable of vibrating more or less freely, in any 106 ELEMENTS OF period lying between certain wide limits. They are accordingly set in vibration by all the notes of their respective instruments ; and by the large surface with which they act upon the air, they contribute in a very high degree to increase the sonorous effect. All stringed instruments are provided with sounding-boards ; and their quality mainly depends on the greater or less readi- ness with which these respond to the vibrations of the strings. D. MUSICAL INSTRUMENTS. 157. .Stringed Instruments. In one class of musical instruments the notes are produced by the transverse vibra- tions of strings. These instruments are called stringed instruments. The rate at which a string vibrates depends upon its length, its weight, and its tension. The shorter, Fig. 109. the tighter, and the lighter a string, the faster it vibrates. Strings may be thrown into transverse vibration by draw- ing a rosined bow across them, as in the case of the violin ; or by plucking them with the finger, as in the case of the harp ; or by striking them with a hammer, as in the case of the piano. In the piano there is a string for every note. In the violin and similar instruments, several notes are obtained from the same string by fingering it so as to change its length and tension. 158. The Sonometer. The sonometer (Figure 109) is an instrument for investigating the laws of the vibration of strings. It consists essentially of a string or wire stretched over a sounding-box by means of a weight. One end of NATURAL PHILOSOPHY. 107 the string is secured to a fixed point at one end of the sounding-box ; the other end passes over a pulley, and carries weights which can be altered at pleasure. Near the two ends of the box are two fixed bridges, over which the cord passes. There is also a movable bridge, which can be employed for altering the length of the vibrating portion. 159. Wind Instruments. In wind instruments the notes are produced by the longitudinal vibrations of columns of air enclosed in pipes. The rate of vibration depends upon the length of the column, and upon whether the pipe is opened or closed. The shorter a column of air \hefaster it vibrates, and the air in an open tube vibrates twice as fast as that in a closed pipe of the same length. This is because the air in a closed pipe vibrates as a whole, while that in an open pipe vibrates in two segments, there being a stationary point or node at the centre of the pipe. In an organ there are as many pipes as notes, only one note being obtained from each pipe. In the case of the flute and similar wind instruments, several notes are obtained from one pipe by opening and closing the holes at the side of the pipe so as to alter the length of the vibrating column of air. and by altering the strength of the blast so as to change from the fun- damental note of the pipe to one or other of its harmonics. In all wind instruments the pipe is made to speak by reso- nance. The sympathetic vibrations in the pipe are sometimes started by the vibrations of the lips, as in the case of the trumpet ; or by the vibrations of a spring called a reed, as in the case of the clarionet ; or by the flutter of a jet of air when blown against a sharp edge, as in the case of the flute. 1 60. Organ Pipes. Organ pipes are made of wood or metal, and they are made to sound either by blowing against a sharp edge so as to produce a flutter, or by blowing against a spring so as to throw it into vibration. Pipes which are made to sound in the first way are called flue-pipes ; and those made to sound in the second way, reed-pipes. Pipes closed at one end are called shopped pipes ; and those open at both ends are called open pipes. io8 ELEMENTS OF Two forms of flue-pipes are shown in Figures no and in ; the one being made of wood, the other of metal. The air passes from the bellows through the tube P into a chamber, which is closed at the top except the narrow slit z. The air compressed in the chamber passes through this slit in a thin sheet, which breaks against a sharp edge #, and there produces a flutter. The space between the edge a and the slit below is called the mouth of the pipe. The metal reed commonly used in organ Fig. no. Fig. in. pipes is shown in Figures 112 and 113. It consists of a long strip of flexible metal V V, placed in a rectangular opening, through which the current of air enters the pipe. As soon as the air begins to enter the pipe, the force of the blast bends down the spring of the reed so as to close the opening. The elasticity of the reed causes it to fly back at once, so as to open the pipe and allow the air to enter again. It thus breaks up the current of air into a regular succession of little puffs. NATURAL PHILOSOPHY. I0 9 161. The Organ of the Human Voice. The organ of voice in man is situated at the top of the windpipe, or trachea, which is the tube through which the air is blown from the lungs. A pair of Figs. 113 Fig. elastic bands, called the vocal chords, stretched across the top of the windpipe so as nearly to close it, form a double reed. When air is forced from the lungs through the slit between the chords, these are made to vibrate. By changes in their tension, their rate of vibration is varied, and the sound raised or lowered in pitch. The cavity of the mouth and nose acts as a resonant tube* and by altering the shape of this cav- ity we can give greater promi- nence to either the fundamental note of the vocal chords or to any of their harmonics. 162. Singing Flames. The air in an open tube may be made to give a sound by means of a luminous jet of hydrogen, coal gas, etc. When a glass tube about twelve inches long is held over a lighted jet of hydrogen (Figure 114), a note is produced which, if the tube is in a cer- tain position, is the fundamental note of the tube. The current of air passing up through the tube over the flame causes the flame to flutter, and the air in the tube reinforces some pulsations of this flutter by sympathetic vibration..- The vibration of the column of air in the tube re- acts upon the flame, and causes it to vibrate more regularly and no ELEMENTS OF more powerfully. The note depends on the size of the flame and the length of the tube. If, while the tube emits a certain sound, the voice is gradu- ally raised to the same pitch, as -soon as the note is nearly in unison with that of the tube, the flame is agitated, jump- ing up and down, but becomes steady when the two sounds are in unison. If the note is then gradually raised in pitch, the pulsations again commence ; they are the optical expres- sions of the beats which occur near perfect unison. If, while the jet burns in the tube, and produces a note, the position of the tube is slightly altered, a point is reached at which no sound is heard. If now the voice or the tuning-fork is pitched at the note produced by the jet, it begins to sing, and continues to sing even after the voice or fork is silent. A mere noise or shouting at an incorrect pitch affects the flame, but does not cause it to sing. Fig. 115- 163. Edison's Phonograph. In Edison's phonograph, the vibrations of the air are first taken up by a thin plate of metal, and are then permanently registered on a sheet of tin-foil. This instrument (Figures 115 and 116) consists essentially of a brass cylinder C and of a mouth-piece F. On the surface of the cylinder is constructed a very accurate spiral groove, the threads of which are about T ^ of an inch apart. The cylinder is turned by the crank D upon the axis A B. On one end of this axis is cut a thread of the same fineness as the groove on the cylinder. A sheet of tin-foil is fastened smoothly on the surface of the cylinder. The mouth-piece (Figure 1 16) is supported on a post G, and may be moved to and from the cylinder by the lever H. At the bottom of the mouth-piece there is an iron plate A about T ^ T of an inch thick. Under this plate are two NATURAL PHILOSOPHY. II I pieces of rubber tubing x and x, which separate it from a spring supported by E, and carrying a round steel point P, which rests upon the tin-foil on the cylinder, just over the spiral groove. If the crank is turned, the thread on the axis causes the cylinder to move forward so as to keep the groove always under the point. When the iron plate is at rest, if we turn the crank the point marks a spiral line of uniform depth on the tin-foil. If \ve speak or sing into the mouth-piece, the vibrations of the air are communicated to the iron plate, and from this to the point Fig. 116. by means of the rubber tubing. If the crank is turned while a person is speaking or singing into the mouth-piece, the point will mark a dotted line on the tin-foil. The depth of the indentations will exactly represent the densities of the different Portions of the sound-waves which encounter the disc. The forms of the sound-waves are thus registered on the tin-foil, and may be studied at leisure with the microscope. If, after talking into the mouth-piece, we set the cylinder back to the 'starting-point and then turn the crank, the point will follow the indentations in the tin-foil, and so be compelled r 112 ELEMENTS OF to vibrate exactly as it did when it made these indentations in the foil. The vibrations of the point will be communicated to the thin iron plate by means of the rubber, and by the plate to the air. Thus the words spoken into the mouth-piece will be exactly repeated, and by the use of a properly constructed mouth-piece they may be rendered audible throughout a large hall. By resetting the cylinder they may be repeated several times, though more feebly each time the foil is passed under the point, the indentations being gradually smoothed out. E. THE HUMAN EAR. 164. The Human Ear. A section of the ear is shown in Figure 117. The external opening is closed at the bottom by a circular membrane called the tympanum, behind which is the cavity called the drum of the ear. This cavity is sep- arated from the space between it and the brain by a bony partition, in which are two openings, the one round and the other oval. These also are closed by delicate membranes. Across the cavity of the drum stretches a series of four little bones : the first, called the hammer, is attached to the tym- panum ; the second, called the anvil, is connected by a joint with the hammer ; a third little round bone connects the anvil with the stirrup bone, which has its oval base planted against the membrane of the oval opening, almost covering it. Behind the bony partition, and between it and the brain, is the labyrinth, which is filled with water, and over the lining of which the fibres of the auditory nerve are distributed. The tympanum intercepts the vibrations of the air in the ex- ternal ear, and transmits them through the series of bones in the drum to the membrane which separates the drum from the laby- rinth ; and thence to the liquid within the labyrinth itself, which in turn transmits them to the nerves. The transmission, how- ever, is not direct. At a certain place within the labyrinth, ex- ceedingly fine elastic bristles, terminating in sharp points, grow up between the nerve fibres. These bristles of Schultze (so called from the discoverer) are exactly fitted to sympathize with those vibrations of the water which correspond to their proper periods. Thrown thus into vibration, the bristles stir the nerve fibres which lie between their roots, and the nerve transmits the NATURAL PHILOSOPHY. impression to the brain, and thus to the mind. At another place in the labyrinth we have little crystalline particles, calle'd oto- litks, embedded among the nervous filaments, and exerting, when they vibrate, an intermittent pressure upon the adjacent nerve fibres. The otoliths appear to be fitted, by their weight, to receive and prolong the vibrations of evanescent sounds which might otherwise escape attention. The bristles of Schultze, on the contrary, are peculiarly fitted for the transmission of con- tinuous vibrations. Finally, there is in the labyrinth the organ of Corti (named from the discoverer^, which is to all appearance Fig. 117. a musical instrument, with its chords so stretched as to receive vibrations of different periods, and transmit them to the nerve filaments which traverse the organ. Within the ear of man, and without his knowledge or contrivance, this lute of 3000 strings has existed for ages, receiving the music of the outer world, and rendering it fit for reception by the brain. Each musical'tremor which falls upon this organ selects from its tense fibres the one appropriate to its own pitch, and throws that fibre into sympathetic vibration. And thus, no matter how compli- cated the motion of the external air may be, these microscopic strings can analyze it, and reveal the elements of which it is composed. - 114 ELEMENTS OF III. HEAT. I. EFFECTS OF HEAT. / A. EXPANSION. 165. Expansion of Solids. As a rule, bodies expand ivhen heated, solids being the least expansible, liquids next, and gases the most expansible. The linear expansion of a solid may be illustrated by means of the apparatus shown in Figure 118. The metal rod A is sup- ported on two standards. It is fastened at the end B by the binding screw ; the other end passes loosely through its stand- ard, and presses against the short arm of the index K, which Fig. 118. moves over a graduated arc. Under the rod there is a vessel filled with alcohol. The rod is adjusted so that the index shall be at zero on the scale, and the alcohol is lighted. As the rod becomes heated, the index rises, showing that the rod has ex- panded in length so as to move forward the short arm of the index. If a brass and iron rod of the same length and thickness are tried in succession, and each is raised to a bright red heat, it NATURAL PHILOSOPHY. 115 will be found that the brass rod will expand considerably more than the iron. As a rule different solids expand unequally when heated equally. The cubical expansion of a solid may be illustrated by means of the ring and ball shown in Figure 119. When cool, the ball will just pass through the ring. If we heat the ball by holding it for a time in the flame of the lamp, it will no longer pass through the ring ; but if allowed to cool, it will again pass through. If, while the heated ball rests on the ring, this is heated equally with the ball, the latter will again pass through the ring, the two being equally expanded by the heat. 1 66. Force of Expansion of Solids. The force of ex- pansion is very great, being equal to that which would be Fig. necessary to compress the body to its original dimensions. Thus, for instance, iron when heated from 32 to 212 increases by .0012 of its original length. In order to produce a corresponding change of length in a rod an inch square, a force of about 15 tons would be required. It would be useless to attempt to offer any mechanical resist- ance to a force so enormous ; the only thing that can be done, in the case of structures in which metals are employed, is to ar- range the parts in such a manner that the expansion shall not be attended with any evil effects. Thus, in a railway, the rails do not touch each other, a small interval being left to allow room for the variations of length. Iron beams employed in buildings must have the ends free to move forward, without encountering any obstacles, which they would inevitably overthrow. Sheets u6 ELEMENTS OF of zinc or lead employed in roofing are so arranged as to be able to overlap one another on expansion. 167. Compensating Pendulum. Suppose a clock to keep exact time at a certain temperature ; then, if the temperature rises, the length of the pendulum will increase (62), and with it the duration of each oscillation, so that the clock will lose. The opposite effect would be produced by a fall of temperature. Hence the clock is liable to go too fast in winter, and too slow in Fig. 120. Fig. 121. _J I F f f 1 q c c T~ C summer ; and we must move the ball of the pendulum from time to time in order to insure its regularity. The effect of temperature may be notably diminished by means of compensating pendulums, of which there are several different kinds. Harrison's gridiron pendulum (Figures 120 and 121) consists of four oblong frames, the uprights of which are alternately of NATURAL PHILOSOPHY. llf brass, C, and of steel, F. These are so put together that the expansion of the steel rods alone would tend to lower the ball, while the expansion of the brass rods alone would tend to raise it. The lengths of the rods are so adjusted that the expansion of one set of rods shall just balance that of the other, thus keeping the ball of the pendulum all the time at exactly the same distance from the point of suspension. Graham's pendulum consists of an iron rod carrying at the bottom a frame which holds one or two tubes containing mercury I Figure 122). The mercury takes the place of the ball of the pendulum. The expansion of the rod tends to lower the centre of gravity of the mercury, while the expansion of the mercury, since it is free to expand only upward, tends to raise the centre of gravity. The quantity Fig. 123. of mercury is adjusted so that its expan- sion shall balance that of the rod, and thus keep the centre of gravity of the mercury at the same height all the time. 1 68. Compensation Balance-Wheel. The rate of a watch is controlled by the vibration of the balance-wheel. The larger this wheel the slower it vibrates. and the smaller it is the faster it vibrates. Hence changes of temperature have the same effect on the rate of watches as on that of clocks. The rim of the compensation balance-wheel (Fig- ure 123) is made in sections, which are weighted at their free ends, and are composed of two metals, the more expansible of which is on the outer side of the sections. The expansion of the spokes tends to carry the weights away from the centre of the wheel and so to make the wheel larger. When the sections of the rim expand, they become more curved, since they expand more rapidly on the outside than on the inside ; hence they tend to carry the weight in towards the centre and so to make the wheel smaller. The parts of the wheel are so adjusted that the expansion of the sections of the rim just balances that of the spokes. 169. Expansion of Liquids. The expansion of a liquid may be illustrated by means of a bulb with a projecting n8 ELEMENTS OF Fig. 124. tube (Figure 124), filled with water or other liquid up to the point a. If the bulb is immersed in a vessel of hot water, the liquid in the stem at first falls to />, and then gradually rises to a. The liquid falls at first, because the bulb, being the first heated, is also the first to expand, and its capacity is thus increased. After- wards, as the liquid becomes heated, it expands more rapidly than the globe ; hence it rises in the tube. If two bulbs, with projecting tubes, and of exactly the same size, are filled, one with water and the other with alcohol, and are then heated equally, the alco- hol will be seen to expand more rapidly than the water. In general, different liquids when heated equally expand un- equally. 170. Anomalous Expansion and Contraction of Water. If we fill a bulb and tube with water, and surround the bulb with a freezing mixture, the water in the stem will steadily fall till the temperature of the water has reached 39 ; it will then begin to rise again, and will continue to rise till the temperature reaches 32. If now the bulb is gradually heated, the water will fall in the stem till the temperature reaches 39 ; it will then begin to expand, and will continue to expand until it boils. Water at 39 will expand whether it is heated or cooled. It follows from this, that water is at its greatest density at 39. Hence this point of temperature is called its point of maximum density. 171. Expansion of Gases. The expansion of air may NATURAL PHILOSOPHY. Fig. 125. be illustrated by means of the bulb and tube shown in Figure 125. The bulb is filled with air, which is separated from the external air by a small column of liquid in the stem, which serves also as an index. When the globe is warmed by the hands, the index is rapidly pushed up. It has been found that all gases expand equally for the same rise of tem- perature, and that under a uniform pres- sure a gas will expand so as to double its volume for a rise of temperature of about 490. 172. Expansion due to an Increase of Molecular Motion. The molecules of bod- ies are all the time moving rapidly to and fro. When heat is applied to a body, its molecules are made to move more rapidly, and this increased agitation causes them to move farther apart, and the body to expand. B. MEASUREMENT OF TEMPERATURE. 173. Temperature. When we wish to indicate hoiv hot a body is, we say that it has a certain temperature. The word temperature is the noun which corresponds to the adjective hot. We estimate how hot a body is from its power of imparting heat to other bodies. The body which has the greater power of imparting heat is said to be the hotter, or to have the higher temperature. Temperature is the thermal condition of a body considered with reference to its power of imparting heat to other bodies. An instrument used/0/- measuring temperature 'is called a thermometer. 174. jThe Mercurial Thermometer. In ordinary ther- mometers changes of temperature are indicated and meas- I2O ELEMENTS OF Fig. 126. ured by the expansion and contraction of mercury. The instrument is called a mercurial thermome- ter. It consists essentially (Figure 126) of a tube with a very fine calibre, closed at one end, and having a reservoir at the other end, usually in the form of a globe or cylinder. The bulb and a portion of the stem are filled with mercury. As the temperature changes, the top of the column of mercury in the tube rises and falls. A scale is either engraved on the stem or placed behind it. 175. How the Mercurial Thermometer is Graduated. The two fixed points of tempera- ture are those at which ice melts and water boils. The former is called \\\e freezing-point, and the latter the boiling-point. In order to determine the position of the freezing-point on the stem, the bulb and the lower part of the stem are surrounded by melting ice, contained in a perforated vessel so as to allow the water pro- duced by the melting to escape (Figure 127). When the column in the stem ceases to fall, a mark is made on the tube, with a fine diamond, at the top of the mercurial column. This mark in- dicates the position of the freezing- point for this particular thermometer. In order to obtain the position of the boiling-point, the bulb and stem of the thermometer are enveloped in steam from boiling water, as shown in Figure 128. The height to which the mercury rises is then marked on the stem. 176. The Fahrenheit and Centigrade Scales. There are two thermometer scales in common use, the Fahrenheit and the Centigrade. The ordinary scale in use in this country Fig. 127. NATURAL PHILOSOPHY. 121 and in England is the Fahrenheit scale. On this scale the freezing-point is marked 32 and the boiling-point 212. The space between the freezing and boiling points is divided into 1 80 equal parts, each of which is called a degree. These divisions are continued on the scale above the boiling-point and below the freezing-point to the ends of Fig. 128. the tube. A Fahrenheit degree is T |Q of the difference of temperature between the freezing and boiling points. On the Centigrade scale the freezing-point is marked o and the boiling-point 100, and the space between the two is divided into 100 equal parts, the divisions being con- tinued to the ends of the tube. A Centigrade degree is T y of the difference of temperature between the freez- 122 ELEMENTS OF ing and boiling points. A Fahrenheit degree is f of a Centigrade degree. The zero of the Centigrade scale is the temperature of melting ice. The zero of the Fahrenheit scale is 32 below the melting-point of ice. It was the lowest temperature that Fahrenheit could obtain with a mixture of salt and ice. 177. Alcohol Thermometers. Mercury freezes at a temper- ature of about 40 below zero, or of 40 F.; hence it cannot be used for measuring temperatures below that point. Low temperatures are sometimes measured by means of an alcohol thermometer. This is constructed in the same way as a mer- curial thermometer, but the bulb is rilled with alcohol instead of mercury. As alcohol boils at a temperature of about 175 F. an alcohol thermometer cannot be used for measuring high temperatures. 178. Pyrometers. Mercury boils at a temperature of about 670 F. ; hence it cannot be employed to measure temperatures above that point. Very high temperatures are often measured by the expansion of solids. The instrument used is called a Pyrometer. One form of pyrometer (Figure 129) consists of a Fig. 129. bar of iron lying in^the groove of a porcelain slab. One end of the iron bar presses against the end of the groove, and the other end against the arm of an indicator. As the bar expands it moves the index point, the position of which indicates roughly the temperature to which the bar is exposed. Such pyrometers are not very accurate. 179. The Differential Thermometer. Leslie's differential thermometer (Figure 130) enables us to measure small varia- tions of temperature. A column of sulphuric acid, colored red, stands in the two branches of a bent tube, which terminates in two globes of equal volume. When the air contained in NATURAL PHILOSOPHY. I2 3 Fig. 130. the two globes is at the same temperature, the liquid stands at the same height in the two branches. This point is marked zero. One of the globes being then maintained at a constant tempera- ture, the other is raised through, for instance, 5 degrees, when the column rises on the side of the colder globe up to a point a, and descends on the other side to a point b. Suppose the space trav- ersed by the liquid in each branch to be divided into 10 equal parts, each part will be equivalent to a quarter of a degree. This division is continued upon each branch on both sides of zero. QUESTIONS ON THERMOMETER SCALES. 72. Oil of vitriol freezes at 30 F. This is equivalent to what temperature on the Centigrade scale ? 73. Lead melts at 620 F. What is the temperature at which lead melts on the Centigrade scale ? 74. Iron melts at 2800 F. What is the equivalent tempera- ture on the Centigrade scale ? 75. What temperature on the Fahrenheit scale corresponds to 50 C. ? To - 25 C. ? To 380 C. ? C. CHANGE OF STATE. /. FUSION AND SOLIDIFICATION. 1 80. The Fusing-Point. When any solid is sufficiently heated it will melt, but different solids melt at very different temperatures. The temperature at which a solid melts is called its melting-point or fusing-point. Mercury melts at 40 F., ice at 32 F., lead at 608 F., and silver at 1832 F. Most substances expand on melting, but a few, like ice, con- tract. When a substance expands on melting, an increase of 124 ELEMENTS OF pressure upon it will tend to hinder its melting, and will there- fore raise its melting-point ; but if it contracts on melting, an increase of pressure will tend to help its melting, and will accordingly lower its melting-point. The passage from the solid to the liquid state is generally abrupt, but this is not always the case. Glass, for instance, before reaching a state of perfect liquefaction, passes through a series of intermediate stages in which it is of a viscous con- sistency, and can be easily drawn out into exceedingly fine threads, or moulded into different shapes. 181. Constant Temperature during Fusion. During the entire time of fusion the temperature remains constant. Thus, if a vessel containing ice is placed on the fire, the ice will melt more quickly as the fire is hotter ; but if the mixture of ice and water is constantly stirred, a thermom- eter placed in it will indicate the temperature 32 without variation, so long as any ice remains unmelted ; it is only after all the ice has become liquid that a rise of tempera- ture will be observed. 182. Latent Heat of Fusion. As we have just seen, all the heat that enters the body while it is undergoing fusion is employed in changing its state. The heat thus employed is said to be rendered latent, and is called the latent heat of fusion, or, since it exists in the latent state in the liquid formed, the latent heat of the liquid. 183. Solidification. Were any substance sufficiently cooled, it would become solid. This conversion of a sub- stance into a solid by a reduction of temperature is called solidification, or congelation. 184. Change of Volume in Congelation. In passing from the liquid to the solid state, bodies generally undergo a diminution of volume ; there are, however, exceptions, such as ice, bismuth, silver, cast-iron, and type-metal. It is this property which renders these latter substances so well adapted for casting, as it enables the metal to penetrate completely into every part of the mould. NATURAL PHILOSOPHY. 125 The expansion of ice is considerable, amounting to about ^ of its bulk ; its production is attended by enormous mechanical force, just as in the analogous case of expansion by heat (166). Its effect in bursting water-pipes is well known. Major Williams at Quebec filled a 1 2-inch shell with water, and closed it with a wooden plug, driven in with a mallet. The shell was then ex- posed to the air, the temperature being 18 F. The water froze, and the plug was projected to a distance of more than 100 yards, while a cylinder of ice of about 8 inches in length was protruded from the hole. In another experiment the shell split in halves, and a sheet of ice issued from the rent (Figure 131)- Fig. 131. It is the expansion and consequent lightness of ice which enables it to float on the surface of the >vater, and to protect animal life beneath. //. EVAPORATION AND CONDENSATION. 185. Evaporation of Liquids. The majority of liquids, when left to themselves in contact with the atmosphere, evaporate, that is, gradually pass into the state of vapor and disappear. This occurs much more rapidly with some liquids than with others, and those which evaporate most readily are said to be the most volatile. Thus, if a drop of ether is let fall upon any substance, it disappears almost instantaneously ; alcohol also evaporates very quickly, but water requires a much longer time. The change is in all 126 ELEMENTS OF cases accelerated by an increase of temperature; in fact, when we dry a body before the fire, we are simply availing our- selves of this property of heat to hasten the evaporation of the moisture of the body. Evaporation may also take place from solids. 1 86. Gas and Vapor. The words gas and vapor have no essential difference of meaning. A vapor is the gas into which a liquid is changed by evaporation. Every gas is probably the vapor of a certain liquid. The word vapor is especially applied to the gaseous condition of bodies, which are usually met with in the liquid or solid state, as water, sulphur, etc. ; while the word gas generally denotes a body which, under ordinary conditions, is never found in any state but the gaseous. When the air or any other gas contains all the vapor it can hold, it is said to be saturated with that vapor. The amount of vapor required to saturate a gas increases with the temperature. This may be shown by the following experiment. Pour a few drops of water into a glass flask, and then apply heat till the water is entirely evaporated and the flask appears dry. If the flask is allowed to cool, moisture will collect on its inner surface. 187. Dry Air and Currents of Air favorable to Evapora- tion. The dryer the air the more rapid the evaporation, be- cause the more readily will the atmosphere take up the vapor formed. Currents of air favor evaporation, because they pre- vent any layer of air from remaining long enough in contact with the liquid to become saturated with' vapor. Other things being equal, wet clothes will dry much faster on a windy day than on a still day. 1 88. Latent Heat of Evaporation. Evaporation is a cooling process. If a few drops of ether are allowed to fall on the hand, they will evaporate rapidly, and a sensation of cold will be experienced. If the bulb of a thermometer is dipped in ether and removed, the ether which adheres NATURAL PHILOSOPHY. 12? to it will quickly evaporate, and the mercury will fall sev- eral degrees. The heat consumed in evaporating a liquid is called the latent heat of evaporation, or the latent heat of the Tapor. 189. Ebullition. When a liquid contained in an ojjen vessel is subjected to a continual increase of temperature, it is gradually changed into vapor. This action is at first confined to the surface ; but after a certain time bubbles of vapor are formed in the interior of the liquid, which rise to the top, and set the entire mass in motion with a characteristic noise ; this is what is meant by ebullition, or boiling. If we observe the gradual progress of this phenomenon, for example, in a glass vessel containing water, we shall per- ceive that after a certain time very minute bubbles are given off ; these are bubbles of dissolved air. Soon after, at the bot- tom of the vessel, larger bubbles of vapor are formed, which decrease in volume as they ascend, and disappear before reach- ing the surface. This stage is accompanied by a peculiar sound, and the liquid is said to be singing. The sound is probably caused by the collapsing of the bubbles as they are condensed by the colder water through which they pass. Finally, the bubbles increase in number, growing larger as they ascend, until they burst at the surface, which is thus kept in a state of agitation ; the liquid is then said to boil. 190. Difference between Evaporation at the Boiling-Point and below the Boiling- Point. Below the boiling-point evaporation takes place only at the surface ; the tension, or elastic force, of the vapor is less than that of the atmos- phere ; and only a part of the heat received by the liquid is used in converting the liquid into vapor, the tempera- ture of the liquid rising all the time that heat is applied to it. At the boiling-point evaporation takes place through- out the liquid ; the tension of the vapor formed is equal to that of the atmosphere ; and all the heat received by the liquid is used in converting it into steam, the temperature 128 ELEMENTS OF remaining stationary. The elastic force of the vapor given off by a liquid increases with the temperature, until we reach the boiling-point, when it equals that of the atmos- phere. The boiling-point of a liquid is therefore the tem- perature at which the elasticity of the vapor is equal to the pressure of the atmosphere on the surface. It follows from this that the boiling-point must vary with the pressure. Under a pressure less than that of the atmosphere the boiling-point of water is below 212, and under a greater pressure than that of the atmosphere is above 212. -191. Franklin's Experiment. Boil a little water in a flask long enough to expel all the air from the flask. Remove the Fig. 132. flask from the source of heat, cork it securely, and invert it with its corked end under water. Ebullition ceases almost instantly. Pour cold water over the flask (Figure 132) and the liquid will begin to boil, and will continue to do so for some time. The contact of the cold water with the flask lowers the temperature and tension of the steam which presses on the surface of the water, and the diminution of pressure allows the water to boil at a lower temperature. 192. Papin^s Digester. In a confined vessel water may be raised to a higher temperature than in the open air, but it will not boil. This is the case in the apparatus called, from its in- ventor, Papiii's digester (Figure 133)- It is a bronze vessel of great strength, covered with a lid secured by a powerful screw. It is employed for raising water to very high temperatures, and thus obtaining effects which would not be possible with water at 212, such, for example, as dissolving the gelatine con- tained in bones. NATURAL PHILOSOPHY. 12 9 Fig. 133- The tension of the steam increases rapidly -with the tempera- ture.. Thus, at 392 the pressure is that of 16 atmospheres, or about 240 pounds 'on the square inch. In order to obviate the risk of explosion, Papin introduced the device known as the safety-valve. It consists of an opening, closed by a coni- cal valve or stopper, which is kept down by a lever loaded with a weight. Suppose the area of the lower end of the stopper to be i square inch, and that the pressure is not to exceed 10 atmospheres, cor- responding to a temperature of 356. The magnitude and position of the weight are so arranged that the pressure on the whole is 10 times 15 pounds. If the tension of the steam exceeds 10 atmos- pheres, the lever will be raised, the steam will escape, and the pressure -will be thus relieved. 193. Condensation of Vapors. Condensation, or the conversion of a vapor into a liquid, is the reverse of evap- oration. In condensation, the heat rendered latent in evaporation is again set free as sensible heat. As an in- crease of temperature and a diminution of pressure pro- mote evaporation, so a diminution of temperature and an increase of pressure promote condensation. 194. Distillation. Distillation consists in boiling a liquid and condensing the vapor evolved. It enables us to separate a liquid from the solid matter dissolved in it, and to effect a partial separation of the more volatile constituents of a mixture from the less volatile. The apparatus employed is called a still. One of its simpler forms, suitable for distilling water (Figure 134), consists of a retort a, the neck of which c communicates with a spiral tube dd, called the worm, placed in a vessel e, con- taining cold water. The water in the retort is boiled, the steam 9 13 ELEMENTS OF given off is condensed in the worm, and the distilled ivater is col- lected in the vessel^". As the condensation proceeds, the water of the cooler becomes heated, and must be renewed. For this purpose a tube descending to the bottom of the cooler is sup- Fig. plied with a continuous stream of cold water from above, while the warm water, which rises to the top, flows out by the tube i. 195: The Spheroidal State. This is a peculiar condition assumed by liquids when exposed to the action of very hot metals. If we let fall a drop of water upon a smooth plate of iron or Fig. 135. silver, the drop will evaporate more rapidly as the temperature of the plate is increased up to a certain point. When the tem- perature exceeds this limit, which, for water, appears to be about 300, the drop assumes a sphe- roidal form, rolls about like a ball or spins on its axis, and fre- quently exhibits a beautiful rip- pling (Figure 135). While in this condition it evaporates much more slowly than when the plate was at a lower temperature. If the plate is allowed to cool, a moment arrives when the globule of water flattens out, and boils rapidly away with a hissing noise. If the temperature of the liquid is measured by means of a NATURAL PHILOSOPHY. 131 thermometer with a very small bulb, it is always found to be below the boiling-point. \ n the spheroidal state the liquid and the metal plate do not come into contact. To prove this, the plate used must be quite smooth and accurately levelled. When it is heated, a little water is poured upon it and assumes the spheroidal state. By means of a fine platinum wire the globule is kept at the centre of the plate. It is then very easy, by placing a light behind the globule, to see dis- tinctly the space between the liquid and the plate (Figure 136). This separation is maintained by the rush of steam from the under surface of the globule, which is also the cause of the pe- Fig. 136. culiar rippling movements. In consequence of the separation, heat can pass to the globule only by radiation, and hence its comparatively low temperature. D. . MEASUREMENT OF HEAT. 196. The Unit of Heat. The temperature of a body indicates its thermal condition, but not the amount of heat in it. The thermometer shows a pound of iron and ten pounds of iron to be of the same temperature, when, of course, the latter has ten times as much heat in it as the former. In the measurement of heat we need some unit in which amounts of heat can be expressed. The English unit of heat is the amount of heat required to raise one pound of water at 32 one degree in temperature. 197. Specific Heat. If equal bulks of water and of mercury are exposed to the same source of heat, it will be found that the temperature of the mercury will rise faster than that of the wa- ter, though the mercury is more than 12 times as heavy as the 132 ELEMENTS OF water. It has been 'found that it requires very different amounts of heat to raise the same weight of different substances one de- gree in temperature. The specific heat of a substance is the amount of heat re- quired to raise one pound of it one degree in temperature. The specific heat of water is I, and it is higher than that of any other substance, with the single exception of hydrogen. 198. A Body in Cooling \ gives out just as much Heat as it takes to Heat it i. Boil a quarter of a pound of wa- ter in a beaker, and the bulb of a thermometer plunged into it will indicate a temperature of 212. Remove the beaker from the source of heat, and pour the water into another beaker containing a quarter of a pound of water at a temperature of 70. Stir the mixture a short time with the bulb of a delicate thermometer, and the tempera- ture will be found to be 141. The first quarter of a pound of water has then lost 71, and the second has gained 71 ; in other words, the first in cooling one degree has given out just heat enough to warm the second one degree. The same is true of all other bodies. 199. The Water Calorimeter. A calorimeter is an instru- ment/br measuring quantities of heal. The water calorimeter is a vessel containing water into which a heated substance may be introduced. As the substance cools it imparts some of its heat to the water, and the amount of heat given up by the sub- stance may be calculated from the weight of the water in the calorimeter and the number of degrees the temperature is raised. The number of units of heat received by the water will be equal to the product of the rise of temperature in degrees and the weight of the water in pounds. This method of measuring heat is called the method of mixture. 200. The Latent Heat of Water. By the latent heat of water we mean the amount of heat required to melt a pound of ice. This is found to be 143 units. 201. The Ice Calorimeter. Another method of finding spe- cific heat is by melting ice. The substance is first weighed, NATURAL PHILOSOPHY. 133 then heated to a certain temperature, as 100, and placed in the vessel M (Figure 137). This vessel is placed within the vessel A, the space between the two being filled with ice. The vessel A is placed in another, B, from which it is also separated by ice. Since the vessel A is surrounded by ice, the heat which melts the ice within it must come wholly from the vessel J/. As the ice in A melts, the water runs off through the pipe D. As we know how much heat is required to melt one pound of ice, we need only know 010 much ice is melted by any substance Fig. 137- within the box J/, in order to find how many units of heat it has given up. Dividing this by the weight of the substance and by the number of degrees it has cooled, we get its specific heat. 202. The Latent Heat of Steam. The latent heat of watery vapor, or steam, is higher than that of any other vapor, being 967 units. The latent heat of steam may be found by allowing a quan- tity of steam to pass into a water calorimeter. The steam will be condensed, and the water formed will be cooled to the re- sulting temperature of the water in the calorimeter. The heat given out in this condensation and cooling will raise the tem- perature of the water in the calorimeter. The amount of this heat may be calculated, as well as the amount of heat given out 134 ELEMENTS OF in the cooling of the water formed from the steam. The dif- ference between these two amounts will be the amount of heat set free in the condensation of the steam. This, divided by tlie weiglit of the steam, will give its latent heat. II. RELATIONS BETWEEN HEAT AND WORK. 203. Heat consumed in the Performance of Work. In expansion, liquefaction of solids, and evaporation, the molecules are always pushed into new positions against some kind of resistance, either internal or external ; that is to say, work is done upon the molecules. This work is always done at the expense of heat, either of that already in the body or of that communicated to the body. Hence, whenever any of these kinds of work are done without the application of heat to the body, some of the heat in the body is consumed and its temperature falls , and whenever the work is done by the application of heat, the temperature of the body rises less than it would with the same application of heat were no work done. 204. Heat consumed in Expansion. If a thermometer bulb is introduced into the receiver of an air-pump through an opening into which it is fitted air-tight by means of a rubber cork, and the pump is worked, as the exhaustion proceeds the air in the receiver will expand more and more, and the mercury in the stem of the thermometer will fall several degrees, indicating a reduction of temperature. The air is always chilled when any expansion takes place in it ivithoiit the application of heat. It takes 6.7 units of heat to raise the temperature of a cubic foot of air 490 when the air is confined so that it cannot expand, and 9.5 units to raise the temperature the same amount when the air is free to expand. In the latter case the air will expand enough to double its volume (171). So that 2.8 units of heat are consumed in expanding a cubic foot of air enough to double its volume. The heat consumed in expansion is called the latent heat of expansion. The conversion of sensible into latent heat NATURAL PHILOSOPHY. '35 Fig. 138. is simply the transformation of kinetic into potential energy. When the air contracts again, the potential energy is trans- formed again into kinetic energy, and the latent heat again becomes sensible. 205. Heat consumed in Liquefaction. Place some pul- verized nitrate of ammonia in a small beaker glass, add an equal bulk of water, and stir the mixture with the bulb of a thermometer. The solid will be rapidly dissolved, and the temperature of the mixture will quickly fall 40 or 50 degrees. If put upon a wet board, the beaker will be quickly frozen to it. In the liquefaction of a solid a part of its kinetic energy is transformed into potential energy, and sensible heat becomes latent heat. In the solidification of the liquid the potential energy is transformed back again into kinetic energy, and the latent heat again becomes sensible heat. In the melting of a solid all the kinetic energy that enters the body is transformed into potential energy by the conversion of the solid into a liquid, and hence there is no rise of temperature while the solid is melting. 206. Heat consumed in Evapo- ration. The consumption of heat in evaporation may be illustrated by means of the cryophorus (Fig- ure 138). It consists of a bent tube with a bulb at each end. It is partly filled with wate^an^hermetically sealed while the liquid is boiling, thus expelling the air. When an experiment is to be made, all the liquid is passed into B, and A is plunged into a freezing mixture, or into pounded ice. The cold condenses the vapor in A, and thus pro- duces rapid evaporation of the water in B. Needles of ice soon appear on the surface of the liquid. , 3 6 ELEMENTS OF Pour a little water into a small test-tube, and place the tube in a wineglass of ether (Figure 139); then blow a current of air through the ether by means of a pair of bellows. The rapid evaporation of the ether will reduce the temperature sufficiently to freeze the water in the tube in a short time. In evaporation as in liquefaction, the conversion of sensible into latent heat is merely the transformation of kinetic energy into potential energy. 207. Freezing Mixtures. The ordinary freezing mixture is a mixture of salt and ice. The salt causes some of the Fig. 139 ice to liquefy, and this liquefaction consumes so much heat that the temperature of the mixture is reduced suffi- ciently to freeze cream within a can which is surrounded by the mixture. A mixture of solidified carbonic acid and ether, in the re- ceiver of an air-pump from which the air has been exhausted so as to promote the evaporation, evaporates with very great ra- pidity, and the consumption of heat is so great as to reduce the temperature of the mixture to 166 F. NATURAL PHILOSOPHY. 137 A mixture of solidified nitrous oxide and bisulphide of carbon, under similar circumstances, evaporates still more rapidly, and reduces the temperature to 220 F. 208. Solidification of Gases. If any gas is liquefied by the combined action of cold and pressure, and then allowed to escape into the atmosphere in a fine stream, so as to evaporate freely, the temperature will be reduced to 'such an extent that a portion of the vapor will be frozen, so that the gas can be obtained in a solid state. In the case of hydrogen, and some other gases, which cannot be liquefied by the direct action of cold and pressure, if the gas Fig. 140. is reduced to the greatest possible degree of density by the com- bined action of cold and pressure, and then is allowed to expand by a sudden removal of the pressure, the sudden expansion chills the gas sufficiently to freeze a portion of it (204). Hydrogen frozen in this way is heard to rattle like hail when it falls on the table. Faraday was the first to conduct methodical experiments in the liquefaction of gases. The apparatus employed by him (Figure 140) consists of a very strong bent glass tube, closed at both ends. v One end of this contains the ingredients which, on the application of heat, evolve the gas to be tried, while the other 138 ELEMENTS OF is immersed in a freezing mixture. The pressure produced by the evolution of the gas in large quantity in a confined space combines with the cold of the freezing mixture to produce lique- faction of the gas, and the liquid collects in the cold end of the tube. 209. Mechanical Equivalent of Heat. Meyer found the equivalent of a unit of heat in foot-pounds , by converting heat into mechanical energy through the expansion of air. In the expansion of air the work done is wholly external, namely, that of pushing aside the surrounding air. We have seen (204) that it takes 2.8 units of heat to expand a cubic foot of air to double its volume. To ascertain the amount of work done in pushing away the surrounding air, Meyer imagined his cubic foot of air at the bottom of a prismatic box whose section was a foot square, so that the air could expand only upward. The upper surface of the cubic foot of air contains 144 square inches. Hence the weight of the column of air pressing upon this surface is about 144 X 15 = 2160 pounds; and when the cubic foot of air ex- pands so as lo double its volume, this weight must be raised one foot high. Hence 2.8 units of heat are equivalent to 2160 foot- pounds of mechanical energy, and one unit of heat is equivalent to ni foot-pounds. This is known as the mechanical equivalent of heat. 210. The Steam- Engine. The molecular energy of heat can be made to do mechanical work by means of the arrangement shown in Figure 141. The steam derives its expansive power from the heat, and this expansive power is made tp work a pis- ton in the cylinder of the steam-engine. The steam from the boiler passes through the tube x into the steam-box d. Two pipes run from this box, one a to the top and the other b to the bottom of the cylinder. A sliding- valve y is so arranged as always to close one of the pipes to the steam-box and open it to the exit-pipe O, and, at the same time, to open the other pipe to the steam-box and close it to the exit-pipe. In the right-hand figure the lower pipe b is open, and the steam can pass in under the piston and force it up. At the same time the steam which has done its work on the other side of the piston passes out from the cylinder through the pipes a and O. The sliding- valve is connected by means of the rod /with the NATURAL PHILOSOPHY. '39 crank of the engine, so that it moves up and down as the piston moves down and up. As soon, then, as the piston has reached the top of the cylinder, the sliding- valve is brought into the posi- tion shown in ihe left-hand figure. The steam now passes into the cylinder above the piston through the pipe a, and forces the Fig- 141. piston down, and the steam on the other side which has done its work goes out through b and O. The sliding-valve is now again in the position shown in the right-hand figure, and the piston is driven up again as before ; and thus it keeps on moving up and down, or in and out. III. DISTRIBUTION OF HEAT. A. CONDUCTION. 211. Illustration of Conduction. If heat is applied to one end of a bar of metal, it is slowly propagated through the substance of the bar, producing a rise of temperature 140 ELEMENTS OF which is first perceptible near the heated end, and after- wards in more remote portions. The transmission of heat from molecule to molecule through the substance of the body is called conduction. If the application of heat to one end of the bar is continued for a sufficiently long time, and with great steadiness, the differ- ent portions of the bar will at length cease to rise in tempera- ture, and will retain steadily the temperatures which they have acquired. We may thus distinguish two stages in the experi- ment : ist, the variable stage, during which all portions of the baf are rising in temperature ; and 2d, the permanent state, which may subsist for any length of time without alteration. In the former, the bar is gaining heat ; that is, it is receiving more heat from the source than it gives out to surrounding bodies. In the latter, the receipts and expenditure of heat are equal, not only for the bar as a whole, but for every small portion of it. In the permanent state no further accumulation of heat takes place. All the heat which reaches an internal particle is trans- mitted by conduction, and the heat which reaches a superficial particle is given off partly by radiation and air-contact, and partly by conduction to colder neighboring particles. In the earlier stage, on the contrary, only a portion of the heat received by a particle is thus disposed of, the remainder being accumu- lated in the particle, and serving to raise its temperature. 212. Conducting Power of Solids. Different solids are found to vary much in conductivity, or conducting power. The following experiments are often adduced in illustration of the different conducting powers of different solids. Fig. 142. Two bars of the same size, but of different materials (Figure 142), are placed end to end, and small wooden balls are attached NATURAL PHILOSOPHY. 141 by wax to the under surfaces at equal distances. The bars are then hc.ited at their contiguous ends, and, as the heat extends along them, the wax melts, and the balls successively drop off. If the heating is continued till the permanent state arrives, it may generally be concluded that the bar which has lost most balls is the best conductor. The apparatus shown in Figure 143 consists of a copper box having on one side a row of holes in which rods of different materials can be fixed. Fig I43 The rods having been pre- viously coated with wax, the box is filled with boil- ing water, which comes into contact with the inner ends of the rods. The wax gradually melts as the heat travels along the rods ; and if the experiment is continued till the melting reaches its limit, those rods on which it has extended furthest are, generally speaking, the best conductors. It is thus found that different metals are not equally good conductors of heat, and that the more familiar ones may be arranged in the following order, beginning with the best conductors : Silver, copper, gold, brass, tin, iron, lead, platinum ^ bismuth. Metals, though differing considerably one from another, are as a class greatly superior in conductivity to other substances, such as wood, marble, brick, etc. This explains several familiar phenomena. If the hand is placed upon a metal plate at the temperature of 50, or plunged into mercury at this temperature, a very marked sensation of cold is experienced. This sensation is less intense with a block of marble at the same temperature, and still less with a piece of wood. The reason is that the hand, which is at a higher temperature than the substance to which it is applied, gives up a portion of its heat, which is con- ducted away by the substance ; consequently a larger portion of heat is parted with in the case of the body of greater conducting power. 213. Conducting Power of Liquids. With the exception of mercury and other melted metals, liquids are exceedingly 142 ELEMENTS OF Fig. 144. bad conductors of heat. This can be shown by heating the upper part of a column of liquid, and observing the variations of tempera- ture below. These will be found to be scarcely perceptible, and to be very slowly produced. If the heat were applied below (Figure 144), we should have the process called convection of heat ; the lower layers, made lighter by expansion, would rise to the sur- face, and be replaced by colder ones from above, which would be heated and rise in their turn, the circulation thus producing a general heating of the liquid. When heat is applied above, the expanded layers remain in their place, and the rest of the liquid can be heated only by conduction and radiation. The following experiment is an illustration of the very feeble conducting power of water. A piece of ice is placed at the bottom of a glass tube (Figure 145), which is then partly filled with water ; heat is applied to the middle of the tube, and the upper portion of the water may be made to boil without melting the ice below. 2 1 4. Conducting Power of Gases. Of the conducting power of gases it is almost impossible to obtain any direct proofs, since it is ex- ceedingly difficult to prevent the interference of convec- tion and direct radiation. We know, however, that they Fig. 145- NATURAL PHILOSOPHY. 143 are exceedingly bad conductors. In fact, in all cases where ^ases are enclosed in small cavities where their movement t5 is difficult, the system thus formed is a very bad conductor of heat. This is the cause of the feeble conducting powers of many kinds of cloth, of fur, eider-down, felt, straw, saw- dust, etc. Materials of this kind, when used as articles of clothing, are commonly said to be warm, because they hinder the heat of the body from escaping. If a garment of eider-down or fur were compressed so as to expel the greater part of the air, and to reduce the substance to a thin sheet, it would be found to be a much less warm cov- ering than before, having become a better conductor. We thus see that // is the presence of air which gives these sub- stances their feeble conducting power, and we are accordingly justified in assuming that air is a very bad conductor of heat. B. CONVECTION. 215. Convection Currents. Although liquids and gases are very poor conductors of heat, they allow heat to be distributed through them readily by convection currents. When heat is applied to any portion of a fluid, the heated portion expands, becomes lighter, and rises, allowing colder portions to take its place and become heated in turn ; that is, the system of currents shown by the arrows in Figure 144 is formed. There will be an upward cur- rent at the centre of the heated region, an outflow in every direction above, downward currents on every side, and an inflow from every direction below. It is chiefly in this manner that heat is distributed through liquids and gases. C. RADIATION AND ABSORPTION. 216. Illustration of Radiation. When two bodies at different temperatures are brought opposite to each other, an unequal exchange of heat takes place through the inter- 144 ELEMENTS OF vening distance ; the temperature of the hotter body falls, while that of the colder rises, and after some time the tem- perature of both becomes the same. This propagation of heat across an intervening space is what is meant by radia- tion, and the heat thus transmitted is called radiant heat. Instances of heat communicated by radiation are the heat of a fire received by a person sitting in front of it, and the heat which the earth receives from the sun. 217. Radiations will traverse a Vacuum. This last in- stance shows us that radiation as a means of propagating heat is independent of any ponderable medium. But since the solar heat is accompanied by light, it might still be questioned whether non-luminous heat could in the same way be propagated through a vacuum. This was tested by Rumford in the following way. He con- Fig. 146. structed a barometer, the upper part of which was expanded into a globe (Figure 146). A thermometer was hermetically sealed into the top, so that the bulb of the thermometer was at the centre of the globe. The globe was thus a Torricellian vacuum-chamber. By melting the tube with a blow-pipe, the globe was sep- arated, and was then immersed in a vessel containing hot water, when the thermometer immediately rose to a temperature higher than could be clue to the conduction of heat through the stem. The heat had therefore been com- municated by direct radiation -through the vacuum between the sides of the globe and the bulb a of the thermometer. 218. Radiant Heat travels in Straight Lines. In a uniform medium the radiation of heat takes place in straight lines. If, for instance, between a ther- mometer and a source of heat there are placed a number of screens, each pierced with a hole, and if the screens are so arranged that a straight line can be drawn through the holes from the source to the thermometer, the temperature NATURAL PHILOSOPHY. 145 of the latter immediately rises ; if a different arrangement is adopted, the heat is stopped by the screens, and the thermometer indicates no effect. The heat which travels along any one straight line is called a ray of heat. Thus, we say that rays of heat issue from all points of the surface of a heated body, or that Mich a body emits rays of heat. 219. Molecular Theory of Radiation. According to the molecular theory, radiations originate in the vibrations of the atoms within the molecule. Each kind of atoms seems to have certain characteristic rates of vibration, and when the molecules in their motions come into collision, their atoms are thrown into vibration ; these vibrations are communicated to the surrounding ether (3), and are propagated through the ether in minute waves and with enormous velocity. As the tempera- ture of the body rises the agitation of its molecules becomes more energetic, and the more violent collisions of the molecules produce more powerful vibration of the atoms. Hence the radiation becomes more intense as the temperature rises. 220. Different Kinds of Radiation. At low tempera- tures bodies emit only obscure radiations. When the tem- perature reaches a certain point, the body becomes red-hot, and begins to emit luminous radiations. At a still higher temperature it becomes white-hot. 221. Diathermanous Bodies. A body, like air, which will allow thermal rays to pass readily through it is said to be diathermanous. If a polished plate of glass is held in front of a body heated to dull redness, it will stop nearly all the heat emitted by it. If the same plate of glass is held in front of a body at bright white heat, it will allow considerable heat to pass through it. Glass is diathermanous to luminous radiations, but only slightly so to obscure thermal radiations. A solution of alum is still less diathermanous to obscure thermal rays, although it allows the luminous rays to pass readily through it. A solution of iodine in bisulphide of carbon, on the contrary, is perfectly diathermanous to the obscure thermal rays and per- 146 ELEMENTS OF fectly opaque to the luminous rays. A polished plate of rock salt is diathermanous to both the obscure and luminous rays. 222. The Effect of Rise of Temperature on Radiation. If the temperature of a body is gradually raised to the highest possible point, and a cell of the iodine solution is used to cut off the luminous radiations, the obscure thermal radiations will be found to grow more and more intense, both before and after the body begins to emit luminous radiations. A rise of tempera- ture, then, has two effects upon the radiation of a body ; it causes its obscure radiations to become more intense, and gives rise to new radiations. The latter radiations differ from the former in having quicker vibrations and shorter waves. The radiations of longest and shortest wave-lengths are obscure, while those of medium wave-lengths are luminous. The radiations of all wave-lengths are thermal, but the thermal power is greatest in radiations of long wave-lengths, and least in those of short wave-lengths. All radiations are capable of producing certain chemical effects, but the chemical or actinic power is least in radiations of long waves and greatest in the short waves. The radiations of bodies have, accordingly, been divided into three classes ; namely, obsciire thermal, luminous, and obscure actmic. At low temperatures bodies emit only the first class of radia- tions ; at higher temperatures, the first and second classes ; and at still higher temperatures, all three classes. 223. Absorption. Absorption is the reverse of radiation. When the minute waves of the ether encounter the mole- cules of gross matter, they throw the atoms into vibration, provided they can vibrate at the same rate as the particles of the ether in the waves. In this way the rays are taken up and absorbed by bodies. It is only those rays which are absorbed by a body that heat it. Bodies are not warmed at all by the rays which they transmit. 224. Good Radiators are Good Absorbers. Rough blackened surfaces are better radiators than smooth pol- ished surfaces, and they are also better absorbers. This may be shown by the following experiment. Two metallic plates A and B (Figure 147) of the same size are NATURAL PHILOSOPHY. mounted on standards which move to and fro on a sliding bar at the bottom. Between these plates there is a rod for supporting a ball at the height of the centre of the plates. A is coated with polished nickel on both sides, and B with nickel on one side and lampblack on the other. B is made to turn on its standard so that the sur- face coated with lampblack may be turned either towards the ball or from it. First, turn the nickel faces of the plate towards the ball, heat the ball to dull redness, place it upon its rod, and move both plates up against it so that they may be heated equally. Place a differential ther- mometer (179) as shown in the figure, so that its bulbs shall be equally distant from the two plates. One of the bulbs will be heated by radiation from the nickel surface, and the other by radiation from the blackened surface. The liquid in the stem will move towards the former bulb, showing that the latter bulb is hotter, and that the radiation is more powerful from the blackened surface. Now reverse plate B, turning its blackened face towards the ball, remove the ball, and allow both plates to cool. Place each plate against one of the bulbs of the ther- mometer, and arrange them so that they shall be equally distant from the ball. Heat the ball and replace it on the rod. The plates will now become heated by absorption of radiations from the ball. They will receive equal radiations, but the thermome- ter will indicate that the plate with the lampblack coating towards the ball is the hotter. Hence the blackened surf ace is the better absorber. Different gases, as well as different solids and liquids, differ in their absorptive power and in the kind of rays which they absorb. Watery vapor among gases corresponds to glass among solids and a solution of alum among liquids. It is dia- thermanous to luminous rays, but much less so to obscure rays. Stoves .and radiators, which are designed to give out heat, should have rough blackened surfaces ; while a teapot, which 148 ELEMENTS OF is designed to keep the liquid in it hot, should have a bright polished surface. 225. Hot-Houses. A hot-house is a structure covered with glass. On a sunny day the temperature will be several degrees higher within such a structure than on the outside. The lumi- nous heat which comes from the sun passes readily through the glass and falls upon the objects within. These absorb the heat and in turn send back obscure heat. This heat is stopped by the glass. Hence the heat accumulates within the hot-house. A hot-house may be described as a trap to catch sunbeams. Even at night and on a cold cloudy day it will be warmer within a hot-house than on the outside, the glass preventing the ob- scure radiations from passing off into space. The watery vapor in the atmosphere acts just like the glass of the hot-house- NATURAL PHILOSOPHY. 149 IV. LIGHT. A. RADIATION. 226. Luminous Bodies. Bodies, like a gas-jet or the sun, which emit light of their own, are said to be luminous. Light is now believed to originate in extremely minute and rapid vibrations of the atoms of matter. These vary in rapidity from about 400 million million to about 760 million million a second. The atoms of all luminous bodies are supposed to be vibrating at this enormous rate. When a body is heated its atoms are thrown into more and more rapid vibration, and when the rate of vibration reaches 400 million million a second the body begins to become lumi- nous. In the case of a candle-flame or gas-jet, these rapid vibrations are produced by the clashing of the atoms of oxygen, hydrogen, and carbon as they rush into combination. A black- smith may heat a nail red-hot by vigorously hammering it. Each blow of the hammer throws the atoms of the nail into more rapid vibration, till they finally vibrate fast enough to develop light. 227. Propagation of Light by the Ether. As the atoms of matter vibrate in the ether (3) in which they are im- mersed, they communicate their vibration to it. The vibrations thus started are propagated through the ether in every direction in minute waves and with an inconceivable velocity. These ethereal waves vary in length according to the rate gf the atomic vibrations. It takes somewhat more than 35,000 of the longest of these waves, and somewhat 150 ELEMENTS OF less than 70,000 of the shortest, to make the length of an inch. The vibrations are transverse, so that each luminous wave is made up of crest and hollow, like a water wave. Light and luminous radiations are the same thing. 228. Velocity of Light. The velocity of light is about 186,000 miles a second. It was first determined by Roemer, a Danish astronomer, by a study of the eclipses of one of Jupiter's moons. He found, by examining a long series of observations, that the mean interval between two successive eclipses of the moon was about 42^ hours, but that the interval varied according to the motion of the earth with respect to Jupiter. When the earth was moving away Fig. 148. from Jupiter from T to T' (Figure 148), the intervals were longer than the mean, till at T' the eclipse occurred about 16^2 minutes late; when the earth was moving towards Jupiter, from T 1 to 2] the intervals were shorter than the mean. Now we cannot be aware of the eclipse till the light which left the moon just as.it entered Jupiter's shadow has reached the earth ; and the distance this light has to travel is continually increasing as the earth travels from T to T', and decreasing as the earth travels from T 1 ' to T. Roemer concluded that this must be the reason why the intervals between the eclipses were longer than the mean in the one case and shorter in the other. As the NATURAL PHILOSOPHY. 151 eclipse occurred 16^ minutes late at J 7 ', he concluded that it must take light about i6*4 minutes to cross the earth's orbit. As this distance is about 184,000,000 miles, light must travel at the rate of about 186,000 miles a sec- ond. This velocity would carry light around the earth in about % of a second. Great as is this velocity, it is believed that the nearest fixed star is so distant that it would take light over three years to reach us from it, while the most distant stars are, at least, a thousand times more remote. Were all the stars in the heavens blotted out of existence to-night, it would be over three years before we should miss any of them, a quarter of a century before we should miss many, and thousands of years before we should lose them all. The light which will enter our eyes as we glance at some star to-night probably started on its journey before the building of the great pyramids, and has been travelling eight times the distance around the earth every second since. Fig. I49 . 229. Rectilinear Propagation of Light. When sunlight enters through an opening into a darkened room, it illu- mines the dust in the atmosphere in its path, which may then be easily traced. This path is always found to be ELEMENTS OF straight. Light always traverses a homogeneous medium in straight lines. A single line of light is called a ray, and a collection of rays a beam. 230. Images produced by Small Apertures. If a white screen is placed opposite a small opening in a shutter of a darkened room, an inverted picture of the outside landscape will be formed on the screen (Figure 149). The smaller the opening, the sharper the image. The formation of this image is due to the rectilinear propaga- tion of light. The point A (Figure 150) is sending out rays in all Fig 150. directions in straight lines. The rays from this point which pass through the small opening must fall upon A 1 of the screen. In the same way the rays from B must fall ^^\ A u P n B'. As A sends light to no part of the o'\. screen except A', and as A' receives light \J B from no part of the object but A t the color and brightness of the spot A' will depend upon the color and brightness of A ; in other words, A' will be the image of A. In like manner B' will be the image of B, while the points of the object between A and B will have their images at corresponding points between A' and Fig. 151. NATURAL PHILOSOPHY. '53 B'. An inverted image of AB will thus be formed between A' and B'. Hold a card with a large pin-hole in it between a candle and a screen (Figure 151), and an inverted image of the candle will be formed on the screen. Fig. .52- When the sun shines through a small hole into a room with the blinds closed, whatever may be the shape of the opening, the image of the sun formed on the floor or wall will be round or oval, according as it falls upon a surface which is perpendicular or oblique to the rays (Figure 152). When the sun shines through the foliage of trees, the spots of light on the ground will always be round or oval, whatever may be the shape of the openings through which the light comes, provided they are suf- ficiently small. When the sun is undergoing eclipse, the progress of the eclipse may be watched by noticing the shape of these spots, which will always be that of the uneclipsed portion of the sun's disc. 231. Shadows. Bodies which, like glass, allow light to pass readily through them, are said to be transparent. Bodies which do not allow light to pass through them are said to be opaque. Owing to the rectilinear propagation of light, opaque bodies in front of a light must necessarily cast shadows, that is, shut off the light from some of the space behind them. 154 ELEMENTS OF If the luminous body 6" (Figure 153) is a mere point, the body /I/will cast a well-defined shadow GH upon the screen PQ. If the straight line SG is kept fast at S, and carried round the sphere J/, touching it all the time, it will describe a cone. Fig. 153- The part M G, as it passes round, will exactly mark the limits of the shadow cast by M. If the luminous body is not a mere point, the shadow of M (Figure 154) upon the screen will be indistinct in outline. Prolong the line GS to A. Keep the point A fixed and carry the line A G around the spheres S and M, keeping it in contact with both. The line will describe a cone, and the part Fig. 154- M G will mark out the space from which the light is entirely ex- cluded. This is called the iimbra of the shadow. If the line S C is kept fixed at B, and then carried round the two spheres, it will describe a double cone, whose apex will be at B. The partvVCof this line will mark the extreme limits of the shadow. From the part outside of the umbra only a portion of the light is excluded^ and the farther we pass from the umbra the less the light excluded. This part of the shadow is called the penumbra. It will be seen at once from the figure, that the light from S will reach all the space between D and G, and the light from L all the space between Cand //. NATURAL PHILOSOPHY. 232. Illumination. The illuminating power of a source of light diminishes as the square of the distance from the illu- minating body increases. In Figure 155 the disc CD is held parallel with the screen A B< and half-way between the screen and the source of light L. The diameter of the shadow on the screen will be twice that of the disc, and the area of the shadow four times that of the disc. The disc receives all the light that would fall upon the space covered by the shadow, were the disc removed. Hence the illumination of the disc is four times as intense as that of the screen. If the disc were held one third of the way from L to the screen, the area of the disc would be one ninth that of its shadow, and the illumination of the disc would be nine times as intense as that of the screen. Fig. 156. 233. Photometry. Photometry is the measurement of the relative illuminating power of different sources of light ; and the instrument used is called a photometer. 156 ELEMENTS OF Riimf or ds photometer, based upon the comparison of shadows, is one of the simplest of these instruments. An opaque rod M (Figure 156) is placed in front of a ground-glass screen. The lights L and B to be compared are placed so that each casts a separate shadow of the rod upon the screen. These distances are then made such that the two shadows a and b are of exactly the same intensity. The screen must then be receiving the same illumination from each light ; for the shadow cast by B is illumined by L, and that cast by L is illumined by B. Hence the illuminating power of the two lights will be to each other as the squares of the distances of the lights from the screen. B. REFLECTION. 234. Diffusion. When light meets the surface of a new medium, a portion of it is diffused, that is, thrown back and scattered irregularly in every direction. It is by means of the light thus diffused that we are enabled to see the sur- faces of non-luminous bodies. Smooth polished surfaces diffuse less light than rough irregular ones, but the most highly polished mirror diffuses enough light to enable us to see its surface, though sometimes with difficulty. 235. Reflection. On meeting the surface of a new me- dium, a portion of the light is reflected, that is, thrown back Fig I57 in a definite direction. In Figure 157 IP R AB represents the surface of the new medium, 1C the ray coming to it, or the incident ray, and CR the reflected ray. PC is a perpendicular to the surface of the medium at the point C. The angle TCP is called the angle of incidence, and the angle HCP'is called the angle of reflection. In reflection, the angles of incidence and reflection are always equal. The smoother the surface of a medium, the greater the proportion of the light reflected from it. Good reflecting surfaces are called mirrors. NATURAL PHILOSOPHY. 157 236. Images formed by Plane Mirrors. It is by reflected light that we see images of objects in reflecting surfaces. These visible images formed by reflection correspond to the echoes formed by reflection in the case of sound. Figure 158 represents a pencil of rays emitted from the highest point of a candle-flame to the Fig i g eye of an observer. The rays have exactly the same degree of divergence after reflection as before, and if prolonged back- ward would meet just as far behind the mirror as the point from which they come is in front of it. The same would be true of the rays coming from every point of the object. Hence an image seen in a plane mirror will seem just as far behind the mirror as the object is in front of it. This is not only true of the image as a whole, but also of each part of it. Fig- 159- 237. Images formed by two Mirrors at an Angle to each other. Figure 159 shows the images that would be formed by two mirrors at right angles to each other, one being horizontal and the other vertical. Figure 160 shows the images that would be formed if an ob- '58 ELEMENTS OF ject were placed between two mirrors facing each other at an Fig . j6o- angle of 60. When the mirrors are inclined to each other, the im- ages formed are always arranged in the circumference of a circle, whose centre is at the intersection of the mirrors, while its circum- ference passes through the object. 238. The Kaleidoscope. The kaleidoscope is an optical toy, in- vented by Sir David Brewster. It consists of a tube containing two glass plates, extending along its whole length, and inclined at an angle of 60. One end of the tube is closed by a metal plate, with a hole in the centre, through which the observer looks in; at the other end there are two plates, one of ground and the other of clear glass (the latter being next the eye), with a num- ber of little pieces of colored glass lying loosely between them. These colored ob- jects, together with their images in the mirrors, form symmetrical patterns of great beauty, which can be varied by turning or shak- ing the tube, so as to cause the pieces of glass to change their positions (Figure 161). C. REFRACTION. 239. Refraction. If a beam of light is allowed to fall obliquely upon water, it will be seen to be bent on enter- ing the water, though it will continue to move on in a straight line after it has passed into the water. This bending of a ray of light, in passing obliquely from one me- dium to another, is called refraction. NATURAL PHILOSOPHY. '59 Fig. 163. If a coin or other object m n (Figure 162) is placed on the bottom of a vessel with Fi g . , 62- opaque sides, so as just to be concealed from an eye at O, and the vessel is then filled with water, the bottom of the vessel will seem to rise and the object will come into view. This is because the pencils of rays coming from the object at m will be suddenly bent on entering the air and will reach the eye as if they came from /', where the object will ap- pear to be. For a similar reason, a stick partly immersed in water, in an oblique position, will appear bent, as shown in Figure 163. When a ray of light passes obliquely from a rarer into a denser medium, it is bent towards a perpejidicular drawn to the sur- face of the medium at the point of contact of the ray. In Figure 164 A B represents the surface of a denser me- dium, 1C the incident ray, C R the refracted ray, and P C H a perpendicular to the surface of the medium at the point C. The Fig- '64- Fig. 165. , p U IP angle R CH is the angle of refraction. In this case the angle of refraction is less than the angle of incidence. When a ray of light enters a rarer medium obliquely, it is bent/ram a perpendicular to the surface of the medium at the point of contact. i6o ELEMENTS OF In Figure 165 A B represents the surface of a rarer medium, /Cthe incident ray, C R the refracted ray, and P C H the per- pendicular. In this case the angle of refraction is greater than the angle of incidence. When a ray of light enters any medium perpendicularly, there is no refraction. 240. Total Reflection. The angle of incidence may have any value from o up to 90. When light enters a denser medium, the angle of refraction is less than the angle of incidence, and hence always less than 90. But when ! H light enters a rarer medium, there is always a certain angle of incidence I C P (Figure 166) at which the angle of refraction H C R is equal to 90. F 'g- i6 7 . This angle is called the limiting angle, or the critical angle. When the media are air and water, this angle is about 48^ degrees. For air and the differ- ent kinds of glass it ranges from 38 to 41. When the angle of incidence exceeds the limiting angle, none of the light will enter the medium, however transparent it may be. 'In this case the light will be totally reflected, the angle of reflection being equal to that of incidence. NATURAL PHILOSOPHY. l6l If a glass of water, with a spoon in it, is held above the level of the eye (Figure 167), the under side of the surface of the water is seen to shine like polished silver, and the lower part of the spoon is seen reflected in it. The rays of light which pass upward through the water at a certain angle are totally re- flected on meeting the air. D. DISPERSION. 241. The Dispersion Spectrum. If a glass prism (Fig- ure 1 68) is held with its edge down to the path of a thin beam of light, the spot of light on the screen will be raised kFig. 168. and be changed into a beautifully colored band, in which the colors are arranged in the order of red, orange, yellow, green, blue, indigo, and violet. The colored band produced by the passage of a beam of light through a prism is called the dispersion spectrum. The raising of the spot of light on the screen is due to the bending of the beam as a whole by the prism ; and the formation of the colored band, to the unequal bending of the different colored rays of which white light is composed, red being bent the least and violet the most of all the rays. The separation of the colored rays by refraction is called dispersion. The refrangibility of light is found to depend upon the length of its waves ; the shorter the waves, the more refrangible the ray. The violet rays are more refrangible than the red because they have shorter waves. II 1 62 ELEMENTS OF In the case of sunlight and of light from any intense source of heat, it is found that the thermal or heating powe'r of the spectrum extends considerably beyond the red, and the actinic or chemical power considerably beyond the violet. The com- plete spectrum is composed of three parts, a luminous portion at the centre, an obscure thermal portion beyond the red, and an obscure actinic portion beyond the violet. Every portion of the spectrum is thermal, but the thermal power increases rapidly as we approach the red end, and is greatest just beyond the red. Every part of the spectrum is also actinic, but the greatest actinic power is in the region of the blue. Only the central part of the spectrum is luminous, and the greatest luminosity is in the region of the yellow and green. 242. Achromatic and Direct- Vision Prisms. The refractive power of a substance is independent of its dispersive power. Hence, by using different kinds of glass, it has been found pos- sible to construct prisms which shall have equal refractive powers and unequal dispersive powers, or equal dispersive and unequal refractive powers. If two prisms of crown and flint glass are constructed so as to have equal powers of bending a beam of light as a whole, the flint-glass prism will produce greater dis- persion than the crown-glass. If, on the other hand, the two prisms are constructed so as to produce equal dispersion, the crown-glass prism will bend the ray as a whole more than the flint-glass. When two prisms of equal dispersive and unequal refractive powers are combined, with the thicker part of one beside the thinner part of the other (Figure 169), they form what is called Fig. 169. an achromatic prism. Such a prism produces refraction without disper- sion. Achromatic means 'without color. When two prisms of equal re- fractive and unequal dispersive powers are combined as above, they form what is known as a direct-vision prism. Such a prism produces dispersion without refraction. In using it we look directly at the object, while with any other prism we NATURAL PHILOSOPHY. 163 are obliged to look somewhat away from the object (Fig- ure 170). Fig. 170. 243. The Spectroscope. The spectroscope is an instrument for examining spectra. A simple spectroscope is shown in Fig. 171. Figure 171. The tube at the right is called the collimator tube. 164 ELEMENTS OF The light to be examined is admitted through a narrow opening at the end of the tube, and the rays are rendered parallel by means of a lens within it. The light is then dispersed by the prism, and the spectrum examined by means of the telescope at the left of the prism. The tube in front of the prism has a scale engraved on glass in the opening at the end next to the candle. The light from the candle which shines through this scale is reflected from the side of the prism into the telescope, so as to form an image of the scale alongside that of the spectrum. 244. Three Kinds of Spectra. On examining with the spectroscope the light from an incandescent solid, its spectrum will be found to be a continuous band of colors, changing by in- sensible gradations from red at one end to violet at the other. Such a spectrum is called a continuous spectrum. Incandescent solids and liquids give continuous spectra. If we examine with the spectroscope the light from lumi- nous strontium vapor, its spectrum (see frontispiece) will be seen to be made up of bright lines and dark spaces. Such a spectrum is called a bright-lined or broken spectrum. Vapors and gases, when luminous, give bright-lined spectra. The spectra of different gases and vapors differ in the number and position of these lines. Hence a vapor may be recognized by its spectrum. The dark spaces of these spectra are due to the absence of certain rays. While incandescent solids and liquids emit rays of all degrees of refrangibility, luminous vapors and gases emit those only of particular degrees of refrangibility. Each vapor or gas emits just as many sets of rays as there are bright lines in its spectrum. The number of these lines ranges from one up to several hundred. The analysis of light by means of the spectroscope is called spectrum analysis. The spectrum of an incandescent solid or liquid, when shining through a luminous vapor or gas, is made up of dark lines separated by bright spaces, there being a dark line for every bright line which the gas alone would give. Such spectra are called reversed spectra, the spectrum of the gas being reversed by the light of the solid which passes through it. NATURAL PHILOSOPHY. E. LENSES. 245. Forms of Lenses. A lens is a transparent medium having at least one curved side. Lenses are usually made of glass, and are circular in outline. Their curved sur- faces are usually spherical. They are divided into two classes, according to their shape, namely, convex lenses and concave lenses. Every convex lens has at least one convex surface, and is thickest at the centre; and every concave lens has at least one concave surface, and is thickest at the margin. There are three forms of each class of lenses. These six forms of lenses are shown in section in Figure Fig. 172. C D 172. The first three are convex and the last three con- cave lenses. A is a double-convex lens, having two convex surfaces. B is a plano-convex lens, having one plane and one convex surface. C is a concavo-convex lens, having a concave and a convex surface, the convex surface having the greater curvature. This lens is often called a meniscus^ D is a double-concave lens, having two concave surfaces. E is a plano-concave lens, having a plane and a concave surface. F is a convexo-concave lens, having a convex and a concave surface, the concave surface having the greater curvature. 246. The Optical Centre of a Lens. There is for every lens a point, any straight line drawn through which will meet on opposite sides of the lens portions of surface which are par- allel. This point is called the optical centre of the lens. 1 66 ELEMENTS OF 247. Axes and Foci of Lenses, Any straight line drawn through the optical centre of a lens is called an axis. An axis which passes through the centre of curvature of a lens is called the principal axis, and every other axis a second- ary axis. Every ray of light which coincides with an axis will emerge from a lens with the same direction it had before entering, since it will pass through a portion of a medium having parallel sides. Every other ray which passes through a lens will be deflected towards the thicker part of the lens. In the case of a convex lens the deflection will be towards the centre of the lens, and of a concave lens towards the margin. When the rays, on emerging from a lens, are either convergent or divergent, the points towards which they con- verge or from which they diverge are called foci. When the rays are convergent on emerging from the lens, the focus is real ; and when they are divergent, it is virtual. 248. Parallel Rays with Lenses. Parallel rays with a convex lens (Figure 173) become convergent on emerging from the lens, and have a real focus on the opposite side of the lens to that on which they enter and on the axis to which the rays are parallel. Parallel rays with a concave lens (Figure 174) become di- Fig. I74 . vergent, and have a virtual focus on the same side of the lens as that on which the rays enter and on the axis to which the rays are parallel. NATURAL PHILOSOPHY. i6 7 249. Principal Foci and Focal Length. The focus for parallel rays is called the principal focus of the lens. It may be real or virtual, and on the principal axis or on a secondary axis. The distance from the optical centre of a lens to the principal focus is called the focal length of the lens. The greater the curvature of a lens, and the greater the refractive power of the material of which it is com- posed, the shorter the focal length of the lens. Fig. 175. A 250. Divergent Rays -with Lenses. Divergent rays with a convex lens (Figure 175), the point of divergence being beyond the focal length of the lens, become convergent on emerging from the lens, and have a real focus on the opposite side of the lens to that on which the rays enter, on the same axis as the point of divergence, and at a distance greater than the focal length. Divergent rays with a convex lens (Figure 176), when the Fig. 176. point of divergence is within the focal length of the lens, become less divergent on emerging from the lens, and have a virtual focus on the same side of the lens as that on which the rays enter, on the same axis as the point of di- vergence, and at a distance from the lens greater than that of the point of divergence. Fig. 177. Fig. 178. Divergent rays with a concave lens (Figure ^7) become more divergent, and have a virtual focus on the same side of the lens 1 68 ELEMENTS OF as that on which the rays enter, on the same axis as the point of divergence, and nearer the lens. 251. Convergent Rays with Lenses. Convergent rays with a concave lens, the point of convergence C (Figure 178) being at the focal length, on emerging from the lens, become parallel with the axis on which the point of convergence lies. When the point of convergence is beyond the focal length of Fig. 179. the lens (Figure 179), the rays, being less convergent on meet- ing the lens than in the previous case, become divergent on emerging from the lens, have a virtual focus on the same side of the lens as that on which the rays enter, on the same axis as the point of convergence, and farther from the lens than the focal length of the lens. Fig. 180. Convergent rays with a convex lens (Figure 180) become more convergent on emerging from the lens, and have a real focus on the opposite side of the lens to that on 3J-"""'"" which the rays enter, on the same axis as the point of convergence, and nearer the lens. 252. Images formed by Lenses. Rays are diverging from every point on the surface of an object ; that is to say, every such point is a point of divergence. The focus of a point is a copy or image of that point, and the foci of all the points on the surface of an object form an image of the object. To find the image of an object it is necessary to find only the foci of its extremities. To find these foci, we have only to draw axes through the extremities of the object, and locate the foci on these axes, according to the case of divergent rays under which they come. NATURAL PHILOSOPHY. i6 9 (i.) Figure 181 represents the case of an object AB beyond the focal length of a convex lens. The image a b is real, because made up of real Fig . l8l . foci ; inverted, because the axes cross between the image and the object ; and in this case larger than the object, because farther from the lens. Were the object distant, the image would be nearer than the object to the lens, and consequently smaller than the object. The nearer the object to the principal focus of the lens, the more distant and tne larger the image. (2.) Figure 182 represents the case of an object A B within the focal length of a convex lens. The image a b is virtual, because made up of virtual foci ; erect, because the axes do not cross between the image and the object ; and larger than the object, because farther from the lens. The nearer the object to the principal focus of the lens, the more distant and the larger the image. Fig. 182. Fig. 183. (3.) Figure 183 represents the case of an object AB with a concave lens. The image ab is virtual, because made up of virtual foci ; erect, because the axes do not cross between the image and the object ; and smaller than the object, because nearer the lens. ' Virtual images can be seen only by looking through the lens at the object. 253. Magnifying Power of Lenses. (i.) When an object is 40 or 50 feet distant, the rays from it which fall upon a small lens*are sensibly parallel, and are brought to a focus 170 ELEMENTS OF nearly at its focal length. The image of a distant object is, therefore, formed nearly at the focal length of a lens ; hence the longer the focal length the larger the image of such an object. (2.) When we can place the object very near the princi- pal focus of the lens, the shorter the focal length the larger the image it will form. Fig. 184. This is readily seen from Figure 184. The two lenses I and 2 are represented as in the same position. F' is the principal focus of the first lens, and F" that of the second lens. A B represents the same object placed near the principal focus of each lens, so that each will form an image of it at the same dis- tance on the other side of the lenses. The image a' >', formed by the first lens, is seen to be smaller than the image a" b", formed by the second lens. 254. Spherical Aberration. The rays which pass through an ordinary lens near the margin are brought to a focus a little nearer the lens than those which pass through near the centre (Figure 185). This action of the lens is called Fig. 185. Fig. 186. spherical aberration. It causes the image to appear blurred. It is obviated by grinding the lens to a special form, which can be exactly ascertained only by trial. 255. Chromatic Aberration. An ordinary lens not only NATURAL PHILOSOPHY. 171 refracts, but also disperses the rays of light, so that the violet rays, which are most refrangible, are brought to a focus at i (Figure 186), while the red rays, which are least refrangible, are brought to a focus at 2. pig. is 7 . The other rays are brought to a focus between these points. This action of the lens is called chromatic aberration. It causes the image to be fringed with colors. It can be overcome by combining a convex lens of crown glass with a concave lens of flint glass, which has an equal dispersive power, but a smaller refractive power. Such a combination of lenses (Figure 187) is called an achromatic lens. Fig. 188. 256. Concave Mirrors correspond to Convex Lenses. Lenses act by refraction, and mirrors by reflection. The Fig. 189. result of the action of a concave mirror on rays of light is the same as that of a convex lens. A concave mirror 172 ELEMENTS OF causes parallel rays atter reflection to converge to a principal focus (Figure 188); rays diverging from a point beyond the principal focus to become convergent (Figure 189) ; and rays diverging from a point within the principal focus to become less divergent (Figure 190). Fig. 191. It follows that a concave mirror will form the same im- ages as a convex lens. The image formed by such a mir- ror of an object beyond its focal length (Figure 191) is real and inverted; while the image of an object placed within its focal length (Figure 192) is virtual, erect, and larger than the object. NATURAL PHILOSOPHY. To avoid spherical aberration, the reflecting surface of a concave mirror should have a curvature as nearly that of the parabola as possible. Fig> J. vA\ ''I'.V-H/ 286. Lines of Magnetic Force. Place a sheet of drawing- paper stretched on a frame over a bar-magnet, and sift fine iron filings upon it. Tap the paper gently, and the filings will arrange themselves in a system of curved lines (Figure 217). If a horseshoe-magnet is held under the 13 194 ELEMENTS OF paper with its poles against the paper, the filings. will form the system of curves shown in Figure 218. These curves mark the lines along which the magnetic force acts, and show the direction and intensity of the force at each point. The curves are nearest together about the poles of the magnet, where the magnetism is most intense. The space near a magnet which is pervaded by its force is called the magnetic field. 287. Magnetic Induction. If a bar-magnet is brought near a piece of soft iron, it develops magnetism in it by an action called induction. If iron filings are scattered over the soft iron while under the influence of the magnet, they will adhere to its ends, as shown in Figure 219. The soft Fig. 219. . . iron will have two poles and a neutral portion between them. The near end of the soft iron will be the opposite pole to that of the bar presented to it ; and the far end, the other pole. Remove the magnet, and the iron filings NATURAL PHILOSOPHY. J 95 fall off from the piece of iron, showing that the iron retains no traces of magnetism, or only very slight ones. The attraction of pieces of iron by a magnet is always pre- ceded by induction, the magnet developing in the portion of the iron nearest it a magnetic pole nulikd its own. Hence pieces of iron are attracted with equal readiness by either pole of a magnet. A piece of iron which has become magnetic by contact with a permanent magnet may attract a second piece of iron, and this a third, and so on (Fig- ure 220). A magnetic chain may thus be formed, each com- ponent of which has two mag- netic poles. Each piece of iron in the filings which cling to the poles of a magnet becomes a magnet through induction, and these pieces are held together by their dissimilar poles. A piece of steel also becomes magnetic by induction when acted upon by a magnet, but it is not so powerfully magnetized as the soft iron. It is harder to magnetize the steel than the iron, but the steel retains its magnetic power after the magnet has been withdrawn. 288. Magnetization of Steel Bars. Permanent magnets are bars of steel. These may be magnetized either by the method called magnetization by single touch, or by that called magnetization by double touch. In the former method, the bar to be magnetized is laid on a board (Figure 221), near one end of which is a stop whose height is less than Fig. 221. the thickness of the bar. The magnet is held in a sloping position and is drawn over the bar several times, always in the same 196 ELEMENTS OP Fig. 222. direction and with the same end down. If the marked end of the magnet is drawn over the bar from a to d, the end a will become a marked pole. If the magnet is drawn over the bar in the opposite direction, or the other pole of the magnet is held downward, the end b will become the marked pole. In the method by double touch, two magnets are held one in each hand with dissimilar poles downward over the centre of the bar to be magnet- ized, as shown in Figure 222. They are now drawn apart quite over the ends of the bar, lifted, replaced at the centre, and again drawn over the ends. This pro- cess is repeated several times. The end of the bar over which the unmarked end of the magnet has been drawn will be the marked pole, and vice versa. 289. Compound Magnets. The lifting power of a magnet generally increases with its size, but small magnets are usu- ally able to sustain a greater multiple of their own weight than large ones. Compound magnets consist of a num- ber of thin bars laid side by side, with their similar poles all pointing the same way. Figure 223 represents such a compound magnet composed of twelve elemen- tary bars, arranged in three rows of four bars each. Their ends are inserted in masses of soft iron, the ex- tremities of which constitute the poles of the system. Figure 224 represents a compound horse- shoe-magnet, whose poles N and S support a Fig. 223. Fig. 224. NATURAL PHILOSOPHY. I 97 keeper of soft iron, from which is hung a bucket for holding weights. By adding fresh weights day after day, the magnet may be made to carry a greater and greater load ; but if the keeper is torn away from the magnet, the additional power is in- stantly lost, and the magnet is able to sustain only its original load. 290. Magnetic Needles. Any magnet suspended at the centre so as to turn freely is called a magnetic needle. The needle may be suspended so as to turn in a horizontal plane (Figure 225) or in a vertical plane (Figure 226). The former is called a horizontal needle, and the latter a dipping needle. Fig. 225. Fig. 226. 291. Terrestrial Magnetism. If a steel bar, exactly bal- anced in a horizontal position in the frame shown in Figure 226, which is suspended by a thread, is then mag- netized, it will no longer remain in equilibrium in any posi- tion in which it may be placed, but it will place itself in a particular vertical plane, and will take a particular direc- tion in this plane. The needle takes this position in obe- dience to the force of terrestrial magnetism. The earth acts upon the needle as if it were itself a magnet. The vertical plane of the needle is called the magnetic meridian. This plane usually lies several degrees from 198 ELEMENTS OF a north and south direction. The difference between true and magnetic north, or the angle between the geographical Fig. 227. Fig. 228. and the magnetic meridian, is called the declination. The direction of the needle in the vertical plane is seldom hori- zontal, but inclined more or less to the horizon. The angle NATURAL PHILOSOPHY. I 99 which the needle makes with the horizon is called the dip. Both the declination and the dip of the magnetic needle are very different in different parts of the earth. As a rule, the north pole of the needle dips at places north of the equator, and the south pole at places south of the equator. In the neighborhood of the equator there is a line around the earth on which neither pole dips. This line is called the magnetic equator. The dip increases as we proceed north and south from the magnetic equator. The magnetic meridians and lines of equal clip are shown in Figures 227 and 228. It will be seen that the magnetic poles are at some distance from the geographic poles. The magnetic pole north of the equator is a south magnetic pole, and vice versa. Fig. 229. 292. The Mariners Compass. The mariner's compass is a declination compass used in guiding the course of a ship. Fig- ure 229 represents a view of Fig. 230. the whole, and Figure 230 a vertical section. It consists f of a cylindrical case, B B', which, to keep the compass in a horizontal position in spite of the rolling of the vessel, is supported on gimbals. These are two concentric rings, one t 200 ELEMENTS OF of which, attached to the case itself, moves about the axis x d, which plays in the outer ring A / and this moves in the supports P Q, about the axis m n, at right angles to the first. In the bottom of the box is a pivot, on which is placed a magnetic bar ab, which is the needle of the compass. On this is fixed a disc of mica, a little larger in diameter than the length of the needle, on which is traced a star with thirty-two branches, making the points of the compass (Figure 231). The branch ending in a small star (Figure 229), and marked A 7 ", is in a line with the bar a (Figure 230), which is underneath the cisc. The compass is placed near the stern of the vessel, in sight of the helmsman. NATURAL PHILOSOPHY. 2OI VI. ELECTRICITY. / FRICTIONAL ELECTRICITY. A. ELECTRICAL ATTRACTIONS AND REPULSIONS. 293. Electrical Excitation. If a dry stick of sealing- wax is rubbed with a piece of dry flannel, or a vulcanite tube with a piece of dry fur, it acquires the power of at- tracting light bodies, such as bits of paper, pieces of straw, pith balls, etc. The body rubbed is said to be electrified, and the force which it manifests is called electricity. Elec- tricity is developed whenever any two unlike bodies are rubbed together, though some bodies become electrified much more readily than others. The ancients noticed that amber, which the Greeks called electron, acquired the power of attracting light bodies when rubbed ; hence the terms elec- trified and electricity. Electricity can be most readily and conveniently excited by rubbing a smooth vulcanite tube, 18 inches or so in length and % of an inch in diameter, with a cat-skin ; or a glass tube of tht same dimensions with a silk pad, composed of three or four layers of silk, and 8 or 10 inches square. The silk pad is much more effective when covered with amalgam, a mixture of I part by weight of tin, 2 parts of zinc, and 6 of mercury. The pad should be first smeared with lard, and then the powdered amalgam sprinkled over it. The tubes and rubbers work best when they are dry and hot. 202 ELEMENTS OF 294. Electrical Attraction. A pith ball hung on a silk thread (Figure 232) will be attracted if we present to it either an excited glass or vulcanite tube, without allowing it to touch the ball. Fig. 232. Fig. 233. An" ordinary walking-stick placed in a wire loop, sus- pended by a narrow silk ribbon (Figure 233), may be pulled around by either of the excited tubes. Fig. 234. An ordinary lath balanced on an egg in an egg-cup (Figure 234) is sensibly attracted by the glass or vulcanite tube when electrified. 295. Electrical Repulsion. Place an electrified glass tube in the loop shown in Figure 233, and present another excited glass tube to it. The tube in the loop will be NATURAL PHILOSOPHY. 203 repelled. An electrified vulcanite tube placed in the same loop will also be repelled on presenting a second electrified vulcanite tube to it. If the pith ball of Figure 232 is allowed to touch either the electrified glass or vulcanite tube, it will soon be repelled, and it cannot again be in- duced to touch the tube (Figure 235). 296. Two Kinds of Electricity. If an electrified vulcanite tube is placed in the wire loop of Figure 233, and an elec- trified glass tube is presented to it, the vulcanite will be attracted ; while, as we have seen, it will be repelled on present- ing an electrified vulcanite tube to it. So, also, if an excited glass tube is placed in the loop, it will be repelled by an ex- cited glass tube, but attracted by an excited vulcanite tube. There are thus'/nw kinds of electricity : one appearing on glass when rubbed with silk, and the other on vulcanite when rubbed with fur. The former is called/0.r///z>s tubes, or vacuum tubes. The light of the auroral discharge has great power of 'exciting fluorescence (283). If any portion of the glass of the tube is col- ored with a fluorescent substance, as uranium, or any portion of the tube passes through a fluorescent liquid, as a solution of sulphate of quinine, when the discharge takes place, the ura- nium glass glows with a soft green light, and the sulphate of quinine with a soft blue, each becoming fluorescent. The accompanying plate represents a vacuum tube. The spiral portion near each end passes through a solution of sulphate of quinine contained in a wider external tube. The green por- tions are colored with uranium. The red shows the natural color of the discharge in rarefied air. The sulphate of quinine is quite colorless by ordinary daylight, and the uranium very nearly so. 321. The Glow Discharge. When a metallic point is attached to the conductor of an electrical machine in ac- tion, it wijl be seen in the dark to be covered with a soft glow of light. A stream of molecules of air sets off from 220 ELEMENTS OF the point (314), carrying electricity away with them, and so discharging the conductor. This discharge is called con- vective discharge. The surfaces between which convective discharge is taking place are covered with a faint glow of light. Hence convective discharge is often called glow dis- charge. In spark discharge the electricity leaps from mole- cule to molecule through the intervening air, while in convective discharge the electricity is carried along by the molecules which traverse the intervening space. 322. The Brush Discharge. Remove the condenser from under the discharging rods of a Holtz machine, put the machine in action, and separate the rods. Instead of the ordinary spark discharge we shall find the space be- tween the rods filled with a pale, diffused purplish light. From the form of this light, this discharge has been called the brush discharge. Fig. 257. The brush discharge seems to be a blending of the spark and the convective discharge. The electricity is some of the time NATURAL PHILOSOPHY. 221 carried by the molecules of the air, and some of the time it leaps along from molecule to molecule. In a darkened room brushes of light will be seen on various parts of a powerful Holtz machine in action. The brush sometimes assumes the form shown in Figure 257. II. VOLTAIC ELECTRICITY. A. DEFLECTION OF THE NEEDLE. 323. The Electric Current. The flow of electricity through a conductor is called the electric current. The phenomena of electricity in motion, or of current electricity, are usually classed together under the head of voltaic elec- tricity, to distinguish them from those of electricity at rest, or of frictional electricity. The former department of electricity is sometimes called dynamical electricity, electro- dynamics, or electro-kinetics ; and the latter, statical electricity, or electro-statics. 324. The Action of the Current on the Magnetic Needle. Oersted discovered, in 1819, that a current flowing through a wire near a magnetic needle will deflect the needle. If the Fig. 258. Fig 259. wire is held over the needle (Figure 258), the needle will be deflected in one direction. If the same wire is held under the needle (Figure 259), the needle will be deflected /;/ the opposite direction. If the current is made to flow in the opposite direction through the wire while over or under the needle, the needle will be deflected in the opposite direc- tion to what it was before. If two currents flow, one over the needle in one direction, and one under the needle in the opposite direction, they will 222 ELEMENTS OF both tend to turn the needle the same way. In any case, the stronger the current the greater the deflection of the needle. If the wire conveying it is bent round the needle, as in Figure 260, the current will flow in opposite directions above and below the needle. Hence both portions of the current will tend to turn the needle the same way, and the deflection will be greater than when the current flowed simply over Fig. 260. Fig. 261. or under the needle. If the wire is carried a second time around the needle (Figure 261), the deflection of the needle will be increased, since there will now be two cur- rents above the needle and two below it, all tending to turn the needle the same way. Fig. 262. 325. Ampere's Rule. Ampere has given the following rule for ascertaining the direction of the deflection of the needle in any case : Imagine a little swimmer in the electric current, always swimming with the current, and with his face to the needle. The north pole of the needle will always be deflected to his left (Figure 262). NATURAL PHILOSOPHY. 22 3 Fig. 263. 326. The Simple Galvanometer. A galvanometer is an instrument for showing the presence, direction, and strength of an electrical current. The simple galvanometer consists of a magnetic needle, free to turn in a horizontal or vertical plane, and surrounded with a coil of wire. This galva- nometer shows the presence of a current in the wire with which it is connected, by the deflection of the needle ; the direction of the current, by the direction of this deflection ; and the strength of the current, by the amount of the deflection. 327. The Astatic Needle. The directive action of the earth upon a magnetic needle impedes its deflection by the current. This action may be neutralized by com- bining two needles. The needles (Figure 263) are fastened together rigidly at the centre ; and the poles of one needle are the reverse of those of the other. As there is a north and a south pole at each end, each needle must neutralize the directive action of the earth upon the other. Such a combination of needles is called an astatic needle (unsteady needle). 328. The Astatic Galvanometer. An astatic galvanometer is one in which an astatic needle is used. The two needles of the combination are almost, but not quite, of the same strength. They are hung on a fibre of silk, and the wire is coiled around the lower needle (Figure 264). It will be seen by Ampere's rule (325) that the current that flows between the needles will tend to turn both needles the same way, while that which flows under the lower needle will tend to turn the needles in opposite directions. Owing to the greater distance, its action on the upper needle will be much feebler than its action on the lower needle. Such a galvanometer is very sensitive, since 224 ELEMENTS OF Fig. 266. the directive action of the earth is nearly neutralized, while the ef- fective action of the current is increased by using two needles. When it is desired to make this galvanometer extremely sensitive, the needles are made very light, and hung on a single fibre of silk, and the wire is coiled sev- eral thousand times around the lower needle. In this case the wire is very fine, and is wound on a flat reel (Figure 265). The whole is enclosed in a glass case, to Fig. 265. protect the needle from currents of air (Figure 266). B. FLOW OF ELECTRICITY THROUGH CONDUCTORS. 329. Electromotive Force. The flow of electricity through a wire connecting two conductors is analogous to the flow of water through a pipe connecting two reservoirs. When the water is at the same level in both reservoirs, no water will flow through the pipe. When the water is at different levels in the reservoirs, it will flow through the pipe from the higher level to the lower. The greater the difference between the levels, the greater the energy of the current in the pipe. In like manner, no current of electricity will flow through a wire connecting two conductors, when the conductors are at the same potential. When the conductors differ in potential, a current will flow through the wire from the higher potential to the lower. The greater the difference of potential between the two conductors, the greater the energy of the current. NATURAL PHILOSOPHY. 225 The force which urges electricity through a conductor is called the electromotive force. The electromotive force is ahvays equal to the difference of potential between the points connected by the wire. A certain standard electromotive force has been selected as a unit, and is called a volt. A conductor designed to convey a current is called a circuit. 330. Electrical Resistance. Every known substance offers some resistance to the passage of the current through it, but different substances differ greatly in the amount of resistance which they offer. The resistance of a wire varies with its material, its length, and its thickness. The longer and thinner a wire, the greater its resistance. The metals offer comparatively little resistance to the passage of the current, and silver the least of them all. Copper stands next to silver. The less the resistance any substance offers to the passage of the current, the better conductor it is. A certain standard of resistance has been chosen as a unit, and is called an ohm. It is about the resistance of 250 feet of copper wire ^ of 5 each, forming 4 com- ^^;;^ pound cells, which are con- f ^\^" \ \ \ \ p nected side by side. The 1 ^.fr fr fr fr electromotive force of this V. battery is 5 times that of a single cell, and its resistance is f that of a single cell. 232 ELEMENTS OF II. ELECTROLYSIS. 343. Electrolytic Action. If two platinum wires, con- nected with the poles of a battery in action, are immersed in dilute sulphuric acid, the acidwill be decomposed. Hydro gen will be set free at the wire connected with the negative pole of the battery, while oxygen will appear at the other wire. This can be shown to a class by placing the dilute acid in a tank with parallel glass sides, and throwing an image of the wires in the tank on a screen. Torrents of bubbles of gas will be seen to rise from the wires. The decomposition -of the acid is the work of the electric cur- rent, and is called the electrolytic action. If a solution of sulphate of copper is used instead of the dilute sulphuric acid, copper is deposited on the negative wire, while oxygen is set free at the positive wire. 344. Faraday's Nomenclature of Electrolysis. Faraday called the decomposition of a substance by means of elec- tricity, electrolysis ; the substance decomposed, the electro- lyte; the poles at which the decomposition takes place, the electrodes ; the one connected with the positive pole of the battery the anode, and the one connected with the negative pole of the battery the cathode; the products of the decom- position, the ions ; the one going to the anode the anion, and the one going to the cathode the cation. 345. The Voltameter. The voltameter is an instrument for measuring the quantity of the current. It was invented by Faraday, and consists of a dish filled with acidulated water and fitted with electrodes (Figure 278). Receivers over the electrodes collect the gases as they are set free. The quantity of the gas liberated per minute measures the mean strength of the current during the time, and the total quantity of the gas collected measures the total quantity of electricity which has passed through the circuit. It is necessary to collect the gases separately, as chemically clean platinum has the power to cause the hydrogen and oxy- NATURAL PHILOSOPHY. 233 gen to reunite. The receiving tubes are first filled with water and inverted over the electrodes. As the gas rises it displaces the water. The receivers are graduated so as to show the amount of the gas collected. Fig. 278. 346. Electro-Metallurgy. Whenever solutions of com- pounds of metals are decomposed, the metal is deposited upon the cathode. This deposition of metals by means of the electric current is called electro-metallurgy, and is of great practical importance. The two chief processes of electro- metallurgy are electrotyping and electroplating. The former is copying by means of electricity, and the latter is coating the baser metals with the more noble by means of electricity. 347. Electrotyping. Anything may be electrotyped of which a mould may be taken in wax. The chief use of electrotyping is in copying the face of printers' type and wood-engravings, after they have been arranged for the pages of a book. A mould is first taken in wax of the article to be copied, and the wax is coated with a thin film of some conducting substance, such as graphite powder. The mould is then hung up in a trough filled with a solution of sulphate of copper, called the bath. The mould is connected with the negative pole of the battery, so as to make it a cathode. A plate of copper is hung in the bath opposite the mould, and connected with the positive pole of the battery, so as to make it an anode. On the passage of the cur- rent through the bath, copper is deposited from the solution upon the mould in a uniform coherent sheet, while the anode is 234 ELEMENTS OF gradually eaten away, and keeps the bath of uniform strength. The moulds are usually hung in the bath at night, and in the morning they are removed, and the wax melted off. The cop- per casts are made sufficiently firm for use in printing by back- ing them with type-metal. 348. Electroplating. The ordinary table-ware, such as knives, forks, tea-sets, etc., is plated with silver by electrolysis. The article to be plated is very carefully cleaned, and hung up in a bath containing a solution of cyanide of silver. It is then connected with the negative pole of a battery, while a piece of silver hung in front of it is connected with the positive pole. On the passage of the current, silver is deposited from the so- lution upon the article which forms the cathode, while the silver of the anode is gradually eaten away, and keeps the solution of uniform strength. If the article is thoroughly cleaned, and the current is maintained at the right strength, the silver will be deposited uniformly over its surface, and will adhere firmly to it. When the article is to be gilded, or coated with gold, the bath must contain a solution of the cyanide of gold, and the anode must be of gold. In other respects the process is the same as in silver-plating. In nickel-plating the bath contains a solution of some com- pound of nickel, and the anode is a piece of nickel. D. ELECTRO-MAGNETIC INDUCTION. 349. An Electric Whirl constitutes a Magnet. If a cur- rent of electricity is sent round a wire bent in the form of a Fig. 279. ring (Figure 279), the ring will act in all re- spects like a short magnet. The left-hand side of the ring to a person swimming round it with the current, and with his face towards the [j )] centre of the ring, will be a north pole, and the other side of the ring a south pole. If the wire is wound round and round in the form of a coil, the multiplication of the rings will produce a stronger magnet. By changing the strength of the current in such NATURAL PHILOSOPHY. 235 a coil, we change the strength of its magnetism, and by changing the direction of the current we reverse the poles of the magnet. 350. The Electro-Magnet. If a bar of soft iron is placed within the axis of the coil, and a current sent through the coil, the iron becomes a magnet, with its north pole to the left hand of a person swimming around the coil with the current and with his face towards the axis of the coil. A wire coiled round a bar of soft iron constitutes an electro-magnet. Such a magnet is active only while the current is passing through its coil. It loses its magnetism the moment the current stops. Its poles are reversed by reversing the current in its coil. As the strength of the current increases the magnetism of the magnet increases, but less and less rapidly, till it reaches a certain point, beyond which an increase in the strength of the current produces no increase of magnetism. At this point the magnet is said to be sat- urated. Below the point of saturation every change in the strength of the current, however slight, produces a corre- sponding change of magnetism. Electro-magnets are usually made of the horseshoe form (Figure 280), and they are much Fi 2go stronger than the ordinary steel mag- nets. The iron core of each coil is often a separate bar, and the two bars are connected by a straight bar at the base. 35 1. Magneto- Electric Currents. If a wire is moved in the neighborhood of a magnet in any direction whatever, except along a line of magnetic force, a difference of poten- tial will be produced at the ends of the wire which would cause a current to flow through a wire connecting the ends and not acted on inductively by the magnet If a magnetic pole is moved in the neighborhood of a 2 3 6 ELEMENTS OF wire, in any direction except parallel to it, a current will be induced in the wire. If, for instance, a magnet N S (Figure Fig. 281. 2 8i) is moved suddenly in or out of the coil of wire, a current will be induced in the coil, which will be in one direction on in- serting the pole, and in the other on withdrawing it. If the mag- net is reversed so as to use the other pole, the current will be reversed. If a coil of wire through which a current is passing is used instead of a steel magnet (Fig- ure 282), precisely similar results are obtained. The more suddenly the steel magnet or the coil conveying a current is moved in or out of the coil, the stronger the current induced. Fig. 282. - If the small coil is left within the larger coil, any change whatever in the current in the inner coil, whether of strength or direction, will develop a current by induction in the outer coil. So, too, if any two coils of wire, through one of which a current is passing, are near together, any movement of the coils with respect to each other, or any change in the current in the first, will induce a current in the second. If a bar of soft iron is inserted in the inner coil of Fig- NATURAL PHILOSOPHY. 2 37 tire 282, the current induced in- the outer coil, either by motion or change of current, will be very much stronger. Fig. 283. 352. The Bell Telephone. Figures 283 and 284 show the Bell telephone, in section and in perspective. It consists of a steel magnet M around one end of Fig. 284. which is wound a coil of fine wire B. The coil and magnet are enclosed in a wooden case, which serves as a handle. One end of this case is enlarged and hollowed out at E, so as to serve as a mouth-piece or an ear-piece. A diaphragm of thin iron D is stretched across the wide end of the case, just in front of the pole of the magnet, which it does not touch. The transmitting and receiving instruments, which are exactly alike in construction, are connected to- gether by a wire. On speaking into the mouth-piece, the air in it is thrown into vibration, and the vi- brations are communicated to the diaphragm. The vibrations of the iron plate produce slight temporary alterations in the magnetism of the steel magnet. These changes of magnetism in the magnet induce corresponding cur- rents in the wire of the coil, which are transmitted over the wire which connects the two instruments. Hence pulsations of electricity exactly corresponding to the vibrations of the dia- 23 8 ELEMENTS OF phragm of the first instrument will be transmitted over the wire and through the coil of the receiving instrument. These pulsa- tions of the current in the coil will induce in the magnet of the receiving instrument exactly the same changes of magnetism as those by which they were produced in the sending instrument. These changes of magnetism cause the magnet to pull upon the iron plate in front of it with a varying force, and, consequently, to make it vibrate exactly like the diaphragm of the transmitter. These vibrations are communicated to the air, and then to the ear of the operator, which is placed at the mouth of the re- ceiver. The words spoken into the transmitter are thus repro- duced in the receiver. Figure 285 shows the way in which the two instruments are X_L\ connected. The wire at each end is connected with the earth by means of a copper plate sunk in the ground, so that the cir- cuit is completed by the earth. Otherwise two wires must be used between the instruments. The Bell telephone is a beautiful illustration of electro- magnetic induction. 353. The Edison Telephone. In the Bell telephone no battery is used. In the Edison telephone a battery is used, and a current transmitted from the battery is thrown into undula- tions by an arrangement called the carbon button. In Figure 286 b is a disc or button of carbon, in the form of compressed lampblack ; a and c are metallic plates placed against the front NATURAL PHILOSOPHY. 239 Fig. 286. and back of the disc. One of the poles of the battery B is connected with a, and the other with c. The current is obliged to pass from the plate a to c through the carbon. An increase of pressure upon the metallic plates a and c diminishes the resist- ance of the button, either by increasing the density of the carbon or by improving the contact between the plates and the disc. The button is exceedingly sensitive to varia- tions of pressure, the slightest alteration of pressure producing a change in the strength of the current which traverses the carbon. One form of the Edison transmitter is shown in Figure 287. The mouth-piece is of vulcanite. Back of this is the vibrating Fig. 287. disc, and behind this is a little hemispherical button of alumin- ium. This button rests upon the metallic plate in front of the carbon disc. This plate is of platinum. Behind the carbon disc is a second platinum plate, held in position by means of the screw at the back of the instrument. The battery wires are connected with the two platinum plates in such a way that the current must traverse the carbon disc. On speaking into the mouth-piece, the disc is thrown into vibration. The vibrations are communicated to the platinum plate and the carbon disc by means of the aluminium button, thus producing undulations in the current exactly correspond- ing to the vibrations of the disc. 240 ELEMENTS OF The receiving instrument of the Edison telephone is similar to that of the Bell telephone. Changes of magnetism are in- duced in it by the undulating current which traverses its coil, and these changes of magnetism cause the disc in front of the magnet to vibrate exactly like that of the transmitter. 354. The Induction Coil. The induction A?// consists of two coils: an inner m primary coil of coarse wire, enclos- ing pieces of soft iron, usually in the form of wires ; and an outer or secondary coil oijine wire. The coils are care- fully insulated from each other. A current of electricity is sent through the primary coil, and any change in the strength of this primary current develops by induction a cur- rent in the secondary coil. The induced current is much less in quantity (331) than the primary current, but it has a far greater electromotive force (329). 355. The Use of the Induction Coil with the Telephone. The induced currents from the induction coil are better adapted for working the telephone than the direct current from the bat- tery. Figure 288 shows the way the coil is used with the tele- phone, b is the carbon disc of the transmitter, a and c are the platinum plates, B is the battery, d is the primary coil of the in- duction coil, and ee its secondary coil. The battery is connected with the plates a and c, and with the primary coil d. One end of the wire of the secondary coil is connected with the earth by the wire G; and the other end to the line Z, which runs to the receiving instrument. The un- dulations of the current in the primary coil induce correspond- ing undulations of greater electromotive force in the secondary coil. These latter undulations pass over the line, and work the receiving instrument. 356. The Microphone. When there is an imperfect contact at any point of a circuit carrying a battery current, any change Fig. 288. NATURAL PHILOSOPHY. 241 in the quality of the contact will produce a change in the strength of the current, and cause a sound in a telephone re- ceiver included in the (circuit. When the imperfect contact is between pieces of carbon lightly pressed together, variations of the current are produced by the slightest sounds occurring near the carbons. ' The microphone consists of three pieces of carbon, C, A, and C' (Figure 289). The wires from the battery B are con- Fig. 289. nected with Cand C' in such a way that all the pieces of carbon are in the circuit. The wires X and Y run to the receiver of a telephone. The lowest whisper spoken near the microphone is loudly reproduced in the telephone. As the carbon rod A is thrown into vibration by the pulsations of sound, it alternately lengthens and shortens. These alterations of length alternately improve and impair the contact at C and C'. Fig. 290. To intensify the effect, the microphone is usually placed on a sounding-board D (Figure 290). The sound caused by a fly walking on the sounding-board is distinctly audible at the dis- 16 242 ELEMENTS OF tant telephone. The ticking of a watch on the sounding-board sounds like the blows of a hammer. 357. Magneto-Electric Machines.^ The fact that electric currents are produced in a wire by any change of mag- netism near it, or by moving the wire in the neighborhood of a magnet, has been utilized in the construction of ma- chines for the development of very powerful currents of electricity. These machines are called magneto-electric or dynamo-electric machines. The former name is applied more especially to the machines in which the electric cur- rents are produced by changes of magnetism, and the latter to those in which the currents are produced mainly by the motion of wires in the neighborhood of magnets. In all the dynamo-electric machines the currents are produced by revolving coils of wire between the poles of powerful horseshoe-magnets, which are sometimes steel magnets, but usually electro-magnets. Fig. 291. E. TELEGRAPHY. 358. The Principal Instruments of the Simple Morse Tele- graph. The principal instruments of the simple Morse telegraph are the key, the relay, and the sounder. 359. The Key. The key (Figure 291) is used for opening and closing the circuit. Its essential parts are NATURAL PHILOSOPHY. 243 shown in outline in Figure 292. K is the lever ; a is the axis on which it turns ; b is a platinum point connected with the lever ; c is a stationary platinum point directly under b, called the anvil; and d is a vulcanite button by which the lever is pressed down. There is a spring under the lever of the key which keeps it up so as to separate the platinum points when the lever is not pressed down. Fig. 292. K 293- K U In Figure 293 the key is shown in the circuit of a bat- tery. One pole of the battery is connected with the anvil by a wire, and the other with the lever at the axis. When Fig. 294. the lever is up, the circuit is opened at a by the separation of the platinum points, and the current is stopped. When the lever is pressed down, the circuit is closed by the con- tact of the platinum points at a, and the current starts. 244 ELEMENTS OF 360. The Sounder. The sounder is shown in Figure 294. Its essential parts are shown in outline in Figure Fig. 295. 295. A is an electro-magnet ; L b S L is a lever ; b is the axis on which the lever turns ; c is a spring which pulls the lever up ; e is a piece of soft iron, fastened across the lever just over the electro- magnet ; and d is a piece of metal against which the lever strikes when it is drawn down. Figure 296 shows the sounder and key in circuit. One Fig. 296. K ~ D pole of the battery is connected by a wire with the circuit of the key ; the other pole is connected with one end of the wire of the electro-magnet of the sounder, and the other end of the wire of this magnet is connected with the lever of the key at the axis. When the lever of the key is up, the circuit is broken at a, the current is stopped, the electro-magnet of the sounder is inactive, and the lever of the sounder is thrown up by the spring. If the lever of the key is pushed down, con- tact is made at a, which closes the circuit; the current starts, the electro-magnet of the sounder becomes active, and the lever of the sounder is drawn down by the pull of the magnet upon the iron above it. As the lever is drawn down, it clicks from striking the metallic stop at the end. The clicking of the sounder is controlled by the key, even when these are miles apart, for the sounder clicks every time the lever of the key is depressed. Letters and NATURAL PHILOSOPHY. 2 45 words are indicated by combinations of long and short inter- vals between the clicks. The operator listens to the sounder just as we listen to one who is talking to us, and soon becomes able to follow it as readily. 361. The Register. Sometimes an instrument called the register is used for receiving the message instead of the sounder. The essential parts of this instrument are shown in Figure 297. It resembles the sounder in construction and action. At the back end of the lever there is a point B, and just above this point a strip of paper C is carried Fig. 298. along by clockwork between two rollers at Z>. When the lever is drawn to the magnet, the point is thrown against the paper and scratches a line on it. This line will be long or short according to the time the lever is held down. 246 ELEMENTS OF Fig. 299. The long lines are called dashes and the short lines dots. These dots and dashes correspond to the short and long intervals between the dicks of the sounder, and their combina- tions form the letters of the alphabet. 362. The Relay. On long lines, in which there are a num- ber of stations, the current from the main battery is not strong enough to work the sounders with sufficient force. This neces- sitates the use of an instrument called the relay (Figure 298). Its essential parts are shown in outline in Figure 299. A is an electro-magnet ; / is the lever, which turns upon an axis at b ; c is a piece of soft iron fastened across the lever in front of the electro- magnet; f is a spring for pulling the lever back ; d and e are two platinum points, the former fastened to the lever and the latter stationary. Figure 300 shows the way in which the key, relay, and sounder are connected. The full line represents the circuit of Fig. 300. K-*- 'UB. the main battery M ; and the dotted line, of the local battery L. One pole of the main battery is connected with the anvil of the key, and the other with one end of the wire of the electro- magnet of the relay. The other end of the wire of this magnet is connected with the lever of the key at the axis. One pole of the local battery is connected to the lever of the relay, and the other pole to the electro-magnet of the sounder and then to the stationary platinum point of the relay. When the lever of the key is up, the main circuit is opened at a, the current is stopped, the electro-magnet of the relay is inactive, the lever of the relay is drawn back by the spring, the local circuit is NATURAL PHILOSOPHY. 247 opened at by the separation of the platinum points, the electro- magnet of the sounder is inactive, and the bar of the sounder is thrown up by the spring. When the lever of the key is pushed down, contact is made at a, the main circuit is closed, the electro-magnet of the relay becomes active, the lever of the relay is drawn forward, contact is made at b, the local circuit is closed, the electro-magnet of the sounder becomes active, and the lever of the sounder is drawn down. Thus, the levers of the relay and sounder vibrate in unison, but each is worked by a different battery. The vibration of the lever of the relay is controlled by the key, and controls the vibration of the lever of the sounder by opening and closing the local circuit. 363. The two Terminal Stations of a Line. Figure 301 shows the arrangement of the instruments and circuits for two terminal stations. For convenience, half of the main battery is placed at each station. There is also a key, a relay, and a sounder at each station. One pole of the main battery, say the negative, at New York is connected with the earth by a wire running to a large copper plate E sunk in the ground. A wire runs from the positive pole of the battery to the anvil of the key A", then from the lever of the key to the electro-magnet of the relay /?, then from the relay to the line and along the line to Boston, then to the electro-magnet of the relay R ', then to the lever of the key Af ', then from the anvil of the key to the negative pole of this part of the main battery, and from the posi- tive pole of the battery to the copper plate E' in the earth. The circuit is completed by the earth, the electricity passing one way over the line and back through the earth. Each local bat- tery is connected with its relay and sounder as in the previous section. When the line is not in operation, the main circuit is closed at each key by pulling the side lever H seen in Figure 291 up against the anvil. This connects the axis of the lever with the anvil, and closes the circuit, although the levers of the keys are up. The electro-magnets of both relays are now active, the levers of both relays are drawn forward, both local circuits are closed, the electro-magnets of both sounders are active, and the levers of both sounders are drawn down. When the ope- rator at one of the stations wishes to send a message, he pulls 248 ELEMENTS OF a NATURAL PHILOSOPHY. 249 back the side lever of his key. This opens the main circuit, and causes all the electro-magnets to become inactive, and all the levers to be thrown back. On working his key, the levers of both relays and of both sounders are made to vibrate. His own sounder elides as well as that at Boston. When the operator has finished his message, he closes his key by pulling the side lever against the anvil. Should both operators start at the same instant to send messages, the fact would be revealed by the confusion of ,the signals given by each sounder, and one operator would close his key and wait for the other to finish. Should the operator at the receiving station desire to interrupt the one sending the message to ask him to repeat, or for any other purpose, he Las merely to open his key so as to break the circuit. 364. A Way Station. One of the simplest methods of introducing the instrument of a way station into the circuit is shown in Figure 302. A and B are two brass buttons, turning on pivots at the top. Under the bottom of each button, as it stands in the diagram, is a metallic disc D, E. A wire runs from one of the metallic discs to the electro-magnet of the key K', and thence to the anvil of the key K' '. A wire runs from the other disc to the lever of the key. There is a third metallic disc at C between the buttons. When the buttons are on the discs D and E, the key and the electro-magnet of the relay are in the main circuit. The sounder and local circuit are arranged precisely as in the terminal stations. When not in operation, the key is kept closed by means of the side lever. It will be seen at once that the levers of the relay and sounder will vibrate when the key at either terminal station is worked, and also that the levers of the relays and sounders at the terminal stations will vibrate on working the key at the way station. When the buttons A and B are both turned upon the disc C, the instrument" of the way station will be cut out of the circuit, which will be completed through the buttons, these being now in contact with each other. When any key at any station is worked, the sounders of every station which is not cut out will click. The name of the station for which the message is designed is first called, and only the operator at that station attends to the message. 250 ELEMENTS OF -D NATURAL PHILOSOPHY. 251 There are means at each way station to connect one of the wires with the ground and the other wire with the line on either side, so that the operator may use that side alone, in case the line is injured in any way on the other side>of his station. The chief reason for dividing the main battery between the terminal stations is to enable a way station to use the line on either side in case of necessity. F. TRANSMISSION OF POWER BY MEANS OF ELECTRICITY. 365. Electro- Motors. The current produced by moving a magnet near a wire, or a wire near a magnet, always opposes the motion which produces it ; that is to say, it tends to produce motion in the opposite direction. Hence, if a cur- rent of electricity from any external source were sent through the coils of a magneto-electrical machine in the direction of the one produced in these coils by the action of the machine, it would cause the cylinder to revolve in the opposite direction to that in which it must be turned to produce a current. Hence electricity when sent through the coils of such a machine becomes a source of power. A machine driven by electricity is called an electro-motor. It is proposed to employ electricity as a motive power for a great variety of purposes. Companies have been formed to develop electric currents at one or more centres in cities, and send them through wires laid in the streets to the houses, to be used for a variety of domestic purposes, such as driving clocks, working sewing-machines, pumping water, etc. It is thought that electricity will be found to be the medium by which power can be most efficiently and economically trans- mitted to a distance. For instance, if water-power is abun- dant in places remote from the localities where the power is needed, the energy of the water may be converted into that of electricity by means of dynamo-electrical machines, then the electricity conducted to the distant points through wires, and used as a source of power with similar dynamo-electrical ma- chines (357). 252 ELEMENTS OF Fig. 33- Fig. 304. G. ELECTRO-THERMAL ACTION. 366. Thermo- Electric Piles. When two metals are soldered together, so as to form a closed circuit, as shown in Figure 303, and one of the junctions is heated more than the other, a current flows around the circuit. The direction and strength of the current vary with the metals used. Such a combination of two metals is called a thermo-electric pair. Antimony and bismuth form the best combination among the metals. In this combination the current flows across the heated junction from the bismuth to the antimony. With a single pair of metals only a feeble current is obtained. These pairs may be combined so as to form batteries, or piles. The pairs are sol- dered together at alternate ends, as shown in Figure 304. Several hundred pairs are often combined in a pile. The least difference of temperature be- tween the ends of such a pile gives rise to a current. When used in connection with a delicate galvanometer the thermopile becomes an exceedingly sensitive differential thermometer (179). No current is obtained from the pile when the two faces are heated equally. 367. The Development of Heat by means of the Ctirrent. Whenever a powerful current of electricity flows through a wire it heats it. The flner the wire, and the lower the con- ducting power of the material of which it is composed, the more intense the heat developed. The more powerful the current employed, the more intense the heat with the same conductor. Fine wires of the most refractory metals are heated white-hot, and even fused, on the passage of power- ful currents. NATURAL PHILOSOPHY. 2 53 368. Electric Illumination by Incandescence. There has been for a long time an effort to make electricity available as a source of light, and at last the many practical diffi- culties that have been met with seem to have been nearly, if not quite, surmounted. Illumination by means of a poor conductor heated to a white heat on the passage of the cur- rent, is called illumination by incandescence. The great difficulty encountered in illumination by incandescence is that the conductor which is heated to incandescence is also apt to be destroyed by the current. Even so refrac- tory a substance as platinum is very likely to fuse when heated to incandescence. If the current is sent through a very thin rod of carbon, the carbon becomes heated to incandescence ; but at the high temperature the carbon is liable to be destroyed by combining with the oxygen of the air. Even when the carbon is placed in an exhausted receiver, or in one which has been first exhausted of air and then filled with some gas which is a non-supporter of combustion, the rod or filament is liable to disintegration. 369. The Edison Lamp. The Edison lamp for incandescence is shown, in section, in Figure 305. The upper portion of the lamp is a glass globe, from which the air has "been exhausted, and which is hermeti- cally sealed. In the centre of this globe is the carbon filament, bent in the form of a ring. The ends of this filament are held in little clamps, connected with the platinum wires which pass through the glass of the smaller globe under the ring, and thence out through the bottom of the lamp, where they are connected with the wires of the circuit. The permanent success of this and simi- lar lamps for illumination depends solely upon whether the Fig. 305. 254 ELEMENTS OF carbon filament is found, in practice, to be sufficiently durable. The Edison filament is constructed of bamboo-wood. The re- sistance of the loop is from 100 to 300 ohms (330), and the amount of light that can be safely obtained from it varies from 2 to 10 candles. These lamps will be arranged in the houses just as gas- jets are now, and electricity will be conducted to them by wires in the streets, just as gas is conducted to the gas-jets by pipes in the streets. Edison's plan is to measure the electricity used in each house by a kind of voltameter (345), in which sulphate of copper is decomposed instead of sulphuric acid. The copper is deposited on one of the electrodes and so increases its weight. The increase in weight of the plate will show the amount of elec- tricity which has passed through the instrument. Illumination by incandescence is especially adapted for light- ing rooms of the ordinary size. Fig. 306. 370. The Voltaic Arc. If two pencils of coke carbon are brought in contact in a circuit through which a power- ful current of electricity is passing, and are then separated a little, intense light and heat will be developed at the point of separation (Figure 306). The ends of the pencils will be heated white-hot, and they will be connected by a luminous bridge. This bridge is called the voltaic arc. NATURAL PHILOSOPHY. 2 55 The light and heat of the voltaic arc are the most intense that can be obtained by artificial means. If the carbons are separated far enough to stop the current, it will not start again till they have been again brought in contact. After the current has been started, it will continue to flow after the carbons are separated, pro- vided they are not separated too far. As the carbons Fig. 307. begin to separate, the current which is passing detaches little particles from each of them and transfers these to the other carbon, and so bridges over the space between the points with carbon dust. The air thus filled with particles of carbon offers less resistance to the current than the -air free from carbon dust which separates the points before they are brought into contact Heated air 256 ELEMENTS OF moreover, offers less resistance than cold air. The intense heat of the voltaic arc is due to the resistance which the current encounters in the space between the carbon points. The end of the positive carbon becomes concave, and that of the negative carbon pointed, as shown in Figure 307. Both carbons are consumed, but the positive more rapidly than the negative. 371. Illumination by the Voltaic Arc. In order to ob- tain illumination by the voltaic arc, a lamp is needed to keep the carbons all the time at the right distance apart, and to bring them together, in case the current should stop, and then to separate them again when it has started. In the best lamps for this purpose, the points are moved by means of clock-work, which is so constructed that it can be made to move the points either together or apart. The clock- work is controlled by an electro-magnet by means of a lever. The current passes through the coil of this electro-magnet on its way to the carbons. When the carbons become too far apart, the current is weakened, the lever is released, and the clock-work is made to turn so as to move the carbons together. When the carbons come too near together, the current becomes strong enough to draw the lever down, and this causes the clock-work to turn so as to separate the points. When the points are at just the right distance apart, the lever is held in such a position as to stop the clock-work entirely. Illumination by the voltaic arc is too intense for rooms of the ordinary size, but is especially adapted for out-door illumination, and for large halls and workshops. NATURAL PHILOSOPHY. 257 VII. METEOROLOGY. I. CONSTITUTION OF THE ATMOSPHERE. 372. The Term Meteorology. The term meteor was formerly applied to any natural phenomenon occurring within the limits of the atmosphere ; hence the term meteorology as applied to that branch of Natural Philosophy which treats of the atmosphere. 373. The Composition of the Atmosphere. The atmos- phere is composed chiefly of oxygen and nitrogen in a state of mechanical mixture, and not of chemical combination. In every 100 volumes of air there are nearly 79.1 volumes of nitrogen and 20.9 volumes of oxygen. Owing to the tendency of these two gases to diffuse into each other, and to the currents which exist in the atmosphere, these proportions are sensibly the same in all parts of the globe and at all accessible elevations above its surface. In addition to the oxygen and nitrogen, the atmosphere contains also a little carbonic acid and watery vapor. The amount of carbonic acid varies, in the open country, from 4 to 6 parts in a thousand. The amount of moisture is very variable, ranging from 4 parts in one hundred to i part in a thousand. 374. The Height of the Atmosphere. The atmosphere is held to the earth by gravity, and it must terminate at that height at which the attraction of the earth is balanced 258 ELEMENTS OF by the repulsion of the particles of the air. At the height of 50 miles the atmosphere is wellnigh inappreciable in its effect upon twilight. The phenomena of lunar eclipses indicate an appreciable atmosphere to the height of 66 miles ; while the phenomena of shooting stars and of the auroral light show that such an atmosphere exists at the height of 200 or 300 miles, and probably of more than 500 miles, above the earth's surface. 375. The Weight of the Atmosphere. The weight or downward pressure of the air at any point is ascertained by the use of the barometer (126). It is different in different parts of the earth, and is in a state of constant fluctuation at the same place. If we observe the height of the barometer every hour of the day, and then divide the sum of the observed heights by 24, we obtain the mean height for the day. By dividing the sum of the daily means for a month by the number of days in the month, we obtain the mean height for the month. By dividing the sum of the monthly means for a year by 12, we obtain the mean height for the year. If we divide the sum of the annual means for a series of years by the number of years in the period, we obtain the mean height for the place. This at Boston is 29.988 inches. Fig. 308. BOJ BO.O 39.8 30.6 89.4 29.2 70' 60" 60* 40^ 30 20 10" 0" 10 20 SO? W ?0> BO' 376. The Mean Height of the Barometer at Different Lati- tudes. The curve in Figure 308 shows the mean height of the barometer at different latitudes from 75 north to 80 south. The numbers at the bottom show the latitude, and those at the side the height of the barometer in inches. The height at which the curve crosses the vertical lines of the diagram shows NATURAL PHILOSOPHY. 2 59 the mean height of the barometer at that latitude. The height is found by following the horizontal lines to the left ; and the l.ititude, by following the vertical lines to the bottom. It will be seen from the diagram, that the mean height of the barome- ter is greatest at 32 north and 25 south of the equator, and lowest at 64 north and about 70 south of the equator ; also that the mean height of the barometer is generally greater north of the equator than south of it. There is a belt of low pressure at the equatdr. 377. The Mean Height of the Barometer for Different Months. The mean height of the barometer varies somewhat from month to month during the year, being generally higher in winter than in summer. In many places the mean height in winter exceeds that of summer by half an inch, while in other places the inequality almost entirely disappears. At Pekin, China, the mean height of the barometer for January exceeds Fig. 309- X JFMAMJJASONDJ that for July by three quarters of an inch. At Boston the mean pressure does not differ more than one tenth of an inch for any two months of the year. The same is true of London and Paris. The four curves B, L, H, and P (Figure 309) show the monthly fluctuations of the mean pressure at Boston, London, Havana, and Pekin. The spaces and letters at the bottom represent the months, and the verti- cal lines the height. 378. Hourly Fluctuation of the Barometer. When the in- dications of the barometer for each hour of the day for a long period are averaged, it will be found that these averages are not equal. The height of the barometer is greatest about 10 A. M. and least at about 4 P. M. There are also smaller fluctuations at night, the barometer attaining a second maximum at about 10 P. M. and a second minimum at about 4 A. M. This diurnal oscillation is greatest at the equator, and decreases as we approach either pole. 379. Fluctuation depending on the Position of the Moon. There is a small fluctuation of the barometer depending on the 260 . ELEMENTS OF position of the moon, but this variation is exceedingly minute and can be detected only by taking the mean of the most accu- rate observations continued for a long time. These fluctuations indicate a feeble tide in the atmosphere similar to those of the ocean. 380. Irregular Fluctuations. The irregular fluctuations of the barometer are far greater than the periodic ones. The difference between the greatest and least heights of the barom- eter for a single month is called the monthly oscillation, and by combining observations extending over a series of years we obtain the mean monthly oscillation. This is least at the equa- tor, and increases as we proceed towards the poles. At the equator it is about ^ of an inch ; in latitude 30 it is ^ of an inch ; in latitude 45, over the Atlantic Ocean, it is I inch; in latitude 65 it is \\ inches. The extreme fluctua- tions are much greater than the mean monthly oscillations. The greatest and least observed heights of the barometer at Boston are 31.125 inches and 28.47 inches, the difference being 2.655 inches. The greatest observed difference at London is 3 inches; and at St. Petersburg, 3.5 inches. II. TEMPERATURE OF THE ATMOSPHERE. 381. How the Atmosphere becomes Heated. The atmos- phere becomes heated partly by absorbing the direct rays of the sun, partly by contact with the warmer earth, and partly by absorbing the obscure heat radiated from the earth. A -portion of the heat emitted by the sun is absorbed by our atmosphere before it can reach the earth's surface. It is esti- mated that on a clear day our atmosphere absorbs about one fourth of the rays which traverse it vertically. The heat thus absorbed raises the temperature of the atmosphere. It is mainly the obscure rays (220) that are absorbed by the atmos- phere, and this absorption is done chiefly by the watery vapor in the atmosphere. The rays of the sun which reach the earth's surface are absorbed by it. The surface thus becomes heated, and communicates heat to the air which rests upon it. This NATURAL PHILOSOPHY. 26l heated air, becoming lighter through expansion, rises and gives place to colder air from above, which in turn becomes heated by contact with the earth. As the surface of the earth becomes warmed by the direct rays of the sun, it radiates obscure" heat back into the atmos- phere. These rays are partially absorbed by the atmosphere, especially in the lower layers, where watery vapor is most abundant (224, 225). 382. Hourly Variations of Temperature. The temper- ature of a place varies from hour to hour according to the elevation of the sun above the horizon. The average of observations taken for a long period shows that the mean hourly variations of temperature are extremely regular. The curve in Figure 310 shows the mean hourly variations Fig. 310. ; oo- 5i ; ^^ -~ -" / (>_ / \ 4S'- 4G= / .. X s. / v 42 iu- \ / 12 2 4 G 8 10 n 2 4 6 8 10 12 of temperature at New Haven. There is a maximum and minimum of temperature each day, the minimum occurring about an hour before sunrise, and the maximum about two hours after noon. The highest temperature of the day, other things being equal, occurs when the amount of heat lost each instant by radiation is just equal to that received from the sun. Before midday the earth receives more heat from the sun than it loses by radia- tion, and the temperature rises. After noon the earth receives, each instant, less heat from the sun than it did at noon ; but for some time it still receives heat faster than it parts with it. Hence the. maximum of temperature occurs some time after noon. During the night we receive no direct heat from the sun, 262 ELEMENTS OF and the earth cools by radiation. About an hour before sunrise the heat received from the returning sun becomes equal to that lost by radiation, and the temperature ceases to fall. 383. Mean Temperature of a Day. The mean temper- ature of a day is the average temperature of the 24 hours. This is found by taking the average of three observations, one at 6 A. M., one at 2 P. M., and one at 9 P. M. 384. Monthly Variations of Temperature. The curves of Figure 311 show the mean temperature and also the Fig. 3 ir. mean maximum and minimum temperatures for each month of the year at New Haven, accord- ing to observations extending through 86 years. The months are given on the horizontal line at the bottom, and the degrees of temperature on the vertical ^ ne at ^ e k^ ^ ie warmest months of the year for this place are July and August, the maximum occurring about the 24th of July. The coldest month is January, the mini- mum occurring about the 2ist of this month. The differ- ence between the maximum and minimum temperature is greater for the cold than for the warm months. The chief reasons why it is colder during the winter months than during the summer months are that the sun is farther from the zenith and is a shorter time above the horizon. The earth is receiving the most heat from the sun at the time of the summer solstice, but the temperature continues to rise as long as the earth receives more heat from the sun during the day than it loses by radiation during the night. During the autumn the loss at night is much greater than the gain by day, and the temperature rapidly falls. The temperature continues to fall till the gain by day is again equal to the loss by night. This does not occur till some time after the winter solstice. 385. Irregular Fluctuations of Temperature. Besides NATURAL PHILOSOPHY. 263 the periodic variations of temperature, there are irregular fluctuations of temperature which are liable to occur any hour of the day and any day of the year. 386. Variations of Temperature with the Latitude. As we proceed from the equator to the poles, the temperature generally falls, but not at a uniform rate, and the rate of fall is different on different meridians. Hence the lines of equal temperature on the surface of the earth do not coincide with the parallels of latitude. Lines which con- nect places of equal mean temperature are called isothermal lines. The isothermal lines for every ten degrees are shown on the accompanying map (Figure 312). They are much more irregular on and around the continents than in the oceans. 387. The Temperature of the two Sides of the Atlantic. It will be seen from the map in Figure 312 that the mean temperature of the eastern side of the Northern Atlantic Ocean is considerably higher than that of the western side at the same latitude. The temperature of Dublin is as high as that of New York, though the former is 13 farther north, while near Lake Superior, in latitude 50, we find the same mean temperature as at the North Cape, in lati- tude 72. The high temperature of the European coast is due to the high temperature of the Northern Atlantic and the prevalent westerly winds. The Gulf Stream conveys the warm water of the equatorial region into the North Atlantic. The temperature of the North Atlantic is thus raised considerably above what is due to its latitude, and the prevalent westerly winds of the middle latitudes carry this heat to the eastern side of the Atlan- tic and away from its western side. 388. The Temperature of the two Sides of the Pacific. Owing to the currents of the Pacific Ocean, there is a cor- responding difference of temperature between its eastern and western coast, the temperature of the east coast being 264 ELEMENTS OF NATURAL PHILOSOPHY. 265 higher than that of the west. This causes a marked dif- ference of temperature between the eastern and western coasts of North America at places on the same parallel. The same isothermal line will be found 10 or 15 degrees farther north on the Pacific coast of North America than "on the Atlantic coast. 389. The Temperature of the Northern and Southern Hemispheres. The mean temperature of the northern hemisphere is nearly three degrees higher than that of the southern hemisphere. The unequal temperature of the two hemispheres is probably due to the unequal distribution of land and water. The north- ern hemisphere contains more land and less water than the southern. In the southern hemisphere the sun's rays fall chiefly upon water, and a large amount of heat is consumed in evapo- ration. In the condensation of vapor the heat is again liberated. Observations show that there is more condensation in the northern hemisphere than in the southern. Thus the southern hemisphere is cooled more by evaporation and warmed less by condensation than the northern hemisphere. 390. Mean and Extreme Temperatures of a Place. Two places having the same mean temperature may differ greatly in their extreme temperatures. New York and Liverpool have the same mean temperature, but the difference between the mean temperature of the three summer months and that of the three winter months is twice as great in New York as in Liverpool. In some localities the mean temperature of the hottest month of the year is less than 5 above that of the coldest, while in other localities it is 70 or 80 above. 391. Marine and Continental Climates. The tempera- ture of water changes less than that of land. The specific heat (197) of water being much higher than that of land, a \nuch greater amount of heat is consumed in raising the temperature of an equal mass of water the same number of degrees, and a much greater amount of heat is liber- ated in the cooling of an equal mass of water. Hence when land and water are receiving or losing heat at the same rate, the 266 ELEMENTS OF temperature of the former will rise higher or fall lower than that of the latter in the same time. The high latent heat of watery vapor (202) tends to keep the temperature of water uniform, a large amount of heat being rendered latent by evapo- ration when the temperature is rising, and an equally large amount being liberated by condensation when the temperature is falling. Again, the sun's rays penetrate water to a greater depth than land, and at the same time the currents in the ocean tend to equalize the temperature of the water at different depths. Hence, while land becomes heated only at the surface, water becomes heated to a considerable depth below the sur- face. The greater depth of water heated and cooled as the temperature rises and falls would cause the temperature to change less at the surface of water than of land. When the temperature of a place is controlled mainly by the ocean, the temperature is equable, and the climate is called marine; when, on the contrary, it is controlled mainly by the continent, the temperature is extreme, and the climate is called continental. On the eastern coast of the United States, where the prevalent winds are from the land, there is a great annual range of temperature and a continental climate ; while in the western part of Europe, where the prevalent winds are from the ocean, the temperature is more uniform and the climate marine. 392. Change of Temperature with the Elevation. As we ascend in the atmosphere from the earth, the tempera- ture falls. The rate of decrease varies with the latitude of the place, with the time of the year, and with the hour of the day. It is more rapid in warm countries than in cold, and in the hot months than in the cold. It is most rapid about 5 P. M., and least rapid about sunrise. The change is also most rapid near the earth, and decreases as we ascend. There are two main reasons why the temperature of the atmosphere falls as we ascend : (i) The air of the earth's sur- face becomes heated and expanded, and tends to rise because of its diminished specific gravity. As the air ascends it meets NATURAL PHILOSOPHY. 267 with less pressure and therefore expands ; this expansion con- sumes heat (204), and causes the temperature to fall. (2) The moisture in the air becomes less and less as we ascend, and hence there is less absorption of the solar rays, and it is only the rays which are absorbed that tend to raise the temperature ; there also is less hindrance to the escape into space of the heat radiated from the atmosphere. 393. The Line of Perpetual Snow. Since the tempera- ture of the atmosphere falls as we ascend, the tops of high mountains, even "within the tropics, are covered with perpetual snow. The snow-line depends more upon the temperature of the hottest month than upon the mean tem- perature of the year. It is not therefore the line whose mean temperature is 32. It depends also to a consider- able extent upon the annual snow-fall. Under the equator the height of the snow-line varies from 15,000 to 16,000 feet, where the mean annual temperature is 35. On the Alps the average height of the snow-line is 8800 feet, where the mean annual temperature is 25 ; while on the coast of Norway its height is only 2400 feet, where the mean annual temperature is 21. 394. The Atmosphere a Regulator of Temperature. During the day the atmosphere absorbs a portion of the sun's rays, so that they are less excessive on reaching the earth. A considerable portion of the heat thus absorbed during the day is rendered latent by expansion. At night the air intercepts a part of the rays emitted by the earth, and so keeps the heat from escaping into space. At the same time, as the air is cooled, it contracts, and so liberates the heat that was rendered latent by expansion during the day. Were it not for the atmosphere the days would be very much hotter and the nights very much colder than they are now. It is chiefly by means of the watery vapor present in the atmosphere that it acts thus as a regulator of temperature (381). 2 68 ELEMENTS OP III. HUMIDITY OF THE ATMOSPHERE. 395. The Hygrometer. An instrument capable of meas- uring the moisture of the air is called a hygrometer. A hygroscope is an instrument which merely shows that there are changes of moisture, without being capable of measuring xthe amount of moisture present. t Mason's hygrometer (Figure 313) consists of two thermome- ters. The bulb of one of these is kept moist by being covered with muslin or silk, the fibres of which dip into a reservoir of water. The water is drawn up to the bulb by capillary action, and the evaporation from its surface lowers its temperature. Hence the wet-bulb thermometer will always show the lower tem- perature. The greater the dif- Fig. 313- ference of reading between the thermometers, the faster the evaporation from the wet bulb and the drier the air. 396. The Humidity of the ^2>. The amount of moist- ure which a cubic foot of air can hold increases with the temperature. When the air contains all the moisture it can hold at that temperature, it is said to be saturated with moisture. By the humidity of the air we do not mean the absolute amount of moisture in it, but its degree of satura- tion. If the air is half saturated, its humidity is 50: if three-quarters saturated, 75 ; etc. NATURAL PHILOSOPHY. 269 397. The Dew- Point. The dew-point is the temperature at which the air would become saturated with the moisture in it, and its moisture begin to be deposited as dew. It is not a fixed temperature, like those of the freezing and boiling points, but varies with the temperature and humidity of the air. The greater the humidity of the air, the less the temperature would have to fall to reach the dew- point. 398. Diurnal Variation in the Vapor in the Atmosphere. The amount of vapor in the atmosphere is subject to great fluctuations, some of which are irregular and others periodic. As a rule, the amount is least about an hour before sunrise, and greatest just before sunset, the mean diurnal variation amounting to about }& of the average amount of vapor present. The curve in Figure 314 shows the diurnal variation at Philadelphia, the figures at the Fig 3 , 4 left indicating the pressure of the vapor in inches of mercury & at the hours given at the bot- - 30 torn. This variation is due to the diurnal change in tempera- ture. As the temperature rises during the day, more water is evaporated from the ocean and the moist earth, and the amount of vapor in the air increases. During the night a portion of the vapor is condensed in the form of dew and hoar-frost, and the amount present in the air decreases. 399. Annual Variation in the Amount of Vapor in the Atmosphere. In the northern hemisphere the mean amount of vapor in the atmosphere is greatest in July, when the mean temperature is highest, and least in January, when the mean temperature is lowest. This is due to the more rapid evapora- tion in summer than in winter. 400. Variation in the Amount of Vapor with the Elevation. The humidity of the atmosphere as a rule decreases as we rise above the earth, though there is a slight increase of humid- ity for the first 3000 feet. At the highest elevations at which 810D.2 4 6 270 ELEMENTS OF observations have been taken the air has never been found entirely free from moisture. 401. Diurnal Variation of the Pressure of the Gaseous Atmosphere. The earth is really enveloped in two atmos- pheres, one of vapor and one of permanent gases. These two atmospheres are mixed together, and by their combined pres- sure cause the rise of the barometer. Other things being equal, the greater the amount of vapor present in the atmos- phere the higher the barometer, and vice versa. Fluctuations in the height of the barometer are caused by changes in the temperature of the air and the amount of vapor present in the atmosphere. A diminution of vapor and an increase in temperature both tend to cause the barometer to fall. If we subtract the pressure of the vapor in the atmosphere from that of the whole atmosphere, the remainder will be the pressure of the gaseous at- mosphere. At Philadelphia this pressure is greatest about an hour after sunrise and least about 4 P. M., as is shown by Fig. 315- 33.2 .60 1 IDT the curve of Figure 31 5. 402. Annual Variation of the Pressure of the Gaseous Atmosphere. In the northern hemisphere the pressure of the gaseous atmosphere '^greatest in January, when the temperature is lowest, and least in July, when the temperature is highest. The difference between the summer and winter pressures of the gaseous atmosphere is very unequal in different countries., In the eastern part of the United States this difference amounts to about half an inch, while in Central Asia it amounts to above an inch, and at the equator is scarcely appreciable. IV. MOVEMENTS OF THE ATMOSPHERE. 403. Winds.- Wind is air in motion. Although the winds are proverbially variable and fickle, they are gov- NATURAL PHILOSOPHY. 271 erned by laws as fixed and definite as those which regulate the temperature and pressure of the atmosphere. The force of a wind is estimated either by its velocity in miles per hour or by its pressure in pounds per square foot. The character, velocity, and pressure of various winds are given in the following table, taken from Loomis : Character. Velocity in Miles per Hour. Force in Pounds per Square Foot. 2 o Gently pleasant 008 Pleasant brisk .... T->I/ Very brisk - *-/2 **7i *i no