THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA FROM THE LIBRARY OF PROFESSOR CARL COPPING PLEHN 1867-1945 HANDBOOK OP NATURAL PHILOSOPHY, FOR SCHOOL AND HOME USE. BY W. J. ROLFE, FORMERLY HEAD MASTER OF THE HIGH SCHOOL, CAMBRIDGE, MASS. AND J. A. GILLET, PROFESSOR OF MATHEMATICS AND PHYSICS IN THE FEMALE NORMAL AND HIGH SCHOOL OF THE CITY OF NEW YORK. SECOND EDITION, REVISED. NEW YORK: WOOLWORTH, AINSWORTH, & CO. 1871. Entered according to Act of Congress, in the year 1869, by W. J. ROLFE AND J. A. GILLET, In the Clerk's Office of the District Court of the District of Massachusetts. By the same Authors, HANDBOOK OF CHEMISTRY. HANDBOOK OF THE STARS. These are elementary manuals of Chemistry and Astronomy, on the same plan ai this book. In each of the three, the more difficult and theoretical portions of the sub- ject are treated in the Appendix. Also, THE CAMBRIDGE COURSE OF PHYSICS, IN THREE VOLUMES : 1. CHEMISTRY. II. NATURAL PHILOSOPHY. III. ASTRONOMY. CAMBRIDGE: PRESS OF JOHN WILSON AND SON. PREFACE. l'7/ THE great favor with which the Natural Philosophy of the Cambridge Physics has been received has en- couraged the authors to comply with the urgent demand for a brief and elementary text-book on the same subject. It is impossible to prepare a book which shall be adapted to all schools ; but it is hoped that the plan of this man- ual is such that it may meet the wants of quite a wide range of schools. In the body of the book, little is at- tempted beyond a clear and brief statement and illus- tration of those facts in Physics which are of special importance on account of their practical or theoretical bearing. It is hoped that this part may furnish all that is needed' for the higher classes in Grammar Schools. This is followed by an Appendix, which contains chap- ters on the physics of the atmosphere, on the theory of molecular motions, and on the origin and transformation of energy. This part is intended to fit the book for the use of those High Schools which have not time for a larger work. There is no overlapping of subjects ; but ' the Appendix is a more difficult chapter which naturally follows. The material of the book is drawn in the main from the sources enumerated in the Preface of the larger Natural Philosophy. We have not forgotten the great advance recently made in the practical applications of the physical forces, IV PREFACE. as well as in the theories of the science. In the body of the book, we have given the preference to facts which are of practical interest. It is for this reason that frictional electricity occupies so little space compared with current electricity. A few years ago, frictional electricity held the first place in the school books ; but in practical importance it has dwindled into insignificance, while voltaic and magnetic electricity have become of im- mense value in the arts. Electricity now means some- thing more than toy experiments with attractions and repulsions, and the explosion of gunpowder and gaseous mixtures. If the teacher thinks that we have varied somewhat from our rule in bringing the double refraction and polarization of light into the body of the book, 'he can omit those sections. The chapter on Machines is certainly not too full for boys j and it is very easy to abridge it for classes of girls. The Appendix also contains problems and notes which give a full account of the apparatus needed for the book, and directions for performing difficult experi- ments. For numerous illustrations which the teacher can use in oral instruction, we would refer him to our larger Natural Philosophy. These could not be added here without making the book too bulky ; and it is our conviction that such illustrations come from the teacher's lips with a force which no written statement can give them. CAMBRIDGE, February 15, 1869. TABLE OF CONTENTS. COHESION AND ADHESION. PAGE COHESION ' ...'... 3 SUMMARY 16 ADHESION 18 SUMMARY 27 MECHANICS. PRESSURE 29 WEIGHT 29 CENTRE OF GRAVITY -31 SUMMARY 36 PRESSURE OF LIQUIDS 36 SPECIFIC GRAVITY 43 SUMMARY 46 PRESSURE OF GASES 47 SUMMARY . 59 MOTION 60 FIRST LAW OF MOTION 60 SECOND LAW OF MOTION 62 THIRD LAW OF MOTION ..65 SUMMARY " 68 THE PENDULUM 69 SUMMARY 73 MACHINES 74 THE LEVER 74 VI CONTENTS. PAG* THE WHEEL AND AXLE 78 THE PULLEY 82 THE INCLINED PLANE 85 THE WEDGE 86 THE SCREW 87 SUMMARY 87 WATER POWER 89 STEAM POWER , 91 SUMMARY . . . ' 99 SOUND. NATURE AND PROPAGATION OF SOUND . . . 100 SUMMARY 104 MUSICAL SOUNDS 105 SUMMARY 116 MUSICAL INSTRUMENTS 117 STRINGED INSTRUMENTS 117 SUMMARY . 118 WIND INSTRUMENTS 119 SUMMARY 126 SOUNDING FLAMES 127 SUMMARY . . . . , 128 THE HUMAN VOICE AND EAR 128 SUMMARY . . . , 130 LIGHT. PROPAGATION OF LIGHT ! 3 i RADIATION, REFLECTION, AND REFRACTION .... 131 SUMMARY 138 DISPERSION, ABSORPTION, INTERFERENCE, AND PO- LARIZATION 139 SUMMARY 146 CONTENTS. Vli PAGE OPTICAL INSTRUMENTS . 147 LENSES 147 SUMMARY 150 THE EYE 150 SUMMARY . 163 THE MICROSCOPE AND TELESCOPE 164 THE MAGIC LANTERN 168 SUMMARY 168 MIRRORS * 169 SUMMARY 172 HEAT. PROPAGATION OF HEAT 173 SUMMARY 176 EFFECTS OF HEAT ON BODIES 177 SUMMARY 188 THERMAL INSTRUMENTS 190 SUMMARY 194 ELECTRICITY. MAGNETISM . 195 SUMMARY 198 VOLTAIC ELECTRICITY 198 SUMMARY 204 ELECTRO-MAGNETISM 206 SUMMARY 213 ELECTROLYSIS 214 SUMMARY 217 POWER OF THE CURRENT TO DEVELOP HEAT AND LIGHT 218 SUMMARY 219 Vlll CONTENTS. PAGE MAGNETO-ELECTRICITY 219 SUMMARY 221 THERMO-ELECTRICITY 222 SUMMARY 223 FRICTIONAL ELECTRICITY 223 SUMMARY 229 APPENDIX. THE PHYSICS OF THE ATMOSPHERE ..*.... 231 MOLECULAR MOTION AS MANIFESTED IN SOUND, LIGHT, HEAT, AND ELECTRICITY 266 SOURCES AND CONVERSION OF ENERGY 275 FRENCH WEIGHTS AND MEASURES 285 PROBLEMS 287 NOTES ON EXPERIMENTS , . . . . 295 THE SPECTROSCOPE AND THE DIFFERENT KINDS OF SPECTRA 305 PHOTOGRAPHY 308 NOTES . .' 310 QUESTIONS FOR REVIEW AND EXAMINATION . . . 315 INDEX 325 HANDBOOK OF NATURAL PHILOSOPHY. COHESION. 1 . Matter is made up of Molecules. When a piece of ice is heated to a temperature of 32, it melts and be- comes water. The particles of the ice hold together firmly, but in melting they have been loosened so that they move among themselves with the greatest ease. If water be heated to a temperature of 212, it boils and becomes steam. Its particles are still farther sepa- rated from one another. The particles of which all bodies are built up, and which are loosened and separated when a solid melts and a liquid boils, are called molecules. Molecule is a word from the Latin, and means a little mass. 2. Molecules are exceedingly small. It is impossible to grind a solid so fine as to convert it into a liquid. A piece of gold may be divided into particles so small, that each can barely be made out with a powerful microscope, yet the gold is solid still. When heated, however, the pulverized gold becomes a liquid ; that is, each minute piece is separated into molecules. These molecules, then, are much too small to be seen with the best micro- scope. 3. The Molecules are not in actual con- Fi s- tact. If a brass ball, which at the ordi- nary temperature will just pass through a ring (Figure i), be plunged into a freezing mixture and left until it becomes very cold, it will then pass through the ring very eas- ily, not touching it at all. COHESION. Fig. 2. If a bulb with a projecting tube be filled with water up to a certain point on the tube, and the bulb be then plunged into a freezing mixture (Figure 2), the water will fall in the tube. If a similar bulb be filled with air, and the end of the tube be held under water (Figure 3), and the bulb be cooled by means of a freezing mix- ture, the water at once rises in the tube ; showing that the air occupies less space when cooled. Fig. 3 . We find, then, that solids, liquids, and gases contract when cooled ; and there seems to be no limit to this contraction, for they continue to con- tract, however much they are cooled. Now this contraction is best ex- plained by supposing that the mole- cules come nearer together ; and since, so far as we know, a body may continue to contract indefinitely, it follows that the mole- cules are never in actual contact. 4. The Spaces between the Molecules are immense in comparison 'with the Size of the Molecules. Though the spaces between the molecules are very minute, since they cannot be discerned even with the most powerful microscope, there are good reasons for believing that they are immense in comparison with the bulk of the molecules themselves.* * The molecules of a body maybe compared to the earth, sun, moon, and stars, and the spaces between the molecules to the spaces between these heavenly bodies. If we imagine a being small enough to live on one of the molecules in the centre of a stone, as we live on the earth, he would, on looking out into the COHESION. 5 5. An Attractive Force and a Reptdsive Force act between Molecules. If we attempt to pull any solid asunder, we perceive at once that the particles of which it is composed are held together more or less firmly. That which holds them together is called an attractive force. If a glass rod be dipped into water, a drop hangs from its end when taken out. This drop is made up of molecules which are evidently held together. In the case of liquids, the molecules are held together but feebly, and the attractive force seems to be slight. If a rubber bag partially filled with air, and closed so as to be air-tight, be placed under the receiver of an air- pump, and the air exhausted from the receiver, the air within the bag will at once expand, as we see by the filling out of the bag. This shows that gases when left to themselves expand ; that is, their molecules separate. The force which separates the molecules is called a repulsive force. Since these forces act between molecules, they are called molecular forces. 6. These two Forces act together. A brass ball (see Figure i ) which will just pass through a ring at the ordi- nary temperature, will not pass through the ring after being heated ; showing that the molecules of the ball have been pushed apart. If, however, while the solid is heating, we attempt to pull it asunder, it resists ; show- ing that the molecules are still held together by an attrac- tive force. It is evident, then, that both forces act together. space about him, see here and there, at immense distances, other molecules, as we see the scattered stars in the heavens at night. The molecules, though exceedingly minute, are perfectly distinct and definite masses, like the earth, moon, and stars ; and they are separated by spaces many thousand times as great as that occupied by each molecule. 6 COHESION. 7. The Three States of Matter. When the attrac- tive force is considerably stronger than the repulsive force, matter is in the solid state.; when the two forces are nearly balanced, it is in the liquid state; and when the repulsive force is the stronger, in the gaseous state. 8. Cohesion and Adhesion. The force which holds the molecules of a solid or liquid together is evidently the excess of the attractive over the repulsive force ; for if the two forces were just equal, they would just neutralize each other, and the molecules would not be held together in the least. In the case of iron or water, molecules of the same kind are held together. When we mark on a blackboard \vith a piece of chalk, or write on paper with ink, mole- cules of different kinds are held together. The force which holds together molecules of the same kind is called cohesion ; that which holds together molecules of different kinds^is called adhesion. 9. These Forces act only through insensible Dis- tances. Two pieces of lead will not cohere if their sur- faces are rough ; but if we make them perfectly smooth and clean, and press them firmly together, they cohere quite strongly. Plates of glass, from simply resting upon one another in the warehouse, have been known to cohere so firmly that they would break elsewhere as readily as where they came in contact. 10. Solids have considerable Cohesion. Matter, as we have seen, exists in three states, the solid, the liquid, and the gaseous. The distinguishing characteristic of solids is that the attractive considerably exceeds the re- pulsive force. In solids, therefore, the cohesion is al- ways considerable. The various properties of solids result from modifications of this molecular force. 1 1 . Tenacity. We find on trial that it is much eas- ier to pull in two a rod of lead than a rod of steel of the COHESION. 7 same thickness; showing that the molecules of some solids cohere more strongly than those of others. When a solid is thus pulled in two, it is said to be rup- tured. The power which a solid has of resisting rup- ture is called tenacity. The relative tenacity of different solids is determined by finding how much force is required to rupture rods of the same thickness made of them. If it takes twice as much force to pull asunder one rod as another, the first solid is said to have twice the tenacity of the second: The relative tenacity of solids may be found by means of a machine called a dynamometer. This name is made up of two Greek words, and means force-measurer. Fig. 4- One form of the machine is shown in. Figure 4. It consists of a heavy iron frame, at one end of which is a box containing a stout steel spring. A pointer connected with this spring moves over a graduated arc on the top of the box. On the frame are two movable blocks, or slides, one of which is attached to the spring, while the other may be carried backward and forward by a screw and crank. The rod whose tenacity is to be tried is stretched be- tween the two slides, and the crank is then slowly turned so as to pull upon the rod until it breaks. The force thus brought to bear upon the rod bends the spring ; and the 8 COHESION. position of the pointer when the rod breaks shows how much force it took to break it. 12. Hardness and Softness. If we indent apiece of india-rubber with the finger-nail, or strike a piece of lead a smart blow with a hammer, we see that it is possible to displace the molecules of a solid. When it is easy to displace the molecules, as in the case of wax, the solid is called soft ; when it is difficult to displace them, as in the case of glass, the solid is called hard. To find which of two solids is the harder, see which will scratch the other. The one which scratches is al- ways harder than the one scratched. Diamond is the hardest solid known ; hence it is used for cutting glass, which is also a very hard substance. 13. Elasticity, Brittleness, Ductility, and Mallea- bility. When molecules have been displaced, one of three results must follow, they will return to their orig- inal positions as soon as they are left to themselves, or they will take up new positions, or they will fall entirely asunder. If we bend a steel rod moderately, it straightens as soon as it is released ; showing that displaced molecules sometimes tend to return to their former positions. This tendency of molecules to return to their original posi- tions after being displaced is called elasticity. A steel rod may be bent a good deal, and yet straighten when released ; but if it be bent beyond a certain point, it will no longer straighten, showing that the molecules, after they have been displaced beyond a certain limit, tend to remain in their new positions. The greatest ex- tent to which the molecules of a solid can be displaced, and yet go back to their former positions, is called the limit of elasticity for that solid. All solids are found to be elastic, but they differ very much in the limit of their elasticity. The molecules of steel and india-rubber can COHESION. 9 be displaced a good deal without becoming fixed in new positions, while those of glass ^and pipe-clay can be dis- placed but slightly. If a glass rod be bent within a certain limit, it will straighten when released ; but if it be bent beyond this limit, it will not remain bent, but w^ill break. When the displaced molecules cannot take up permanently new positions, the solid is said to be brittle. Hard solids are likely to be brittle also ; but hardness and brittleness are, as we have seen, entirely different things. When the molecules after being displaced can take up permanently new positions, the solid is ordinarily described as malleable or ductile. It is said to be mal- leable when it can be hammered or rolled out into sheets; ductile when it can be drawn out into wire. Gold is one of the most malleable of the metals. In the manufacture of gold leaf, it is hammered out into sheets so thin that it takes from 300,000 to 35-0,000 of them to make the thickness of a single inch. Wire is made by drawing a rod of metal through a series of conical holes in a hardened steel plate. Each hole is a little smaller than the preceding, so that the rod becomes lengthened and diminished in thickness as it is drawn through one after another. In the drawing of iron wire, the molecules are sepa- rated, yet the tenacity of the iron is greatly increased, so that fine iron wire is the most tenacious of substances. A bar one inch square of the best wrought-iron will sus- tain a weight of thirty tons ; a bundle of wires one-tenth of an inch in diameter, containing the same quantity of material, will sustain a weight of from thirty-six to forty tons ; and if the wires have a diameter of only one-twen- tieth or one-thirtieth of an inch, the same quantity will sustain from sixty to ninety tons. Hence cables made of fine iron wire twisted together are much stronger than 10 COHESION. bars or chains of the same weight. The cables of sus- pension bridges are madejn this way. The following Table gives the most useful metals in the order of their tenacity, malleability (both under the hammer and the rolling-mill), and ductility: Tenacity. Iron Copper Platinum Silver Zinc Gold Lead Tin 14. Solids are somewhat Compressible. Some metals are permanently diminished in bulk by hammer- ing ; and so also by the pressure to which they are sub- jected in the process of coining. The stone columns of buildings are frequently shortened by the great weight resting upon them. This was found to be the case with the columns supporting the dome _of the Pantheon at ^ability under ; Hammer. Malleability under the Rolling-Mill. Ductility. Lead Gold Platinum Tin Silver Silver Gold Zinc Silver Copper Tin Lead Iron Copper Gold Copper Platinum Zinc Platinum Zinc Tin Iron Iron Lead 15. The Molecules sometimes arrange themselves in Crystals. If alum be added to hot water as long as it will dissolve, and then the water be allowed to cool slowly, a part of the alum will be deposited on the bot- tom of the dish, not in a confused mass, but in beautiful and symmetrical forms, -called crystals. Melt some sulphur in a crucible, and let it cool slowly till a crust forms on the surface ; then carefully break the crust, and pour off the remaining liquid. The crucible (Figure 5) will be found lined with delicate needle-shaped crystals. COHESION. II As a general rule, the molecules of a solid tend to arrange themselves in crystals. The same solid usually crystallizes in the same form, but different solids in different forms. In the cases of crystallization which we have already described, the solid is first brought to the liquid state, that the molecules may have freedom of motion. The building of a crystal out of molecules is much like building a house out of bricks. The bricks must be taken one by one and laid in regular order before they are cemented together. So, in forming a crystal, the molecules must be arranged one by one in regular order before they are fastened together by the cohesive force. Large crystals of many solids can be obtained by dis- solving 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 gradual the for- mation, the larger are the crystals. The large crystals seen in cabinets of minerals were probably centuries in forming. The water in which the solid was dissolved found its way into a cavity of a rock, and there slowly evaporated. The tendency of the molecules to form crystals is strik- ingly_ 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 brittle, and on breaking show the smooth faces of the crystals which have been formed. The continued jar- ring gives the molecules a slight freedom of motion, and crystals are slowly built up;^" Many solids are crystalline in structure which do not 12 COHESION. appear to be so. Thus a piece of ice is a mass of the most perfect crystals, but they are so closely packed to- gether that we cannot readily distinguish them. 1 6. The Molecules cohere more strongly on some sides than on others. It is easy to cleave a piece of mica or other crystal in certain directions, but difficult to cleave it in other directions. The molecules cohere more strongly on some sides than on others. Iron and other solids are not so tenacious when crystalline in structure as when not crystalline. This is because the molecules in crystals are arranged in layers, so that the weakest sides are brought face to face. 17. Annealing and Tempering. If melted glass be dropped into cold water, it forms the well-known Ru- pert's drops, which are so brittle that, if we break off the small end or scratch them slightly w.ith a file, they fly in pieces. When glass is allowed to cool in the air at the ordinary temperature, it is also very brittle. In order to make it tough enough for ordinary use, it must be cooled very slowly, or annealed. This is done by pass- ing it slowly through a long oven, which is kept very hot at one end and cool at the other. Steel, also, when suddenly cooled from a high temper- ature, is very hard and brittle ; but when slowly cooled, it is very tough and pliable. The process of giving steel various degrees of hardness is called tempering. The steel is first heated white hot, and then suddenly cooled by plunging it into cold water. It is thus rendered very brittle. It is then reheated, and allowed to cool slowly. When it is to be made quite hard, it is reheated but slightly ; when quite soft, it is reheated a good deal. The more it is reheated, the softer it becomes on cooling. These different conditions of glass and steel are probably owing to differences in the arrangement of the molecules. 1 8. Liquids have little Cohesion. The chief char- COHESION. 13 acteristic of liquids is that the attractive and repulsive forces acting between the molecules are very nearly bal- anced, the attractive force being slightly the greater. Hence in liquids the cohesion is slight, and the mole- cules are free to move among themselves. If a piece of lead be carefully measured, then melted and measured again, it will be found to have increased in bulk. Hence, when any substance is in a liquid state, the molecules are farther apart than when it is in a solid state. This explains why, in moulding bul- lets, the mould is never quite filled by the bullet. There are a few exceptions to this rule. If, for in- stance, a bottle be filled with water and tightly corked, and allowed to freeze, the bottle will burst. The molecules of ice, then, must be farther apart than those of water. 19. Liqtiids are but slightly Com- Fi s- 6 - pressible. The apparatus repre- sented in Figure 6 consists of a very thick vessel of glass closed at top and bottom. Within the vessel are a piston which can be moved by the thumb-screw at the top, and a glass bulb which is prolonged by a very fine tube, bent as represented. Fill the bulb and tube with any liquid, as water, and plunge the end of the tube in the mercury which covers the bottom of the vessel. Then fill the vessel with water, and apply pressure by turning the screw. The mercury will rise in the tube, show- ing that the liquid in the bulb has been compressed. This compres- sion, however, is but slight, amount- ing at most to a few millionths of the bulk of the liquid. 14 COHESION. 20. Liquids are perfectly Elastic. However much the screw, in the above experiment, may be turned down, or however long it may be left, the moment we loosen it the mercury will fall inside the tube to a level with the mercury outside ; showing that liquids are perfectly elastic. This elasticity is developed only when the liquid is compressed; that is, when the molecules have been brought nearer together. In whatever other way the molecules may be displaced, they show no tendency to return to their former positions. 21. The Molecules in Liquids when left to themselves collect into Spheres. If a mixture of water and alcohol be made, which is just as heavy as sweet-oil, bulk for bulk, and a quantity of the oil be carefully introduced 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. This shows that when the molecules of a liquid are left to themselves, they at once collect into spheres. Rain-drops, dew-drops, and the manufacture of shot illustrate this tendency of the molecules of liquids. In making 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. 22. Gases have no Cohesion. In gases, as has al- ready been shown, the repulsive molecular force exceeds the attractive. Hence there is no cohesion in this state of matter, and the molecules move among themselves with greater freedom than those of liquids. The molecules of any substance are farther apart in the gaseous state than in either the solid or the liquid state. Fill a test-tube nearly full of water, then close it tightly with a cork through which a fine tube passes nearly to COHESION. the bottom of the test- tube. Boil the water so as to convert a portion of it into steam, which is a gas, and the water will be driven forcibly out of the fine tube (Figure 7) ; showing that the steam occupies more space than the water from which it Fig. 7. comes. 2 3 are readily Compressible. The Fig- ure represents a U-tube closed at one end and open at the other, with a nipper-tap * at the bend. Pour in mercury enough to cover the bend. The closed end is now filled with air. Pour in more mercury and this column of air rapidly shortens; showing that gases are highly compressible. 24. Gases are perfectly Elastic. Open the nipper- tap that the mercury may run out, and it is entirely driven out of the closed arm of the tube. To prove that it is the elasticity of the air which drives out the mercury from this arm, fill the closed arm and a part of the open arm with mercury, and open the nipper- tap. The mer- cury will flow out from the open arm, and not from the closed arm. Air and other gases are perfectly elastic. * See, in Appendix, Notes on Experiments. i6 COHESION. SUMMARY. Matter is made up of particles too small to be seen, called molecules, (i, 2.) These molecules are not in actual contact with one another. It is probable that the spaces which separate them are immense in comparison with the size of the molecules themselves. (3, 4.) There is an attractive molecular force, which holds the molecules together, and a repulsive molecular force, which pushes the molecules apart. (5.) These two molecular forces act together, and the re- pulsive molecular force is increased by heat. (6.) There are three states of matter : the solid state, in which the attractive force is considerably the greater ; the liquid state, in which the two forces are nearly equal ; and the gaseous state, in which the repulsive force is the greater. (7.) The force which holds together molecules of the same kind is called Cohesion ; that which holds together mole- cules of different kinds, Adhesion. (8.) Cohesion is the excess of the attractive over the repul- sive molecular force. In solids, it is comparatively strong ; in liquids, it is weak ; in gases, it does not exist. The properties of solids depend on the action of the cohesive force. (10.) The tenacity of a solid is its power of resisting rup- ture, (n.) A solid is called hard when it is difficult to displace its molecules ; soft, when it is easy to displace them. (12.) Elasticity is the tendency of the molecules, on being displaced, to return to their original positions. All solids are elastic, but differ greatly in the limit of their elas- ticity. COHESION. 17 A solid is said to be brittle when its molecules cannot take up permanently new positions. It is said to be malleable or ductile when they can take permanently new positions : malleable, -when it can be hammered or rolled into sheets ; ductile, when it can be drawn into wire. (13.) Solids are somewhat compressible. (14.) The cohesive force often arranges the molecules of a solid into regular forms called crystals. (15.) The cohesive force is stronger on some sides of the molecule than on others. (16.) The molecules are farther apart in the liquid than in the solid state ; yet liquids are less compressible than solids. (19.) Liquids are perfectly elastic j but their elasticity is developed only when the molecules are brought nearer together. (20.) The molecules of a liquid, when acted upon only by cohesion, tend to collect into spheres. (21.) In the gaseous state, the molecules are farther apart than in the liquid state. (22.) Gases are readily compressible, and when compressed are perfectly elastic. (23, 24.) ADHESION. 25. Adhesion between Solids and Solids. Adhesion has already been defined as the force which holds to- gether unlike molecules. The sticking of the chalk to the blackboard, of the graphite of the pencil to paper, and of dust to furniture, prove the existence of this force between solids and solids. The use of the various cements also illustrates this force. When solids are held together by cements, cohesion and adhesion are both brought into play. When, for instance, two pieces of wood are held together by means of gkie, the adhesive force holds the wood on each side to the glue, and cohesion holds together the molecules of the glue. When furniture breaks, we 'often see that the wood splits instead of separating from the glue. So also stones are sometimes cemented together so firmly that the stone itself will break sooner than separate from the cement. The adhesive force between two solids is frequently stronger than the cohesive force of the solids them- selves. 26. Adhesion between Solids and Liquids. If we dip the hand in water, it comes out wet. This fact, with others equally familiar, proves that there is also an adhesive force between liquids and solids. 27. The Adhesion between a Liquid and a Solid is sometimes not strong enough to overcome the Cohesion of the Liquid. If a glass disk be suspended from one pan of a balance and counterpoised by weights, and then ADHESION. brought in contact with mercury, it will require addi- tional weight to raise the disk from the mercury, and the disk comes off dry. This proves, first, that there is adhe- Fig. 9. sion between glass and mercury, and, secondly, that this adhesion is not strong enough to overcome the cohesion of the mercury. 28. The Adhesion between a Solid and a Liquid is sometimes strong enough to overcome the Cohesion of the Liquid. If a glass plate be laid upon the surface of water and then removed, it comes off wet, that te to say, covered with a film of water ; showing that the ad- hesion between a solid and liquid is sometimes strong enough to overcome the cohesion of the liquid. Since adhesion takes place only at the surface, it is evident that we may increase the adhesion of a solid for a liquid by increasing the surface of the solid. If we take a stone, and break it in two, it evidently has all the surface it had before it was broken, and, in addition, the two surfaces exposed by the breaking. The more it is broken up, the more surface it expos.es. The readiest way, then, to increase the surface of a solid is to pulverize it. 2O ADHESION. If pulverized bone-black be mixed with vinegar, or with wine, and the liquid be separated again by pouring the mixture upon unsized paper placed inside a funnel, the liquid that runs through will be colorless. All vege- table colors can be removed from liquids in the same way. The process is called clarifying the liquid. Bone-black is obtained by burning bones in closed ves- sels. It is pulverized that it may present more surface. Other substances may be used for clarifying liquids. Next to bone-black, ordinary charcoal is the best and the. most frequently used. The bone-black evidently removes the coloring matter by means of the adhesive force which exists between the two. The coloring matter adheres to the bone-black more strongly than to the liquid, or the two would not be separated. 29. The Adhesion between a Solid and a Liquid is sometimes strong enough to overcome the Cohesion of the Solid. If some Epsom salts be put into water, the salts will speedily become liquid. The adhesive force be- tween the water and the salts overcomes the cohesive force of the solid, since it reduces the solid to the liquid state. 30. Three Cases of Adhesion between Solids and Licfuids. We have, then, three well-marked cases of adhesion between solids and liquids : ist, When the adhesive force is not strong enough to overcome the cohesion of the liquid. In this case, the liquid cannot wet the solid. 2d, When the adhesive force is strong enough to over- come the cohesion of the liquid. In this case, the liquid can wet the solid. 3d, When the adhesive force is strong enough to over- come the cohesion of the solid. In this case, the liquid can dissolve the solid. The liquid which dissolves the solid is called a solvent, and the liquid in which the solid has been dissolved is called a solution. ADHESION. 21 31. Heat promotes Solution. We find on trial that Epsom salts will dissolve more rapidly and in greater quantity in hot than in cold water. We have already found (i, 6) that heat tends to overcome cohesive force. As a general rule, solids dissolve in greater quantities and more readily in hot than in cold liquids ; but there are exceptions, among which are lime and Glauber's salts. 32. Capillarity. If one end of a fine and clean glass tube be put into water, the water will rise inside the tube above the surface of the water outside. If one end of such a tube be put into mercury, the mercury will fall inside the tube below the surface of the mercury outside. This action of liquids inside tubes is called capillarity. The force which draws some liquids into tubes and pushes others out, has been called capillary force. This name is a convenient one, though capillarity really results from the combined action of certain other forces. We have seen that water will wet glass (28), while mercury will not (27). We have, then, two distinct cases of capillarity, corresponding to two cases of adhe- sion between solids and liquids ; for those liquids 'which 'will wet a tube are drawn into Fig. 10. it) while those which will not wet it are driven out. Mercury will wet zinc, and it is drawn into a tube of zinc, just as water is into a tube of glass. We find by using glass tubes of different sizes, that the finer the tube, the higher the water rises and the lower the mercury falls ; that is, the more marked is the capillarity. The word capillary comes from a Latin word (capillaris) , which t means hair- like. The force was called capillary because its action is most powerful in hair-like tubes. This force, however, acts in tubes of every size, and in fact a tube is not ne- 22 ADHESION. cessary for its action. Put two plates of glass together as represented in Figure 1 1 , and then dip them into water Fig. ii. or mercury. The water will rise between the plates, and the mercury will fall. 33. Illustrations of Capil- larity. A lamp-wick is full of tubes and pores ; and capil- lary force draws the oil up through these to the top of the wick, where it is burnt. When one end of a cloth is put into water, capillary force draws the water into the.tubes and pores of the cloth, and the whole soon becomes wet. In the same way, a lump of sugar, or other porous substance, soon becomes wet throughout, if a corner of it is put into water. Blotting- paper is full of pores into which the capillary force draws the ink. The use of a- towel for wiping any thing which is wet depends on the same principle. 34. Strength of the Capillary Force. When a piece of cloth is wet, it is quite impossible to wring or squeeze it dry. This shows that the capillary force which holds the water into the pores of the cloth is very strong. Many other facts prove the strength of the capillary force. 35. Capillary Force never causes a Liquid to Jlow through a Tube. If we take a glass tube, in which the capillary force will raise water two inches, and put the tube into water so that not more than half an inch shall be above the surface, the water will not overflow the tube. If, however, the water be removed as soon as it comes to the top, more will rise to take its place. When a lamp is burning, the oil is passing up con- tinually through the wick, because it is burnt as soon as it reaches the top ; but when the lamp is not burning, ADHESION. 23 the oil does not overflow the wick. The wick of an alcohol lamp must be covered with a cap when not in use, or the alcohol will evaporate as fast as it comes to the top of the wick, and so all pass out of the lamp. 36. Adhesion between Solids and Gases. If a piece of boxwood charcoal be put into a jar of ammonia gas over mercury, the mercury rapidly rises into the jar.* The ammonia gas, then, is drawn into the charcoal by an adhesive force ; showing that there may be adhesion between the molecules of a solid and those of a gas. When a gas is taken up in this way by any substance, it is said to be absorbed. When the ammonia gas is absorbed by the charcoal, it must occupy less space than before. When a gas is absorbed by a solid, then, the repulsive force of the gas has to be overcome. We know that cold helps to over- come the repulsive force (3). Hence we should expect that a solid would absorb a gas when cold more readily than when hot ; and this is found to be true. Heat, on the other hand, increases the repulsive force. If a solid which has absorbed a gas be heated, the repul- sive force of the gas is increased, so that it finally over- comes the adhesion of the solid for the gas, which then leaves the solid. The charcoal is heated before it is put into the jar, in order to expel the air from its pores. 37. Adhesion between Liquids and Liquids. If oil be poured upon water, the oil, which is the lighter, soon rises to the top and remains entirely separate from the water. If alcohol, which is also lighter than water, be poured into water, the two will thoroughly mix.f This proves that the molecules of the alcohol adhere to those of the water, and that this adhesion is strong enough to overcome the cohesion of the liquids. * See, in Appendix, Notes on Experiments. t This may be shown better by using colored water. 2 4 ADHESION. Nearly all liquids will mix when poured together, though some will mix much more readily than others. 38. Diffusion of Liquids. Put some colored alcohol into a tall glass jar, and then with a funnel carefully Fig. 12. pour in some water (Figure 12). The water will remain for a time at the bottom of the jar, and its separation from the alcohol will be sharply de- fined ; but on standing a few days, the two liquids will become thoroughly mixed. This mixing of liquids on being merely brought into contact is called diffusion of liquids. Different liquids diffuse into each other at very different rates ; while some, as oil and water, will not diffuse at all. 39. Osmose of Liquids. Fasten a bladder air-tight to the end of a long glass tube, fill the bladder with alcohol, and put it into a vessel of water (Fig- ure 13). The liquid will gradually rise in the tube; showing that the water has passed into the bladder. At the same time the alcohol passes slowly out and mixes with the water. The mixing of liquids when separated by a thin mem- brane or porous substance is called osmose of liquids. Liquids do not mix at the same rate when separated by a thin membrane or porous substance as when they mix by simple diffusion. The rate of mixing is modified in a striking manner by the presence of the membrane or porous substance. 40. Adhesion between Liquids and Gases. Let a small glass jar inverted over mercury be filled with ammonia gas, and then pour some water over the sur- face of the mercury. Raise the jar carefully, and, as ADHESION. soon as its mouth comes in contact with the water, the latter rises and completely fills the jar. The ammonia is absorbed by the water, Fig I3> showing that the mole- cules of the gas adhere to those of the water. The same gas is not absorbed with equal read- iness by all liquids. Am- monia gas, which is ab- sorbed so greedily by water, is not absorbed at all by mercury. 41. Cold and Pressure promote Absorption. When a gas is absorbed by a liquid, as when ab- sorbed by a solid (36), the molecules are brought nearer together and the repulsive force overcome. Both cold and pressure, as we have seen, help to overcome this force ; hence they favor the absorption. The effect of pressure on the absorption is illustrated in soda-water, which owes its agreeable taste mainly to the presence of carbonic acid gas in the water. Water and carbonic acid are brought in contact in the fountain, and subjected to very great pressure. When the water is drawn from the fountain, this pressure is removed ; and the carbonic acid escapes in thousands of little bubbles, causing the liquid to foam, or effervesce. Ordinary aqua ammonia is water which has absorbed ammonia gas. If it be heated, the gas escapes. The heat increases the repulsive force of the gas, and thus overcomes its adhesive force, for the liquid. THis is the 26 ADHESION. ordinary way of freeing a liquid "from a gas which it has absorbed. Common spring-water owes much of its pleasant taste to the presence of carbonic acid and other gases which it Fig . I4 . absorbs from the air. When this water is boiled, these gases escape, and it becomes very insipid. The constant agitation of running water helps it to absorb gases, _ since it is thus made to pre- sent more surface to the air. 42. Diffusion of Gases. Two bottles are connected by a long glass tube (Fig- ure 14). The lower bottle is then filled with carbonic acid and the upper with hy- drogen gas, which is very much lighter than carbonic acid. After a time, the hy- drogen will be found to have passed down and mixed with the heavier carbonic acid, and the carbonic acid to have mixed with the hydrogen in the upper bottle. We may prove that there is carbonic acid in the up- per bottle by pouring lime-water into it and shaking it. Carbonic acid makes lime-water milk-white, while hy- drogen has no effect upon it. The mixing of gases 'when brought in contact is called diffusion of gases. Different gases diffuse into each other at very different rates. As a general thing, the more the gases differ in weight, the more rapidly they diffuse into each other. 43. Osmose of Gases. A long glass tube is fastened air-tight, by means of a cork and sealing-wax, into the ADHESION. open end of an unglazed porcelain cup. The cup is then held so that the end of the tube dips beneath the sur- face of water, and a large F ' i s- is- bell-jar of hydrogen is held over the cup. There is an instant rush of bubbles from the end of the tube up through the water, showing that the hydrogen has passed through the pores of the cup and mixed with the air inside. Remove now the jar of hydrogen, and the water at once rises in the tube ; showing that the hy- drogen inside the cup has passed out through the pores to mix with the air outside. The mixing of gases when separated by a porous sub- stance or thin membrane is called osmose of gases. SUMMARY. Adhesion is the force which holds together molecules of different kinds. It acts between molecules of solids and solids, solids and liquids, solids and gases ; also between liquids and liquids, and liquids and gases. It is doubtful whether it acts between the molecules of different gases. The adhesion between two solids is sometimes stronger than the cohesion of the solids themselves. (25.) There are three cases of adhesion between solids and liquids : 28 ADHESION. ist, When the adhesion is not strong enough to over- come the cohesion of the liquid, and the liquid cannot ivet the solid. 2cl, When it is strong enough to overcome the cohe- sion of the liquid, and the liquid can wet the solid. 3d, When it is strong enough to overcome the cohe- sion of the solid, and the liquid can dissolve the solid. (26-30.) Heat generally promotes solution, since it helps to overcome the cohesion of the solid. (31.) Capillary force acts upon liquids in tubes. Liquids which can wet a tube are drawn into it, while liquids which cannot wet it are driven out of it. The finer the tube, the more marked is the capillarity. (32.) The capillary force is very strong ; but acting al6ne it never makes a liquid flow through a tube. (33, 35.) When a gas is absorbed by a solid or by a liquid, the adhesive force between the molecules of the solid or liquid and those of the gas must be strong enough to overcome the repulsive force of the gas. (36, 40.) Heat hinders absorption, since it increases the repul- sive force between the molecules of the gas. Hence gases absorbed by solids or liquids can be separated from them by means of heat. (36, 41.) The same gas is absorbed by some solids or liquids more readily than by others. (40.) The adhesive force between the molecules of different liquids causes the liquids to mix. The mixing of liquids on mere contact with each other is called diffusion of liquids. (38.) Liquids also mix when separated by a thin membrane or porous substance. This mixing is called osmose of liquids. (39.) Gases, like liquids, mix by diffusion and by osmose. (4 2 > 43-) MECHANICS. PRESSURE. WEIGHT. 44. Matter is acted upon by Gravity. Thus far we have been dealing with forces which act between the molecules of matter. We are now to study a force which acts between masses of matter. When a stone falls to the earth, x it is because this force acts between the stone and the earth to draw them together. We know that the moon is continually moving round the earth. Were it not for this force acting between these two great masses, the moon would flyt>fFin a straight line, and we should never see her again. As it is, while moving onward, she is all the while falling towards the earth, and her path is thus bent from a straight line into a curve. It is found that the strength of this force diminishes as the square of the distance increases; that is, at double the distance 'its strength is one-fourth, at thrice the distance one-ninth, and so on. It can be proved that the moon obeys this law and falls towards the earth just as fast as a stone would fall if it were as far off. It is the same force which keeps the earth in its path about the sun, and which guides all the stars of heaven in their appointed courses. It acts upon every mass of matter in the universe, from the dust that floats in the air, to moons and planets and suns, compared with MECHANICS. whose vast bulk this earth of ours is a floating particle of dust. This force is called gravity.* ! 45. Weight. When a stone is held in the hand, it is felt to press downward. This is because gravity is drawing it toward* the earth. The downward pressure which gravity causes a body to exert is called its weight. When different bodies, as iron and wood, are taken in the hand, it is easy to feel that some are heavier than others ; but it is not so easy to tell exactly how much they differ in weight. 46. The Spring Balance. But the weight of a body may be made to bend a spring, and, when different bodies are made to bend the same spring, we can readily tell how much heavier one is than another by seeing how much more it bends the spring. If it bends the spring twice as much, it is twice as heavy ; and if three times as Fig. 16. much, it is thrice as heavy. An instrument ^ ^ for finding the weight of a body in this way is called a spring balance; and one form of it is shown in Figure 16. It con- sists of a steel spring wound into a coil. One end of this coil is fastened to a ring, and the other to a hook. The body to be weighed is fastened to the hook, and the whole raised by the ring. The weight of the body straightens or draws out the spring. A pointer moving over a plate in front, which is divided into equal parts, shows how much the spring has been drawn out. A body which will straighten the spring a certain amount * We have already referred (see foot-note on page 4) to the analogy between the molecules in a mass and the great masses in solar and stellar systems. The analogy can be extended to the forces acting among the units which make up the two. MECHANICS. is said to weigh a pound ; one which will straighten it half as much, half a pound ; one fourth as much, a quarter of a pound ; twice as much, two pounds ; and so on. 47. The Balance. An- other instrument for rind- ing the weight of a body is called a balance, and is shown in Figure 17. It consists of a bar turning on a pivot in the centre, and having pans hung from each end for holding the body to be weighed and the 'weights, which are pieces of iron or brass whose weight is known. The body to be weighed is placed in one pan, and weights are put into the other until they balance it. The body weighs as much as the weights used. 48. The Steelyard. Yet another weighing instrument is the steelyard, shown in Figure 1 8. It differs from the balance in having one long and one short arm. The weight P can be moved upon the long arm, and shows the weight of the body by its distance from C. Fig. 18. THE CENTRE OF GRAVITY. 49. The Centre of Gravity. The centre of gravity of a body is a point such that the force of gravity act- ing upon the part of the body on one side of this point always balances the force of gravity acting upon the part on the opposite side, no matter how the body may be placed. 32 MECHANICS. 50. The Centre of Gravity is not always in the Body itself. If a straight strip of metal or wood be fastened to the sides of a ring so as to pass through its centre, it will be found that the ring will rest in any position when the centre is supported ; and that it will not thus remain at rest on any other point. The centre of gravity, then, of a. ring which is exactly alike throughout its whole extent is at the centre of the ring. If one part of the ring is heavier than the other, the centre of gravity will be. found to be between the centre and the heavier part. When two balls of the same weight are connected by a straight rod (Fig- ure 19), the centre of gravity will be found to be at the centre of the rod. If one ball be twice as heavy as the other, the centre of gravity will be in the rod at a point twice as near the heavier ball as the lighter ball. If the heavier ball be three times the weight of the lighter ball, the centre of gravity will be thrice as near this ball as the other. If the balls are connected by a curved rod, the centre of gravity will no longer be in the rod, but in a straight line which joins the balls. Its distance from the balls will be as explained above. 51. Equilibrium. When a body is at rest, it is said to be in equilibrium. When it is at rest in such a posi- tion that on being slightly disturbed it again returns to this position, it is said to be in stable equilibrium. When it is at rest in such a position that on being slightly disturbed it seeks a new position of rest, it is said to be in unstable equilibrium. Wlien a body remains at rest equally well in any position, it is said to be in indifferent equilibrium. >r- 52. The Centre of Gravity always seeks the Lowest Point. In every case, it will be found that the centre of "\ MECHANICS. 33 gravity of a body seeks the lowest position that it can take. Hence, when a body is so situated that its centre of gravity is raised by tipping it in any direction, it is in stable equilibrium ; when any disturbance of the body tends to lower its centre of gravity, it is in unstable equilibrium ; when, on being disturbed, its centre of gravity neither rises nor falls, it is in indifferent equilibrium. ^L. 4 In Figure 20, g e shows the path which the centre of gravity g must take when the body is tipped. Until g reaches the point e, the body tends to go back, because in so doing the centre of gravity would fall ; but as soon as g passes e, the body tends to go over, because in so doing the centre of gravity would fall, h e shows how mucn the centre of gravity must be raised to overturn the body ; and this distance is seen to be greater when the Fig. 20. V ^. c &*+ n~" I A z X *-. ^s s tody is resting on the side a b than when it is resting on the side b c. It will be found that much more force will be required to overturn it in the latter case than in the former. Hence, the more the centre of gravity of a body has to be raised in order to overturn it, the more stable its equilibrium. It will also be seen from Figure 20 that the broader the base of a body compared with its height, the more stable its equilibrium. 3 34 MECHANICS. If, however, the body is not upright, it may be in un- stable equilibrium even when the base is broad. In Figure 2i,g e is the path which the centre of gravity^ Fig. 21. (l r ~ , O. O, -, I must take when the body a b c d is overturned ; and it Fig. 22. will be seen that, as soon as g is moved at all in the direction g e, it begins to fall, and the body will go over. In the body / m n a, the centre of gravity g is not sup- ported, and the body will fall over of itself. It is evident, then, that a body may lean and yet be in equilibrium, provided the centre of gravity is directly over any point of the base. If this point be well Fj g . 23 . within the base, the equilibrium m be very stable, as in the case of the famous leaning tower at Pisa. On the other hand, a body may be in stable equilibrium even when the base is very narrow. Thus a cork may rest upon the point of a needle, and yet be in stable equilibrium. This may be proved by sticking two forks into the cork, as shown in Figure 22. The forks bring the centre of gravity below the point of support, so that the cork cannot be tipped without raising the MECHANICS. 35 centre of gravity. In the same way, the image in Fig- ure 23 is balanced on its toe by means of the two heavy balls beneath. So, too, in F - the u prancing horse " (Figure 24) the centre of gravity is brought below the point of support by the leaden ball at the end of the curved rod. 53. How to find the Centre of Gravity of a Solid. When a stone, as in Figure 25, is hung by the cord A, the centre of gravity must be directly under the point of support ; that is, somewhere in the line A B. If the same stone be hung by the cord C, its centre of gravity must still be below the point of support, somewhere in the line C J). Since the centre of gravity is in both the Fig. 25. lines A B and C D, it must be at the point G, where they cross. To find the centre of gravity of a solid, then, suspend it from any. point of its surface by means of a cord, and notice the direction which the cord takes. Then suspend it from ^another point, and again notice the direction of the cord. . The point within the body where lines drawn in these directions would cross each other will be the centre of gravity. Of course, if the solid be of regular shape and of uniform density, the centre of gravity is at the centre of magnitude. 36 MECHANICS. SUMMARY. Matter is acted upon by gravity, which gives it -weight. (44, 45.) * The weight of bodies may be found by the spring balance (46), the balance (47), or the steelyard (48). A point can always be found such that the force of gravity acting upon the part of a body to the right of it is always balanced by the force of gravity acting upon the part to the left of it, no matter in what position the body may be placed. This point is called the centre of grav- ity, and sometimes lies within a body and sometimes without it. (49, 50.) A body at rest is in equilibrium. Its equilibrium .may be stable, unstable, or indifferent. (51.) The centre of gravity always seeks the lowest position which it can take. The stability of equilibrium depends upon the position of the centre of gravity, and upon how much it must be raised to overturn the body. (52.) The centre of gravity of a solid may be found by sus- pending the body from two points of its surface. (53.) PRESSURE OF LIQUIDS. 54. How to find the Weight of a Liquid. If we weigh a cup and then fill it with water and weigh it again, we shall find that it weighs more in the second case. Liquids, as well as solids, are acted upon by grav- ity, which causes them to exert a downward pressure. The weight of the water in the cup is the weight of the cup when full of water less the weight of the empty cup. If the cup be filled with quicksilver, it will be found to weigh much more than when filled with water ; show- ing that some liquids are heavier than others. MECHANICS. 37 55. Liquids 'when acted upon by Gravity-press, not only downward, but also upward and sideways. Fix a long tube into the top of a wooden cask, and put a stop-cock into the top, and another into the side of the cask. Fill the cask and the tube with water, and open the stop-cocks, and the water will be driven out of both. This shows that the water in the cask presses upward and sideways as well as downward. The pressure which liquids exert sideways is called lateral pressure. 56. The Upward, Downward, and Lateral Pres- sures are equal for the same Depth of Liquid. In Figure 26, we have a glass vessel, into the top of which are inserted three glass tubes of exactly the same size, with their mouths at the same distance from the bottom. One of these tubes opens downward, one upward, and one sideways. If we fill the vessel with water, through the funnel, the liquid rises to the same height in all three tubes. Now it is the upward pressure which causes it to rise in the tube opening downward, the lateral pressure which causes it to rise in the tube opening sideways, and the downward pres- sure which causes it to rise in the tube opening upward ; and since the tubes are all of the same size, and the water rises to the same height in each, these pressures are all evidently equal. 57. The Upward, Downward, and Lateral Pres- sures of a Liquid increase with the Depth, but are not altered by the Size or Form of the Vessel which holds the Liquid. The more water we pour into the vessel, in Figure 26, the higher the water rises in the tubes. The upward, downward, and lateral pressures increase 38 MECHANICS. with the depth of the liquid, since the lower layers of molecules are themselves acted upon by gravity, and have also to sustain the pressure of the water above them. That the pressure is independent of the size and shape of the vessel is seen when vessels of different sizes* and shapes are connected (Figure 27), and a liquid is poured into one of them. It rises to the same height in all. Fig. 27. 58. When a closed Vessel is filled 'with a Liquul, and any additional Pressure is brought to bear on any Particle of this Liquid, every Particle is made to exert the same additional Pressure, upward, downward, and sideways. Suppose the four tubes in Figure 26 are all of Exactly the same size, and that the vessel is full of water. Pour water into the left-hand tube until it rises to the line c d. The water rises in all the tubes to the same height. The water poured into the first tube brings an additional pressure to bear upon the particles of water at its mouth, and it is the additional pressure which the particles at the end of the other tubes are made to exert that causes the water to rise in them. Since they are all of the same size, there must be the same number of parti- cles at the end of each ; therefore, the particles at the end of the three tubes are made to exert the same ad- ditional pressure upward, downward, and sideways, as that brought to bear upon the particles at the end of the left-hand tube. 59. The Hydrostatic Press. It follows, from what has just been shown, that by means of a liquid a small pressure upon a small surface may be made to exert a MECHANICS. 39 great pressure upon a large surface. In Figure 28, we have two cylinders, with a plunger, or piston, in each. Fig. 28. Suppose that the surface of the larger piston, P, is thirty times that of the smaller, p; if the latter is pressed Fig. 29- downward by a weight of one pound, an upward pres- 4 o MECHANICS. sure of one pound will be brought to bear upon each portion of the surface of P equal to that of p. The whole upward pressure on P will then be thirty times the downward pressure on p. If the surface of P had been sixty times that of p, one pound on the latter would have balanced sixty on the former ; and so on. Advantage is taken of this fact in the construction of the hydrostatic press, shown in Figures 29 and 30. The two cylinders A and JB are connected by the pipe d. Fig. 30. The piston #, in the small cylinder A, is worked by the handle 0, and forces water into the large cylinder j??, where it presses up the piston C. If the end of the piston C is 1,000 times as large as that of the piston a, a pressure of 2 pounds on a would exert a pressure of 2,000 pounds, or one ton, upon C. If a man in working the 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, testing cannon, boilers, etc., and for raising ships out of the water. MECHANICS. 60. Springs and Artesian Wells. -^All natural col- lections 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 to- gether, 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 com- posed 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 de- rive 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 3 1 , suppose A B and C D to be two strata of clay, and K K to be a stratum of sand or gravel between Fig. them. The 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 42 MECHANICS. its escape. If now a hole be bored down 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. An Artesian well in Paris has a depth of 548 metres, or about i ,800 feet, and the water flows out at the rate of 656 gallons a minute, or nearly a million gallons a day. One in this country, at St. Louis, is 2,199 feet deep, and affords 75 gallons a minute. 61. A Body is buoyed up ivhen placed in a Liquid. If a stone be weighed under water, it will seem to be lighter than when weighed in the air. We have already seen that, at the same depth in a liquid the upward and downward pressures are equal, but that these pressures increase with the depth. The bottom of the stone in the above experiment being deeper in the water than the top, the upward pressure of the Fig. 32. water against the bottom of the stone is greater than the downward pressure upon the top of the stone. The stone is accordingly lifted up a little when plunged under water, and, being thus buoyed up, seems to be lighter than in the air. 62. A Body is buoyed up in Water by a force just equal to the Weight of the Water 'which it displaces. In Figure 32, A is a cup into which the cylinder B exactly fits. This cup, then, will hold just as much water as B displaces when under water. Hang this cup and cylinder to the hydrostatic balance, and balance it with weights. Immerse the cylinder B in a vessel of water, and we find that it is more than balanced by the weights. Now care- MECHANICS. 43 * fully fill the cup A with water from the vessel, and the cup and cylinder are seen to be again just bal- anced by the weights. This shows that a body when immersed in water is buoyed up by a force just equal to the weight of the water which it displaces. Of course, if a solid weighs exactly as much as the water it displaces when fully immersed, it will neither rise nor sink in the water. If it weighs more than the water it displaces, it will sink ; if less, it will rise. When a body floats upon the water, it displaces exactly its own weight of water. It is well known that a lump of iron will sink, but the same lump of iron may be hammered out into a vessel which will displace its own weight .of water without being wholly immersed. In this way, ships may be made of iron which will float upon water as well as ships made of wood. SPECIFIC GRAVITY. 63. Substances vary in Density. The same bulks of different solids and liquids are found to be very differ- ent in weight. A substance which weighs more, bulk for bulk, than another substance is said to be more dense, or to have a greater density. It is often desirable to know the relative weights of the same bulks of bodies which vary in density. In such cases, it is convenient to compare the weight of each substance with the weight of some given substance ; and water is taken for this purpose. The weight of a given substance compared with the weight of the same bulk of water is called its specific gravity. 64. Specific Gravity of Solids. To find the specific gravity of a solid or liquid, we must know the weight of the substance and that of the same bulk of water. The weight of a bulk of water equal to that of the 44 MECHANICS. solid can be found by weighing the solid in water, and subtracting its weight in water from its weight in air. The difference of these weights is (62) just equal to the weight of the water it displaces ; and this is, of course, a bulk of water just equal to its own bulk. Hence we have the rule : divide the weight of the body by its loss of weight in water, and the quotient will be its specific gravity. If the body will not sink in water, fasten it to a piece of iron or other substance which will make it sink, and find the weight lost by the two in water. The difference between what Jboth lose and what the iron weighed alone loses will, of course, be what the lighter body loses. 65. Specific Gravity of Liquids. The specific grav- ity of liquids is most conveniently found by means of an instrument, shown in Figure 33, called a hydrometer. Fig- 33- It consists of a hollow glass cylinder, with a stem and scale-pan above, and a small bulb filled with mercury below, by which it is made to float upright in a liquid. The instrument is placed in water, and weights are added until it sinks to a point marked upon the stem. MECHANICS. 45 The weight of the hydrometer, together with the weights in the pan, is equal to the weight of the water displaced (62). If now the instrument be placed in a liquid of dif- ferent density, as alcohol, and made to sink by weights to the mark on the stem, the weight of an equal bulk of that liquid can be found. Of course, the specific grav- ity of the liquid will be the weight of the liquid divided by the weight of the water. A more common form of hydrometer is shown in Fig- ure 34. It consists of a glass tube and bulb loaded with mercury at the bottom. This, when put into a liquid in which it will float, always displaces just its own weight (62). It is first put into pure water, and the point to which it sinks is marked upon the stem. If it be now put into a liquid of less density, it will sink deeper ; if into one of greater density, it will not sink so deep. By means of the scale on the stem, the specific gravity of the liquid into which it is put is indicated. Another way to find the specific gravity of a liquid is the following : Fill a small bottle with water, and then with the liquid, and find the weight of each ; then di- vide the weight of the liquid by the weight of the water, and the quotient will be the specific gravity required. A specific gravity bottle is a bottle which is made to hold a definite weight of water, as 1,000 grains. If it holds 790 grains of alcohol, the specific gravity of the alcohol is .79 ; if it holds 1,860 grains of sulphuric acid r the specific gravity of the acid is i .86 ; and so on. Again, since the weight which a body loses when im- mersed in a liquid is equal to the weight of its own bulk of that liquid (23), we can find the specific gravity of a liquid by dividing the weight which a body loses in that liquid by the weight which it loses in water. Thus, if a piece of copper loses 200 grains when weighed in water,, and 158 grains when weighed in alcohol, the 46 MECHANICS. specific gravity of the alcohol is equal to 158 divided by 200, or .79. SUMMARY. Liquids have weight, and press upward, downward, and sideways. (54, 55.) The upward, downward, and lateral pressures are always equal for the same depth of the liquid. (56.) These pressures increase with the depth of the liquid, but are not altered by the size or shape of the vessel. (57-) When any pressure is brought to bear upon one parti- cle of a liquid, every particle is made to press with the same force upward, downward, and sideways. (58.) On this account, when a small force acts upon a few particles of a liquid, an enormous force may be brought to bear on a large surface in contact with the same liq- uid. This is illustrated by the hydrostatic press. (59.) Springs and Artesian wells illustrate the tendency of water to seek a level in connected vessels. (60.) A body is buoyed up in water by a force equal to the weight of the water which it displaces. (61, 62.) The specific gravity of a solid or liquid is the weight of the solid or liquid compared with the weight of the same bulk of water. (63.) To find the specific gravity of a solid, divide its weight by its loss of weight in water. (64.) The hydrometer is an instrument for finding the spe- cific gravity of liquids. (65.) e Problems on the pressure and weight of liquids, given in the Appendix, are intended to be used at this point. MECHANICS. 47 THE PRESSURE OF GASES. 66. Gases have Weight. Weigh very carefully a thin copper globe when filled with air; then weigh it again after exhausting the air from it, and it will be found to weigh less than before. This shows that air has weight, and the same is true of all other gases. 67. Gases, like Liquids, press upward, downward, and sideways. Figure 35 represents two brass hemi- Fig. 36. Fig. 35- spheres, some four inches in diameter, the edges of which are made to fit tightly together. 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 4 8 MECHANICS. Fig. 37- hemispheres, from Otto von Guericke, of Magdeburg, by whom it was invented. If a small bell-jar, open at both ends, be covered with the palm of the hand, and the air be then exhausted from it, the hand will be held down with considerable force by the pressure of the air upon it. If a wet bladder be tied over the same bell-jar and dried, and the air be exhausted as before, the bladder will burst with a loud noise. These two experiments illustrate the downward pres- sure of the air. In Figure 37, A is a strong glass cylinder, open at both ends ; B a piston, working air- tight within it ; and C a brass plate, covering it closely, and having a hole in the centre to which a hose may be screwed fqr connecting it with the air- pump. When the air is ex- hausted from the cylinder, the piston rises, even if a heavy weight be fastened to it. This experiment affords a very striking illustration of the upward pressure of the air. Fig s8 68. Gases have an Expansive Force. If an india-rubber bag, par- tially filled with air, be closed air- tight and placed under the receiver of the air-pump, the bag fills out as shown in Figure 38, when the air is exhausted from the receiver. All gases thus tend to expand. 69. The Air-Pump. An instru- MECHANICS. 49 t for removing the air from a vessel is called an air-pump. One form of it is shown in Figure 39. It consists of a cylinder, in which a piston moves air-tight. In this piston is a valve opening upward. At the top of the cylinder is another valve also opening upward. The bottom of the cylinder is connected with the pump-plate by a tube. On this plate is placed the vessel, or re- ceiver, from which the air is to be exhausted. As the Fig. 39- piston is forced down, the expansive force of the air below pushes open the valve in the piston to get into the space left behind it. When the piston is drawn up again, the expansive force of the air above closes this valve and opens the valve at the top of the cylinder, so that this air escapes. The expansive force of the air in the tube and receiver causes it to fill the space behind the piston. When the piston is again pushed down, the 4 5O MECHANICS. downward pressure of the air outside closes the valve at the top of the cylinder, while the expansive force of the air below opens the valve in the piston, and some of the air passes through it. On drawing up the piston again, this air is removed as before. By continu- ing this process, the air is nearly all withdrawn from the receiver. It cannot be wholly withdrawn, because as it becomes more and more exhausted, the expansive force becomes less and less, until at last it is not sufficient to open the valve in the piston. 70. A Body is buoyed up in the Air. If a hollow sphere be balanced in the air by a piece of lead, and then the whole apparatus be put under the receiver of an air-pump and the air exhausted, the lead will no longer balance the sphere. This shows that a body is buoyed up in the air as well as in a liquid (61). Bodies seem to be lighter in the air than in a vacuum (that is, a space from which the air has been exhausted], for the same reason that a body seems lighter in water than in the air. The upward pressure of the air upon the bottom of the body is somewhat greater than the down- ward pressure upon the top of the body. A body in the air, then, is buoyed up by a force just equal to the weight of the air which it displaces. If a body weighs more than the air it displaces, it sinks through the air ; if it weighs less than the air it displaces, it rises in the air. 71. Balloons. Balloons rise in the air because they are Jilled with some substance which makes them lighter than the air which they displace. If a glass bulb and tube filled with air be arranged, as in Figure 40, with the end of the tube under MECHANICS. water, and the bulb be heated by means of *. lamp, the air in it expands, and a part of it is driven out in bubbles through the water. This shows that air ex~ panels' ivhen heated. Paper balloons are sometimes made which are sent up by fastening a light just under an opening in the bottom of the balloon. The light heats the air inside, and causes it to expand, and a part to pass out. The remainder is then lighter than the air displaced by the balloon, which consequently rises. Large balloons are made of strong silk', and filled with some very light gas, such as coal-gas. This makes the balloon so much lighter than the air it displaces, that it will rise, carry- Fig. 41. ing a car with two or three persons in it. 72. The Pressure of the Atmosphere will sustain a Column of Liquid in an in- verted Vessel. Fill a glass jar with water and invert it in a dish of water, keeping the mouth of the jar all the time under water ; and the liquid will not flow out of the jar when it is raised. Now place the dish and jar under the receiver of an air- pump, and exhaust the air ; and the water will flow out from the jar. This shows that it is the pressure of flic atmosphere on the sur- face of the water in the dish which keeps the water in the inverted jar. 52 MECHANICS. 73. The Atmospheric Pressure will sustain a Col- umn of Mercury about 30 Inches high. If a glass tube closed at one end and about 34 inches long be filled with mercury, and inverted in a cup of mercury, as shown in Figure 41, a part of the mercury will run out, leaving a column about 30 inches high in the tube. 74. The Atmospheric Pressure is equal to about 15 Pounds to the Square Inch. If the tube in the above experiment be one inch square, it follows, from the way in which liquids press, that the downward pressure at the bottom of the tube will be just equal to the down- ward pressure of the atmosphere on each square inch of the surface of the mercury in the vessel. If now we weigh the mercury in the tube, we shall find that there are about 15 pounds of it. This column of mercury then exerts a pressure of 15 pounds at the bottom of the tube. The air then presses with a weight of 15 pounds upon every square inch of surface. We do not perceive this great pressure, because the air presses equally in every direction. 75. The Atmospheric Pressure varies from Day to Day. If a glass tube be filled with mercury, and then inverted in a cup of mercury and left standing, and the height of the mercury column noted from day to day, it will be found to vary considerably, being sometimes as much as two inches higher than at other times. This va- riation must be due to changes in the pressure of the air. 76. The higher the Place, the less the Atmospheric Pressure. If the tube just described be carried to the top of a mountain, the mercury will fall considerably. This shows that the atmospheric pressure becomes less, the higher we go above the surface of the earth. The atmosphere is a great ocean of air which sur- rounds the earth, and at the bottom of which we live, as the fishes live at the bottom of the sea. The changes in MECHANICS. 53 the height of the mercury just described show that the pressure increases with the depth.* 77. The Barometer. An instrument for measuring the pressure of the atmosphere is called a barometer. One form of it is shown in Figure 42. It consists of a cup and tube filled with mer- cury, as in the experiment illustrated by Figure 41. These are fastened to a wood- en frame. At the upper part of the tube, there is a scale with a sliding index, for measuring the height of the mercury. H is a thermometer. The mercury is often put into a leather bag instead of an open cup as here, since it is less likely to be spilled. As the leather is flexible, the pressure of the air is brought to bear upon the mercury through the bag. 78. Uses of the Barometer. When we have found at what rate the atmospheric pressure diminishes as we go up, we can readily find the height of mountains by means of the barometer. The difference between the readings of the barometer at the level of the sea and at the top of the mountain, will show how much the pressure has diminished", and from this we can find he height of the mountain. The barometer is also of considerable use in indicating the approach of storms, espe- cially of violent winds. It has been ob- served that such storms are very likely to occur immediately after a sudden diminu- tion of atmospheric pressure, which is shown * See, in the Appendix, the chapter on The Physics of the Atmosphere. 54 MECHANICS. by a rapid fall of the mercury.' On the other hand, a gradual rise of the mercury usually indicates the ap- proach of fair weather. The mere height of the mercury tells us little about the weather, but a careful study of its movements en- ables us to judge pretty accurately what changes are likely to occur in the weather. 79. Pumps. As water is somewhat more than thir- teen times lighter than mercury, the pressure of the atmosphere will sustain a column of this liquid about thirteen times thirty inches in height, or considerably more than thirty feet. If the tube is open at the top, it is necessary to remove the air from it, before the water will rise into it. An instrument for raising water in this way is called a pump. The common lifting-pump is shown in Figure 43. It is really an air-pump. When the piston P is forced down, the air below it, by its expansive force, opens the valve 0, through which it escapes. When the piston is drawn up again, the valve O is kept shut by the pressure of the air above, and the air in A expands, pushes open the valve 6 1 , and rushes into the vacuum above. The air being thus partly removed from A, the pressure of the air upon the water in the well outside is greater than that inside the pipe, and consequently forces the water up the pipe and through the open valve S. When the piston is pushed down again, the pressure of the water in the cylinder shuts the valve S^ and opens the valve O. The water thus gets above the piston, which, on going up again, lifts it so that it flows out at the spout, as shown in the figure. Figure 44 represents the force-pump. In this pump, the piston P is solid. When it is drawn up, the water below, by its upward pressure, opens the valve S, and fills the cylinder. When the piston is pushed down, the MECHANICS. valve 6 1 being shut by its own weight, and the pressure of the water upon it, the water is forced up through the Fig- 44- valve O into the pipe D. When the piston goes up again, the valve O is closed by its own weight and that of the water above, the valve 5 opens, and the cylinder is filled as before. In Figure 45, we have these two pumps combined. The air is pumped out through the valves .5 and O, and the water is forced up into the cylinder through the pipe A and the valve S, just as it was in the litting- pump ; and the water is then forced through the valve O and the pipe Z?, as in the force-pump, just described. MECHANICS. In both these forms of force-pump, the water is driven out of the pipe D only when the piston is going down. It may be made to flow out in a steady strearn by adding an air-chamber above the valve 0, as shown in Figure 46. As the water is forced into this chamber, it corn- Fig. 45- Fig. 46. presses the air, which, by its expansive force, exerts a continuous pressure on the water, and drives it in a steady stream up the pipe. In tint fire-engine, two force-pumps are usually con- nected with one air-chamber. The pumps are so arranged that the piston of one is going down while that of the other is going up, thus forcing water into the air-chamber all the time. 80. The Siphon. Bend a tube into the form of the let- ter U, making one arm somewhat longer than the other ; fill it with water, and close both ends with the fingers ; then invert it, and place the short end under the surface of water in a vessel. If now both ends be opened, the water will flow out of the vessel through the tube. A bent tube used in this way is called a siphon. To explain the action of a siphon, let us suppose it MECHANICS. 57 Fig- 47- filled, and the short arm placed in the water. The pressure then acting on C (Figure 47), and tending to raise the water in the tube, is the atmospheric pressure less the weight of the column of water CD. In like manner, the pres- sure on the end of the tube B is the atmospheric pres- sure less the pressure of the column of water A B. But as this latter column is longer than C D, the force acting at B is less than the force acting at C, and consequently the water will be driven through the tube by a force equal to the difference of these two forces. The flow will therefore be the faster, as the difference of level between C and B is greater. Si. Tantalus's Cup. This is a glass cup, with a siphon tube passing through the bottom, as shown in Figure 48. If water be poured into the cup, it will rise both in- side 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 than the siphon car- ries 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 again as before ; and so on. In many places there are springs which flow at inter- Fig. 4 8. 58 MECHANICS. vals, like the siphon in this experiment, and whose action may be explained in the same way. A cavity under ground 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. 82. The Air- Gun and the Condenser. The expan- sive force of gases increases 'when they are compressed. This is illustrated by the air-gun, which consists of a tube, connected by a stop-cock with a small air-tight vessel of very great strength. If a large amount of air be forced into this vessel, and the stop-cock be then opened, the expansive force of the gas will drive a bul- let from the tube, as if it were fired from a musket. The firing of a musket is, in fact, another illustration of the very same kind. When the gunpowder is set on fire, it forms an immense amount of gas, which, being confined in a small space, has a great expansive force, and therefore exerts a great pressure upon the bullet. An instrument used for compressing air is called a condenser. It consists of a strong cylinder, with a pis- ton and valves, arranged precisely as in the force-pump in Figure 44. It works, too, in the same way as the force-pump ; the air rushing in through the valve S when the piston is raised, and being driven out through the valve O when the piston is pushed down. The ves- sel into which the air is to be forced is screwed to D. 83. Mariotte's Law. The bulk of a gas becomes less just in proportion as the pressure upon it becomes greater ; or, in other words, the volume of a gas is in- versely as the pressure which it bears. The elasticity of a gas becomes greater just in propor- tion as its bulk becomes less, or as the pressure upon it becomes greater ; or, in other words, the elasticity of a gas is inversely as its volume, and directly as the pres- MECHANICS. 59 sure which it bears. These facts concerning gases are known as Mariettas law, from their discoverer. 84. The Spirit Level. The spirit level (Figure 49) consists of a closed glass tube, A B, very slightly curved on the upper side. It is filled with spirit, with the ex- Fig. 49- D ception of a bubble of air which tends to rise to the highest part of the tube. It is set in a case C *D ; and when it is placed on a perfectly level surface, the bubble is exactly in the middle of the tube, as in the figure. SUMMARY. Gases have weight, and, like liquids, press upward, downward, and sideways. (66, 67.) Gases are acted upon by an expansive force, which is increased by heat and by pressure. (68, 71, 82.) Bodies are buoyed up in air by a force equal to the weight of the air which they displace. (70.) The atmospheric pressure balances a column of mer- cury about thirty inches high, and is equal to about fifteen pounds to the square inch. (73, 74.) This pressure varies from day to day, and becomes less as the height of the place increases. (75, 76.) The barometer is an instrument for measuring the at- mospheric pressure. (77? 7^0 The action of pumps, and of the siphon, is to be ex- plained by the pressure of the atmosphere. (79, 80.) The bulk, or volume, of a gas is in the inverse ratio of the pressure which it bears. The elasticity of a gas is in the inverse ratio of its volume, or the direct ratio of the pressure it bears. (83.) 60 MECHANICS. MOTION. FIRST LAW OF MOTION. 85. Inertia. We know that a stone, or other body, when at rest, will not begin to move of itself, but only on the application of some force ; and that, when any body, as a ball, is in motion, it requires some force to stop it. The inability of a body, whether at rest or in mo- tion, to change its state, is often called inertia. 86. A moving Body, when left to itself, will always move in a straight Line and at the same Rate. Mathematicians, from the study of certain motions, have come to the conclusion that a moving body, when left to itself, will always move in a straight line and at the same rate. This is the first law of motion. 87. An unbalanced Force must act upon a Body in order to put it in Motion, or to change the Direction or the Rate of its Motion. A ball, held in the hand, remains at rest, because the downward pull of gravity upon the ball is just balanced by the resistance offered by the hand. If the hand is removed so that the force of gravity is unbalanced, then the ball begins to move. If we push with the hands against the opposite sides of a book, the book will remain at rest as long as the push of one hand is just balanced by that of the other. Take away one hand, so that there shall be nothing to balance the push of the other, and the book begins to move. So, in every case, a body begins to move only when an unbalanced force acts upon it. And when a body is once in motion, it changes the direction and rate of its motion only when an un- MECHANICS. 6 1 balanced force is acting upon it. When a body is once in motion, it is just as natural for it to move on in a straight line, with uniform speed, as it is for it to remain at rest when once it is at rest. 88. The Effect of a Force acting for a Moment only. When a body is acted upon by a force only -for an instant, as when a ball is struck with a bat, or a bullet is fired from a gun, it has its greatest speed at first, and its motion is gradttally wasted by the resistance it meets in passing through the air or over the earth. 89. The Effect of a Force acting continuously. When a body is acted upon continuously by a force, as in the case of a railway train, "or a steamboat, the mo- tion, slow at first, gradually increases till it reaches a certain point, when the speed remains unchanged so long as the moving force is unchanged. When the moving force is increased, the speed increases; and, when it is diminished, the speed diminishes. 90. The Resistance a moving Body meets increases as the Square of its Velocity. The steamboat, in moving, has to push aside a certain amount of water in a second, and this is the chief resistance it meets. Now, as the speed of the boat increases, more water must be pushed aside in a second, and each particle of water must be moved aside more quickly. Hence, the faster it moves, the greater the resistance. Suppose die speed of the boat to be doubled, twice as many par- ticles of water must be pushed aside in a second, and each particle must be pushed aside in half the time. Hence, the resistance becomes fourfold when the velocity is doubled. The resistance, then, increases as the square yf the velocity. 91. A moving Body may be in Equilibrium. A body at rest is in equilibrium, because the forces acting upon it are balanced. When a train of cars is starting, 62 MECHANICS. the force of the steam is not wholly balanced by the re- sistance ; hence it imparts motion to the train. But as the speed of the train increases, the resistance also in- creases, until it finally equals the force of the steam. All the force of the steam is now used in balancing the resistance, and the speed no longer changes. Since the two forces acting upon the moving body balance each other, it must be in equilibrium. Every body moving in a straight line, and with uniform speed, is in equilibrium. SECOND LAW OF MOTION. 92. A Force has the same Effect in producing Mo- tion, whether it acts upon a Body at Rest or in Motion, and whether it acts alone or with other Forces. When a ball is thrown horizontally, two forces act upon it, one to throw it forward in a straight line, and the other to draw it to the earth in a straight line ; and it is found that it is drawn just as far towards the earth in a given time as a ball that is let fall from a state of rest. The same is true, in whatever direction the ball may be thrown. For example, if the force used would send the ball forward 30 feet in a second, and if gravity will pull it from a state of rest 16 feet towards the earth in the same time, the ball at the end of the second will be just 16 feet below the point it would > have reached had not the force, of gravity acted upon it. So, were a ball thrown directly upward with a velocity of 100 feet a second, at the end of the second it would be only 84 feet high ; that is, 16 feet below the point it would have reached had not the force of gravity acted upon it. If it were thrown directly downward from the top of a high tower with the same velocity, it would be at the end of MECHANICS. 63 a second 116 feet below the top of the tower ; that is, 16 feet below the point it would have reached had not gravity acted upon it. Now 16 feet is just the distance in each case that gravity would have pulled the ball in a second from a state of rest. Again, if the current in a stream is strong enough to carry a boat down stream one mile in an hour, and if a person attempts to row the boat directly across the stream at a rate which would take him across in an hour, at the end of the hour the boat will be at the opposite bank just a mile down stream. 93. A Body thrown horizontally or Fig. 50. obliquely, when acted upon by Grav- ity, describes a curved Path. When both the forces acting upon the body are instantaneous, it moves in a straight line; when one is instan- taneous, and the other continuous, as in the case of gravity acting on a ball thrown horizontally or obliquely, the path is curved. Hence a cannon- ball describes a curved path ; if fired at a distant object, it must be aimed above it. 94. All Bodies would fall at the same Rate, were it not for the Resist- ance of the Air. As we see bodies, light and heavy, falling through the air, we come to think that the force of gravity causes heavy bodies to fall more rapidly than light ones ; but if we place a coin and a feather in a long glass tube and exhaust the air com- pletely (Figure 50), the two bodies will fall through the tube in the same time. It must, 64 MECHANICS. then, be the resistance of the air which causes a lighter body to fall more slowly through the atmosphere than a heavy one does. When the force of gravity is unimpeded in its action, it will cause every body, whatever may be its size, shape, or density, to fall with exactly the same speed. 95. When a Body is moving directly downward, Gravity increases its Velocity at the Rate of 32 Feet a Second. A body falls 16 feet the first second, and acquires a velocity of 32 feet during the time. As grav- ity has the same effect upon a moving body as upon one at rest, a falling body will gain in velocity 32 feet each second. When therefore a body is moving directly down- ward, gravity increases its velocity at the rate of 32 feet a second. 96. How to find the Distance a Body falls in a given Time. The distance a body falls the first second, or 16 feet, is exactly the mean between o, its velocity at start- ing, and 32, its velocity at the end of the second. As it would gain a velocity of 32 feet during the next second, it would have a velocity of 64 feet at the end of that second. The velocity it has already acquired would cause it to fall 32 feet the second second, and the force of gravity acting upon it during that time would cause it to fall 16 feet more ; hence it would fall 48 feet during the second second. It will be noticed that 48 is just the mean of 32, its velocity at the beginning of the second, and 64, its velocity at the end of the second. During the first two seconds, the body would fall 48 -|- 16 ==. 64 feet. This is just twice the mean of o and 64. Hence, to find the distance that any body would fall when acted upon by gravity alone during any number of seconds, find its mean velocity during the time, and multiply it by the number of seconds. To find the velocity of a falling body at the end of MECHANICS. 65 any second, multiply 32 feet by the number of seconds it has been falling. 97. When a Body is moving directly upward, Grav- ity retards its Velocity at the Rate of 32 Feet a Second. We know that gravity has the same effect on a body in motion as on one at rest (92). Since, then, it causes a body in falling from a state of rest to acquire a velocity of 32 feet a second, it must, in the case of a body mov- ing directly upward, diminish its velocity at the rate of 32 feet a second. And it must also cause it to rise each second 16 feet less than if it were not acting upon it. 98. How to Jind the Distance a Body, when thrown upward, will rise in a given Time. To find this dis- tance, take the mean velocity of the body during the time, and multiply it by the number of seconds. To find the velocity at any particular second, multiply the number of seconds the body has been rising by 32, and subtract this from the velocity the body has at starting. THIRD LAW OF MOTION. 99. Momentum. The product of the velocity of a body multiplied by its mass is called its momentum. By the mass of a body, we mean its quantity of mat- ter. The same force acting upon bodies containing different quantities of matter does not give each the same velocity ; but it does give each the same momen- tum, or quantity of motion; that is, if the quantity of matter in each be multiplied by its velocity, the prod- ucts will all be equal. 100. A moving Body cannot impart Motion to another Body without itself losing the same Quan- tity of Motion. This third law of motion results from 5 66 MECHANICS. the fact that a moving body is unable of itself either to increase or to lessen its quantity of motion. On meeting another body, it may impart some of its own motion to it ; but it cannot give motion to this body, and at the same time retain all its own motion. This is often called the law of action and reaction, and stated thus : action and reaction are always equal and in opposite directions. When any force acts in op- posite directions, it is usually said to act in one direction, and react in the opposite. Thus in firing a cannon, the expansive force of the gases set free by the burning powder acts equally in all directions. It acts upon the sides with equal and opposite forces which neutralize each other unless the cannon bursts. It also acts toward the muzzle and breech with equal forces, which produce equal effects, one upon the ball and the other on the can- non, causing the recoil. The ball and the cannon both have the same momentum ; but the ball, since it has a much less mass, gets a much greater velocity. This expansive force is said to act upon the ball and to react upon the gun. So, too, in walking, we are said to react upon the earth. The truth is, that the bent leg acts like a bent spring between our bodies and the earth ; and when the spring straightens, it pushes us away from the earth and the earth away from us ; the earth being moved as much less than our bodies as its mass is greater. 101. It requires Time to impart Motion to a Body as a Whole. The forces which impart motion to a body often act directly upon only a few of its particles. When a ball is struck by a bat, only a small part of it receives the blow, and when a bullet is shot from a gun, the gases (46) act only upon one-half of it. In such cases, it is clear that the motion must be transmitted from particle to particle; and this transmission of MECHANICS. 67 motion from particle to particle requires time, ab- though this time may be exceedingly short. If the force acts so suddenly that there is not time enough for this transmission, the part acted upon is flattened or chipped off. Thus a musket-ball may be fired through a window-pane, making a clear round hole without cracking the glass. If the ball had been thrown by the hand, the whole pane would have been shattered. In the first case, the speed of the ball was so great that the particles in front of it had not time to transmit their motion to those about them ; hence they moved on alone, leaving the others at rest. If the pane had been suspended by a fine thread, the ball would have passed through it in the same way, without breaking the thread, or causing the pane to swing in the least. So a door half open may be pierced by a cannon-ball without being shut. The end of a musket in a soldier's hand has been known to be carried away by a cannon- ball without his being aware of it. A tallow candle may be fired through a board, since it gets through it before the parts of the tallow have time to yield. In this way, a soft missile may hit as hard as lead, if fired with sufficient speed. \Ve see, then, that when a moving body meets with another it seldom expends all its power in imparting motion to that body as a whole, but also pierces it more or less. The .power of a body to pierce another in- creases as the square root of its velocity; that is, if a body is to pierce another twice as far, it must have four times the velocity ; if three times as far, nine times the velocity ; and so on. 102. Reflected Motion. When an elastic ball is thrown against the floor, it rebounds. If it is thrown directly downward, it retraces its path in its rebound. If it is thrown obliquely, it rebounds obliquely in an 68 MECHANICS. opposite direction. In Figure 51, if the ball is tnrown Fig. 5 i. in the direction af, it will rebound in the direction^* b. If the line e j be drawn at right angles to the sur- face, the angle formed by the two lines # j^and e f\ called the angle of' incidence, and is always equal to the angle formed by the two lines b f and e f. This last angle is called the angle of reflection. In reflected motion, the angle of incidence always equals the angle of reflection. SUMMARY. The inability of a body, whether at rest or in motion, to change its state, is called inertia. (85.) A moving body, when left to itself, will always move in a straight hne and at the same rate. (86.) An unbalanced force must act upon a body in order to put it in motion, or to change the direction or rate of its motion. (87.) When a force acts upon a body for a moment only, the motion which it imparts is gradually wasted away, owing to the resistance which the body meets. (88.) The resistance which a moving body meets increases as the square of the velocity of its motion. (90.) .A body moving in a straight line and with uniform velocity is in equilibrium. (91.) An unbalanced force has the same effect, whether it act upon a body at rest or in motion, and whether it act alone or with other forces. (92.) A body thrown horizontally or obliquely, when acted upon by gravity, is made to move in a curved' path. (93-) MECHANICS. 69 Were it not for the air, a light body would fall as fast as a heavy one. (94.) Gravity acting alone causes a body to fall from a state of rest about 16 feet in a second. When a body is mov- ing directly downward, gravity increases its velocity at the rate of 32 feet a second. When a body is moving directly upward, gravity retards its velocity at the rate of 32 feet a second. (95, 97.) The same force always gives to a body the same quantity of motion, or momentum. The momentum of a body is found by multiplying its weight by its velocity. (99-) A. moving body cannot impart motion to another body without itself losing the same quantity of motion. (.00.) When the same force acts in opposite directions, it is often said to act in one direction and to react in the opposite. (100.) It takes time to give motion to a body as a whole. (101.) In reflected motion, the angle of incidence equals the angle of reflection. (102.) For Problems under the Laws of Motion, see Appendix. THE PENDULUM. 103. A Pendulum is a heavy Body hung from a fxed Point by means of a Cord or Rod. When the centre of gravity of the body is directly under the point of support, the body remains at rest ; but if the body be drawn out of this position and let go, it will fall towards a vertical line passing through the point of support ; and when it has reached this line, it will, owing to its inertia, pass beyond it. On coming to rest, it again falls toward MECHANICS. Fig. 52. this vertical line and again passes beyond, and thus continues to swing from side to side. 104. First Law of the Vibration of the Pendulum. Suppose d, in Figure 52, to be a leaden ball hanging by a fine silk thread. Pull it to one side so that it shall swing through a very short arc, and count the number of its vibrations in a minute. Now bring it to rest again, and draw it to one side so that it shall swing through a little longer arc, and again count its vibrations in a minute. Again bring the ball to rest, then cause it to swing through an arc yet longer, and count the vibrations in a minute. In all three cases, the number of vibrations in a minute will be equal. By a vibration is meant the whole of the pendulum's movement in one direction. The arc through which the pendulum swings is called the amplitude of its vibration. When the length of the pendulum remains the same, the pendulum always vibrates in nearly the same time, whatever be the amplitude of the vibration.* This singular property of the pendulum is called isoch- ronism, from two Greek words, signifying equal times, and the vibrations of the pendulum are said to be isochronous. ' 105. The Second Law of the Vibration of the Pen- dulum. Let d and c, in Figure 52, be two pendulums exactly alike, except that the ball of one is lead, and of the other ivory. It will be found that, making allowance * If the amplitude does not exceed 3, the time of vibration will always be exactly the same. MECHANICS. 71 for the resistance of the air, each performs the same number of vibrations in the same time. For pendulums of the same length, the time of the vibration* is the same, whatever the pendulum may be made of. 106. Third Law of the Vibration of the Pendulum. Let b, in Figure 52, be a pendulum one-fourth the length of c, and a another, one-ninth the length of c. It will be found that b vibrates twice as fast as c, and a three times as fast as c. This shows that, for pendu- lums of unequal length, the time of the vibration is proportional to the square root of the length j that is, the lengths of the pendulum being made 4, 9, and 16 times greater, the times of vibration will be only 2, 3, and 4 times longer. 107. Fourth Law of the Vibration of the Pendulum. It is found that when a pendulum of a given length is placed on different parts of the earth's surface, the time of the vibrations is not always the same. Towards the poles it is found to vibrate more rapidly than at the equator. Mathematicians have shown that this is be- cause the force of gravity is stronger at the poles. They have shown that, in different parts of the earth, the time of vibration for pendulums of the same length is in the inverse ratio of the square root of the intensity of gravity; that is, if the intensity of gravity were four times as great in one place as in another, the time of vibration for a pendulum of the same length would be half as great, and so on. 108. The Use of the Pendulum for Measuring Time. The most important use of the pendulum is for measuring time. The common clock is merely a con- trivance for recording the beats of the pendulum, and keeping up its motion. The essential parts of such a clock are shown in Figure 53. The toothed wheel R, called the scape-wheel, is turned by a weight or spring, MECHANICS. Fg- S3- and its motion is regulated by the escapement n m, which swings on the axis o; the vibrations of the pen- dulum being communicated to it by means of the forked arm a b. When the pendulum is at rest, one of the teeth of the scape-wheel rests upon the upper side of the hook m, and the clock does not go. If now the pendulum be set in motion, so that the hook m is moved from the wheel, the tooth which rested on it is set free, and the wheel begins to turn ; but it is soon stopped by the hook 72, which moves up to the wheel as m moves away from it, and catches on its under side the tooth next below. As the pendulum swings back, the hook n moves away, the wheel again begins to turn, but is stopped again on the oppo- site side by the hook m, which catches the tooth next to the one it held before ; and thus each vibration of the pendulum allows the scape-wheel to move forward through a space equal to one-half of one of its teeth. If, then, the wheel has thirty teeth, it will turn round once in sixty beats of the pendulum. Upon the axis of this wheel the second- hand of the clock is placed. It is connected with another wheel, which takes sixty times as long to revolve, and which carries the minute-hand; and this latter wheel is connected with another, which turns in twelve times the period, and carries the hour-hand. Thus the second- hand registers the pendulum-beats up to sixty, or one minute ; the minute-hand registers the revolutions of the second-hand up to sixty, or one hour ; and the hour-hand those of the minute-hand up to twelve, or half a day. MECHANICS. 73 Were it not for the pendulum and escapement, these wheels would be whirled round very fast by the action of the weight or spring, and the clock would soon run down. On the other hand, were there not some means of keeping up the motion of the pendulum, it would soon be brought to rest by the resistance of the air and the friction at the point of suspension. Its motion is kept up by means of the escapement, which is so constructed as to give it a slight push at each vibration. The ends of the two hooks have inclined surfaces against which each tooth of the wheel, as it leaves them, presses with considerable force, so as to throw the escapement for- ward a little. This impulse is communicated, through the axis o, and the arm a b, to the pendulum. SUMMARY. A pendulum is a .heavy body hung from a fixed point by means of a cord or rod. (103.) The laws of the pendulum are four : \st, When the length of the pendulum remains the same, the pendulum vibrates in nearly the same time, whatever be the amplitude of the vibration. (104.) id, For pendulums of the same length, the time of the vibrations is the same, whatever the pendulum may be made of. (105.) ^d, For pendulums of different lengths, at the same place, the time of the vibrations is proportional to the square root of the lengths. (106.) \th, In different parts of the earth, the time of the vibrations for pendulums of the same length is in the inverse ratio of \the square root of the intensity of gravity. (107.) The pendulum is used for measuring time. (108.) 74 MECHANICS. MACHINES. THE LEVER. 109. There are three Kinds of Lever. When a workman wishes to raise a large stone, he places an R iron bar under it, as in Figure 54, with a block under the bar near the p stone, and then presses down upon the other end of the bar ; or else he places the end of the bar under the stone, as in Figure 55, so that one end of it rests upon the ground, and then lifts upon the other end. The bar Fig. 55. thus used constitutes one of the simple machines. It is called the lever. , The mass to be raised is called the weight. The moving- force applied at the other end of the bar is called the power; and the point on which the bar rests is called the fulcrum. The parts between the fulcrum and the points where the power and weight act are the arms of the lever. In the first case, the fulcrum was between the weight and the power ; in the second case, the weight was between the fulcrum and Fig S6 the power. In the fishing-rod , (Figure 56), one hand, f, is the fulcrum ; the other hand, P, is the power ; and the fish is the weight. Here the power is applied between the ful- crum and the weight. There are, then, three kinds of lever : (i) That with the fulcrum between the weight and power. MECHANICS. 75 (2) That 'with the -weight between the fulcrum and power. (3) That with the power between the fulcrum and the weight. These three kinds of lever ate shown in Figure 57 Fig. 57- 1 10. The Law of the Lever. In the lever of the first kind, if the fulcrum is just half-way between the weight and power, then the weight and power will move through equal distances. In this case, the weight and power must be equal in order to balance each other, or to be in equilibrium. If the power were twice as far from the fulcrum as the weight, then the weight would move through only half the distance that the power does, and in this case the power need be only half the weight in order to balance it. Thus we see that, in the case of the lever, the weight and power will balance each other when the power, multiplied by the distance through which it moves, equals the weight multiplied by the distance through which it moves; that is, if the fulcrum of a lever be so placed that one end of the lever will move through a thousand inches while the other end moves one inch, then a power of one pound on the former will balance a weight of a thousand pounds on the latter. ^>s in. The Law of Machines in General. The same / 76 MECHANICS. is found to be true in the case of every machine, how- ever complicated ; namely, that the power and 'weight 'will balance each other when the power, multiplied by the distance through which it moves, equals the weight multiplied by the distance through which it moves. There is no real gain of mechanical force in a lever or a machine of any kind. A machine is only an arrange- ment by which a small force acting through a great distance is converted into a great force acting through a small distance, or else a great force acting through a small distance is converted into a small force acting through a great distance. When a small force, by acting through a great dis- tance, is made to raise a great weight, or do a great deal of work, there is said to be a gain of power in the machine. When, on the contrary, a great force, in mov- ing through a small distance, lifts only a small weight, or does very little work, there is said to be a loss of power in the machine. But whenever there is a gain in power, there is a corresponding loss in speed; and whenever there is a loss in power, there is a corre- sponding gain in speed. For if, in the machine, a power of one pound is made to move a weight of ten pounds, then the weight moves only one-tenth as fast as the power. But when a power of ten pounds is made to move a weight of one pound, then the weight moves ten times as fast as the power. 112. Gain and Loss of Power in the Lever. In a lever of the first kind, when the fulcrum is just half- way between the weight and power, there is neither gain nor loss in power. If the fulcrum is nearer the weight than the power, there is a gain in power and a loss in speed. If the fulcrum is nearer the power than the weight, there is loss in power and gain in speed. MECHANICS. 77 In a lever of the second kind, the power is always farther from the fulcrum than the weight, and con- sequently it always moves through greater distance. Hence, in this kind of lever, there is always a gain in power and a loss in speed. In a lever of the third kind, the weight is always farther from the fulcrum than the power, and must move the greater distance. In this kind of lever, then, there is always a loss in power and a gain in speed. 113. The Compound Lever. Sometimes two or more simple levers are combined, as shown in Figure 58. Fig s8t Suppose that P be five times as far from the fulcrum f 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 is five times as far from the fulcrum F as W is, the five pounds of pull on J3 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 W. But it will be found on trial that by pulling P down one inch, W will be raised only one twenty-fifth of an inch. Such a combination of levers is called a compound lever. 114. Bent Levers. Sometimes the arms of the lever are bent, as shown in Figure 59. In such a lever, the lengths of the arms are straight lines drawn from the fulcrum at Flg< S9> right angles to the lines which ^^~~~^^ = --'-y c show the direction in which the f" power and weight act. The common claw-hammer, as used for drawing nails, is an illustration of this kind of lever. 7 8 MECHANICS. THE WHEEL AND AXLE. 115. The Rack and Pinion. In Figure 60, we have a machine called the rack and pinion. The crank A turns a small toothed wheel called the pinion. The teeth of the pinion, one k after another, catch under the teeth of \ an upright bar B, called the rack, and each tooth raises the bar a little. If the rack is placed under the weight, it will carry up the weight as it rises. 1 1 6. The Rack and Pinion is a Modification of the Lever. In the rack and pinion, the crank takes the place of the long arm of the lever ; the rod, or axle, upon which the pinion turns takes the place of the fulcrum; and the pinion takes the place of the short arm. Each tooth of the pinion is, in fact, the short arm of a lever, and the pinion is a contrivance by which the lever is furnished with several short arms instead of one. These short arms act upon the weight one after another, so that it can be raised a considerable distance without interrup- tion. With the simple lever, it is evident that a weight can be lifted but a little way at a time. 117. The Windlass. In the windlass (Figure 61), a thick axle, or barrel, takes the place of the pinion, and a rope that of the rack. When the crank is turned, the rope is wound upon the barrel, and the weight raised. In one turn of the crank, the rope is wound once round the barrel, * and the weight is raised a dis- tance equal to the circumference of the barrel ; while the Fig. 61. MECHANICS. 79 power at the end of the crank moves through a path like the dotted line in Figure 60. If the power moves ten times the distance the weight moves in the same time, a power of one pound at the end of the crank ought to balance ten pounds of weight hung from the barrel (in). 1 1 8. The Capstan. In the windlass, the longer the crank and the smaller the barrel, the greater the gain of power. If, however, the barrel be made very small, it will not be strong enough ; while if the crank be made very long, it cannot be conveniently turned with the hand. But instead of one crank there may be a num- ber of spokes ; and, if the barrel be placed upright, a man may pull upon one spoke after another as they come within Ijis reach, and thus turn the barrel, or several men may 'walk round it, pushing against the spokes. Such an upright windlass, with long spokes, is called a capstan, and is much used on board ships. Sometimes the capstan (Figure 62) is arranged with a single long arm, to which a horse can be harnessed. Fig. 62. 119. The Wheel and Axle. This machine is simply a wheel with a thick axle, like the barrel of the wind- 8o MECHANICS. Fig. 63. lass. The wheel takes the place of the crank of the windlass, or the spokes of the capstan. Power is applied to the wheel, either by means of pegs upon its rim, as in Figure 63, or by means of a rope- or band, as in Figure 64. Suppose that the circumference of the wheel is eight times that of the axle. If we hang a weight of one pound to the wheel, we must hang a weight of eight pounds to the axle in order to balance it ; and the former will move eight inches, while the latter moves one (in). 120. The Ratchet. The ratchet is an arrangement to keep the 'wheel from turning except in one direc- tion. It consists of a catch c (Figure 64), which plays Fig. 6* into the teeth of the wheel A B. It thus allows the wheel to turn to the left, but keeps the weight from pulling it back towards the right. 121. Wheel-work. In the wheel and axle, the larger the wheel and the smaller the axle, the greater the gain of power. But, as has already been said (118), if the barrel be made very small, it may not be strong enough ; and, on the other hand, if the wheel be made very large, it will be too heavy and take up too much room. Instead of using such a large wheel, we may have several wheels and axles acting upon one another, like the levers in the compound lever (113). Such a combination, or train, of wheels and axles is often called wheel-work. The power is applied to the circumference of the first wheel, and the weight is hung to the axle of the last wheel. Sometimes one wheel turns the other by rubbing MECHANICS. Fig. 65. against it, or by friction. The most common way, however, is by means of teeth or cogs on the surfaces of the wheels and axles, as shown in Figure 65. If the teeth project from the side of Fig the wheel, as in Figure 66, it is called a crown-wheel. If their edges are sloped, as in Figure 67, the wheel is called a bevel-wheel. Again, the wheels and axles may be made to act upon one another by means of a belt, or band, passing over them both. Fig. 67. J MECHANICS. They may thus be at any distance apart, and may turn either the same way or contrary ways, according as the belt does or does not cross between them. THE PULLEY. 122. In Figure 68, we have a fixed ring through which passes a cord with a weight hung to it. By pulling down the cord at P, the weight is drawn up. It is often desirable thus to change the direction of the power. Fig. 68. if we use a r i n g f or this purpose, much of the power will be wasted by the friction, or rubbing, of the rope against the ring. We may get rid of much of this friction by using, instead of the ring, a pulley. This is simply a 'wheel 'with a grooved rim to keep the cord in place. There would be no gain in power by the use of the Fig. 69. MECHANICS. 83 pulley. It is evident that one pound on one side of the wheel would balance just one pound on the other side ; and that if the former were drawn down one inch, the latter would be drawn up just one inch. A very common use of the pulley in changing the direction of the power is illustrated in Figure 69. 123. Fixed and Movable Pulleys. In Figure 70, the frame of the pulley D C is fastened to the ceiling ; the frame of the pulley AB rises as the Fig. 7 o. rope P is drawn down. A pulley like D C is called a fixed pulley; one like A B, a movable pulley. The frame of the pulley is often called the block. 124. The Law of the Pulley. In the combination, or system, of pulleys in Fig- ure 70, it is evident that the rope must have the same tension, or strain upon it, from one end to the other. This fact, namely, that a cord when stretched must have the same strain upon it through- out its length, is called the law of the pulley. 125. Systems of Pulleys with one Rope. In Figure 70, the tension or strain of the rope is equal to the power P, since it balances the power. If a weight of one pound is hung to the rope at P, there will be a strain of one pound on the part of the rope on that side of the pulley. There must then be a strain of one pound upon the part of the rope between A and D, and a strain of one pound between 3 and H. These two tensions, AD and B H, will evidently sustain a weight of two pounds at W. In this system of pulleys, then, a power of one pound balances a weight of two pounds. But here, as in every other machine (m) 5 what is gained in power is lost in speed. If the power P is drawn down one foot, the weight W will rise only half a foot ; for of the one foot added to the length of 8 4 MECHANICS. one-half will be taken from AD and one-half from B H. In the system of pulleys shown in Figure 71, we see that one pound at P will balance three pounds at W, Fig. 71. since each of the three parts of the rope on that side of the pulley C has a tension of one pound. But P must be drawn down three feet in order to raise W one foot. In Figure 72, we have a system of pulleys in which the weight is four times the power; and in this case the power evidently moves four times as far as the weight. 126. Systems of Pulleys 'with more than one Rope. Figure 73 represents a system of pulleys, in which two ropes are used. Here a weight of four pounds is balanced by a power of one pound. The parts of the rope A D and A B must each have a tension equal to the power. The rope A C B balances the two tensions, B P and B A, and must therefore have a tension of twice the power. The three tensions supporting the pulley A amount therefore to four times the power. MECHANICS. In the system shown in Figure 74, four ropes are used. The tensions of the several ropes will be readily under- Fig. 73. Fig. 74. stood from the numbers. In this case, the power is doubled by each movable pulley which is added. THE INCLINED PLANE. 127. When a heavy cask is to be raised into a cart or dray, a ladder is often used. One end of the ladder is placed upon the cart behind and the other end upon the ground, and the cask is rolled up the inclined surface thus formed. One man may thus raise a load of several hundred weight with comparative ease. An inclined surface used in this way is called an inclined plane. We often see inclined planes on a large scale in roads. 128. The Law of the In- Fig 7S dined Plane the same as that of other Machines. In Figure 75, we have an inclined plane. W is the weight, which is balanced by the power P. B C is the height of the inclined 86 MECHANICS. plane, and A C is its length. It is evident that the power must descend a distance equal to the length of the inclined plane, in order to raise the weight a distance equal to its height. Now it is found on trial that, if the length of the inclined plane is sixteen feet, and its height four feet, a power of one pound will balance four pounds of weight. But one multiplied by sixteen equals four multiplied by four; that is, the power multiplied by the distance through 'which it acts equals the weight multiplied by the distance through which it is raised. It follows from the above, that the greater the length of the inclined plane, compared with its height, the less the force necessary to raise a weight, and the slower the weight rises. THE WEDGE. 129. Instead of lifting a weight by moving it along an inclined plane, we may do the same thing by push- ing the inclined plane under the weight. When thus used, the movable inclined plane is called the wedge. A wedge which is used for splitting wood has p. 6 usually the form of a double inclined plane, as in Figure 76. 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. 130. Uses of the Wedge. ^ 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 upright again by driving wedges under that side. So, too, ships are often raised in docks by driving wedges under MECHANICS. Fig. 77. their keels. Cutting and piercing instruments, such as razors, knives, chisels, awls, pins, needles, a.nd the like, are different forms of wedges. THE SCREW. 131. The screw (Figure 77) is a movable inclined plane, in which the inclined surface winds round a cylinder. The cylinder is the body of the screw, and the in- clined surface is its thread. The screw usually turns in a block N, called the nut. Within the nut there are threads exactly corresponding to those on the screw. The threads of the screw move between those of the nut. The power is usually applied 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. 132. The Endless Screw. In Fig- ure 78, the thread of the screw works between the teeth of the wheel, and turns it. Since as fast as the teeth at the left escape from the screw those on the right come up to it, the screw acts on the wheel continually ; hence the name of the machine. Fig. 78. SUMMARY. A machine is a contrivance by which force is made to do work. In a machine there is no real gain of force, but a force may be changed in direction, and a small force 88 MECHANICS. acting through a great distance may be converted into a large force acting through a small distance, or a large force acting through a small distance converted into a small force acting through a great distance. (109, in.) The first simple machine is the lever. There are three kinds of levers, depending upon the relative position of the weight, the fulcrum, and the power. (109.) In every machine, the power and weight will balance each other when the power multiplied by the distance which it moves is equal to the weight multiplied by the distance which it moves in the same time, (m.) A compound lever is a machine in which two or more simple levers are combined. (113.) The rack and pinion is a lever whose short arm is multiplied in the pinion. (116.) In the windlass, the barrel and the rope take the place of the pinion and the rack. (117.) In the wheel and axle, the long arm of the lever is mul- tiplied as well as the short one. (119.) Several wheels are often combined so as to act upon one another. The wheels may be made to act upon one another by means of cogs, or by means of belts.} (121.) The direction in which a force acts may be changed by means of a single fixed pulley. (122.) In a system of pulleys, the mechanical advantage de- pends upon the fact that a stretched rope will have the same tension throughout its whole length. (124.) The fourth simple machine is the inclined plane. The fifth simple machine is the wedge. This is really a movable inclined plane which is pushed under the weight to be raised. (129.) The sixth simple machine is the screw. This is also a movable inclined plane arranged round a cylinder. (131.) MECHANICS. WATER POWER. 8 9 Fig. 79- J 33' Water Wheels. An important source of me- chanical power is falling water. The falling or run- ning water is made to turn a wheel, called a 'water wheel, and this wheel is made to drive machinery. Water wheels are of various forms. Some turn on an upright axis, and others on a horizontal axis. The latter are called vertical water wheels ; and the former, horizontal water wheels. 134. Vertical Water Wheels. One of the most common forms of vertical water wheels is the breast- wheel, represented in Figure 79. It consists of a series of boxes, or buckets, arranged on 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 constructed that they hold the water as long as possible while they are going down, but al- low it all to run out be- fore they begin to rise on the other side. 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. The undershot wheel has boards projecting from its circumference, 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. 9O MECHANICS. Fi 135. Barkers Mill. In Figure 80, we have a hol- low upright cylinder, with two horizontal arms at the bottom, and turning on an axis. The cylinder is open at the top, but closed below, except that it has two holes on opposite sides of the arms near the end, as shown in the figure. If water be poured in at the top, the cylinder begins to turn round, and will continue to turn as long as the supply of water 1S k 6 ?* U P* ^ tne holes in the arms are stopped up, the cylinder ceases to move. This apparatus is known as Barker's mill. Its action is easily understood when we recollect that liquids press equally in all directions (56). If the holes in the arms are plugged up, the water presses forward against the plug ; and it presses backward against the opposite part of the arm with an equal force, so that there will be no motion. If now we remove the plug, there will be no pressure against that part of the arm to balance the backward pressure against the opposite side ; and the arm consequently turns backward. As the holes in the arms are gn oppo- site sides of the tube, the backward pressure on each arm tends to turn the cylinder in the same direction. Fi s- 8l - This machine gains in power by curving the arms (Figure 81) ; for the water is thus made to press more powerfully against the bend of the arm as it flows through the tube. 136. The Turbine Wheel. The power of Barker's mill would evidently be increased by increasing the num- ber of the arms. Instead of these arms we might have curved partitions placed between two flat disks, forming a wheel (Figure 82). MECHANICS. 91 Suppose now that the wheel were cut round where the dotted circle is seen in the figure, and that the outer part were arranged to turn round freely while the central part was kept stationary. If water were poured into the wheel from above, the outer part would of course turn round just as the whole wheel did before it was cut. For the action of the water against the partitions would evidently be the same as before, and it was this action which turned the wheel. The central partitions may be so curved that the water will strike the outer partitions nearly at right angles. The direct force of the current is thus very much in- creased, and may become far greater than the reactionary force already explained. This is the arrangement in the turbine wheel^ the most efficient water wheel yet devised. STEAM POWER. 137. The Steam Engine. The elastic force of con- fined steam (71, 82) can be made to work a piston. The steam coming from the boiler by the tube x (Figure 83) passes into the box d. From this box two pipes, a and , carry the steam, one above and the other below, the piston. A sliding valve y is so arranged that it always closes one of these pipes. 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 through the pipes a and O. The sliding valve is connected by mea'ns of the rod i with the crank of the engine, so. that it moves up and 9 2 MECHANICS. 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 position shown in the Fig. 83. left-hand figure. The steam now passes into the cylinder above the piston through the pipe a and forces the 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. This kind of motion is called reciprocating motion. Fig. 84. In using the engine for doing work, it is generally necessary to change this reciprocating motion into a rotary one ; that is, to MECHANICS. 93 make the piston, as it moves up and down, turn a wheel. This is usually done by means of a crank. The crank is sometimes connected with the piston-rod directly, the cyl- inder being placed either horizontally, as shown in Figure 84, or upright, as in the engine represented in Figure 86. In other cases, the piston-rod turns the crank by means of a ivalking- beam, the arrangement and action of ~ J which will be evident from Figure 85. The walking- beam is much used for large engines, especially on steamboats. In Figure 86, we have a picture of a small stationary steam-engine, which shows how the parts of the ma- chine already described are put together, and also illus- trates those parts which have not yet been mentioned. On the right is the cylinder P, which is supplied with steam from the boiler by the pipe x. TJie waste steam is carried away by the pipe L. Within the cylinder is the piston moving up and down as explained above. The piston-rod A moves the crank M, and thus turns the axle D, which may be connected with the machinery to be driven, by means of a belt X, as here, or by a train of wheels, or in various other ways. J^> is a pump, like that shown in Figure 45, which supplies the boiler with water, through the pipe R. It is worked by the engine itself by means of the rod g and the cam, or eccentric, E. 138. The Governor. The governor is a contrivance by which the engine regulates its own speed, so that it may not be too suddenly quickened or retarded by vari- ations in the work to be done. It consists of two arms, k r (Figure 86), carrying heavy iron balls, m, n, at one end, and attached by joints at the other end to the rod c. The whole is made to rotate by means of the bevel-wheels a 94 MECHANICS. and b (121), which are turned by the engine itself. If the speed of the engine is quickened, the governor rotates Fig. 86. MECHANICS. 95 faster, and the arms and balls tend to separate more and more ; just as two balls hung side by side will do when the strings by which they are held are twirled by the hand. As the arms spread out, they raise the ring r, which slides freely on the rod c; and as r rises, it acts upon the levers s, /, and O, which partially close a valve in the pipe x. This valve is seen at v in Figure 83. The supply of steam from the boiler is thus diminished, and the speed of the engine is retarded. The governor now rotates less rapidly, the arms drop a little, the ring r slides down, the valve in x is opened a little more, let- ting steam pass to the cylinder more freely, and the speed of the engine is quickened again. Thus any ten- dency to go faster or slower corrects itself very promptly ; and the engine runs at almost exactly the same speed, however much the resistance may vary. 139. The Fly -Wheel. As the crank turns round, it will be seen that there are two points where the pis- ton-rod is pushing exactly in the direction of the point round which the crank moves ; and that at these points it does not tend to turn the crank at all. There must therefore be some means of carrying the crank past these dead points, as they are called. This is the office of the fly-ivheel V, a heavy iron wheel attached to the axle D. The great momentum (99) of this heavy mass tends to carry the axle round with a uniform motion, notwith- standing the variations in the power acting upon it. 140. High Pressure and Loiv Pressure Engines. When the steam, after doing its work in the cylinder, is carried into a cold chamber, the engine is said to be of low pressure; when it is forced out into the air, the engine is said to be of high pressure. In the former case, the steam is condensed into 'water in the cold chamber, and a vacuum is thus formed behind the piston. In the latter case, the piston has to act against 96 MECHANICS. the pressure of the atmosphere, which, as we have learned (74), is equivalent to a weight of 15 pounds on each square inch of its surface. It is evident that a greater pressure of steam will be necessary to move the piston in the latter case. 141. The Boiler. In the boiler, the steam is pro~ duced, and confined until it is used in moving the piston. Boilers are usually made of plates of wrought iron or copper riveted together. Copper is the best material, but iron is generally used on account of its cheapness. In order to get the full effect of the fire, the hot gas and smoke from it are usually made to pass through Jlues or tubes in the body of the boiler; and the water comes directly in contact with these flues or tubes. This is illustrated in the Cornish boiler, as it is called, shown in Figure 87, and considered one of the best forms of Fig. 8 7 . boiler. It is a cylinder, frequently more than forty feet long, and from five to seven feet in diameter, with two cylindrical flues, B B, extending its whole length. These flues serve as the fur- nace in which the fire is built. The hot gas and smoke, after passing through the flues, circulate round the out- side of the boiler before escaping into the chimney. Figure 88 represents the usual form of the boiler of a locomotive engine. The furnace, or Jire-box, A, is with- in the boiler, and is surrounded by water except beneath and at the door D. A large number of stout tubes extend from the fire-box through the boiler to the smoke-box 1$. The hot gases and smoke pass through these before they escape into the chimney. E is the steam-dome, from the top of which a large tube conveys the steam into the MECHANICS. 97 chamber F, from which it passes by tubes on each side to the cylinders. The waste steam from the cylinders Fig. 88. passes into the chimney through two pipes meeting at K, and thus increases the draught of the furnace. 142. The Locomotive Engine. This machine is shown in full in Figure 89. The boiler XX has just been described. D is the fire-box ; Y, the smoke-box ; # , the tubes connecting the two ; 0, the door for putting in fuel ; H, the vent-cock, by which the water can be drawn off from the boiler ; R R, the feeders which con- duct water from the tender to two force-pumps (not seen in the figure) by which it is forced into the boiler. At i are the safety-valves, kept down by spiral springs in the cases e. When the pressure of steam in the boiler becomes too great for safety, the valves open and, by allowing a part of the steam to escape, reduce the pres- sure, g is the steam-whistle; G, a rod which controls the valve /, by which steam is let into the steam-pipe A. The engineer is represented as holding in his hand the lever by which this valve is opened more or less, to regulate the speed of the engine. The steam-tube A passes through the boiler, as shown by the dotted lines, into the smoke-box, where it branches off to the two cylinders. In this engine there is no chamber, like that 7 MECHANICS. marked F, in Figure '88. One of the cylinders is seen at F, laid open to show the piston P. The sliding valve rig. 8 9 . MECHANICS. 99 by which- the steam is admitted to the cylinder is pre- cisely like the one figured and described above (137) ; but, being behind F under the boiler, it does not appear here. E is the pipe by which the waste steam is dis- charged into the smoke-pipe J^. K is the connecting- rod, by means of which the piston turns the crank M on the axle of the driving-wheels. In starting the engine, the valves must be moved by hand. This is done by means of the lever J3 and the rod C. 1 1 are stop-cocks, through which any water condensed in the cylinders can be driven out ; v, the rod for opening these cocks. The locomotive is always a high pressure engine. SUMMARY. The downward and lateral pressure of water is a source of mechanical power. (133.) The downward pressure of water is made to turn a vertical water wheel. ( 1 34. ) The lateral pressure of water is made to turn a hori- zontal or reaction water wheel. The turbine wheel is a reaction wheel, and the most efficient water wheel known. (135, 136.) The elastic force of steam is used as a source of mechanical power in the steam engine. (137-) The essential parts of the steam engine are the boiler, in which the steam is generated ; the cylinder, in which the expansive force of the steam is made to work a piston ; and the crank, by which the motion of the piston is made to turn a shaft, (141? I37-) In the low pressure engine, a vacuum is formed be- hind the piston by condensing the steam which has been used ; in the high pressure engine, this steam is forced out against the pressure of the air. (140.) SOUND. NATURE AND PROPAGATION OF SOUND. 143. A Sounding Body is a Vibrating Body. If a glass bell-jar held by the knob be struck with the knuckle, it gives out a sound. If a bit of metal, ivory, or other hard substance be placed within the bell, as seen in Figure 90, it is tossed up and down rapidly, showing that the bell is vibrating. Fig. 90. Every body vibrates while giving out sound^ and it is only by causing a body to vibrate that it can be made to give out sound. 144. Sound will not pass through a Vacuum. In Figure 91, the bell B is suspended by silk threads under the receiver of the air-pump. The bell is struck by means of clock-work, set in motion by the sliding rod r. If the bell be struck before exhausting the air, it can be distinctly heard ; but as the air is exhausted, the sound becomes fainter and fainter, until at last it can hardly be perceived even with the ear close to the receiver. Sound, then, cannot pass through a vacuum. SOUND. 101 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. 145. Sound passes through all Gases. If hydrogen or any other gas be now al- lowed to pass into the re- ceiver, the sound of the bell will be heard again. 146. Sound passes through Liquids and Solids. If a bell be 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 be 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 liquids and solids. A slight scratch upon the iron rail, which could not be heard at all through the air, is heard distinctly when the ear is placed against the rail ; showing that the solid transmits the sound better than the air. If the ear be placed near the ground, the tramp of horses or the tread of men can be heard at a great distance, the sound being conveyed by the solid earth. A vibrating body throws the molecules of air, or other elastic medium around it, into vibration, and these vibrations are sent on from molecule to mole- cule until they reach the ear. IO2 SOUND. 147. The Intensity of Sound depends upon the Amplitude of the Vibrations. If the bell-jar in Figure 90 be struck lightly, it will give out a faint sound, and the bit of metal will be but slightly agitated ; if it be struck a harder blow, it will give out a louder sound, and the metal will be more violently agitated. It is evident that in the latter case the bell-jar moves backward and forward through a greater space than in the former ; in other words, that the amplitude of its vibrations is greater. The intensity, or loudness, of sound, then, depends upon the amplitude of the vibra- tions of the sounding body. 148. The Intensity of Sound diminishes as the Square of the Distance of the Sounding Body in- creases. If we place a bell ten yards off, and four bells of the same size twenty yards off, we shall find that the sound of the one bell will be just equal to that of the four bells. At the distance of thirty yards, nine bells would be necessary to produce a sound equal to that of the one bell at ten yards. Sound, then, dimin- ishes in intensity as the square of the distance from the sounding body increases. 149. Speaking -Tubes. If the sound is prevented from spreading in all directions, it loses 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 three-quarters of a mile off. The sides of the pipe kept the sound from spreading. Conversa- tion can be carried on between distant parts of a large building by means of small tubes, called speaking- tubes. 150. Sound travels through the Air at the Rate of i ,090 Feet a Second. The velocity of sound in air has been several times determined by experiment. In 1822, the French Board of Longitude chose two heights near SOUND. I0 3 Paris, and from the top of each fired a cannon at inter- vals of ten minutes during the night. The time between seeing the flash and hearing the report was carefully noted at both stations, and the average of the results showed that sound travels through the air at the rate of 1,090 feet a second. In such experiments, the time taken by the light to pass between the stations is too small to be perceived. 151. The Velocity of Sound in Water is about 4,700 Feet a Second. This was determined at the Lake of Geneva, in 1826, by Colladon and Sturm. They found that, when a bell was struck under water on one side of the lake, the sound could be distinctly heard at a distance of nine miles on the other side by putting the ear to one end of a tube whose other end was in the water. It was thus found that the velocity of sound in water is about ^floofeet a second. 152. Sound travels through Solids faster than through Air. It is found by the experiment with the iron rail mentioned above (146) that the velocity of sound in a solid body is greater than in the air. 153. Sound is rejlected on meeting a new Medium. Experiments show that when sound meets a new medium, it is reflected ; and that, as in reflected motion (102), the angle of reflection is equal to the angle of incidence. -^y^ 154. Echoed When there is a sufficient interval between the direct and the reflected sound, we hear the latter as an echo. The reflected sound has the same velocity as the direct sound, so that the echo of a pistol- shot from the face of a cliff 1,090 feet distant is heard two seconds after the explosion. An echo in Woodstock Park repeats seventeen syllables by day, and twenty by night ; one on the banks of the Lago del Lupo, above the fall of Terni, repeats fifteen. 104 SOUND. In the whispering gallery of St. Paul's, the faintest sound is conveyed from one side of the dome to the other, but is not heard at any point between. At Carisbrook Castle, in the Isle of Wight, is a well, 210 feet deep and 12 wide, lined with smooth masonry. When a pin is dropped into the well, it is distinctly heard to strike the water. In some cases, the sound is reflected several times, and a succession of echoes is heard, each feebler than the pre- ceding, since a part of the sound is lost at each reflection. Sounds are also reflected from the clouds. When the sky is clear, the report of a cannon on an open plain is short and sharp ; while a cloud is sufficient to produce an echo like the rolling of distant thunder. A feeble echo also occurs when sound passes from one mass of air to another of different density. SUMMARY. Sound originates in a vibrating body. (143.) It is not propagated through a vacuum. (144.) It is propagated through all elastic substances, whether gases, liquids, or solids, by vibrations of their molecules. (145, 146.) Its intensity increases with the amplitude of the vibra- tions, and diminishes as the square of the distance from the sounding body increases. (147, 148.) The velocity of sound in air is 1,090 feet a second. (150.) The velocity of sound in water is about 4,700 feet a second. Its velocity in solids is greater than in the air. On meeting a different medium, sound is reflected. (153-) Echoes are due to reflected sound. (i54') SOUND. 105 Fig. 92. MUSICAL SOUNDS. [55. Difference between Noise and Musical Sounds. -In Figure 92, we have an instrument called the gyro- scope, consisting mainly of a heavy brass ring d surround- ing a disk which rests upon a steel axis. To this axis is fastened a small toothed wheel W. If a card c be held against the edge of the wheel when it is spinning rapidly, a very shrill musi- cal sound is produced; as the speed is checked some- what, the sound becomes less shrill. The more the speed is diminished, the less shrill the sound becomes, until finally we hear the separate taps of the teeth against the card. We see, then, that "when the taps are sufficiently frequent, they blend so as to produce one continuous sound, or a musical sound, as it is called. In this experiment, the card is made to vibrate by strik- ing the teeth of the wheel ; and, as the teeth are at equal distances, the vibrations follow one another at equal inter- vals. A musical sound, then, is one in which the vibra- tions recur at regular intervals. If they do not recur at regular intervals, the sound is called a noise. 156. The Pitch of Musical Sounds. We have seen that, the faster the wheel turns, and the more rapid the vibrations of the card, the shriller is the sound, or the IO6 SOUND. higher its pitch. Hence the pitch of musical sounds depends on the rapidity of the vibrations. In musical sounds, as in all other sounds, the loudness depends upon the amplitude of the vibrations. 157. The Tuning-Fork. The tuning-fork (Figure 93) consists of a bar of steel bent into the form of the Fig. 93- letter U, and attached to a standard. A B is a wooden case open at both ends, by which the intensity of the sound produced by the fork is increased. The fork may be set vibrating by striking it, or by drawing a violin bow across it. The elasticity of the steel causes the prongs to vibrate regularly, and thus to give out a musical sound. 158. The Siren. The siren (Figure 94) is an in- strument for producing musical sounds, and at the same time registering the number of vibrations. The disk d e is pierced with holes, and is made to rotate by blowing into the tube t. As it rotates, the holes are alternately opened and closed, so that the air escapes from the cylinder in a regular succession of puffs, giving rise to vibrations, which produce a musical sound. The number of times the disk rotates is registered SOUND. 107 by the apparatus shown in the upper part of the figure. On the axis of the disk is an endless screw s (132), which carries a pair of toothed wheels. These are con- nected with pointers moving over dial- plates on the front of the instrument. The stops m, n, o, p, are used to open or close ;the different sets of holes. 159. The Rate at 'which a Sounding Body vibrates may be determined by means of the Siren. If we force air into the siren with a bellows, the disk is made to rotate faster and faster, and the pitch of the sound produced rises higher and higher, as the force of the blast in- creases. In this way, the siren may be made to produce a sound of the same pitch as that of a tuning-fork, or of any other sounding body ; and, by means of the registering apparatus, the number of vibrations in a second may be ascer- tained. 1 60. The Octave. A sound is the octave of another when it is produced by vibrations twice as rapid. IOS SOUND. 161. The Sonometer. The sonometer (sound meas- urer}, shown in Figure 95, consists of the sounding-board M N, above which the string B B 1 is stretched upon Fig. 95- two movable bridges by means of the weight W. It is used to illustrate the laws of the vibrations of strings. \62. The Rapidity with which a String vibrates is inversely as its Length. Cause the string B B 1 to vibrate by pulling it to one side, or drawing a bow across it, and notice the pitch of the sound. Place one of the movable bridges at the centre of the string, so as to divide it into two equal parts, and cause either part to vibrate. The sound will be the octave (160) of the one given out by the whole string. The half of a string, then, vibrates twice as fast as the whole string, when the tension (or the tightness with which it is stretched) re- mains the same. In the same way, it can be proved that one-third of a string vibrates thrice as fast as the whole ; and so on. While the string is equally stretched, the rapidity of its vibrations is inversely as its length. 163. The formation of Nodes. If we hold a feather against the centre of the wire of the sonometer (Figure SOUND. 109 96), and draw a bow across one-half of it, we get the octave of the note given by the whole string, showing that one-half vibrates by itself. If now a little rider of Fig. 96. red paper be placed across the middle of one part of the string, and the other part be made to vibrate while the feather is still held at the centre, the rider is thrown off; showing that both halves of the string vibrate. These vibrating halves are separated by a node, or stationary point, formed where the feather touches the string. Hold now the feather one-third of the way from the end of the wire (Figure 97), and place a blue rider on Fig. 97- the longer portion of the wire, so as to divide it into two halves, and red ones on the middle of these halves. Now draw the bow across the shorter portion of the no SOUND. wire, and the blue rider will remain at rest and the others be thrown off, as shown in the figure ; showing that the longer portion of the wire has been divided into two vibrating parts separated by a node. In the same way, the wire may be divided into four, five, or any number of vibrating parts separated by nodes. 164. Formation of Nodes in Vibrating Plates. In Figure 98, we have a metallic plate supported at its Fig. 98- centre. If fine sand be sprinkled over the plate, and a bow be drawn across the middle of one edge while the thumb and finger are held against the opposite edge, the sand instantly collects into lines, as seen in the figure ; showing that the vibrating plate is at rest along these lines. The sand has all been tossed away from the vibrating portions between the lines. A. vibrating plate may, then, be broken up into different vibrating parts ; and the lines which separate these parts are called nodal lines. By holding the thumb and finger against different parts of the plate, a great variety of nodal lines may be obtained, all of which may be made visible by means SOUND. Ill of sand, as in the above experiment, nodal forms are shown in Figure 99. Fig. 99- Some of these Nodes may be formed in a similar way in bells, and in all other sounding bodies. 165. Overtones or Harmonics. It is found that, even when a sounding body is made to vibrate as a whole, it always does at the same time vibrate in parts ; so that a vibrating body never gives out a simple tone. The tone given out by a string, or other body, as a whole, is called its fundamental note; the higher tones produced by the vibrations of the parts are called harmonics, or overtones. The tone produced by the halves of a string is called the first harmonic; that produced by the thirds of a string, the second harmonic ; and so on. 112 SOUND. Fig. 100. 1 66. Quality. In every vibrating string, a great number of these higher tones are produced, which, mingling with the fundamental tone, give rise to what is called the quality of the sound. It is this union of high and low tones which enables us to distinguish one musical instrument from another. A flute and a violin, though tuned to the same fundamental note, do not give the same sound. The overtones of the one are different from those of the other; and the mixtures formed by these and the fundamental note are therefore different. 167. Musical Sounds are transmitted through Liquids and Solids. In Figure 100, M is a long tube filled with water, which is placed between the tuning-fork 1? and the sounding-box A JB. If the fork be set vibrat- ing in the air away from the tube, it can scarcely be heard ; but if the foot of it be placed upon the "water in the tube, it can be heard as distinctly as wljen it is placed upon the sounding-box. In both cases, the box is the real sounding body, and is set vibrating by means of the tuning-fork. Musical vi- brations, then, are trans- mitted through the water in the tube. Similar experiments prove that they are transmitted through all liquids. By using a rod of wood in place of the tube, it may SOUND. 1 13 be shown that musical sound is transmitted through solids as well as through liquids and gases.* 1 68. Sympathetic Vibrations. Place two tuning- "' forks which sound the same note, mounted on their boxes, upon the table, 18 inches apart, and draw the bow vigorously across one of them. If now we stop the agitated fork, the sound is weakened, but by no means quenched. The vibrations conveyed through the air and through the 'wood have been taken up by the un- touched fork, and it is this fork which we now hear. Attach a bit of wax to one of the forks, and sound it again ; the very slight change in the rate of vibration has destroyed the sympathy between the two forks, and no response is now possible. Remove the wax, and the un- touched fork responds as before. \ * An experiment first tried by Wheatstone and repeated by Tyndall is very striking. A piano was placed in a room under- neath the lecture-room, separated from the latter by two floors. Through the two floors passed a tin tube 2i inches in diameter, with a wooden rod inside of it, the end of which projected into the lecture-room. The rod was clasped by India-rubber bands which completely closed the tube. The lower end of the rod rested upon the sounding-board of the piano. The piano was played, and no sound was heard in the lecture-room ; but when a violin was placed against the end of the rod, it became musi- cal, not with the vibrations of its own strings, but with those of the piano. On taking away the violin, the music ceased; but when a guitar was put in its place, the sounds were heard again; and also when a sounding-box was substituted for the guitar. The end of the rod was then placed against the sounding-board of a harp, and every note of the piano was reproduced as before. An ordinary music-box may be used instead of the piano in this experiment. f The vibrations may be communicated through the air alone. Every one knows that a piano-string is sometimes set vibrating when the note of the string is sounded by the voice or a flute, even at the other end of the room. 114 SOUND. When a body is thus thrown into vibration by its neighbor, its vibrations are said to be sympathetic. 169. Two Sounds may Interfere so as to destroy each other and produce Silence. There are certain posi- tions in which the sound of one prong of a tuning-fork is wholly destroyed by that of the other. These positions are easily found by making the fork vibrate, and then turning it round before the ear. When the back or the side of a prong is parallel to the ear, the sound is heard ; when the corner of a prong is held toward the ear, the sound is utterly destroyed. This case of interference, as it is called, may be ren- dered more striking by means of a resonant jar (180). In Figure 101, the jar is of such a length as to resound Fig. 101. powerfully to the fork. Rotate the fork above the mouth of the jar. When the back or sides of the prongs face the jar, a loud sound is obtained ; but when the corners of the fork face the jar, there is no sound. When the corner of the fork is over the jar, slide a pasteboard tube over one prong so as to cut off its vibra- tions, and the jar begins to resound. SOUND. 115 1 70. Beats. If two tuning-forks which vibrate nearly at the same rate be made to sound together, the sound, instead of being continuous, rises and falls in quick succession, producing what are called beats. Beats are thus produced 'whenever two musical sounds of nearly the same pitch are uttered together, and the number of beats per second is always equal to the dif- ference between the two rates of vibration. iji. Combination of Musical Sounds. Take two tuning-forks, each of which gives 256 vibrations in a second, and set them vibrating. The two musical sounds flow together in a perfectly blended stream, and produce what is called unison. In this case, the ratio of the vibrations is I : I. Take now two forks, one of which makes 256 vibra- tions a second, and the other 512. For every vibration sent to the ear by the one fork, two vibrations are sent by the other, and the two notes blend harmoniously. This combination, as we have seen, is called an octave (160) ; and the ratio of the vibrations is 1:2. Take another pair of forks, which give 256 and 384 vibrations in a second. The combination of the two sounds is very pleasing to the ear, but the consonance is hardly so perfect as in the case of the octave. The ratio of the vibrations is 2 : 3. This is the most pleasing com- bination next to the octave, and is called a. fifth. If we take two forks whose vibrations are in the ratio 3 : 4, the interval is called a fourth. This combination is still agreeable, but not quite so agreeable as the fifth. Thus, then, with perfect unison the ratio of the vibrations is i : i ; with a note and its octave it is i : 2 ; with a note and its fifth it is 2 : 3 ; and with a note and its fourth it is 3 : 4. The combination of two notes is the more pleasing to the ear, the smaller the two num- bers which express the ratio of their vibrations. Il6 SOUND. Take now two forks whose rates of vibration are in the ratio 4 : 5, or a major third apart ; the harmony is less perfect than in any of the cases which we have examined. With the ratio 5 : 6, or that of a minor third, it is usually less perfect still ; and we now approach a limit beyond which a musical ear will not tolerate the combination of two sounds. If, for example, we sound together two forks whose vibrations are in the ratio of 13 : 14, their combi- nation is altogether discordant. An agreeable combination of two notes is called a chord; a disagreeable one, a discord. SUMMARY. When the vibrations of a sounding body take place at regular intervals and often enough, they give rise to a musical sound. In a noise, the vibrations follow one an- other at irregular intervals. (155.) The pitch of the sound increases with the rapidity of the vibrations. By means of the siren, we may ascer- tain the number of vibrations answering to any given pitch. (156, 159.) Strings, plates, and all sounding bodies may vibrate in parts separated by nodes. (163, 164.) Sounding bodies always vihrate in parts, giving rise to overtones or harmonics; and the blending of these vibra- tions gives to the sound its quality. (165, 166.) Musical sounds are transmitted through solids, liquids, and gases. (167.) A vibrating body may throw another body into sympa- thetic vibration. (168.) Two musical sounds may interfere so as to produce silence. (169.) SOUND. 117 When two musical sounds of nearly the same pitch are sounded together, beats are produced. (170.) When the combination of two notes is agreeable, they form a chord; when it is disagreeable, a discord. The simpler the ratio of the vibrations of two notes, the more agreeable the chord which they form. (171.) MUSICAL INSTRUMENTS. STRINGED INSTRUMENTS. \ J A 172. Stringed Instruments. In stringed instru- ments the sounds are produced by the vibrations of strings or wires. 173. Sounding- Boards. Some kind of a sounding- board is necessary in all stringed instruments. It is not the chords of a piano, or harp, or violin, that throw the air into sonorous vibrations. It is the large surfaces connected with the strings, and the air enclosed by these surfaces. The merit of such instru- ments depends mainly upon the quality and arrange- ment of their sounding-boards. 1 74. Laws of the Vibration of Strings. The first law of the vibration of strings has already been found (162), and is stated thus: The rapidity of the vibra- tions is inversely as the length of the string. 175. The Rapidity with which a String vibrates varies as the Square Root of the Weight which stretches it. If a string be stretched on the sonome- ter (161) with a weight of one pound and made to vibrate, a note of a certain pitch is obtained. If the weight be made four pounds, the pitch will be raised Il8 SOUND. an octave; if sixteen pounds, it will be raised another octave ; and so on. The rapidity of the vibrations, then, varies as the square root of the weight by which the string is stretched. 176. The Rapidity with which a String vibrates varies inversely as its Thickness. If strings of the same material, but of different thickness, be stretched by equal weights, the thicker strings will give the lower notes. If one string is just twice as thick as another, its note will be an octave lower. Other things being equal, the rapidity of the vibrations of a string varies inversely as its thickness. 177. The Rapidity with which a String vibrates is inversely as the Square Root of its Density. If a platinum and an iron wire of the same length and thick- ness be stretched by equal weights, they will not give notes of the same pitch. It is found that the pitch of the sound rises as the square root of the density diminishes. The last two laws, taken together, may be stated thus : The rapidity with which strings vibrate is inversely proportional to the square root of their weight. In one class of stringed instruments, like the violin, violoncello, and guitar, notes of a great variety of pitch are obtained from a few strings by Jingering the strings, so as to change their length. In another class, like the harp and piano-forte, many strings are used, varying in length and thickness, each of which gives but one note. SUMMARY. Musical sounds may be produced by the vibrations of strings, but a sounding-board is necessary to make them audible. (172, I73-) SOUND. 119 The laws of vibrating strings are three in number : (1) The rapidity with which a string vibrates varies inversely as its length. (2) The rapidity with which a string vibrates varies as the square root of the weight which stretches it. (3) The rapidity with which a string vibrates is in- versely as the square Joot of its weight. In some stringed instruments many notes are produced by a few strings ; in others, there are as many strings as there are notes given. (174-177*) WIND INSTRUMENTS. 178. The Longitudinal Vibrations of Rods free at one End. A smooth wooden or metallic rod, with one of its ends fixed in a vice, yields a musical note when rubbed with resined leather. The rod lengthens and shortens in quick succession, or, in other words, is thrown into longitudinal vibration. The pitch of the note increases as the length of the rod diminishes. Figure 102 shows a musical instrument whose notes are produced by the longitudinal Fig. 102. vibrations of wooden rods of dif- ferent lengths. 1 79. Longitudinal Vibrations of Rods free at both Ends. Clasp a long glass tube at its centre with one hand, and rub a wet cloth over one of its halves with the other. A musical sound is produced. A solid glass rod of the same length will give the same note. In this case, the centre of the tube, or rod, is a node (163), and the two halves 120 SOUND. lengthen and shorten in quick succession. In Figure 103, a b is a brass rod held at its centre by the clamp Fig. 103. s; and an ivory ball hung by two strings from the points m and n rests against the end b of the rod. On drawing a piece of resined leather gently over the rod Fig. 104. near # , we throw it into longitudinal vibrations. The centre s is at rest, but the motion of the ivory ball shows that the end b is in a state of tremor. Rub the rod more briskly, and its vibrations become more intense, and the ivory ball is thrown off violently whenever it comes in contact with the end of the rod. If a long glass tube be held at the centre, and one-half of it be rubbed briskly with a wet cloth, the strain upon the glass, caused by the longi- tudinal vibrations, may be sufficient to shiver the other end, as shown in Fig- ure 104. 1 80. Resonance. When a tuning- fork is detached from the sounding-box, and made to vibrate, it can hardly be heard. Let, now, the fork be SOUND. 121 Fig. 105. held over a glass jar AB (Figure 105), some 18 inches deep, and the sound is still very faint. Keep the fork in this position, and pour water with the least possible noise into the jar. As the col- umn of air under the fork becomes shorter, the sound becomes louder ; and when the water has reached a certain level, it bursts forth with great power. Continue to pour water into the jar, and the sound becomes weaker and weaker, until it is as faint as at first. Pour the water care- fully out, and we reach a point where the sound is reinforced again. In this way, we find that there is one particular length of the column of air 'which causes the fork above it to give the loudest possible sound. This reinforcement of sound is called reso- nance.* The columns become shorter as the forks vibrate faster. * "Most travellers in Switzerland have noticed the deafening sound produced by the fall of the Reuss at the Devil's Bridge. The noise of the fall is raised by resonance to the intensity of thunder. The sound heard when a hollow shell is placed close to the ear is a case of resonance. Children think they hear in it the sound of the sea. The noise is really due to the reinforcement of the feeble sounds with which even the stillest air is pervaded. The channel of the ear itself is also 122 SOUND. 181. A Column of Air may be made to vibrate by blowing across the End of a Tube. Select two jars, and two tuning-forks to which they will resound. Make both forks vibrate, and hold them both over one of the jars. Only one of them is heard. Hold them both over the other jar, and the other fork alone is heard. If twenty forks were held over either of these jars, it would select and reinforce the sound of the one to which it naturally resounds. Blow, now, across the open mouth of this same jar, or across the mouth of a glass tube of the same length as the jar, and f of an inch in diameter (Figure 106). Fig. 106. A fluttering of the air, a mere medley of vibra- tions, is thus produced at the mouth of the tube. The tube selects the set of vibrations, or pulse, to which it can resound, and re- inforces it so that it becomes a musical sound. The sound is the same as that produced by the proper tuning-fork held over the tube. The column of air in the tube has, in fact, made its own tuning-fork ; for it has made the air blown across the tube vibrate in uni- son with itself. On blowing across the mouth of a tube of any length, a musical sound is produced ex- actly like that obtained when the proper tuning-fork is held over the tube. 182. The Rate of Vibration of a Column of Air in a Tube is inversely proportional to its Length. Take three tubes, 6, 3, and ij inches long, and blow gently a resonant cavity. When a poker is held by two strings, and when the fingers of the hands holding the poker are thrust into the ears, on striking the poker against a piece of wood a sound is heard *s deep and sonorous as that of a cathedral bell." Tyndatt. SOUND. I2 3 across the mouth of each, so as to bring out its funda- mental note (165). The note of the 3-inch tube will be the octave of the note of the 6-inch tube, and that of the i^-inch tube the octave of that of the 3-inch tube. In other words, the rate of vibration is in- versely proportional to the length of the tube. 183. Vibrations in Open Tubes. The tubes which have been used thus far have been closed at one end. Such tubes are called stopped tubes. We will next examine the vibrations of tubes open at both ends, or open tubes. If we take a stopped tube and an open tube of the same length, and blow gently across the mouth of each so as to get its fundamental note, we find the note of the latter an octave higher than that of Fig. 107. Fig. 108. I 2 4 SOUND. the former. An open tube always yields the octave of the note given by a stopped tube of the same length. 184. Organ- Pipes. Organ-pipes are nothing more than resonant tubes. There are various ways of agitat- ing the air at the mouth of such tubes, so as to set the columns of air within them into vibrations. In one kind of organ-pipes, this is done by blowing a thin sheet of air against a sharp edge. This produces a flutter, some pulse (181) of which is converted into a musical sound by the resonance of the air in the tube. Figures 107 and 108 represent open organ-pipes. The air passes from the bellows through the tube JP into a chamber, which is closed at the top except the narrow slit t. The air compressed in the chamber passes through this slit in a thin sheet, which breaks against the sharp edge , and there produces a flutter. The space between the edge a and the slit below is called the mouth of the pipe. In a stopped organ-pipe, the upper end is closed. Instead of producing a flutter at the mouth of the pipe by a blast of air, \ye may get the same effect by hold- Ing at the mouth of the pipe (Figure 109) a tuning-fork whose vibrations are in uni- son with those of the pipe. Select several pipes of differ- ent lengths, and tuning-forks in unison with each. Begin- ning with the longest pipe, make the fork of lowest pitch vibrate near its mouth. The pipe speaks loudly. Blow in- to the same pipe ; its tone is SOUND. '25 exactly the same as when the fork was held at its mouth. Try each pipe in the same way, and the note which each gives when blown into is exactly that given when the proper fork is at its mouth. If all the forks are held at the same time at the mouth of any one of the pipes, the pipe will select and reinforce the sound of but one. So also the current of air striking against the sharp upper edge of the mouth of the pipe gives rise to a great variety of pulses, from which the pipe selects and reinforces but one. 185. Reed Pipes. A column of air may be made to vibrate by means of a spring of metal, or wood, called a reed. The metal reed commonly used in organ-pipes is shown in Figure no. It consists of a long and flexi- ng, no. ble strip of metal, V V, placed in an opening through which the 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 suc- cession of little puffs. The action of the reed may be illustrated by a com- mon straw. With a penknife raise a strip of the straw near a knot, as shown at r r 1 in Figure in. This strip 126 SOUND. serves as a reed, and the straw as a pipe. Blow into it, and it gives a musical note. Fig. in. s In the horn, trumpet, and similar instruments, the lips of the player take the place of the reed. 1 86. Two Classes of Wind Instruments. In one class of wind instruments, as the flute and fife, a single column of air is made to give a great number of notes, the length of the column being varied by keys. In an- other class, as the organ, there is a pipe for every note. SUMMARY. Longitudinal vibrations may be illustrated by means of rods free at one end or at both ends. (178, 179.) The sound of a tuning-fork is reinforced when it vi- brates over the mouth of a jar of air of a certain depth. This reinforcement of sound is called resonance. (180.) Jars and tubes may be made resonant by blowing across their open mouths, and give the same note as when made to resound by a tuning-fork. The shorter the column of air, the faster it vibrates. (181, 182.) An open tube gives a note which is the octave of a closed tube of the same length. (183.) Organ-pipes are resonant tubes. When open at both ends, they are called open pipes ; when closed at one end, stopped pipes. One kind of organ-pipe is made to resound by blowing a thin sheet of air against a sharp edge at its mouth. (i8 4 .) A column of air may be made to vibrate by means of a reed. The trumpet and many other wind instruments are reed-pipes. (185.) SOUND. SOUNDING FLAMES. 127 Fig. 112. 187. Friction is always Rhyth- mic. When we draw a bow across a string, or rub a wet ringer round the edge of a glass, a musical sound is produced, showing that the fric- tion has been broken up into rhyth- mic pulses. Close the lower end of the tube A B (Figure 112) with a metallic plate, pierced by a round hole whose diameter is equal to the thickness of the plate. Plug the hole, and fill the tube with water. Remove the plug, and, as the water - sinks in the tube, a very sweet musi- cal note is given out by the liquid column. This note is due to the in- termittent flow of the water through the hole, by which the column above is thrown into vibrations. The same intermittence is observed in the dense smoke which rolls in rhythmic rings from the funnel of a steamboat. A rifle-ball sings as it passes through the air. u The whispering pines " owe their music to the rubbing of the wind against their branches and foliage. The whistling of the wind is also produced by the rhythmic friction of the air. If we blow gently against a candle-flame, the fluttering noise announces a rhythmic action. We have learned (184) that a pipe will select a pulse from a flutter, and raise it by resonance to a musical sound. In like manner, the noise of a flame may be converted into a musical note. This is done by enclosing the flame in a tube. 128 SOUND. 1 88. Sensitive Flames within Tubes. Place a tube 12 inches long over a small gas-flame, so that the flame shall be about an inch and a half from trie bottom of the tube. If the note to which the tube would resound be sounded at some distance, the flame is seen to tremble. Lower the tube, so that the flame shall be about three inches from the bottom, and the flame begins to sing. Somewhere between these two points we may find a point where the flame will burn silently ; but if it be excited by the voice, it will sing, and keep on singing. Flames which are thus affected by musical sounds are called sensitive flames. SUMMARY. Friction is always rhythmic. When a gas-flame is surrounded by a tube, the air in passing over it is made to vibrate, and musical sounds are produced. A silent flame within a tube may be made to sing by sounding the note of tfye tube near it. (187, 188.) THE HUMAN VOICE AND EAR. 189. The Organ of Voice is a Reed Instrument. The organ of voice in man is situated at the top of the windpipe, or trathea, which is the tube through which the air is blown from the lungs. A pair of elastic bands, called the vocal chords, stretched across the top of the windpipe, so as nearly to close it, form a double reed. When the air is forced from the lungs through the slit between these chords, they 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. SOUND. I2 9 The action of the vocal chords may be imitated by Fig. n 3 . means of india-rubber bands. If the open end of a glass tube (Figure 113) be closed by two strips of india-rubber, leaving a slit between them, and the air be blown through this slit, the strips are thrown into vibration, and a musical sound is produced. 190. The Human Ear. The external opening of Fig. 114. the ear (Figure 1 14) is closed at the bottom by a mem- brane, called the tympanum. Behind this is the cavity called the drum of the ear. This is separated from the space between it and the brain by a bony partition, in which there are two openings, the one round and the other oval. These also are closed by delicate mem- branes. Across the cavity of the drum stretches a series of four little bones : the first, called the hammer, is at- tached to the tympanum ; the second, called the anvil, 9 I3O SOUND. 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. Behind the bony partition is the labyrinth, which is filled with water, and over the lining of which the fibres of'the auditory nerve are spread. The tympanum receives the vibrations of the air, and transmits them through the series of bones to the mem- brane which separates the drum from the labyrinth ; and thence to the liquid within the labyrinth, which transmits them to the nerves. The nerve transmits the impression to the brain and thus to the mind. 191. The Range of the Human Ear. There must be at least 16 vibrations in a second, in order that they may be heard as a continuous sound (155) ; and the sound ceases to be audible when the vibra- tions reach 38,000 in a second. Starting with 16 and multiplying continually by 2, we find that the nth octave will have 32,768 vibrations. Thus the entire range of the human ear extends to about 1 1 octaves. The practical range of musical sounds is about 7 oc- taves, or from 40 to 4,000 vibrations in a second. SUMMARY. The organ of voice in man is a reed instrument, the vocal chords forming the reed. (189.) The human ear consists of three parts : the outer ear, the drum, and the labyrinth. The sonorous vibra- tions are first intercepted by the tympanum, then trans- mitted to the fluid in the labyrinth, by which they are communicated to the auditory nerve. (190.) The range of human hearing embraces about eleven octaves. (191.) LIGHT PROPAGATION OF LIGHT. RADIATION, REFLECTION, AND REFRACTION. 192. A Luminous Body sends out Light in Every Direction. A body in which light is developed is called a luminous body. All other bodies are said to be non-himinous. If a lighted lamp is placed in the middle of a room, it illumines every part of the room ; showing that the light proceeds from the luminous body in every direction. A body through which light passes, as air and glass, is called transparent. Other bodies are called opaque. 193. Light travels through Space in Straight Lines. If a room be darkened, and the sunlight be allowed to enter through a small hole in the shutter, it will illumine the floating particles of dust in the air Fig. 115. through which it passes, so that we can trace its path ; and in every case we find that it moves in a straight line. I 3 2 LIGHT. An opaque body placed before a luminous one cuts off the light from the space behind it, producing a shadow* If the luminous body S (Figure 115) is a mere point, the body J/will cast a ivell-dejlned shadow G If upon the screen Pjg. If the luminous body S L (Figure 116) is not a mere point, the shadow cast by M N will have an indistinct Fig. 116. outline. The dark central portion G //of the shadow is called the umbra; the less dark outer portion is called the penumbra. Umbra is the Latin word for shadow, while penumbra means almost a shadow. Since a luminous body gives out light in every direc- tion in straight lines, it is said to radiate light. A single line of light is called a ray. A collection of rays is called a pencil. If the rays are parallel, it is a par- allel pencil, or a beam; if the rays diverge, it is a diver- gent pencil ; if they converge, a convergent pencil. 194. The Velocity of Light is about 190,000 Miles a Second. Light moves so fast that it seems to require no time at all to pass over any distance on the earth. Its velocity was first determined by Roemer, a Danish as- tronomer, in 1675, by observing the eclipses of Jupiter's moons. Jupiter, li^e the earth, is a planet which revolves about the sun, but at a much greater distance than the earth. He is accompanied by four moons, which are eclipsed when they pass into his shadow ; and the pre- LIGHT. '33 cise time when these eclipses occur can be calculated by astronomers. Roemer found that the eclipses did not always take place at the computed time, but appeared about sixteen minutes later when the earth was farthest from Jupiter than when she was nearest to him. He therefore concluded that it takes light sixteen minutes to traverse the difference of these distances, which is about 183,000,000 miles. Its velocity, then, would be about 190,000 miles a second, and this agrees very nearly with the velocity as determined by wholly different methods. 195. The Intensity of Light diminishes as the Square of the Distance from the Luminous Body increases. In Figure 117, the disk C D is held half- Fig. u 7 . way between the luminous point L and the screen A B. If the disk be held parallel to the screen, the diameter of the shadow on the screen will be twice that of the disk, and its surface will be four times that of the disk. The disk receives all the light that the space covered by the shadow would receive if the disk were removed. The light on the disk must then be four times as intense as that upon the screen. If the disk be held one-third of the way between L and the screen, the shadow will cover a surface nine times that of the disk, and the intensity of the light on the disk will be nine times as great as that upon the screen ; and so on. The intensity of the light, then, diminishes as the square of the distance increases. 134 LIGHT. 196. Reflection and Refraction. If a ray of sun- light be made to fall upon a looking-glass in a darkened room, it will be seen to be thrown back, or reflected, from the glass. A piece of glass cut into the form shown in Figure 118 is called a prism. Fig. 1 1 8. Fig. 119. If a ray of light, a b, be allowed to fall obliquely upon one side of such a prism, as shown in Figure 119, a part of the light is reflected in the direction b c, and another part, b d, enters the prism. The part which enters the prism is bent from the direction of the original ray. When this part meets the air at the opposite side of the prism, a part of it is again reflected in the direction d e, and a part passes into the air, taking a different direc- tion, df, from that which it had while in the prism. We see, then, that when light travelling in the air meets the glass, it is partly reflected and partly trans- mitted ; and that when light travelling in the glass meets the air again, it is also partly reflected and partly trans- mitted. In both cases, the transmitted portion is turned aside from its course. Light thus turned aside is said to be refracted. In general, when light meets a transparent medium different from that which it has been traversing, it is partly reflected and partly transmitted. The trans- mitted portion, when it enters the medium obliquely, is refracted. LIGHT. 135 197. The Law of Reflection. In Figure 120, we have a mirror L fastened at right angles to the rod m n, Fig. 120. I/ and turning upon a pivot at n. As the mirror is turned to the right or left, the rod passes over the graduated arc a b. If a ray of light be allowed to fall upon the mirror in the direction of the dotted line a n, it will be reflected in the direction of the line n b; and it will be seen that the angle a n m is equal to the angle b n m. The former is called the angle of incidence, and the latter the angle of reflection. If the mirror be turned, the direction of the reflected ray changes in such a way that the angle of incidence always equals the angle of reflection. This is known as the law of reflection. 198. Diffused Light. Since non-luminous bodies are not visible in the dark, but become visible when light falls upon them, they must send to our eyes some of the light they receive. This light must be sent out in every direction, since we can see them as well from one posi- tion as another. The light which they thus throw off is said to be diffused. It is this diffused light which ena- bles us to see the body itself; while reflected light enables us to see another body in it. The most perfectly polished mirror does not reflect all the light it receives. It diffuses a portion, so that we see the mirror as well as the objects reflected in it. i 3 6 LIGHT. Fig. 121. 199. The Law of Refraction. When a ray of light passes obliquely from air into water, it is bent towards a perpendicular drawn to the sur- face of the water. Thus the ray a b (Figure 121) is bent towards the per- pendicular c d, and takes the direction b e after passing into the water. This is found to be always true when the light passes from a rarer to a denser medium. When it passes from a denser to a rarer medium, it is bent away from a per- pendicular drawn to the surface of the latter medium. Fig. 122. & is owing to refraction that a stick placed obliquely in the water appears bent, as in Figure 122. Each part of the stick in the water appears to be lifted up a little by refraction. 200. Total Rejection. When a ray of light passes from a denser to a rarer medium, as from water into air, the angle of refraction is greater than the angle of incidence (199). Hence when light passes through water from S to O (Figure 123), there is always a value of the angle of incidence SOB such that the an- Fig . I23 gle of refraction A O R is a right angle. In this case, the ray cannot pass from the water into the air. If the incident angle be made any larger, the light is thrown back in the direction of jg, and is said to be totally reflected. 201. Mirage. In hot climates, especially on the Sahara in Africa, the ground has often the appearance of a tranquil lake, on which are seen LIGHT. 137 reflected houses and trees. This is caused by total re- flection. The layers of air near the ground are more heated, and therefore less dense than those higher up. A ray of light, then, coming from A (Figure 124) is Fig. 124. bent round more and more as it passes down through the successive layers until it reaches the point 0, where the angle of incidence becomes such that it is totally reflected, and reaches the eye as if it came from B. The same will be true of light coming from other parts of the tree, so that the tree will appear inverted, as if reflected in water. This phenomenon is called mirage, and often deludes the thirsty traveller on the desert with the appearance of water which vanishes as he draws near it. Another form of mirage is often seen on the water. In this case, the layers of air near the water are colder and more dense than those above, so that the rays of light passing upward from an object are bent round more and more, until at last they are totally reflected downward to the eye of the observer, who thus sees the object inverted in the air. 138 LIGHT. 202. Path of Rays through a Medium tvith Parallel Faces. When light passes through a medium with parallel faces, as a pane of common window-glass, the rays leave this medium at the same angle at 'which they entered it. Since the ray in passing into the air is bent away from the perpendicular just as much as it was bent towards it in passing into the glass, the ray leaves the glass at the same angle at which it en- tered it; and its direction, therefore, is unchanged. 203. Path of Rays through a Prism. In Figure 125, Fig. I2S . the ray of light O D on pass- ing into the prism A B C is bent towards a perpendicular drawn to the surface at D. On passing out into the air again, it is bent away from a perpendicular drawn to the surface at K. We see, then, that a ray of light in passing through a prism is bent twice in the same direction j provided it meets neither face at right angles. _ SUMMARY. A luminous body gives out light in every direction, which passes through space in straight lines. A single line of light is called a ray; and a collection of rays, a beam, or pencil. (192, 193.) The velocity of light is about 190,000 miles a second. The intensity of light diminishes as the square of the distance increases. (195.) When light falls on a transparent medium different from that in which it is moving, it is partially reflected LIGHT. 139 and partially transmitted. The transmitted portion, if it meets the medium obliquely, is refracted. (196, 199.) The angle of reflection equals the angle of incidence. (197-) All bodies diffuse light, and it is by means of this diffused light that we see them. (198.) On meeting a rarer medium at a certain angle, light is totally reflected. (200.) Mirage, and other atmospheric phenomena of the kind, are caused by total reflection. (201.) When a ray passes through a medium with parallel sides, it comes out with its direction unchanged. (202.) On passing through a prism, a ray is usually bent twice in the same direction. (203.) DISPERSION, ABSORPTION, INTERFERENCE, AND POLARIZATION. \ 204. The Solar Spectrum. Allow a beam of sun- light, S A (Figure 126) to pass through a small opening Fig. 126. into a darkened room, and fall upon the prism P. If the prism be placed at the proper angle, the beam of 140 LIGHT. light is not only bent from its course, but is spread out so as to form a long band of light on the opposite wall. This band is not white, like ordinary sunlight, but made up of the seven colors of the rainbow, violet, indigo, blue, green, yellow, orange, and red. This colored band is called the solar spectrum, and the colors are often called the prismatic colors. This spreading out of a beam of light is called dispersion; and the power of any substance to pro- duce this effect is called its dispersive power. The dispersive power of a substance is not in proportion to its refractive power. Thus the refractive power of flint-glass is almost the same as that of crown-glass, but its dispersive power is nearly double. 205. Achromatic Prism. By combining a flint-glass prism C D F (Figure 127), with a crown-glass prism Fig. 127. C JB F, the dispersive power of the latter may be neutralized, with- out wholly neutralizing its refract- ive power. The prism CDF, in order to have the same dispersive power as C B F, need be only half as thick as the latter; so that the edges B Cand F D are still inclined as though they were sides of the larger prism A B F. Such a combination of prisms is called an achromatic (colorless} prism, since light passes through it without being separated into the prismatic colors. 206. The Prismatic Colors are Simple. If all the colors of the spectrum except one be cut off by a screen, and that one be made to fall on a second prism (Figure 128), it will be again refracted, but will not be separated into different colors. These colors, then, are simple. 207. The Prismatic Colors are unequally Refrangi- ble. The position of the colors in the spectrum shows LIGHT. that they are not equally refracted. The red is least, and the violet most refracted. Fig. 128. 208. The Composition of White Light. These ex- periments with the prism seem to show that white light is not simple, but made up of the seven prismatic colors. The same may be shown by mixing these colors in the eye. This can be done by painting them in the proper proportions upon a circular disk (Figure 129) and mak- Fig. 129. Fig. 130. ing this disk whirl rapidly, as shown in Figure 130. The impression of each color remains in the eye while the 142 LIGHT. disk turns completely round, so that the seven are blended into one, and the disk appears 'white. If we mix two or more of these colors, we get a tint different from any one of them. Thus red and yellow produce orange ; blue and red, purple ; and so on. In fact, all the varied colors we see are formed by the mixture of the prismatic colors. It is probable that white light is made up of only three simple colors; for if red, green, and blue be mixed, a color is obtained which cannot be distinguished from white. Moreover, all the other prismatic colors can be formed by mixing these three. According to some authorities, red, yellow, and blue are the three simple colors ; but it has been shown that no mixture of these will produce all the prismatic colors. If the spectrum be divided into any two parts, and the colors in each part be mixed, they will form what are called complementary colors ; that is, one will con- tain what the other needs to make white light. 209. Absorption of Light. If light be made to pass through a piece of colored glass, and then to fall upon a prism, the spectrum will be wanting in certain colors. If red glass is used, the spectrum will contain little be- sides red light ; if blue or green glass is used, the spec- trum will be rich in blue or green, and deficient in other colors. A part of the light is retained in the glass, and is said to be absorbed by it. All transparent bodies absorb a portion of the light which falls upon them. If they absorb all colors equally, they appear colorless ; if they absorb some colors more than others, their color will be complementary to what they thus absorb (208). 210. The Color of Bodies. Opaque bodies, as well as transparent ones, absorb light. Hence, when white light is falling upon non-luminous bodies, they do not all appear of the same color. They are really sifting the LIGHT* 143 light which they receive, absorbing a part and reflecting, diffusing, or transmitting the rest. Their color depends upon the light 'which they rejlect or diffuse. Thus a body which absorbs all the prismatic colors except red appears red ; one which absorbs all except green appears green ; and so on. Bodies sometimes transmit a color different from that which they rejlect, and appear of a different color ac- cording as they are seen by transmitted or rejlected light. Gold appears yellow by reflected light, and green by transmitted light, as may be seen by holding a piece of gold-leaf between the eye and the sunshine. 211. Two Rays of Light may Interfere so as to Destroy each other. If a slightly curved piece of glass be pressed down upon a flat plate of glass (Figure 131), colored rings are formed around the centre (Figure 132). Fig. 131. If any homogeneous > (that is, lignt oj one kind}, as red, be used, the rings are red and separated by black spaces. If violet light be used, the rings are violet and smaller. As we pass from the violet end of the spectrum to the red end, the rings grow larger and broader. Hence, when white light is used, we get seven sets of rings, which somewhat over- lap one another. This explains why there are several colors in each ring. The dark rings are caused by the interference of the rays of light which are reflected from the lower surface of the upper glass and the upper sur- face of the lower glass. Hence two rays of light, like two sounds (169), may interfere so as to destroy each other. These colored rings are seen in soap-bubbles, and in all cases where there are two reflecting surfaces very near each other. They are known as Newton's rings^ since he was the first to study them. 144 LIGHT. 212. Diffraction Fringes. Let a beam of sunlight fall upon a small glass lens * in a darkened room. The light will be concentrated into a point a little way from the lens, and will then diverge from it in a luminous cone, and may be received upon a screen. Place any small opaque body within this cone of light, so that it may cast a shadow upon the screen. This shadow, in- stead of being sharply defined, as we should expect (193), is somewhat larger than it should be, and is surrounded by three colored fringes. If homogeneous light (211) is used, instead of the fringes we get bright rings sepa- rated by dark spaces, the breadth of the rings varying with the color of the light. When white light is used, these different sets of colored rings blend so as to produce the fringes. If the opaque body is long and very narrow, as a hair or a very thin strip of card, besides the colored fringes already described, others are seen within the shadow, parallel to its length, and arranged on the two sides of a central white line. When light is transmitted through a very narrow slit, the fringes become even more curious and complicated. These fringes are called diffraction fringes, and are caused by interference. 213. Double Refraction of Light. Figure 133 rep- resents a crystal of Iceland spar (crystallized carbonate Fig. i 33 . of lime). A crystal of this shape is called a rhomb. It has six faces, which are equal parallelograms. If now a ray of light be allowed to fall on one face of this crystal in a darkened room, it will be * The focal length of the lens should be about an inch. LIGHT. 145 doubly refracted, or divided into two rays. One of these rays conforms to the law of ordinary refraction (199), and is therefore called the ordinary ray. The other ray does not conform to this law. It is therefore called the extraordinary ray. Since the opposite faces of the crys- tal are parallel (202), the ordinary and extraordinary rays emerge parallel to the incident ray and to each other, but quite near together. If, however, the crystal be cut into the form of a prism, the ordinary and extraordinary rays, alter leaving the prism, will diverge, so that Fig. 134. we may easily examine them separately. Such a prism may be rendered sufficiently achromatic by combining with it a second prism of glass, whose dispersive power (204, 205) is different from that of the crystal. This prism is usually mounted as shown in Fig- ure 134. 214. The Ordinary and Extraordinary Rays are loth Polarized. Let a beam of ordinary light fall on a double-refracting prism, cut off the extraordinary ray by a screen, and let the ordinary ray fall on a second similar prism. If this second prism be turned round, we find a position in which the ray is refracted singly and ordi- narily, and another position in which it is refracted singly but extraordinarily. Half-way between these two positions, it will be doubly refracted. If the ordinary ray be cut off, and the extraordinary ray be allowed to fall on the second prism, it will be singly or doubly refracted when the prism has been turned round 90 from the position in which the ordinary ray was singly or doubly refracted. In this way, we find that neither of the doubly refracted rays is the same on the right and the left as it is above and below ; in other words, both rays have acquired sides. In this respect, they differ from a ray of ordi- 10 146 LIGHT. nary light, which is doubly refracted in every position of the prism, and is therefore the same on all sides. Light which has thus acquired sides is said to be polarized. The corresponding sides of the two rays are at right angles to each other ; in other words, the extraordinary ray is like the ordinary ray turned round through 90. / SUMMARY. Nkjn passing through a prism, a beam of white light is dispersed, and forms a spectrum of seven colors. Since different substances disperse light differently, two prisms may be combined so as to form an achromatic prism. (204, 205.) Prismatic colors are simple and unequally refrangible. (206, 207.) The blending of the seven prismatic colors produces white light. It is probable that there are but three simple colors, red, green, and blue. Two colors, whose mixture will produce white light, are said to be complementary. (208.) Different bodies absorb light of different colors. It is the sifting of the rays of light by absorption which gives bodies their color. (209, 21 a.) Soap-bubbles and other thin films, when exposed to light, exhibit colored rings. These rings are always seen when light is reflected from two surfaces sepa- rated by a very small interval ; and they are caused by interference. (211.) When small bodies are seen in divergent light, they appear surrounded by colored fringes, called diffraction fringes. These are caused by interference. (212.) When a ray of light passes through a crystal of Ice- LIGHT. land spar, it is doubly refracted; one of the refracted rays being called the ordinary, and the other the ex- traordinary ray. (213.) Both the doubly refracted rays have acquired sides, and are said to be polarized. Their corresponding sides are at right angles to each other. (214.) , OPTICAL INSTRUMENTS. LENSES. 215. Forms of Lenses. Lenses are pieces of glass, r other transparent substance, bounded on one or both sides by a curved surface. The forms of lenses used in optical instruments are shown in Figure 135. Fig. 135- ABC D F A is bounded by two spherical surfaces, and is called a double-convex lens. B has a spherical surface on one side, and a plane surface on the other, and is called a plano-convex lens. C has a convex surface on one side, and a slightly concave surface on the other, and is called a meniscus, from a Greek word meaning a crescent. D has two concave surfaces, and is called a double-concave lens. E has a concave and a plane surface, and is called a plano-concave lens. F has a concave surface on one side and a slightly convex sur- face on the other, and is called a concavo-convex lens. 148 LIGHT. 2 1 6. Convex Lenses cause Parallel Rays to Converge] Concave Lenses cause them to Diverge. Allow a beam of sunlight to fall upon a double-convex lens in a dark- ened room. On leaving the lens, the rays ivill converge to a point, called the focus (the Latin word for fire- place), since the heat as well as the light is concen- trated there. This action of the lens upon the light will be understood from Figure 136. It will be seen Fig. 136. that the lens is somewhat like two prisms placed back to back ; and it will be remembered that a ray of light, in passing through a prism (196), is bent twice in the same direction. The rays falling upon the upper part of the lens will be bent downward, and those falling on the lower part will be bent upward, and they will all meet at F. If a plano-convex lens, or a meniscus, be used, the results will be similar. Parallel rays are made to -meet at the focus of a convex lens. If, on, the other hand, the rays diverge -from the focus, they will become parallel on passing through the lens. If they diverge from a point nearer the lens than the focus is, they will be so divergent on entering the lens that they will not be made parallel on leaving it, but merely less divergent. If they diverge from a point farther off than the focus, they will be so little divergent that they will become convergent on leaving the lens. If, however, we use any one of the concave lenses, LIGHT. I 49 it will be found that the rays of light, instead of con- verging, are made to diverge, F i g I37 on leaving the lens ; as shown in Figure 137. Since the convex lenses all cause parallel rays to con- verge, they are called converg- ing lenses ; while the concave lenses are called diverging lenses, since they cause parallel rays to diverge. 217. Images formed by Lenses. Place a lighted candle before a double-convex lens in a darkened room, and a screen behind it. At a certain distance from the lens, a distinct inverted image of the candle will be formed upon the screen. Move the candle nearer the lens, and the image will become blurred, but will be- come distinct again on moving the screen farther from the lens. If the candle be moved away from the lens, the image becomes blurred ; but it becomes distinct again when the screen is brought nearer the lens. The nearer the candle is to the lens, the larger the image formed. The more convex the lens used, the nearer the candle must be brought to it, and the larger the image. Fig. 138. i Instead of using a more convex lens, we may add a second convex lens, with the same effect. I5O LIGHT. An image is formed behind a lens because the rays which diverge from every point of an object are made to converge, on passing through the lens, so as to meet at corresponding points behind the lens ; as shown in Figure 138. The image is always included between liries drawn from the extremities of the object through the centre of the lens. SUMMARY. There are two classes of lenses. One class causes parallel rays to converge, and the other causes them to diverge. (215, 216.) When objects are placed in front of a converging lens, images of them are formed at its focus behind it. The magnitude of the image increases with its dis- tance from the lens, and also with the convexity of the lens. (217.) THE EYE. 218. The Camera Obscura. If a converging lens be placed before an opening in the shutter of a darkened room, a small and beautiful picture of the landscape will be seen upon a screen placed a short distance be- hind the lens. An arrangement of this kind is called a camera obscura (Latin for a dark chamber). Figure 139 represents the camera used by photog- raphers. C is a dark chamber ; E is the screen of ground glass upon which the image is received; A is a tube containing the combination of lenses used to form the image. This camera can be adjusted to objects at dif- ferent distances by changing the position of the screen, or of the lenses (which may be moved by the screw /?), or both. LIGHT. 15* 219. The Eye is a Camera. The eyeball is com- posed, in the first place, of a tough, firm, spherical case, Fig. 139- Scl (Figure 140). The greater part of this case is white and opaque, and is called the sclerotic coat, or Fig. 140. M.I. the white of the eye. In front this case becomes trans- 152 LIGHT. parent and more convex, and is called the cornea, Cn. This case of the eye is kept in shape by being filled with fluids called the humors. The aqueous humor, Aq, fills the corneal chamber ; and the vitreous humor, Vt, the sclerotic chamber. Between these chambers is the double-convex crystalline lens, Cry, which is denser, and has a greater refractive power than either humor. The choroid coat, Ch, is of a dark color and highly vas- cular (that is, full of vessels}, and it lines the whole inner chamber of the eye. At the front part of the chamber, its inner surface becomes raised into ridges, called the ciliary processes, C. p. The iris, Ir, is a curtain with a round hole in the middle called the pupil. The iris has two sets of muscular fibres, by the action of which the pupil is enlarged or contracted. It gives the color to the eye ; and hence its name, iris being the Latin for rainbow. The optic nerve, Op, enters the back of the eye a lit- tle way from the centre towards the nose. It then spre'ads out over the choroid coat, forming the retina, Rt. The eyeball is thus seen to be a camera obscura. In an ordinary camera, a screen, or diaphragm, is used to moderate the light, and to cut off all the rays except those which fall on the central part of the lens. In the eye, the iris acts as a diaphragm, and has the advantage of being self -regulating. It dilates the pupil and admits more light when the illumination is too weak ; it contracts the pupil, and cuts off a part of the light when there is too much of it. 220. The Adjustment of the Eye. That the eye must adjust itself in order to see distinctly at different distances, may be shown by a very simple experiment. Stick two stout needles into a piece of wood, so that one of them shall be about six inches from the eye, and the other about twelve, very nearly in the same LIGHT. 153 direction. If now you look at one needle, you will see it distinctly and without the least sense of effort; but the image of the other will be blurred. Try now to make this blurred image distinct, and you find that you can do it, but not without effort. In proportion as one image becomes distinct, the other becomes blurred, and no effort 'will enable you to see both distinctly at the same time. When a lighted taper is held near, and a little to one side of a person's eye, any one, on looking into the eye from the proper position, will see three images of the flame ; one reflected from the cornea, one from the front surface of the crystalline lens, and one from its rear surface. Suppose, now, the person's eye be steadily fixed on a distant object, and then adjusted to a nearer one in the same direction. The position of the eyeball, of course, remains the same. It is also found that the images reflected from the cornea and from the rear surface of the lens, remain unchanged ; while the image reflected from the front surface of the lens changes its position and its size Fi gt I4I . in such a way as to show that this surface has been brought forward and at the same time made more convex. The eye then adjusts itself to different dis- tances by altering the convexity of the crystalline lens. This change in the form of the lens is shown in Figure 141. The half A shows the form of the lens when the eye is adjusted for distant objects ; and the half B, when it is adjusted for near objects. 221. The Structure of the Retina. Figure 142 rep- resents a portion of the retina highly magnified, since LIGHT. Fig. 142. th e w hole thickness of this membrane does not exceed -^ of an inch. Next to the choroid coat it consists of a great number of minute rod-like and conical bodies, e, arranged side by side. This is the layer of rods and cones. The fibres of the optic nerve are all spread out between b and a. At the entrance of the optic nerve, the nerve fibres predominate, and the rods and cones are wanting. Exactly at the centre of the back of the eye, there is a slight circular depression of a yellowish hue, called the macula lutea, or yellow spot. In this spot, the cones are abundant without the rods and nerve fibres. , 222. The Action of Light on the Optic Nerve. The fibres of the optic nerve are in themselves as blind as any other part of the body. To prove this, we have only to close the left eye and with the right look steadily at the cross on this page, holding the book ten or twelve inches from the eye. The black dot will be seen quite plainly as well as the cross. Now move the book slowly towards the eye, which should be kept fixed on the cross. At a certain distance the dot will suddenly disappear ; but on bringing the book still nearer it will come into view again. Now it is found, that, when the dot disappears its image falls exactly upon the point where the optic nerve enters the eye, and whe^e there are no rods and cones, but merely nerve fibres. Again, the yellow spot is the most sensitive part of the retina, though it contains no nerve fibres. LIGHT. 155 It would appear, then, that the optic nerve is not directly affected by light, but only through the rods and cones. These remarkable bodies are like so many finger-points, endowed^ with a touch delicate enough to feel the impulses of light and communicate the impres- sion to the optic nerve. 223. The Sensation of Light may be excited by Other Causes. The sensation of light may be excited by any thing which can excite the optic nerve. Thus an electric shock sent through the eye causes an apparent flash of light. If the finger be pressed on one side of the eyeball, a luminous image is seen. In the same way, a blow on the head may make one " see stars." 224. The Duration of the Impression on the Retina. The impression made by light on the retina does not cease the instant the light is removed, but lasts about the eighth of a second. If the impressions are separated by a less interval, they appear continuous. Thus, if a stick with a spark of fire at the end be whirled round rapidly, it gives the impression of a circle of light. The spokes of a wheel in rapid motion cannot be distinguished. The optical toy called the thaumatrope illustrates the same principle. One form of it, known as the zoetrope, consists (Figure 143) of a cylindrical FJ paper box turning on an upright axis. Near the top of the box is a row of upright slits. The successive positions which a moving body assumes are rep- resented in order upon a strip of pa- per ; and this paper is put within the box, which is then whirled round rap- idly. If we look at the pictures through the slits, they come before the eye one after another, and the impression of each picture lasts till the next ar- rives, so that they all blend into one, and the object IS* LIGHT. appears to be really going through the evolutions repre- sented. 225. Irradiation. A white or very bright object seen against a black ground appears larger than it really is; while a black object on a white ground ap- pears smaller than it really is. The two circles given in Figure 144 illustrate this. The black one and the Fig. 144. white one are of just the same size, but the former appears to be the smaller. This effect is called irradiation. It arises from the fact that the impression produced by a bright object on the retina extends beyond the outline of the image. We have a marked case of irradiation in the new moon, which seems much larger than the old one which it is said to " hold in its arms." 226. The Sensibility of the Retina is easily ex- hausted. When we look at a bright light, and then turn the eye towards a moderately lighted surface, a dark spot is seen ; showing that the part of the retina on which the bright light fell has lost for the moment its sensibility, or become blind. If the bright object be of one color, the part of the retina on which its image falls becomes insensible to rays of that color, but not to those of other colors. If a red wafer be stuck upon a sheet of white paper, and viewed steadily for some time with one eye, and then the eye be turned to another part of the LIGHT. 157 paper, a greenish spot will appear of the size and shape of the wafer. The red image has made the retina blind to red light, but it has left it sensitive to the remaining colors which make up white light (208) ; and when red is taken from white light the combination of the other colors gives a greenish hue. If the wafer is green, the spot seen will be red. 227. Color- Blindness. In some persons the retina appears to be affected in one and the same way by different colors, or even by all colors. The most com- mon form of this color-blindness, as it is called, is an inability to distinguish red and green. Thus to many persons the leaves of the cherry-tree and its fruit seem of the same color. In some cases, persons who were color-blind without being aware of it, and who have been employed on railways, have mistaken the color of signal-lights, and serious accidents have been the result. This blindness may arise either from a defect in the retina, or from some peculiarity in the absorptive powers of the humors of the eye. 228. The Optical Axis and the Visual Angle. A line drawn from the centre of the yellow spot through the centre of the pupil is called the optical axis. When we look at any object we must turn the eye so as to direct this axis toward it. This gives us the direction of the object. The image of an object on the retina is contained between lines drawn from the extremities of the object through the centre of the crystalline lens (217). The angle contained between lines thus drawn is called the visual angle of the object, and of course measures the length of the image on the retina. All objects which have the same visual angle form images of the same length on the retina. 158 LIGHT. 229. How we estimate the Size of a Body. The visual angle evidently gives us no information as to the real size of a body ; for we see from Figure 145 that the Fig- 145- visual angle of a body diminishes as its distance in- creases, and also that bodies at different distances may have the same visual angle, though they are not of the same size. Thus A B and A f B 1 are the same object, but / A r B 1 which is farther off has the smaller visual angle. Again C D and A 1 B 1 have the same visual angle, but A 1 B 1 is the larger. Hence, we must know the distance of a body in order to estimate its size; but when we know this distance we estimate its size instinctively. Thus a chair at the other side of the room has a visual angle only half as large as that of a chair half as far from the isye, yet we cannot make it seem smaller if we try. If we are in any way deceived as to the distance of an object, we are also deceived as to its size. 230. How we estimate the Distance of an Object. If we refer to Figure 146, we see that when the eyes are directed to a distant object, as C, they are turned inward but slightly ; while they are turned inward considerably when directed to the nearer object D. The muscular effort we have to make in turning the eyes inward so as to direct them upon an object is one of the best methods we have of estimating its distance. We also judge of the distance of an object from the distinctness with which we see it. The more obscure LIGHT. 159 it is, the more distant it seems. It is for this reason that objects seen in a fog sometimes appear enormously large. Fig. 146. They appear indistinct, and we cannot rid ourselves of the impression that they are far off; and hence they seem large, though they may really be small and near us. When we know the real size of an object we judge of its distance from the visual angle ; but we judge of the distance of unknown objects mainly by comparing it with the distance of known objects. This is one reason why the moon appears larger near the horizon than over- head, though she is really nearer in the latter case. When she is on the horizon we see that she is beyond all the objects on the earth in that direction, and there- fore she seems farther off than when overhead, where there are no intervening objects to help us to judge of the distance. 231. Why Bodies near us appear Solid. Hold any solid object, as a book, about a foot from the eyes, and look at it first with one eye and then with the other. It will be seen that the two images of the object are not exactly alike. With- the right eye we can see a little more of the right side of the object, and with the left eye a little more of its left side. It seems to be the blending of these two pictures which causes objects to appear solid. 1 60 LIGHT. 232. The Stereoscope. The principle just stated ex- plains the action of the stereoscope. Two photographs Fig. 147. f an object are taken from slightly different points of view, so as to obtain pictures like those formed in the two eyes. These photographs are placed before the eyes in such a manner that each eye sees only one, but both are seen in the same position. The pictures (Figure 147) are placed at A and JB. The rays of light from them fall upon the lenses m and n, and in passing through them are bent so that they enter the eye as if they came from the direction C. The lenses are portions of a double- convex lens, arranged as shown in the figure. 233. The Laws of Distinct Vision. To see an ob- ject distinctly, a clear image of it must be formed on the retina. When an object is brought quite near the eye, it becomes indistinct ; showing that there is a limit to the power which the eye has (220) of adjusting itself for different distances. The rays are now so divergent that the lens cannot bring them to a focus on the retina. The nearest point at ivJiich a distinct image is formed upon the retina is called the near point of vision, and the greatest distance at which such an image is formed is called the far point. In perfectly formed eyes, the near point is about 3^ inches from the eye, and the far point is infinitely distant. In such eyes, parallel rays are brought to a focus exactly at the retina when the eye is at rest ; that is, when the crystalline lens is of its natural convexity. The pupil of the eye is so small that the rays LIGHT. l6l which fall upon it from objects 1 8 or 20 inches distant diverge so little that they may be regarded as parallel. The distance of the near and far ^0/7zy,_however, is not the same for all eyes. In some cases, the near point is considerably less than 3^ inches from the eye, while the far point is only 8 or 10 inches. In other cases, the near point is 12 inches from the eye, and the far point infinitely distant. The former are called near-sighted eyes ; the latter, far-sighted ones. It was once thought that near-sightedness was due to the too great convexity of the cornea or the crystalline lens, or of both, and far-sightedness to the too slight convexity of the same. But actual measurement has shown that their real cause lies in the shape of the eyeball, which in far-sighted people is flattened, and in near-sighted people elongated, in the direction of the axis. In Figure 148, the curve N shows the form Fig. 148. of the normal, or perfect eye ; N', of the far-sighted eye ; and N", of the near-sighted eye. The eye is represented as at rest, and we see that the parallel rays A and A are brought to a focus on the retina of the normal eye, while only the convergent rays A and A are brought to a focus on the retina of the far-sighted eye, and only the divergent rays A" on the retina of the near-sighted eye. A" then is the far point for the near-sighted eye, since the lens has now its least convexity ; and this point must ii 1 62 LIGHT. be within 18 or 20 inches, since the rays from an object farther off are virtually parallel and cannot be brought to a focus on the retina. The near point must be less than for the normal eye, since the retina is farther from the lens, and therefore rays of greater divergence can be brought to a focus upon it. In the far-sighted eye, the retina is nearer the lens than in the normal eye ; hence the near point is farther away. While, then, the normal eye sees distant objects distinctly without adjustment, the far-sighted eye must adjust itself to see them. The defect of far-sighted eyes can be in great meas- ure remedied by wearing convex glasses, 'which help to bring the rays to a focus on the retina, and thus diminish the distance of the near point. The defect of near-sighted eyes can be remedied by the use of con- cave glasses, which render parallel rays divergent, and thus increase the distance of the far point. T\\e first law of distinct vision, then, is that a distinct image of the object must be formed on the retina. Again, it is well known that, as evening approaches, objects become indistinct. Here, of course, the image on the retina is distinct, but it is not brilliant enough to produce the proper effect upon the optic nerve. The second law of distinct vision, then, is that the image must be sufficiently illuminated. Again, some objects are so small that they cannot be seen, however much they may be illumined. Here the image is too minute to affect the optic nerve. The third law of distinct vision, then, is that the image must be of sufficient magnitude. 234. Old Eyes. As the eye grows old it loses its power of adjustment, the crystalline lens becoming less elastic. Hence old eyes can see distinctly only distant objects. This, however, is quite a different thing from far-sightedness. In the far-sighted eye, there is no lack LIGHT. 163 of power to change the convexity of the lens, but this power becomes useless because of the distance of the retina. This defect of vision caused by age can be remedied by the use of convex glasses. SUMMARY. The camera obscura is an apparatus by which an image of an object can be formed on a screen in a f dark- ened chamber. (218.) The eye is a camera obscura. (219.) Ths eye adjusts itself to light of varying intensity by varying the size of the pupil. (219.) It adjusts itself to various distances by changing the convexity of the crystalline lens. (220.) The optic nerve is blind. The light acts upon the rods and cones, which trans- mit the impression to the optic nerve. (222.) Any thing which excites the optic nerve produces the sensation of light. (223.) The impression on the retina lasts a short time after the object which produced it has been removed. (224.) The impression of a bright object extends beyond the image, giving rise to irradiation. (225.) The sensitiveness of the retina for any color is readily exhausted. (226.) We judge of the direction of an object by the direc- tion of the axis of the eye when turned towards it. The visual angle of an object depends on its size and distance. (228.) We judge of the size and distance of an object by means of its visual angle, the direction of the optical axis, and the distinctness of the image. (229, 230.) 164 LIGHT. Near bodies seem solid, because the images in the two eyes are not exactly alike. (231.) The stereoscope causes pictures on a plane surface to appear solid. (232.) In order that vision may be distinct, a distinct image must be formed on the retina, the image must be suffi- ciently illuminated, and must have sufficient magnitude. Perfect eyes can adjust themselves to any distance from 3^ inches to infinity. Near-sighted eyes can adjust them- selves only to short distances, and far-sighted eyes only to long distances. (233.) Eyes lose their power of adjustment as they grow old. (234-) Near-sightedness and far-sightedness are due to defec- tive forms of the eyeball. These defects and that caused by age can be partially remedied by the use of glasses. ( 2 33> 234.) THE MICROSCOPE AND THE TELESCOPE. 235. The Simple Microscope. We have seen (233) that an object must form upon the retina an image of a certain magnitude, in order to be distinctly seen. Now the magnitude of the image may be increased indefi- nitely by bringing the object nearer the eye ; but when it is brought too near, the eye is not able to bring the rays from it to a focus on the retina. We may accom- plish this, however, by the aid of a convex lens. Such a lens is the simplest form of a microscope. It is called a microscope (from two Greek words meaning to see small things) because it enables us to see things smaller than the unaided eye can distinguish. The more convex the lens, the nearer can the object be brought to the eye, and the larger will be the image on the retina. LIGHT. 165 236. The Compound Microscope. In Figure 149, we have what is called a compound microscope. M is a Fig. 149- lens; A B is an object placed near it. An enlarged image of A B is formed at a b, and this image is viewed through the lens N, in the same way that an object is viewed with the single lens of a simple microscope. The lens Mis called the object-glass or the objective; and TV 7 ", the eye-piece. The latter is usually a combina- tion of two lenses. We have seen (216) that a convex lens causes the rays passing through it to meet at a focus. In reality, how- ever, this focus is not exactly the same for all the rays. Those falling near the margin of the lens meet a little sooner than those falling upon its centre, causing what is called aberration. The more convex the lens, the greater the aberration, and the less distinct the image. This aberration can be diminished by diminishing the size of the lens, so that all the rays must fall near its centre. Hence the objective of a compound microscope, which is a very convergent lens, is made very small. The magnifying power of a microscope is commonly expressed in diameters. If it makes the breadth of the object appear 50 times as great as it really is, it is said to magnify 50 diameters. Of course the surface of the object is increased as the square of its diameter; or in this case 2,500 times. The most powerful compound microscopes magnify 1,500 diameters, or even more. Of course, there is no more light on this enlarged 1 66 LIGHT. image than there is on the object itself; hence the ob- ject must be strongly illuminated in order that the light when thus diluted may be sufficient to affect the eye. 2.37. The Telescope. As an object is moved farther and farther from the eye, its image becomes smaller and smaller, until at last it may cease to affect the eye, even though the object itself may be very large. An instru- ment for examining distant objects is called a telescope.^ The word is made up of two Greek words meaning to see far off. Its construction (Figure 150) is very much Fig. 150. like that of the compound microscope. It has an object- glass^ M, for forming an image, a b, of the object A B, and an eye-piece, N, for examining this image. It differs from the microscope mainly in the fact that the image is always smaller than the object. Since the object is very distant, the rays which fall upon the object-glass are virtually parallel ; hence this glass may have a great diameter without making the image indistinct through aberration. The larger the diameter the better, since it will collect and concentrate the more light on the image. The size of the image increases with its distance from the object-glass. To make this distance as great as possible, the object-glass has very slight convexity. The object-glass of the telescope is made as large as possible, with very slight convexity ; while that of the microscope is made as small as possible, with very great convexity. The eye-piece is the same in both LIGHT. i6 7 instruments. The magnifying is chiefly done by th& eye-piece. >We have seen that light is dispersed when passing through a prism (204) ; and that a double-convex lens is somewhat like two prisms placed back to Fig. 151. back (215). Such a lens therefore disperses the light which passes through it, giving rise to colored fringes round the* image. This can be prevented by the use of a second lens made of glass of different dispersive power (204). A lens thus corrected (Figure 151) is called an achromatic (colorless) lens. 238. The Terrestrial Telescope. The image in the telescope described above will be inverted. An erect image may be obtained by using additional lenses. The first inverted image (Figure 152) is formed at a 6. Fig. 152. The lens P renders the rays diverging from this image parallel, and J brings them to a focus again at a 1 b 1 . These two lenses then act as one, and form an inverted image of the inverted image, .or an erect image. Fig. 153- 239. The Opera -Glass. M (Figure 153) is the ob- ject-glass, and is a converging lens. R is the eye-piece, and is a diverging lens. The rays of light coming from i68 LIGHT. the ends A and B of the object would be brought to a focus at a b, where an inverted image would be formed. But on falling upon the eye-piece R they are turned aside, so that they enter the eye as if they came from the points a' and b 1 . Hence the eye sees the object A B erect and under a greater visual angle (228) than if it had been viewed directly. The telescope invented by Galileo was an opera-glass. ,THE MAGIC LANTERN. 240. In the photographic camera (Figure 139) a small inverted image of the object is formed upon the glass screen E. If E be a transparent picture, and 'a strong light be sent through it from behind, an enlarged and upright image of the picture will be formed by the lenses in the tube A, and may be received upon a screen in a darkened room. The nearer the picture is to the lens, the farther off and the larger will be the image. An instrument for thus projecting pictures upon a screen is called a magic lantern. SUMMARY. The microscope is an .instrument which enables the eye to see an object at less distance than it otherwise could. With the simple microscope, the object is viewed directly ; with the compound microscope, an enlarged image of the object is viewed. (235, 236.) The telescope is an instrument for viewing a distant object. An image of the object is formed in the focus of the object-glass and viewed with a microscope. The object-glass of a telescope is made achromatic by combining lenses of different dispersive power. (237.) LIGHT. 169 In terrestrial telescopes, two or more lenses are com- bined so as to make the object appear upright. (238.) The magic lantern forms a magnified image of an object upon a screen in a darkened room. (240.) MIRRORS. 241. Plane Mirrors. A mirror is a smooth reflect- ing surface. If the surface \sjlat, it is a plane mirror. In Figure 154, suppose a point of light A to be in front of the plane mirror N M. The rays diverging from A, as A I? and A C, are re- Fig. 154- fleeted from the mirror so as to make the angle of reflection equal to that of incidence. After reflec- tion they enter the eye O just as if they came from the point a. This point will therefore appear to be just as far behind the mirror as A is in front of it. A plane mirror simply alters the direction of the rays, and makes them appear to come from a point as far behind the mirror as the object is in front of it. Now, as we always see an object in the direction which the rays have on entering the eye, the object will appear to be behind the mirror. No image is formed; for, in order to form an image, the rays diverging from the object must be made to converge so as to meet. 242. Concave Mirrors. A concave mirror is a por- tion of the inner surface of a hollow sphere. In Figure 155, C is the centre of the sphere of which the mirror is a part. The radii C A, C B, and C D are perpendicular to the surface of the mirror at the points A, JB, and D. Parallel rays, as H, G, and L, on meeting the mirror, are reflected so as to make the angle I7O LIGHT. of reflection equal to that of incidence ; that is, making CB H equal to CB F, C D G to CDF, etc. Hence Fig- iSS- the reflected rays are made to converge. If the mirror is not more than 8 or 10 in breadth, the rays will all meet at F, half-way between C and A.. This point is called the principal foctis of the mirror. If rays diverge from a point nearer the mirror than the principal focus is, they will still diverge on reflec- tion. If they diverge from a point farther off than the principal foc2ts, they 'will converge on reflection. 243. Images formed by Concave Mirrors. If an object be in front of a concave mirror, and outside of the principal focus, an inverted image of it will be formed Fig. 156. in front of the mirror (Figure 156) ; for the rays which diverge from it will be made to converge and meet. The size of the image will increase with its distance from the mirror ; and its distance from the mirror becomes greater as the mirror is made less concave, and as the object is brought nearer. LIGHT. 171 244. Convex Mirrors. A convex mirror is a portion of the surface of a sphere. Such a mirror (Figure 157) renders parallel rays di- vergent, and divergent rays more divergent. Hence Fig- 157- an object reflected in it appears smaller than it really is. A concave mirror affects the rays like a convex lens, and a convex mirror like a concave lens. 245. The Reflecting Telescope. A concave mirror may be used instead of the object-lens of a telescope, as Fig. 158. is shown in Figure 158. The rays from an object falling upon the concave mirror M are reflected so as to form an image at the focus, and this image is viewed with the eye-piece o. As the image is formed by reflected light, the instrument is called a reflecting telescope. The or- dinary telescope is called a refracting telescope, since the image is formed by refracted light. 172 LIGHT. 246. Parabolic Mirrors. The mirror shown in Fig- ure 159 has what is called a parabolic surface, and is Fig I5g therefore called a para- bolic mirror. The point F is called the focus, and the line A X the axis, of the mirror. If parallel rays fall upon such a mirror, they are reflected exactly to the focus F, whatever may be the breadth of the mirror. On the other hand, if a light be placed at the focus, its rays will be reflected from the mirror in parallel lines. This is because a parabolic surface is curved in such a way that if a perpendicular be drawn to any point, as M, the angle which it makes with the line ML, drawn parallel to the axis, is equal to the angle it makes with the line M F drawn to the focus. Parabolic mirrors are used for the lanterns placed in front of locomotive engines and in many light-houses. SUMMARY. An object is seen reflected in a plane mirror without enlargement, but it appears as far behind thje mirror as it really is before it. (241.) An inverted image of ah object placed outside the principal focus is formed in front of a concave mirror. A concave mirror may be used in place of the object- glass in a telescope. (243, 245.) In a convex mirror an object appears smaller than it really is. (244.) A parabolic mirror renders the rays which diverge from its focus parallel. (246.) HEAT. PROPAGATION OF HEAT. 247. Heat is Radiated in all Directions. When we come near a stove we feel its heat, no matter on what side of it we may be ; that is, the stove radiates its heat in all directions. Radiant heat, like light, diminishes in intensity as the square of the distance increases, and for the same reason. 248. Heat traverses Space in Straight Lines and with the Velocity of Light. Heat and light come to the earth together in the sun's rays, and we have seen that these move in straight lines and with a velocity of about 190,000 miles a second. 249. Luminous and Obscure Heat. Heat which is radiated from a non-luminous source, as from a ball heated below redness, is called obscure heat ; while that radiated from a luminous source, as from the sun or from a ball heated to redness, is called luminous heat. 250. Diathermanous Bodies. Some substances, as air, allow radiant heat to pass readily through them, and are called diathermanous. The term is derived from the Greek words dia, through, and thermos, heat. If a plate of glass be held up before an iron ball heated to dull redness, a delicate thermometer held behind the plate will be scarcely, if at all, affected. If, however, a plate of rock salt be put in place of the glass, the ther- mometer rapidly rises. Rock salt is the most diather- manous of all known solids, and is to radiant heat what glass is to light. 1 74 HEAT. A solution of iodine in bisulphide of carbon is wholly opaque to luminous heat, and perfectly diathermanous to obscure heat. 251. Obscure Heat always accompanies Luminous Heat. If a luminous beam, as that from the lime light, be allowed to fall upon a cell with glass sides, filled with the iodine solution (250), all the luminous heat is cut off. Place a differential thermometer * behind the cell in the dark space, and we find that a beam of obscure heat is passing through the cell. Obscure is found always to accompany luminous heat ; and the hotter the source, the more intense are the obscure rays. This may be shown by heating a coil of platinum wire gradually from dull redness to a white heat, and then cutting off the luminous rays by the iodine cell, and letting the obscure rays fall on a differential thermometer. 252. Heat is Reflected and Refracted in the Same Way as Light. Let a beam of light fall upon a mir- ror, and hold one bulb of a differential thermometer in its path after it has been reflected. The luminous heat will be found to be reflected with the light. Now cut off the luminous heat with the iodine solution, and hold the bulb again in the path which the reflected beam took. It will be found that the obscure heat has also been reflected in the same path as the light. Let the luminous beam fall upon a prism, and examine it in the same way after refraction. It will be found that both luminous and obscure heat are refracted like light. 253. tfeat is Dispersed in the Same Way as Light. Experiments have shown that radiant heat is dispersed like light on passing through a prism ; and that obscure heat is less refrangible than luminous heat. * A thermometer for finding the difference of temperature at two points (291). HEAT. 175 254. The Spectrum is made up of three Parts. The spectrum is found to be made up of three parts : (i) a luminous portion ; extended, at the red end, by (2) an obscure thermal portion ; and, at the violet end, by (3) an obscure chemical portion. The luminous portion is also both thermal and chemical. Black lines (called, from their discoverer, Fraun- hofer's lines} can be seen crossing the luminous part of the spectrum. These dark lines are found to be also cold and chemically inactive. Similar cold lines are found in the obscure thermal part. 255. Calorescence and Fluorescence. If a jet of mixed hydrogen and oxygen be set on fire, it produces wh'at is called the oxy-hydrogen flame. This flame has very little light, but its heat is intense. The radiations are mainly the obscure thermal ones. But if a small cylinder of lime be put into the flame, the light becomes most dazzling. The obscure thermal radiations have been changed into luminous ones. This change is called calorescence. If a paper washed with a solution of quinine be held in the extreme violet end of the spectrum, the obscure chemical part of the spectrum becomes luminous. This change of the obscure chemical rays into luminous ones is called fluorescence. 256. Different Solids, Liquids, and Gases absorb Heat 'with different Degrees of Readiness. If we cause rays of heat to fall upon different solids, liquids, and gases, and measure with a delicate thermometer the heat which passes through, we find that they absorb the same kind of heat very differently. Again, if we use platinum wire (251) as a source of heat, we shall find that glass absorbs obscure heat better than luminous heat ; and, in general, that a given sub- stance absorbs different kinds of heat in different 176 HEAT. proportions. Among gases the best absorber of ob- scure heat is watery vapor. 257. Good Absorbers are good Radiators. Place a heated copper ball just half-way between two plates of tin, one of which is bright and the other coated with lamp-black ; and hold the bulb of a differential ther- mometer against the back of each plate. The coated plate will be found to be hotter than the other, showing that it is the better absorber v Again, place the plates against the ball, with the coated side of the blackened plate outward ; and hold a differential thermometer near each to receive the heat radiated by it. It will be found that the coated plate is the better radiator. Good absorbers always prove to be good radiators. cfc SUMMARY. Heat is radiated from its source in all directions, in straight lines, with the velocity of light. (247, 248.) Radiated heat may be luminous or obscure. (249.) Bodies which allow heat to pass readily through them are called diathermanous. (250.) Radiant heat is reflected, refracted, and dispersed in the same way as light. (252, 253.) The spectrum is made up of three parts: (i) a lumi- nous part; (2) an obscure thermal part; and (3) an obscure chemical part. (254.) Calorescence is the change of the obscure thermal rays into luminous rays. Fluorescence is the change of the obscure chemical rays into luminous. (255.) Different solids, liquids, and gases absorb heat very differently. (256.) Good absorbers are good radiators. (257.) HEAT. 177 EFFECTS OF HEAT ON BODIES. 258. The Molecules of a Body transmit Heat to one another. When one end of a poker is placed in the fire, it soon becomes red hot, and the heat slowly travels from this end to the other. This heat cannot have been radiated, since radiant heat travels at the rate of 190,000 miles a second. Fig. 160. This transmission of heat from molecule to molecule of a body is called conduction. 259. Different Solids conduct Heat differently. If several thermometer bulbs be inserted in a metallic rod, as shown in Figure 160, and one end of the bar be heated, the mercury will begin to rise in the ther- mometer nearest the heated end, and then in the others successively. If rods of other metals of the same length and thickness be tried in the same way, it will be found that the metals differ 'widely in conductive power. Those which are good conductors of heat are also good conductors of electricity. 260. Liquids and Gases are Poor Conductors of Heat. In Figure 161, a differential thefmometer (251) 12 HEAT. Fi s- l6x - is placed in a glass vessel filled with water. Heat is applied to the surface of the water by means of a dish of heated oil. If the water conducted the heat, the upper bulb w T ould become heated sooner than the lower one, and the thermome- ter would at once indicate a dif- ference of temperature between the two bulbs. But the thermometer is scarcely affected. All liquids are poor conductors of heat ; and gases are poorer ones. 261. Heat raises the Temperature of a Body. The most obvious effect of the heat absorbed by a body is a rise of temperature. This rise is indicated by the sense of touch, but more accurately by a thermometer. 262. A Body in cooling i gives out just as much Heat as it takes to heat it l. Boil half a pound of water, and plunge the bulb of a thermometer into it, and it will indicate a temperature of 212. Remove the water from the source of heat, and add half a pound of water of a temperature of 70. Stir the mixture a short time with the bulb of a delicate thermometer, and the temperature will be found to be 141. The first half-pound of water has then lost Ji and the second has gained 71 ; in other words, the first in cooling i has given out just heat enough to warm the second i. The same is true of all other bodies. 263. It requires different Amounts of Heat to raise the Temperature of the same Weight of different Bodies i. Heat a piece of tin to 212 by plunging it into boiling water, and then plunge it into its own weight of water at 70. The resulting temperature will be considerably below 141 ; showing that tin in cooling HEAT. 179 i does not give out heat enough to raise the water i. But the tin in cooling i gives out just as much heat as it takes to raise its temperature i. Hence it takes more heat to raise the temperature of a pound of water i than to raise that of a pound of tin i. If copper be used instead of tin, the resulting temperature will be higher, but still below 141. It requires, then, less heat to raise the temperature of a pound of copper i than to raise that of a pound of water i, but more than it takes to raise that of a pound of tin i. In this way, w r e find that it takes very different amounts of heat to raise the tem- perature of the same weight of different substances i. 264. Unit of Heat. The thermometer indicates the rise of temperature in a body, but not the amount of heat required to raise the temperature. It is therefore desir- able to have some -unit by which the heat received by a body may be expressed. The unit usually taken is the amount of heat required to raise the temperature of a pound of water i. A unit of heat, then, is the amount of heat required to raise the temperature of one pound of water i. 265. Specific Heat. The amount of heat required to raise the temperature of a pound of any substance i, expressed in units, is called the specific heat of that substance. Thus it requires -fa of a unit of heat to raise the temperature of one pound of mercury i ; and the specific heat of mercury is therefore ^ or .033. 266. Heat causes Solids to melt. Place a dish of water at the temperature of 32 and a dish of ice at the same temperature side by side in a warm room, and hold a thermometer bulb in each. The temperature of the water will gradually rise, while that of the ice will not rise until the whole is melted. The heat, then, which has been absorbed by the ice has melted it, or changed its state. 180 HEAT. The second effect of heat upon a body, then, is to change its state. 267. The Melting-Points of different Solids are very different. Ice, as we have seen, has a temperature of 32. Mercury melts at 40; and alcohol at a temper- ature lower than we have yet been able to produce. On the other hand, phosphorus melts at 111 ; iron at 2012; and charcoal at a higher temperature than we are able to produce. The melting-point of any one substance is, under the same circumstances, always the same. Certain bodies become soft or viscous before they melt. Sealing-wax, when cold, is quite brittle, but when heated it first grows plastic, and finally melts. In like manner, iron before melting becomes soft in such a manner that pieces may be easily welded to- gether or moulded into any form. 26$. Latent Heat of Liquids. If a pound of ice at 32 be mixed with a pound of water at 212, the tem- perature, when the ice is melted, will be 50.5. It has then taken 161.5 units of heat to melt a pound of ice and to raise its temperature from 32 to 50.5, or 18.5. It therefore takes 143 units of heat to melt a pound of ice. Heat always disappears in melting a solid ; and this heat is called the latent heat of fusion, or the latent heat of the liquid, since it is concealed in the liquid. By the latent heat of a liquid, then, we mean the num- ber of units of heat required to melt one pound of the substance. Thus the latent heat of water is 143 units, which is greater than that of any other liquid. When the liquid passes back into the solid state again, its latent heat reappears as sensible heat. 269. Heat causes Liquids to boil. Under the ordi- nary pressure, if water be raised to a temperature of 212, it begins to boil, and its temperature then remains the same until it is all converted into steam. The heat, HEAT. l8l then, which the water absorbs changes it from the liquid to the gaseous state. Other liquids can be made to boil, but at very different temperatures. Any given liquid, under the same circumstances, always boils at the same temperature. 270. Latent Heat of Gases. If a thermometer be held in the steam just over boiling water, it will indi- cate a temperature of 212. Now, as water is receiving heat all the time it is boiling, this heat must be latent in the steam. The latent heat of different gases is found to vary greatly. The latent heat of steam and watery vapor is greater than that of any other gas or vapor, hydrogen alone excepted. 271. The State of a Body depends upon its Temper- ature. When a solid is heated, its temperature rises till it reaches the melting-point, where it remains sta- tionary until the solid is melted. It then rises again until it reaches the boiling-point, where it again remains stationary until the liquid is converted into a gas. When a gas is sufficiently cooled, it goes through the same changes in the reverse order. It is because different substances have very different boiling-points that they can exist in nature, some as solids, some as liquids, and some as gases. 272. The Boiling- Point of Water falls as the Pres- sure on its Surface diminishes. Fill a flask two-thirds full of water, boil it for some time, cork it tightly, remov- ing it at the same time from the source of heat, and invert it, as shown in Figure 162. Pour cold water upon the flask, and it begins to boil again. At first the upper part of the flask is full of steam, whose elastic force causes it to press upon the water. When cold water is poured upon the flask, this steam is condensed, the pressure is diminished, and the water boils, though at a lower temperature. 182 HEAT. Fig. 162. The height of a mountain can be estimated quite ac- curately from the dif- ference between the boiling-points at its summit and at its base. Steam occupies very much more space than the same weight of wa- ter, and there is no cohesion among its molecules (22). When, therefore, water Boils, both the cohesion of the liquid and the pressure of the atmosphere must be overcome, since both of these tend to keep the molecules together. Hence, when either the cohesive force or the external -pressure is changed, the boiling-point will also change. 273. The Spheroidal State. If two or three drops of water be poured into a red-hot metallic cup, they gather into a globule, which runs about without boiling. The water is now said to be in the spheroidal state. Fig. 163. Turn a cup c bottom up (Figure 163), heat it to red- ness, and carefully put a drop of water d upon it with a HEAT. 183 dropping-tube. Place behind the drop a platinum wire a b, heated to a white heat by a battery. With the eye at e, the platinum wire can be seen between the drop and the cup, showing that the drop does not touch the cup. As soon as the drop comes near the heated cup, steam is generated beneath it, and acts like an elastic spring to lift the drop from the surface. As the cup cools, this spring gives way, and the water, on touching the surface, is suddenly converted into steam. Boiler ex- plosions are probably often caused by this sudden change from the spheroidal state to steam. 274. Evaporation. If water is exposed in an open vessel at the ordinary temperature, it gradually disap- pears, passing off in the form of vapor. This vapor is formed slowly and only at the surface; while, in boil- ing, steam is formed rapidly and throughout the liquid. Water is thus evaporated into the atmosphere at all tem- peratures, but more rapidly as the temperature rises. 275. Condensation. A gas condenses at the same point at which its liquid boils; and, as pressure raises the boiling-point, it also raises the point at which a gas will condense. Under the combined action of pressure and cold, almost every known gas has been liquefied. 276. Freezing- Mixtures. When a solid melts, or a liquid evaporates, a large amount of heat is rendered latent. Advantage is taken of this fact to obtain an arti- ficial reduction of temperature. One of the most com- mon freezing-mixtures is composed of salt and pounded ice. The substance to be frozen is placed in a small vessel which is put in a larger one and packed round with this mixture. The ice rapidly melts, and in doing so absorbs a large amount of heat, thus reducing the temperature of the inner vessel. A much greater degree of cold is obtained by the rapid evaporation of a liquid than by the melting of a solid. 184 HEAT. If solid carbonic acid be mixed with ether, it evapo- rates very rapidly. By means of such a mixture, 20 or 30 pounds of mercury may be readily frozen. If the mixt- ure be placed under an exhausted receiver, the evapora- tion is greatly quickened. Faraday thus reached a tem- perature of 1 66 F. 277. Solids are expanded by Heat; but different Solids expand unequally for the same Rise of Tem- perature. We have already learned (6) that solids are expanded by heat. If now a bar of iron and one of cop- per be riveted together and then plunged in boiling water, so that the temperature of both may be raised to the same point, the compound bar will become curved, the copper being the convex side. This is because copper is ex- panded more than iron for the same rise of temperature. Scarcely any two solids are expanded alike by heat. 278. Liquids are expanded by Heat; but different Liquids expand unequally for the same Rise of Tem- perature. Fill a test-tube with water, and then close it with a rubber cork through which passes a fine glass tube. Plunge the test-tube in boiling water, and the liquid will rise in the tube ; showing that it has been expanded by heat. Fill a second test-tube with alcohol, and plunge both into boiling water. The alcohol will rise higher in the tube than the water will, showing that it is expanded more by the heat. Different liquids, then, expand un- equally for the same rise of temperature. 279. Gases are expanded by Heat, and different Gases expand equally for the same Rise of Temper- ature. Close a pint flask with a cork through which passes a bent tube, and connect the tube with a jar in- verted over water. Plunge the flask into boiling water, and bubbles of air rush over into the jar. All gases are thus expanded by heat. HEAT. '85 Fill now the same flask with hydrogen, oxygen, or any other gas ; connect it with the same jar as before, and again plunge the flask into boiling water. Precisely the same amount of gas will pass over as at first. Solids, liquids, and gases are expanded by heat; solids and liquids unequally, and gases equally, for the same rise of temperature. 280. Convection. Since the molecules of liquids and gases are free to move, their expansion, when they are heated unequally in different parts, will create currents. The unexpanded and heavier portions will tend to dis- place the lighter ones and to compel them to rise. As these heavier portions become heated, they in turn tend to rise and give place to colder portions ; and so on. These currents tend to distribute the heat, and this mode of distribution is called convection. J - 281. Convection of Liquids. In Figure 164, we have a glass beaker filled with water heated by a lamp below. A little sawdust is added to the water, and its motions show that a current is passing up the centre of the vessel and down at the sides, as indicated by the arrows in the figure. Each molecule is thus seen to come to the bottom to get heated, and then to return to the sur- face. It is in this way that water, which is a bad conduc- tor, is readily heated when the heat is applied below. 282. Oceanic Currents. Oceanic currents are produced by convection. The temperature of the sea in the tropics is about 50 higher than at the poles, and the Fig. 164. 1 86 HEAT. specific gravity of the water is therefore muth less. To restore the equilibrium, the warmer and lighter water of the tropical regions flows towards the poles, and the colder and denser water of the polar regions flows towards the equator. If the whole earth were covered with water of the same saltness, we should everywhere have a surface-current from the equator towards the poles, and an under-current from the poles towards the equator. But owing to the obstructions offered by the land and by the inequalities in the bed of the ocean, and to the different degrees of saltness, and therefore of density, in different parts of the sea, these two great currents are broken up into innumerable minor currents and counter-currents. The most remarkable of these currents is the Gtilf Stream, which issues from the Gulf of Mexico, and, crossing the Atlantic in a north-easterly direction, washes the western coast of Europe. 283. Convection of Gases. If a lighted candle be held in the crack of a door which opens from a warm into a cold room, the flame will be blown outward at the top of the door and inward at the bottom, while half-way up it will burn steadily. A current of cold air is passing into the room at the bottfem, driving out a current of warm air at the top. It is mainly by convection that the air in a room is heated. The air near the stove is heated and expanded, and then forced upward by the current of colder air. When a building is heated by a furnace, this is placed in the cellar and encased in brick-work or in sheet iron. The space between the fire-pot and the casing is con- nected by the air-box with the outer atmosphere, and by flues or pipes with the rooms to be heated. The air about the fire-pot first becomes heated, and is driven up through the pipes by the cold air from without. HEAT. 187 284. The Relation of Water to Heat and Climate. Water, from its high specific and latent heat, has a marked influence on climate. It makes the transition from winter to summer and from summer to winter more gradual. In the spring, when the snow begins to melt, a large amount of heat is absorbed from the air and ren- dered latent. After the snow and ice are all melted, such is the specific heat of water that it requires a great deal of heat to raise its temperature. In the fall, on the other hand, as the water cools down and freezes, it gives out all the heat which it had absorbed in the spring. 285. The Irregular Expansion and Contraction of Water. If water at the temperature of 39 be either warmed or cooled, it expands. This temperature is hence called the point of maximum density of water. We can now understand why water often bursts the pipe or vessel in which it freezes. Water is the only liquid 'which has such a point of maximum density, and there are but very few substances which expand when they become solid. Iron is one, and it is owing to this property that it is so well adapted for castings. As it solidifies, it expands so as completely to fill the mould. This irregular expansion of water is of the greatest importance. Before freezing it begins to grow lighter, so that the freezing begins at the surface ; and the ice, being lighter still and also a poor conductor of heat, floats upon the water and keeps it from freezing very deep. If water continued to contract as it cooled, it would begin to freeze at the bottom, and during the winter our lakes and rivers would become solid masses of ice. This would be fatal to all animal life in the water ; and, as water is a very poor conductor of heat, it would melt only to the depth of a few feet during the summer. 1 88 HEAT. 286. Heating by Steam. It is now quite common to warm buildings by steam. Pipes run from the boiler through the rooms to be heated, and then back to the boiler again. The steam passes from the boiler into these pipes, where it is condensed and runs back as water to the boiler. Now every pound of water con- verted into steam in the boiler takes up over 900 units of heat, and every pound of steam which condenses in the pipes gives out the same amount of heat into the rooms. The water thus acts as carrier of heat between the furnace and the room where it is wanted. 287. A Hot-House is a Tra t catch Sunbeams. A hot-house is covered with glass. Now we have seen that luminous heat, like that from the sun, passes readily through glass, while obscure heat can scarcely pass through it at all. As, therefore, the sunbeams beat down upon the roof of a hot-house, they easily pene- trate the glass ; but, when they fall upon the plants and furniture within, they are radiated back as obscure heat, and are unable to make their way through the glass except by the slow process of conduction. It is because the sunbeams are thus caught in a trap, that the temperature inside a hot-house on a sunny day is always higher than outside. SUMMARY. Heat is transmitted from molecule "to molecule of bodies by conduction. Liquids and gases are poor con- ductors. (258, 260.) The heat which a body absorbs is partially used in raising its temperature. (261.) A body in cooling i gives out just as much heat as it takes to warm it i. (262.) HEAT. 189 It takes a different amount of heat to raise the tem- perature of the same weight of different substances i. The amount of heat required to raise the temperature of one pound of water i is called a unit of heat. The amount of heat required to raise the temperature of one pound of any substance i, expressed in thermal units, is called its specific heat. (263-265.) The heat which a body absorbs is sometimes used in changing its state. 1 (266.) The melting and boiling points are the same for the same substance under the same pressure ; but those of different substances are different. (267, 269.) When a substance melts or boils, a certain definite amount of heat is rendered latent. The latent heat of water is higher than that of any other liquid ; and that of steam is higher than that of any other vapor. (268, 270.) The boiling-point of water is raised by increasing the pressure. (272.) When water is put into a red-hot vessel, it is prevented . from coming in contact with the heated surface by a layer of steam, and is said to be in the spheroidal state. (273.) Liquids evaporate at all temperatures, but more rapidly as the temperature rises. Vapors condense at the same point as that at which their liquids boil. (274, 275.) The heat absorbed by a body is used partially in pushing the molecules apart, or expanding it. Dif- ferent solids and liquids expand unequally, and different gases equally, for the same rise of temperature. (277- 279-) When a gas or a liquid is heated beneath its surface, currents are produced which distribute heat by convec- tion. It is in this way that the Gulf Stream and other oceanic currents are produced. (280-283.) 190 HEAT. Water, by its high specific and latent heat, tends to make the change of seasons more gradual. Its irregu- lar expansion and contraction prevent the lakes and rivers from freezing solid in the winter. (284, 285.) THERMAL INSTRUMENTS. 288. The Mercurial Thermometer. The common thermometer is used, as its name implies, to measure temperature. In making a thermometer, the bulb and tube are first filled with mercury. The mercury is then heated up to the highest temperature which the thermometer is in- tended to measure, and the end of the tube is sealed air-tight by melting the glass. As the bulb cools again, the mercury falls in the tube, leaving a vacuum above it. On the thermometer scale there are two fixed points : that at ivhich ice melts, or the freezing-point; and that at which water boils, or the boiling-point. The freezing-point is found by plunging the bulb into melting ice, and noting the position of the mercury in the tube. Melting ice is used rather than freezing water, because it is found that if water be kept perfectly still it can be cooled several degrees below the freezing-point before it congeals ; while ice, at the ordinary pressure, always melts at the same temperature. The boiling-point of water is not always the same (272) ; but its steam always has the same temperature at the ordinary pressure. The boiling-point is therefore found by enclosing the bulb and tube in a steam-bath. On the Fahrenheit scale, which is the one in common use in this country and England, the freezing-point is marked 32, and the boiling-point 212; the space be- tween the two being divided into 180 equal parts, or degrees. These equal divisions are continued above the HEAT. boiling-point and below the freezing-point; but not be- low 38 nor above 576, since mercury freezes at the former point and boils at the latter. On the Centigrade scale, which is the one commonly used in France, and the one generally preferred by scien- tific men, the freezing-point is marked o, and the boil- ing-point 100. 5 of this scale, then, are equal to 9 of the Fahrenheit scale. A third scale, known as Reaumur's, is in general use in Germany. On this scale the freezing-point is marked o, and the boiling-point 80. 289. The Alcohol Thermometer. When tempera- tures below 38 are to be measured, alcohol is used instead of mercury. An alcohol thermometer is not, however, so accurate as a mercurial one. 290. The Air Thermometer. There are various ways of measuring temperatures above the boiling-point of mercury, but the best is by means of the air ther- mometer. The expansive force of air is very regular for all known temperatures, but it expands so rapidly that to measure the ordinary range of temperatures would require too long a tube. The expansion of the air in the tube is indicated by the movement of a column of liquid upon which it acts. 291. The Differential Thermome- ter. This instrument shows the dif- ference in temperature between two neighboring substances or places. In the one invented by Leslie (Figure 165), two bulbs, A and B, filled with air, are connected by a bent tube. A little colored liquid fills the lower part of this tube, and rises to the levels C and D when both bulbs are Fig. 165. I9 2 HEAT. of the same temperature. But should A become warmer than >, since air expands very much for an increase of temperature, the column of liquid will be pushed down at C and made to rise at JD; and this motion will be reversed when B becomes warmer than A. The slightest difference of temperature is therefore indicated at once. Sulphuric acid, or some other liquid which is not volatile, is used in the tube. 292. Effect of Temperature upon Measures of Time. The rate of a clock depends upon the time in which its pendulum vibrates, and that of a watch upon the time in which its balance-wheel oscillates. Now since the change of temperature alters the length of a pendulum, it likewise alters its time of vibration (106). The higher the temperature, the more slowly does it vibrate. In like manner, a change of temperature, by altering the dimensions of the balance-wheel of a watch and the force of the spring, will cause it to vibrate more slowly in hot weather than in cold. Fig. 166. 293. Graham's Mercurial Pendulum. The first attempt to compensate for change of length in a pendulum was made by Graham, an English clockmaker. The rod of his pendulum (Figure 1 66) was made of glass, to the lower end of which was attached a cylindrical vessel containing mer- cury. As the glass rod expands by heat, the bottom of the vessel which contains the mercury will of course be carried farther from the point of suspension ; but since the mercury resting on this base expands upwards, its centre of gravity is raised, or brought nearer the point of suspen- sion. The lowering of the centre of gravity, due to the expansion of the glass, may thus be counteracted by the rise of the same, due to the expansion of the mercury. HEAT. 193 294. Compensation Balance - Wheel. The balance- wheel of a watch is sometimes made, as in Figure 167, not with one continuous rim, but with pig. 167. a broken rim of several separate pieces, all of which are fixed at one end and free at the other, the free ends being loaded ; and each piece is composed of two metals, of which the more expansible is placed outside. On a rise of temperature, then, the loaded ends 'will approach the centre. This is made to counteract the effect produced on the rate of the watch by the expansion of the wheel, which carries the cir- cumference farther from the centre. 295. Other Effects of Expansion. The force ex- erted by solids in contracting or expanding, or by liquids in expanding, is very great. If a strong vessel be en- tirely filled with a liquid and then sealed tightly, the vessel will burst if considerably heated. In the arts it is of great importance to bear in mind the intensity of this force, sometimes with the view of guarding against its action, and sometimes in order to make it useful. Thus, bars of furnaces must not be fitted tightly at their extremities, but must at least be free at one end. In making railways, also, a small space must be left between the successive rails. For a similar reason water-pipes and gas-pipes are fitted to each other by telescopic joints. 296. Wet and Dry Bulb Hygrometer. A hygrome- ter is an instrument for measuring the amount of moisture in the air. The one invented by Mason con- sists of two thermometers (Figure 168) placed side by side, one having a dry bulb and the other a bulb covered with muslin, kept moist by means of a string dipping in water. The wet bulb is chilled by the evaporation of 13 HEAT. l68 - the water from it, since this evaporation renders some of its heat latent. The drier the air, the more rapid the evaporation, and the greater the difference be- tween the readings of the two thermometers. 297. Edson's Hygrodeik. This is an improved form of Mason's hygrometer. It differs from all other hygro- meters in having a dial and pointer, showing at a glance the temperature, the degree of humidity, the absolute amount of vapor in each cubic foot of air, and the dew-point. The dew-point is the tem- perature at which the moisture of the air begins to be deposited as dew. SUMMARY. The thermometer is used to measure temperature. The thermometer scales most used are Fahrenheit's, the Centigrade, and Reaumur's. (288-290.) The differential thermometer serves to measure the difference of temperature at two places. (291.) The expansive power of heat may be made to regu- late the rate of clocks and watches. (292-294.) The hygrometer and hygrodeik are instruments for measuring the amount of moisture in the air. (296, 297.) ELECTRICITY. MAGNETISM. 298. Magnets. If we bring one end of an ordinary bar magnet in contact with a pile of iron tacks, we find that some of the tacks cling to the magnet. The force residing in a magnet and shown by its attracting iron is called magnetism. There is a certain iron ore which has the power of attracting iron. This ore seems to have been first found near Magnesia, a city of Asia Minor ; hence the name magnet. Natural magnets are called loadstones (more properly lodestones), that is, stones that lead or draw iron. 299. The Power of a Magnet resides chiefly at the Ends. If a small iron ball, suspended by a string, be moved alongside a bar magnet, it is scarcely attracted at Fig. 169. the middle of the bar. As it approaches either end, it is attracted more and more, and near the ends the attrac- tion is much the strongest. 196 ELECTRICITY. Lay a piece of stiff drawing-paper upon a strong magnetic bar, and strew fine iron-filings over it. The particles of iron (Figure 169) arrange themselves in lines radiating from the poles, called lines of mag- netic force, or magnetic curves. 300. The Forces at the Ends of a Magnet act in Opposite Directions. Suspend a bar magnet by a string (Figure 170) so that it can turn freely. Bring Fig. 170. one en d of a bar magnet near one end of the suspended magnet, and the latter is drawn towards it. Re- verse the ends of the bar magnet, and the end of the suspended mag- A ^r net is repelled. This shows that the forces at the ends of a magnet act in opposite directions. The ends of the magnet, or the points where the opposite forces reside, are called poles. 301. The Magnetic Needle. A bar magnet poised or suspended so as to turn freely is called a magnetic needle. One of its poles will always point to the north, and is called the north pole. The opposite pole is called the south pole. 302. The Earth acts like a Magnet. If a small needle which is free to move horizontally be placed upon a bar magnet, its south pole will always point towards the north pole of the latter. If a small dip- ping needle, that is, a needle which is free to move vertically, be placed above the middle of a bar magnet, it stands parallel with the bar magnet. If it be moved towards the north pole of the magnet, the south pole dips more and more towards the magnet. If it be moved from the centre of the bar magnet towards the south pole, its north pole dips in the same way. Now, a magnetic needle (301) points north and south ELECTRICITY. I 9 7 when held above the earth. A dipping needle near the equator stands horizontally ; when carried north from the equator, its north pole dips towards the horizon ; and when carried south from the equator, its south pole dips. We see, then, that the earth acts upon a magnetic needle like a magnet 'whose poles are near the poles of the earth. 303. Like Poles of Magnets repel and unlike Poles attract each other. Bring the north pole of a bar magnet near the north pole of a needle, and the latter will be repelled. Bring the south pole of this magnet near the north pole of the needle, and it will be at- tracted. The experiment with the bar magnet and the dipping needle (302) also illustrates this law. 304. Magnetism is developed in Iron or Steel by Induction. When a piece of soft iron is brought in contact with the pole of a magnet, it will attract other pieces of iron, showing that magnetism is developed in the iron by contact 'with the magnet. Magnetism can be developed, or induced, in a piece of steel in the same way. The iron loses its magnetism as soon as it is taken away from the magnet, 'while the steel retains it. The iron or steel need not come in actual contact with the magnet. Magnetism Fig. 171. will be induced in it, if it merely be brought very near the pole. 305. Forms of Magnets. Ordinary magnets are made of steel. When straight, they are called bar magnets; when bent into the shape of the letter U, they are called horseshoe magnets. Several bar or horseshoe magnets con- nected (Figure 171) constitute a mag- netic battery. 198 ELECTRICITY. SUMMARY. The force which enables a magnet to attract iron is called magnetism. (298.) This force resides chiefly at the ends, or poles, of a magnet. It radiates from these poles in curved lines, called lines of magnetic force, or magnetic curves. (299, 300.) The forces at the poles of a magnet act in opposite directions. (300.) The earth acts upon a needle like a magnet. Its magnetic poles are situated near the poles of its axis. Like poles of magnets repel, and unlike poles attract, each other. (303.) A magnet can develop magnetism in iron or steel by induction. Soft iron loses its magnetism as soon as it is withdrawn from the influence of the magnet, while steel retains its magnetism permanently. (304.) VOLTAIC ELECTRICITY. 306. The Voltaic Pair. If a strip of amalgamated zinc (zinc which has been immersed in mercury) and another of copper be placed in a cup of dilute sulphuric acid, no action takes place so long as the zinc and copper are not connected. If we join the plates by means of a wire, bubbles of hydrogen gas at once appear at the cop- per plate, and the acid begins to dissolve the zinc plate. If a small magnetic needle be held near the wire when the plates are connected (Figure 172), the needle will ELECTRICITY. 199 Fig. 172. be turned aside, showing that there is some new force in the wire. This new force is called electricity; and, as it seems to flow through the wire, it is called in this case the electric current. It is produced by the chemical action between the acid and the zinc. Two plates thus connected form a voltaic pair or cell. The zinc is called the active plate, and the copper the passive plate. The passive plate is often made of other substances. The active plate is also called the negative pole, and the passive plate the positive pole of the cell. What- ever connects the poles is called the circuit. The electric current is always assumed to Row from the passive plate, or positive pole, through the wire to the active plate, or negative pole. 307. Bunseris Cell. When the above voltaic cell is in action, bubbles of hydrogen collect upon the passive plate so as nearly to cover it. This prevents contact be- tween the plate and the liquid, and Fig. 173. interferes with the chemical action of the cell. In Bunseris cell this collection of hydrogen is prevented by surround- ing the passive plate with strong nitric acid, which takes up the hydrogen. This cell (Figure 173) consists of the following parts : a large earthen or glass cup ; a piece of zinc rolled into a cylinder and open down one side ; a porous porcelain cup, small enough to go inside the zinc cylinder; and a piece of coke carbon, small enough to stand inside the 200 ELECTRICITY. Fig. 174. porcelain cup. The larger cup is filled with dilute sulphuric acid, and the smaller cup with the strongest nitric acid.* The carbon is the passive plate. In Grove's cell, a strip of platinum is used for the pas- sive plate, instead of carbon. In other respects it is essentially the same as Bunsen's. 308. DanielVs Cell. This cell is shown in Figure 174. The outer vessel is of copper, and serves .as the passive plate. Inside this is a vessel of porous earthen-ware, containing a rod of zinc. The space between the copper and the porous cup is filled with a solution of blue vitriol, which is kept saturated by crystals of the salt lying on a perforated shelf. The porous cup is filled with dilute sulphuric acid. The porous partition keeps the fluids from mingling, but does not hinder the passage of the current. The blue vitriol in contact with the passive plate serves to take up the hydrogen. 309. The Electric Battery. Several cells joined together constitute a battery. There are two ways in which the cells may be joined : (i) the zinc of the first cell may be joined to the carbon of the second, and the zinc of the second to the carbon of the third, and so on throughout, and the free carbon of the first cell joined to the free zinc of the last by a wire, as in Fig- Fig- 175- * Instead of nitric acid, we may use a mixture of equal parts of strong sulphuric acid and a concentrated solution of bichro- mate of potash. ELECTRICITY. 2OI ure 175 ; or (2) the zincs may all be joined together, and the carbons all joined together, and then the zincs and the carbons joined by a wire, as in Figure 176. 310. Quantity and Intensity. Arrange a battery of three cells according to the first method, and connect the poles by a short, thick copper wire, which passes over a needle, and observe how much the needle is turned aside, or dejlected. Then arrange the same cells according to the second method, and connect the zinc and carbon by the same wire ; and the needle will be dejlected more than in the former case. When the battery, then, is arranged according to the second method, the current has the greater power to dejlect the needle. Fig. 176. If now the cells be again arranged in the Jirst way, and a piece vijine steel wire, two or three feet long, be put into the circuit, the needle will be dejlected consid- erably less than when the circuit is completed with the short, thick copper wire; showing that the current is resisted in passing through thejine wire. If the same piece of fine wire be put into the circuit when the battery is arranged according to the second method, the needle will be dejlected considerably less than before ; showing that the current produced by \hejirst form of battery has the greater power of overcoming resistance. The power of the current to dejlect a needle is called its quantity, and its power to overcome resistance in the circuit is called its intensity, or its tension. The Jirst form of the battery develops electricity of the greatest tension, and is called a battery of tension, or 2O2 ELECTRICITY. Fig. 177. intensity battery; while the second form of the battery develops electricity in the greatest quantity, and is called a battery of quantity, or quantity battery. When electricity in considerable quantity and of considerable tension is required, the two methods of ar- ranging the battery are combined, as represented in Figure 177* C3ii. Conductors and Non- Conductors. If a piece >f glass, sealing-wax, or dry wood be put into the circuit, no current passes. Substances which will not allow the electric force to pass through them are called non-con- ductors; while those through which it passes freely are called conductors. Metals are generally good conduc- tors. Copper is one of the best conductors, and is gen- erally used for transmitting the ' electric current. When the circuit is composed entirely of conductors, it is called a closed circuit ; when there is a non-conduc- tor in any part of the circuit, it is called an open cir- cuit. 312. The Rheotome and the Rheotrope. An instru- ment for breaking the current is called a rheotome, a name derived from two Greek words, and signifying current-cutter. An instrument for changing the di- rection of the current is called a rheotrope; that is, a current-turner. These two instruments are often com- bined in one. 313. A Magnetic Needle tends to place itself at right angles with a Wire through which a Current isjlowing. If the current be made to flow over a needle from its north end to its south end, the north pole of the needle will turn to the left hand of an observer who is facing that pole. If it be made to pass over the needle ELECTRICITY. 203 from its south pole to its north, its north pole will turn to the right. If it be made to flow under the needle, the north pole will turn in just the opposite direction. We see, then, that the needle always tends to place itself at right angles to a wire through which a current is flowing. 314. The Rheoscope, or Galvanometer. An instru- n ment used for detecting or measuring a current is called a rheoscope, or a galvanometer. The first name means a current-examiner; the second, a measurer of galvanism. Current electricity is often called galvan- ism, from its discoverer, Galvani. If the magnetic needle used to detect the electricity (306) moves over a graduated arc, it will be found to move a greater number of degrees when the current passes entirely round it, than when it merely passes over it or under it. The effect is the same as if two currents of equal strength were passing over or under the needle, and both in the same direction. Every time, therefore, that the wire conducting the current is coiled round the needle, the effect of the current is multiplied. A current which is too weak to deflect the needle by simply passing over or under it, may be made to deflect it decidedly by coiling the conducting wire many times round the needle. 315. The Astatic Needle. When a single needle is deflected by the current, the directive action of the earth, which tends to make the needle take a north and south position, offers a resistance to the deflection. In order to neutralize this directive action, two needles of equal magnetic strength are fastened together, so that the north pole of one faces the south pole of the other, as in Figure 178. Since the earth will pull each end of such a compound needle towards the north and towards the south with equal strength, it will 204 ELECTRICITY. Fig. 178. h ave no tendency to point north and south. This needle is called an astatic needle (from a Greek word meaning unsteady) ; that is, one having no directive power. An astatic galvanometer is one in which the needle is of this kind. 316. The Resistance of Conductors. It has been proved that the resistances of 'wires of the same ma- terial and of uniform thickness to the current are in the direct ratio of their lengths, and in the inverse ratio of the squares of their diameters. Thus a wire of a certain length offers twice the resistance of its half, thrice that of its third, and so forth. Again, wires of the same metal, whose diameters are in the ratio of i, 2, 3, etc., offer resistances which are to each other as i, , , etc. Therefore, the longer the wire, the greater the resistance; the thicker the wire, 'the less the resistance. The same holds true of liquids, but not with the same exactness. SUMMARY. A voltaic pair or cell consists of two plates, usually of metal, immersed in a liquid which will act chemically upon one of them. The plate acted upon is called the active plate, the other the passive plate. The two plates are called the poles of the cell ; the passive the positive pole, and the active the negative pole. That which is employed to connect the poles is called the circuit. (306.) A force called electricity resides in a wire which con- nects the poles. Since this force seems to flow through the wire, it is called a current. We always consider the ELECTRICITY. 2C>5 current as starting from the positive pole, and passing to the negative pole. (306,311.) When two or more cells are connected, the apparatus is called a battery. The carbon of one cell may be connected with the zinc of the next, and so on throughout ; or the carbons may all be connected, and also all the zincs. In the first case, the free zinc of the first cell and the free carbon of the last are the poles of the battery ; in the second, the united carbons constitute one pole, and the united zincs the other. (309.) The power of the current to turn a needle is called its quantity; its power to overcome resistance, its intensity. The first form of battery gives electricity of greater intensity than the second form ; while the latter gives electricity of greater quantity than the other. (310.) Substances which allow the current to pass readily , through them are called conductors; those which will not allow it to pass are called non-conductors. A closed circuit is made up entirely of conductors. If there is a non-conductor in the circuit, it is said to be open. (311.) An instrument for breaking the current is called a rheotome; an instrument for changing the direction of the current, a rheotrope. (312.) A magnetic needle tends to place itself at right angles to a wire through which a current is passing. The direc- tion in which the needle turns depends on the direction of the current, and upon the position of the needle with reference to the wire. (313.) An instrument for indicating and measuring the cur- rent is called a rheoscope, or galvanometer. (314.) The resistance to the deflection of the needle caused by the magnetic attraction of the earth is neutralized in the astatic needle, which is therefore more sensitive to the action of the current. (315.) 2O6 ELECTRICITY. The effect of the current upon a needle is multiplied by coiling the wire round the needle. (314.) The resistances oif wires of the same material and thickness are directly as their lengths, and inversely as the squares of their diameters. (316.) ELECTRO-MAGNETISM. 317. The Current can make Iron magnetic. If a part of the wire of the circuit be wound into a coil, a piece of soft iron placed inside this coil becomes strongly magnetic while the current is passing, and is called an electro-magnet. The coil is called a helix. When the current passes through the coil in the direc- tion of the hands of a watch, the end at which it enters will be a south pole, as in Figure 1 79 ; so that, by Fig. 179. reversing the current, the poles of the 1 electro-magnet "will be reversed. When the current is broken,* the soft iron instantly loses its magnetism. A steel rod retains its magnetism after the current is broken. If the wire is wound around ' Fig. 180. the iron in several layers, the strength of the magnet is greatly increased. The strongest electro-magnets are of the horseshoe form. They far exceed ordinary magnets in power. Small electro - magnets have been made which support 3,500 times their own weight, and large ones which hold up a weight of 2,500 pounds. These magnets are much stronger when pro- ELECTRICITY. 207 vided with a keeper, or armature; that is, a piece of soft iron to connect the poles, as in Figure 180. 318. The Wire through which a Current is passing is a Magnet. If the current be sent through a coil such as is shown in Figure 181, and the end Fig. 181. of a rod of soft iron be brought near the opening in the centre, it is at once drawn into the coil. Coils have been made which would draw up a weight of 600 pounds. If the wire joining the poles of a battery is brought in contact with fine iron filings, they adhere to the wire ; showing that any 'wire through which the current is flowing is magnetic. 319. Electricity as a Source of Mechan- ical Power. All the electro-magnetic ma- chines which have been invented for doing work, depend on the property of an electro- magnet to acquire or to lose its magnetism when the current flows or is interrupted; or to reverse its poles when the direction of the current changes. Page's rotating machine (Figure 182) illustrates one method of making the electric force do work. It consists of a horseshoe magnet, in the axis of which is an upright shaft. To this a piece of soft iron is fixed, with its, ends fa- cing the poles of the magnet. The soft iron is surrounded with a coil of copper wire, so that it is an elec- tro-magnet. The ends of the wires of the coil are fastened to two metal- lic strips, which are attached to the shaft. The current comes to the coil through two springs which Fig. 182. 208 ELECTRICITY. press against these strips, and which act as a rheotrope to reverse the current when the shaft has turned half-way round. The machine is so arranged that, at starting, the poles of the two magnets facing each other are of the same kind. They therefore repel each other, and when the shaft is once started, they send it around a quarter of the way; then unlike poles begin to approach each other, and their attraction causes the shaft to complete half a rotation. The current then changes its direction, the poles of the electro-magnet are reversed, and like poles again face each other and are repelled. The rotation is kept up by the self-acting rheotrope. The shaft may be made to rotate 2,000 times a minute, caus- ing 4,000 changes of polarity in that brief time. 320. Electric Clocks. The electric force has also been used to regulate the movements of clocks, called copying clocks. They are of -the usual construction, except that the pendulum balls are hollow coils of copper wire, which become mag- netic when a current is sent through them. In Figure 183, R represents a part of the rod, and B the ball, of such a pendulum. Permanent mag- nets, NS and S ' N, are fastened against the sides of the clock-case opposite the ends of the coil B, with like poles towards the coil. The hollow of the coil, as it swings, can pass a little way up the length of each magnet. If the south poles of the magnets are turned towards the coil, as in the figure, and a current is sent through the wire, one end of the coil becomes a north pole, which is attracted by the magnet near it, and the other end a south pole, which is repelled by the magnet near it. Fig. 183. f- ELECTRICITY. 209 This attraction and repulsion both tend to send the coil in one direction. If, now, at the instant that B is drawn to one side, the direction of the current is changed, the poles of the coil are reversed, and it is carried to the other side. The pendulum thus vibrates every time the current is reversed. This is done by means of a regulating clock. Every time the pendulum of this clock vibrates, the current is reversed ; so that the pendulums of all the copying clocks vibrate exactly at the same rate as the pendulum of the regulating clock. Figure 184 shows one of the ways in which the pendu- lum, A) of the regulating clock can change the direction Fig. 184. ! 1 '-} 1 1 ! i i A i C B > /rf. ! C D C S r 'N J c 3 | G 1 E of the current. The spring e is connected with the neg- ative pole of the battery G, and the spring d with the positive pole of the battery F. The other poles of these batteries are connected with the plates m and n, buried in the earth. B and C are the pendulums of the copy- ing clocks. When the regulating pendulum touches the spring the cumulo-stratus; by six, the stratus. 24. Cirrus Cloud. The cirrus (or curl) cloud consists of parallel, -wavy, or diverging fibres which may increase in any or in all directions. Of all clouds it has the least density, the greatest elevation, and the greatest variety of figure. It is the cloud first seen after serene weather, appearing as slender fila- ments stretching like white lines pencilled across the blue sky, and thence spreading in one or more directions, laterally, or upward, or downward. Sometimes the thin lines of cloud are arranged parallel to each other, the lines lying in the northern hemisphere from north to south, or from south-west to north- east ; sometimes they diverge from each other in the form of the \ 248 APPENDIX. tail of a horse; while at other times they cross each other in different ways like rich, delicate lace-work. It is probable that the fine particles of which this cloud is composed are minute crystals of ice or snow-flakes. The duration of the cirrus varies from a few minutes to many hours. It remains for a short time when formed in the lower parts of the atmosphere and near other clouds, and longest when it appears alone in the sky and at a great height. 25. Cumulus. This name is applied to convex or conical heaps of clouds increasing upwards from a horizontal base. They are usually of a very dense structure ; are formed in the lower regions of the atmosphere; and are carried along in the current next the earth. The cumulus has been well called the cloud of the day, being caused by the ascending currents of warm air which rise from the heated ground. Its beginning is the little cloud not bigger than a man's hand, which is the nucleus round which it increases. The lower surface remains roughly horizontal, while the upper rises into towering heaps, which may continue comparatively small, or swell into a size far exceeding that of 'mountains. When these clouds are of moderate height and size, of a well- defined curved outline, and appear only during the heat of the day, they indicate a continuance of fair weather. But when they increase with great rapidity, sink down into the lower parts of the atmosphere, and do not disappear towards even- ing, rain may be expected. If loose fleecy patches of cloud begin to be thrown out from their surfaces, the rain is near at hand. 26. Stratus. The stratus, as its name implies, is a widely- extended, continuous layer or sheet of cloud, increasing from below upwards. It is, besides, the lowest sort of cloud, its lower surface commonly resting on the earth. The stratus may be called the cloud of night, since it generally forms about sunset, grows denser during the night, and disappears about sunrise. It is caused by the vapors which rise during the day, but towards evening fall to the earth with the falling temperature. Since during night the cooling of the air begins on the ground, the APPENDIX. 249 250 APPENDIX. stratus first appears like a thin mist floating near the surface of the earth ; it thence increases upwards as successive layers of the air are cooled below the point of saturation. It includes all those mists already described, which in the calm evening of a warm summer day form in the bottom of valleys and over low- lying grounds, and then spread upwards over the surrounding country like an inundation. When the morning sun shines on the upper surface of the stratus cloud, it begins to be agitated and to heave up in dif- ferent places into the rounded forms of the cumulus, and the whole of its lower surface begins to rise from the ground. As the heat increases, it continues to ascend, breaks up into de- tached masses, and soon disappears. This indicates a continu- ance of fine weather. 27. Cirro-cumulus. This cloud is composed of well-defined, small, roundish masses, lying near each other, and quite separated by intervals of sky. It is formed from the cirrus cloud, the fibres of which break, and gather into these small masses. It is com- monly known among sailors as a mackerel sky. 28. Cirro-stratus. The cirro-stratus partakes partly of the characteristics of the cirrus and stratus. It consists of long, thin, horizontal clouds, 'with bent or undulated edges, and either separate or in groups. It is a marked precursor of storms. 29. Cumulo-stratus. This cloud is formed by the blending of the cirro-stratus ivith the cumulus, either among its piled-up heaps, or spreading underneath its base as a horizontal layer. It is formed when the cumulus becomes surrounded with small fleecy clouds just before rain begins to fall, and also on the approach of thunder-storms. 30. Cumulo-cirro-stratus, or Nimbtis. This is the well-known rain-cloud, consisting of a cloud, or system of clouds, from which rain is falling. It sometimes has its origin in the cumulo- stratus, which increases till it overspreads the sky, and becomes black or bluish-black in color; but, this soon changing to gray, the nimbus is formed, and rain begins to fall. Its name, cumulo-cirro-stratus, suggests the way in which it is more frequently formed. At a considerable height, a sheet of APPENDIX. 251 cirro-stratus cloud is spread out, under which cumulus clouds drift from the windward ; these rapidly increase and unite, form- ing one continuous gray mass, from which the rain falls. The breaking-up of the lower gray mass indicates that the rain will soon cease. s^ When a rain-cloud is seen approaching at a distance, cirri appear to shoot out from its top in all directions ; and the more copious the rain-fall, the greater is the number of these cirri. RAIN, SNOW, AND HAIL. 31. Rain.-^ Whatever lowers the temperature of the air may be considered as a cause of rain. It is chiefly brought about by the ascent of air into the higher regions of the atmosphere. Moist air-currents are forced up into the higher parts of the atmosphere by colder, drier, and therefore heavier, wind-cur- rents which get beneath them. Ranges of mountains also oppose their masses to the winds, so that the air forced up their slopes is cooled, and its vapor condensed into showers of rain or snow. Moist air-currents are also drawn up into the higher regions of the atmosphere over the area of least pressure at the centre of storms ; and in such cases the rain-fall is gen- erally very heavy. The temperature of the air is lowered, and the amount of the rain-fall increased, by those winds which convey the air to higher latitudes. This occurs in temperate regions, or in those tracts traversed by the return trade-winds, which in the north temperate zone blow from the south-west, and in the south temperate zone from the north-west. The meeting and mixing of 'winds of different temperatures is also v a cause of rain, since the several portions, when combined into one, cannot hold as much vapor as before. The rain-fall is also increased if the prevailing winds are directly from the sea, and are therefore moist; but it is diminished if they have passed over large tracts of land, particularly mountain-ranges, and are therefore dry. The quantity of rain is influenced by sandy deserts, which allow radiation, by day or night, to take im- 252 APPENDIX. mediate effect in raising or depressing the temperature; and also by forests, which retard or counteract radiation. Rain rarely or never falls in certain places, which are, on that account, called rainless regions; as, for example, the coast of Peru in South America, the Sahara in Africa, and the desert of Gobi, in Asia. The Sahara is bounded on the north and on the south by ranges of mountains. When the north-east trade-wind strikes the northern range, a part of its vapor is condensed. As it moves southward, it reaches warmer latitudes, where there is a greater capacity for moisture. Since there are no opposing winds to force it upwards, it sweeps on across the vast sandy plain until it arrives at the southern mountains, where its vapor is precipitated in abundant rains. In the few spots in the desert where hills or mountains occur, there are occasional rains. On the desert of Gobi, the prevailing winds are from the .south-east, and are very dry, because they have precipitated nearly all their moisture in passing, over the Himalaya Moun- tains. The rainless district in Peru is caused by the Andes, which condense nearly all the vapor of the south-east trade-wind in copious rains on their eastern slopes. On the other hand, in such places as Chili and Patagonia, it rains almost every day. "XT^ 32. Rain-fall 'within the Tropics. At places within the tropics, where the trade-winds blow regularly and steadily, the rain-fall is small. Since these winds come from higher latitudes, the temperature is increasing, and they are thus more likely to take up moisture than to part with it. Where, however, the trade- winds are forced up the slopes of mountain ranges, they bring rain in copious showers. 33. The Region of Calms. This tropical belt (see page 235) is the region of constant rains. Here the sun almost invariably rises in a clear sky; but about midday clouds gather, and the whole face of the sky is soon covered with black clouds, which pour down prodigious quantities of rain. Towards evening the clouds disappear, the sun sets in a clear sky, and the nights APPENDIX. 253 are serene and fine. The reason of this is, that the air, being greatly heated by the vertical rays of the sun, ascends, drawing with it all the vapor which the trade-winds have brought with them, and which has been largely increased by the rapid evap- oration from the belt of calms ; and this vapor is condensed as it rises. The rain is sometimes so copious that fresh water has been collected from the surface of te sea. As evening sets in, the surface of the earth and the air near it being cooled, the as- cending currents cease, and the cooled air descends ; the clouds are thus dissolved, and the sky continues clear till the returning heat of the following day. 34. The Rain-fall of India. Over a great part of the tropics disturbing influences draw the trade-winds out of their course, and sometimes, as in the case of the monsoons, give rise to winds which blow from the opposite point of the compass. These winds affect the rain-fall of India, and but for them the eastern districts of Hindostan would be constantly deluged with rain, and the western districts constantly dry and arid. As it is, each part of India has its dry and wet seasons, summer being the wet season of the west and interior as far as the Himalaya, and winter the wet season of the east, and especially the south-east. So far as known, the heaviest annual rain-fall at any place on the globe is 600 inches, on the Khasia Hills. About 500 inches of this fall in seven months, during the south-west monsoons. These hills face the Bay of Bengal, from which they are sepa- rated by only 200 miles of swamps and marshes. Hence the southerly winds not only arrive heavily laden with vapor from \Jthe Indian Ocean, but they get more moisture in passing over the 200 miles of swamp. They are, therefore, ready to burst in torrents, even before they are suddenly raised, by the hills they encounter, into the cooler regions of the atmosphere. ~S 35. Snotv. Snow is the frozen moisture which falls from the /clouds when the temperature is 32 or lower. The particles of f >which snow is composed are crystals, which are usually in the form of six-pointed stars. About 1,000 different kinds of snow- crystals have been already observed, a few of which are shown 254 APPENDIX. in Figure 199. The forms of the crystals of the same fall of snow are generally similar to each other. Snow-flakes vary from an inch to T ^j- of an inch in diameter, the largest being observed when the temperature is near 32, and the smallest at very low temperatures. The limit of the fall of snow at any time of the year coincides nearly with 30 N. latitude, which includes almost the whole of Europe. On traversing the Atlantic this line rises to 45, but on nearing the American continent it descends to 33 ; it rises in the west of America to 47, and again falls to 40 in the Pacific. Snow is unknown at Gibraltar; at Paris, it falls 12 days on an average annually, and at St. Petersburg, 170 days. The white color of snow is caused by the combining of the different prismatic rays which issue from the minute snow- crystals. When the crystals are looked at separately, some Fig. 199- appear red, others green, purple, and, in short, all the colors of the spectrum; but when a mass of snow is looked at, the different colors blend into white. Red snoiv and green snow have been occasionally met with in the arctic regions and in other parts of the world. These colors are due to the presence of vegetable organisms, about y^g-^ of an inch in diameter, which grow and flourish in the region of eternal snow. From its loose texture, and from its containing about ten times its bulk of air, snow is a very bad conductor of heat ; and thus is an admirable covering to preserve the earth from the effects of its own radiation. It not unfrequently happens in times of great cold, that the soil is 40 warmer than the surface APPENDIX. 255 of the snow which covers it. The flooding of rivers, from the melting of the snow on mountains in spring and summer, carries fertility into regions which would otherwise remain barren wastes. 36. Hail. Hailstones are generally of a conical or of a round shape, and when cut across are found to be composed of alternate layers of clear and opaque ice, enveloping a white snowy nucleus. Less frequently they are composed of crystals radiating from the centre outwards. They vary much in size, some being as small as the smallest shot, while others are several inches in diameter. In August, 1813, hailstones the size of eggs fell upon the British army among the Pyrenees ; the storm lasted twenty minutes, and was not accompanied with thunder or lightning. June 4th, 1814, hail, from 13 to 15 inches in diameter, fell in Ohio. In the Orkney Islands, July 24th, 1818, during thunder, a very remarkable shower of hail took place; the stones were as large as a goose's egg, and mixed with large masses of ice. The origin of hail is not fully understood ; but it appears to be formed by a cold current of air forcing its way into a mass of air much warmer and nearly saturated, the temperature of the united mass being below the freezing-point. The warm moist air is easily accounted for, since hail generally falls in summer and during the day; but it is difficult to account for the in- tensely cold current which is sufficient to reduce the warm saturated mass below 32. In mountainous regions, cold currents from the fields of snow, rushing down the sides of the mountains and mixing with the heated air of the valleys, are no doubt frequent causes of hail; and such places are peculiarly subject to hailstorms. The sudden ascent of moist warm air into the upper regions of the atmosphere, where a cold current prevails at the time, is, in all probability, a common cause of hail. This is confirmed by the sultry, close weather which generally precedes hailstorms, the slight but sudden fall of the barometer, the whirlwinds and ascending currents which accompany them, and the fall in the temperature which follows after the storm has passed. 256 APPENDIX. ATMOSPHERIC ELECTRICITY. j. Electricity in the Air. The identity of lightning and electricity was first suspected by Wall in 1708, but it was re- served to Franklin to prove it. In 1749, he suggested, as the mode of proof, the erection of pointed metallic conductors prop- erly insulated. Acting on this suggestion, Dalibard erected near Paris a pointed iron rod, 40 feet in length, and insulated; and, on the loth of May, 1752, obtained electrical sparks from it. In June of the same year, Franklin, impatient at the delay in erecting the spire for his pointed conductor, tried the experi- ment of obtaining electricity from the clouds by flying a kite. The kite was held by a hempen string, to the lower end of which a key was attached ; and the whole was insulated by tying a silk ribbon to the key, the other end of the ribbon being attached to a post. On the approach of the thunder- cloud, he raised the kite, and soon the fibres of the hempen string began to repel each other; and, at last, when the rain had moistened the string, he had the satisfaction of drawing sparks from the key. When the sky is cloudless, the electricity is always positive; but the intensity increases with the height. When the sky is clouded, the electricity is sometimes positive and sometimes negative, according to the electrified condition of the clouds. In relation to the air, the earth's surface is always negative. The electricity of the atmosphere is stronger in winter than in summer, increasing from June to January, and decreasing from January to June. It is subject to a double maximum and minimum each day. 38. Sources of Atmospheric Electricity. (i) Evaporation. Electricity is produced when impure water is evaporating, or water in which chemical decomposition is going on ; none whatever being produced by the evaporation of pure water. Evaporation from water containing an alkali or a salt gives off negative electricity to the air, and leaves positive electricity APPENDIX. 257 behind ; but when the water contains acid, positive electricity is given off, and negative is left behind. Hence it is supposed that seas, lakes, and rivers are abundant sources of electricity, particularly of the positive sort. (2) Vegetation. The vege- table kingdom is also a source of electricity; (a) from the evap- oration going on by which water is separated from the sap of the plants, and () from the giving off of oxygen gas during the day, and carbonic gas during the night. In these cases, positive electricity arises from the plants, and negative is left behind. (3) Combustion. During the process of burning, bodies give off positive electricity, and become themselves neg- atively electrified. This is frequently seen on a grand scale during volcanic eruptions. (4) Friction. Wind, by the fric- tion it produces upon terrestrial objects, the particles of dust, and the watery particles which it carries with it, contributes to the electricity of the air. Electricity is not generated if the moisture be in the form of pure vapor. 39. Effect of the Condensation of Vapor. When a great mul- titude of molecules of vapor are condensed by cold into a drop, or snow-spangle, that drop probably collects and retains on its surface the whole electricity of the molecules from which it is formed. If a thousand such globules coalesce into one, the electricity will be increased a thousand-fold, and, being spread entirely over the surface, will have a tenfold tension. This view (which is Sir John Herschel's) explains the electricity ob- served in the lower stratum of air when detv is being deposited, and the highly electrical state of fogs and clouds. It also ex- plains the annual fluctuation ; for, since in winter the conden- sation of vapor is greater and more frequent than in summer, the average quantity of electricity will be greater in winter. 40. Thunder-storms. The thunder-storm probably originates, like cloud and rain, in the condensation of vapor ; but the con- densation is more copious and more rapid, so as to bring about an accumulation of a sufficient quantity of electricity. If the condensation is not copious, the electricity will be too weak; and if not sudden, it escapes before enough collects for a dis- charge. 17 258 APPENDIX. Thunder-storms occur most frequently within the tropics, and diminish in frequency towards the poles. They are also more frequent in summer than in winter; during day than during night ; after midday than before it ; and in mountainous coun- tries than in plains. Within the tropics they prevail most in the region of calms and during the rainy season ; and least in arid deserts and during the dry season. 41. Lightning. Arago has divided lightning into three kinds; zigzag lightning, sheet lightning, and ball lightning. When the electric flash darts through the air, it takes the path of least resistance ; and, since the conducting power of different portions of the atmosphere is unequal, the lightning frequently appears zigzag. When branches are given off at different points of its course, the lightning is said to be forked. Sheet lightning is the most common, appearing as a glow of light illuminating the sky. The flashes often follow each other in quick succession, and the thunder which accompanies them is low and at a considerable distance. Analogous to this is silent lightning, often called heat lightning, which generally occurs during serene summer evenings, lighting up the sky for hours with repeated faint flashes, attended with no thunder. It is probable that this kind of lightning is almost always the reflection of the lightning of distant storms from the vapor of the upper regions of the atmosphere. Ball lightning is the least common. It appears as a globular mass, moving slowly or sometimes remaining stationary, and- in a short time explodes with violence. It has not yet been satisfactorily explained. The duration of a flash of lightning, like that of an electric spark, is less than the thousandth part of a second. For this reason a wheel rotating so fast that the spokes are invisible will ap- pear stationary when lighted up with the electric spark or by lightning. 42. Thunder. Thunder is probably the noise produced by the rush of the air to fill the vacuum left by the lightning along the path of the discharge. The sound emitted by flames is a familiar phenomenon of the same kind. Flashes of lightning frequently extend two or three miles in length ; and since the thunder is APPENDIX. 259 produced along its whole course nearly at the same instant, the prolonged rolling noise arises from the different intervals of time it takes the sound to reach the ear. Reverberations from clouds and from mountains frequently heighten the effect and prolong the peal. Thunder has not been heard at a greater distance than 14 miles from the flash. 43. Effects of Lightning. Electrical discharges generally pass into the air, or into other clouds less highly electrified ; a very few only take place between the cloud and the earth. By this latter class innumerable lives have been destroyed, the strongest trees rent to pieces, heavy bodies displaced, iron and steel magnetized, metals and rocks softened and fused, and com- bustible substances set on fire. When the thunderbolt falls upon sand, it usually produces fulgurites, or fulminary tubes, which are silicious tubes of various sizes vitrified within. 44. Return Shock. The return shock sometimes proves fatal to living beings, even at great distances from the place of the electric discharge. It is caused by the inductive action of the electrified cloud, by which bodies become charged with the elec- tricity opposite to that of the cloud. When the cloud has dis- charged its electricity into the ground, the induction ceases, and the rapid change of the bodies from the electrified to the neutral state gives them a severe shock. 45. Lightning-Rods. The lightning-rod was invented by Franklin in 1755. The chief advantage gained by it is not that it protects the building in case of a discharge by allow- ing a free passage for the electric fluid to the earth ; but by quietly and gradually keeping up the communication, it tends to maintain the electric equilibrium, and thus. prevent a dis- charge. The best rods are made of copper, not less than three- quarters of an inch thick, and pointed at the upper end. They should be of one piece throughout, fastened vertically to the roof of the building, and thence carried down into the ground. The lower extremity should part into two or three branches bent away from the house, and carried far enough into the soil to meet water, or permanently moist earth. The conductor should be connected with all metallic surfaces on the roof or 26o . APPENDIX. other parts of the building, in order to prevent the occurrence of lateral discharges, or discharges from the conductor to these surfaces, which are often very destructive. ^V~ 46. St. Elmo's Fire. This meteor is the Castor and Pollux of the ancients, and is frequently mentioned in classic writings. The finest and most beautiful displays occur at sea during storms, when it appears as a light resting on the masts. The light which is seen on a point held near the conductor of an electric machine explains St. Elmo's fire. It takes place when the electricity of a cloud and that of the earth combine, not in flashes of lightning, but slo-wly and continuously from different points. 47. The Aurora Borealis. The aurora borealis % is a luminous appearance in the northern sky. It is observed also in the neighborhood of the south pole, and is there called aurora australis. When fully developed, the aurora consists of a dark segment of a hazy or slaty appearance, surmounted by an arch of light, from which luminous streamers quiver and dart up- wards. Several auroral arches are sometimes seen at once. X\ Sometimes the streamers appear to unite near the zenith, form- ing what is called the corona of the aurora, towards which the dipping needle at the time points. Auroras are very unequally distributed over the earth's sur- face. At Havana, but six have been recorded within a hundred years. As we travel northwards from Cuba, they increase in frequency and brilliancy; they rise higher in the heavens, and oftener attain the zenith. If we travel northwards along the meridian of Washington, we find, on an average, near the par- allel of 40, only ten auroras annually. Near the parallel of 42, the average number is twenty annually; near 45, it is forty; and, near 50, it is eighty. Between this point and the parallel of 62, auroras are seen almost every night, high in the heavens, and as often to the south as the north. Farther north, they are seldom seen except in the south, and from this point they diminish in frequency and brilliancy as we advance towards the pole. If we make a like comparison for the me- ridian of St. Petersburg, we shall find a similar result, except APPENDIX. 26l that the auroral region is situated farther northward than it is in America. Auroras are more frequent in the United States than they are in the same latitudes of Europe. The aurora is of great extent, having been sometimes ob- served simultaneously in Europe and America. The height varies from about 45 to 500 miles above the earth. 48. Relations of the Aurora to Magnetism. Many facts show a connection between the aurora and terrestrial magnetism. The magnetic needle is much agitated when the aurora is vis- ible. When the arch is motionless, so is the needle; but as soon as streamers are shot out, its declination changes every moment, and this happens though the aurora does not appear , at the place of observation, but is seen near the pole. It is v probable that magnetic disturbances of the earth are due to the sun, but not to his heat and light; and that they are invariably accompanied by the aurora and by electric currents on the surface of the earth. The secular periods of the sun's spots, of the variation of the magnetic needle, and of the fre- quency of auroras, coincide in a remarkable way, indicating 1;hat these phenomena are regulated by astronomical causes. * OPTICAL PHENOMENA. 49. The Rainbow. The rainbow, in its most perfect form, consists of two colored arches projected upon falling rain on which the sun is shining from the opposite quarter of the heavens. The lower or inner arch is called the primary bow; the upper or outer, the secondary bow. Each contains all the colors of the spectrum, but the order of the colors in one is the reverse of that in the other. Red is outermost in the pri- mary bow, and innermost in the secondary. The primary bow is the narrower and brighter of the two, and when it is of unusual brightness narrow red arches are seen just within it, called supernumerary bows. These are sometimes three or four in number, but they can be traced only a short distance. The * See Handbook of the Stars, p. 91. 262 APPENDIX. common centre of the bows is in a line drawn from the sun through the eye of the observer. The rainbow is produced by the refraction and reflection of the sunlight within the rain-drops. Its colors are due partially to the dispersion, and partially to the interference of the light thus refracted and reflected. Rainbows in the morning are always seen in the west, and indicate the advance of the rain-cloud from the west at the time that it is clear and bright in the east. Since the fall of rain at this time of the day when the temperature should be rising is an additional evidence of increasing moisture, a morning rain- bow is a prognostic of a change to wet, stormy weather. On the contrary, a rainbow in the evening shows the passing of the rain-cloud to the east, and a clearing up in the west at the time of day when the temperature has begun to fall ; thus further indicating a change from wet to dry weather. Hence the popu- lar rhyme : " A rainbow in the morning, Sailors take warning ; A rainbow at night Is the sailor's delight." 50. Lunar Rainbows. Rainbows are also produced by the light of the moon falling on rain-drops, exactly in the same way as solar rainbows. They are by no means of rare occur- rence. Owing to the feeble light of the moon, the bow is generally without colors ; but when the sky is very clear and the moon is full, the prismatic colors appear, though in sub- dued splendor. 51. Coronas. The corona is an appearance of faintly colored rings encircling the moon when seen behind the light, fleecy cloud of the cirro-cumulus. When the corona is perfect, the rings form several concentric circles, the blue prismatic color being nearer the centre than the red. When large, the ring has generally a whitish, nebulous appearance. Coronas are also very frequently formed round the sun ; but to see them it is necessary to look through smoked glass, or at the image of the-sun reflected from still water. APPENDIX. 263 52. Anthelia. Glories of light, otherwise called anthelia, because formed opposite the sun, are sometimes seen when the shadow of an observer is cast on fog; and the shadow of his Fig. 200. Fig. 201. Fig. 202. Fig. 203. Fig. 204. Fig. 205. head is surrounded with the prismatic circles. The phenomenon is seen in the polar regions whenever sunshine and fog occur at the same time. 264 APPENDIX. 53. Halos. Halos are circles of prismatic colors around the sun (Figures 200-203), or the moon (Figures 204 and 205), but they are not to be confounded with coronas. Halos are of comparatively rare occurrence; coronas, on the contrary, may be seen every time a light, fleecy cloud comes between us and the sun or moon. The structure of halos, as seen from the figures, is often very complicated, circle cutting circle with mathematical exactness, the circles being generally very large. The structure of the corona, on the other hand, is simple, the circles concentric, the inner one small, the diameter of the second being double, and that of the third treble, the diameter of the first. N In halos, the red prismatic color is next the centre; in coronas, the blue. Halos are formed by the refraction and reflection of the rays of light by the minute snow-crystals of the cirrus cloud ; while coronas arise from the interference of the rays passing on each side of the globules of vapor. At the points where the circles of the halo intersect, images of the sun or moon generally appear, from the light concentrated at these points. The images of the sun are called parhelia, or mock- suns ; and those of the moon, paraselene, or mock-moons. These also exhibit the prismatic colors of the halo. * 54. Colors of Clouds. The red and golden clouds which fire the western sky at sunset, are the accompaniment of cumulus clouds as they slowly sink, while dissolving, down into the lower and warmer parts of the atmosphere; and consequently they disappear from the sky shortly after sunset. Such sunsets are therefore prophetic of fine 'weather. A green or yellowish-green sky, on the other hand, is one of the surest prognostics of rain in summer, and snow in winter. If, after a storm, the yellow tint becomes of a sickly green, more rain may be expected ; but if it deepens into orange and red, the atmosphere is getting drier, and fine weather may be looked for. It has been shown that high-pressure steam, while trans- parent, and in the act of expansion, readily absorbs the violet, blue, and part of the green rays, thus letting the yellow, orange, and red pass. It is found, also, that successive layers of air, with visible vapor diffused through them, separate the APPENDIX. 265 transmitted light more and more perfectly from its more re- frangible rays. The blue rays are first absorbed, then the yellow rays, and finally the red rays. It is in the lower layers of the atmosphere that dust, smoke, watery vapor, and small rain- drops are chiefly suspended. When the sun is high in the heavens, the thickness of the vapor-screen between the sun and the eye has no perceptible action on the rays of light, which consequently appear white ; but as the sun descends to the horizon, the thickness of the vapor is greatly increased, and, at sunset, the light of the sun has to pass through 200 miles of the air in illuminating a cloud a mile above the earth. Hence, as the rays fall more and more obliquely on the clouds, they appear successively yellow, orange, and finally red. The varied colors often seen at sunset are due to the fact that the clouds appear at different heights and in different parts of the sky, so that various thicknesses of vapor are interposed between them and the sun. At dawn, the clouds first appear red ; but, as the sun rises higher, the yellow light ceases to be absorbed, and they appear orange, yellow, and finally white. These changes are well described in Dante's Purgatorio: The dawn was vanquishing the matin hour, Which fled before it, so that from afar I recognized the trembling of the sea. . . . Already had the sun the horizon reached, . . . So that the white and the vermilion cheeks Of beautiful Aurora, where I was, By too great age were changing into orange. LongJ f eltou?s Translation. A high red dawn is a prognostic of settled weather, because the redness seen in clouds at a great height while the sun is yet below the horizon, may be occasioned by the great thickness - of the vapor-screen through which the rays must pass before reaching the Clouds, and not by any excess of vapor in the air itself. But if the clouds be red and lowering in the morning, it is a sign of rain ; since, the thickness traversed by the rays being now much less, the red color must arise from an unusual amount of vapor in that stage of partial condensation, when the blue rays are absorbed, and the yellow and red pass. 266 APPENDIX. MOLECULAR MOTION AS MANIFESTED IN SOUND, LIGHT, HEAT, AND ELECTRICITY. i. Sound-waves. When water is agitated, the molecules vibrate in sets, one set moving upward while the next set is moving downward, thus giving rise to a wave. When two sets of water-waves meet and cross, they are found at certain points to increase, and, at others, to diminish each other's volume. The former takes place when they meet in the same phase, that is, when the hollow of one meets the hollow of the other, or the crest of one meets the crest of the other ; while the latter occurs when they meet in opposite phases, that is, when the crest of one meets the hollow of the other. If the waves are of the same size, they will in the one case destroy each other, and, in the other case, form a wave of double the height. Now we have seen that two sounds may meet so as to destroy each other, or, as in the case of beats, so as alternately to in- crease and diminish each other. This must be because, in sonorous vibrations, the 1 molecules vibrate in sets, so as to produce waves. When a string, for instance, vibrates, the air about it is alternately compressed and extended ; and these compressions and extensions run on in the direction in which the sound travels, and constitute sound-waves. The molecules vibrate longitudinally, that is, backward and forward ; and not, as in the water-wave, transversely, that is, at right angles to the direction in which the wave moves. Sound-waves interfere so as to destroy each other when they fc meet in opposite phases ; that is, when the compression of the one meets the extension of the other. As the pitch of the sound rises, the vibrations become more rapid and the waves shorter; for the length of a sound-wave is the distance that the sound travels while the sounding body is making a single vibration. Sounds give beats when they differ slightly in pitch. The waves which then flow out from the sounding bodies differ APPENDIX. 267 slightly in length, and encounter each other alternately in the same and opposite phases. 2. Reflection of Sound. The transmission of sound through air, or any other elastic medium, is best illustrated by a row of ivory balls. If the balls are all of the same size, each gives up all its motion to the next, and itself comes to rest. If one of the balls is larger than the next, it gives up only a part of its motion to it. If it is smaller than the next, it puts that in mo- tion, and itself rebounds. When sound is travelling through the same medium, we have the condition of the balls of the same size. Each molecule gives up all its motion to the next, and itself comes to rest. When the sound meets a denser me- dium, we have the condition of a smaller ball striking against a larger one. The molecules of the denser medium are set vibrating, while those of the rarer medium rebound and trans- mit their motion backward, so that a part of the sound-wave is reflected. When the sound-wave meets a rarer medium, we have the condition of a larger ball striking a smaller one. The molecules forming the last layer of the denser medium retain a part of their motion, and transmit it back again to the mole- cules behind. In this case, also, the wave is partially reflected. Hence, whenever a sound-wave meets a medium different in density from that in which it has been travelling, it is partially reflected and partially transmitted. 3. Refraction of Sound. So long as sound is traversing the medium in which it originates, the advancing wave will have a spherical outline, since the sound travels with equal speed in all directions. But when the wave passes into a medium in which it travels at a different rate, its outline is changed. If it travels faster in the new medium, the portion of the wave in it will be rounded out, or become more convex; if it travels slower, it will be flattened, or become less convex. The direction in which any portion of a sound-wave is travelling will be repre- sented by a line drawn perpendicular to the surface of that portion. Let a b (Figure 206) be a portion of a sound-wave moving in the direction of the arrow, and a c be the surface of a medium O of different density from M, in which the wave has 268 APPENDIX. been moving. If the elasticity of O is such that the wave will move faster in it than in M, the portion a of the wave which enters O first will move on faster than the portion b while the Fig. 206. Fig. 207. latter is moving in M. When a b is wholly within 0, the second arrow shows the direction in which it will be moving; and it will continue to move in this direction so long as it is wholly in this medium. When the direction of a wave is thus bent, it is said to be refracted. In this case, it is bent away from a perpen- dicular P <^ drawn to the surface of the medium O. If the elasticity of O is such that the sound-wave moves slower in it than in M, the portion a of the wave (Figure 207), when it has entered O, moves slower than b while the latter is in M. In this case, it will be seen that the direction of the wave will be bent towards the perpendicular P ^. It is evident that, if a b had not met the medium O obliquely, both ends of it would have entered O at the same time, and its direction would not have been changed. We see, then, that when a sound-wave passes obliquely into a medium of different density, it is refracted, and that, if it travels more rapidly in the new medium, it will be bent away from a perpendicular drawn to the surface of that medium ; while, if it travels less rapidly in the new medium, it will be bent towards a perpendicular drawn to its surface. This refraction of a sound-wave has been shown by the ex- APPENDIX. 269 periment illustrated in Figure 208. B is a collodion balloon filled with carbonic acid gas; w is a watch hung near it; and i is a glass funnel. By placing the ear at /, and moving the Fig. 208. Fig funnel about, a point will be found where the ticking of the watch will be louder than elsewhere. This shows that the sound- waves have been converged to that point. Figure 209 shows how the sound-waves are refracted in passing through the carbonic acid, a b is a portion of the sound-wave. In passing into the carbonic acid, a medium in which it moves more slowly than in air, it is bent into the form of m o ! n. On passing out from the carbonic acid, it is bent still farther in the same di- rection, and thus the two parts of the wave are made to converge. 4. Light is propagated by Vibrations and Waves. We have seen that Newton's rings are produced by the interference of rays of light. This interference of light leads us to the conclu- sion that light is also propagated by waves, which augment or destroy each other, according as they meet in the same or opposite phases. These waves, of course, like those of water and sound, must be made up of vibrating molecules. But light will traverse a vacuum as well as the air. The medium, then, which transmits it, must exist in a vacuum and among the 270 APPENDIX. molecules of all transparent substances. This medium is called the luminiferous ether, or simply the ether. The existence of luminous waves is the only evidence of the existence of the ether, but this evidence is of such a kind that scientific men generally deem it conclusive. The ether fills not only the spaces between the earth and the sun and stars, but the spaces between the molecules of all bodies. Since light, like sound, is propagated by vibrations, it is probable that it originates in vibrations. Moreover, in ordinary combustion, which is the most familiar source of light, the atoms of the oxygen in the air are rushing into combination with the atoms of the burning body; and the collision of these atoms will be very likely to set them vibrating. The vibrating molecules first communicate their vibrations to the molecules of the ether about them, and these transmit the vibrations with the enormous velocity of 190,000 miles a second. When the vibrations meet a new medium, a part of them may pass on through the spaces among its molecules without disturbance, and thus some of the light is transmitted. A part of the vibrations may rebound, and thus some of the light is reflected. Another part may be taken up by the molecules of the medium, and thus some of the light is absorbed. 5. The Length of the Luminous Wave. As the length of the sound-wave is the distance which sound travels while the sounding body is vibrating once, so the length of the luminous wave is the distance which light travels while the molecules of the luminous body are making one vibration. Of course the quicker the vibrations, the shorter the waves. The length of the luminous waves can be found by means of Ne-wtorfs rings. If the curved glass (Figure 210) be pressed down upon the plate beneath, and perpendicular rays of red light be allowed to fall upon it, the centre a will be black, and black rings will appear at i, 2, 3, and 4. Since the centre is black, the waves reflected from the two surfaces must meet there in opposite phases, although the two surfaces are in contact. This is because a wave of light when reflected from a rarer medium changes its phase, while it does not when reflected from APPENDIX. 271 a denser medium. The light reflected from b must travel a wave- length farther than that reflected from i, in order that the waves reflected from these points may meet in opposite phases, and so give a dark ring. Now the wave reflected from b must evidently travel over the space i b twice : hence i b must be i the length of a luminous wave. For a similar reason, 2 c is a a b . c d e wave-length ; 3 d , a wave-length and a half; 4 e, two wave- lengths. Now we can easily find the length of 4 e. 4 m is half the diameter of the fourth dark ring, and is found by measure- ment. We can also measure the radius 4 C, and 4 m C is a right-angled triangle. In this triangle, we know the length of the hypothenuse 4 C, and of the side 4 m ; hence we can find C m. The radius C a Cm = a #2 = 4 e. If violet light be used, the fourth ring is smaller, and 4 e is shorter. In this way, the wave-lengths in the following Table are found: Colors. Length of waves in parts of an inch. Number of waves in an inch. Number of waves in a second. Extreme Red .0000266 37> If we take a long rubber cord fastened at one end, and alternately stretch and relax it, we have a rude representation of a ray of sound made up of longi- tudinal vibrations. The cord is evidently alike all round, and has no sides. But if we shake the cord so that it shall vibrate transversely to its length, we shall at once see that it is not the same above and below as it is to the right and the left ; in other words, that it has sides. Hence we conclude that the luminous vibrations must be transverse. In an unpolarized ray the vibra- tions are transverse, but are executed in every plane ; so that such a ray is alike all round. It is only by forcing the vibrations all into one plane that a ray can be polarized. 8. Heat and Light are one and the same. We have seen that radiant heat and light are reflected, refracted, and dispersed in precisely the same way. It has also been found by difficult and delicate experiments that radiant heat is capable of interference and polarization in the same way as light. These facts lead to the conclusion that light and heat are the same thing, and the following fact proves this beyond a doubt. We have learned that the solar spectrum is crossed by dark lines, known as Fraunhofer's lines. Now an examination of the spectrum with a very delicate thermopile has shown that these dark lines are also devoid of heat, and, furthermore, that simi- 18 274 APPENDIX. lar dark or cold lines exist in the obscure part of the spectrum beyond the red end, where the heat is most intense. Again, these dark lines have been shown to be chemically inactive, and similar inactive lines are found beyond the violet end in the obscure chemical part of the spectrum. The existence of these .blank lines throughout the whole length of the spectrum, in the obscure as well as in the luminous part, and the absence of both heat and chemical activity in the dark lines found in the lumin- ous part, prove conclusively that the thermal, the luminous, and the chemical rays are one and the same thing. Passing from the obscure end of the spectrum beyond the red to the obscure end beyond the violet, we meet with vibrations of greater and greater rapidity, but differing in nothing else. A portion of these vibrations at the lower or thermal end of the spectrum are too slow to be seen, but may be felt by the nerves which give us the sensation of heat. Another portion, including the luminous part of the spectrum, can be both seen and felt, and can also develop chemical action. A third portion, or those beyond the violet end, are too rapid to be seen or felt, but are able to cause chemical action. Luminous heat and light, then, are exactly the same thing; and obscure heat differs from lumi- nous heat only as one color of the spectrum differs from an- other. If there is need of further proof that obscure heat differs from light only in the rapidity of the vibration, it is furnished by an experiment of Dr. Draper's. He gradually raised the tempera- ture of a platinum wire till it was of a white heat, and exam- ined its spectrum throughout the process. At first the spectrum contained only the obscure thermal rays; then the least re- frangible red rays appeared, followed in' succession by the orange, yellow, green, blue, indigo, and violet; and after these came the obscure chemical rays. 9. Electricity is a Mode of Molecular Motion akin to Heat . Suppose the liquid used with the voltaic pair to be muriatic acid. "The zinc plate, in virtue of the powerful affinity of zinc for chlorine, attracts the chlorine atoms, which rush towards it with immense velocity; and the sudden arrest of motion which APPENDIX. 275 attends the union of the chlorine with the zinc has the effect of an incessant volley of atomic shot against the face of the plate. Each of the atomic blows must give an impulse to the molecules of the metal itself, which will be transmitted from molecule to molecule through the material of the plate and the connecting wire, in the same way that a shock is transmitted along a line of ivory balls." The electric current is merely " a wire or other con- ductor filled with innumerable lines of oscillating molecules." We know nothing of the mode of the molecular motion in the metallic conductor. It is apparently allied to heat, but is capable of producing very different effects. This peculiar mode of molecular motion may also be de- veloped by heat, by magnetism, and by friction or percussion. In the same way, heat may be developed, not only by chemical action, but also by friction and percussion. 10. The Molecules of all Bodies are in Motion. It would seem, then, that all the molecules of gross matter are in con- stant vibration; and that, when acted upon by heat or other force, these molecules are made to perform their fundamental vibrations with greater energy, and to add to these higher and higher harmonics. Our organs of sense are instruments for intercepting these vibrations and transmitting them to the brain, where they tell us nearly all that we know of the external world. SOURCES AND CONVERSION OF ENERGY. 11. Kinds of Energy. Every moving mass is said to have actual or dynamical energy. Every mass so situated that it can be moved by the forces acting upon it is said to have possible or -potential energy. The energy of a visible body in motion is called mechanical ; that of moving molecules, or atoms, is called molecular or atomic. The energy manifested in the bodies of animals is called muscular energy, or nerve-force. 12. Affinity, Cohesion, and Gravity tend to convert potential into actual Energy. When visible masses are separated, gravity tends to pull them together, and to convert their potential into 276 APPENDIX. dynamical energy. When the molecules of a body are separated, as in melting or boiling, cohesion tends to draw them together again, and thus to convert their potential into actual energy, which appears as heat. Again, when the atoms of a body are separated, affinity tends to bring them together and to convert their potential into actual energy, which appears, in ordinary chemical action, as heat and electricity, and, in respiration, as heat and nerve-force. 13. Mechanical Energy may be converted into Heat. ji VjQ have a familiar illustration of this in the lighting of a friction match. A part of the energy used in rubbing the match is con- verted by the friction into heat, which ignites the phosphorus. Here there is a double transfer of energy. The muscular energy of the arm is converted into mechanical energy in the moving match, and a part of this into heat by the friction. Before matches were invented, the flint and steel were used for the same purpose. The steel was struck against the flint, and the spark obtained was caught in tinder. A part of the mechanical energy of the steel appeared as heat in the spark. Indians are s.aid to obtain fire by vigorously rubbing together two pieces of dry wood. In this case, too, the heat is nothing but mechanical energy appearing in a new form. Iron can be heated red-hot by hammering it. And, generally, heat is developed by friction and percussion. 14. All Mechanical Energy is ultimately converted into Heat. When a falling body strikes the earth, it becomes heated. In this case, the whole energy of the body is converted into heat. "When bodies are rubbed together, their energy, as we have seen, is converted into heat. The energy of a running stream is gradually converted into heat by the friction against its banks and bed and among its particles. If it is made to turn the wheels of a factory on its way, the rubbing of the parts of the machinery against each other and against the air, together with the various kinds of work done by the machinery, converts the mechanical energy of the water-wheel into heat. A railway train is really stopped by the conversion of its APPENDIX. 277 motion into heat. When this has to be done quickly, the change is hastened by increasing the friction by means of the brakes. On the other hand, in order to prevent the loss of energy while the train is in motion, the axles of the wheels are kept carefully oiled, that they may turn with as little friction as possible. When unlike substances are rubbed together, a part of the energy is first converted into electricity, but ultimately into heat. 15. When Mechanical Energy is converted into Heat, the same Amount of Energy always gives rise to the same Amount of Heat. This was first shown by Joule, who began his experiments in 1843, and continued them till 1849. He converted mechanical energy into heat by means of friction. He first examined cases of the friction of solids against liquids. The apparatus used for this purpose is shown in Figure 211. B is a cylindrical box holding the liquid. In the centre of the box is an upright axis, Fig. 2X1. to which are attached eight paddles, like the one shown in the figure. These revolve between four stationary vanes, which prevent the liquid from being carried round. The paddles are turned by means of the cord r and the weight W. The size of the weight is such that it descends without acquiring anjr 278 APPENDIX. velocity, and hence all its energy is expended in the friction of the paddles. The degree to which the liquid becomes heated by the friction, is shown by a thermometer at t. Knowing the weight of the liquid, its specific heat, and the rise of temperature during the experiment, the amount of heat generated can be readily calculated. With this machine Joule found that, whatever the liquid he used, a weight of one pound falling through 772 feet, or 772 pounds falling one foot, generated heat enough to raise one pound of water one degree Fahrenheit in temperature, or one unit of heat, as it is called. He also found that, when solids were rubbed together by the action of a falling weight, one pound falling through 772 feet generated a unit of heat. In this experiment, iron disks were made to rotate together, one against the other, in a vessel of mercury. If a metallic disk be put into rapid rotation, and then brought between the poles of a powerful electro-magnet, it soon comes to rest. It will now be found very difficult to turn it, and it be- comes heated as it rotates. Joule found in this case, as in the others, that, if the disk is turned by a falling weight, one pound descending 772 feet generates a unit of heat. The force necessary to raise one pound one foot is called a foot-found; and this is the same force which a pound acquires in falling one foot from a state of rest. We see, then, that when mechanical energy is converted into heat, the same amount of energy always gives rise to the same amount of heat, and that 772 foot-pounds of mechanical force are equivalent to one unit of heat. For this reason, we call 772 foot-pounds the mechanical equivalent of heat. 16. Heat may be converted into Mechanical Energy. The steam-engine is a contrivance for converting heat into mechan- ical energy. The heat converts the water into steam, and gives to this steam an expansive force ; and this expansive force is made to move a piston, as explained on pages 91-93. The animal body is a machine for converting the molecular energy developed by affinity into mechanical energy. APPENDIX. 279 17. The Same Amount of Heat always gives rise to the Same Amount of Mechanical Energy. In Figure 212, C is a box a foot square. Suppose a a to be a partition one foot F - 2J2 from the bottom, so as to shut in a cubic foot of air. Suppose this partition to be immovable, and the air beneath to be heated. Its elastic force will be increased, but it cannot expand. We will next suppose that a a is movable, but without weight, and that the air beneath is heated as before. On raising its temperature 490, its volume will be doubled, and a a will of course be raised one foot to b b. In raising a a one foot, it has had to raise the air above it. Now this air presses with a force of 15 pounds upon every square inch, or 15 x 144 = 2,160 pounds upon the whole surface. From the specific heat of air, we know that to raise the temperature of a cubic foot of air 490, when it is free to expand, 9.5 units of heat are required. But we have seen that a part of the heat which enters a body is used in expanding it, and a part in raising its temperature. In the above experiment, how much heat is used in raising the temperature? This is equivalent to asking how much heat is required to raise the cubic foot of air 490 when it is not allowed to expand. It has been found that the computed velocity of sound in air is less than its observed velocity, and that this is owing to the heat developed in the compressed portion of the sound-wave. From the ratio between the observed and the computed velocity, it is found that the specific heat of air when free to expand must be 1.42 of its heat when not allowed to expand. Hence the heat required to raise the temperature of the cubic foot of air 490, when it is not allowed to expand, is found by the following proportion to be 6.7 units : 1.42 : i = 9.5 : 6.7. The amount of heat, then, used in expanding the air that is, in raising 2,160 pounds one foot high is 2.8 units. Divid- ing 2,160 by 2.8, we get 772, nearly. Since there is no cohesion among the particles of air, the whole expansive force is used in raising the weight. 280 APPENDIX. \Ve see, then, that 772 foot-pounds of mechanical force are equivalent to a unit of heat, and that a unit of heat is equivalent to 772 foot-pounds of mechanical force. We have seen that merely to melt a pound of ice at a tem- perature of 32 Fahrenheit requires 143 units of heat, which is equivalent to the force required to lift 110,396 pounds, or about 55 tons, a foot high. And to convert a pound of boiling water into steam requires 967 units of heat, equivalent to the force required to lift 746,524 pounds, or about 373 tons, a foot high. The force of gravity is almost as nothing compared with this molecular force. The strength of affinity is shown by the amount of heat developed by the combination of oxygen and hydrogen. It is found that, when oxygen unites with one pound of hydrogen, 61,000 units of heat are generated. Hence the force which has combined the two gases is equal to 61,000 X 772 = 47,092,000 foot- pounds, or the force necessary to raise 23,546 tons a foot high, or to throw one ton to a height of morfi* than four miles. A pound of carbon, in combining with oxygen, gives out about 14,500 units of heat, equivalent to 11,194,000 foot-pounds. We see, then, that the force even of cohesion is insignificant com- pared with that of affinity. 18. Energy may be transmuted, but not destroyed. We have now seen that mechanical motion may be converted into the molecular motions of heat and electricity, and that these molec- ular motions may be converted into mechanical motion. Energy, like matter, may assume a great variety of forms; but, like matter, it is wholly indestructible. 19. Source of Energy. If left to itself, affinity would soon bring all dissimilar atoms together, and lock them up in com- pounds ; cohesion would bring all the molecules of these com- pounds together, and lock them up in solids ; and gravity would bring all these solids together, and hold them in its iron grasp ; while the heat developed by these forces would be radiated into space, and our earth become one dreary waste, void of all signs of life and activity. What, then, is the source of the energy which is thus manifesting itself in Protean forms ? APPENDIX. 28l Let us consider, first, the energy developed by gravity. This energy is seen in the winds, the falling rain, and running streams. The atmosphere, on each side of the equator, is an immense wheel. The side of this wheel next the equator is continually expanded, and thus made lighter, by the heat of the sun. Hence gravity pulls down the colder and heavier side in the polar regions, and thus the wheel is made to turn. Were it not for the sun's heat, it would soon come to rest. Again, the heat of the sun evaporates the waters of the ocean, and in their gaseous state they are swept round with the atmos- pheric wheel till they come to colder regions, where they are condensed, and fall to the earth as rain, and flow to the ocean in rivers. It is due, then, to the heat which comes to the earth in the sunbeam, that gravity can thus unceasingly manifest its energy. The energy of chemical affinity, which is manifested in heat, light, and muscular force, is developed by its action between oxygen and carbon. How are these elements separated from carbonic acid, so that they may be reunited by affinity? Place a leafy plant in a glass vessel, and let a current of car- bonic acid stream over it in the dark, and no change takes place. Let the same gas stream over the plant in the sunshine, and a part of it will disappear, and be replaced by oxygen. When acted upon by the sunbeams, leaves of plants remove carbonic acid from the air, separate its carbon and oxygen, retain the former, and give the latter back to the air. When plants are consumed by combustion in our furnaces, and by respiration in our bodies, this oxygen combines with carbon and develops energy, which appears as mechanical force in our engines, and as muscular force in our bodies. In the summer, when more sunshine than we need is poured upon the earth, a part of it is absorbed by the leaves of plants, and used to decompose carbonic acid, to build up the varied forms of vegetable life. In this way, the forests and the fields become vast storehouses of force which has been gathered from the sunbeam. When, therefore, we burn fuel in our stoves and food in our bodies, the light, heat, and muscular force developed 282 APPENDIX. are only the reappearance in another form of the sunbeams stored up in plants. But this process of gathering force from the sunlight has been going on for ages ; and when we burn anthracite or bituminous coal, we are merely releasing the sunbeams im- prisoned in plants which grew upon the earth before it became the dwelling-place of man. The energy of affinity, then, like that of gravity, is nothing but transmuted sunshine. The only form of energy known to us which does not come to the earth in the sunbeam is that developed by the ebb and flow of the tidal wave. This wave is dragged round the earth mainly by the attraction of the moon ; and it acts as a brake upon the earth's rotation, since it is drawn from east to west while the earth is turning from west to east. The energy of this wave, then, is developed at the expense of the earth's motion on its axis; and it must tend to retard this motion, though to so slight a degree that the observations of thousands of years have not served to make it appreciable. 20. The Amount of Heat given out by the Sun. Making allow- ance for the heat absorbed by the atmosphere, it has been calcu- lated that the amount received by the earth during a year would be sufficient to melt a layer of ice 100 feet thick and covering the whole earth. But the sun radiates heat into space in every other direction as well as towards the earth ; and if we conceive a hollow sphere to surround the sun at the distance of the earth, our planet would cover only of its surface. Hence * 2,300,000,000 the sun radiates into space 2,300,000,000 times as much heat as the earth receives. 21. Source of the Sun's Heat. It has been supposed by some that the materials of the sun are undergoing combustion, and that this combustion develops the light and heat which it sends forth. There are, however, no substances known to us whose burning would produce so much heat for so long a time as we know the sun has been shining. Carbon is one of the most combustible substances with which we are acquainted ; but if the sun, large as he is, were a mass of pure carbon, and were APPENDIX. 283 burning at a rate sufficient to produce the light and heat that he is giving out, he would be utterly consumed in 5,000 years. It seems hardly possible, then, that the solar light and heat can be generated by ordinary combustion. One of the most satisfactory theories of the origin of the solar heat is that developed in 1848 by a German physician, Mayer, and known as the meteoric theory. We have seen that a pound-weight which has fallen through 772 feet will, when its motion is arrested, generate a unit of heat. Now, we know that a body falling that distance will acquire a velocity of about 223 feet a second. Hence a pound ball moving with a velocity of 223 feet a second will generate a unit of heat when its motion is arrested. We know, too, that the velocity with which a falling body strikes the ground is in proportion to the square root of the height from which it falls; that is, in order to double or treble its velocity, a body must fall from four or nine times the height. A pound ball, then, moving with a velocity of twice 223 feet a second will be able to generate 4 units of heat; one moving with thrice this velocity, 9 units of heat ; and so on. When, therefore, we know the weight of a body and the speed with which it is moving, we can easily cal- culate how much heat will be generated on stopping it. Were the earth's motion arrested, its elements would melt with fervent heat, and most of them would be converted into vapor. Were the earth to fall into the sun, the heat generated by the shock would be sufficient to keep up the solar light and heat for 95 years. We know that countless swarms of meteoric bodies are revolving in rings about the sun, and that they must be moving in a resisting medium. If so, they must eventually be drawn into the sun, and, from the velocity with which they must strike, it has been shown that they could fall in sufficient numbers to generate all the light and heat of the sun, without increasing his magnitude enough to be detected, since accurate measures of his diameter were first made. 22. The Nebular Hypothesis. According to Laplace, the material of our solar system was once a nebulous mass of ex- treme tenuity, and the sun, moon, and planets were formed by 284 APPENDIX. its gradual condensation. Let us suppose such a nebulous mass slowly rotating, and gradually cooling by radiation into space. As it cools, it must begin to contract; and as it contracts, its rotation must be quickened, since the matter at the surface must be moving faster than nearer the centre. It thus goes on con- tracting and rotating faster and faster, until the centrifugal tendency becomes so great that cohesion and gravity can no longer hold it together. A ring is then detached from the circumference, which continues to rotate by itself. The central mass goes on contracting and rotating with ever-increasing velocity, until a second ring is thrown off. In this way, ring after ring is detached, and all these rings continue to rotate round the central mass in the same direction. But the rings themselves would go on condensing, and at last they would be likely to break up, each forming one or several globular masses. These would, of course, all revolve about the central mass in the same direction, and their condensation would cause them to rotate on their axis ; and it has been proved that, with the exception of one or two of the outer ones, they must all rotate on their axis in the same direction in which they revolve in their orbits. - But as these masses condensed, their rotation would be ac- celerated, and they would be likely to throw off rings, which would either remain as rings, or be condensed into globes. The central mass, of course, forms the sun ; the rings which it throws off, the planets; and the rings thrown off by the planets, the moons. In the case of Saturn, a part of the rings still remain uncondensed, while a part appear as moons. The rings thrown off by the central mass usually condensed into one body, but, in the case of the minor planets and the meteoric rings, into many. 23. Helmholtz's Theory of Solar Heat. Helmholtz has made the nebular hypothesis the basis of his theory of solar heat, an account of which is given by Tyndall as follows : " He starts from the nebular hypothesis of Laplace, and, assuming the nebulous matter in the first instance to have been of extreme tenuity, he determines the amount of heat generated APPENDIX. 285 by its condensation to the present solar system. Supposing the specific heat of the condensing mass to be the same as that of water, then the heat of condensation would be sufficient to raise their temperature 28,000,000 Centigrade. By far the greater part of this heat was wasted ages ago in space. . . . Helrnholtz sup- poses this condensation to continue ; that a virtual falling down of the superficial portions of, the sun towards the centre still takes place, a continual development of heat being the result. However this may be, he shows by calculation that the shrink- ing of the sun's diameter by .0001 of its present length would generate an amount of heat competent to cover the solar emis- sion for 2,000 years ; while the shrinking of the sun from its present mean density to that of the earth would have its equiv- alent in an amount of heat competent to cover the present solar emission for 17,000,000 of years." Mayer's theory is evidently not inconsistent with that of Helrnholtz, but supplementary to it. The former merely as- sumes that the meteors and planets, which were thrown off from the nebulous mass as it condensed, are slowly falling into it again. When these shall all have fallen into it, and the con- densation shall have ceased, our sun will cease to shine, like many other stars which have disappeared from the heavens. FRENCH WEIGHTS AND MEASURES. The names of the higher orders of units, or the multiples of the standard unit, are formed from the name of the stand- ard unit (the metre, litre, etc.), by means of prefixes taken from the Greek numerals; namely, deca- (10), hecto- (100), kilo- (1,000). The names of the lower orders of units, or the subdivisions of the standard unit, are formed in a similar manner by means of prefixes taken from the Latin numerals ; namely, deci- (10), centi- (100), milli- (1,000). 286 APPENDIX. TABLE OF LINEAR MEASURE. io millimetres = i centimetre = 0.3937 inch. 10 centimetres = i decimetre = 3-937 " io decimetres = i metre = 39-37 io metres = i decametre = 393-7 io decametres = i hectometre = 328 ft. i inch. io hectometres = i kilometre = 3280 " io " TABLE OF MEASURES OF SURFACE, loocentiares = i are = 119.6 square yards. loo ares = i hectare = 2.471 acres. The centiare is a square metre, or 1,550 square inches. TABLE OF MEASURES OF CAPACITY. 10 millilitres = i centilitre = 0.6102 cubic inches. 10 centilitres = i decilitre = 6.1022 " " 10 decilitres = i litre 1.0567 wine quarts. 10 litres = i decalitre = 2.6417 " gallons. 10 decalitres = i hectolitre = 26.417 " " 10 hectolitres = i kilolitre =264.17 " " The kilolitre is a cubic metre, and is also called a stere. The decastere == 10 steres. TABLE OF WEIGHTS. 10 milligrammes = i centigramme = 0.1543 grains. 10 centigrammes = i decigramme = 1.5432 " 10 decigrammes = i gramme = 15.432 " 10 grammes = i decagramme = 0.3527 oz. avoirdupois. 10 decagrammes = i hectogramme = 3-5274 " " 10 hectogrammes = i kilogramme = 2.2046 pounds " The millier or tonneau is equal to 1,000,000 grammes, or 2204.6 pounds avoirdupois. The English equivalents given above are those which were established by Congress, in July, 1866, and are sufficiently accurate for all practical purposes. APPENDIX. 287 PROBLEMS. Teachers can use either the English or the French weights and measures, or both. The French weights are not equivalents of the English, unless the nature of the problem requires it. WEIGHT OF I^IQUIDS. i. A glass flask, when full of water, weighs 9 ounces (180 grammes). The flask itself weighs 4.2 ounces (84 grammes). How many ounces (grammes) of water does the flask hold? 2. The same flask, when full of mercury, weighs 69.1 ounces, (1,382 grammes). How many ounces (grammes) of mercury does it hold? 3. The same flask, full of alcohol, weighs 8 ounces (160 grammes). How many ounces (grammes) of alcohol does it hold? 4. The same flask, full of sulphuric acid, weighs n ounces (220 grammes). How many ounces (grammes) of sulphuric acid does it hold? THE PRESSURE WHICH LIQUIDS EXERT BY REASON OF THEIR WEIGHT. In these problems, it is assumed that in liquids the pressure increases at exactly the same rate as the depth. 5. When water is one foot (centimetre) deep in a vessel, it exerts a pressure of 62.5 Ibs. (one gramme) on every square foot (centimetre) of surface at the bottom of the vessel. What would be the pressure exerted upon every square foot (centi- metre) of surface at the bottom, if the water in the vessel were 3 feet (centimetres) deep ? 6. What would be the pressure upon 9 square feet (decimetres) of surface at the bottom, if the liquid were 6 feet (centimetres) deep ? 7. What upon 13 square feet (decimetres) at the bottom, if the liquid were 7.5 feet (17 centimetres) deep? 8. A closed vessel is 9 inches (3 decimetres) deep, and has a tube projecting from the top to the height of one yard (metre). The bottom of the vessel has a surface of 100 square inches (50 square decimetres), and the vessel is filled with water to the top 288 APPENDIX. of the tube. What is the whole pressure upon the bottom of the vessel ? 9. What would be the pressure upon a square inch (centimetre) of surface on the side of the above vessel, the centre of the sur- face being 3 inches (centimetres) from the bottom ? 10. What would be the pressure upon a square inch (centi- metre) of surface at the top of the vessel? 11. What would be the pressure upon the whole upper surface of the vessel, supposing it to contain 100 square inches (50 square decimetres) ? 12. A cubical vessel, every side of which is a square yard (metre), is filled with water. What would be the pressure upon its bottom? 13. What would be the pressure upon each of its sides ? * 14. Suppose the top of the above vessel were closed, and a tube one yard (metre) in length were inserted into it, and were filled with water, what would be the pressure exerted upon the top of the vessel ? 15. What would be the pressure upon the bottom of the vessel when the tube is full of water? 16. What would be the pressure upon the sides of the vessel in the last case ? THE HYDROSTATIC PRESS. 17. The end of the small piston in a hydrostatic press has a surface of 10 square inches (centi- metres) ; and the end of the large piston a surface of a square foot (decimetre). A pressure of 10 pounds (kilogrammes) upon the small piston would bring what pressure to bear upon the large piston? 18. If the small piston be the same as above, and the end of the large piston contain a square yard (metre) of surface, 5 pounds (kilogrammes) upon the small piston will cause what pressure to be brought to bear upon the end of the large piston ? 19. A pressure of 75 pounds (kilogrammes) on the small * To find the pressure upon any surface at the sides of a vessel, take the average depth of the surface, that is, the distance from the top of the water to the middle of that surface. APPENDIX. 289 piston would cause what pressure to be exerted upon the end of the large piston ? THE BUOYANCY OF LIQUIDS. A cubic inch of water weighs 252.458 grains, the grain being y^-^ of a pound avoirdupois. For ordinary calculations, a cubic foot of water may be assumed to weigh 1,000 ounces, or 62.5 pounds, avoirdupois. A cubic centimetre of water weighs I gramme. 20. A body weighs 50 pounds (kilogrammes) in air, and has a bulk of 432 cubic inches (40 cubic decimetres). How much does it weigh in water ? 21. A stone weighs 80 pounds (kilogrammes) in the air, and 55 pounds (kilogrammes) in water. What is its bulk? 22. A hollow vessel of copper weighs one pound (kilogramme). What must be its bulk in order that it may just float in water? 23. A hollow vessel of iron weighs 15 pounds (kilogrammes). What must be its bulk in order that it may sink one-half in water ? 24. A boat displaces 12 cubic yards (metres) of water. What is its weight? SPECIFIC GRAVITY. 25. A body weighs 15 pounds (150 hec- togrammes) in air, and weighs 2 pounds (2 kilogrammes) in water. What is the weight of a bulk of water equal to that of the body? 26. A flask full of water weighs 6.2 ounces (62 grammes) : a piece of lead weighs 44 ounces (44 decagrammes) in the air. It is put into the flask, and the flask is filled with water. It is found that the lead and water together weigh 46.2 ounces (462 grammes). What is the weight of a bulk of water equal to that of the lead ? 27. A piece of lead weighs 3 pounds, 8 ounces (56 grammes) in the air, and 3 pounds, 3 ounces (51 grammes) in water. What is the specific gravity of lead ? 28. A flask holds 15 ounces (75 grammes) of water : a lump of copper, which weighs i pound (160 grammes) in the air, is put into the flask, and it is found that the water and the copper together weigh i pound, 5.9 ounces (219 grammes). What is the specific gravity of copper? '9 290 APPENDIX. 29. The specific gravity of iron is 7.8. What weight of water will 45 pounds (kilogrammes) of iron displace? 30. The specific gravity of zinc is 7.2. What is the bulk of 90 pounds (kilogrammes) of zinc? 31. A piece of wood which weighs 5 ounces (25 grammes) in the air, is fastened to a piece of iron whose weight is i pound (80 grammes) ; and on immersing both in water and weighing them, it is found that they together weigh 9 ounces (45 grammes). What is the weight of the water displaced by the wood? 32. A piece of wood, weighing 4.2 ounces (42 grammes), is fastened to a piece of zinc weighing 8.6 ounces (86 grammes), and both are weighed under water, and are found to weigh 3.4 ounces (34 grammes). What is the specific gravity of the wood? 33. A flask weighing 2 ounces (20 grammes) weighs 2 pounds, ii ounces (430 grammes) when full of water, and 34 pounds, 11.5 ounces (5555 grammes) when full of mercury. What is the specific gravity of mercury ? 34. A hydrometer weighing 5 ounces (50 grammes) requires a weight of 8 ounces (80 grammes) to sink it to the neck in water, and a weight of 13.5 ounces (135 grammes) to sink it to the same depth in sulphuric acid. What is the specific gravity of sulphuric acid? 35. A vessel holds 100 pounds (kilogrammes) of water. How much mercury would it hold ? 36. How much alcohol will it hold, if the specific gravity of alcohol is .79? WEIGHT OF GASES. The specific gravity of a gas is its weight compared with that of an equal bulk of atmospheric air. 37. A glass globe of the capacity of 61 cubic inches (one litre) weighs 29.27 ounces (83 grammes) after the air has been ex- hausted from it; and 29.73 ounces (84.292 grammes) when full of air. What is the weight of 61 cubic inches (a litre) of air? 38. The same globe, when full of ammonia gas, weighs 29.54 ounces (83.759 grammes). What is the weight of 61 cubic inches (a litre) of ammonia gas? APPENDIX. 291 39. The same flask, when full of carbonic acid, weighs 29.96 ounces (84.964 grammes). What is the weight of 61 cubic inches (a litre) of carbonic acid ? 40. The same flask, full of hydrogen, weighs 29.3 ounces (83.089 grammes). What is the weight of 61 cubic inches (a litre) of hydrogen? 41. What is the specific gravity of ammonia gas? 42. What is the specific gravity of carbonic acid ? 43. What is the specific gravity of hydrogen? 44. A vessel of the capacity of 34 cubic feet (985 litres) would hold how many ounces (grammes) of air? of carbonic acid? of hydrogen ? PRESSURE CAUSED BY THE WEIGHT OF GASES. The atmos- pheric pressure (74) is about one kilogramme upon every square centimetre of surface at the level of the sea. 45. The body of an ordinary-sized man has a surface of about * 2,340 square inches (16,000 square centimetres). How many pounds (kilogrammes) of pressure does the atmosphere exert upon a man's body? 46. A room is 12 yards (metres) long, 9 yards (metres) wide, and 5 yards (metres) high. How many pounds (kilogrammes) of pressure does the atmosphere exert upon the floor of the room ? 47. How many pounds (kilogrammes) of pressure does it exert upon each end of the room ? How many on each side ? 48. How many pounds (kilogrammes) of air does the room contain ? 49. The atmospheric pressure will balance a column of mer- cury 30 inches (76 centimetres) high, and the specific gravity of mercury is 13.5. It will balance a column of water how many feet (metres) high ? 50. If water is to be raised 45 feet (1,200 centimetres) high by means of the lifting-pump, how much of this distance must the water be lifted ? 51. Water is to be carried over a hill 68 feet (1,350 centimetres) high? Can it be done by means of the siphon? Why? BUOYANCY OF GASES. 52. A block of wood has a bulk of 900 cubic yards (metres). How much is it buoyed up in the air? 292 APPENDIX. 53. A balloon when filled with gas weighs 1,000 pounds (500 kilogrammes). How many cubic feet (litres) of bulk must it have, in order that it may just float in the air? 54. A balloon has a bulk of 1,000 cubic yards (metres), and weighs 50 pounds (25 kilogrammes). It is filled with coal-gas, whose specific gravity is .6. By how many kilogrammes of pres- sure is it forced upward? If a car, which, with all its fixtures, weighs 96 pounds (48 kilogrammes), be attached to the balloon, with what pressure will the whole be forced upward ? SECOND LAW OF MOTION. Gravity causes a body to fall from a state of rest 4.9 metres in a second, and increases its velocity 9.8 metres in a second (95). 55. A body falls from a state of rest. What will be its velocity at the end of the third second ? 56. A body is thrown downward with a velocity of 50 yards (metres) a second. What will be its velocity at the end of 7 seconds ? 57. A body is thrown downward with a velocity of 23 yards (metres) a second. What will be its velocity at the end of 9 seconds ? 58. A body is thrown upward with a velocity of 42 yards (metres) a second. What will be its velocity at. the end of 4 seconds ? At the end of 6 seconds ? 59. A body is thrown upward with a velocity of 98 yards (metres) a second? How long will it continue to rise? 60. How high will the above body rise ? 61. How far will it rise the first 3 seconds? 62. How far will it rise the last 3 seconds ? 63. How far will it rise from the beginning of the 3d to the end of the 8th second. 64. Two bodies are thrown upward, one with a velocity of 224 feet (68.6 metres) a second, and the other with a velocity of 448 feet (137.2 metres) a second. How many seconds will it be before each begins to fall? 65. To what height would each rise ? 66. A ball falls from a state of rest, and reaches the earth in 12 seconds. With what velocity does it strike the earth? APPENDIX. 293 67. From what height did the ball in the last example fall ? 68. How far did it fall the first 5 seconds? 69. How far did it fall the last 5 seconds? 70. How far did it fall from the beginning of the 3d to the end of the 5th second ? 71. How far did it fall from the beginning of the 8th to the end of the nth second? 72. A ball is thrown downward with a velocity of 125 yards (metres) a second, and reaches the earth at the end of 7 seconds. What is its velocity on reaching the earth ? 73. From what height was the ball in the last example thrown ? 74. Through what distance did it pass from the beginning of the 3d to the end of the 6th second ? 75. A stone falls from a state of rest, and is 4 seconds in reaching the earth. With what velocity does it strike the earth? Through what distance does it fall ? 76. If the stone had reached the earth in 8 seconds, what velocity would it have acquired, and through what distance would it have fallen? 77. If the stone had reached the earth at the end of 12 seconds, with what velocity would it have reached the earth, and through what distance would it have fallen ? * 78. A body in falling from a state of rest through 16 feet (4.9 metres) acquires a velocity of 32 feet (9.8 metres) a second. Through what distance must it fall in order to double this velocity? To treble this velocity? 79. A stone falls from a height of 64 feet (19.6 metres). With what velocity does it reach the earth ? THIRD LAW OF MOTION. To find the momentum of a body, multiply its weight in founds {grammes) by its velocity in feet (metres). * When we know the velocity a body acquires in falling through a certain distance a, and we wish to know what velocity it will acquire in felling through any other dis- tance 6, divide the distance b by a, extract the square root of the quotient, and multiply the velocity the body acquires in felling through the distance a by the number thus obtained. If, on the other hand, we wish to know how far the body must fall to acquire any velocity c, divide the velocity c by the velocity a body acquires in felling through the distance a, square the quotient, and multiply the distance a by this number. 294 APPENDIX. 80. A body weighs 50 pounds (kilogrammes), and is moving at the rate of 12 yards (metres) a second. What is its mo- mentum? 81. The same body is moving at the rate of 5 yards (metres) a second. What is its momentum? 82. With what velocity must a body weighing 6 pounds (grammes) move, in order to have the same momentum as a body weighing 10,000 pounds (500 kilogrammes), and moving at the rate of 2 yards (metres) a second ? 83. A certain force gives to a body weighing 45 pounds (kilo- grammes) a velocity of 9 yards (metres) a second. What velocity would the same force give to a body weighing 3 ounces (grammes) ? MACHINES. 84. In a lever, the short arm is 5 inches (deci- metres) long, and the long arm 61 inches (decimetres) long. How far will the end of the long arm move while the end of the short arm moves through 3 inches (centimetres) ? 85. In a lever, the short arm is 2 yards (metres) long, and the long one 15 feet (50 decimetres) long. A power of 2 pounds (kilogrammes) is applied to the end of the long arm. What weight at the end of the short arm will it balance? 86. While the weight in the last example is moving through 3 inches (decimetres), how far will the power move? 87. A weight of 5 pounds (60 decagrammes) is applied at the end of the long arm of the lever in the above example. What power must be applied at the end of the short arm to balance it? 88. In a wheel and axle, the circumference of the wheel is 4 yards (metres) and that of the axle 9 inches (30 centimetres). What weight will a power of 3 pounds (grammes) balance? 89. In a train of wheels, a power of i ounce (gramme) balances a weight of 450 pounds (43 kilogrammes). What distance must the power move through while the weight moves through 12 feet (50 decimetres) ? 90. In a system of pulleys, a power of I ounce (gramme) balances a weight of 1,200 pounds (245 kilogrammes). How far will the weight move while the power is moving through i foot (metre)? APPENDIX. 295 NOTES ON EXPERIMENTS. In the following notes, we shall mention all the apparatus necessary for performing nearly all the experiments in this book. In the larger Natural Philosophy of the Cambridge Physics, many additional pieces of apparatus are described, and many additional experiments and illustrations are given. The teacher should have that book for reference and for use in oral instruction. For priced list of apparatus, see the end of the book. This list has been very carefully prepared by Mr. Ritchie, under the supervision of the authors. The articles whose prices are car- ried out in the right-hand column are all that are really neces- sary for the thorough illustration of this book. The others are, however, very desirable, if one has the means to get them. COHESION. i. Ring and ball, for 3. A bar and gauge will perhaps be better for showing contraction and expansion by change of temperature. 2. Two half-pint flasks, provided with rubber corks, through which glass tubes of small bore pass. These can be used in all cases, instead of a bulb with projecting tube ; and the flasks will be useful for many other experiments. 3. A pair of lead hemispheres, for 9. 4. Two evaporating dishes ; for making crystals, and for other purposes. 5. A crucible, for sulphur crystals. 6. A dozen Rupert's drops. 7. Two glass two-quart jars, with ground mouths and plates to cover them. 8. A dropping-tube. This is to be used in the experiment in 21, which we advise all teachers to try. Mix half the desired quantity of alcohol and water to a density near that of the oil, but a little less, so that a drop of oil will slowly sink in it; and mix the other half to a density a little greater than that of the oil, so that a drop of oil will slowly rise in it. Then pour the 296 APPENDIX. heavier mixture under the lighter, through a long tube. Next fill the bulb and stem of the dropping-tube with sweet oil, close the top with the thumb, and put the small end into the centre of the mixture. Remove the thumb, and keep the tube steady till the oil runs out. If the mixture is made in one of the two-quart jars (No. 7) and covered, the sphere of oil can be kept for a number of days. 9. Half a dozen 6-inch test-tubes, one of which is to have a rubber cork and tube for the experiment in 22. 10. A U-tube and nipper-tap, for 23 and 24. 11. Wooden retort-holder, for holding U-tube and for other purposes. 12. Eight or ten pounds of mercury for experiments with U-tube, and also for experiments in 27, 36, 40, and 72. ADHESION. i. Glass disk with hook, for the experiment in 27- 2. A shallow glass dish. 3. Two small glass funnels, and a pack of filters. 4. A set of capillary tubes. 5. A pair of capillary plates. 6. Two glass cylinders : one, i inch in diameter and 5 inches deep; the other, i in diameter and 7 deep. These should have ground mouths and ground-glass plates for covers. The small one is to be used for 36 and 40, and the large one for 38. For method of filling the cylinder with ammonia, see Hand- look of Chemistry, page 189, 23. Do not fail to try these experi- ments. 7. Glass tube, about 10 inches long ; to be used, with a small funnel, for experiment in 38, which is simple and striking. 8. Bladder and tube, for 39. The tube should have as small a bore as possible, that the rise of the liquid may be quickly seen. With proper care, the alcohol can be poured in through a small funnel. A better form of apparatus would be a glass bell, with a tube projecting from its top; the bladder being stretched over the mouth of the bell. APPENDIX. 297 9. Bottles and tube, for 42. For the preparation of hydrogen, see Handbook of Chemistry -, page 182, ii. For preparation of carbonic acid, see same book, page 29, 42. For the method of filling the bottles with the gases, see same book, page 181, i. The upper bottle and tube should be together filled with hydrogen. The end of the tube should then be closed with the thumb and inserted into the other bottle. The cork of the lower bottle should be left on the tube. 10. Cup and tube, for 43. Instead of a bell-jar, one of the jars in No. 7 of Cohesion may be used. The last two experiments are very striking, and can be easily performed. MECHANICS. i. Set of balls, rods, etc., for illustrating centre of gravity. 2. Bottle with tubes (Figure 26). 3. Equilibrium tubes (Figure 27). 4. Illustration of hydrostatic press. 5. Hydrometer (Figure 34). 6. Cylinder and cup, for 62. 7. An air-pump. For all the experiments in this book, a table air-pump will answer. 8. Receiver, with sliding-rod. 9. Quart receiver and small bolt-head. 10. Apparatus for illustrating weight and buoyancy of air. n. Magdeburg hemispheres. 12. Hand-glass. 13. Small rubber bag. 14. Barometer tube. 15. Model of lifting pump. 16. Model of force pump. 17. Glass siphon. 18. Tantalus's cup. 19. Condenser. 20. Condensing chamber, with air-gun and jets. 21. Guinea and feather tube. 22. Illustration of pendulum. 298 APPENDIX. Fig. 214. 23. Illustration of first law of motion (Figure 214). When the ring is in rapid rotation, it as- sumes the form shown bj the dotted line, in consequence of the ten- dency of its parts to move in straight lines, or what is usually called the centrifugal force. 24. Models of lever and com- pound lever. 25. Models of wheel and axle, capstan, and pulleys; with stand and weights. 26. Models of inclined plane, wedge, and screw. 27. Model of Barker's mill. 28. Wollaston's illustration of low-pressure engine. SOUND. i. Bell, for 144. A sliding- rod is not necessary, as the bell can be rung by tilting the pump. 2. Toothed wheel, for 155. If one has an ordinary gyro- scope, a toothed wheel can be readily fitted to its axle. 3. Tuning-fork and sounding-box. 4. Sonometer and strings. This is the most important piece of apparatus for sound. "In Ritchie's Improved Sonometer the case is of mahogany, thirty-six inches in length, with sounding-board of spruce, fitted for two wires, with tension-keys and wrench, and a brass lever with two weights, for measuring tension. The upper line of fig- ures on the lever is for the smaller, and the lower line for the greater weight. There are two scales marked on the instru- ment : one, the diatonic scale, with letters and syllables for the intervals of tones and semitones, and the ratio of length of chord, and number of vibrations ; and the other, a scale of sixty equal parts. There are also movable bridges for one or both wires to rest upon. "To produce the notes of the scale, move the bridge to the letters on the scale, and sound with the bow. " To show that the rapidity of vibration is as the square root APPENDIX. 2QQ of the tension, attach one wire to the lever, place the weight on some number, tighten the wire until the lever is brought to a level, and tune the other wire to unison. Then change the weight to some number on the lever corresponding to a chord. A change from 2 to 8 will give an octave ; i to 16, two octaves ; 4 to 9, a fifth ; etc. " To show that the rapidity of vibration is inversely as the square root of the 'weighty place the large wire, which is four times as heavy as the other, on the lever, and the weight at 16; tune the other wire to unison, then change the large wire for one of the same size as the second one, and raise the weight as before. The new wire will sound an octave higher than the other. Place the weight at 4, and it will give the unison. " If the weight be changed considerably, it will be necessary to tighten or loosen the screw to allow for the stretching of the wire. " For producing overtones, or harmonics, touch the wire with a feather, or lightly with the finger, at one of the equal divisions, and draw the bow gently across it. The wire will vibrate be- tween the feather and fixed bridge, and also in equal divisions on the other side of the feather, but having points of rest, or nodes, at the divisions. For example, touch the feather at 20, and a node will appear at 40, or touch at 12, and other nodes will appear at 24, 36, and 48, dividing the wire into three or five equal portions, vibrating at equal times. Put paper riders, blue and red, on the wire before sounding; some on the nodes, and some of another color on intermediate places. The former will remain stationary, while the latter will be instantly thrown off. " For showing sympathetic vibrations, tune one wire to unison (or an octave) with the organ-pipe, or vibrating plate ; or sound the note with the voice, and the wire will be thrown into vibra- tion and distinctly heard. It is essential that the unison or chord be perfect, or the wire will not respond. Draw the piston of the pipe while sounding it; the wire will respond to the note which was for the instant of the same number of vibrations. " By tuning the wires nearly to unison, the effects of interfer" ence, or beats, are produced." 3OO APPENDIX. 5. A violoncello bow. 6. Vibrating plate, for 164. 7. Four rods, for 178. 8. Brass rods, for 179. 9. Iron screw-press, for last three instruments. 10. Ivory ball and stand, for use with No. 8. 11. A resonant jar, for 180. The nitric-oxide jar (Handbook of Chemistry, page 184, 18) is just right for the purpose. 12. Three glass tubes, for 182. 13. Organ-pipe, with sliding piston." 14. Reed pipe. 15. Jet and tube for singing flame. LIGHT. It is very desirable to have a room which can be darkened, and into which direct sunlight can be admitted through a hole in a shutter. The hole should be four inches in diameter, with a diaphragm for reducing it. The beam of light may be received upon a mounted mirror inside the room, and thus thrown wherever desired. It is better to introduce the light by means of a porte-lumiere.* Some experiments may be per- formed by means of the light from a common solar lamp, having an opaque chimney with an aperture opposite the flame. 1. Condensing lens, mounted. 2. Prism for refraction, etc. 3. Mounted prism. 4. Achromatic prism. 5. Apparatus for revolving disks, with set of disks. These are circles of cardboard and paper of a variety of brilliant colors, including Newton's disk for recomposing white light. A great variety of interesting and beautiful effects are produced by the set of disks made by Ritchie, f 6. Apparatus for Newton's rings. 7. Zoetrope. * See Ritchie's new Catalogue of Apparatus. t The brief duration of the light of the electric spark (see 41, p. 258) may be shown by discharging a Leyden jar, so that the light produced shall fall upon one of the disks in rapid rotation. APPENDIX. 301 8. Stereoscope, with diagrams. 9. Convex and concave mirrors. 10. Mounted mirror. 11. Double-convex and double-concave lenses. HEAT. i. Iodine cell, for cutting off luminous radiations in the sunbeam. , 2. A differential thermometer. 3. A conductometer. 4. A pair of tin plates and balls, for 257 and 263. 5. Compound bar, for 267. 6. Apparatus for convection of gases. 7. Mason's hygrometer. 8. Edson's hygrodeik. 9. Reflectors and ball. 10. Fire-syringe. 11. Spirit lamp. ELECTRICITY. i. Bar magnet. 2. U-magnet. 3. Voltaic pair (Figure 172). 4. Bunsen's cell. 5. Needle and stand. 6. Dipping needle. 7. Oersted's galvanometer. 8. Electro-magnet (Figure 180). 9. Lifting-coil (Figure 181). 10. Page's rotating apparatus (Figure 182). 11. Helix and ring. 12. Model of electro-magnetic telegraph (Figure 185). 13. Relay magnet (Figure 186). 14. Decomposing cell, 327. 15. Thermo-electric series. 16. Small induction coil. 17. Induction coil, with separable helices (Figure 188). 18. Powder cup. 19. Vulcanite cylinder (for frictional electricity). 20. Small electrical machine. 21. Holtz's electrical machine. 302 APPENDIX. Fig. 215. This machine, as im- proved by Ritchie (Fig- ure 215), consists of a thin revolving glass plate, near to which, on opposite sides of the axis, are placed two (or four) sectors, or plates of thin glass. These have pieces of paper pasted upon both sides, covering a small portion of the sectors. On the edges, meeting the plate in its revolution, a tongue of paper pro- jects beyond the glass, to collect the electricity from the revolving plate. On the reverse side of the rotating plate, and opposite to the paper coatings, are sets of collecting points, like those of the frictional machine. These are insulated, but connected by metal rods with two insulated pillars, in which slide discharging rods with ball ends. The machine is excited by bringing near to one of the sectors, while the plate is rotating, a piece of vulcanite which has been charged by rubbing it upon a piece of cat-skin. The plate at once shows electrical excitement, which increases till it reaches a maximum, accompanied by a rushing sound ; while at the same time a perceptible increase of force is required to turn the plate. Seen in the dark, the sector first charged shows a beau- tiful play of electrical streamers flowing apparently from the plate to the sector and more strongly to the collecting points, while the opposite set of points show bright stars ; the one set of points giving negative, and the other positive electricity. By connecting one of the dischargers with a prime conductor and the other one with the earth, the discharge is intensified. A very remarkable modification is made by connecting both APPENDIX. 303 the sets of points by means of metal conductors with one prime conductor, while a third set of collecting points is placed half- way between the others, but without a sector over it, and con- nected with the earth. As thus connected, the sectors and points continue to exhibit negative and positive electricity, and the prime conductor gives positive electricity when the sector, whose tongue points towards the third or "earth" set of col- lecting points, is excited by means of the vulcanite, and nega- tive electricity when the opposite sector is first excited. No satisfactory explanation of the action of the machine has yet been given. In power it greatly exceeds the frictional machine. The quan- tity of electricity obtained is many times greater, so that it serves well for experiments with vacuum tubes, Geissler's tubes, Gassiot's cascade, and the like. 22. Insulated conductor, for 346. 23. Gold-leaf electroscope. 24. Ley den jar. 25. Diamond jar. 26. Discharger. 27. Electric wheel. 28. Spotted tube (for electrical light). 29. Stand and bells. 30. Gassiot's cascade. 31. Geissler's tube. THE INDUCTORIUM, OR RUHMKORFF'S COIL. This machine is shown in Figure 216. The relative position and construction of the primary helix, with its enclosed core of iron wire, the sur- rounding secondary helix of fine insulated wire of great length, and the rheotome, or break-piece, have been described in 336. In that instrument (Figure 188), the induced electric current is of comparatively low intensity. Hence it will not give a spark in the atmosphere, though in a vacuum or highly rarefied gas the current will pass in a beautiful glow. The spark or flash at the break-piece is immensely magnified by the extra cur- rent in the primary coil. Fizeau found that by connecting the 304 APPENDIX. Fig- 216. wires on each side of the break to the two coatings of a Leyden jar, this extra current may be drawn off and the flash or spark re- duced to that of the direct action of the battery, but the in- tensity of the secon- dary current is enor- mously increased. In the inductorium the Leyden jar is thus introduced, and is made of many sheets of oiled silk coated with tinfoil, which are equivalent to a Ley- den jar of from twenty to one hundred square feet of surface. This is the condenser, which is in the base of the instrument. As the tension of the induced current is increased, we must increase the insulation between the spirals of the coil and the courses of the bobbin, as well as between the helices. No one succeeded in doing this, except for very low tensions, until Rit- chie, of Boston, wound the secondary helix in planes perpen- dicular to the axle, thus separating the portions of wire under different tension so far that a discharge cannot take place be- tween them. With this arrangement, the secondary helix may contain thirty miles of wire, and a spark of fifteen inches or more may be obtained. The invention of every part of the so-called " Ruhmkorff's coil," except the condenser, is due to our own countrymen, Page and Ritchie. It was not until RuhmkorfF unwound one of Ritchie's coils, and thus learned the secret of its structure, that he was able to make an instrument that would give a spark of more than three-quarters of an inch. He has, however, made no acknowledgment of his indebtedness to Ritchie. APPENDIX. 305 THE SPECTROSCOPE AND THE DIFFERENT KINDS OF SPECTRA. i. The Spectroscope. This instrument (Figure 217) consists of a prism, P, and three tubes, A, JB, and C. The tube A is an Fig. 217. ordinary telescope. The tube B has a narrow slit in its outer end, through which a beam of light is admitted. This beam is concentrated by a lens upon the prism P. The tube C has at its outer end a fine scale marked on glass. The light from the candle F shines through this glass, and is reflected by the face of the prism into the telescope A, so that on looking into this telescope an enlarged image of the scale is seen. The light from the tube B, on passing through the prism, is dispersed into a spectrum, which is examined by means of the telescope A. This simple instrument was invented in 1859, ty two German professors, Bunsen and Kirchhoff, and it has already led to very remarkable discoveries in both Chemistry and Astronomy. 2. The Spectra of Incandescent Solids and Liquids. When the light from an incandescent solid or liquid is examined by 20 306 APPENDIX. means of the spectroscope, the spectrum is seen to be an un- broken band of colored light. Such a spectrum is called a con- tinuous spectrum. Dense vapors when incandescent also give continuous spectra. 3. The Spectra of Incandescent Gases. If we dip a platinum wire into a solution of some sodic salt, and hold it in the color- less flame of a Bunsen's lamp, so as to color it with incandes- cent sodium vapor, we shall get a spectrum, consisting of a single yellow line, as shown at III. in the chromolithic plate at the beginning of this book. Color the flame in a similar manner with incandescent potassium vapor, and we get a spectrum like II. in the plate, continuous in the middle, with a bright line at each end. The incandescent vapors of the rare metals c&sium and rubidium give spectra like IV. and V. in the plate. As a rule, the spectra of incandescent gases are broken, or made up of bright lines separated by dark spaces. The spectrum of each element is unlike that of every other element, either in the number or the position of its bright lines, and usually in both. The position of these lines 'can be ascertained with great accuracy by means of the scale, which is seen in the telescope in the same position as the spectrum ; and for the same sub- stance the position of the bright lines is always the same. 4. Reversed Spectra. Kirchhoif found on examining the brilliant light from incandescent lime, after it had passed through a flame colored with sodium vapor, that its continuous spectrum was crossed by a single black line, and that this black line was exactly in the position of the bright sodium line. The bright yellow line became a dark line when seen against the background of the lime-light. By allowing the lime-light to traverse the vapors of potassium, barium, strontium, etc., the bright lines which they would have given were found to be con- verted into dark lines. This reversal of the bright lines of the metallic vapors is owing to the fact that each vapor has the power to absorb rays having the same refrangibility as those it emits, and no others. Each vapor, therefore, absorbs from the lime-light all those rays which would fall in the part of the spectrum occupied by its own bright lines ; and, as its own light is feeble in compari- APPENDIX. 307 son with the lime-light, the bright lines appear dark in contrast with the rest of the spectrum. The dark lines produced thus by absorption constitute the reversed spectra of the absorbent vapors. 5. Fraunhofer 's Lines. When sunlight is examined by means of the spectroscope, its spectrum is found to be crossed by a great number of very fine dark lines. These dark lines were first noticed by Wollaston in 1802 ; but they were first studied and described in detail by Fraunhofer in 1814. Fraunhofer mapped the lines, and designated the most conspicuous of them by the letters A, a, B, C, D, E, b, F, G, If: they are therefore generally known as Fraunhofer's lines. The dark line A (see I. of the chromolithic plate at the begin- ning of this book) is at the extremity, and B at the middle, of the red ; C at the boundary of the red and orange ; D in the orange ; E in the green ; F in the blue ; G in the indigo ; and H in the violet. Of the other prominent lines just mentioned, a is in the red, and b in the green. In the case of sunlight, the position of the dark lines is fixed and definite. Similar dark lines are found in the spectra of starlight, but their position is somewhat different. Of the solar lines, however, all are not invariable in position and distinctness; some of the feebler lines being seen only when the sun is near the horizon, or in certain states of the atmosphere. The invariable ones are the true Fraunhofer's lines, and belong to the sun. The others are sup- posed to be due to the absorptive action of our atmosphere, and are therefore called atmospheric or telluric lines. Fraunhofer counted more than 600 dark lines, distributed irregularly from the extreme red end of the spectrum to the extreme violet end. Brewster counted 2,000. By causing the light to traverse several prisms in succession, the number of the lines has been increased to 3,000, and several which had been supposed to be single have been shown to be double. Fraunhofer's lines are undoubtedly the reversed spectra of the incandescent vapors of the sun's atmosphere. [For the applications of the spectroscope in Chemistry see our "Elements of Chemistry," or "Handbook of Chemistry;" and for its applications in Astronomy see the " Elements of Astronomy," or the " Handbook of the Stirs."] 308 APPENDIX. PHOTOGRAPHY. 1. Photography is the art of fixing the image of the camera (218) permanently to the surface upon which it falls. This is done by the chemical action of light. The various photographic processes may be considered under three heads : photography on metal, photography on paper, and photography on glass. 2. Photographs on Metal. It was in the year 1839 t na t the problem of taking pictures by light was first successfully solved by a Frenchman named Daguerre. The Daguerreotype picture is taken on a plate of copper coated with silver. The plate is first carefully polished, and then ren- dered sensitive by exposing its silvered surface to the vapor of iodine, which forms upon it a thin layer of argentic iodide. If the picture is to be taken quickly, the surface must be made still more sensitive by the action of bromine. All these operations must be performed by candle-light. The plate is now put into a little wooden case, and exposed in the camera. After a little time, it is removed to a darkened room. No change perceptible to the eye has taken place ; but when the plate is exposed to the vapor of mercury, an image appears exactly like that formed in the camera. The mercury condenses upon those parts of the plate that have been most strongly illumined, and thus develops the picture which before was latent. The action of the light gives the molecules of the argentic iodide a tendency to decom- pose, and the tendency of the mercury to unite with the silver completes the decomposition. In the shades of the picture, the molecules of the iodide have acquired no tendency to break up, and those parts are not attacked by the mercury. If, after the development of the picture, the plate were ex- posed to the light, the iodide on all parts of the surface not attacked by the mercury would gradually blacken, and the picture become obliterated. In order to fix the picture, it is necessary to dissolve and remove this iodide, which is usually done by a solution of sodic hyposulphite. The picture is next toned by immersing the plate in a solution of auric chloride. Some of the gold of this compound unites APPENDIX. 309 with the mercury and silver of the parts attacked, an'd greatly increases the intensity of the lustre. The lights of the picture consist of the amalgam of mercury, silver, and gold ; and the shades, of metallic silver. 3. Photographs on Paper. Photographs on paper are ordi- narily printed from negatives on glass. If gun-cotton be put into a mixture of alcohol and ether, it dissolves and forms collodion. If this solution is poured over any surface, the alcohol and ether quickly evaporate, leaving a film of solid collodion behind. To obtain a sensitive surface on glass, a solution of collodion is first impregnated with potassic iodide, or a mixture of potassic iodide and ammonic bromide, and poured out upon the surface of a glass plate, so as to coat it with a thin film. The plate thus coated is dipped into a bath of argentic nitrate, so as to form a film of argentic iodide, or a mixture of argentic iodide and bromide. The plate is now exposed a short time in the camera, and again removed to a darkened room. As before, no image is perceptible. The light has not decomposed the com- pounds of silver, but merely given them a disposition to de- compose. Their decomposition is completed, and the picture developed, by pouring over the plate a solution of ferrous sul- phate or of pyrogallic acid. The picture is then fixed by dis- solving off the argentic iodide from the unaffected part by means of the solution of sodic hyposulphite. The glass is rendered less transparent by the presence of the metallic silver: hence, when viewed by transmitted light the lights of the image appear dark, and the shades light; and the picture is therefore said to be a negative. From this nega- tive picture any number of positive pictures may be printed on paper. For this purpose, paper is impregnated with argentic chloride, by dipping it first into a solution of common salt (sodic chloride), and then into a bath of argentic nitrate. The nega- tive is then placed on a sheet of this paper in a copying-frame, and exposed to the action of light. The chloride gradually blackens, and most rapidly where the glass is most transparent. In this way the tints of the negative are reversed, and the picture becomes a positive. After sufficient exposure, the picture is 310 APPENDIX. fixed by dissolving off the remaining chloride by a solution of sodic hyposulphite, and toned in a bath of auric chloride. 4. Photographs on Glass. The picture on glass, which ap- pears negative by transmitted light, will become positive if it be backed with a coating of black varnish or a piece of black cloth, so that it shall be seen by reflected light. Beautiful positive pictures on glass may be obtained by the following process : prepare the plate in the same way as for negatives, but expose it a much shorter time in the camera; develop the picture by pouring over it a solution of ferrous sul- phate, which gives a negative image ; then pour a solution of potassic cyanide over the plate, and this negative is rapidly converted into a positive. NOTES. B3^ These notes are numbered to correspond with the sections to which they refer. 257. Many familiar illustrations of the fact that good absorbers are good radiators, and vice versa, might be given. Put equal quantities of boiling water into two teakettles, one of which is polished and the other rough, and the former will cool more slowly than the latter. Put the same kettles full of cold water before an open fire, and the rough one will become hot sooner than the other. Dark colors absorb and radiate heat better than light ones. The former are therefore the better for winter clothing, and the latter for summer. For a similar reason, snow melts very slowly even under the direct rays of the sun ; but a piece of black cloth laid upon the snow causes it to melt quite rapidly. Since a stove is meant to radiate heat, it is better that its sur- face should be rough than that it should be polished. On the other hand, a tea-urn, or any vessel intended to keep its contents hot as long as possible, should be polished rather than rough. APPENDIX. 311 276. A still lower temperature, of 220, has been obtained bj placing a mixture of liquid nitrous oxide and carbonic di- sulphide (bisulphide of carbon) in an exhausted receiver. Water may be readily frozen by the evaporation of ether. Put the water in a small test-tube ; and place the test-tube, surrounded with cotton moistened with ether, in a wine-glass or tumbler. Put the nozzle of a bellows into the cotton, and blow vigorously. The current of air passing over the cotton acts on a very large surface of ether, which is thus evaporated fast enough to freeze the water in the tube. 277. The force exerted in the expansion and contraction of bodies is very great. A curious application of this force was made by the architect Molard, at the Conservatoire des Arts et Metiers, in Paris. The walls of a vaulted gallery in this build- ing had been pushed outward by the weight of the stone roof, and it was feared that the whole would fall. Molard put iron bars across the gallery through the walls, the ends of the bars having a screw-thread fitted with nuts. He then heated the bars throughout their whole length, screwed them up tight, and allowed them to cool. The gradual contraction of the iron drew the walls nearer together without injuring them. The process was repeated several times, until the walls were restored to a vertical position. The bars were left to keep them in place, and may be seen to this day. Advantage is taken of the force of contraction in putting tires on wheels. The tire is put on hot, when it fits loosely; but as it cools it contracts, and grasps the wheel with very great force. For other illustrations of the kind, see 295. 287. The vapor in the atmosphere acts in the same way as the glass of the hot-house : the luminous rays from the sun easily penetrate it, and fall upon the earth ; but they cannot make their way back through it when radiated from the earth as obscure heat. See the chapter on the Physics of the Atmosphere, 2. Saussure made a wooden box, blackened within, having one of its sides formed of three panes of glass, separated by thin layers of air. He then put a vessel of water in the box, and 312 APPENDIX. exposed the glass side to the rays of the sun ; and in this way he succeeded in making the water boil. The luminous heat easily passed in through the glass and the air, and was absorbed by the blackened surface ; but when radiated back as obscure heat, it could not escape from the box, and after a time it had accumulated sufficiently to boil the water. 307. The zinc used for battery purposes should, in all cases, be amalgamated. Full directions for the process are given in the Natural Philosophy, page 379. 312. To make a simple rheotome and rheotrope, fill two small cups with mercury, and put the ends of the battery wires into them. Put the end of another wire into each cup, and use these latter wires to convey the current where you wish to use it. The current can be instantly broken by taking one of these wires out of the mercury; and the direction of the current can be changed by shifting the wires from one cup to the other. For a description of Foucault's self-acting rheotome, see Natural Philosophy, Part II., page 301. 333- Various arrangements have been invented for giving steadiness to the electric light by keeping the carbon points within such a distance of each other that the current can pass between them. Foucault, aided by Duboscq, was the first (in 1849) to construct an electric lamp of this kind. In it, by means of an electro-magnet and of clock-work, the points are made to travel towards each other at rates corresponding to those of their combustion, the positive pole moving faster than the negative. The electric lamp has not yet been used successfully for light- ing streets. The light may be kept up for hours, but even then it is not perfectly steady, and the apparatus cannot be safely left without an attendant. It has, however, been used with excellent effect where a limited space had to be lighted for a few nights, as in building bridges. It has also been used with success for light- houses, in England and France. The power of the electric light to penetrate fogs is found to be far superior to that of the usual oil light. APPENDIX. 313 When an electric current is made to pass through highly rarefied air, a very beautiful effect is produced. This may be shown by Getssler's tubes (so called from the inventor), which are combinations of bulbs and tubes, filled with rarefied gases and liquids, and then sealed air-tight, so as to be ready for use at any time. One of them is represented in Figure 218. When Fig. 218. 'the current is sent through these tubes, they exhibit lights of various tints according to the gases contained in them. A very pleasing illustration of the electric light in rarefied air is afforded by the " guinea and feather tube," shown in Figure 50. If the ends of the tube are connected with the poles of the inductorium, or with the electrical machine, purple flashes of auroral light mark the passage of the current through the tube when the air is exhausted. In all experiments of this kind, the room should be darkened. Gassiofs cascade is a simple and inexpensive piece of apparatus for showing the electric light in a vacuum. It consists of a large glass goblet (uranium glass is best), the inside of which is coated nearly to the top with tinfoil. Place the vessel on the plate of the air-pump, cover it with a receiver which has a sliding rod through the top, bring the sliding rod in contact with the tinfoil coating, and connect one pole of the induc- torium (or one conductor of the electrical machine) with the rod, and the other with the pump-plate. When the air is ex- hausted, and the current sent through the receiver, streams of blue light flow from the tinfoil over the side of the vessel to the pump-plate. A variety of beautiful effects are produced by different degrees of exhaustion, and by changing the direction of the current. The apparatus known as the Abbt Nollefs Globe also furnishes very pretty displays of the electric light in rarefied air. It con- sists of a glass globe suspended in the upper part of a glass bell- jar, and arranged so that it can be partially filled with water, and then connected with the inductorium or the electrical ma- 314 APPENDIX. chine by a chain dipping into the water. The light in this case flows in lambent streams from the globe to the pump-plate. A variety of pieces of apparatus for showing the electric light are made by pasting bits of tinfoil, about -^ of an inch apart, on glass, oiled silk, or other non-conducting substance. Letters, outline figures, etc., may thus be formed, which appear in lines of scintillating light when the current is sent through them. The pieces of tinfoil may be pasted in a spiral on the inside of a long glass tube, and lighted up in the same way. The diamond jar, as it is sometimes called, is a Leyden jar,- the coatings of which are composed of small pieces of tinfoil, separated from one another. Brilliant sparks pass between these pieces when the jar is charged or discharged. 336. A Ruhmkorff 's coil of moderate size readily yields sparks of from four to five inches, with a battery of six Bunsen's cells. The power of the induced current to turn a needle, and to effect electrolysis, is very slight. This shows that it is very much in- ferior to the inducing current in quantity, though muck superior in tension. The physiological effect is very powerful, and care must be taken not to allow any part of the body to form the con- nection between the poles, as the shock might be disagreeable, if not dangerous. 347. When an insulated conductor is brought near a charged body, it is first polarized ; and the nearer it is brought, the higher the polarization rises. If the conductor discharges its force at the end nearest the polarizing body, it becomes charged with the same electric force as the polarizing body; if it dis- charges from the opposite end, it becomes charged with the force opposite to that on the polarizing body. If the conductor can discharge quite readily at both ends, but more readily at one end than at the other* there will be three steps in the process. It will first become polarized, then charged, and finally neutralized. If the conductor can discharge quite readily, and with equal readiness at each end, there will be only two steps in the process : it will be first polarized, and then neutralized. QUESTIONS FOR REVIEW AND EXAMINATION. GSF* The numbers refer to the sections of the book. COHESION. i. Show that bodies are made up of molecules. What are molecules? 2. Show that molecules are very small. 3. State the effect of cold upon solids, liquids, and gases. What follows from this ? 4. What is true of the spaces between mole- cules? 5. What forces act between molecules? Prove this. 6. Show that these forces act together. 7. Define the three states of matter. 8. What is cohesion ? adhesion ? 9. Through what distances do these forces act? Prove this. 10. What is true of cohesion in solids? n. Define tenacity. Describe the dynamometer, and explain its use. 12. When is a solid hard? When soft? What is the test of hardness ? 13. Define and illus- trate elasticity. What is meant by the limit of elasticity? When is a body brittle? When malleable? When ductile? How is gold-leaf made? Wire? What facts about iron wire ? 14. Show that solids are compressible. 15. What are crystals? How may we get crystals of alum? of sulphur? In order to crystallize, in what state must the substance be? Why? How are large crystals obtained? Explain the formation of crystals in iron axles, etc. What is said of ice ? 16. What is true of the differ- ent sides of molecules? Prove this. 17. Describe Rupert's drops. Explain annealing and tempering. 18. What is true of cohesion in liquids? Of the spaces between the molecules in liquids? 19. Are liquids compressible? How may this be proved? 20. Are liquids elastic? Show this. 21. How do the molecules of liquids tend to arrange themselves? Give illustra- tions. 22. What is said of cohesion in gases? Of the molecules of gases? 23. What of the compressibility of gases? 24. What of their elasticity? Recite the Summary of Cohesion. 316 APPENDIX. ADHESION. 25. Give illustrations of adhesion between solids. What is sometimes true of this adhesion? 26. What is said of adhesion between solids and liquids? 27. Describe the experi- ment with balance and glass disk. What does it show? 28. What is shown by the experiment with a glass plate laid on water? What is the effect of pulverizing a solid? Why? Ex- plain the clarifying of liquids. 29. What is shown by the experiment with Epsom salts? 30. State the three cases of adhesion between solids and liquids. 31. How does heat affect solution? Why? 32. What is capillarity? The origin of the word? State the different cases of capillarity. 33. Give illus- trations of capillarity. 34. Show the strength of capillarity. 35. Will a liquid overflow a capillary tube? Show this. Ex- plain the burning of a common lamp. Why must an alcohol lamp have a cap? 36. Describe the experiment with ammonia and charcoal. What does it show? Why is the charcoal first heated? 37. Give the facts concerning the adhesion of liquids to liquids. 38. What is the diffusion of liquids? Illustrate by experiment. 39. Describe and illustrate osmose of liquids. 40. What experiment shows the adhesion of liquids and gases? 41. Illustrate the effect of cold and of pressure on this kind of ab- sorption. What is said of aqua ammonia? of spring-water? 42. Describe and illustrate diffusion of gases. 43. What is osmose of gases? Illustrate. Recite the Summary in full. PRESSURE. 44. What is gravity? What law of gravity is mentioned? 45. What is weight? 46. Describe the spring balance. 47. Describe the balance. 48. The steelyard. 49. Define centre of gravity. 56. What is sometimes true of the position of this centre? Illustrate. 51. Define equilibrium. Its kinds? 52. Show that the centre of gravity seeks the lowest point. On what does stability of equilibrium depend? Prove this. What does the experiment with the cork balanced on a needle show? What other illustrations of the same kind? 53. How do we find the centre of gravity of a solid? 54. How is the weight of a liquid found ? 55. How do liquids press when acted on by gravity? 56. What is true of the pressure while the depth of the liquid remains the same? Erove this.' 57. At varying APPENDIX. depths, what is true of the pressures? Prove this. 58. Explain the effect of additional pressure exerted on any particle of a liquid in a closed vessel. 59. Describe the hydrostatic press. Explain its working. Its uses? 60. What is said of springs? Of Artesian wells? 61. Show that a body is buoyed up by a liquid. 62. How much is it thus buoyed up? Prove this. When will a body float in a liquid? How can iron be made to float on water? 63. What is true of the density of bodies? What is the specific gravity of a body? 64. How do we find the specific gravity of solids? 65. Describe the two forms of hydrometer. Their use? Give other ways of finding the specific gravity of liquids. 66. Prove that gases have weight. 67. What is true of the pressure of gases ? Show this by experiments. 68. Show that gases have an expansive force. 69. Describe the air-pump, and explain its action? 70. Prove that bodies are buoyed up in air. How much? 71. Why do balloons rise? How are they made? 72. Show that the pressure of the air will sustain a column of liquid in an inverted vessel. 73. How high a column of mercury will it sustain ? 74. How much is the pressure of the air on a square inch ? Show this. 75. Is the pressure always the same? 76. How is the pressure affected by the height of the place? 77. What is a barometer? Describe the form given here. 78. What are the uses of the barometer? 79. Describe and ex- plain the lifting-pump. The different forms of force pump. The fire-engine. 80. What is a siphon? Explain its action. 81. Describe Tantalus's cup. What is said of certain springs? 82. What does the air-gun illustrate? Describe it. Explain the action of gunpowder on a bullet. Describe the condenser. 83. State Mariotte's law. Why is it so called? 84. Describe the spirit level. MOTION. 85. Define inertia. 86. What is the first law of motion ? 87. What is necessary to make a body move, or to change the rate of its motion ? Show this to be so. 88. What is the effect of a force acting for a moment? 89. Of a force act- ing continuously? 90. What is true of the resistance a moving body meets ? 91. When is a moving body in equilibrium ? Illus- trate. 92. What is the second law of motion? Illustrate it. 318 APPENDIX. 93. When does a body move in a straight line? a curved line? 94. How does gravity tend to make all bodies fall? Prove this by an experiment. 95. How does gravity affect the velocity of a body moving downward? 96. How far will a body fall in a given time? 97. What is the effect of gravity on a body moving upward ? 98. How high will such a body rise in a given time ? 99. Define mass and momentum. 100. What is the third law of motion ? What is it often called ? Give illustrations of the law. 101. Show that it takes time to give motion to a body as a whole. On what does the piercing power of a projectile depend? 102. What is reflected motion ? Its law? 103. What is a pendulum? 104. What is the first law of the pendulum? Explain the word isochronis'm. 105. The second law of the pendulum ? 106. The third law? 107. The fourth law? 108. The chief use of the pendulum? What is a clock? Describe its parts, and their working. MACHINES. 109. What is a lever? The weight? The power? The fulcrum? The arms of the lever? The three kinds? no. What is the law of the lever? Illustrate, in. The general law of machines? When does there seem to be a gain of power in a machine? When a loss of power? 112. Explain the gain and loss of power in the three kinds of lever. 113. Describe and explain the compound lever. 114. What is said of bent levers? 115. Describe the rack and pinion. 116. Of what is it a modifi- cation? Show this. 117. Describe the windlass. 118. The capstan. 119. The wheel and axle. Show the application of the general law to this machine. 120. Describe the ratchet. Its use? 121. What is wheel-work? Why used? Describe the dif- ferent kinds of wheels. How are they made to act on one another? 122. For what is the pulley used? 123. Define fixed and movable pulleys. 124. The law of the pulley? 125. Show the application of the law of machines to systems of pulleys with one rope. 126. Describe systems with more than one rope. 127. What is an inclined plane? 128. The law of the inclined plane? 129. What is a wedge? Its law? 130. Its uses? 131. What is a screw? Its parts? 132. Describe the endless screw. 133. What kinds of water-wheels? 134. Describe the breast APPENDIX. 3 19 wheel. The overshot wheel. The undershot wheel. 135. Describe Barker's mill. Explain its action. 136. What is said of the turbine? 137. Show how steam maybe made to move a piston. What is reciprocating motion? How changed to rotary motion ? Describe the engine in Figure 86. 138. De- scribe the governor. Its use ? 139. What is the fly-wheel ? Its use? 149. What is a high-pressure engine? A low-pressure engine? 141. The purpose of the boiler? Its construction? Describe the Cornish boiler. The locomotive boiler. 142. De- scribe the other parts of the locomotive. SOUND. 143. Show that a sounding body vibrates. 144. Show that sound does not pass in a vacuum. 145. Show that it passes through all gases. 146. Does sound pass through liquids? Solids? Prove this. How is sound produced? 147. On what does its intensity depend ? Show this. 148. The law of the intensity of sound for different distances? 149. Explain speaking-tubes. 150. The velocity of sound in air? How found? 151. Its velocity in water? When and how found? 152. Its velocity in solids? 153. When is sound reflected? The law of the reflection ? 154. What are echoes? Mention some remark- able echoes? 155. What is noise? musical sound? Describe experiment. 156. On what does the pitch of musical sounds depend? 157. Describe the tuning-fork. 158. Describe the siren. 159. Its use? 160. What is an octave? 161. Describe the sonometer. Its use? 162. On what does the rapidity of the vibration of a string depend? 163. What are notes? Give ex- periments illustrating their formation in strings. 164. How may nodes be formed in plates ? What are nodal lines ? 165. What are overtones? 166. What is quality in sound? Illustrate. 167. Show the transmission of musical sounds through liquids and solids. 168. What are sympathetic vibrations? Illustrate. 169. Illustrate the interference of sounds. 170. When are beats produced? 171. What is unison? A fifth? A fourth? Are they equally pleasing to the ear? What is a major third? A minor third? A chord? A discord? 172. What are stringed instru- ments? 173. What is the use of sounding-boards? 174-177. State the laws of the vibration of strings. What two classes 32O APPENDIX. of stringed instruments? 178. What is said of longitudinal vibrations in rods free at one end? 179. In rods free at both ends? 180. Give experiment illustrating resonance? 181. How may a column of air in a tube be made to vibrate? 182. At what rate does such a column vibrate? 183. What is true of the vibration in open and in stopped tubes ? 184. What are organ- pipes? Explain their action. 185. What is a reed? How does it produce sound? 186. What two classes of wind instruments? 187. Show that friction is always rhythmic. How may the noise of a flame be changed to music? 188. What is said of sensitive flames within tubes? 189. Describe the organ of voice in man. How may its action be illustrated? 190. Describe the human ear? 191. What is the range of human hearing? LIGHT. 192. What is a luminous body? What is true of it? What are transparent bodies? opaque bodies? 193. Show that light traverses space in straight lines. Explain shadows. De- fine ray, beam, pencil, divergent pencil, and convergent pencil. 194. What is the velocity of light? How first determined? 195. How does the intensity of light vary with the distance? 196. When is light said to be reflected ? What is a prism ? When is light refracted ? 197. What is the law of reflection ? 198. What is diffused light? How distinguished from reflected light? 199 What is the law of refraction ? 200. When is light totally re- flected? 201. Describe and explain mirage. 202. What is true of rays passing through a medium with parallel faces ? 203. What of the path of rays through a prism? 204. What is meant by the solar spectrum? What are its colors called? Define dispersion and dispersive power. 205. Describe and explain the achromatic prism. 206. Show that prismatic colors are simple. 207. Show that they are unequally refrangible. 208. What is the composition of white light? How may this be shown ? How many simple colors are there? What are they? What are com- plementary colors? 209. What is said of the absorption of light? 210. To what is the color of bodies due? What is some- times true of the color they transmit? 211. Describe Newton's rings. What causes them? 212. What are diffraction fringes? Their cause? 213. What is double refraction? 214. Describe APPENDIX. 321 the polarization of light? 215. What are lenses? Their differ- ent forms? 216. How do convex lenses affect parallel rays? How do concave lenses? What are they respectively called? 217. How may images be formed by convex lenses? On what does the size and position of the image depend? 218. Describe the camera obscura? 219. Describe the parts of the eye. What purpose does the iris serve? 220. Show that the eye must adjust itself for different distances. How does it do this ? 221. Describe the structure of the retina. 222. Show that the optic nerve is blind. 223. How may the sensation of light be excited? 224. How long does the impression on the retina last? Prove this. Describe the zoetrope. 225. Explain and illustrate irradiation. 226. Show that the sensibility of the retina is soon exhausted. 227. What is color-blindness? 228. What is the optical axis? the visual angle? 229. How do we estimate the size of bodies? 230. Their distance? 231. Why do near bodies appear solid? 232. Describe and explain the stereoscope. 233. What are the laws of distinct vision? Explain near-sightedness and far-sight- edness. How may these defects be remedied ? 234. How is the eye affected by age ? How may this defect be remedied ? 235. What is a microscope? A simple microscope? 236. Describe the compound microscope. What is aberration ? How may it be lessened? How is the magnifying power of a microscope estimated? 237. What is a telescope ? How constructed? How does it differ from the microscope ? How can a lens be rendered achromatic? 238. Describe the terrestrial telescope. 239. The opera-glass. 240. The magic lantern. 241. What is a mirror? A plane mirror? How does it affect the rays falling on it from an object? Why is no image formed? 242. What is a concave mirror? How does it affect parallel rays? other rays?- 243. When is an image of an object formed by a concave mirror? On what does its size depend? 244. What is a convex mirror? Its effect on different kinds of rays? 245. Describe the reflecting telescope. What is a refracting telescope? 246. How does a parabolic mirror affect parallel rays? How does it affect rays diverging from the focus ? Why is this ? HEAT. 247. How is heat radiated ? 248. What is the velocity 21 322 APPENDIX. of radiant heat? 249. Define luminous and obscure heat. 250. When is a body diathermanous ? Illustrate. 251. Show that ob- scure always accompanies luminous heat. 252. Show that heat may be reflected and refracted. 253. How do the two kinds of heat compare in respect to refrangibility? 254. Of what is the spectrum made up? What are Fraunhofer's lines? 255. What is calorescence ? Fluorescence ? 256. What facts are given con- cerning the absorption of heat? 257. Show that good absorbers are good radiators. 258. What is conduction? 259. What is true of the conductivity of solids? 260. Of liquids? of gases? 261. What is the first effect of heat on bodies? 262. How much heat does a body give out in cooling i? Show this. 263. What is true of the heat required to raise the temperature of different bodies i? 264. What is a unit of heat? 265. Define specific heat. 266. What is the second effect of heat on bodies? 267. What is said of the melting-points of different solids? What change do some bodies undergo before melting? Illustrate. 268. What is the latent heat of a liquid? 269. What is said of the boiling of liquids? 270. Show that gases have latent heat. 271. Show the relation of the state of a body to its temperature. 272. Is the boiling-point of water always the same? Why is this ? 273. Explain the spheroidal state. 274. What is said of evaporation? 275. At what point does a gas condense? 276. On what principle do freezing-mixtures depend? Illustrate. 277-279. What is true of the expansion of solids by heat? Of liquids? Of gases? 280. What is convection? 281. How may convection in liquids be shown ? 282. How are oceanic currents caused ? 283. Illustrate the convection of gases. Explain heat- ing by a furnace. 284. State the relation of water to heat and climate. 285. What is peculiar in the expansion and contraction of water? Is the fact of any importance ? Why? 286. Explain heating by steam ? 287. Show that a hot-house is a trap for sunbeams. 288. Describe the making and graduating of a com- mon thermometer. Explain the Fahrenheit, Centigrade, and Reaumur's scales. 289. When is an alcohol thermometer used? Why? 290. Describe the air thermometer. 291. Describe Les- lie's differential thermometer. 292. How are clocks and watches APPENDIX. 323 affected by temperature? 293. Describe Graham's pendulum. 294. Describe the compensation balance-wheel. 295. Give illus- trations of the force exerted by bodies in expanding and con- tracting. 296. Describe Mason's hygrometer. 297. What is the hygrodeik ? ELECTRICITY. 298. What is magnetism? The origin of the name? What are lodestones? Why so called? 299. Where does the power of a magnet chiefly reside? Show this. What are magnetic curves? 300. What are the poles of a magnet? What is true of the forces at the poles? 301. Describe the mag- netic needle. 302. Show that the earth acts like a magnet. 303. What is the law of magnetic attraction and repulsion? 304. Describe and illustrate magnetic induction. 305. What are the kinds of magnets? 306. Describe the voltaic pair, giving the names of its parts. What is electricity? The electric current? Why so called? 307. Describe Bunsen's cell. Grove's cell. 308. Daniell's cell. 309. What is an electric battery ? What two ways of connecting the cells ? 310. What is quantity? Intensity? A quantity battery? An intensity battery? How may we obtain both quantity and intensity? 311. Define conductors and non- conductors. 312. What is a rheotome? A rheotrope? Give the origin of the words. 313. What position does a needle take with reference to a conducting wire? 314. What is a rheoscope? What other name has it? On what principle does the instru- ment depend? 315. Describe the astatic needle. 316. What law concerning the resistance of conductors? 317. Show that the current can make iron magnetic. What is a helix? An electro- magnet? 318. Show that the wire conducting a current is mag- netic. 319. On what principles do electro-magnetic engines depend? Describe Page's rotating apparatus. 320. How can electricity be made to regulate the motion of clocks? 321. What is a telegraph? What four things essential to an electric tele- graph ? What is the receiving instrument in the needle telegraph ? In Bain's telegraph? 322. Describe the receiving instrument of the Morse telegraph. 323. What is said of the earth as a tele- graphic wire? 324. What is the purpose of the relay? De- scribe the instrument. 325. Describe the telegraphic fire-alarm. 324 APPENDIX. 326. Define electrolysis, electrolyte, electrode, anode, and cath- ode. What compounds may become electrolytes? 327. De- scribe the electrolysis of blue vitriol. 328. What is electrotyping? Describe the process. Its uses? 329. What is electro-plating? Describe the process. 330. Describe electro-gilding. 331. De- fine electro-metallurgy. What two kinds? Illustrate. 332. What law in regard to the heat developed by a current? Ex- plain blasting by means of electricity. 333. How is the electric light produced? What is the voltaic arc? What is said of its heat. 334. Show that a current may be induced by a magnet. 335. In magneto-electric machines, how is the electricity in- duced? 336. Describe the induction coil in full. 337. What is the extra current? 338. What is thermo-electricity? How is it generated? 339. Describe the thermopile. Explain its use as a thermometer. 340. What is frictional electricity? When is it developed? 341. Describe the electrical machine. 342. What is true of the quantity and intensity of frictional electricity? How does it compare with voltaic electricity? 343. Describe the electroscopes mentioned. Their use? 344. Show that the forces on the two conductors act in opposite directions. 345. What are these forces called, and what is true of their develop- ment? 346. What is induction? Illustrate. When is a body polarized? When charged? 347. Show that the charge on a solid conductor is on the surface. 348. Describe the Leyden jar. How is it charged ? How discharged ? 349. Describe the forms of Leyden battery. How do they differ in their operation? 350. Explain the effect of points on a conductor. 351. Describe the electric wheel. INDEX. ?or concise statements of the leading topics of the book, see the SUMMARIES, which will be readily found by means of the Table of Contents. The references in this Index are only to the fuller treatment of subjects in the body of the work. Abb6 Nollet's globe, 313. Action and reaction, 66. Adhesion, 6. of gases and liquids, 24. solids, 23. liquids, 23. and solids, 18, 20. solids, 1 8. Air (see Atmosphere). Air-gun, the, 58. Air-pump, the, 48. Annealing, 12. Anode, 214. Anthelia, 263. Apparatus, list of, 295. Artesian wells, 41. Atmosphere, buoyancy of the, 50. composition of the, 231. elasticity of the, 48. electricity in the, 256. heating of the, 231. moisture of the, 242. pressure of the, 52, 232. resists the fall of bodies, 63. Aurora borealis, the, 260. Balance, the, 31. Balance-wheel, the compensation, 193. Balloons, 50. Barker's mill, 90. Barometer, the, 53. Battery, Bunsen's, 199. Daniell's, 200. Grove's, 200. Leyden, 227. magnetic, 197. thermo-electric, 222. Beats, 115. Blue vitriol, electrolysis of, 215. Boiling, 181. Brittleness, 8. Buoyancy, 42, 50. C. Calms, region of, 235, 252. Calorescence, 175. Camera obscura, the, 150. Capillarity, 21. Capstan, the, 79. Cathode, 214. Centre of gravity, the, 31. Chords, 1 1 6. Clocks, construction of, 71. electric, 208. Clouds, 246. colors of, 264. Cohesion, 6. in gases, 14. liquids, 12. solids, 6. Coils, induction, 220. Collodion, 309. Color-blindness, 157. Colors, 142. complementary, 142. prismatic, 140. Condensation of vapors, 183. Condenser, the, 58. Coronas, 262. Crank, the, 93. Crystals, 10. Current, the electric, 199 (see Electricity). Curves, magnetic, 196. D. Daguerreotype, the, 308. Density, denned, 43. Dew, 243. Diamond jar, the, 314. Diathermancy, 173. Diffraction fringes, 144. Discharge, convective, 229. glow, 229. Discharger, the, 228. Discords, 116. Ductility, 8. Dynamometer, the, 7. 326 INDEX. Ear, the human, 129. range of, 130. Earth, as a telegraphic wire, 211. Echoes, 103. Elasticity, 8. Electric battery, 200. clocks, 208. lamp, 312. light, 218, 313. telegraph, 210. wheel, 229. Electrical machine, the, 224. Electricity, a source of mechanical power, 207. atmospheric, 256. conductors of, 202. developed by friction, 223. heat, 222. magnetism, 219. develops heat and light, 218. intensity of, 201. makes iron magnetic, 206. nature of, 274; positive and negative, 226. quantity of, 201. resistance to current of, 204. voltaic, 198. Electrodes, 214. Electro-gilding, 217. Electrolysis, 214. Electrolyte, 214. Electro-magnets, 206. Electro-metallurgy, 217. Electro-plating, 216. Electroscopes, 225. Electrotypmg, 215. Energy, conversion of, 275. kinds of, 275. source of, 280. transmuted, not destroyed, 280. Equilibrium, 32. of moving bodies, 61. Evaporation, 183, 242, 256. Expansion by heat, 184, 193, 311. Experiments, notes on, 295. Eye, the, 151. adjustment of, 152. affected by age, 162. F. Falling bodies, 63. Farmer's alloy, 222. Far-sightedness, 161. Fire-engine, the, 56. Flames, sensitive, 128. sounding, 127. Fluorescence, 175. Fly-wheel, the, 95. Fogs, 244. Force-pump, the, 54. Fraunhofer's lines, 175, 273. Freezing-mixtures, 183. French weights and measures, 285. Friction, always rhythmic, 127. electricity developed by, 223. G. Galvanometer, the, 203. Gases, buoyancy of, 50. cohesion in, 14. compressibility of, 15. diffusion of, 26. elasticity of, 15. expansive force of, 48, 58. osmose of, 26. pressure of, 47. specific gravity of, 290. Gassiot's cascade, 313. Geissler's tubes, 313. Governor, the, 93. Graham's pendulum, 192. Gravity, the centre of, 31. curves the path of projectiles, 62. increases speed of falling bodies, 64. specific (see Specific Gravity). Gulf Stream, the, 186. Gunpowder, action of, 58. H. Hail, 255. Halos, 264. Hardness, 8. Harmonics, or overtones, 1 1 1. Heat, absorption of, 175, 310. causes liquids to boil, 180. solids to melt, 179. conduction of, 177. convection of, 185. conversion of, 278. developed by electricity, 218. dispersion of, 174. expansion by, 184, 193, 311. latent, 180, 181. luminous, 173. mechanical equivalent of, 278. obscure, 173, 231, 311. of the atmosphere, 231. promotes solution, 21. radiation of, 173, 176, 310. reflection of, 174. refraction of, 174. solar, 282. specific, 179. the same as light, 273. unit of, 179. Heating by steam, 188. Helix, 206. Holtz's electrical machine, 301. Hot-houses, 188, 311. Hydrometer, the, 44. Hydrostatic press, the, 38. Hygrodeik, the, 194. Hygrometer, the, 193. I. Iceland spar, 144. Inclined plane, the, 85. Induction coils, 220, 303. electrical, 227. INDEX. 327 Inductorium, the, 303, 314. Inertia, 60. Instruments, stringed, 117. wind, 119. Irradiation, 156. Lamp, Bunsen's, 306. the electric, 312. Lenses, 147. achromatic, 167. Level, the, 59. Lever, the, 74. Leyden battery, the, 227. jar, the, 227. Light, absorption of, 142. chemical action of, 308. composition of, 141. diffusion of, 135. dispersion of, 140. double refraction of, 144. intensity of, 133. interference of, 143. length of waves of, 270. polarization of, 145. radiation of, 131. reflection of, 134, 143. refraction of, 134, 136, 273. total reflection of, 136. undulatory theory of, 269. velocity of, 132. Lightning, 258. rods, 259. Liquids, buoyancy of, 42. cohesion in, 12. C9mpressibility of, 13. diffusion of, 24. elasticity of, 14. osmose of, 24. pressure of, 37. specific gravity of, 44. weight of, 36. M. Machines, 74. law of, 75. Magdeburg hemispheres, 47. Magic lantern, the, 168. Magnetism, 195, 261. developed by electricity, 206. of the earth, 196. Magneto-electricity, 219. Magnets 195, 197. Malleability, 9. Mariotte's law, 58. Mass, defined, 65. Matter acted upon by gravity, 29. made up of molecules, 3. states of, 6. Melting-point, the, 180. Microscopes, 165. Mirage, 136. Mirrors, 169 Mists, 244. Molecular forces, 5. Molecules of bodies are in motion, 273. size of, 3. Momentum, 65. Monsoons, 237. Motion, 60. laws of, 60, 62, 65. quantity of, 65. reciprocating, 92. reflected, 67. resistance to, 61. rotary, 92. Musical instruments, 117. sounds, 105, 112. N. Near-sightedness, 161. Nebular hypothesis, the, 283. Needle, the astatic, 203. the dipping, 196. Nodal lines, no. Nodes in sounding bodies, 109. Noise defined, 105. O. Oceanic currents, 185, 232, 244. Octave, defined, 107. Opera-glass, the, 167. Optic nerve, action of light upon, 154. Optical axis, the, 157. Organ-pipes, 124. Osmose of gases, 26. liquids, 24. Overtones, m. P. Page's rotating apparatus, 207. Parhelia and paraselenae, 264. Pendulum, the, 69. . Graham's, 192. Penumbra of shadow, 132. Photography, 308- Pisa, the Leaning Tower of, 34. Polarization of electricity, 227, 314. light, 145. Pressure (see Air, Gases, and Liquids). Prisms, 134. achromatic, 140. double refracting, 144. path of rays through, 138. Problems, 287. Pulley, the, 82. Pumps, 54. air, 48. R. Rack and pinion, the, 78. Rain, 251. Rainbow, the, 261. Ratchet, the, 80. Rays of light, 132. Reaction, 66. Reed pipes, 125. Relay, the, 211. INDEX. Resonance, 120. Retina, duration of impression on, 155. structure of, 153. Rheoscope, the, 203. Rheotome, the, 202, 312. Rheotrope, the, 202, 312. Rods, longitudinal vibrations of, 119. Kuhmkorit's coil, 303, 314. Safety-valve, the, 97. Saint Elmo's fire, 260. Screw, the, 87. Shadows, 132. Simoom, the, 241. Siphon, the, 56. Siren, the, 106. Snow, 253. Softness, 8. Solids, adhesion of, 18, 20, 23. cohesion of, 6. compressibility of, 10. Solution, 20, 21. Sonometer, the, 108, 298. Sound, caused by vibrations, 100. intensity of, 102. interference of, 114. quality of, 112. reflection of, 103, 267. refraction of, 267. transmission of, 101. velocity of, 102, 103. will not pass through a vacuum, 100. Sounding-boards, 117. Sound-waves, 266. Speaking-tubes, 102. Specific gravity, 43. of a gas, 290. Spectroscope, the, 305. Spectrum, the solar, 130, 175. Spheroidal state, the, 182. Spirit level, the, 59. Spring balance, the, 30. Springs, 41. Steam engine, the, 91. locomotive, 97. heating by, 188. latent heat of, 181. Steelyard, the, 31. Stereoscope, the, 160. Storms, 238. Strings, vibrations of, 108, 117. T. Tantalus's cup, 57. Telegraph, Bain's, 210. fire-alarm, 212. four things essential to, 210. Morse's, 210. needle, 210. Telescope, the, 166. reflecting, 171. refracting, 171. terrestrial, 167. Temperature affects time pieces, 192. of the atmosphere, 232. Tempering, 12. Tenacity, 6. Thaumatrope, the, 155. Thermo-electricity, 222. Thermometers, 190. differential, 191, 223. Thermopile, the, 222. Thunder, 258. Thunder-storms, 257. Tornadoes, 239. Trade-winds, 235. Transparency, 131. Tubes, vibrations in, 122. Tuning-fork, the, 106. V. Vacuum defined, 50. Vibrations, longitudinal, 119. of columns of air, 122. sympathetic, 113. Vision, laws of, 160. Visual angle, the, 157. Voice, the human, 128. Voltaic arc, the, 218. electricity, 198. pair, the, 198. W. Water, electrolysis of, 214. expansion of, 187. frozen by evaporation of ether, 3n- power, 89, specific and latent heat of, 187. wheels, 89. Waterspouts, 241. Wedge, the, 86. Weight, 30. in air, 50. liquids, 42. Wells, Artesian, 41. Wheel and axle, the, 79. Wheels, kinds of, 81. Wheel-work, 80. Whirlwinds, 239. dust, 240. Wind instruments, 119. Windlass, the, 79. Winds, 234. Wire, 9. Zoetrope, the, 155. Cambridge : Electrotyped and Printed by John Wilson and Son. APPARATUS. The following articles named in the List on pages 295-303 can be furnished at the prices affixed: COHESION. No. i. Bar and gauge . . $2.25 2. Two half-pint flasks and tubes . . . . . 1.25 3. Lead hemispheres . . i.oo . . $1.00 5. Crucible . . .25 . . .50 7. Two-quart cylindrical jar . . 1.50 8. Dropping-tube ........ . . .50 9. Six test-tubes . . .50 . . 2.50 ii. Retort-and- tube-holder . . 3.50 12. Mercury . . 5.00 5.00 ADHESION. No. i. Glass disk, with cord . . 1.50 . . 1.50 3. Two glass funnels, and niters . . . . . I.OO 4. Set of capillary tubes . . I.OO 5. Pair of capillary plates . . 1.50 . . 1.50 7. Glass funnel tube . . .25 . . 1.75 9. Bottles and tube . . I.OO 10. Cup and tube . . I.OO APPARATUS. Fig. i. MECHANICS. No. I. Illustrations of Centre of Gravity (Fig. i) $5.00 2. Bottle with tubes . . $3.50 3. Liquid equilibrium tubes 3.50 4. Illustration of hydrostatic press .... 9.00 5. Hydrometer 1.25 6. Cylinder and cup 2.50 7. Ritchie's school air-pump (Figure 2) The plate is eight inches in diameter, and forms the top of a cylinder four inches high, which prevents any flexure or change in its form. The pump cylinder is placed horizontally beneath the plate, and is thus protected from injury. The base is of mahogany, and has a screw table clamp. This pump is essentially automatic in its action, and will produce a vacuum more than twice as high as any pump with valve action ; this is of great importance in all experiments with electricity. It is worked with ease, and is warranted to be trustworthy and durable. A patent has been applied for. 25.00 8. Sliding-rod receiver, complete 5.00 9. Plain quart receiver i.oo 10. Apparatus for weight and buoyancy of air (See Figure 2) 7.50 ii. Magdeburg hemispheres 7.50 12. Hand glass 1.25 13. Rubber bag, with screw cap and hook . . 2.25 APPARATUS. Fig. 2. No. 14. Barometer tube $1.50 15. Model of lifting pump 9.00 1 6. Model of force pump, with stand and cis- tern for both pumps $13.50 17. Siphon 0.50 1 8. Tantalus's cup 2.00 19. Condenser 9.00 20. Condensing chamber, with air-gun and jets for water 9.50 21. Guinea and feather tube (fitted also for electrical experiments) 8.00 22. Illustration of pendulum 3.50 23. Illustration of central forces 3.75 24. Models of simple and compound levers . 5.50 25. Models of wheel and axle, capstan, and pulleys, with stand and set of weights (Figure 3). This arrangement for the illustration of these simple ma- chines will be found very convenient and complete. The teacher can thus have before his class those only that illustrate the lesson. 2O.OO 26. Models of screw, wedge, and inclined plane, with car 7.50 APPARATUS. Fig- 3- No. 27. Model of Barker's mill $2.25 28. Wollaston's illustration of low-pressure engine. This is a cylinder with a thin copper globe attached, piston and rod, and handle. Pour a teaspoonful of water into the globe, and hold over a spirit-lamp ; steam will be generated and drive up the piston : then plunge the globe in cold water ; the steam will be condensed and the pis- ton forced down by atmospheric pressure. 5'5^ SOUND. No. i. Bell for vacuum 2. Revolving toothed wheel . . . 3. Tuning-fork and case .... 4. Sonometer, with wires, complete 5. Violoncello bow 6. Vibrating plate 7- Four rods on bar 8. Brass rods . 3-50 $3-25 7.50 n.oo 25.00 2.00 3-50 1.50 APPARATUS. Fig. 4. Fig- 6. Fig. 5- Fig. 8. Fig. 7- No. 9. Iron screw-press for Nos. 6, 7, and 8 (Fig- ure 4) $7-50 10. Ivory ball and stand, for No. 8 .... 2.25 ii. Resonant jar 2.00 12. Three glass tubes $0.50 13. Organ pipe, with sliding piston .... 4.50 14. Reed pipe, with glass chamber .... 4.75 15. Jet for singing flame i.oo LIGHT. No. i. Condensing lens, mounted 10.00 2. Prism, for refraction 2.00 3. Prism, No. 2, mounted (Figure 5), $6.00 ; (difference compared with No. 2) ... 4.00 4. Achromatic prism 7.25 5. Revolving disk apparatus, with disks . - . IO-75 6. Apparatus for Newton's rings, brass frame 6.50 7. Zoetrope 5.00 8. Stereoscope, with 12 diagrams 4.50 9. Convex and concave mirrors, ground and polished 4.50 10. Mounted mirror 4.25 ii. Double-convex and double-concave lenses 3.00 APPARATUS, Fig. 12. Fig. 9. Fig. 10. Fig. xi. HEAT. No. i. Iodine cell $5.00 2. Differential thermometer $3.50 3. Conductometer 4.50 4. Pair of plates, with copper and tin balls . 3.25 5. Compound bar 1.25 6. Illustration of convection of gases . . . 3.50 7. Mason's hygrometer 4.00 8. Edson's hygrodeik 15.00 9. Pair of reflectors, and ball 12.50 10. Fire syringe and tinder 3.00 ii. Spirit-lamp i.oo ELECTRICITY. No. i. Bar magnet (Figure 6) i.oo 2. U-magnet (Figure 7) ........ i.oo 3. Voltaic pair 1.50 4. Bunsen's cell . 4.50 5. Magnetic needle (Figure 8) 1.50 6. Dipping needle 2.50 APPARATUS. Fig. 13- Fig. 14. Fig. 15. No. 7. Oersted's galvanometer (Figure 9). A base and pillar supporting a wire frame, within which is suspended a magnetic needle on a centre point. The wire has three pole cups arranged so that the battery current may pass above, below, or around the needle. The frame must be placed north and south. $4-75 8. Electro-magnet 3.00 9. Lifting coil 3.00 10. Page's rotating apparatus 8.00 ii. Helix and ring (Figure 10). Two semi-circular pieces of soft iron, with handles, and a helix of copper wire. Connect the helix with the bat- tery, and great force is required to separate the ring. $4- 2 5 12. Model of telegraph (Figure 1 1) .... 8.00 13. Model of relay magnet 9.50 14. Decomposing cell 3.25 15. Thermo-electric series 2.00 1 6. Vibrating shocker, or induction coil (Fig- ure 12). A helix enclosing an iron rod, or bundle of wires, with a vibrating break-piece ; another helix, of great length, of fine wire, entirely separated, surrounds the former. 7-5 17. Separable helices, $ 1 8.00; (difference, com- pared with No. 1 6) 10.50 1 8. Powder cup (for explosion of powder by battery) i-oo 19. Vulcanite cylinder (for friction) .... 1.25 20. Electrical machine 25.00 8 APPARATUS. No. 21. Holtz's machine, $50.00 ; (difference com- pared with No. 20) ....... $25.00 22. Insulated conductor ........ 12.50 23. Gold-leaf electroscope . ...... 6.00 24. Leyden jar ............ $2.00 25. Diamond jar (Figure 13) ...... 3.50 26. Discharger ........... 2.00 27. Electric wheel ....... ... 1.25 28. Spotted tube (for electric light) .... 4.00 29. Stand and bells (Figure 14). A basement with pillar and bell, and a similar bell to screw to the stem of a Leyden jar. A little ball suspended between the bells will be alternately attracted and re- pelled between them, vibrating for a long time, and gradually discharging the jar. 5'^Q 30. Gassiot's cascade (Figure 15) ..... 2.50 31. Geissler's tubes, $2.00 to . ..... 5.00 SUMMARY. COHESION ................. $12.75 ADHESION ................ 7 50 MECHANICS ............... 124.50 SOUND ..... . . ......... . 70.00 LIGHT .......... ........ 26.75 HEAT .................. 24.00 ELECTRICITY ............... 84.50 TOTAL (for articles priced in right-hand column) . $350.00 A charge for boxing and packing will be made of two per cent on the amount of the bill. The above list of apparatus, or any considerable portion of it, will be delivered free of freight, and insured against dangers of transportation or breakage, if a draft on Boston or New York is received with the order. Orders maybe sent to E. S. RITCHIE & SONS, Manufacturers, 149 Tremont Street, Boston ; or to WOOLWORTH, AINSWORTH, & Co., New York. NEW AND VALUABLE TEXT-BOOKS IN PHYSICS FOR GRAMMAR AND DISTRICT SCHOOLS, HIGH SCHOOLS, AND ACADEMIES, BY W. J. ROLFE AND J. A. GILLET, TEACHERS IN THE HIGH SCHOOL, CAMBRIDGE, MASS. THE CAMBRIDGE COURSE IN PHYSICS IN THREE VOLUMES : I. CHEMISTRY, $2.00. II. NATURAL PHILOSOPHY, $2.00. III. ASTRONOMY, $2.00. $iT New and revised editions of these books have been prepared, and the Series is now complete in a permanent form* The Electricity of the old " Chemistry and Electricity " has been transferred to the '" Natural Philosophy " in the new edi- tion, and has been wholly rewritten, made somewhat briefer, and brought fully down to the present state of the science. There has also been added to the Appendix of the " Natural Philosophy " a chapter on the Physics of the Atmosphere, or Meteorology, containing all the recent discoveries and theories in this important and interesting field. As thus revised, the " NATURAL PHILOSOPHY " is complete in itself, containing Mechanics (under which head are included Hydrostatics, Hydraulics, Pneumatics, Motion, Machines, etc.), Sound, Light, Heat, Electricity, and Meteorology. The "CHEMISTRY" has been carefully rewritten and ex- panded so as to fill the space occupied by the Electricity in the old edition. New chapters on Crystallography and Organic Chemistry, from the freshest sources, have been added, and the description of Elements has been enlarged. This edition (June, 1869) gives the nomenclature as adopted by the London Chemical Society, as taught at Harvard College, and as generally used in scientific journals. The new edition of the "ASTRONOMY " contains, in addition to the Astronomy proper, a chapter on the Conservation of Energy and an account of the Constellations, illustrated by 17 full-pa^e Star Maps from Argelander. These books are inductive in method, fresh in matter, simple in style, fully illustrated, and handsomely printed, and they ex- actly meet the wants of our advanced Seminaries and Acade- mies, and of those High Schools which can devote considera- ble time to these subjects. THE HANDBOOK SERIES IN THREE VOLUMES : I. HANDBOOK OF CHEMISTRY, $ 1.25. II. HANDBOOK OF NATURAL PHILOSOPHY, $ 1.25. III. HANDBOOK OF THE STARS, $1.50. These books contain (aside from the Appendix) respectively 159, 230, and 159 pages, in clear, open type, with no fine print, and they treat of all the topics usually included in school manuals of these sciences. The more theoretical portions of the subject are discussed briefly in Appendixes, and descrip- tions of apparatus and directions for performing experiments are added. Omitting the Appendixes, the books are not too difficult for the upper classes in Granxmar and District Schools. With the Appendixes, they are exactly adapted to the wants of those High Schools and Academies which have not time for larger books. They are not abridgments of the larger works by the same authors, but are wholly new and independent books, differing from the others in the selection, arrangement, and treatment of topics, so far as w^is necessary to fit them for a briefer and easier course of study. They are simple in style, and emi- nently ^rad&a/, yet thoroughly scientific, and giving the results of the latest discovery and research. They are sure of a hearty welcome from teachers who desire books that shall be brief without being dry, and easy without being puerile. IgOr" E. S. RITCHIE & SONS, of Boston, will furnish a set of apparatus for the thorough illustration of the Handbook of Chemistry for $30, and a set for the thorough lustration of the Handbook of Natural Philosophy for $ 350. *** Circulars, containing notices and testimonials from emi- nent teachers, will be furnished on application. Copies for examination will be supplied at one half the advertised price, with twenty-five cents additional for postage. Special terms will be given for first introduction of any of the books. WOOLWORTH, AINSWORTH, & CO., NEW YORK. TESTIMONIALS. BELOW we give extracts from a few of the most recent testimonials to the merits of this popular series : The Pennsylvania School Journal (April, 1869,) speaks thus of the series : " The progress of science teaching in our schools has un- doubtedly been retarded by the lack of suitable text-books. That want has been, in a great measure, velieved by the recent labors of Messrs. Rolfe and Gillet, in their double course, a course of Hand- books for those who do not desjre anything beyond elementary in- struction, and another of more comprehensive text-books on the same sciences, the last of which has just been published. These text- books commend themselves as the work of men whose experience in the class-room has taught them the most effective methods of present- ing scientific truth, and whose design has been to present the results of the latest investigations in the several departments of each science treated. They aim throughout at nothing more than clearness, nothing less than accuracy. We remark, especially, the absence of any loose statement which could mislead the pupil or leave a half-formed idea. Teachers all know the difficulty of banishing a false impression which has for a time been accepted and applied as fact. Instead of the weakness which tends to enfeeble the growing mind by presenting the study of science as a play lesson, a mere succession of interesting experiments, etc., we have scientific truth here set forth as a study which the schoolboy may feel an honest pride in mastering. In none of these works is system sacrificed to simplicity, as in some others of their class ; yet the text-books of the Cambridge Course yield to none in point of interest At the end of each division of the subject, a carefully prepared Summary has been inserted, thus binding together and again classifying all the matter previously given Indeed, take the Cambridge Physics throughout, the Course is greatly in ad- vance of any heretofore issued in this country. The publishers have TESTIMONIALS. also done their part well. It is a luxury to sweep the hand over these smooth, solid, glossy pages, beautiful also to the eye, in their old- style type and in their wealth of scientific illustration, and think of the books as specially designed for our Common Schools." The San Francisco Bulletin, (March 20, 1869,) in a review of the whole series, says : " These works embody the latest results of sci- entific discovery. The compilers wisely discard theory, however plausible and fascinating, unless it rests on a solid groundwork of truth. The arrangement and divisions of subjects are judicious ; the method of teaching is based on correct principles. The definitions are clear and concise ; the notes are models of perspicuity. There is no useless verbiage ; no vague generalization ; no rhapsodies of style. The student is directly introduced to the subject, and kept rigidly to it until he has mastered it. At the close of each section the ground gone over is reviewed, and the principles educed are summed up in a few pithy axioms. While these volumes are more immediately de- signed for the use of schools, they have high claims to recognition as scientific treatises. We can hardly think of any other souree where so much valuable knowledge of physics can be found in so short a compass. The subjects are discussed with a freshness and oftentimes a grasp of thought rare in books of the kind." The Boston Courier says of the whole series : " They are in ad- vance, by a great stride, of other text-books in common use, not only because they pursue the only rational method, so long ago instituted by Bacon, and yet so much neglected, of deducing principles from facts, instead of supporting rules laid down by examples, but also be- cause they have kept pace with the progress of constantly accumulat- ing knowledge and furnish us with the latest results. They are MODEL BOOKS." The Boston Daily Advertiser says : It is in their attempt to keep up with the progress and present condition of scientific knowledge, that these volumes differ most widely from the text-books generally used in our schools. Chemistry and electricity heat, light, and sound wear, in this Cambridge Course of Physics, a very different aspect from that which they present in similar treatises of five-and- TESTIMONIALS. twenty years ago. .... We rejoice to believe that many myriads of the young and not of the young only will here be introduced to discoveries and speculations of so much interest and grandeur." The Commonwealth (Boston), in noticing the " Handbook of Natu- ral Philosophy," says : " The merit of this, as of the other volumes, is that it breaks away from the traditional method of preparation of such works, and by original arrangement, the introduction of the latest discoveries and experiments, and the amplest illustration, gives at once the most complete and accurate data of the subject-matter treated. It is fresh and pertinent throughout, and is equally valuable in school, counting-house, or family." The Boston Journal of Chemistry (March, 1869,) says of the series : " We have carefully examined these books, and find them to be compiled with great accuracy and care ; and the arrangement of top- ics and the general style are admirable. The pleasing perspicuity and commendable exactness, with which the elementary principles and facts of the physical sciences are presented in these treatises, are in marked contrast with a number of text-books which have somehow found their way into many of our schools." The Round Table (New York) says of the " Handbook of the Stars " : " It is a very admirable specimen of the abilities of the authors. There is scarcely anything in it which young pupils cannot readily comprehend. The illustrations are really beautiful, and the collection of celestial maps at the end adds greatly to the value of the work. An Appendix discusses with considerable thoroughness some of the more abstruse subjects touched upon in the body of the book. The name scarcely expresses the full scope of this manual. It is really an elementary treatise on astronomy without mathematics, and is very good reading for any one with a taste for science but neither the time nor the inclination to go de'eply into its study. It is brought down to the very latest dates, another advantage in these days of stereotype plates and non-revision. We hope that Messrs. Rolfe and Gillet will, at least once in every three or four years, go carefully over their text-books and bring them down to the time of the latest cor- rections and discoveries. By so doing, they will very effectually keep the start of those lazy writers who, when they have finished a school- TESTIMONIALS. 7 book on a progressive science, imagine it is to last without revision as long as they remain in the world to draw an income from its sales." Sillimaifs Journal (March, 1869,) says of the "Handbook of Chem- istry " : " On the whole, the book is a valuable addition to our mea- gre collection of text-books on the new system, and we commend it to the notice of teachers." La Renaissance Louisianaise (New Orleans) says of the " Natural Philosophy " : " Get ouvrage instructif convient a 1'usage des gens du monde aussi bien qu!a celui des etudiants. C'est un manuel qui traite avec une grande clarte demonstrative sur tous les sujets ele- mentaires de la Physique, d'apres les plus recentes decouvertes Les auteurs ont, selon nous, completement reussi a produire un ou- vrage utile au plus haut point et dont personne ne devrait se dispenser." Mr. S. M. Capron, of the High School, Hartford, Conn., where the " Natural Philosophy " has been adopted, says : " We have ex- amined all the recent" text-books on this subject which have appeared, and feel convinced that this is the best arranged of all for our purpose, and most fully up to the present state of scientific research." Professor Edward Conant, of the Vermont State Normal School, writes that his pupils have used the same book " with constant de- light, and, of course, with profit." Mr. L. R. Williston, of Cambridge, Mass., writes thus : " I will express my good opinion of the ' Handbook of Natural Philosophy ' by simply saying that I intend to use it in my school. I shall also continue to use the ' Handbook of the Stars,' and shall use your book in Chemistry, if I use any." Mr. W. B. Stickney, Master of the High School, Chicopee, Mass., says : " The ' Handbook of the Stars ' bears the test of the school- room. My class is delighted with it." 8 TESTIMONIALS. Professor W. S. Smyth, of Wyoming Seminary, Kingston, Pa., who has adopted the same book, says : " For logical arrangement, clear- ness of expression and illustration, as well as for mechanical execution, it is unsurpassed." Professor John B. Bttrwell of the Charlotte Female Institute, North Carolina, writes : " I have been using the books for the last two or three years, and consider them superior in all respects to any others I have ever met with. I can also add the recommendation of Dr. Philips, whose reputation as a teacher is known throughout the South." THE following is from the official report of the regular meeting of the Chicago Board of Education, May 7, 1869 : " Mr. Carter moved to adopt the next recommendation of the Com- mittee, to wit : Rolfe and Gillet's Chemistry, in place of Wells's Chem- istry. " Carried. Yeas Messrs. Ballahtyne, Bond, Bonfield, Briggs, Carter, Guilford, Holden, King, Meserve, Runyan, Shackford, Tink- ham, and Walsh 13. Nays None." *** This popular course of Physics has been officially adopt- ed by the State Board of Maryland and Minnesota, and is al- ready used, in whole or in part, in the cities of Baltimore, Pitts- burg, Wheeling, Richmond, Savannah, Charleston, Mobile, New Orleans, Galveston, Memphis, Nashville, Louisville, St. Louis, Chicago, Milwaukee, Racine, Bloomington, Detroit, Cin- cinnati, Columbus, Dayton, Cleveland, St. Joseph, Wheeling, Buffalo, Rochester, Newark, Worcester, Taunton, Lowell, Ban- gor, Lawrence, Haverhill, Bath, Milford, Hartford, New London, New Bedford, Boston, Cambridge, Dover, Concord, Nashua, Burlington, Dorchester, Manchester, Pittsfield, Chelsea, Chico- pee, Northampton, San Francisco, etc., etc. THE mw LATIN COURSE. PREPARATORY LATIN PROSE BOOK, CONTAINING ALL THE LATIN PROSE NECESSARY FOR ENTERING COLLEGE; WITH REFERENCES TO THE GRAMMARS OF HARKNESS, ANDREWS AND STODDARD, ALLEN, AND BULLIONS. BY J. H. HANSON, A. M., PRINCIPAL OF THE WATERVILLE CLASSICAL INSTITUTE. II. A HANDBOOK OF LATIN POETRY, CONTAINING SELECTIONS FROM VIRGIL, OVID, AND HORACE; WITH NOTES, AND. REFERENCES TO THE GRAMMARS OF HARKNESS, ANDREWS AND STODDARD, ALLEN, AND BULLIONS. BY J. H. HANSON, A. M., AND W. J. ROLFE, A. M. III. SELECTIONS FROM OVID AND VIRGIL. A SHORTER HANDBOOK OF LATIN POETRY ; WITH NOTES AND GRAMMATICAL REFERENCES. BY J. H. HANSON, A. M., AND W. J. ROLFE, A. M. This volume comprises all the Latin Poetry, Notes, and References contained in the larger volume, with the exception of Horace. No. 1 embraces all the Latin prose requisite to preparation for col- lege, with reference to the grammars most in use, Critical and Explan- atory Notes, and a Vocabulary. No. 2 completes the plan, furnishing all the requisite Latin poetry. The two volumes comprise all the Latin necessary to be read in preparing for a collegiate course, and all that is needed to complete the Latin reading of pupils who terminate their classical studies in our High Schools and Academies. No. 3 is the same as No. 2, omitting the Selections from Horace. MAGILL'S FRENCH COURSE. I. A FRENCH GRAMMAR: BEING AN ATTEMPT TO PRESENT, IN A CONCISE AND SYSTEMATIC FORM, THE ESSENTIAL PRINCIPLES OF THE FRENCH LAN- GUAGE : TO WHICH IS ADDED A FRENCH, ENGLISH, AND LATIN VOCABULARY. Eleventh Edition. Enlarged and Improved. II. AN INTRODUCTORY FRENCH READER CONTAINING SELECTIONS FOR READING AND DECLAMATION. III. FRENCH PROSE AND POETRY: BEING AN ADVANCED FRENCH READER : CONTAINING SELECTIONS FROM THE PRINCIPAL CLASSICAL FRENCH POETS AND PROSE-WRITERS DURING THE PAST TWO HUNDRED YEARS, WITH BIOGRAPHICAL NOTICES OF THE AUTHORS; THE WHOLE CHRONOLOGICALLY ARRANGED. BY EDWARD H. MA GILL, A. M., PROFESSOR OF ANCIENT AND MODERN LANGUAGES IN SWARTHMORE COLLEGE, PENNSYLVANIA. No. 1 now contains a complete course of Grammar, illustrated by copious exer- cises, English-French and French-English, together with a very full treatise on pronunciation, brought down to date according to the most recent authorities. No. 2 Contains selections progressively arranged ; and its very full vocabulary gives the derivations of the words as well as their definitions and pronunciation, an entirely new feature in a work of this character. Both this work and No. i are highly recommended by M. Bescherelle aine", author of the Dictionnaire National. No. 3 is a combination of the best materials to make a useful French Reader which the author could obtain during a residence of some months in France, some of them already widely used in the French schools, and others, new selections, taken from the original sources. The whole series forms a very complete course of instruction in French, according to the most approved modern method, for our schools and colleges. 10 A NEW ELEMENTARY COURSE IN THE GERMAN LANGUAGE, FOR THE USE OF SCHOOLS. BY GABRIEL CAMPBELL, M.A., PROFESSOR IN THE STATE UNIVERSITY OF MINNESOTA. I2tno. pp. 200. THE aim of this work is to make a practical application of the improvements developed by the growth of the modern science of Comparative Philology. The author presents the German language to American learners, who are presumed to be acquainted with the English language, by way of comparison with the English in its points of similarity and of difference. The plan is simple, philosophical, and practical, and the work is proving itself eminently successful. It has received very flattering encomiums from high authorities in all parts of the country where German is taught. The book is divided into three parts : PART I. General Principles ; PART II. Synopses Forms of Words ; PART III. Special Principles, Reading and Analysis ; followed by a German and English Vocabulary to Part III. It con- tains also an English and German Vocabulary to Part I, 11 BARTHOLOMEW'S DRAWING SERIES, DESIGNED FOR THE PKIMAEY, GRAMMAR, AND HIGH SCHOOL. BY WILLIAM N. BARTHOLOMEW, PROFESSOR OF DRAWING IN THE ENGLISH HIGH AND GIRLS* HIGH AND NORMAL SCHOOLS, AND DIRECTOR OF DRAWING IN THE GRAMMAR SCHOOLS OF BOSTON. Bartholomew's Primary-School Writing and Drawing Slate. Bartholomew's Drawing-Books. NEW SERIES. In twelve numbers; with "Teacher's Guide" for No. I, No. 2, No. 3, and No. 4. Bartholomew's Drawing-Cards for Blackboard Use. Bartholomew's Progressive Picturesque Drawing- Cards. In four numbers. Bartholomew's Linear Perspective. One vol. 8vo. 64 pp. Bartholomew's Sketches from Nature. In five numbers. BARTHOLOMEW'S DRAWING-BOOKS. This series of Drawing- Books embraces twelve numbers. Each con- taining twelve plates, executed in the highest style of lithographic art, and twenty-four pages of drawing-paper of superior quality. Instruction relating to the examples is given on the covers of the books. The subject-matter of each book is as follows : No. i. Horizontal and vertical lines, together with plane figures and ornamental forms composed of these lines. No. 2. Inclined lines and ornamental forms composed of horizon- tal, vertical, and inclined lines, curved lines, circles, and ornamental forms composed of curved lines. No. 3. Initiatory lessons in Perspective ; The method of drawing from objects explained ; The Laws of Light ; Shade and Shadow pre- sented. No. 4. Advanced lessons on the subjects presented in No. 3. No. 5. Lessons in drawing Fruit and Flowers. No. 6. Initiatory lessons on Foreground and Foliage. No. 7. Lessons on Landscape-drawing. No. 8. Marine Views and Landscape. No. 9." Initiatory lessons on Animal-drawing. No. 10. Advanced lessons on Animal-drawing. No. n. Initiatory lessons on Figure-drawing. No. 12. Advanced lessons on Figure-drawing. 12 Bartholomew 's Drawing Series. The object aimed at in the first four numbers is to give to pupils in our public schools that facility of hand, that discipline of eye, and that knowledge of the principles of drawing which all should possess. The remaining numbers of this series are intended for the use of those who have the time and opportunity to pursue the study further. For the assistance of teachers the author has prepared a series of Manuals, called " The Teacher's Guide." With the aid afforded by these manuals, any good teacher may guide a class to successful results. BARTHOLOMEW'S PRIMARY-SCHOOL SLATE, WITH A SERIES OF PROGRESSIVE LESSONS IN WRITING AND DRAWfNG. This is one of the most simple, practical, and useful arrangements which ingenuity has yet devised in the way of a slate for primary schools. BARTHOLOMEW'S PROGRESSIVE PICTUR- ESQUE DRAWING-CARDS. Four sets, or numbers. Each containing twelve cards, accompanied with instructions. These cards afford pleasing subjects for drawing. The object aimed at, however, is not so much to teach the art of drawing, as it is to nourish in the child a love for it, afford him a source of innocent occupation and amusement, and lead him to observe nature. No. i. Elevations of familiar objects, principally of buildings ; subjects simple in outline and treatment No. 2. Buildings and familiar objects in perspective. No. 3. Buildings and foliage. No. 4. Landscape. BARTHOLOMEW'S LINEAR PERSPECTIVE. I VOLUME, IN WHICH THIS SUBJECT IS SCIENTIFICALLY TREATED. BARTHOLOMEW'S SKETCHES FROM NATURE. IN FIVE NUMBERS, TAPER COVERS, EACH NUMBER CONTAINS FOUR PLATES, II BY 14. Accurate copies of the author's pencil sketches. Affording a pleas- ing variety of subjects, remarkable for simplicity and power. To those who have had some little practice in landscape drawing, these sketches will prove exceedingly useful as subjects' for further study. BARTHOLOMEW'S DRAWING-CARDS, FOR BLACKBOARD USE. 13 PAYSON, WJHTON, & SCIUBNER'S NATIONAL SYSTEM OF PENMANSHIP IS USED ALMOST EXCLUSIVELY IN New England, the British Provinces, the Southern States, and the States of the Pacific Coast. It has been re-engraved and republished in England, Scotland, and Canada. Large sales have been made in the West Indies, Sand- wich Islands, and New Mexico. The Publishers of this popular system 'of penmanship have spared no pains to make it worthy of the leading position which it holds in the country. We have endeavored to combine every practical point of excellence which can be secured through eminent sagacity and ingenuity of au- thorship, and the most artistic skill and precision in the mechanical execution of these books and charts. Our effort to advance the standard of good penmanship is shown in the progressive character of our succeeding editions ; the favorable reception which the books have met with, and the enviable reputation which they now enjoy, is regarded a reasonable subject of congratula- tion. The first four numbers have been recently revised, rearranged, and superbly engraved. The system comprises three distinct series, COMMON SCHOOL SEKIES, Nos. i, 2, 3, 4, 5, and 6. BUSINESS SERIES, Nos. 7, 11, and 12. LADIES* SERIES, Nos. 8, 9, and 10. 14 HANAFORD & PAYSON'S BOOK-KEEPING, COMPRISED IN THREE BOOKS, BY L. B. HANAFORD, A. M., AND J. W. PAYSON. SINGLE ENTRY Common School Edition, with Blanks. DOUBLE AND SINGLE ENTRY High School Edition, with Blanks. ACADEMIC EDITION with Blanks. This work completely meets the wants of the older pupils in our Common Schools and Academies ; it has met a hearty reception, and given universal satisfaction. CROSBY'S GREEK SERIES. The series comprises the following books : GREEK LESSONS. Consisting of selections from Xenophon's Anabasis, with Directions for the Study of the Grammar, Notes, - Exercises in Translation from English into Greek, and a Vocabu- lary. By ALPHEUS CROSBY. i2mo. Price, $ i.oo. XENOPHON'S ANABASIS. Revised Edition. A Narrative of the Expedition of Cyrus the Younger, and of the Retreat of the Ten Thousand. By XENOPHON of Athens. Edited by ALPHEUS CROSBY. I2mo. Price, $ 1.25. GREEK TABLES. For the Use of Students. By ALPHEUS CROSBY. I2mo. Price, 62 cents. A GRAMMAR OF THE GREEK LANGUAGE. Re- vised Edition. By ALPHEUS CROSBY, late Professor of the Greek Language and Literature in Dartmouth College. I2mo. Price, $ 1-75- 15 PAYSON, DUNTON, & SCRIBNER'S STEEL PENS. Having added ONF NEW PEN to our series, we feel that it embraces variety enough to meet all wants and suit all tastes. These PENS are made expressly for us by the best manufacturers in England and America ; and in quality of material, finish of points, easy action, and durability are unsurpassed by any in the market. No. 333. EXTRA FINE. No. 44,5. THE NATIONAL PEN. No. 7. THE BUSINESS PEN. No. 8. THE LADIES' PEN. No. 111. COMMERCIAL PEN. No. 117. THE EXCELSIOR PEN. These Pens are neatly put up in gross and quarter-gross boxes. Sample card of six pens (one of each kind) sent to any address on receipt of ten cents. These Sample Cards offered to the trade at 80 cents per dozen. RICHARD'S LATIN LESSONS. SAWYER'S LATIN PRIMER. WILSON'S TREATISE ON ENGLISH PUNCTU- ATION. BASCOM'S WORKS. 1. ^Esthetics ; or, The Science of Beauty. 2. Philosophy of Rhetoric* CHAMPLIN'S WORKS. 1. Text-Book in Intellectual Philosophy. 2. First Principles of Ethics. WOOLWORTH, AINS WORTH, & CO., PUBLISHERS, NEW YORK. 16 RETURN CIRCULATION DEPARTMENT TO""^ 202 Main Library 642-3403 LOAN PERIOD 1 HOME USE 2 3 4 5 6 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 1 -month loans may be renewed by calling 642-3405 6-month loans may be recharged by bringing books to Circulation Desk Renewals and recharges may be made 4 days prior to due date DUE AS STAMPED BELOW FORM NO. DD 6, 40m, 6'76 UNIVERSITY OF CALIFORNIA, BERKELEY BERKELEY, CA 94720 U.C.BERKELEY LIBRARIES COL13L356G